diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000..ff51641 Binary files /dev/null and b/.DS_Store differ diff --git a/module 6/.DS_Store b/module 6/.DS_Store new file mode 100644 index 0000000..c2be648 Binary files /dev/null and b/module 6/.DS_Store differ diff --git a/module 6/PengRobinson_Et_heat_capacity_fix.ipynb b/module 6/PengRobinson_Et_heat_capacity_fix.ipynb new file mode 100644 index 0000000..563ad2f --- /dev/null +++ b/module 6/PengRobinson_Et_heat_capacity_fix.ipynb @@ -0,0 +1,466 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f225380f", + "metadata": {}, + "source": [ + "# Homework: Calculate the heat capacity of ethane at different pressures\n", + "\n", + "The argument we made for using departure functions is that the heat capacity for a real substance depends on pressure (or molar volume). Here we will calculate the constant pressure heat capacity at different pressures for ethane.\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst \n", + "November 2025\n", + "\n", + "----" + ] + }, + { + "cell_type": "markdown", + "id": "28594ad2", + "metadata": {}, + "source": [ + "As ususal, we import the *numpy* and *matplotlib* libraries. We'll also use the *SciPy* constants library." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "8ba8e9f4", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import constants\n", + "import scipy.optimize as opt\n", + "\n", + "R = constants.R # Set the gas constant to R" + ] + }, + { + "cell_type": "markdown", + "id": "8672870c-eb49-47d7-b862-437a5b5515d6", + "metadata": {}, + "source": [ + "## Problem statement\n", + "\n", + "Using a Jupyter Notebook, plot the constant pressure heat capacity of ethane between 30°C and 200°C for the pressures 0.1, 2, and 4 MPa. Compare these to the ideal gas values $ C_p (T) $ given by the correlation in Appendix A.II." + ] + }, + { + "cell_type": "markdown", + "id": "d2e66192-d13c-4c0d-9677-6a0e88410ff3", + "metadata": {}, + "source": [ + "To solve this problem, I will calculate the enthalpy of ethane as a function of temperature at constant pressure. From these values, I will take the numerical derivative to find\n", + "\n", + "$$ C_p(T) = \\left ( \\frac{\\partial \\underbar{H}}{\\partial T} \\right )_P \\approx \\left ( \\frac{\\Delta \\underbar{H}}{\\Delta T} \\right ) _P .$$\n", + "\n", + "The change in enthalpy will be calculated with departure functions\n", + "$$ \\Delta \\underline{H} = \\Delta \\underline{H}^\\mathrm{IG} + \\Delta [ \\underline{H} - \\underline{H}^\\mathrm{IG}] $$\n", + "\n", + "\n", + "or\n", + "\n", + "$$\\Delta \\underbar{H} = \\Delta \\underline{H}^\\mathrm{IG} + [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2 - [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_1.$$\n", + "\n", + "The specific departure functions we will use are derived from the generalized Peng-Robinson equation of state. " + ] + }, + { + "cell_type": "markdown", + "id": "9cacacf5", + "metadata": {}, + "source": [ + "# Generalized Peng-Robinson Equation of State\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS,\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "f3d2f917", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Solve for the compressibility factor given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_compressibility(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "74031b60-3999-49f8-91a2-eebfeeb09d83", + "metadata": {}, + "source": [ + "## Data for ethane\n", + "\n", + "For ethane, we need the critical pressure and temperature and Pitzer's acentric factor:\n", + "\n", + "$P_c = 4.884$ MPa \n", + "$T_c = 305.4$ K \n", + "$\\underline{V}_c = 0.184\\,\\mathrm{m^3/kmol} = 9.9\\times10^{-5}\\,\\mathrm{m^3/mol}$ \n", + "$\\omega = 0.098$ \n", + "\n", + "We also need heat capacity data in the ideal state. We use the empirical equation in SIS A.II:\n", + "\n", + "$$ C^*_p(T) = A + BT + CT^2 + DT^3 $$\n", + "\n", + "The code block below has values for several molecules, including ethane." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "7579e5f6", + "metadata": {}, + "outputs": [], + "source": [ + "# Critical values for Ethane and the acentric factor\n", + "# pressure in Pa, temperature in K\n", + "Pc = 4.884e6\n", + "Tc = 305.4\n", + "omega = 0.098\n", + "\n", + "# Heat capacity data for N2, O2, CO2, CH4, C2H6\n", + "params = np.array([\n", + " [28.83, -0.157, 0.808, -2.871, 1800],\n", + " [25.46, 1.519, -0.715, 1.311, 1800],\n", + " [22.243, 5.977, -3.499, 7.464, 1800],\n", + " [19.875, 5.021, 1.268, -11.004, 1500],\n", + " [6.895, 17.255, -6.402, 7.280, 1500]\n", + " ])\n", + "\n", + "i = params[4,:] # equation parameters for ethane" + ] + }, + { + "cell_type": "markdown", + "id": "79739b7d", + "metadata": {}, + "source": [ + "## Function to calculate the heat capacity $C_p^*(T)$\n", + "\n", + "Here, the ideal state constant pressure heat capacity $ C_p^*(T)$ is given by an empirical equation\n", + "\n", + "$$ C_p^*(T) = a + bT + cT^2 + dT^3 \\tag{Table A.II}$$\n", + "\n", + "where $T$ is in absolute temperature Kelvins and $C_p^*$ is in units J/(mol K)." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "7f48f67a", + "metadata": {}, + "outputs": [], + "source": [ + "# Calculate the heat capacity using SIS correlation in Appendix A.II\n", + "\n", + "def calc_Cp_IG(T, params):\n", + " A, B, C, D = params[:]\n", + " B *= 10**-2\n", + " C *= 10**-5\n", + " D *= 10**-9\n", + " return A + B*T + C*T**2 + D*T**3" + ] + }, + { + "cell_type": "markdown", + "id": "9b0c2408-14d8-4e9b-b593-414804278b6d", + "metadata": {}, + "source": [ + "## Function to calculate the enthalpy change in the ideal state\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = \\int_{T_1}^{T_2}C_p^*(T)dT$$\n", + "where we will use the ideal state heat capacities summarized in SIS Appendix A.II,\n", + "$$C^*_p(T) = A + BT + CT^2 + DT^3$$\n", + "resulting in\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = A(T_2-T_1) + \\frac{1}{2}B(T_2^2 - T_1^2)+ \\frac{1}{3}C(T_2^3 - T_1^3) + \\frac{1}{4}D(T_2^4 - T_1^4)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "b587ff94-888c-455a-b216-f68a3a7ff462", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def calc_deltaH_IG(T1,T2,params):\n", + " A, B, C, D = params[:4]\n", + " B *= 10**-2\n", + " C *= 10**-5\n", + " D *= 10**-9\n", + " deltaHIG = A*(T2-T1) + B*(T2**2-T1**2)/2 + C*(T2**3-T1**3)/3 + D*(T2**4-T1**4)/4\n", + " return deltaHIG" + ] + }, + { + "cell_type": "markdown", + "id": "4133d8cd", + "metadata": {}, + "source": [ + "## Function for Generalized Peng-Robinson departure function \n", + "The enthalpy departure function in $(P,T)$ control variables for the Peng-Robinson equuation of state is\n", + "\n", + "$$[\\underline{H} - \\underline{H}^\\mathrm{IG}] = RT(Z-1) + \\frac{T\\frac{da}{dT}-a}{2\\sqrt2 b}\\ln \\left [ \\frac{Z+(1+\\sqrt2)B}{Z+(1-\\sqrt2)B} \\right ] \\tag{Eq. 6.4-29}$$\n", + "\n", + "where we need to evaluate the compressibility factor,\n", + "$$Z = \\frac{P\\underline{V}}{RT}$$\n", + "the scaled value of $b$,\n", + "$$B = \\frac{bP}{RT}$$\n", + "and the deriviative of $a(T)$ with respect to temperature given in SIS (p. 264),\n", + "$$\\frac{da}{dT} = - 0.45724 \\frac{R^2T_c^2}{P_c} \\kappa \\sqrt{\\frac{\\alpha}{T T_c}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "b9c7dd01-8aca-45eb-9d06-7eb0d1d1c084", + "metadata": {}, + "outputs": [], + "source": [ + "# With Z already calculated, we define a function to calculate the departure function\n", + "\n", + "\"\"\"\n", + "Enthalpy departure function from the Peng-Robinson equation of state (eq. 6.4-29)\n", + "For convenience, we recalculate b, kappa, sqrtalpha, and a(T) here, but we could\n", + "use the earlier functions, too.\n", + "\n", + "Uses globals Tc, Pc, R\n", + "\"\"\"\n", + "def calc_depH(T,P,Z):\n", + " b = 0.07780*R*Tc/Pc\n", + " B = b*P/R/T\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " a = 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + " dadT = -0.45724*R*R*Tc*Tc/Pc*kappa*sqrtalpha/(T*Tc)**0.5\n", + "\n", + " depH = R*T*(Z-1)+(T*dadT-a)/(2*np.sqrt(2)*b) \\\n", + " *np.log((Z+(1+np.sqrt(2))*B)/(Z+(1-np.sqrt(2))*B))\n", + " return depH" + ] + }, + { + "cell_type": "markdown", + "id": "ad238854-9629-4ce9-9f2a-0c92edcecc92", + "metadata": {}, + "source": [ + "# Enthalpy calculation function\n", + "\n", + "We will define a function to calculate the enthalpy." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "327f42c7", + "metadata": {}, + "outputs": [], + "source": [ + "def del_H(T1, T2, P1, P2, params):\n", + " '''\n", + " params should include: A, B, C, D for Cp correlation '''\n", + "\n", + " # Calculate the compressibility factor\n", + " # Use the maximum value in case there are multiple roots\n", + " Z1 = np.max(PR_compressibility(P1,T1,Pc,Tc,omega))\n", + "\n", + " # Calculate the first departure function\n", + " depH1 = calc_depH(T1,P1,Z1)\n", + "\n", + " # Calculate the compressibility factor\n", + " # Use the maximum value in case there are multiple roots\n", + " Z2 = np.max(PR_compressibility(P2,T2,Pc,Tc,omega))\n", + "\n", + " # Calculate the second departure function\n", + " depH2 = calc_depH(T2,P2,Z2)\n", + "\n", + " # Calculate the ideal gas contribution\n", + " deltaH_IG = calc_deltaH_IG(T1,T2,params)\n", + "\n", + " # Add for the total change in enthalpy\n", + " return deltaH_IG + (depH2 - depH1)\n" + ] + }, + { + "cell_type": "markdown", + "id": "2dd02464", + "metadata": {}, + "source": [ + "# Routine to calculate heat capacity" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "bb8d3194-40ce-463c-9914-5eed37d4f7de", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Heat capacity for ethane at different pressures')" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Known values in problem\n", + "# The initial and final temperatures are\n", + "Ti = 30 + 273.15 # Beginning temperature in K\n", + "Tf = 200 + 273.15 # final temperature in K\n", + "delta_T = 1 # use increments to calculate numerical derivative\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for P in [0.1e6, 2e6, 4e6]:\n", + "\n", + " T = np.arange(Ti, Tf + 1, delta_T)\n", + "\n", + " cp_values = np.zeros_like(T, dtype=float)\n", + "\n", + " for idx, T0 in enumerate(T):\n", + " # Compute ΔH over 1 K interval for each temperature\n", + " dH = del_H(T0, T0 + delta_T, P, P, i[:4])\n", + " cp_values[idx] = dH / delta_T\n", + "\n", + " ax.plot(T, cp_values, label=f'P = {P/1e6:.1f} MPa')\n", + "\n", + "cp_ideal = calc_Cp_IG(T, i[:4])\n", + "ax.plot(T, cp_ideal, '--', label='Ideal Gas')\n", + "\n", + "ax.legend()\n", + "plt.xlabel('T (K)')\n", + "plt.ylabel(\"$C_p$ (J/molK)\")\n", + "plt.title('Heat capacity for ethane at different pressures')" + ] + }, + { + "cell_type": "markdown", + "id": "c5e87754", + "metadata": {}, + "source": [ + "This makes sense. The isotherms on the pressure-enthalpy plot tend to bend toward lower values of enthalpy with higher pressures. That is, $(\\partial P/\\partial \\underbar{H})_T$ has a lower and negative slope on the plot. Thus, at $P = 4$ MPa, for each 10 degree difference in temperature, there is nearly double the amount of enthalpy change. Pretty interesting!\n", + "\n", + "Second, the non-lienar behavior also makes sense. This isobar eventually intersects the VLE curve (it’s below the critical pressure) and so you expect the heat capacity to diverge! Why? Think of the intersecting isotherm and what the slope represented by looks like in the VLE region. Then, as you go to higher temperatures along the isobar away from the VLE curve, you begin to recover more ideal-like behavior (and its temperature dependence)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 6/PengRobinson_Et_throttle_problem.ipynb b/module 6/PengRobinson_Et_throttle_problem.ipynb new file mode 100644 index 0000000..bceae41 --- /dev/null +++ b/module 6/PengRobinson_Et_throttle_problem.ipynb @@ -0,0 +1,517 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f225380f", + "metadata": {}, + "source": [ + "# Homework: Calculate the temperature of ethane in a throttling process\n", + "\n", + "These are codes to calculate the enthalpy departure function from the complete, generalized Peng-Robinson equation of state as given in SIS 5th edition equations 6.4-2 and 6.7-1 to 6.7-4. \n", + "\n", + "We use it to calculate analyze an isenthalpic expansion of ethane through a throttling process.\n", + "\n", + "Eric Furst \n", + "November 2025\n", + "\n", + "----" + ] + }, + { + "cell_type": "markdown", + "id": "28594ad2", + "metadata": {}, + "source": [ + "As ususal, we import the *numpy* and *matplotlib* libraries. We'll also use the *SciPy* constants library." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8ba8e9f4", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import constants\n", + "import scipy.optimize as opt\n", + "\n", + "R = constants.R # Set the gas constant to R" + ] + }, + { + "cell_type": "markdown", + "id": "8672870c-eb49-47d7-b862-437a5b5515d6", + "metadata": {}, + "source": [ + "## Problem statement\n", + "\n", + "Ethane gas undergoes a rapid, adiabatic expansion through a continous throttling process from upstream conditions ${\\text{100}^\\circ}\\text{C}$ and 100 bar to atmospheric pressure.\n", + "\n", + "Calculate the downstream gas temperature.\n" + ] + }, + { + "cell_type": "markdown", + "id": "d2e66192-d13c-4c0d-9677-6a0e88410ff3", + "metadata": {}, + "source": [ + "To solve this problem, we will calculate the enthalpy of methane such that it satisfies an isenthalpic condition. In terms of the departure function values, this is \n", + "$$\\Delta \\underline{H} = \\Delta \\underline{H}^\\mathrm{IG} + \\Delta [ \\underline{H} - \\underline{H}^\\mathrm{IG}] = 0$$\n", + "or\n", + "$$\\Delta \\underline{H}^\\mathrm{IG} + [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2 - [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_1 = 0$$\n", + "The specific departure functions we will use are derived from the generalized Peng-Robinson equation of state. " + ] + }, + { + "cell_type": "markdown", + "id": "9cacacf5", + "metadata": {}, + "source": [ + "# Generalized Peng-Robinson Equation of State\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS,\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f3d2f917", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Solve for the compressibility factor given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_compressibility(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots" + ] + }, + { + "cell_type": "markdown", + "id": "74031b60-3999-49f8-91a2-eebfeeb09d83", + "metadata": {}, + "source": [ + "## Data for ethane\n", + "\n", + "For ethane, we need the critical pressure and temperature and Pitzer's acentric factor:\n", + "\n", + "$P_c = 4.884$ MPa \n", + "$T_c = 305.4$ K \n", + "$\\underline{V}_c = 0.184\\,\\mathrm{m^3/kmol} = 9.9\\times10^{-5}\\,\\mathrm{m^3/mol}$ \n", + "$\\omega = 0.098$ " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7579e5f6", + "metadata": {}, + "outputs": [], + "source": [ + "# Critical values for Ethane and the acentric factor\n", + "# pressure in Pa, temperature in K\n", + "Pc = 4.884e6\n", + "Tc = 305.4\n", + "omega = 0.098\n", + "\n", + "# Known values in problem\n", + "T1 = 373 # Inlet temperature in K\n", + "P1 = 10.e6 # Inlet pressure in Pa\n", + "P2 = 101325 # Outlet temperature in Pa" + ] + }, + { + "cell_type": "markdown", + "id": "ad238854-9629-4ce9-9f2a-0c92edcecc92", + "metadata": {}, + "source": [ + "# Enthalpy calculation\n", + "\n", + "## Start by calculating $Z$ for the inlet condition" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "43ba6036", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.2213490504256714 2.0475020475020473\n" + ] + } + ], + "source": [ + "TR1 = T1/Tc # Reduced temperature\n", + "PR1 = P1/Pc # Reduced pressure\n", + "\n", + "print(TR1,PR1)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0bdc3b7d-bbe1-4358-91a2-8aeaa0d33040", + "metadata": {}, + "outputs": [], + "source": [ + "TR1 = T1/Tc # Reduced temperature\n", + "PR1 = P1/Pc # Reduced pressure\n", + "\n", + "# Use the PR_vol function to calculate the molar volume\n", + "Z1 = np.max(PR_compressibility(P1,T1,Pc,Tc,omega))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ca49e458-2711-465b-add8-198d80ff5131", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Z1 = 0.61\n" + ] + } + ], + "source": [ + "print(f\"Z1 = {Z1:.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "4133d8cd", + "metadata": {}, + "source": [ + "## Function for Generalized Peng-Robinson departure function \n", + "The enthalpy departure function in $(P,T)$ control variables for the Peng-Robinson equuation of state is\n", + "\n", + "$$[\\underline{H} - \\underline{H}^\\mathrm{IG}] = RT(Z-1) + \\frac{T\\frac{da}{dT}-a}{2\\sqrt2 b}\\ln \\left [ \\frac{Z+(1+\\sqrt2)B}{Z+(1-\\sqrt2)B} \\right ] \\tag{Eq. 6.4-29}$$\n", + "\n", + "where we need to evaluate the compressibility factor,\n", + "$$Z = \\frac{P\\underline{V}}{RT}$$\n", + "the scaled value of $b$,\n", + "$$B = \\frac{bP}{RT}$$\n", + "and the deriviative of $a(T)$ with respect to temperature given in SIS (p. 264),\n", + "$$\\frac{da}{dT} = - 0.45724 \\frac{R^2T_c^2}{P_c} \\kappa \\sqrt{\\frac{\\alpha}{T T_c}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b9c7dd01-8aca-45eb-9d06-7eb0d1d1c084", + "metadata": {}, + "outputs": [], + "source": [ + "# With Z already calculated, we define a function to calculate the departure function\n", + "\n", + "\"\"\"\n", + "Enthalpy departure function from the Peng-Robinson equation of state (eq. 6.4-29)\n", + "For convenience, we recalculate b, kappa, sqrtalpha, and a(T) here, but we could\n", + "use the earlier functions, too.\n", + "\n", + "Uses globals Tc, Pc, R\n", + "\"\"\"\n", + "def calc_depH(T,P,Z):\n", + " b = 0.07780*R*Tc/Pc\n", + " B = b*P/R/T\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-(T/Tc)**0.5)\n", + " a = 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + " dadT = -0.45724*R*R*Tc*Tc/Pc*kappa*sqrtalpha/(T*Tc)**0.5\n", + "\n", + " depH = R*T*(Z-1)+(T*dadT-a)/(2*2**0.5*b)*np.log((Z+(1+2**0.5)*B)/(Z+(1-2**0.5)*B))\n", + " return depH" + ] + }, + { + "cell_type": "markdown", + "id": "c8640217", + "metadata": {}, + "source": [ + "## Calculate the inlet departure function $[\\underbar{H}-\\underbar{H}^\\mathrm{IG}]_1$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c3dc8ef7-f035-4079-8e90-bb4cc500fbf9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "*** depH1 = -5108 J/mol\n" + ] + } + ], + "source": [ + "depH1 = calc_depH(T1,P1,Z1)\n", + "\n", + "print(f\"*** depH1 = {depH1:.0f} J/mol\")" + ] + }, + { + "cell_type": "markdown", + "id": "1fb6ec34", + "metadata": {}, + "source": [ + "## Guess an outlet temperature\n", + "\n", + "Now, the challenge here is that the outlet temperature is not known. So, we have to guess an outlet temperature and calculate both the ideal contributino and the outlet departure function value." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "02096ffe", + "metadata": {}, + "outputs": [], + "source": [ + "# GUESS OUTLET TEMP\n", + "T2 = 284.4 # outlet temp in K\n", + "T2R = T2/Tc # reduced outlet temperature" + ] + }, + { + "cell_type": "markdown", + "id": "9b0c2408-14d8-4e9b-b593-414804278b6d", + "metadata": {}, + "source": [ + "## Function to calculate the enthalpy change in the ideal state $\\Delta \\underbar{H}^\\mathrm{IG}$\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = \\int_{T_1}^{T_2}C_p^*(T)dT$$\n", + "where we will use the ideal state heat capacities summarized in Appendix A.II,\n", + "$$C^*_p(T) = A + BT + CT^2 + DT^3$$\n", + "resulting in\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = A(T_2-T_1) + \\frac{1}{2}B(T_2^2 - T_1^2)+ \\frac{1}{3}C(T_2^3 - T_1^3) + \\frac{1}{4}D(T_2^4 - T_1^4)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b587ff94-888c-455a-b216-f68a3a7ff462", + "metadata": {}, + "outputs": [], + "source": [ + "# Heat capacity data for N2, O2, CO2, CH4, C2H6\n", + "params = np.array([\n", + " [28.83, -0.157, 0.808, -2.871, 1800],\n", + " [25.46, 1.519, -0.715, 1.311, 1800],\n", + " [22.243, 5.977, -3.499, 7.464, 1800],\n", + " [19.875, 5.021, 1.268, -11.004, 1500],\n", + " [6.895, 17.255, -6.402, 7.280, 1500]\n", + " ])\n", + "\n", + "i = params[4,:] # equation parameters for ethane\n", + "\n", + "deltaHIG = i[0]*(T2-T1) + i[1]*10**-2*(T2**2-T1**2)/2 + i[2]*10**-5*(T2**3-T1**3)/3 + i[3]*10**-9*(T2**4-T1**4)/4" + ] + }, + { + "cell_type": "markdown", + "id": "2dd02464", + "metadata": {}, + "source": [ + "## Calculate the enthalpy change of the ideal state" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "bb8d3194-40ce-463c-9914-5eed37d4f7de", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "*** Delta HIG = -5043 J/mol\n" + ] + } + ], + "source": [ + "print(\"*** Delta HIG = {:.0f} J/mol\".format(deltaHIG))" + ] + }, + { + "cell_type": "markdown", + "id": "a5cf19a3-a21e-4fc0-a034-30d48834da91", + "metadata": {}, + "source": [ + "## Calculate the outlet departure function $[\\underbar{H}-\\underbar{H}^\\mathrm{IG}]_2$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "04bda783-43d6-4fb6-8f69-e87dc1a5a2be", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "depH2 = -63 J/mol\n" + ] + } + ], + "source": [ + "# Use the PR_compressibility function to calculate the molar volume and compressibility factor\n", + "Z2 = np.max(PR_compressibility(P2,T2,Pc,Tc,omega))\n", + "\n", + "depH2 = calc_depH(T2,P2,Z2)\n", + "#print(P2/Pc)\n", + "print(f\"depH2 = {depH2:.0f} J/mol\")\n", + "# , deltaH = {:.0f} J/mol <-- should be zero\".format(depH2,deltaHIG+depH2-depH1))" + ] + }, + { + "cell_type": "markdown", + "id": "b59d01f8", + "metadata": {}, + "source": [ + "## Check if the sum is zero $\\Delta \\underbar{H}^\\mathrm{IG} + [\\underbar{H}-\\underbar{H}^\\mathrm{IG}]_2 - [\\underbar{H}-\\underbar{H}^\\mathrm{IG}]_1 = 0$\n", + "Since $\\Delta \\underbar{H} = 0$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "b30ecfe0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "delta_H = 2 J/mol\n", + "for T2 = 284.40 K\n" + ] + } + ], + "source": [ + "print(f\"delta_H = {deltaHIG + depH2 - depH1:.0f} J/mol\")\n", + "print(f\"for T2 = {T2:.2f} K\")" + ] + }, + { + "cell_type": "markdown", + "id": "8044d9eb", + "metadata": {}, + "source": [ + "If this doesn't equal zero (or is close to zero), guess another $T_2$ and recalculate $\\Delta \\underbar{H}^\\mathrm{IG}$ and $[\\underbar{H} - \\underbar{H}^\\mathrm{IG}]_2$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "edee9974", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 6/PengRobinson_Me_throttle_example.ipynb b/module 6/PengRobinson_Me_throttle_example.ipynb new file mode 100644 index 0000000..04e33c1 --- /dev/null +++ b/module 6/PengRobinson_Me_throttle_example.ipynb @@ -0,0 +1,576 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f225380f", + "metadata": {}, + "source": [ + "# Example: Departure functions from Peng-Robinson equation of state\n", + "\n", + "These are codes to calculate the enthalpy departure function from the complete, generalized Peng-Robinson equation of state as given in SIS 5th edition equations 6.4-2 and 6.7-1 to 6.7-4. \n", + "\n", + "We use it to calculate analyze an isenthalpic expansion of methane through a throttling process.\n", + "\n", + "Eric Furst \n", + "November 2024\n", + "\n", + "Version updates: \n", + "Revisions in layout, calculation of PR EOS (11/2025)\n", + "\n", + "----" + ] + }, + { + "cell_type": "markdown", + "id": "28594ad2", + "metadata": {}, + "source": [ + "As ususal, we import the *numpy* and *matplotlib* libraries. We'll also use the *SciPy* constants library." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8ba8e9f4", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import constants\n", + "import scipy.optimize as opt\n", + "\n", + "R = constants.R # Set the gas constant to R" + ] + }, + { + "cell_type": "markdown", + "id": "8672870c-eb49-47d7-b862-437a5b5515d6", + "metadata": {}, + "source": [ + "## Problem statement\n", + "\n", + "Methane gas undergoes a rapid, adiabatic expansion through a continous throttling process from upstream conditions ${\\text{13}^\\circ}\\text{C}$ and 184 bar to a lower pressure at ${\\text{-43}^\\circ}\\text{C}$ .\n", + "\n", + "Calculate the downstream gas pressure.\n" + ] + }, + { + "cell_type": "markdown", + "id": "d2e66192-d13c-4c0d-9677-6a0e88410ff3", + "metadata": {}, + "source": [ + "To solve this problem, we will calculate the enthalpy of methane such that it satisfies an isenthalpic condition. In terms of the departure function values, this is \n", + "$$\\Delta \\underline{H} = \\Delta \\underline{H}^\\mathrm{IG} + \\Delta [ \\underline{H} - \\underline{H}^\\mathrm{IG}] = 0$$\n", + "or\n", + "$$\\Delta \\underline{H}^\\mathrm{IG} + [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2 - [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_1 = 0$$\n", + "The specific departure functions we will use are derived from the generalized Peng-Robinson equation of state. " + ] + }, + { + "cell_type": "markdown", + "id": "9cacacf5", + "metadata": {}, + "source": [ + "# Generalized Peng-Robinson Equation of State\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS,\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f3d2f917", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Solve for the compressibility factor given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_compressibility(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots" + ] + }, + { + "cell_type": "markdown", + "id": "74031b60-3999-49f8-91a2-eebfeeb09d83", + "metadata": {}, + "source": [ + "## Data for methane\n", + "\n", + "For methane, we need the critical pressure and temperature and Pitzer's acentric factor:\n", + "\n", + "$P_c = 4.6$ MPa \n", + "$T_c = 190.6$ K \n", + "$\\underline{V}_c = 0.099\\,\\mathrm{m^3/kmol} = 9.9\\times10^{-5}\\,\\mathrm{m^3/mol}$ \n", + "$\\omega = 0.008$ " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7579e5f6", + "metadata": {}, + "outputs": [], + "source": [ + "# Critical values for Methane and the accentric factor\n", + "# pressure in Pa, temperature in K\n", + "Pc = 4.6e6\n", + "Tc = 190.6\n", + "omega = 0.008\n", + "\n", + "# Known values in problem\n", + "T1 = 286 # Inlet temperature in K\n", + "P1 = 18.4e6 # Inlet pressure in Pa\n", + "T2 = 230 # Outlet temperature in K" + ] + }, + { + "cell_type": "markdown", + "id": "ad238854-9629-4ce9-9f2a-0c92edcecc92", + "metadata": {}, + "source": [ + "# Enthalpy calculation\n", + "\n", + "## Start by calculating $Z$ for the inlet condition" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0bdc3b7d-bbe1-4358-91a2-8aeaa0d33040", + "metadata": {}, + "outputs": [], + "source": [ + "TR1 = T1/Tc # Reduced temperature\n", + "PR1 = P1/Pc # Reduced pressure\n", + "\n", + "# Use the PR_vol function to calculate the molar volume\n", + "Z1 = np.max(PR_compressibility(P1,T1,Pc,Tc,omega))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ca49e458-2711-465b-add8-198d80ff5131", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Z1 = 0.77\n" + ] + } + ], + "source": [ + "print(\"Z1 = {:.2f}\".format(Z1))" + ] + }, + { + "cell_type": "markdown", + "id": "4133d8cd", + "metadata": {}, + "source": [ + "## Calculate the departure function for the inlet condition\n", + "The enthalpy departure function in $(P,T)$ control variables for the Peng-Robinson equuation of state is\n", + "\n", + "$$[\\underline{H} - \\underline{H}^\\mathrm{IG}] = RT(Z-1) + \\frac{T\\frac{da}{dT}-a}{2\\sqrt2 b}\\ln \\left [ \\frac{Z+(1+\\sqrt2)B}{Z+(1-\\sqrt2)B} \\right ] \\tag{Eq. 6.4-29}$$\n", + "\n", + "where we need to evaluate the compressibility factor,\n", + "$$Z = \\frac{P\\underline{V}}{RT}$$\n", + "the scaled value of $b$,\n", + "$$B = \\frac{bP}{RT}$$\n", + "and the deriviative of $a(T)$ with respect to temperature given in SIS (p. 264),\n", + "$$\\frac{da}{dT} = - 0.45724 \\frac{R^2T_c^2}{P_c} \\kappa \\sqrt{\\frac{\\alpha}{T T_c}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b9c7dd01-8aca-45eb-9d06-7eb0d1d1c084", + "metadata": {}, + "outputs": [], + "source": [ + "# With Z already calculated, we define a function to calculate the departure function\n", + "\n", + "\"\"\"\n", + "Enthalpy departure function from the Peng-Robinson equation of state (eq. 6.4-29)\n", + "For convenience, we recalculate b, kappa, sqrtalpha, and a(T) here, but we could\n", + "use the earlier functions, too.\n", + "\n", + "Uses globals Tc, Pc, R\n", + "\"\"\"\n", + "def calc_depH(T,P,Z):\n", + " b = 0.07780*R*Tc/Pc\n", + " B = b*P/R/T\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-(T/Tc)**0.5)\n", + " a = 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + " dadT = -0.45724*R*R*Tc*Tc/Pc*kappa*sqrtalpha/(T*Tc)**0.5\n", + "\n", + " depH = R*T*(Z-1)+(T*dadT-a)/(2*2**0.5*b)*np.log((Z+(1+2**0.5)*B)/(Z+(1-2**0.5)*B))\n", + " return depH" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c3dc8ef7-f035-4079-8e90-bb4cc500fbf9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "*** depH1 = -3134 J/mol\n" + ] + } + ], + "source": [ + "depH1 = calc_depH(T1,P1,Z1)\n", + "\n", + "print(f\"*** depH1 = {depH1:.0f} J/mol\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "6132bf00-dc64-4bbf-99cc-4e749d5f676b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.93\n" + ] + } + ], + "source": [ + "# I'm calculating this number to compare with corresponding states later...\n", + "print(f\"{-depH1/Tc/4.184:.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "9b0c2408-14d8-4e9b-b593-414804278b6d", + "metadata": {}, + "source": [ + "## Calculate the change in enthalpy in the ideal state\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = \\int_{T_1}^{T_2}C_p^*(T)dT$$\n", + "where we will use the ideal state heat capacities summarized in Appendix A.II,\n", + "$$C^*_p(T) = A + BT + CT^2 + DT^3$$\n", + "resulting in\n", + "$$\\Delta\\underline{H}^\\mathrm{IG} = A(T_2-T_1) + \\frac{1}{2}B(T_2^2 - T_1^2)+ \\frac{1}{3}C(T_2^3 - T_1^3) + \\frac{1}{4}D(T_2^4 - T_1^4)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "b587ff94-888c-455a-b216-f68a3a7ff462", + "metadata": {}, + "outputs": [], + "source": [ + "# Heat capacity data for N2, O2, CO2, CH4, C2H6\n", + "params = np.array([\n", + " [28.83, -0.157, 0.808, -2.871, 1800],\n", + " [25.46, 1.519, -0.715, 1.311, 1800],\n", + " [22.243, 5.977, -3.499, 7.464, 1800],\n", + " [19.875, 5.021, 1.268, -11.004, 1500],\n", + " [6.895, 17.255, -6.402, 7.280, 1500]\n", + " ])\n", + "\n", + "i = params[3,:] # equation parameters for methane\n", + "\n", + "deltaHIG = i[0]*(T2-T1) + i[1]*10**-2*(T2**2-T1**2)/2 \\\n", + " + i[2]*10**-5*(T2**3-T1**3)/3 \\\n", + " + i[3]*10**-9*(T2**4-T1**4)/4" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "bb8d3194-40ce-463c-9914-5eed37d4f7de", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Delta HIG = -1875 J/mol\n" + ] + } + ], + "source": [ + "print(\"Delta HIG = {:.0f} J/mol\".format(deltaHIG))" + ] + }, + { + "cell_type": "markdown", + "id": "0d72851d-90a5-43f0-9839-02f5f495744b", + "metadata": {}, + "source": [ + "Now solve\n", + "$$[ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2 = [ \\underline{H} - \\underline{H}^\\mathrm{IG}]_1 - \\Delta \\underline{H}^\\mathrm{IG}$$\n", + "\n", + "We are looking for a value of the departure function:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "9907b191-2e60-4a7b-8f04-e2655ed4474c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "depH2 must equal -1259 J/mol\n" + ] + } + ], + "source": [ + "print(\"depH2 must equal {:.0f} J/mol\".format(depH1-deltaHIG))" + ] + }, + { + "cell_type": "markdown", + "id": "a5cf19a3-a21e-4fc0-a034-30d48834da91", + "metadata": {}, + "source": [ + "Do this by guessing an outlet pressure, calculating $[ \\underline{H} - \\underline{H}^\\mathrm{IG}]_2$ and iterating (guessing new values of $P_2$) until the condition above is met." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "04bda783-43d6-4fb6-8f69-e87dc1a5a2be", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "depH2 = -1259 J/mol, deltaH = 0 J/mol <-- should be zero\n" + ] + } + ], + "source": [ + "# Guess:\n", + "P2 = 4.145e6 # guess a pressure\n", + "\n", + "# Use the PR_compressibility function to calculate the molar volume and compressibility factor\n", + "Z2 = np.max(PR_compressibility(P2,T2,Pc,Tc,omega))\n", + "\n", + "depH2 = calc_depH(T2,P2,Z2)\n", + "#print(P2/Pc)\n", + "print(\"depH2 = {:.0f} J/mol, deltaH = {:.0f} J/mol <-- should be zero\".format(depH2,deltaHIG+depH2-depH1))" + ] + }, + { + "cell_type": "markdown", + "id": "acfea36c-cb4a-4a12-8577-059d4790340e", + "metadata": {}, + "source": [ + "---\n", + "\n", + "# Change in molar entropy\n", + "\n", + "Now we can calcuate the change in molar entropy of the methane,\n", + "\n", + "$$\\Delta \\underline{S} = \\Delta \\underline{S}^\\mathrm{IG} + \\Delta [ \\underline{S} - \\underline{S}^\\mathrm{IG}]$$\n", + "\n", + "Since the throttling process is adiabatic, this change represents the rate of entropy generation, $\\underline{\\dot{S}}_\\mathrm{gen}$.\n", + "\n", + "The entropy departure function for the Peng-Robinson equation is\n", + "$$[ \\underline{S} - \\underline{S}^\\mathrm{IG}] = R\\ln(Z-B) + \\frac{da/dT}{2\\sqrt{2}b}\\ln \\left [ \\frac{Z+(1+\\sqrt2)B}{Z+(1-\\sqrt2)B} \\right ] \\tag{Eq. 6.4-30}$$\n", + "and the entropy change of the real fluid in an ideal state with $P$ and $T$ control variables is\n", + "$$\\Delta \\underline{S}^\\mathrm{IG} = \\int_{T_1}^{T_2}\\frac{C_p^*(T)}{T}dT - R\\ln\\frac{P_2}{P_1}$$\n", + "with $C_p^*(T)$ given above, \n", + "$$\\Delta \\underline{S}^\\mathrm{IG} = A\\ln\\frac{T_2}{T_1} + B(T_2-T_1) + \\frac{1}{2}C(T_2^2-T_1^2) + \\frac{1}{3}D(T_2^3-T_1^3) - R\\ln\\frac{P_2}{P_1}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "cea15f29-14c8-4b4e-91bc-b070b56856d1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(12.433452523746052)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "deltaSIG = i[0]*np.log(T2/T1) + i[1]*10**-2*(T2-T1) + i[2]*10**-5*(T2**2-T1**2)/2 \n", + "+ i[3]*10**-9*(T2**3-T1**3)/3 - R*np.log(P2/P1)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "0050af8f-231e-401a-8583-4e536511082a", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Entropy departure function from the Peng-Robinson equation of state (eq. 6.4-30)\n", + "For convenience, we recalculate b, kappa, sqrtalpha, and a(T) here, but we could\n", + "use the earlier functions, too.\n", + "\n", + "Uses globals Tc, Pc, R\n", + "\"\"\"\n", + "def calc_depS(T,P,Z):\n", + " b = 0.07780*R*Tc/Pc\n", + " B = b*P/R/T\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " a = 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + " dadT = -0.45724*R*R*Tc*Tc/Pc*kappa*sqrtalpha/np.sqrt(T*Tc)\n", + "\n", + " depS = R*(Z-B)+dadT/(2*2**0.5*b)*np.log((Z+(1+2**0.5)*B)/(Z+(1-2**0.5)*B))\n", + " return depS\n", + "\n", + "depS1 = calc_depS(T1, P1, Z1)\n", + "depS2 = calc_depS(T2, P2, Z2)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f21e77c3-ac10-4596-bcd1-1e1124cffdd6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T1: 286.0 K, P1: 1.84e+07 Pa, Z1: 0.77\n", + "T2: 230.0 K, P2: 4.14e+06 Pa, Z2: 0.79\n", + "\n", + "delSIG= -7.33, depS2= 4.9, depS1= 1.6\n", + "\n", + "Change in molar entropy: -4.0 J/mol.K\n" + ] + } + ], + "source": [ + "print(\"T1: {:.1f} K, P1: {:0.2e} Pa, Z1: {:.2f}\".format(T1,P1,Z1))\n", + "print(\"T2: {:.1f} K, P2: {:0.2e} Pa, Z2: {:.2f}\\n\".format(T2,P2,Z2))\n", + "print(\"delSIG= {:.2f}, depS2= {:.1f}, depS1= {:.1f}\\n\".format(deltaSIG,depS2,depS1))\n", + "print(\"Change in molar entropy: {:.1f} J/mol.K\".format(deltaSIG + depS2 - depS1))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b2f846c5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 6/Peng_Robinson_EOS.ipynb b/module 6/Peng_Robinson_EOS.ipynb new file mode 100644 index 0000000..c8ae394 --- /dev/null +++ b/module 6/Peng_Robinson_EOS.ipynb @@ -0,0 +1,187 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3c29e0e8", + "metadata": {}, + "source": [ + "# Generalized Peng-Robinson Equation of State\n", + "\n", + "Routines to calcualte the Generalized Peng-Robinson Equation of State\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst \n", + "November 2025\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS (see SIS Table 6.4-3),\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "47da809f", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the molar volume given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_volume(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " # Convert real values of Z to molar volume\n", + " V = real_roots*R*T/P\n", + "\n", + " return V\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2f55b187", + "metadata": {}, + "source": [ + "## Example calculation\n", + "\n", + "Given the PR EOS, calculate the molar volume(s) of ethane given different temperature and pressures for ethane." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "fd028ebd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[6.08349837e-05 2.38749240e-04 1.65668503e-03]\n", + "[494.28796012 125.94804501 18.15070421]\n" + ] + } + ], + "source": [ + "# Given the PR EOS, calculate the molar volume(s) of ethane given different T and P:\n", + "\n", + "# Data for ethane\n", + "Pc = 4.884e6\n", + "Tc = 305.4\n", + "omega = 0.098\n", + "MW = 30.07\n", + "\n", + "P = 1e6\n", + "T = -33+273.15\n", + "\n", + "# molar volume m^3/mol\n", + "print((PR_volume(P, T, Pc, Tc, omega))) \n", + "\n", + "# specific density kg/m^3\n", + "print(1/(PR_volume(P, T, Pc, Tc, omega)/MW*1000)) \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f387f98f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 6/Peng_Robinson_EOS_isotherms.ipynb b/module 6/Peng_Robinson_EOS_isotherms.ipynb new file mode 100644 index 0000000..95470b5 --- /dev/null +++ b/module 6/Peng_Robinson_EOS_isotherms.ipynb @@ -0,0 +1,306 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7af16f2a", + "metadata": {}, + "source": [ + "# Example: Using the Peng-Robinson EOS to plot several isotherms for Nitrogen" + ] + }, + { + "cell_type": "markdown", + "id": "3c29e0e8", + "metadata": {}, + "source": [ + "## Generalized Peng-Robinson Equation of State\n", + "\n", + "Routines to calcualte the Generalized Peng-Robinson Equation of State\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst \n", + "November 2025\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS (see SIS Table 6.4-3),\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "47da809f", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the molar volume given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_volume(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " # Convert real values of Z to molar volume\n", + " V = real_roots*R*T/P\n", + "\n", + " return V\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2f55b187", + "metadata": {}, + "source": [ + "## Example calculation\n", + "\n", + "Given the PR EOS, calculate the molar volume(s) of ethane given different temperature and pressures for ethane." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fd028ebd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'PV diagram for nitrogen')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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B9ed2Bmq2luSg8P17INeGIPH//tPt6+pa6nHdt/eK42UXvgmZT2e9Xduqw91r9oEM9d85fYJwBi789jsc++BDhM+djfS77nD7fuYcrsCn72xGWIQ/brnf/a5hV75+91kUHc3E/L9cjZFT5np0G/lL96CluB5Rp6cicFSU0+tTzAC9GaDih8w07QVlGnTN2P3bo1R6YuxJj0CpDvDo/jEMw/QVx+v1u087PWT+R0/sXdOoyYOCzNCY/oesI+vH2KVb4SMzWT61G213QhTyTksovcG6G6dRmCzy6RZbDaZASoXWFMOgrzfloLlLaLjJnr+6qqnbffWE6ASTH0pJ3hGPb8M3zmSH0FzouHMjQX4sUuJ51/BMS+RKX/hqTUVUQ80xj+8fwzDMYKdPix7pCb1rQCI5H3NAXv9EJusoero2CKVsny4FjYSyoygidEbr66hkPqLLQ7ToTUWTQmvqVugbGj26n4HBvpDLZTAa2lFX0/OQy5iEYeK8JC/b49vQDOkoegpcK3oIym8iSOjvCG1wsjhvqDnq8f1jGIYZ7PRp0UNOx5MmTRJp5pSATGGLr7zyigg5pNRhpv8hpTp3bZ74yOSOOz2WRY9B1+02fTu6PS36Lp2ehnqPi7OQMFO3p6rCs8LJkqiOTk9VWRFam5s8ug3fjqJHV9UMfZP1Y2APcgl3pejxDzG9SWio5k4PwzBMvyx6aFPr3//+N6ZPny5C80jETMUPaXxoxMX0P2QdfzHdxlsd4yt7RQ8VNmq5Shy3dSl6CI3CdMPNHZ0eZYC2R50eIqRjxFVV4VmRYomfNhBBoSazzJJ8z7o9cl8lVB2FWIuLI67Y2Fjx2JGgmfyr7KENNhU9TfWFMBqsReYMwzBMP9neCgoKwqOPPiq8enbu3Illy5aJUD1mYGl64CONt+xvN6kUpqKnRd9doa/p0umR+3cUPY2NaDeaPucuoeH+Xuv0WOt6ejDiknQ9BbUuXV+tVpstGBzpelSaECjVQVR1orE23+P7xzAMM5jp86KHGVjI7Wh6fCRND9rtdns0Djs98i6aHlPBAqMRhmbPNDnSeKvaa0XPsJ6LmSVdj4udHldHXNQNkro9LGZmGIaxDRc9jIeanq7bW1LRY3/EpVaoHXR6TH+KLR2dIrlaDZlKZfbs6VGnp7Ln4y0iOtHU6SnNz/G4+yQVPa2lDTC2Gdwqehx1eghz0VPNYmaGYRhbcNHDeLa91XW8ZbGSbm/EJWl6Wm1oTsydHl1nMaHQanu4tm4qeqoraUTW87X1sKg4KFVqtLU0o6q82KPbUAZpoAhUi/18V7s90gZXRUUFmh10vbQdYubG2ly0t3tWlDEMwwxmuOhhPNL0dN1Yd63T01H06LsXPebtLYuCSWEWM3tW9ASF+MJH5gO9zoj6+hb0FJlcjsg402p4cW6Wx7fjlxAkzpvzXHNQ9vPzQ2hoqNNuj682BjK5CgZ9C1oaSj2+fwzDMIMVLnoYt+ho9HTv9FgUPXBa9DgYb3VoegiFv3+Pih7y6QkO8fXaBhcRm5wuzsmd2VN8E4LFeVOea2Jml3U9Mjn8gxLFMfv1MAzDdIeLHsYr5oRC69MRLdFux6BQLVfbHW+pO4TQzR3bW9adHs+FyOYRl5fEzEOS08xFj6cJLn7xpk5Pa1kDDC363tH1sJiZYRimG1z0MN7R9Ljg1aNSKB2Mt2x1eno23rKMo/DW2npU/FDIZHI01FajvqZ7eKorKALUUIb6mnQ9Lq6uS7qe0tJStLW1OdX1sEkhwzBMd7joYTzz6bHV5ZBGXF1iJiQ0Djo9XVfWvaHpIUI6Oj2V5d4pekjIHBmX1OMRl9TtcVXXExgYKE7UXSoqKrJ7Pf+gBCo/0dZSjbYW18dnDMMMDt555x1cccUVVp87ePAgLr/8cowfPx7z58/Hxx9/bHW50WjEa6+9hjlz5ojrXH/99cjPH5x+X1z0MJ6trNvs9EhRFEYPND3W5oSW21s6D7e3iIgoU4ZXeYlncRb9UdfjMHxUoYFvQKw45hEXw5xYLF26VEQ5WVJdXY2rr74aCQkJ+Oqrr3DLLbfgxRdfFMcSb731Fj777DM8+eSTwiCYiqDrrrvOYVd5oMJFD+O98ZaUtG5P0yMVPTY7PTbGW9qed3oiorXm8ZZe55ovjjNik0y6nsKjh3u8wdVW0QR9Y5uXw0fZr4dhTiRo7H3jjTeKYqZrWPcXX3wBpVKJJ554AkOHDsX555+Pq666Cu+++664nAqbDz74ALfddhvmzZuH4cOH4+WXX0ZJSQlWrVqFwQYXPYxHRY9NDa85mMueT4/ahZV1o1eLnoBADTS+SnF/K7w04opJSqWWF2orS9FY59p4ylYOlzrSNHprzq91q9NTXFwMnc5+YGlAiJS4nuPRfWMYZmCRkZEhCpuVK1d2y63cvn27iHZSKDq91CjvkgK+yfvr0KFDaGxsxIwZM8yX0yh95MiR2LZtGwYbFo5yDOPGynq7g06PBz490nhLChy1Tlpv6NE4LiJKi/xj1WLEFR1rckTuCWqNHyJi4lFelIeiY4eROtazrDjf+CC0ljWiKa8GAcNN+VqOCAkJgVarRUNDgyh8qF1tC21H0dNcXwK9rgkKpUnMzTCMc0g31+qiW7q3UavkZgmBO5BOh062oI5NWpqpOy0RGWkKT6bnEbqciImJ6XYd6bLBBBc9jEedHoMjTY/dlXXn461WKyFzQI9X1omI6ABz0eMtYpPSTUXP0UyPix6/hGDU7ChCs4u6HnoyjI+PF6JEEhnaK3qU6kCo/SLQ2lQutriCI0d6dP8Y5kQseO57YwMOHqvqk+8/IikUz/19tkeFjz1aWlqg6oj0sQwyJlpbW80u77auU1s7+JYheLzFeCdl3Wp7y9AjIbPkf+ONTo9U9HhfzCzpejJ7lrjuA+hqWqCrdc0xmooeIi8vz+H1AkJSxHlDNY+4GOZERqPRdBMkt7a2mt3e6XLC1nV8fU3mroMJ7vQwHmp6PBlvOV9Zp1ttNRjFx5Kmx9jSAqNOB5nS5PPj8QZXqfc3uKpKC9HUUAc/rftjM7laAU10AFqK64Wuh3K5nCF1d6jtTE9SXd+dWY64Kgq3oJ6LHoZxGeqwUKdloI23HBEdHY2ysjKrz5V1fBwVFQW9Xm/+nGX3mD5OTzc9zw0muNPDeN+nx1ngqA1Nj0rmQ00Pq7V1hV+nFkXf6PmIKzImwJy2rvPSk5mvfwDCY0xdl8Kcg57fTscWF+l6XCEoKEiIDGml1JFfj9TpaaovFFlcDMO4BhUdGnpD0gcnbxc8xJQpU7Bjxw4YLJ6XN2/ejOTkZISFhYltLdIKbtmyxXx5XV0dDhw4IL52sMFFD+NFR2bJp8f9lXXxRNPFoJBuT97D/C3CX6uCr59StJEqyno2KrNkSMoIcZ5/xPOih3Q9BOl6XI21cGXEpfINgUoTQr8MNNbkenz/GIYZ2NCKOi0/PPjggzhy5Ai+/vprfPjhh/jb3/4mLqduMRkX0rr7mjVrxDbXHXfcITpEixYtwmCDix7Gw05P98ukpHW74y25fU2PvSgKpeTKXN/DDa5e0PXEDzMJhAuyD3h8G5rYAPjIfaBvaIOu2rWOjNSCduaYqu3o9tSzXw/DnLBQN+c///kPjh49ivPOOw9vvPEG7r33XnEsQR49S5YswUMPPYRLLrkEcrkc77//vliDH2ywpodxC6n7alPI3JG9ZXe8Ze702PaYUYtOj84qdFQu8rdKeyxmjowOQF5OFcq8LGb2kclQV1WOuuoKBIaEu30bMqUcmthAoemhEZeKMrlc7PSQIRmJDaVNjK4EhKagqngHi5kZ5gTi2Wef7fa5sWPH4vPPP7f7NVTk3HPPPeI02OFOD+OVlHWXOj0dQuY2fZvNUY5kUNhqsNHp8dYGlxfFzCq1L6Liknvc7fFL7IikOFbt0vUDAgIQHBwsHkNH7sxSp6exNg9GO4UmwzDMiQQXPYwXYyicaHo6xlvtaEebjRdhyavH0qDQG5oeonO85T1NDxE3VBpx9UDXk2Sh67FwpHal2+NoxKX2DROePe3tBlH4MAzDnOhw0cN4pOlp78H2lvOkdaONTk/PDAojO9bWa6qa0NZquyjzhLihI8xFj6tC5K6oo7SQ+ypgbDOI9XV3dD2OxMykZZK6PTziYhiG4aKH8dicEA62t2wXPTKZDEq50r5BodxB6GgPhMyEn1YltriI8lLvdXuiE4ZBrlCiqb4W1WX2V8gdQcWJb2KIOG48VuNWp6e8vNzsqOooh4v9ehiGYbjoYdxEyhQ1ODQntN9JcRRF4au0Xlm3Knoae16o9MYGl0KpRCwFkIrVdc91Pf4dI66mo67pevz9/REaGiqOXdH1NNTkwujg98IwDHMiwEUP4zVNDzo6PTbbQC6Ejqo7vt5ye0vhhZV1yw0ub4uZifhho8R5Xtb+Hut6WksbYGjSeW3EpfGPgkLpj3ajDk21jlfcGYZhBjtc9DBe0/SYOz12AkeduTLb8ulRiJX1nguZe6vTQySkjRbnhTmHYNB7tiWl0KqhCjc5UDfl1nhV1xMQOkwc11cd8ei+MQzDDBa46GG81+npmH3Z0/RYe/XYDx1ttez0BJoKFV1tndeKntKint+WJWHR8fALCIJe14aiY1ke345fkqTrqXZZ10NFTVVVFerr7RdyAaFDxXldVbbH941hGGYwwEUP47XsLanTAw87PbZW1lUhprFPW41r3Q9HRMcGCnPF+rpWNNR5L4+KCo+E1NE9HnH5J5uKnqZjNS5tglE6MgUGErm59qMmpE5PY80x9uthGOaEhosexsNOj/vbW1ZJ6zaLng4hs6U5YXCIOWnd4GBLyRVUagXCI03jsqKCWngTc9Fz2POiRzMkED4KGQyNbWiraHLpaxITE52OuNR+4VCqg4RfDwmaGYZhTlS46GE8i6Fw5NPTw/GWpU+P3FcDWUfMQltNzwuVmDhTqnmxl4ue+NRR4sGpLMlHQ51r46muyBQy+MZ3pK67OOKSih7q9NjrDpl0PaYRF+t6GGZw88477+CKK67o9nl6jhg/fny3bU+Ksnn88ccxY8YMTJgwAXfddZcYmQ9WuOhhvOjILK2sG1wYb+nsxlBYCpnpBVsZbCoEdF4YcfVW0ePrH4DIIUniOD8ro8dbXK769cTExEChUKCpqQkVFRV2r8diZoYZ/CxduhSvvPJKt89nZ2fjmmuusenp9dhjj2HDhg14/fXX8dFHHyEnJ0cEkA5WuOhhvKfpkcZbdhyZrcZbNjo9ahvmhISqY8TlnaLHVFQU5/f8tnpjxOXfIWZuKaiFUWf/cZSggkcyKnRJ11OXD4Pee3omhmH6HgofvvHGG/Hiiy8iKcn05suy80MJ6kFBpjd8Xb9uxYoVIl198uTJIpj0pZdewrZt27Br1y4MRrjoYTzq9LQbHY23PFxZN5sTGq1GNUpJzFztBTHzkECgF8TMRGLaGLOY2eig8HOEMtQXigA12g3tInndndV1R0WP2jdEZHGh3YiG6qMe3TeGORGg5x5jW0ufnDyNssnIyIBSqcTKlSsxbtw4q8tWr16NZ555Bvfdd1+3r9uxY4c4nz59uvlzycnJYkGCCp/BSMe6DcN4Y3vLFSGzg+2tjk4P3XKrwWjW+Jg3uKo908rYEjNXlDYIMXPaSA28RVTCUGj8tGhpakBxbhaGpAx3+zZonOeXHIy6vaVC1+OfYnJddkXXQ7N6vV4vuj/2uj2thZVixBUUYcoMYximEyo6ij5+EK0FmX3y/dVxwxH716fE84A7zJ8/X5xssXz5cnG+ZcsWm52ekJAQqDt0kxKRkZEoKSnBYKRPOz30S0hPT7d5WrBgQV/eNcYTTY/cDXNCGzEUKrmMmjDdQ0eDg7023upNXQ9liyWmjxXHRw/t7vHqemNOtUvv/MLDw+Hn5ycKnuLiYrvXY78ehnEF9wqOgUxzczNUqs4gaAkqgkjgPBjp004PKcVJQGXJ7t27ceutt+Lmm2/us/vFuNLpsXWhOzEU3f+h6N0NdXfIp8ek6zGFk6rMRU+t14qefTsKvV70EMkjxiNz10YcO7gHs8+42KPb8EsMho/cB7qaFuiqm6EKNTk124MeN+r2HDx4UIy4JI2PvaKnub4Iel0TFErHt8swJxr0v0SdlnZd37zg+yjVbnd5eoJGo0FbW/c3oFTw+Pr6YjDSp50eqjAjIiLMJwpRpNnjeeedh/PPP78v7xpjB8v/x67dns7xlvNOT4uNTo+9KApvanqI2F4WM8vkctRUlKC63H7XxREylQK+Hd2oxuwqt1fX7aFUB4osLhog1nO3h2FsQkWHTKXpk9PxLHiI6Oho1NTUdCt8ysrKzMang41+JWR+++23RbvNluCK6R/IO8ZbNnU9Mte3t9psaHpMl0sGhZ3dos5OT881Pb0tZlZpfM1anqMHPR9x+aV0jrjcETPTjL6lpcWF1XUuehjmRGfSpEkwGo1mQTNx9OhR8TwyZcoUDEb6TdFDZkgffvihWLsL7niRY/qvpsdmp8ecsm6/6NE4GG+ZLrfR6Qnu7PR4ut1wvJyZieTh48X5sR4UPZKAubmwDoZW+50ziYCAAISGhorHx/HqOpsUMgxjgro5ixcvFivrpLHdu3cv7rzzTkydOlUYGQ5G+k3R89lnn4kn7osuuqiv7wrjgqbHVqen05zQ/ou0yixktp0BZcugUDInbNfrYWh0LZ6hr8TMRNII05MFbXA1N3qWDq8K8RXr6ySeoiwuV6BVU+LYsWNOih4ftDSWQtfq3eBVhmEGHk8++aRwY/773/+Oa6+9FikpKXjttdcwWOk3RQ8ZJJ177rlCWMX0X3wcdHogdy5k1pizt+x0ejpuo9kyikKthtzfJLpt89KIqzeLnsCQcJG8Tl2XvMN7vbDF5ZquRzIlo6LHXkeMxMt+AbHimEdcDDP4ePbZZ/HJJ590+/y0adOQmZmJuLg4q8/T5udTTz0lfHno9K9//UussQ9W+kXRc+jQIeTn5+Oss87q67vCuNXpge1Oj8GVTk+by+MtQhnUoevxspi5KM87I7OuJI8Y12Ndj/9Q04irycXVdXoyI4+ehoYGJ5EUPOJiGObEpF8UPdu3b0dYWBiGD3ffzI3pO01P1xdiV8wJOzU99oqe7uMta4NC73n1yOQ+aKhvRU2Vd0ZmliSPmCDOcw/vg0HvXJNjC98hgZCp5DA069Ba4nxMRgWPJGgmMaIzMXMdFz0Mw5xg9Iui58CBA8KQkOn/WNQ83cdbLsRQqDqKnhZDq83uha2kdSuDwlrvFD1Kldw84so/6p2RmSUUPuoXEARdawsKj3rm7uojl3UGkGa7P+KyhzYkmSpUtDVXobWp0qP7xjAMMxDpF0VPeXk5b2wNEMhHQppw2dvecrSyrpGbND1U8OhtFEfSeIsMCnuz00PEJ5nGR3lHXSso3MFHJkPS8HFe2+JqdPE+SmLmwsJCu46qcoUG2iCTr09d5WGP7xvDMMxAo18UPe+99x5efvnlvr4bTA/ztzq3twxOOz12Q0c7Oj2t9jo9Xix6EpJNBUX+Me93eixX1ymSwlPdkF+HmLm1tBH6BucusfTmgU7kvZGXl2f3eoHhaeKcix6GYU4k+kXRwwzU/K2uFzj36VHI5JB3XM+WmNlpp8dL+VtEfEdBUV5Sj+Ym2xqjnhA3bCTkCiXqqytQWVrg0W0o/FVQR2vdMip0ZXU9MCzNLGZ2VKQyDMMMJrjoYdzGx16nx4XxFqGRNrhsrK2bNT1dbsPboaOEv1aNsAj/Xuv2KFVqxA8bKY6PZuzy+Ha0HVtcjUcq3dL1kJjZXofJLzAOcoUvDPoWNNble3zfGIZhBhJc9DBuI5d5nr1lOeKyZVBoT8is6vCN8Kamh4iXRly9oOshUkZNFOdH9m/3+Db8h4WJ86bcGhjbnHdlKHBULpejvr5eOJ3bwsdHhsCwVHHMIy6GYU4UuOhhvKbpcWW8ZSlmttnpkdvx6elwZdbV1jrtJHmi68nrhQ0uImXkRMhkclSW5KO6vMSj21CF+0ERpEa7gdyZnd9PpVJpNiBztLoujbi46GEY5kSBix7G8/FWt+0t50Jm605Pm+sr60GmooeERLp6z6IdHOl6ivJroO9SaHkDjZ8WcUNHiOPs/ds8fry1Hd2ehiPubXE59OvpKHoaa/Oh1zV7dN8YhulfvPPOO7jiiiusPrd27Vqcf/75mDBhAubPn4/nnnvOKpiYNj0ff/xxEUdB17nrrrvsdokHOlz0MJ4Lme2YE8JlTU/3osdP2WlOaHn7MoUCisBAr+t6QsP94a9VwaA3ojjf+5EUxLAxprTiI/s8K3osR1wUSdHe1R/Jga6HVtd1Ots5Z2rfEKj9IqhKZXdmhhkELF26FK+88ko381/K1TrllFPwzTff4NFHH8WPP/4oihyJxx57DBs2bMDrr7+Ojz76CDk5ObjtttswGOGih+nB9lbX8ZZrnR51R/5Wi43xlr+y4zboBb5Nb3ODy5tFD3VRJF1Pb/j1EMkjJwrfnorifNRUlHjuzqxRwNiiF8nrzqDE9cDAQBgMBl5dZ5hBTmlpKW688Ua8+OKL5jc8EsuWLRO5W3R5UlISTjrpJNxxxx347rvv0NbWJr6Wsi8paX3y5MkYO3YsXnrpJZHDtWuX5wsY/RUuehiPNT1dJT3S9hZ1DtrbjU7HW202xltymQ+0Hd2eui5FjzTiaqv2rv6mt4seX//OEdeRfds9Dnr1d2OLi4o5d1bXuehhmIFLRkaG0PKtXLkS48aZTFElrrnmGtx3331Wn5PJZKIDTDl9O3bsEJ+bPn26+XJ67oiKihKFz2DD9LaaYTyIorAbQyGNuDo8d+yNt1rs5G9pVQo06Ayo79bp6Z0NrsQO1+O8nCoYDUbIpPU0L4+48rMyxIhr8slnenQb2mGhqM8oQ8ORSoTPSzZrq+xB7+r27NljXl23df2AkKHw8ZF3RFJUQO0X7tF9Y5jBAv2v2AtE7m3UcpXT/2tbkE6HTrYYOdJkmyGh0+nw4YcfYvTo0aIjTJ0eSlVXq00deInIyEiUlHjWme7PcNHDeF/T07G27gOl250eIlCtRElja7eiRymNt2q9q72JHhIEja8SLc06FBXUIi7RVFx5e4tr3YqPUVGch5qKUgSHR7l9G36JIfBRyKCvbUVbRRPUHR5D9qDwUXpHV1tbi+rqavEE1xW5Qg3/4EQ0VOeIbk8EFz3MCV7wPLLmRWRW5vTJ908PH4on5t/lUeHjCnq9Hvfeey+ysrKE/odobm6GStXplC9BRZC9KJuBDI+3GK9peszjLVH02B9vdXZ6bP9DBahMtXh9q87meMubURTSz5OcahIK5xwuR2/g6x+AuJSOEZeHW1yUuO6XEOTyiIueyHh1nWHcpJcKjr6GRlk33ngj1qxZgzfeeENodwiNRiO0PV2hgsfX1xeDDe70MF706bH4czI4T1pvszPeMhc9doTM3tb0EClpETi4twQ5hysw9xRTEdArI64jGcimEdc8z0Zc/qlhIo6CVtdDZyQ4vX5KSooQMmdnZ2PSpEl2i56iIz+jripbiNAtO3YMcyJBHRbqtAy08ZYzysrKcP3114ttzvfffx9Tppg2Sono6GjU1NSIwsey40NfQ7qewQZ3ehjv+fTQ531kTje4NNL2lsHdoiekV8ZbREqaaaxTkFuNtlbHjtIef49Rpi2u8qI81FaW9Sh1vbW0Abo6563noUOHinN6srP05bDEL3AI5Eo/GCmSotb+phfDnAjQ8xg9R/XFqTcKHhpvX3nllcJ3Z+nSpVYFD0FvhiigWBI0S51h0vp0ve5ggIsexmuaHlejKOjdjMNOj9qkBarvUnxI+VveFjITIWH+CA71g9HQjmPZrmVceTbiGt4jzx4KINXEmfyKGrIqnF6fEtdJy0NPava2uEQkRShHUjDMYOSZZ55Bfn4+XnjhBfFcUF5ebj6RpQV1cxYvXixW1rds2YK9e/fizjvvxNSpUzF+/HgMNrjoYdyG1soJm1vpcucGheqO8ZazTk9dm85m0aOvq4NRr++1bs9RF4oJTxnaYVSYtXerx7cR0HE/Gw67VpxJ3R4acTnT9dRWZHp8vxiG6V9QUUNGhLSxRd2e2bNnW52Ki4vF9Z588knhxkwmhtdee60Yi7/22msYjLCmh3EbqQNrsNnpUQhjQUfjLbWD7C1H4y1lgJbaTKYoitpaqMNM4mNvFj07N+cJXU9vMXTUZPzx7adii6uqtBChUUM80vWUr81BS2Ed9A1tUGi7b15YQk9g5LdBnR7q+NBGV1cCw9PFeVNdAXStDVCqtW7fL4Zh+p5nn33WfEzBw9S5cYafnx+eeuopcRrscKeH8Z4js+UGl6Oix4mQOVBtu+ih2zZvcNV4X9eTNCwc8AHKS+pRX2db/+INo8KE9DHiOHP3Zo9uQxmghiYmQBw3ZDnv9sTGxooNDdL0kLbHFipNEHwDYoUXdl0ld3sYhhmccNHDeG97S1zYoenp0XjLpOlp0hmg77L63psbXH7+KsQMMRVVR3ux25M+foY4P7xns8PVfkdo0zoCSF24n9TZoW6PsxFXULhJb1Rbccij+8QwDNPf4aKH8bjTYyv40htCZgodlVyfG7qOuIK9n79lS9eTndk7fj1E8ojxUKo1qK+uQHGeZ0Gf2o772VxQC32j8/VaqeihIEFnRU9dRabT/DSGYZiBCBc9TK90ehyPt6SV9Va7t69V2llblza4qrzf6SFSR5h8KbIOlolIit5AoVRh6OjJ4jhz1yaPbkMZpIE6SiuSWRuPOM8Mo0gK6viQMzOtrtrCPygBcoUvDPpmXl1nGGZQwkUP0wNNT/fLfOTOk9adaXqIAEnX02VtXR1h6nC0VvTO+CkuKQS+fqZIirxjvVNYWY64aHXd4OEmmtTtcWXERZbykjuzvW4PdekkQTOPuBiGGYxw0cN4tdPj44qmR4qhcOB6Kul6uiatqyMjxHlrqWfmfq4UdKkjTd2ewxml6C2GpAyHX0AwWpsbkXvY+XaFI11PU14NDM3W6/2erq6zrodhmMEMFz2Mxyvrtra3zFEUjjQ9HZ0eg5GEygaHa+tdNT3qyEhx3lree5qb9FFS0VMiAgh7Axo1pY2f1qMRlyrEFyoKHW2HiKXwhjtzYBh1enzQXF+Ethbvb8gxDMP0JVz0MN51ZJa73ulxZW29q0GhOqKj01Ne0WsFCeVwyeUyVFU0obKsEb1F+viZ4vzYod1obWny6DYC3NjiCgoKQlhYmHjc7AWQkj+PX6BpDMar6wzDDDa46GG869Nj3t6yX/QoZArIOjK67ImZteak9S6dnvAw0WoytrX1SgaX+B4aBZKGmYqJzIwS9BbhMfEIjYwVmp7s/dt7pOtpyq2BoUXv3RFXOY+4GIYZXHDRw3is6Wn3cHuLQvWcra0Hdmh6um5vyZRKqEJDelXXQ6SN6n1dDz0OaRNm9GzEFeYnTjC2ozGnyuXVdXJnJot6WwRFdKyuVx7m1XWGYQYVXPQwHhc9tja6zeMtB5oeK4NCe6GjdqIojpeuJ61DzEyp640Nrb33fcZNF+eFRzNRV13R60aFMTExwnK+tbVVhBDagsZbCqU/jIZWNNTYDillGKZ/8s477+CKK66w+hzlb5111lkYO3YsFi5ciPfee8/qTSvF01DW1pw5c0TI6PXXX2/3+WGgw0UP4zZSdJPt7S2FU00PYe702HNlNkdRdN9K0nQUPS1lvVf0BIX4InpIIOhH7M1uT2BIOOKGjqS2GQ7t2NCzEdfRahhtFIldBdTSiOvIkSP2U9fNq+sHPbpPDMMcf5YuXYpXXnnF6nPr16/H3XffjQsvvBA//PAD7r33Xrz11lv4+OOPzdehjz/77DMRPLps2TJRBF133XVoa3NufDrQ4KKH8aqmx5XxlpVBoZPQ0boumh4rr56y3htvESPGxojzjN3Fvft9Js0W5wd3/ulRLIUq3A/KEF+0G9rRkO18xDVs2DBz0WNPDB4UPkKcs66HYfo/paWluPHGG/Hiiy8KI1JLysvLccMNN4juT3x8PBYtWoSZM2fizz//FJdTYfPBBx/gtttuw7x58zB8+HC8/PLLKCkpwapVqzDY4KKH8UiLQrQ79Olxbbxlt9PToelpNRjR1mWOpo7qGG/1YqeHGDWeAjiBo0cqenXElTJqIlRqXxFLQWMuT34fAekdRoWHnI+4EhISoFKp0NjYiOJi2wVdYHga/TLR0liK1ibnhRTDMH1HRkYGlEolVq5ciXHjxlld9pe//AW33367ODYajdi4cSO2bduGWbNmic8dOnRIPBfMmGHSFxKBgYEYOXKkuN5gg4sexm3kPg46PWZNj2vjLXuaHl+FDIqOjlJXXY+0tt7Sy52e0HB/xMQFiYyxQ/t6b4tLqVIjddxUcXzQ0xHXcNNj0ni02qlRoUKhQHJyssMRl0LpB22w6R1jbfkBj+4TwwxE6M2coaWlT06e2nDMnz8fr7/+uujk2KOoqAhjxozB1VdfLc4vueQS8Xnq6Eh6P0siIyPNlw0mOpzkGMZLPj1mc0Jn4y1T0dNqZ7xF3QtaW69p0aG+VYcwX1U3TY/k1SN1nnqDkeNiUFxQi4zdRZg0I7HXvs+ISXOQsfV3sbo+9+zLoNb4ufX16nA/qCL80FbehIasSgSNjXY64srMzBRFD4kXbT2GwREj0VCdg5ryA4hMNI3gGGYwQ88n++5/EPWH+sajKmDEcIx55qleeU6j7s3y5cuRm5uLp556Smh7SP/T3NwsLqfub9fomtpesgXpS7jTw3g3e8sFnx7LTk+rgyiKQDsbXJKmx9jSAn19PY7HiCs3uxINdbZdjL1BVHwKQiJjode14chez1rKAR3dnvpDzsd+1OmRy+UigLSystLmdYIiRppurzobBp3piZFhBj29+CaqL9FqtWJkdfrpp+OBBx7ATz/9JNzZNRqNuLyraJk2PH19fTHY4E4P43kMRbv98RYMrgmZWx2FjgpdT3N3rx6VCsqQYOiqa4SuRxkYiN4iONQPQxKCUZhXgwN7izF1tmks5G3onR0Jmjf+9AUO7liPUVNPcvs2AtIjULk+F815tdA3tEGhtX7n1vVdXGJioggfpW5PeLipkLRE4x8BtV8EWpvKUVt5GKHR1loBhhls0P8hdVqMrb2n4XOETK32epdn+/btootD6+oS6emm7cyysjLzWIuOSe8nQR9L1xtM9ItOz4oVK3DGGWeIOePixYtFBcoMgMBRm47MUsq6vsedHkdePZ1r672r67Hs9vT2Flf6hJnwkclQkpeN6jL3v5cyWANNTIDLnj3SFldWVpbd6wRHmro9teUZbt8fhhmIUNEh12j65NQbYy1aTX/66aetPrdnzx6h7aNNL9rWoi7Qli1bzJfX1dXhwIEDmDJlCgYbfV70fPvtt3jwwQdx2WWXCQ+BM888E3feeSd27drV13eN8UjTI3NtvGXW9DgoeqT8rdbuwlxzBlcvb3ARI8fHUAYn8o9Wobqy97K4/AOCkJhuejdG3R5PCBjRMeI66PxxIb8eepKld3T0JOdoxEWr6+zOzDADj6uuugp79+4Va+i5ubmiqfDCCy/gr3/9K0JCQkQX6PLLLxfr7mvWrBHbXHfccQeio6PFevtgQ9bXorFXX31VPPhU9FBr7aabbhIeAlu3bu3Lu8a4UPTQVlM35K4KmdU96vSoI49f0RMY5IuUVNP327O9oFe/18hJc8T5oZ1/wuBk7d+uUaEP0FJcD12NYw0SOTMPGTLE4RaXNigRcqUfDPpmdmdmmAHIxIkThUvzhg0bcPbZZ+P555/HNddcg3vuucd8HfLoWbJkCR566CGx1UV6v/fff1+swQ82+lTTQ0nPJKQie2xL6MFmBkAMhUOfHheFzHa2txzlb4mvP47jLWL8lDjkHC7H3u0FOOmUNPh0FH7eJnH4WPgFBKGpvhZHD+zCsDHutZdJx+MbHyR0PfWZ5QidZn+FVRpxFRQUiBEXPTna+n2SUWFV8Q6xuh4QanJzZhimf/Lss892+xxtaNLJHlTkUBFkWQgNVmR9XfQQTU1NuPbaa4U50gUXXIC1a9f25d1iepSy7qKmx4Xxlr2kdUIjdXp6MX/LkvQx0SJ9vaaqGbk5tredvIFcrsDIyaYnp/1b1vX6Fpek66E3H/R/aAtaXSdodd1THxGGYRic6EVPQ0ODOL/vvvuEloessMkl8uabb8amTZ6lTjPHM2Udnm9vubKyrnYhdPQ4jLcIpVJuFjTv2dbLI64pJ4kVuYLsA6ipcD/3S5saRr8k4dnTWmG7kJEICgoSJmRUzGRnZ9t1Z/bxkaO1qUJscjEMwwxU+rTokeaF1OU577zzMGLECGGXPXfuXPz3v//ty7vGuLKybrPT46JPjxNzQmtNj65bh0Hy6jE0NUHf0HviYkvGTY4T57S63maj++TNENLE1NHiOGPb725/vdxXCf+kYHHc4EK3JzU1VZwfPnzY9u0pNOaxVk0ZuzMzDDNw6dOiJyoqSpynpaXZ1Bkw/RO5g+0t1wNHXV9Z1xnbRQaX1X3QaKAMCjyuup64pBARTaFrMwiH5t5k9LSTzVtcBr3jWAlHsRQ04nI2kpL+//Ly8szurPa3uLjoYRhm4NKnRc+oUaPg7+8vPAMsoXecliZJzEDS9Mhd9Olxbk6oVsihkstcGHEdn6KH1rsndAiDd2zO69XvRavr/oEhaGlsQPb+HW5/vXZYGHwUMrHB1VpiGiPbIzQ0VJgTUhihvRGXpOuhDS5dm+PbYxiG6a/0adFD9tfXXXcd3nzzTXz//ffinea///1vEXlPoWhMPzcntLW91bGy7mx7S+NCp8ey21NnY5xk9uo5TmJmYvyUeMjkPijKqxGZXL2FTC7HyClzxfH+re4LmmUqOfyHhYnjugPOi0Kp22NvxKXyDYFvAK23t3O3h2GYAUufmxOSaPnWW28Vxknkyvzzzz+LtNhp06b19V1j7ODjKGXdxfGWyoXtra66HntePS2lx6/o8Q9QY+RYk2379o2961szaspc8VgXHc30yKE5cGSEWdfT3mU8aK/oIfOylhbb/j4hUSadUU3pfrfvC8MwTH+gz4segro65AS5f/9+4dC8cOHCvr5LjEuOzN0v85G7Nt7SSOMtFzs9tqMojn+nh5DS1vfvKkJLs/t6G1fRBoUicfg4j7s9fkkhkPspYWjWo/FYtcPrhoWFmUdc9owKgyPHiPO6ysMw6HsvfJVhGGZQFz3MwKIjacKmQLZT02N0qdOjM+jEC609AtUdBoWtfa/pkUhICUVEdIAQNO/d0buC+9FT55kdmimB3R3IQNEcS5FR3uMRl8Y/UgSQtrcbRCwFwzDMQIOLHsargaPoMCeEkwgFTYdPT8+iKI6vV48EjZwmzTAJ7bdvzO1Vw76EtDEICA5Da3Mjjuzb7vbXB4w0PUaN2ZUwtOh7NOKinzskytTtqSnb5/Z9YRiG6Wu46GE8j6HogU+PUq6ED4VEuVj01NnQ9GiiTC/o+oYG6OwEZvYWYyfFQaWWo6K0AdmZvVd0yWQys6A5w4MRlzrSH6owP7Qb2p0mr9OIi04Ot7giTbqe2opDMBp6b7THMIxnUM7WFVdcYffyhx56CPPnz7f6HP3Pv/baayKqYvz48bj++uuRn5+PwQgXPYx3U9YlTY+T7S3qGqhcMSjscGVusNHpIa8eSczclH98fZ00vkpMmGrq9mz5wxSn0luMmDxHpNcX52ahosS9JyJ6nAM6BM31Xtji8guMg1IdBKOhDXWVWW7dF4ZhepelS5filVdesXv56tWrsXz58m6ff+utt/DZZ5/hySefxLJly0QRRJvVbW3ujdQHAlz0MD1IWbd1oZSy7tyxWBpxOdrgCugIHbW1sk74xZtckpv7wMxy6pwkkWhOnZ7ykvpe+z7awBCkjDSFge7btMbtrw8YYeqINRfUQVfrWICcnp4uzo8dO8YjLoYZIJSWluLGG2/Eiy++iKSkJJvXKSsrw8MPP4ypU6dafZ4KG4qAoqT1efPmYfjw4WKbuqSkBKtWrcJgg4sexvMYCptCZplL4y1Co9SI8yZdi0eaHsI3Lq5POj1ESJg/ho+OFsdb1vdut2fsjAXiPHPXJrQ0uxe7oQxUi+R1ov5guddGXCKA1IXfM8MMJEijRzEzfXHyVB+YkZEhYp1WrlyJcePG2fyZ7r//fpxzzjndip5Dhw6hsbFRBH5LBAYGYuTIkdi2bRsGGx1vyxnGdeQOhMw+ClNnpt2JkJnwV/qK8yad7egDy6KnoSN/S/II6tbp6YOih5g+NwWH9pVg7/YCnHx6Ovy1plV8bxObnI6w6DhUlhTg4Pb1mDDnNLe+PnBUJJrza4VRYci0uG6PY9cRFwX+0oiLXNO7og1JhkLpD72uEfXVOQgMM2V3McxAh55j/vvGRhQ4sXjoLeKTQnDV32c6/P+0BWl0uup0LPnwww9RXl6Ot99+W2h+LKGODhETY/Ifk6AgYumywQR3ehgva3pMI6t2J6aDhJ+56GlyWvQY2oEmvaFfdXqI+OQQxMYHQa839qq2h54Ex84w+Vft27TW4Zq/LbRpHbEUVc1OYyksR1y2srh8fGQIijQVQzziYgYb7pUb/R/q5Lzxxht44YUXoFJ1bs1KSP/jXS9Tq9VobbWvtxyocKeH8aojszudHj+V806PUi6Dr0KOZr1BePX4KxU2Oz1tlZXQNzVB4eeH4/1YzF6Qii8+3I6tG45hxrwU+Pp1f2LxBmnjp2Pjz8tRV12O3My9SB4x3uWvlakUIpaC3Jmp26OJCbB7XRpvRUREiHeG1O2x1S4PiRyNysKtqCnLQPzwc0UhxDADHfp/pk4LeXD1BUqV3O0ujyOoaLn77rtx0003Ca2OvTgoSdsjHUtf6+treo4eTPAzFePdTo9U9LjR6Wlss1/0ONP1KLRaKEOCxXFzQSH6gvRRUYiMCRAz+W1/9l40hVKlxsjJc8Tx3o2/uv31NOKSdD1GveNOkfQESe8SbREQlgqZXA1dax0aa3s3fJVhjidis1St6JOTNwsegsK8s7KyRKdnwoQJ4kTjraKiInG8fft281iLhM6W0MdRUVEYbHDRw3jVnNBHLhU9zj1c/JV+Tjs9lmvrtvK3CL/4+D7b4JKcj+csMOlaaMTV6sQEsCeMmbFAPDHmHzmAqrIit77WLzEYCq0KxhY9GrOrXCp6CgoKUF/ffTNNJlMgKGKEOK4p4ywuhumPjB07VmxgUbzTihUrxOniiy8Weh06Hj16tPhf12q12LJli/nr6urqcODAAUyZMgWDDS56GM9X1m1lb3V471DgqLPNHr+O7a1GZ0WPg6R1wjduSJ/qeogR42IQFuGP5iZdrwaRBoaEI6ljrOXu+rqIpRhteudWt6/U8fcJDMSQIabHNTMz0+Z1QjqyuCiAtDddqRmG8QwaVyUmJlqdgoKCoFAoxDFdTlqeyy+/XKy7UwYmdXfvuOMOREdHY9GiRRhscNHDuE1HzWNH09OpuXGm6/FXudjpcbK2LnV6+rLooUJw9oJh4njz7zm9qgmQBM2Ux9XaYl8E7mjE1XSsGrr61h6NuALD0+EjU6C1uRLNDe6nwDMM0z+47bbbsGTJEuHWfMkll0Aul+P9998Xa/CDDS56GC9rejpFvM50PebtrTbHL9ySQaF9r54hfbq2LjF64hAEh/qisaENO7f0ns4lbugIhEbGQtfWikM7Nrj1taoQX/jGBYrj+gzHDs20uk6jNDI+q67uvsIrV6gRFG7a9Kou2ePW/WAYpnd49tln8cknn9i9/NZbb8XatWutPkdFzj333COsKnbt2oV3330XcR2bsYMNLnoYj4seu9lbHZs87Xq9iyvrjl2CA51pehJMnZ6WsjIY+9A2XS6XYdZ8U7dn42/Z0NtYsfcGVIiQtofYu2mN00T7rgRKI679pQ7HUn5+fqIF7qjbExJlGrVVl+7lERfDMP0eLnoYt5E2DOy9yHWurbvW6Wl04NNDaKXxlh1Nj5Jm1FotzdvQXOSeuNfbjJsSh4AgDeprW7BnW+91ntInzIRK44vayjLkHnbPK0ebFg4fpRy6mha0FNS5NOI6ePCgzd83iZl9ZEq0NlWgub5vtucYhmFchYsexqvbW9Zr6zqvaHoCnWh6qAjz7fDracrr2xGXQiHHzJOHiuP1v2ZBp+udbo9KrTGnr+/e8ItbXytTyREwPFwc1+53LGgeNmyYED3SeKvrSqt5xNWxxVXFIy6GYfo5XPQwbiN3oOmxdmXWubS91eTUp8expkfcVsf8ua/W1i2ZND0BgcEa1NW2YNuG3tvkGjfzFJF1VpB9EOVFeR6NuBoyK2B08LiSK2tKSorDEVdo1FizrodHXAzD9Ge46GF6IGS2fbm0wdVu0Lnk09NqaIPewXq7pOlpaNPbLbTMnZ4+FjMTCqUc8041CXw3rDmClmbnnkWeEBAchmGjTT4au9f/7NbXamIDoAz1RbveiPrMCpdGXLS6bm/EJZMp0dZSjaa6fLfuB8MwzPGEix7G85R1u+Mt1/K3fDs6Pc5GXFL0BH23Rrtr6/2n00OMnRyHiCitKHj+/M12Wrk3GD/nVHGetXcrGmpdD0mkkWDgKNc8e5KTk4WXB5kUFhZ21+3I5CoERY4Ux7zFxTBMf4aLHsb7mh4XXZnlMjk0CrXToofGaVqlXBzXOSt6iorRbuib3Jyu3bD5Z5g6JFv+yBHC5t4gKi4ZsUlpMBoN2LtptfuePT5AS1E92qrsi8lJ05Oamupki8uUz1Ultrjc2yZjGIY5XnDRw3jVp8cdIbNVFIUzrx610qErsyo8HDKNRqzJNxeXoD+QNioKcUkh0OuM+H3V4V7v9mRsWYe2VteLK4qk8E8OEcd1+8tcHnEZbBSVQeHDTVlcLTWcxcUwTL+Fix6mBzEUzlbWnRc9ZjGzkw2u4I6ip7qlze64xk+Ko8jtHy+6dJ8WLjZtNu3amo+KsoZe+T7Jw8cjKCxKuDMf3L7era8NHNMx4sooRbs9kRaAhIQE+Pv7o6WlBUePHu12uUyuRDCPuBiG6edw0cP0wnjLte0twq9jbd1Z/laEn2kMVt5kPzrBf6hpy6jhyBH0FxJSQpE6MlIUFL/9ZHs01FNog2v8bFNGzp4/f4XRDbNC/5RQyH0VMDTq0JhjP4RUJpNhxAhTAUdBhI5GXCajQh5xMUxfQCnqV1xxhdXnKF4iPT3d6jR//nzz5fSc8dprr2HOnDkYP348rr/+euTnD86lBC56mB4UPU62t5wIma2jKBwXPeF+pkKqosn+bQakmtyQG7L6T9FDLCBtjw9wcG8JcnMqe+V7DJ84C2pff9RVlyPnwE6Xv85HLkOAJGje63gsOHKkqZOTnZ2N5uZmm1lcMoUGutY6NNT03qo+wzC2Wbp0KV555ZVun6ex9I033ogNGzaYT19++aX58rfeegufffYZnnzySSxbtkwUQddddx3a+tDhvrfgoodxG1nHX419TY/K5fGWv9mV2cVOT7P9To+2Q2zbcCTb7WiG3iQyJhATpyWI419WZNjtkPUEpUqNMdNP9mh9PWhstDhvPFoNXZ39xzciIkKc6AnRVvK6TKZAcMQocVxdstfNn4BhGE+hfDwqaigpPSkpyeoykiEcOXIEo0ePNv8P0yk0NFRcToXNBx98IEJH582bJ/R7L7/8MkpKSrBq1SoMNrjoYTyOofCGkLkzf8u1oqfCwXiLNrhIzGxobkZzYd/GUXTl5NPSodYoUFJYhz3beqdtPGbGQsjkCpTkZaM41/VulyrUF77xQcIToG6f427PqFGjHI64QqOlERcZFfafwpNhBjMZGRkiEX3lypUYN870PyiRl5eHpqYms8loV2gjs7GxETNmzDB/LjAwUHR2t23bhsEGFz2M59tbPVxZJ/xUriWtS+Ot2lY9Wg22X0x95HJoU5LFcUNWFvoT/gFqzF2UJo7X/ngIrS3eNyz0DwhC+vjpHkVTBI2LNnv2OBI007tAKnqLi4tRVdVdAxQQlgq50g/6tgbUV/WvMSPDuAJ1RnRtrX1y8tTRnPQ5r7/+OuLjTeHLlhw+bNocpeT1+fPnY+HChXjiiSeE7xZBHR0iJibG6usiIyPNlw0mTOILhvEkhsJp9pYbmh4nSetkUOinkKNJbxDdniEBpq/rijYtFXUHDqL+8BFEzjeNe/oLU2clYeemXFSWN+KPX7NwylkmjYw3GT/7VBzcsQE5GTtQV1WOwNAIl77Of1iYEDTrG9qEoFk7LMz29fz9RfucNrgohHTWrFndRlwhUWNRUbAZVcW7EBhmKvQYZiBARcdX7zyNEjc6pd4kJjEVf/nbA+ZuujegoocWEaiIefvtt0Xn5/nnn0dWVhY++ugjsz6PDEi7RtDU1tZisMGdHsZjIbO9NyWdmh77mU5dfXqcJa1bi5lbXRAz969ODyFXyHDK2aZCZ8v6o6iqaPT69wiLjkN86ijx5L3LjW6PTNEpaK7d45qgmVrqtt6ZhsZMEOfVpftgdEHXxTD9CR/aOhhE3HTTTdi4cSNuvvlmpKWliU7PCy+8gK1bt2Lfvn3QaEy2IV1Fy62trfD1tf3mciDDnR7GbaQ3IQa74y03trdUrvn0SLqevLpmlDvY4JLEzI3HcmFsa4Osy7uXviZ1RCSGpkcgO7Mcq1YewMXXmLKzvMnEuWcgPytDePZMnX82fLWBLguaa7YXookEzbUtUAZ1xoRYMnToUPEukNrjBQUF3Vrq2uAkqDTBaGupQU35AbPOh2H6O9RhoU6LXtc3W0sKpcqrXR6CujwhISYTUgnJYZ3GV9JYq6ysTPhxSdDHtNo+2OBOD9MLjswqDxyZXSt6nHn1qCMjoAwKFM7MjUf739o0PaEtOmekeAwPZ5Ti8AHHuVeeEDd0BCKHJIkn7r2b1rgvaHaSx0WCSXrHKHV7uuLjIzN3e6qKXV+fZ5j+8j9K25B9cfJ2wUPce++9uOqqq6w+t2/fPnE+bNgwodPTarXYsmWL+fK6ujqxrDBlivfflPU1XPQw3hcyu+XI7OvyeMuVooeeNKRuT30/8+uRiIgKwPSTTJsUP3+zH7o272aF0WMwcd5icUxFT1ur84Kyq6C5dr9jQbM04iK9gE7X/fccGj1RnNdVZELvwu+WYZje4dRTT8WmTZvwxhtvCD3P77//jn/84x8488wzRdeWtDyXX365WHdfs2aN2Oa64447EB0djUWLTKangwkuepgeaHq8uL3lRMhspelpdtx61vZTk0JL5p6SisBgDWqqmrF+tff1RykjJyI4PBqtzY3I2PqHy1+nTSVBsxIGEjRn23doHjJkCIKCgkTBQx4gXfENiIZvQAza2w0cS8EwfciCBQuEYSEVNGeddRYefPBBUcw8/fTT5uuQR8+SJUuEc/Mll1wCuVyO999/X3R1Bxtc9DDej6HwaHur2em6pqVXj73RWn8XM0uo1Aqcdu5ocbxxXTbKS03ro96c40+ce7o43r3hZxhcKEAlh+bA0ZHiuNaBQzN1kywFzbaQuj20xcUwzPHh2WefFevplpx++un45ptvsGfPHuHGfN999wldngQVOffcc4/oCO3atQvvvvsu4uLiMBiR9Qcnya6ZIHT6+uuv+/quMT3V9LixvWVsN6JVb39sRYRoVKBvrTO2o65V57TTQwaF+gbvb0h5i/TRUULYbDS046ev93vs0WH39ifMgH9gMBrrapC5a5PLXxfY4dAsCZrtIRU9ubm5QgPQldCY8WIXpqHmKFqbqz36GRiGYQZV0UPzQ6o4169fb5ULcsYZZ/T1XWOcFj1wMt5y3ulRyZWQ+8hciqJQyHwQqjEVVI42uJSBgdBER/W78FFb3ZLTzhsNhUKGY0cqsX9noVdvX65QCt8eYucfP7kcRKoK8YVvQpDTbk9wcLB5c8tWt4c2uLQhJu1SdQl3exiG6Xv6vOghISSZnZFxkmUuiOQdwPTv8Zat7oQ7MRT0wi8lrbu6tu5MzGzZ7anPNLmR9ldCwvww5xST8JpW2FuavetrM2rqSSKItKaixK0g0qBxpjXWur2lMOrtF0tjxowR5/v32+5UhXVscVXyiIthmH5Anxc9FFxICnJm4CCXd65V2tL1uLO9ZbXB5cbauiODQiKwY/RSs9e0mtmfmTEvBWER/mhsaMNvPx3y6m2r1L4YO2OBON657geXR2jaYaGQa1UwNOvQcLjC7vVo5ZU6tTTeos2QrgRHjYWPjxwtDSVoqu9feWgMw5x49ItOD2X4XHbZZZg5c6ZQjv/xh+vbJkzfxVAQeltFjxvbW5ZJ6650eqQNLkfjLSJ4gskQr/5Qpggg7c8oFHKccb6pY7JtYy6K8mu8evtU9JDpWVnhMRRkH3RZ0GxeX99dbPd6tN1BPh9St6crCqUvgiJGiOOqIvbsYRjmBC569Ho9cnJyRL7HrbfeKhTj48ePxw033CBU5Ez/RC7v/LMx2Aj/7DQndM3VtHODyw2vnmbHnR5NdDTUkZHCpLA2w3YieH8iOTUcoyfEiqTz777Ya/Nx9RRyZB45ea443vn7Dy5/HTk0k3K8pageLaUNdq83erRpC42yfFpaugufw2InifPK4p1oN3rXk4hhGGbAFD0KhUK4QC5btgzTp08XT560Sjd79mzhEcD0T0hQLGErikJmHm85396y9urx3niLtELB48eK45rdA8Mn5tRzRsHXT4nSojpsWpfj1dseP+dU+MhkyD9yAKX5rt22wl8FbVq4OK7dZb/bExUVJXR4BoNBhJB2JTB8OBRKf+jb6lFX2b81VgzDDG76fLxFqc1dRcuUC0Kr7Ez/3t4iDAYbGhE3trfc1fRI463aVj1anXRDgsePH1BFj3+AGos6Akl/X3UYleX2uyvuEhgSjrRx08Xx9t++c/nrgieYBM31h8qFvsdegSl1e2yNuCh5XYqlqCza7tH9ZxiGGfBFD7XDJ06caJX5IT1xkkCS6Z/Qi5yk6zHYWIM2d3pc1vS4vr3lr1TATyF3qdsTNHa0SEdtzi9Aa2UlBgJjJ8chJS0CBr1RjLkcRUG4y+R5Z4rH4+jB3ago7i46toUmNgCqCH+0642o22//jciIESOEwRmFFNp6wxIWO1mc15RlcCwFwzAnZtFDW1spKSl44oknsH37dmRnZ+OZZ57B7t27cdNNN/XlXWNc1PXobXR6Os0JdS5tC/kpNS759HSLo3BS9CgDAqAdNnRAdXuooDzzgjFQquTIy6nCzi2uFSeuEBIZg9QxpgDBbWtd6/aIMWFHt6d2d4nd36evr695C9NWt8cvcIg5lqKqeHcPfgqGYZgBWvSQVf7bb7+NsWPH4vbbb8d5550nbLL/+9//mlOcmf6JQm6/0+MjV3R+4Iorsxs+PdZePc7HZ8HjTVtcNbv3YqAQHOqHk09PF8ervz+IulrvbZ9NPvkscZ6dsQNVpa6ZIQaMiIBMLRfuzOTS7MyzhwxHaUmhK2GxpoKLR1wM03u88847uOKKK6w+Rx3YO++8E5MnT8a0adNw1113ia1pS5YuXSpyuuj1+NJLLxUp64ORPtf0hIeHi+4OuTDv3btXiJrpF8P0b8zjLQedHrfzt9pcG3uES2JmJxtclkVP7R4aFXlvI6q3mTo7GbEJwWht0eOnr7wXUREWHYeUUZMoLRbbf/vepa+RKeUIHG1yuK5xIGhOSEhAQECA2OCi0XVXQqMnAD4yNNXlo7nBvtMzwzCeQYULhYta0tbWhmuuuQZFRUX4+OOPxZY0vTGhpSEJyuV6/vnn8X//938iAopyt66++upuhdFgoM+LHmagj7dsFBIWnR5XNrg6V9adJ60TkR1FT1mj86InID0NMo0GutpaNOV6b1R0PMTiZ104VpxnZpTi4F77xYa7TJlv6vZk7d0inJpdIWi8acRFnZ62mma7nVtJ0ExvYLqiVGsRFG7y7OFuD8N4D9LR3XjjjXjxxRdFwoEl33//PQoLC/HGG2+IvLxx48bh/vvvx9GjR9HQYFqWoInL5ZdfjrPPPlvoaSmBnUbWy5cvx2CDix7GIzqFzDY6PT4+buVvmbe3XBS4mjU9zc5vW6ZUImj0KHFcvWtgaUmiYgIxa4FJ0P/TNxlodmGc5woRsYlIGj5OdI+2r/vB5Twuv6QQp+vrNOKi339BQQEqbYjHw4eYuriVRezZw/RP6P/C2Gbok5OnHV3KviOj0JUrV4qixhKaopAlDE1VJObMmYPVq1dDq9WK/9Njx45hxowZVnYyNHHZtm0bBhsW4guGcb/TY89Ej6IoSMhsdGGDy1NNDwmZKeldygKzR8ikiajevgOVGzcj7i/nYiAxZ+EwHNxTjIqyBvy68iDOvtj6Cc1Tpsw/G8cO7UHmro2YOv9sBIZGOP2a4EmxaDpWjbp9pQidmQC5uvvTB423SNB85MgR0e05+eSTHXr2SG7NDNMfoKKj4H97hSFnX6AZEoi4i01vHNxh/vz54mQL6uhQAfPmm29ixYoVQm9HXnj33HMPAgMDUVJi6vbGxJi6uRKUh0ljsMEGd3qYHhkU2ur0uOvKLG1vNbng00OEaFRkFAydsR11rc6LqrCZ02n2ggZyDO74Bx8oUETFmReOBXyA3dvykZ1Z7pXbjYpPQXzqKKFzcrXb45cUDFWor3hH6mh9nYSQ0rtPnc7698OePUy/x82Co79DIywqdijn8l//+pfYlt6xYwduvvlmUeQ1d8T0qFSdWkyCMvVaW51LCAYa3OlhehQ6atOc0GKDyxVNj+TT02pog95ogEJm8uFxVHCFalRivEUbXMEa63/WrqiCgxE0ZrQQM1ds2Ii4JX/BQCIhORRTZiZi25+5+H75Xtx490lQaxRe6fbkZ2Xg0M4NQucTEBzmfH19UizKfs1G7c5iBE+IhY+FUaUEaQroHSSFkFK23qhRpvGipWdPWd4Gs2ePouP3zzB9Df2NU6elXdc3Sw8+SpnbXR5n0KjKz89PFDxKpUl2EBQUhAsuuAD79u0zmwOT4NkSKnhI1zPY4E4P4xFymQMhs5udHt+OTo9na+uuvROJmDPLdP31GzAQWbB4BIJDfVFb3YzV33tnlTQ2KQ1DUobDaDBg5+8/uvQ1ASMjIdMoxPp6Y7btzQ560pa6PWRB0RX27GH6M/T3K1PJ++Tk7YKHiI6ORnJysrngkVIPCNLeSWMtWmu3hD6miJnBBhc9TA99euyNt1x3ZZbL5NAo1G4VPa4aFEqETp8GH4UCTcdy0ZSXj4GGSq3AWReZ9Dw7NuUh53C5Vze5Dmz/A411NS6tr4sgUlpf32Hf54e2uGibq7i4uNuTqZVnT+HWHtx7hmGcMWXKFKHNsQwDPnzYlIGXmJiIsLAwURRZJiOQ7ocMg+lrBxtc9DA96vTYFTJL21sG16Io3PXq6Uxbd22jidyZgyeMG9DdnuRh4Zg8M1EcU0QFefj0lCEpIxCTmAqDXo+df/zk0tcEkUOzzAfNBXV209cpU0+KkrG1vh4WMxE+PnI01Reiqa6ghz8FwzD2uPjii0VEDBkSZmVlCT3PQw89JEwKpdEz+fiQKTD59dASwj/+8Q9RJC1ZsgSDDS56mB5pevRe6PQQ/ua19d4ZbxHhs2eL84oNf3rN7O94s/BMyzFX90Rzd6F2+uSObk/G1nVorK91+jXKALU5fb1mZ5Hd60mrs5S83lUvoFD5IzjK5OlTXmCdvccwjPcIDQ0VpoXUvbngggtExBNZS5Bvj8SFF16I2267TRgbnn/++cLXh4og+trBBguZmR51eoz2hMxuaHqsDQrdX1t3ldCpUyBTqdBSVIzGnKPQDk3BgBxzXTgOn7y9GTs25WLE2BikdBQgnpKQOhpR8UNRmp8ttD1zzrzE6deETIpFw6FycdLPTYLCv7uYPD4+HiEhIaiurhbtdUnnIxE+ZDqqS/agqngX4tLOhLxjxMkwjOc8++yzNpcLKJ7CEddee604DXa408P0sNNjdLK95eJ4q8Orp7HNPU1PbaserXZGbF1R+PkiZPIkcVy6eg0GKsmplmOuPT0ec1G3Z9op54nj/VvWoqHOfr6WhCYmQCSwtxvaUbu72CVBc9fuWkBoCtS+YTAaWlFdOjACYRmGGdhw0cN4hMJsTuis0+OqpkfjVqfHX6mAn0Ludrcn+tRTxHnZ2nXQNzZioELbXEEhpjHXmh96PuaKHzYSMUkmbc8OFzO5gifGmtPXjXrbhSdpBkhPQGJmssq3xMdHhvC4aeK4gkdcDMMcB7joYXoYQ2Hfkdk9TY/kyuyakJmI1poKpYJ611PIg8aNhW98HIwtLShdvRYDFfLpoTEXsX1jLo5mVXih22PyL8rY9gfqa7pHSHSFdD2KADUMzTrUH7S9TUY+H2lpaeJ49+7u6+nk2UMhpI21eWiqt68PYhiG8QZc9DA9G2/ZNSd0c3tLJW1vuV7AJAaZCqVjNU1uvbjHnrVYHBd//yPaDQM3/4m0PJNmdI652lp7NuaKSxne4dujdymBnYwJg2mTq2N93Z44XBI0kyOs5P4qoVQHIDjCtEFSUcDr6wzD9C5c9DAeoZBW1p12etwTMru6vUUkSUVPrXtjqoh5J0ERoEVrWRmqtg3sKATa5qIxV02Vd7a5pi00aXsObl+Pumrn3aPAsdHCRbatoglNubZ9fmJjY0WOD22PkANsV6QRV1XxThgN3glVZRiGsQUXPYxHyJzFULit6XFve4tIDjYVPXl1zXZNEm0hV6sRdcpCcVz0nWu5U/17zDW2c8x1pGdjrtjkNMQPGwWj0YDta1c6vb5co0DQGJNra/W2QrvdtQkTJphHXMYuhXJgWCpUmhAY9M2oLu3u6cMwDOMtuOhhetTpsRtD4eb2lr/K/aInyl8DjUKGNoMRxQ2dbqOuEHPG6SKEtG5/BhqyczCQSUmLwKQZCeL4u8/39njMNXWhKYn+4M4/UVvZ3U25K8GThohA1ObcGrtmhcOHDxf6nvr6emRnZ9sQNE8VxzziYhimXxY9TU1N4smLVlHz8vIGZRor41zTY3Sasu6uI7PrRY/MxweJgZ6NuNQR4Qifbcrjyv1kKQY6nWOuph6PuWIShyExbYxIYN/mQrdHGaSBNj3CYbeHQg/JEI3YtWuXnVgKHzTUHEVzg/0Ed4ZhmONW9JCr6meffYZLLrkEU6dOxZlnniksrk899VRMmjQJV111FT7//PNu7qvM4N3esitk9nB7q9GN7S0iqWPEdazWva8jEi69WORx1ezajZo9A3usotYorcZcPc3mkro9mbs2orq8xOn1Q6YMEecNmeUijNSeoJlGXfn5+aiosB7DqTRBCIoYIY55fZ1hmD4ver7++mucfPLJeOmllxAXF4d7771X2Fh/8MEHePnll3H33XcjMDBQXL5gwQIsX7681+400498epwJmd3N3tK5N6ZKCvJ3e4NLwjcmGtGnLjJ9/Uefis7GQB9zSaaFKz/fg5Zm1x57W0TFpyBpxHixkbVtzbdOr6+J0sIvMRhotx9ESs8PUh6XrW5PRNx0cV5ZtJ0FzQzD9F0Mxd/+9jeUl5fjkUceEYWPStXdcp6gTg91eX788UeR27Fq1Sq899573r7PTD9AJvn0OFtZd3V7y0LTQy+01BFwZ4OLvHp0BiOUHcWYq8RduASla9aiMTsbFRs2ImKuKZ9rII+5sjPLUV3ZhFXfHsDZF5vWxT1h2sJzcezgbhzeuwUT552B8Oh4h9cPnjJEbHDV7i1F6IwEyH1NfwOWkKCZQg8PHDiAOXPmQKMxeS0RgeHpUPmGoq25SkRTSFtdDMO4DsVNbNiwAZ988on4+IorrsDWrba1cs899xzOPdfU1aV8Lmpi0Gv96NGjRSjpyJEjMdhw6RVi0aJFotNDYyx7BY8EXU4P4ooVK8TXMYO702M3hsJNTY803jK2G9Gid10fFuarglalgKG93S2TQglVcBDi/mL6p8/9dCkMA1ybRtlcotDxAXZvy8fhA57rYyJiEzFszBSgvR2bV33t9PrU6VFH+qNdb7QbTUFd4vDwcLG+vn///m6C5oi4GeK4LH/jgA2FZZi+ggoXCg215PXXXxdFkHRav349Jk+ejNTUVJxyismhntLVn3/+efzf//2feK2n/9Orr74aVVVVOCGLHkpddRd6p06JrswgFzI70/S4ON5SyZXiRNS11rv1d2b26/FgxEXEnnMWVGGhaC0tQ+4nn2Ggk5gShulzTWGq33+xF02Nno+KKJPLRyYTHZ/i3Cynvwvq9hA1u4ph1BncXl8PHzIFPjIFmuuL0Fib6/H9ZpgTCYp4ufHGG/Hiiy+KcFFLgoODERERYT6tWrUKe/fuxWuvvQZ/f5M84O2338bll1+Os88+W4ygn376abFtORhlKh5tb9GmFj1o27dvx7Zt28Rpy5YtWLdunXjQmRMnZV1vdDbecq3ooRfDIHWAOK5tcb3oIaSi56ibG1wSco0Gw265SRwXf/8DajMOYKAz//R0hEdp0VDfip++tu6ouENIRAxGTDRtuW365Sun3ZcAiqYIVMPQpEP9Advr7iNGjBBjrdraWhw9etTqMoXKH6HR48Vxef5Gj+83w3gK/Y3rdLo+OXna3czIyIBSqcTKlSvNDui2qKqqEp2gm266CSkppjdGlZWVOHbsGGbMMHVZpW1L6gbRa/tgwyVNjyVU3FALjJ6wbEGVI4mamcGNwmxO6J3sLSJIE4jypirUutHpsRIze7DBJREyaSIiF8xH2Zq1OPL6mxj/6kvCxHCgolDKcc7F4/HB638iY3cRRoyNxshxpoBQd5my4Bxk7t6EoqOZyMvaL9bZ7eEjlyF4UiwqfjuK6u2FCBwTLeIqLKEnZ9IM0JumnTt3YujQoVaXR8TPFGLm6pK9iEs7G0q11qP7zTDuQkXHsmXLUFTUNzlw5F5OG9Guahol5s+fL07OeO+998Qbjmuvvdb8uZIS03ZmTIwpUkaCXNQPHToEnOidHtrUCgkJEa2xhQsXCt0OtcYuvfRS8Yti4fKJ1emx54Ts7niLCNR41umRnJlLGlrQovc8Syv5mqvEmKuluARH3/8vBjpDEoIxe75pW+qHL/eJro8nBASHYfQ00xPqZur2ONlyCxoTDZlGAV11CxqybAeX0oiLni/I44sS2C3xD4qHX2A82tsNqChks0KG8QYNDQ344osvRMGjtnhDJ+XhddXr0nUGo/+e250eCg186qmnhACK3FWpKj7ppJPEidpz//73v/Huu+/2zr1l+mHgqDMhs+t6kmDzeKvOrfsSqFYiVKNEVYsOubVNSA8z3Y67KLT+GHbrLTjw+FMo/eVXaFNSEH3awBbjzz0lVYiZS4vq8P3yvbjo6sluv4skJs9bjAPb/0B5US6yM3aYBM52kKnkCB4fg6rN+ajekg9tWli370nr65S+Ts8n1O057bTTrC6PjJ+JYxmfo6JgE6KT5wmRM8P0NvR3Sp0WEtr3BTRW8uT/0xVWr14ttqu7anSlDcqu/npU8JCuZ7Dh9jMJCQ+jokxZO4mJiWL9VIK2u2gVlRn8KFxeWXdvvOVJp8dbIy4iZMJ4JF5+qTjOefc/qDvQ8xDPvkSukOHcS8aLrLTDGaXYa8dDxxm+2kBMmH2qON7869cwOkmnpxEXBZG2ljWi6Wi1zeuQoSlx8OBB8S7UkpDocZAr/dDWUoPacn5OYY4fVHTQCLYvTr1V8EhFz0knnSTecFgijbW6dlzpY+m1/oQuehISEsS7MyI5OVm0xnJyTNlFVB03NnomJmUGFjIvmxMSQdJ4y01Nj7Uzc8///oacfx7CZs1Eu8GAQ88+j+bCvpnve4uo2EDMOzVdHP/8zX7U1bi/2k+Mn3MqNP5a1JSX4NDOPx1elzx6gsaZnkyp42NLoElPtkOGDBFvpGiTyxKZXInwIaY8rvL8TR7dX4ZhOiEN3QwLsbJEWFiYeC0nva4EvZbT9adMsd/RPWGKnrPOOktsaH366acIDQ0VgsQnn3wSa9euxZtvvml2XGVOjE6Pt2IorIoeN8dbRE/X1i2hd1upt90C/5Rk6GrrsP/hR9HSIfYbqMycl4LYhGC0tuix8vO9Hm2JqNS+mDzvTHG8dc0K6HWOf7chk4fAR+6DlqJ6NOfXOuz2UIYfjcctMXn2+KCu8jBaGp0HnzIMY5vi4mJUV1eL4F9bXHPNNcJQmPx6jhw5gn/84x9oaWnBkiVLgBO96LnuuuvEzJOepIhHH31UtKdvvvlm0fGheApm8CPv6PTYDRyVu2dOSJhX1j3o9CR2FD0VzW2ob+v5PJ7W2Ec99jB84+PQVlmF/Q8/hpYu7d+B1pk79+LxUChkIpdr5+Y8j26HBM3aoFA01FZj3+a1Dq+r0KrE9hZRtaXA5nVocysoKEg8wdLarSVqv1BzHldZ3gaP7i/DMBAuy5Jnjy0uvPBC3HbbbWKdnTQ/hYWFogiixgZO9KJHJpPhvvvuwwsvvCA+puRkmhWSKpx8egZjO4xxFDhqb7zVoZFvN6LdaOh1TY+fUoEof9NGQq4XRlyEMigIo594DJrYGLSWlWPvvf9AQ461r8xAgnx75i82vdNbtfIAqivdf5wUSiWmLjhHHO9Y9z3aWpqdB5HKfNCcW4OW4nqbzycTJ04UxyRo7tqBikqcI84rC7dD72YYLcOciDz77LPmCAqJsWPHClnK0C72EJbQVtfvv/8uGhrk7Ex+WoMRt4oeMiT86aefur0j02q14kGlc+ZECxy1N97qXH90dYNLKnoa2hqhd7FQ6q0Rl4QqNASjn3wcfokJ0FVXY98DD6F6Z/ewzIHCtNnJSBwaCl2bAd8u24N2O78/RwyfOAvBEdFoaWrArvU/O7yuMkiDgBERZm2PLWhETuux1H7Pzs62ukwbMhS+2hgYjTpOX2cY5vgUPXV1dbjkkktw0UUX4Y477hBzPvLloTkhc2KvrNs1J5R3uiG4OuLSqvwg61hNdieKwtsbXF1Rh4dhzNNPIWjMaBhbWnDgiX8i//PlAzKVnYwCz75oHJQqOfJyqrBlg/udK5lcjumLTGuvVPQ01tU4vH7otDhx3phdhdby7t0l8gehN03Ejh07rO+vjw8iO7o9ZXl/utw1ZBiG8bjooTkfraLfeuutwoOHxluk36HUdW9ClvRkWkaBZ8wAGW/Z6/TI5PTq6FbRQwVPYIf7ricjruRgU9GTVd1g9355Cnn4jHz0IUSdslAEcOZ9tkz4+bRW2Dbf68+EhPlj0dmm9OS1PxxCRan1urgrDB01CdEJQ6HXtQlRsyNUoX7Qpoc77PbQ/z2NugoKCswOsRIUS6FQaaFrrUV16T637yvDMIxbRc9vv/2GO++8U4iV586di6uuukoImDdu3IimJu+8q6bNDYqv8NbtMcdHyGyv0+Px2rqH+VuSM3OASoEmnQGHq9z/emfIlEoM+/tNGHbbLZCpVKjZvQe7br0dJb+sGnBdn4nTE5CSFgG93ogVy3bD6OD3aAvqwMw6/SJxfGDbH6gqLXSp29OQWYG2qu46oICAAPNmSde8H1pfj4jvSF/PW+/W/WQYhnG76CHl96hRo6w+N23aNBgMBq+NuF5//XXWBA3ATo89TY+nrsydYmb319ZlPj4YHxUkjneVOB659ISoBfMx7l/PQ5uWCkNTE7LfekdsdzUPoHEvFS1nXzQWao0CRXk12LjO5LXlDjFJqUgZNVGIjzf+8qXD66ojtfBPCRHH1Vttd3ukJYjDhw+LYERLIuJmwsdHjsbaPDTUHHP7vjIMw7hc9JBRUddcDlozJbyRzUHv7D7//HOhOmcGmJDZUaenQ9fT7oaluzl/ywNNDzEx2rSSuau0BkYPE4tdwS8hHmOf/SeSr70aMrUadfszsPu2O5H3v89haGnBQCAw2BennTdaHK/7JVNEVbjLjFOXwEcmw7GDu1GY4zicMGR6vDivO1AOXU33xyg8PNy8XULGaJZQ6GhojGnLqyyX19cZhvGMHgfaeGJy1lUkTd4+Dz30ULeUV6b/0pm95UKnx9D7+VsSw8MC4KuQobZVj5ya3nUH95HLEXv2mZjw+ssIGjcWxrY25C/7Ajtu/DtKV68Rjs79nbGThiB9VBSMhnas+N9uGPTujblCImIweuo8cfznj587HPP5xgbCNzEYMLajaovtbs/UqSYXZtoQpWw/SyITZ4vz6rJ9aGu2HW3BMAzTq0VPT7NCHnvsMSFiJKdnZrCNt3qQv+Vhp0chk2FsZO+PuCzRREVh1OOPIP3eu6COihSr7Udefwu777xHrLf39I1Bb0L/v4svGAtfP6Xo9Pzxa2eWnqtMmX82lCoNygqPIWuftR6nK2EzE8R53f5Sm92e2NhYczQF+fZY4hcQi4DQYcL7qSzfcQwGwzBMj1LWqTix1NxIT+QPP/ww/P1NWzPSk+hHH33k0m2uWLFCtLG/++47V+8GM6DGWz2JovBciDwhKhhbiqrFiGvJ8CG9GuInQd8jfNZMhE6dguIffkL+F1+i6Viu2PAKHD0KSX+9HAHpaeiPaAPUWLxkDL78eCc2rD2CtFGRGJJg0t+4gl9AECbOPR1bVn+Dzb98haGjJkLeUfB2xXdIIPySgtF0rAZVm/MQdVqazW4P2eGTSRppB6UUaILW1+urjgjPnpiUUyBXmAwpGYZhvNbpIYEhFTZU6Egn6fN+fn5Wn6d3aK7y1VdfobKyEvPmzRPdHjoRtBlGcRfMidjp6dl4ixgdEQilzAflTW0oqPcsXLMnG15Dzj0bk95+U4y+yJma9D57730AB59+Dk15nsU/9DYjx8Vi9IRYYVb4zdLdaGvVux1G6hcQjLrqcqfxFKFStyejDG3V3X8/FH5I+h7a6OwaRBoUPhxqv3AY9C2oKNzq1n1kmBOBd955B1dccYXV52hcTJ+bMGGCeL2l/My2tk7ZAb1uv/baa5gzZw7Gjx+P66+/Hvn5tkfQJ0Snp6ultbegB54ydyxZtGiRyAA5++yze+V7MsdzZd19TU9P8rck1Ao5RkUEYndpLXaW1CA+0OTUfDxRBgYIkTMVPnnLvkDZ2nWo2rIVVdu2I3LeSYi/5EJoIiPRnzj9L6ORm1OFqopGrP7+IM44f4zLX6tUqTHtlHPx29cfYtva7zB80mxofDs7wF21PX5JIWg6Vi18e6JPT+vWNaNuz48//ihGXBRKqlSaCmgfHxmiEuci7+DXKMv9A5HxM02eUAzDiPgI8tWbPHmy+XPkdE6Boqeddhqeeuop5OXlCa89KnSkrMy33noLn332mVgmio6OFjFT1HigKUzXJaYTotNDRoSe0NVSvitRUVFITEy0OklR93QZM3DNCa23t9zX9NS11MPY7rn3jXmL6zjpeuyhjohA6q23YMJrLyNsxjR6S4Wytb9h5023Iuc//4Wu1nb6eF/g66cSbs3E9o25OHLIvYDVERNnIzQyFq3Njdjx2/cOrxs2y9TtqT9gu9uTnp6OwMBANDc3Y//+/dZfGztZmBW2tdSgqsS6E8QwJyKlpaW48cYbRSMhKSnJ6jJyOa+pqcE999wjXmOpm0Ma2vXrTZ5X1PH54IMPRLOBukDkl/Xyyy8Lk9BVq1ZhsOFS0XPDDTeICrCrd4Y9ioqK8MQTT4ivYwYncpnU6XHFp8f1okdyZDa0G9HU5vloisTMtGBW2NCCkoa+XyH3i4/D8PvvxdjnnxFxFrTGX/zd99h+w82iE6RvOr5jOHsMTY/AlFmmJ82Vn+9Bc1ObW/EUM0+/UBzv2fgraipK7V5XExMAP/LtaQeqNnUf+ZE7s+TbQ7o/y7E5mRVGJpg2uUqPrevXQnGGOR7Q+Iq6oStXrsS4caY3LhJSUvr//vc/4a1HrucULCpd79ChQ2hsbMSMGSYDUILecIwcObKbUegJU/SQ4JgqRXJjppbX8uXLxQPV0NAgnozoMvqYWmtU6NCIqra21qM4CUqC/ctf/uLJz8IcRxRS9pbRu47MSrkS/kpfcVzT6rmux1+pQHqYaVRGgub+AomZRz35mNj28h+aIrK88v/3OXb87WYUrfweRp3rj1VvsfDMEQiL8EdDXSt+/Mq6y+KMxPSxSEgdDaPBgI0/f+HSJlf9wXK0VXV3YidDVF9fX2FrQc8vlpBDs0yuRnNDCeoqMt26jwzjCCqiDfq2Pjl5WsDPnz9fGPzGx5u8sCyZOHEibrrpJrz66qsYM2YMFixYICYpUoyUFPvS1TImMjKyWyTMCaPpoa0t6vSQEIpEUo8//rioGLtCSclUGC1btkwkJzODX9ND/6MkZpbGXT3d3pJGXI26ZjHiQmBMj0ZcByrqxYjr9KHR6C+QZiV4/DiMGzsGlZs2I/fT/6GlqAhH3/8vilZ+h/hLLhK6H/IB6gsojPTcSyfgg9f/RMbuIuHjM3riENfjKRZfjPzXHkFOxk4UZB9E3NARNq+riQ6A/9BQEURatSkf0YvTre+HUin0PBs2bMCWLVtE2506QIRC6YeIuGkozf0DJcd+Q1CEKcKCYXoCFR2Z295EY01un3x//+AkpE+52asbp9ScIInKZZddJrSyJFB+5plnxOb1c889J0bIRFftDr2eU/PihF1Zl955kcKb8rGo5UwPHj2gISEhwl+DxFOW66XM4MWyyKFun9yGmNST7S1pg6uovhQ1PVhbJ8ZHBWPp/nwcrW1CeVMrIvz613ozORnTmnvY9GkoXfMb8pd9jtbyChx57U0UffsdUm64DkGjreNfjhdDEoIxZ+Ew/LEqCz9+vR8JKaHCwdkVwqKGCMNC2uLa8MP/cOHfHzMXK7Y2uajoqT9UjtDp8VCFWYvOaduEnmtotE7xFFI+l7S+TsnrDdU5aKzJg3+wqXPEMD2j9y0ujickSqbihV67pddxSlSgDE06Sa/ZpO2xfP2mtAXqtJ7QRY8EralTR4c5cZEcmSVXZqXCO9tbRJDa8/wt69tRYkR4gOj2/JxdiivG9M8XReroRC9aiIiT5qDkx59R8OXXaMrNw/4HH0H43DlIvvpKqEJd983xFnMWpuLIwTIU5dcKfc9l10+Dj42Oni2mLjwXh3dvRkVxPg7uWI9RU06yeT1NlBb+w0LReKQKlX/mIeZs644Nvfukbs+ff/6JzZs3C4Gz9C5YpQlGaMwEVBZtF92eoeOv9MJPzZzI0N8WdVqMbozkvQnp1bztK0ZCZhIoWzKuQ89z7NgxYQZKlJWVISGh8zmSPqb/t8FGjx2ZmRPbnNCRV48n21tEoEbb47V1iTOHmcZjfxZUorLZveLreCNXqzHkvHMw8e03EH3aInoGRsUf67Hz5ltR+O13MLqRYeaV+yOX4dxLJkChkCHncAW2bXQ96NPXPwBTFpwjjjev+hptLfaF2mGzTFubDYcr0FLS0O1y6vZQq508vbKyrB2jo5JMT+Y1ZRloaXRv24xhbEFFh1yh6pNTbxipkn6HtLKWZHZ8TJ5Y1D0lCQuNkCVIR3fgwAHzMsFggosepsfjLXtePZ5sbxHB5qT1nhc9qaFajAgLgKG9HT9lDwxRnjIgAENv+hvGvvAstKmpMDQ349gHH2Lv3fehIdsz+whPCY/SCmEzQd49FWXdixJ7jJk+H8Hh0WhuqMP2dfZX2NUR/ggYGSGOKzd0L6yo4CExJkHdHkuxp682CkERI+mvDKXHfnfrZ2OYEwEaYdF6Ovn35OXlYdOmTXjggQfM6+nUTb388svFuvuaNWvE0sAdd9wh/HpoKWmwwUUP4xH0jkQmefXYKXpkHZoeo7uaHmm85YVOD3FmqqnbsyG//3d7LAlIHYaxzz+NobfcBEWAFo1Hj2HP3fch99PPjuuWF62wJ6eGQ68zYsVnuxwaUloiVygw64yLxPHuDatQW2W/ExM2MxGQ+Yh4iqa87tt2VPTQk3N5eTmOHDlidVl08snivLJoB9paBp/wkmF6Avny0ALSxo0bcc455+DBBx/ESSedJLx4JMijZ8mSJSL4+5JLLoFcLsf7779vNgUdTHDRw3iMwlkURcf2Ftycj3sjisKStFAt0sO0otvz8wDp9liKnUnvM+GNVxE2a4YwNyxY/hV233E36jMPH6f74INzLh4Hja9S6Hs2rLYuOhyRNHwc4oeNgtGgx8afltu9njJYg6Cxpg27yvW53VZ3SWApxdR07fZog5OgDUlBe7tB+PYwzIkMbVp3TVGgIueLL77Arl27sHbtWtHpIW2uBBU5ZF5IXSC6zrvvvou4uDgMRtwqevbu3YuffvpJGCExjCRmtmdQ2NnpafOo6BEr617irA5tz/r8SlQNoG6PhCo4GMPvvRvp990NZVAQmvMLsPf+B5H32TK027CP8Da0uUUxFcQfq7NQaKMbY68jOHvxxeI8e/92FOZY++1YEjojHj4KGVqK64WwuStSHAUJLLu6xMekLBDn5QWbofNSh5BhmBO06CFRE7W8LrroIjHrozbYpZdeiuLi4t6/h0y/d2XWe1nTI+Vv1XjxxYuMCtNDtQNK22OL8JkzRNcn4qS5ouuT//ly7HvgITQX9/7PRIGkI8fFiFBSGnPp2lwrtsKi4zBqqklwvP77/9kNJVb4qxA82bRJUrkhV3wfS2h9lsIQCXpHatntCQhNhX9QAtqNepTmsraHYZgeFD0kgCIl96233iraXhRWRu+0JEdH5sTu9Bjtbm95Ot4yaXpa9a1o0bfCW5wlaXsKKoVvz0CFwkzT7vw/pN11O+T+fmLMtfv2u0SmV29GMlC3ZvGSMdAGqlFZ3og1Pxx0+WunnXIeVBpfVBTn4cA2+0VJyOQhkGkUaKtsErlcXSEvMIVCIbKGLLs9dN9iUhaK4/L8TdC3Nbr98zEMM/hxqej57bffcOedd+Lmm28W/jykBn/00UeFMIqMCpkTE+edHs+EzBqFWsRReHvERd0e2uSikNS3d+agzUVBbn8lYu4cjH/lXwgcOULEWWS9+gaOvPYGDK2txyWUdOuGY8jOLHft6/wDMO0UU7zMpl++QnOj7S0wuUaB0KkmLUHlxjwY9da/I9IhSNoe8u6xLPICw4fDL2AIjIY24dTMMAzjUdFDGxPk4mjJtGnTRBQFj7hOXDrzt+x0ejx0ZBYxDdKIy0tiZomrxiYiQKVAXl0zPt2fN+DDKjWRkRj91ONIuOwSSulE2dp12HvvA2guKuq17zlseCQm07aVm6GkY6adLEZdlMK+5Vf7uXxBE2Ig16qgr2tF3d7uYzvyDpE2ucil2fLvJrpD20NOzXodvyFjGMaDokev13fL5SAba8mqmjkxcZa0bs7e8sDdVBpx1XlZlBrqq8INE5KF0fymwir8nleBgQ45OsdfuESEmJLIuelYLvbcdR8qN3eajXkb8u4JDfdHfW0Lfvp6v8sp7HPPvlwc79+6DmWFts0OZUo5wmaYnGEpk8vYpu+m7SFRM0HdZkuNUHDkKGi00TAaWlGWt8Hjn49hmMFJj1fWB/o7Zabnmh690ZmQ2f1tqcCODa6e5m/ZYnhYAM4fbhLMLjtQgCPVrhvu9WeCx47BuJdfQMCI4TA0NeHQM8/j2Eef9Mp2l0qtwLmXjifTaOzfVSSCSV1hSHI60sZNF0m1v3/7Kdrt/O0Ejo6EMkQDQ7MO1dsKu11ORQ+tsVMm18GDndoiHx+ZeZOrLHcDDPoWj39GhmEGHz0uenrDNpsZWFEURoN3x1uENN7ydqdHYlFyJCZFB4ttLtL35NUOjlGIOixMjLtizz5TfFz49QpkPPYk9A3eL+ziEkMwe0GqOP7hy32orbYfNWHJzDMuhFKlQWl+Ng7t2mjzOj5yGcLnJIljKnr09a3dXJoli3za5KJRu0RI1Fio/SJg0DeLMRfDMIzbRc9jjz2Gv/71r+YTiZkJiqe3/PyVV3Lo34mC2ZHZXqenB+Otzk6PdzU9lsU66XuGaDWobdXj2U2ZIp9rMCBTKJB87dVIv/duyDQa1O7dhz333I+mgu4dk54yd1EqYuOD0NKsw4r/7ba7yWeJNjAEUxacLY43/rwcrc22C07/1DBohgSiXW9E5Z+53S4nQTMJmylBev/+/dbdnqGmTS6KpjDoXCvGGIYZ/LhU9NA7Kn9/fzHKkk7S5+lJx/Lz9jw4mEEsZO6NTo8X87fsoVHIcc+MNIyJCITO2I4P9+bik3150A3wrS6J8FkzMPbZf0IdEY6WomIhcK7ZvcfroaTnXTYBSpUcudmV2LQu26WvGzfzFIRExIhcrq2rV9gtTCPmJYvjuv1laO2S+0VGhbRQIbk06yyiOUKjx0PjHym6PaW563vwEzIMM5gwxWA7oaulNcNYCZmdano8L3pqejlLyV+pwN8nD8WPR0qwMqsYf+RX4FBlPU5NicKMIaFQWqTJD0T8k5Mw9sXncOjp51GfmYmMx59CynXXIGbx6V77HmERWpx27ih898Ve/PZzJlLSIhATZ1p0cJTLNeesy7Dygxexd/MajJgyB+HR8d2up4kJgHZ4OBoOVaD892MYsmSU1Uh97Nix2L59O+rr64VjvCRwpm5P7NBFyNn7qVhfj0yYBYXK32s/M8P0Vyhna8OGDVav2xQ98eabbwpvq5CQEJx66qn4v//7P6GLk6Csrc8++0xsRQ4bNgz33nsvpk+fbvf7ZGVl4YUXXsCePXsgk8lEE+T+++9HbGws+jMD+xmd6R9CZrvbWx01tVGP9nb3uifhfqHivKyx90dOMh8fEUp625Sh0KoUKGtqxSf783Dfb/vxXVYxcmubYBzAgn2KsBj91GOImHeScHHOefc/yPnPB3ZFxJ4wfmo8ho+hral2fP3pTpfcmhNSR2Ho6MnifvyxcqndpYjw2UnwkfugObcGTUerrS4jo0LpiXnLli1oa+sUzQdHjYFvQIzY5GKXZuZEYOnSpcJM2BJ6U/D3v/8dp5xyCr755hvhsffjjz/i8ccfN1/nrbfewhtvvIG77roLK1euFM7nN910E/Lz821+n+rqalx99dWiaKLi6r333hNLBdddd12/3+jmoofxGIV5Zd1xp8eTbk+kNlycVzXVQG+wXlnuLUZHBOGZeaNw0Yg4hGpUqG/Ti+7PU38ewu2/7sXr24/gq0OFWJdbjn1ltcipaUReXROKG5qFw3NNSxsa2/Ro0RvQajAKrVN/KZZkKhVSb78ViVdcJj4u/u4HZL74EowWRUJPoO7LmReMRUCHW/OqlQdc+jrK5VIoVSg6molMO6JmCiMNnmh691jx+7Fu8RTkIRYcHIzm5mbs2LHD4j5Rt+c08yYXZ3IxgxVyKL/xxhvx4osvIinJtAAgsWzZMjEGpsuTkpJE+CjFSX333XfiTQIZDFPRcvfdd+OMM84Q16Ek9vj4eKv/J0tWr14tvu75559HWloaRo8eLbo+2dnZ2LlzJwb8eIthbCFz0ZzQXPQo1W7lb6nlKrQa2lDRVIXogEgcD0jnszA5EvMSI7CjuBpbiqqQVd2AZr0Be8vqxMld6FEizTd1lOikUcigVSqgVSvEOZklkn9QjFYjTuG+asg7ROLehAqTuCV/gToyQrg3V/65CRk1tRjxj/ug0Gp7fPt+/iqcc8kEfPrOZuzYlIthwyOQPtqUnG6PgOAwIWre9POX2PDjMiSmj4Ovf/f7EjItHrX7SkU8Rd2+UgSNi7ZKiJ41axZ++OEHbNu2DePGjTMnSAdFjIBfYDya6vJRcvQ3xA83CagZxh7Ucewrt3aVXObRRjSFgJPGjbo0NMYqLOxcWrjmmmvE+MkSmUwmNHANDQ3ia+kNw+LFi63+p+i27DFjxgzRHbIcj0nfg7I6+zNc9DA97vTYG29BJu94yW93e4NLiFj9w1BQVyxGXMer6JFQyHwwbUioOFFRRx0d8vMpb2oTKe2VzW2io0MCaOro0DkJoG09EvQ5eohoPZ4+oi4QbYyhwf73jvJTIyXEH2mhWqSGBiDM19octKfxFcrgYOHjU5dxQKS1j3r0YSF47ikpaeGYMS8Fm9blCI3PkIRgaAM7nxhtMX72qcjctQlVpYXY9MtyzP/L1TbjKcJmJqB8bY7Y5AoYEQ6ZqvPpKz09XbTx6R0vrbAvWLDA/Hc0ZNipyNr5H5QXbEJU0klQaRzrjZgTu+B5bvNhZFf3TXbbsBB/3Ds9ze3CZ/78+eJki5EjR1p9rNPp8OGHH4ruTGhoKI4ePSrMhjMzM8Vo7NixY0LTQ92giRMn2rzNuLg4cbKEcjmpCJKsJPorXPQwXggctTPe8vER3R4yJ/REzNxZ9PStazJ1XZKD/cXJGZTrRSMt6UTFjtXHRqDFYEBDqx71Oj0a2vRijFbe2IrixhaUNrSgzdiOwoYWcVqfb9I0UdEzMjwAE6NDhLkiFUY9NTIc88yTOPD4P9GcXyA2u0Y++iD8u7TGPeHk09Nx9HAFSorq8O2yPbj0uqnwcXB/5XIFTj73Snz1ztM4sO0PDJ84C7FJad2uR92dml1F0FW3oGprIcJnm6IwpL81ygVcvny5EDTTkzUJNomAsDRog5PRUHMUJTlrkDDSlAHGMLYYzM5zer1eCJRJhEz6H4K6PS0tLSJAnDQ9JET+/PPPhf3MihUrMHToUKe3S7qeTz/9FA899JAopPozXPQwHiONYOx2ejp0Paaix33tSKR/2HETM3sLUzHi+dMmFUbUSSqob0ZWVYM45dY1ic4SFUB08lPKMS4yCFNjQzAyPFCMzDyBCpyxzz+NjMeeQnNBAfY98DBGPvwPEWDaExQKuVhjf+/l9SKQdOufxzBtjmn13B4xSakYOWWuKHrWrfgYF/39MbHh1c2wcG4yir89iJptBQgaHSX0PhIJCQlITk4W71xpe+Wss84yfZ2PD2KHnYrD299GReFWRCXPg9q3fz8xM30D/a1Qp2WgjbdcgYqb22+/HVu3bhWiZdp8lJYBqOj5xz/+IfQ+kk5u165dopAh4bOjztirr76Kf//730L4fMUVV6C/w0JmpseOzPZW1i03uNo9ECNH+pvGLWUNAz8fy1WogAn3U2N8VDAuGBGHf8wajldPGYf/mzIMJyWEI1ClQJPOIHLDXt2WjX+sy8APR4pR0+J+J41QR0Rg7HP/FIUORVdkPPoEqnft7vHPEREdgFPONrXVV39/EKXFzuf8M069ABp/rRhz7f7zF5vX8R8WCt+EILQb2lH++9Ful1O3h140KIi0yCJ0NSB0KAJCU9HebkDRkVU9+tmYwQ39/agV8j459VbBU1ZWhssuuwy7d+8Wq+lScUNER0ebR8SWjwF1eAoKCuzeJo3J7rnnHrz99tt44IEHREE1EOCih+mxI7M9c8Ke5m9Fak2dnvIB1OnpLXH16IhAXD46AS8sGIN7pqfi5MQI0fGhDtCKw8W4/7d9eHfXUeTXuR+nQSLmkY89jOCJE8Q218GnnkHlpp6HlVISe+oIMgg04ptPd0Gvc7zGTgLm2WdcLI63rVmJuqpy21qv+SmimdaYVYmm3Bqry8PDw8W7VOKPP/6wWoMfkmryJqoq3omm+t5LoWeY/gQ5ltOoilbKly5d2k1zM3nyZPF/RQWRBP3fHDlyBImJnSPkrtCY7Oeff8a//vUvc0LDQICLHqbHnR57MRQ9dWU2d3pO8KKnaycoLTQAl46Kxwvzx+DqsYkYGuIvtEPbiqvxxIZDeG3bEbdDVOVqtdjiCpsxHe16PQ49/yLKflvXo/tKT6RnXzQO/loVykrqseaHQ06/Jn3CTAxJGQ69rg2/r/zUpnePOtwfwRNMK+wkbG7vMoqYOXOmaNnTBgut0Er4B8UjJGqcEJMXZv3Uo5+NYQYKzzzzjPDboZXy0NBQYT4onSizjjQ8559/Pp566in8/vvvYjz85JNPii7PpZdeKm6DrkfXpzEY8fXXXwuvHxI7T5061eo2pev0V7joYXosZHbY6elB/pak6altrUeLvn8bXvXV/H9mXBjun5GOh2cPx5SYEKEm2ldeh+c2HcYrW4+IrTNXkSmVSL/nTkTOP1mYGGa98jqKf/y5R/fRP0CNsy8eL463rD+KI4fKnBZK8875K2RyOXIz9yI7w7ZPSOjMBMh9FWKFvWZ3sdVlAQEBZmdm6vZYCu1jU08DfGSoqziE+qojPfrZGKa/Q8UKFSc0iqJuz+zZs61OxcXF5mxNKnxIiHzOOefgwIED+OCDD5CSkiIup+vR9em2iO+//16ck09P19uUrtNfYSEz02Mhsz2fnp52evxVfvBX+qJR1yxGXPFB/dvevC9JCPTDDROScU5aDH7JKcXGgipkVNQhY0MdpsWG4Ny0WKEVcoaPXI5ht94Mua8vin/4ETnvvCe0PuTv4yk04po6OwlbNxwToaR/u2suAhyssYdExmDSSYuxbe1KrP9uKRKGjYJK49t9hX1OEspWHUHVxjwEjIiEwq/TF4pa+LTFRc6xdE4Os4TGLxwRcdNRnr8RBYd/wPBptwoTQ4YZLDz77LNWfjv09+8MpVIpujZ0sgWtp9NKuwQVRAMV/m9nei5kdrDp0BNND8EjLveI8tfgr2MS8cTckZgaY1rZ3lJUjYf/OIBvDxe5tJXiI5Mh+fprEHfhEvFx7idLkffZMrsxEa6w8MwRiIoJQFNDG1Z8trubq3JXJs1bjKCwSDTW1WDTL1/avE7g6CioI/1hbDWgcsMxq8vUarUwUCP+/PNPq5Z7TMopkMnVaKorQHXpPo9/JoZhBh5c9DC93OmRtrc82y4ir54TbYPLG0T6q3H9hGQ8NGs4RoQFCP+g74+U4JE/DmBXSY3TAobGTImXXYLEK00rqPmfL+9R4aNQynH+FZNEGvvRrAr8+ZvjNHaKpjj5vCvF8b7Na1F09HD3+yjzQcQCk4dI3d5StJRY65jImTksLEwUPGRYKKFUa4VJIVGU9ROMxuMTc8IwTN/DRQ/jMXJJyOyo0yP3PGl9oHr19CcSg/xwx9RhuHFCMkI1SrHt9dbOHPx7Zw5qW53/TuL+ci6SrjEVHwVffIm8pf/zuPAJj9Li9PNGi2NKY88/WuX4ew8dKbx7iDVffSDEzV3xHRKIgBER4rh8bbbVfSNb/Hnz5olj2kyprOz8G4pKnAuFSovW5kpUFPR8U41hmIEBFz2MxyhcWln3XNNjGTza167MAxnq2kyKCREjr9OHRoH057tKa/HoHwewubDKaREz5JyzkXytKRqiYPlXyPv0M48Ln3FT4jB6QqwYb329dBeamxyPPWedfhH8AoJRW1mKrWu+tXmd8LlJ8FHK0FJUj/oD1kJpCk8kMSaJmWkzRUKuUCN26CniuDj7Vxj0/XvjhGEY78BFD9PjTo9LQmZDzzo9J7pXjzcg87O/pA8RhocJgSQQN+D9Pcfw5o4ckRDviNizz0TyddeI44Ivv0bux7bXyV0pwBYvGYOQMD/UVjeLfC5Ht6P29cO8c00jtl3rf0Z5UW636ygC1AidniCOK9Ydg6HZ+m+Nuj3U9aFV3JycHPPnw4dMg9ovAnpdI4pz1rj9szAMM/Do86KHWs7k6jh9+nRMmDABN9xwg5W3BjMQYigcjbd62OlhIXOvbHo9MHM4zk2LgdzHB3vKqOtzUKTKOyL2rMVIueFacVz49QrkfvSJR4WPWqPE+VdMhEzug0P7SkQiuyNSRk7EsDFT0G40Ys2XH8Bgw907ZHIsVGF+ouCpWG99e5TBJQUnrlu3TqzxEj4yOeLTTVEVZbnr0drE3USGGez0edFzyy23IDc3VyS0fvnllyKlldwdKeqeGSCdnl5yZLYUMjfpmtHQ1jfJx4N1NLl4WIzw9yHdT5PegLd3HcXH+3JFCrw9YhafgZQbrhPHhd98i2MffuxR4RMbH4wFi00ZX798ewClRY5jKuaedRnUvv6oKM7D7vXdIyoolytyoSRqLkFzl9ujN1W+vr5ihd3SeTYwfDgCw9JEPAWtsDMMM7iR9bU99pAhQ4QTJIWfUdbHzTffLHJCKAWWGSjbW8Ze295SK1QI0gSK47IG7vZ4myEBvsLckLQ+9NukQNN//nnIYZxFzOLTkXLj9eK4aMVKHPvgQ48Kn+lzkjGsI6biq092oq3V/haVX0AQ5px5iTjeumYFqsutDQkJ3/ggBIyKFMdlv2ZbrcXTCjsZpxG0ydXU1GQet8VRt8dHhpqy/aiv4i4zwwxm+rToCQoKErkdaWlp4mPKBvnwww9FANqwYcP68q4xLqCQHJkdaXp6uL1lvcHF44fe6vqQ1ueOqakIUitR3NCCpzdmYl1uud1iJub00zD0pr+J46KV33uk8aGV83MuHgdtoBoVZQ34ZUWG04iKhNTRMOj1WPv1f8W4qyvhJyVDplGgrbwRNTut87VGjx6NiIgItLa2Cu8eCV9ttDAsJPIzv0V7e98kbDMMcwKMtyQefvhhYSb2ww8/4J///Cf8/Pz6+i4xXhlv9UzTY+XVw7qeXmVEeAAenTMC4yKDhK/P0ox8/Hdvrl1Dw+jTFiHlxhvMGp/8ZV+4/T39tWqcd9kEESC6a2s+9u8sdBxRcd6VUKrUKD6WhT0bV3e7Drky0zYXUflnHnT1nfElJGaeP3++OCaXWsmCn4gdughyhS+a64tRUbjN7Z+DYZiBQb8peigX5KuvvsKZZ54pdD4ZGY7f9TH9SMjsSuCoh+Mtgjs9x48AlQK3TErBkuFDxLhrU2EVnt2UifIm29lnMaefiuTrTOvsVPTQZpe7JA8Lx5wFqeL4+y/3obLcflhqYEg4Zp1xkTgmp2ZbY67AMVHQxAagXWdAxdrObS3JTn/kyJHiePXq1eZcLoXKHzEdK+xkWGjQsaaQYQYj/abooXEWtZ+py0M6n08//bSv7xLjcqfHle0tz4TMlhtcvLZ+fKCOyqkpUbhzWqoogvLrmvHUn4ewr6zW5vVjzzrT7NxMkRWF3650+3uetCgV8cmhQtfz5Uc7oNOZNqxsMWrqPMQPGwWDXofVy/8DY8c2luX9jzxlmOgeNWRVojHb2gRx7ty5QuND2kHLXKLI+JmdK+xH17r9MzAM0//p06KHNDw0ztLr9VYtaCqA6AmJGQSaHvP2lhc6PSxkPq4MDwsQMRYpwf5o0hnw+vZsrMwqhtGGdoecm+MvMXVgjn3wEYp/+Mmt7yWTy3D+FRPgp1WhtLgeP3+93+51qaiZf/7VUKl9UZqfI/x7uqKO8EfwpCHiuGx1Noxtnc8x/v7+mDVrljjesGEDGhsbba6wtzSWu/UzMAzT/+nToqeiogJ33nmnVS6OTqcTsfa0ycUMkO0th5qenm1vWbkyN1X2KPSScZ9QXxXunpaKeQnhoEf+u6xivLvrqM219viLLjCnsee8+x+UrOquuXFEYJAv/mKh79mzLd/udQOCwzDnrEvF8ZbVK1BR0v26YTMToAhUQ1/f2s27h3K5IiMjhaj5jz/+sF5hDx8uVtjzDn3Df28MM8jo06KHtrao1Uwr69u2bcPhw4dx//33o66uTnj1MIMge8sLnZ5wv1Dx7l5n0KG2xbGfC+N9lHIZLhudgKvGJAozwx0lNXhh8+FuLs70O0q4/FLEnmPqlmS/9TbKflvn1vdKSYvASYtM25w/fLUPpcX2f9/DJ85C0ojxMBr0WLP8P91MC2UqOSIXmbZAa3cVo7mwzqqjvHDhQnFMb7IKCgo6f4bh58BHpkB9ZRZqOIWdYQYVfa7peemll8TW1h133IELLrgANTU1WLp0KWJjY/v6rjHeSFnvoSMzoZDJEeYbIo5LOG29z5gVHyZ0PlqlHLm1Tfjnn5ni3BIqGpKuvhLRZ5wGtLcj67U3Ub6+cz3cFeYuTBXFj15nFPqe1hbb/j30vU4+7yphWlhelIftv33f7Tr+SSEIHG3y7in9JQtGfWeBHhMTI/zBiDVr1pidmtV+4YhOMgWV5meuhEFvW8TNMMzAo8+LnoCAADz22GNitr5nzx68//77SE01bXIw/RuFzAUhsxdW1on4oBhxnldrekfO9A1poVqR3RWj1aCmVYfnNx/GzpLqbsVIyvXXIuqUhYDRiMMvvYLKTVvc8u8577LxCAjSoLK8Ed8vt5/P5R8QZM7m2v7bdygrPNbtOuHzUiD3V0JX1YzqzdZjMDIsJBd4GrXv3LnT/Pno5PlQ+YZC11qL4hz3xnQMw/Rf+rzoYQYu8g4hs94Vnx6D59tbRFJwvDg/Ws1FT18T4acWLs6jwgOFh8+/dx7Fj0dKrAoTH5kMQ2/+GyLmnSQKn8wXX0LV9h1u+fcsoXwumQ8ydhdh+0b7+VypY6eZs7lWf/Ee9DrrvzW5RoGIBSaNYNXWArSWda7EUzTFSSedJI43btwoOs2ETK5E/PBzxHFp7h9obih1+b4zDNN/4aKH8Rh5R6fH2MuOzERSSJw4P1ZjX9zKHD/8lHLcOnko5idGiI+/OVyEj/blCVNDy8In9bZbED57Ftr1ehx69gXU7OlcEXcGrbAvONOUz7Xq2wMoyjcVJLY46Zwr4KcNRFVZETb+vLzb5QFp4fBPDQOM7Sj95YhVRMWoUaOQkJAgtkh//fVXc/EWHDESQREjgXYj8g+yqJlhBgNc9DA97/S4Yk7Y06Kno9OTV1sEg9G+hwtzfDVdl4yKx2Wj4oWR4Z8FlXhzRzZa9J2/Hx+5HKl33IbQaVPQrtPh4D+fRd2Bgy5/j+lzk5E+OkqMUL/8eAeam2x3DH39A7BgiSkIde/G1cjN7F5cRS4YCplajtbSBtTsKLQax5GoWaFQIC8vTwibJeLTO0TN1dmoLukMKmUYZmDCRQ/jMQq3Yih6Nt6K0oZDo1CLDa6ieh419CfmJUYIF2eVzAf7y+vw4uYs1LV2FrkyhQLp99yF4IkTYGxtxYEn/on6w64FClNBcs7F4xES5oeaqmas+N9uqy6NJYnpYzB2pmkja82X76OpwXrzS6FVCX2PFFHRVtUpwg4JCRELFcS6devM3j1qv1DEpCwwi5r1OvtBrAzD9H+46GF6NWVdptSIc2MXnYW7yHxkSAzuGHGxrqffMS4qGHdNT4NWpUBuXROe2ZiJkoYW8+UypRLD778HQWNGw9DcjIzHnkRDzlGXblvjq8SSv06CXCFD1oEy/LHafsE087QLEBo1RBQ8a7/6oNtIija5/BKD0a43ovSnLKsCavLkycK7p6WlBb/99pv581FJ86Dxj4K+rQEFmd03xBiGGTiYnOMYpreEzCpT0QOjXhgUSivsnpAUHIfMimwcrcnHHEzFiQa9gJc0lONwRQ4K60tQWFciojnqWxtR19YAvVEPchCU+fjAT+kLf5Wf8DiK1kYgOiACQwJjkBqahEBNQK/cP3Juvn9GGl7dli2yup7blIm/Tx6KoSFacblcrcaIB+8XBU/9oUxkPPoExvzzCfglmEaXjoiJC8Li88dg5ed78Puqw+LjtJFR3a6nUKqw6KK/4Ys3n8CxQ3uQsXUdRk872Tqi4tRU5H20Ey3F9ajeVoDQafFm755FixYJy4zMzEyR0ZWSkgKZTIHEUUuQufUtVBZtQ2jMRASGmfx/GIYZWHDRw3hByOyo06M2HxvbWiD39bzoSQ4xvTjlnkBi5hZ9K3YXZ2BLwS5klJEhoHNzRkN7O+rbGsWJiqT9ZZlWl1MRlB4+FONjRmJc9EhoVf5eu79R/hpR+Ly2PVt4+PxrSxZumJCM8VHB4nK5ry9GPvIgMh55HA1HsrH/kccw5ukn4euCL9f4qfFCzEybXN8s3YXrbp+NsAhTQWVJeEy86Phs+OF/2PDDMsQmpyM0svP2lYFqRMxPEZ0eGnP5J4dAHWm6naioKEyaNAnbt28XgaRkkqpSqaANTkJE/HSU529C3oEvMXLmXWLDi2GYgQUXPUzvdnrkCtHdoS5Pe1sL4BvQo06PNN6irge9ax+M0M9GHa2fj/yOHYV70Wqx7q+QKTA0NBGJwUMwJCAaUdoIBKq1CFD7QyVXCUGxod2IJl2z6ABRJ4gKn5KGMhyrKRDdIdPH5fj92GYxNhwePhQz4idhZsIkBKi7FxHuEqhW4p5pqXhn11HsK6/DWztycPnoBMxNMMWJKPz9MfKxh7H/oUfRdCwX+x9+XBQ+miiTiaAjTj1nFEqL6pB/rBpffLgD1942Cyp196excTMXIvfwXuRnZWDVsndwwc0PQd6hLyMCRkaawkiPVKHkp8NIuHw8fDo0ajNnzkRWVhZqa2tFRIXk3Dwk9QzUlB1Aa3MlinN+FR8zDDOw4KKH8YKQ2X6nRxpxtTfrRKenJ8QFxYoXaepgVDZXi9HNYIK20tbnbsUPh9cit6bAKnB1evwkTIwZjWFhSVC50GEIg8nBGrA2+mxoa8SRymPYX3YYu4r2Ib+uGAfKs8Tpw93LMSFmNBamzBZdIHqsPUWtkOOWSUOxNCMP6/Mr8cn+PDS06XH60ChRrCoDAjDq8Uex/8GH0VxQiP0PP4oxzzwFdZgpXNYepOtZcuUkvPfyepSX1Itx1/lXTOxWANO6/MIl1+F/rz6MiuI8bF71NWadcVG3JPa8wp1oK29C5cY8hM9JEpcplUqccsop+PLLL4VhKpmlJiYmQq7QIGHEucje/RFKjv2OkOjx8Atg53iGGUiwkJnpsZCZtKCOvHpkKl/T9dqae/T96MU+LjBm0ImZje1GbMzbjjt/fgJvbf1YFDz0sy5ImY1nTrkfry9+EpePOw8jI1NdKngcQaOs8TGjxO396/RH8MbiJ/HX8ecjOTheFF3bC/fg2fVv4vYfH8OPh9eKjlFP/j6uGJ2AM4ZGmb18lh8qNKe0q4KDMOqJx6CJjkZraRkyHn4MbR3mgI4ICNTggr9OgkzugwN7irFpXY7N6/kHBos0doKS2HMPW+doKfxVovAhqrcWCI2PBBU5FEpK/PLLLyKYlAiOHI3gyDHCuyc340u0tzsu+BmG6V9w0cP0OHDUaf5Wh5hZjLd6iHnEZdEJGciQKPmBVc/ilU3vo7i+TIyXLht7Ht4+6xn8bcplYpTVm2M8SrA/M30hnjv1H/jXaQ/jzLQFQgRN468Pdy3HjSsfwNI936CupbMgcAe67+elD8EFw4eIj389WoYP9+aa/17UYaEY9eSjUEeEo7mwSGh9dHV1LhkXnnbuKHG85oeDyDlsO5MtZeREs5CZ3Job6qwjM7Rp4QgYESEE4CU/HoZR1+kxRGHIQUFBqK+vF2vsEtTtoa5PU10+ynLXe/S4MAzTN3DRw3iMoqPT43RtvaPo6el4y8qZuXpgi5kb25rwn+3/w8NrXhTbaL5KDS4cfZbovJwzYhG0au+Ji10lPigWf52wBG+f9TSum3QJhgRGCyH1t4dW4ZbvH8LHu79CTXOtR7e9KCUKV49NBP3JbCqswr935ogIC0ITGYlRTz4GZUgImnLzxHaXvsHkk+OISTMSMW5KHOWa4qtPdqDGwnfHktmLL0F4TAKaG+uFvsfYESwqQREV5OGjq25GxbrONXoSMJ922mnieP/+/cjJMXWUlOpAxKWdKY4Lj/yMlsYyjx4ThmGOP1z0MD0WMjszKDQXPTpvdHriB3wcxc6i/bjjp8exKvsPtKMd85Jm4PUznsCSUWeI4qev0Sg1WDRsLl467RHcO/smDA1JFGLq7zNX49YfHsEX+79Hiwe/y5lxYbhpYooolveU1eLVbUfQ1NFZ8Y2JwWgqfIIC0ZidgwNPPAV9U7PTLhKtsdP6enOTDl98uB1trd0T2RVKJU679CYoVRoUHc3EtrUru2VzRZ2eJo5r95QIgbNEXFyc2OYiVq1aheZm030KGzIVgWFpaDfqcWz/52hnl3CGGRBw0cP0eGWd0DtKWld6f7xV1lgpuiUDCXKTppERaWZo9TwmIBKPzLsdN0/7a6955/QEKiomDxmLp0+5D/fPuQXDQpNE8fNlxg+47cdHsSZ7g0O7AlvQ6vrtU4ZBo5DhcFUDXtxy2Oze7Bcfh1FPPAqFVov6zMM4+NTTMHRoaeyhUMpx4VWT4adVoaSwDt8u22PTsTk4PBonn3elON7223fIP5JhdTkZFoZMMY3gSn/Jgr6+8/vOmjVLODaTS7NkWkiPTeKoC8SYq7E2D6W5v7v1ODAM0zdw0cN4DCVgSxMux0Jm7423aOwjbW1Zbjj1dyg648HVzwtxMHF66sl44dSHMDoqHf0deoGfGDsa/1x4L+6YeR2i/MNF0fbO9qW4Z9U/hX+QO6SHBeCeaWkIUCmQX9eM5zYdRkWTqcjwT0oS6+xyPz/UZRzAoaefg7HNsZt3UIivKHxI2HxwbzH++NW2Y3Pa+OkYNfUk8gTAqs/fRWOdtWg6bHYi1FH+MLboxRq75OZM21ynn366eBwOHjwo1tkJlSYYcelni+OiI6vQXF/i1uPAMMzxh4sepkeQi62rrsze6PQQSR0mhQNFzEzjLBIr0/0lofJ9c27G1RMv7PEm1vGGXvTJz+el0x/BleOXCMfn/NoiPP7by3hj84eodcE4USIhyA/3Tk9DmK8KZcK9+TAK602jo4DUYcLAUKbRoGb3Hhx6/l8w6hwH1iYkh+LMJWPFMTk2H9hTZPN6c868FGHR8WhuqMOqz9+x6lSRT0/04nT4KGRozqtF9bbOUNKYmBhMmTJFHFMSe0NDgzgOi52MoPARaG834Nj+ZTzmYph+Dhc9TI9QdOh6XBIy92D92ZKUkARxfqg8G/0Z6hSsPLQKz61/C836FoyIGIYXTn0Qk2LHYCCjlCuxOH0BXl/8BBYNnQsf+OCP3C1izX3VkT9cHnlFazW4b0YaYrQa1LTq8Pzmw8ipMQmYA0cMF5EVMpUK1du24/DLr6K9iwDZlmPz9JNMgaIUTFpcUGszpsKk71GjMOcQtq351upyVaifcGsmKjfkoqWkc2uNAkkjIiKErufnn382G2RSRIVc4Yum+kKUHDV18hiG6Z9w0cN4KXTUwXhLKfn0eKfTMzZquDjfV3pQeMv0R9oMOry55SN8uucbIVYmw7+HT/o/hPqa4hgGA+T5c93kS8TYi3x+GnXN+M+O/+GhNS+IDpArhGhUuG96GpKD/YSo+aUtWThQYeoYBY8dg+EP3AsfhQKVf25C1mtvot1JQbXwzBEYOjwCep0Rn3+wDQ113f/mQiJiMO/cTn0PZXRZEjgmCtrUMGFAVfJDJoxtpr8xhUKBxYsXi/Pc3Fzs3LnTvM2VMOI8cVyUsxpNdZ0dIoZh+hdc9DBe8epxKGT28niLBLUBKn/xIptV6VpS9/Gkqa0Zz/zxhuh+kKvxNRMvwvWTL4VCPjgN0MklmsTOV024AL4KDY5UHcN9q57BNwd+dqko9VcpcOfUVIwIC0CrwYjXt2djZ4nJTydk4gSk33sXzVFRvu53ZP/7nW7J6V11ZudfPhHhkVrU1bbg8w+3Q2/hvSORPmEGxkyfL/Q9v37+LmqryqzdmhcNgyKA1thbULb6iPl7hoWFYd68eeJ4/fr1KCszfR25M5NxIZkWHt33GYwW0SEMw/QfuOhhvDLeOl5CZnF7MhnGRo8Qx7uKrbdw+prq5lo8+ttLQtxLBcA/5v4dp6XOG7Q5YRJymRxnpM3Hy6c/KuIyKPH9f/u+FV2fgtpip1+vUchx6+ShmBgVDL2xHW/vPIoN+SbDwbBpU5F25+2i8CldtRpH//OBw8JH46vERddMFueFuTX4fvlem9cn/56o+KFobWnCT5++AV1b58YWBeNGn5EOCjOrP1COuv2l5svGjh2LoUOHwmAw4IcffoBOpxO/34SR50OhChC+PQWHv/fgUWQYprfhoofxkpDZhU6PF3x6JCgjiqAE8v5CSX0ZHl7zgtgqC9IE4rH5d5qLsxOFUL9gIdS+eepfhbNzdlUu7l31NFYc/MVp10cpl4lE9llxYWSQjI/25WFVjqnYiJgzC6m33iyOi7//Ebkff+qw8KH09SV/nQQfmQ/27ijEn2u767/kCgVOv+wW+GoDUVGcj3UrPra6Td/4ILHRRZSvyUFrmUm8TAXOokWL4O/vj6qqKvz+u2ldXanSInm0Kd+L0thryg948AgyDNObcNHDeEfI7MicUOndTg8xrqOYIDdjT12CvUleTaFwVyb/IFrpfnLB3Uju2DI70aCiYF7yDGFuOKGj6/PZ3hV47LeXxePjTCN25ZgELEo2Ja5TVtc3mYWiGImcfzKG3vQ38fnCr1cg//PlDm8rJS0cp51jiqpY++MhZOzurjPSBoXgtEtuEgGlmbs2Yt9mayFyyNQ4+CWHoF1vRPF3h2DoMD/08/MTa+wEhZIeOXJEHAeGpyMycY44zt3/BXStrm+0MQzT+3DRw3jFoNBwHMdbBHVSyCmY2F3St++oKRKD1rZrW+uRGBwnCp5obQROdKjrc39H14dGfZkV2bjnl6ewIXer06JpyfAhOC/NlGD+Y3Yplmbki6DS6NMWIflaU4ho/v8+R8HXKxze1pTZSZg2J9m80ZV/tKrbdYakDMfM0y4Uxxu+/x+Kc7Os7kv0GWlQBKhN+p5fOvU9FEo6efJkcyhpXUdm2JDUM+CrjYFe12hya+ZQUobpN3DRw3gliuJ4CpklxsWM7HNdT05VHh5f9wrq2xpFOOijJ9+OYN+gPrs//bXrQ6v6aWEpaNa14LXN/8Xrm//rMMGdvu6MYdG4bFQ8yWrwe14F/rP7GPRGI2LPPhOJV1wmrpf70Sco+v5Hh/fhlLNHIn1UFAx6I5Z9sA1VFd1zvcbPXoRhY6bAaDTg58/eQmN9rbW+56x0kBNnw+EK1O7u1CjNnj0b0dHRaGlpwffffy90PjKZAsljL4OPTIG6ysMoz9vo4aPHMIy34aKH6REKqdNznLK3LJkQYxpd7C050Cer60cqj+HJda+IOIzUsGSxkk5r3IztNPfH59+JJaMWi4Jmfe5W3PvLP0XKvCPmJUbg+vFJoNp6W3E13tyRIza84pb8BXEXLhHXOfre+yhZ9avDja7zLpuA2HhTRtdn721FU6P1dhXdp/nnX4PQyFjh1PzjJ69Db2GI6BsbiPC5SeK4/LejZv8euVyOM888E2q1GsXFxWKjS1xfG4W4tLPEcUHWD7zGzjD9BC56mB5B1v/OzAl7q9OTGposXIFNq+vHcDyhF+snf39VfO/08KF48KRb4acy+REx9je8Lhx9Jh4/+S5E+IUKfc8ja/+Frw/8BKODEdCU2FD8ffJQqGQ+2F9eh1e2ZqFJp0fCpRcj9lxTDET2W++gbJ39/CuVWoGLr5kiIiuo0/P5f7uvsqvUGpxxxa1Q+/qjND8bv33zoZWwOXhSLPyHhQr/nuKVh2BoMhVFQUFB5jT2HTt2mGMqIuJnIChipAglzdn7KQx67/79MwzjPlz0MD2CErOdxVBI5oTt+jav2vTT5ti4KJOgeXfJfhwvyAn6n7+/LkY1IyJS8eDcv4tNJcY1hkcMFbljsxOmiGJn2b6VwteorqXT/bgroyOCcMfUVPgq5DhS3YgXNmehvk2PpKv+iugzThN+O1mvvoGKPzfZvQ1toAaXXDcVao1CaHtshZNSMCk5NkvC5l3rf7bqBkWdlgZlsAb6ulYUf3/I/PXDhg0zp7GTvqempkZcP2n0RSKjq7WpArkZyx1unDEM0/tw0cN4xZzQlRiK3uj2SKvrm/J2OuwWeIsDZVn45x+vi1iJUZFpeGDuLdB0bKcxrkNdsdtmXCNEzpRBtqfkoFhtP1Ru2oKyxbBQLe6ZnopAlQIF9aag0srmNqRcfy0iF84nsygc/tfLqNy8xe5tREYH4IIrJ4uRF21zrf05s9t14oeNwpzFl4jjjT8vt3JslmsUiDlnBHyUpnyuit87zTHnzJkjMrpaW1uFvkev10Oh9EPy2MsBHxmqS/eiPJ/1PQzTl3DRw3gnhsJBpwfkRCyTe32Di5gaN150WYobyrCzaB96k/2lh0RHolXfirFRI3D/nFugUah79XsOdkjk/PTC+zAkIBpVzTVirZ08fewVsPGBfiKvyxxUuvkwihtbMezmGxE+d47I58p8/l+o2LjJ4Sr7mReYwkn/XHME2zZ0H42OmbHAnMj+y7K3UVnaqclRR/iLjg9Rs6MIdQfLrPQ9Go0GpaWlWLdunfi8NjgRcWmLxXFB5ndorBsYQbkMMxjhoofpEQoXOj3U5u8tMbOvUoOFQ02+KN9lrkFvsafkAJ5Z/xZaDW0YHz0S986+EWqFqte+34lEQvAQPHPKfZidOFUUO+Tp8/z6f6O+1WQG2JVIf4ug0hZTUOmx+hak3X5rZ+Hzwkuo+HOjw3DSeR2Fy08r9ndLZae/2blnXY7Y5HToWlvww8evormx8/4EpIcjZFqcOKY19pZS02WBgYE444wzzP49+/ebxq6RCXMQHDlKpLHn7PkEei+F7zIM4x5c9DBeWVl32OmhF5GOEZC3x1vE6anzIPeR4WB5lnAA9jZbCnbh2fVvQWfQiYiFu2ffCBUXPF6FRoS3TrsKN0y+DEqZAjuL94txl73tLgoqvZeCSoNIyG7Av7ZkIbOmSRQ+EfNOEqOuzBdfRvn6P+1+zzkLUzF5ZiLI/vmbpbtxNMsUe9HVsTkwJAJ1VeX4+bM3YdCbzAmJsFmJncaF3x40C5uTk5NFIjuxevVqlJSUdKSxXwiVJgRtzVXIzSD/Htb3MMzxhosexivjLcpLckRvGBRKhPmFYGaCySTuu8zVXr3t349uxksb3xMr8dPjJ+LuWX8TGhTG+1BhsHDobJHaTuaOlU3VeHTtv/Dj4bU2CwQtBZVOS8XwjqDSV7cdwe7yeqTedotwbxYan5deQfkf6+1+v9POG40RY2NgMBjFRldxgbW7t69/ABb/9TYoVRoU5hzC2q//a74vFHERvTi9U9j8XaewmYoeKZ/r22+/RWNjo9D3pIy7Aj4+ctSUZaDk6G+98jgyDGMfLnoY7wiZHZgTWhY9vdHpIc5KXyjON+fvREVjd9ddT/g5ax3e3PqReJEj7cnt068dtEnp/YmkkHg8u+gBzIifBEO7ER/uWi7MDFv0nYGglkGlt00eiglRQaLw/vfOHGwqrsGwW2/uFDe//JrddXaTh894JA0LQ1urHp+9t6WbeWFYdJzVRtfWNd9aC5vPJWGzHM35tShfm2MuqCimIjQ0FA0NDfjuu+9EAeQfFI/4EeeK6xQd+Rm15Ye8/OgxDOMILnoY7wiZnXR6fHpJ02P5Qjk6Ml1oQr7vYbeHihzyjvlg5+fi49NTT8aNUy43h6syvQ+J02+fcS2uHL8EMh8ZNuRtw0OrXxChrraCSv82IQUzh4SKoNL/7s3FmtwKDLvlJkQtWigKn6xXXkfZWpOwuCsKhRwXXjUZ0bGBaGxow9J3t6Ch3rrASkwfi5POuUIcb1vzLQ7u2GC+TB3uL6IqCHJrrtlp0geRYeE555wDlUqFwsJC/PabqbMTETcd4XHT6C8NR/d9hpYm67EawzC9R58/i5OfxSOPPIK5c+di4sSJuOSSS7B9+/a+vluMu0Lm/2/vLKDjrNI3/oxrJu5uTWNNm7pL6lABWiiFLlJssWX5w2KL7ALLsrCwuBWHFigtVCh1d0lTibvLJDMZ95n/uXeSoalbpMn9nXPP+MyXyZfve/LK814o0uMZOtp5BZyz+0+hl7+XbMfJxjNbkS8GUrdDojvEO4ZwU8pM3DloPj3xMroWEi25LimLjvYgs9aqNLV4etO/cbj2jxbyDoNKB0RjStug0h/za7C6pAFxD9xH53VRH59330fj5o4DRdsRSwRYeO8w+PhJoW4x0oiP2fSHIzMhbdgEZI53FylvW/kVqkv+GH8iT/SHv8exuQyGMne0kUR6Ti1sPnHC3WEY2X8uZN7RcNhNKD36FRxniWIxGIyrT7cfyR9//HEcPXoUb731FlasWIHk5GQsXrwYZWXnt6dn9LCangsVMndyeouQEZKCCTEjaaTmnX2fQ2VsvaTXkxqSf25/BzsrDlCRc3fmLbglfRY9+TK6D2IA+frUZ6jzNZnX9Z/dH+OHE6vgPK1jkMvhYH7/cMztF0pvry1pwA8FdYi5/16EzHAbGJa8/yEaNm4+p3nh7fcPh0wuREOtFsuWHKQpr1MZOfUmJGYMpzO6fv/uAzQ3VHse8x0aDkVaMC2MblhbCIvSnSYjtT2jRo2i17ds2YKamho6n4vU9/CFXjAbGlGR+xMrbGYwervoqaysxJ49e/DSSy/RacWk6+H5559HUFAQzYEzriVzwgsVMks6rZC5HSJOFg9eQCedk4nnpADZ7uh40joXpBboiQ2v0EngJLVCTAenJ07otG1lXBp+Eh+8OOExmmokrMxbj9d2vX9GWzuNDiWEegaVbqtU4ovjlYi6dzFCr5tBhU/pBx+h/rezDyn1C5DhtvuG08hPdYX6jHEVpK5n8rzFtJXdajFh7VdvQ69Rez47aEo8JJHecFodqFuZB3vbjK8RI0YgMTHRU9isVqshFHsjfuCf3IXNjcdZYTOD0dtFj6+vLz799FOkp6d77iMHDrK0Wm13bhrjEsdQXCi95Yn0dFJNTzvEO+f/Rt9HhUtRSxne2rfkvBGfGk093tzzCRVIZHBovG80/jXlKRo1YvQsSBH5XZk349ERd0HEE1IX56c3voays9gUkEGli9sGlR6sU9MC5/C776IT2glln36Omp9XnvVzQsK9aapLIOTRNvafv8nusH/z+ALMvP1h+AaGUsGz5qu3YTEZ6WMcHhehs/tD4CuBXWdB/a/5cNocnsLm4OBgOpH9l19+oZdynxhE9p/jKWxubeq6cSoMRl+kW0UPMfIaP348LfRrh8ytIREgYunO6EWRHk9NT+cPXSTtzg8Pv5OmqEj9x2O/v4TVBZtQramD3mqA2qTB7sqD+N++z/F/G17GwZoccMDBDcnT8fLkJxHmFYy+isOkh6W+DIaiQ9Ae3QTNwbVo3buSLs2h36DN2Qx9/l6Ya4tg16ng6oLRH6dDTAzb29qVRhWe3/Imtpad6cczPMwPDw2Oh4DLwQmlFu8cKkXQokWIXHAzfbzy2+9R8c13Z00rRUT74tbFQ8Hnc1GU14hfl+bAeco+LpbKMevOv0IqV6CloRprv/kfbFZ3XQ5PIkDYjSngivkw1+vQsK6ItrILBALMnTsXXl5eNNLT3tFFBpOSRQubjy+FkTk2MxidBsfVgxLJ2dnZuOeeezB69Gi89957l/z6rKwsT96c0TV8uSYXK7eXYO74eCye7Z6DdTZa9/4C1bbvIB8wEUGzHu6SbStXV2PJkWUobvljPtLZGBY+kE7/Js7AfQkiWKwNFTCW5cBSWwhLYwUc2kvsJOLxIQyIhCgkFsLgWIjCEiAKiQOnC1r7SWTu/QNf4Ujb+JGsuDE0EnS6j1KxSo/3DpfCZHcgwkuCvwyNh2H9elR8+TV9nAwsJfO7SOrqdIrzG2mKy+lwYeDQSMy6eQD152mnub4KKz/9N6xmE6KTMjBz0cPgtf3spIW99ueTcDlc8B4YisCsOBrxaWpqwg8//ACbzUaj3FOmTAFcTpQc/QLaliIIRAr0H/4oTX8xGH2FrC46f/cY0UOcS5944gnawfXRRx/Rds9LhYmeruebdXlYvqUYs8bG4b65f6QpT0dz+He0bFgCWf+RCL7piS7bPtLCvr18H/XcIVEBcqIkUZ0YnwikBSdhdNQQxPlFo69A/twtdcXQHdsGQ+F+OI1nppF5Mh/wvPzBl/uAI5KAwyORWBdcNgtdDrOBiiMS6SEn67OlMiVRqRDHpEGaMBhC//BO/f2SWV0/nlhDtpCmJx8ffS8CZf4dnlelNeKdgyXQWu3wEwup8OHu3YXSjz6ldT5BkyYg4eEHweG5Z8SdSv7xevz8zRHyNAwbE4Npc1M7FLfXVRRh1edvwmG3IWngSEyef49HQOkKm9Gwxu3F4z8mGn4jIul10qjx66+/0t8H6VwdOnQoHDYTCg5+QAubJV7hSBr6IHjM+ZvRR8jqS6Lnu+++w6uvvorp06fj9ddf75DuuhSY6Ol6lm4owLKNhZg5KgZ/vinjnM/THd8G5Zr3IYkbhNBb/47uwmK30hMlmdnVl3DardDlbIX28DrYWmo7CpTodEhi0iAMiYMoKBpcseyi3tPldMCuUcLaWAFLQzmsjeUw1xbCaepYXCwIiICs/wjIkkZAGBzTKd1wZDbau/u+gM5qgJdQhr+MXIwBIckdnqM0Wqhrc6PBAimfh4eGxMPneDaK33mPevn4jxyBfv/3GLiCMx23jx2uwaplOfT6iPFxmDIrucPPQSaxr/v2PdrVNWDUZIy9fqHnceLb025aGDw90d3h1RbZbvfuIYNKk5KSYDGqUHDgXdhtBjqrKy6DFDp3e5Mtg9Hp9BnRs3TpUvzjH//AokWL8Nxzz13RAZGJnq7nx02F+G59AaaNiMbD8wee83n6gn1oWvEmxJHJCPvTK126jX0Zp80C3dFNaN23Cg692zuGwxdSESIfMAGSqBRwruJYDZoya6yAqeIkTOU5MFXkEsXVQQB5ZUyCPG08jSRdTZSGFry15zOUqitpNI/YDcxNntbBY0lnteODw6UobTXQIvx7MmIQU1VMJ7O77Hb4ZA5C/6efBO8skebDeyuxbsWJcwqfwqP7sOmnT+n14ZNvwNCs2Z7HmndWQH2wBqSlLOyGFMji/GiUZ+vWrcjJyaET2m+88UZERUVB31qBosOfwOW0Izh6PCKS3MXXDEZvJqsviJ7y8nLMmjULEyZMwIsvvtjhMbFYTAv+LgUmerqen7cW4+vf8pA1NBKPLcg85/OMpUfR8MMrtO4j4p43u3Qb+yLkz5qkr1o2feWp0yEpK5+Rc+E1YAK4ImmXbAdJhRmLD8NQsB+mshy47O4WbnB5kCZkwisji15yuGemlS4Hq8OGL7N/wpYyt2Py4LB0WtQuE/7x81odTnyWU46cRg1ta785OQJDNPXI/9frcFosUKQkI/m5Z8CXyy5Z+Bzbswm71i6l18fNuo1Gfdp/H42/F0GXpwSHz0XELekQh3pRr6HffvsNRUVFNMJ9yy23UMsOVf1R6tZMiEiajeBo1tjB6N1kddH5u1vjpqRTixTzbdq0CWPGjOmwSLqL0XvGUPzh09N5jswMN3ZtCxp+eJVG1ojg4SkCEDDjfkQ9+AG8h87sMsFD4Ill8Eofj5D5TyH6sc8RMPMBiML7AU4HjEWH0Lj836j++FHaGea0XPm+QYqY7x96Gx0bQqa1kyJn4uJc2fpHR5SQx8WfM+MwMTqQjq0g7s0bhP5Iful58GRSaPPyceLZv8PScuYMNzKVfeZN7tq1/TvKsHF1Xofur4zRUzB0kjvCs3PN9zh50D36ggij4GmJkMb40KnstStyqXkhGW1CWtkjIiJgtVqxcuVKaDQa+IUOQljCDPramsI1UDW4U2sMBuMaT29dTVikp+tZvasUn/16EmMHhuNvi9yTzs8G6QyqXfJ/tEiWnPwYnYP+5C40r/8UTouRpq28R86Bz6gbwRVcemNAZ2JVVkN3bCtdTrO7BogjkkIxMAuKITMh8HGPk7gSiH/Pf/d8SgvYiRi6b8htGBdDZl65IYe+DWWNWFHonpU1JNQHt3hzUPTPV2FTqyEKCkTKi89DGnFmIfaRfZX47Wd3xGf4uFhMnZ3iifiQ993z+4/I2bWB3s6atxjJg8fQ68S0sHb5SdrKzpMKEHHrAAh9JbBYLPjxxx+hVCqpf9mCBQsgkUhQXbAKyuo91MAwIfMeKPwTrvh7YTB6In0i0sPoRbO3ThsJcK4p6501cLSv47LboFz3MZpW/Y8KHlFoAsLveRN+42/tcYKHIAyMhP/kOxD1yCcImH4fBP5hcFmM0BxYg+qPHkbTmg9gU9Vf0WeQrjwyrZ0YTZK0F2lv/+LIjx6XbiJSpseH0LoeHoeDw/Wt+KzJhvhXX4Y4LAyWJiVOPP0cdIVFZ7z34JHRuG6eO+JzYGd5h4gPed/RM27BgJHu1NaWFV/Qeh8CV8hD2E2pEAbK4DDaUPvTSdi0ZtqtSmp6iHcZ8fAh5oUkCh7ZfzZ8gwfA5XKgNOcrGLV/FKEzGIxLh4kextVJb11o9lZbt5TLaukWQ7vens6q++bvtGCZVMr6jL0ZYXf+C8KACPR0iBhWDJ6GiPvfQcgtz0ESO4CmvvTHt9K0V9Oqd2BtvnyzPi+RHM+MfQjzUt1DP9eXbMdL297u4NI9PNwPfxmaAAkxIlTp8VaxCsEvvgB5YiLsOh1OPv8S1EeyLyh8fl95kpoQtgufsbMWIm34RNoSv3n5Zyg5cYg+xhPzET4vFQI/t2szifyQcRVyuRw33XQTrWdsaGigLe12uwMxaQsg942H02FBcfYS2uHFYDAuDyZ6GFcEr82PxO64uEiP2++lrZiVcVXSRLVfPwtLfQm4YjlCFjwHv3G3XLXC4K6CtGWTgubQhS8i7M7XqL8P8QDSn9yJmk8eQ+PKN+nPejmQupmb02bhqbEPQtY2nuSpjf9CbtMfEZzkAC88NTIJ/hIhmowWvHGiDoLHn4DPoIG0uDn/1X+jaau7Pud04XP9/HTalUWKnFf9kANn298CET7jZ9+O5CFj3am0Hz5Gae4R+hhfJkT4vDTwFSLY1GYqfBwmG53KToQPKWqurq6mrs1OFwcJA++ARB4Ku1WP4iOfwmZhY3oYjMuBiR7GFcHnXVwhM0dAvJc4XTaKoi9grs5H3TfP0WJlkh4Kv/t1SOMH4VpHHN4PIbc8i/C734A0idTguGDI34eazx6naS/iDXQ5kE6u16Y+4xlI+/L2d+h4kva0VLiXBM+OSkKsjxRGmwPvHquC6q77EThhHFwOB/XzqVnpNhQ8lcwR0bhh4SDq1Hz8SC1+/jabRmgIxKRw4g13ImnQKLicTmxY9pFH+AgUIoTPTwNPJoC12Yjan3PhMNsREhKCG264AXw+n3a4rlu3DhyeCAmZiyGU+MFiakHR4U9hs3b0Q2IwGBeGiR7GVYn0XDC9xeGCIxR1ydDRvoCpKhf1y16G02yAKDwJYX/6FwS+IehNiELjEDLvb4i49y23+CGRn+NbUfXRw2jZ9CUcZ3GTvhBkXtcrWU9iXPRwalL53bGVdNisqW2fVIgEeGJ4PwwN9QXZpb/JrcGJ6TchdK67I6vy629R9vGnVASdSnpmOG6+YzCdRVdwogE/fH4YVovdE2kixcyJGcPhdDiwfumHKDp2gD5GiphJxIcn4cPSqHdHfMx22s01Z84c6t9TXFyM9evXgy/0Qr/B90Mg8qauzcVHlsBuY92QDMalwEQP44rgtUV6LpTe6uqho71d8JCWdDISQhI3EKG3vQie9NI8ra4lhEHRVPyQtJc4OhVw2Okg1KoPHoR610+XbIMg4gvx0PA7cM/gBeBxeThQcxTPbnodNdp6T0v7PQNjcH2CW0SuL2/ChgFjEb74bqLe0bB+I/JffQ12Y8fPTUoLwa33DKXT2cuKlPj+0wMwm2we4TPl5vs8EZ9NP36C/CNuLyFRoAzhN6efInxO0FRXTEwMdWomr83Pz6ejeoQSX/Qbch/4AhlMulqUZH8Oh9096JTBYFwYJnoYV6WQ+dQJ1OeCjDwguJjouWzMtcVo+OFfHsETPP+pHtmd1Vlpr9Db/oGQBX+nJpcuqwnqnT+i+qNHaOv7pRTIk3qbqQnj8Y+Jj8NP4oNaXQOe2fQ69la5U09cDgdz+oVhcUY0dW7ObmzFd37xCPvbk+AKhVAfOYqTxMunuaXD+8b1C8Tt9w2HSMxHdYUa3368Hwa9W5QQ8TJ53mKkDB1PU2Rbfv4cJw9sO034CGBpNHhqfBISEqiPD9neEydO0HZekTQQiUPuA48vgUFTidKjX8LpcIsrBoNxfpjoYVwRJJxPsF+gZZ3ADAqvDNLC3fATETxmSGIz3IKnjw2kJCd/UrcUvvg/CLrhcfB9guHQq6Fc+wFqv3iKRsEuhX4BcXh96jNIDeoHi92C/+1bQtvabW0iYkS4Px4flgi5kI9KrREfmqXwfuElCHx8YCivwPEnn4a+rLzDe0bG+uGOB0dCKheivkaDL9/bA3WL4ZQanzs87ezbf/0Gx/ZsPEX4kFSXAJamP4RP//79MXXqVPqcY8eO0YgPKWpOHHwvuDwRdOpSlOZ8zYQPg3ERMNHDuDqFzBeo6SEwr57Lx2HQoP6HV+hUdGFIPILnPdnnBM/pNWLylNGIvP8d+E1aRI0NrQ1lqP/2BTT8/B/Y1A0X/V7eYgX+Pv5RzOk/1dPW/vctb6BB7y6YTvST0wLnEJkIrWYb3q81wvLU3yGJjIBVpcKJZ/4O1WF3hKidkHBv3PXwKPj4SaBqNuKLd/egrrq1Qzt75ji34/KutctwePtaGv2hwueWNGpc2C587EYb0tLS6EBmwvHjx7Fx40ZIFRFIyLwbXK4A2pZC6uPDhA+DcX6Y6GFcnULmi4j0/OHVw0TPpRoPNix/HXZ1A/g+QbSzqT1q1tfh8AV0nljUn9+HV+ZUEkqBsfAAqj/5C1q2fEMLvS8GUttzW8YNeHrsQ3RKe7m6mra17692+/MESkV4ZlR/DAhSwOZ04ZsKNYrufQxeGRlwms20pb1u7boOnV3+gXLc9chohIQpYNBb8c1H+1BaqPQIn5HT52No1hx6e/+GFdj92w+03kcU0JbqahM+NT8ch01nQWpqKmbOnElfe/LkSTrGR+YdQ7u6uDwhtC1FKDn6BZwOZgnBYJwLJnoYV6mQ+RIiPUz0XBLNG7+ApbYQXLGM1rNc7enkvQGezBuBM+6nw2xJ6o8WO+9fRTu9tEc3X3S9T2ZYGl6f9iySAuJpRxfp7Pr8yA/U0Vkq4OGhwfGYGe8ucN5Sq8bmmQvgRVJPTifKP/scpR98DKftj2iLl0KMOx4aidjEAFgtDixbchDHj7jNFol4GT55LkbPXEBvkzTX5uVL4HDYIQqQImJBOvheIthUJtQsOw6r2oTk5GSP8MnNzaVdXTKf2DbhI4JOVYLi7C9YcTODcQ6Y6GFcpTEUl1LIzGp6LhZywtYdJTUfHATNeQxC/zPnQDFO6/S69XmE3Pws9S4i6cDmdR+h7stnaBH4xRAg9cOLE/+KucnT6O0NJTvwfFu6ixQ435AUhgcGxULE4yJfpceylNGQ3LWYVCqjcdNm5L7wD1hbNZ73E4kFWHjPMKQNCqMF/78uzcGerSWeqNCgsdMwef694HJ5KMzZh3XfvAub1QKhnxQRt6ZD4CuGXWuhwocMKSU1Pqd2dZEp7RKvKCQOvocKH726tK2ri/1zwWCcDhM9jCuC6xlDcTGFzCzScylY6kvRvOEzet13/ALqWMy4yGLnxMGIuPdt+E2+ExyhhDpW1331NC14JvVRF4LP5WHhgLl4ZlzHdNe+anftzuBQXzw9MgkBEiGaTVZ8IQmD44lnPFPaj/3f36AvK/O8H4/PpQaGI8bH0dtbfiugA0vb/276Z47CzEWPgC8QorLoBH5d8gZMBj0ECjEiFgzwzOoiqS5TnRb9+vWjwof4+BQVFdGRFUJpGPoNJl1dYuhby1F85DPYbcZO+54ZjGsRJnoYVyfSw9JbVxXS4db069s0TSPtNww+o2/s7k265uDw+PAZPguRf34P8gET6H2ktZ0MNNUc+g0uZ0eDwbMxKDQN/5n2HPq3pbve3rsES44so+muCIUEz43uj2R/L1gcTnyrASr++hyE4eGwNjfjxFPPoXn3nj+2h8uh09inzkmh5uTZ+6uol4/J6K7BiemfgTmLn4RIIkNjdSlWfvoatOpmOrIi4pZ0iMO84LQ46JBSQ7kaiYmJ1LlZIBCgsrISy5cvB1cUiMTB7e3sVSg89BGs5guLPAajr8BED+PqDBxlhcxXlZaNX9IWdZ6XPwKvf4h2KzEuD77cF0GzHkHYHf+CMCSOTqFv2fgFapY8AVPlyQu+3l/q2yHdtbFkJ57b/B/UaOppKzsZVjolNog+tkVpxLbb/gzBsOFwWq0ofOMtVH63lBYotzNiXBxuucttYlhR0kI7u1TN7oLr0OgE3Hj/M5ApfKFuqsPPH76MxuqytiGlaZDG+MBld6LulzxoTzYiOjoa8+fP9wwp/eGHH+Dk+iBp6IMQiBQw6xtQeOhDmI3Nnfb9MhjXEuxIyuj6QmbWsn5e9Pn7oDu2pa2O51HwJPLu3qRegTgiCeF3/RsBM+4HVyKHTVmF+u9eROMvb9FJ9Rfq7iLprmfHPQyFSI7K1ho8tek1bCzZAaL7b06OwP1tdT7FGhN+HD4dtvm30tfWLF+B/Fdeg02n87xfUmow7exSeIvRojTg83d2o6LUvQ3+weGY9+fn4B8SCaNei18+e53O6+IKeQi7IQVeyYGA04XG9cVo2VtFZ3UtWLCATmlXqVRYtmwZTDYhkoY+BJHEH1aTCoUHP4BRV9fJ3zCD0fPhuE6fnncNk5WVRS+Jaymja2hSGbH41U0Q8rlY8fqs8z5Xm7MZzb99RCdok7ZrxpnY9Wo6Vdxp1sNn1A3wm3g7rjWMZhtaNGY0t5qg0pphtthhsTlhsztoDZhQwKNLIuLD10sEP4WYLplE0GXb6DDqoN6xDNqjm+hML45ABJ/R82g6jLTBn49WkwYfHPwGxxry6O0hYQPwwLBFVAw16M34KLsMdXozHa87lW9G2GfvwWW1QhQUhP5PPwl5vLuuh6DTmvHjF4dQV60Bl8fB9fMGYOCwSPqY1WLChqUf0RofMv5i9IybMXCMO9rUsrsS6gPuLjBFejCCJsdDZ9Dj559/hlqthkQiwdy5cxHoL0dx9hKYdPW01idh0N2Q+8Z24jfLYPTs8zcTPYwrokVjwp3/3EjTXL++4R7KeC70eXvQ9MtbEEelImzRP7tsG68lGle8AUPBfjpmIfyu18DhdZ0QuBysNgcKK9U4UdqMkppWVNRroVRfXneej1yE8CA5IoLkiArxQr9IX8SFe1OB1FlYGsrQvOFzWGoK6G2+bwgCpt5Nhfn5IMNKfy/ahu+P/wq70w4fsQIPD78TA0KSYbE78F1uNfbXquhz0+R8DP3xC7hqqsERCBB//z0InuJ2ZCbYrA78uiwH+cfds7+Gj43F5FnJ1O2cDCjdtXYpTuzf6n6v4RMxbtZt4PJ4aM2ph3JLKRlCD2mML0Jn94fZbsHKlSvR2NhIi5zJCIv4uCg6qoIUN3O4fMSm3wrf4AGd9p0yGJcDEz2XARM9XU+rzoJFL62n11e/OZt2zpwLY/EROkaBOApHLP5PF27ltYGh4AAaV/yHGuyF3/0fiEJie2wkZ//JBuzKqcXxYiWs9jPruUjUxt+7LYIjFkAo4FLxQlq2LTYHFUtGs51Ggsgi188GEdOxYQr0j/bDgMQApCcEQn6VI0LkEKg/uROqLd/AYXC7JhPR4z/lLgj8Qs/72gp1Dd7Z/zlqtW4H6OuTJuPW9Nngc/nYVd2CZXnVsDtd8BcLMDVnJ0Q73OIlaPIkxN13D3gi99w0l9OF7RuLsGuTu60+Ot4P8xYNhsxLRLfv2J5N2L3uB7KxiExMxbRb/wyxRAZ9aQsa1hTSOh9RkAyhN6TAJeLQNvaytu6xcePGIXPQAJSfWAqNkkSnOIjodx2Cosed9++VwehKmOi5DJjo6Xr0Rituff53ev3X/8zyzOI6G6bKXNR/9wL1T4l84L0u3Mqej8NsQM0nf6FzpHxG3Qi/ibehp1FcrcbqXWXYc6wOtlOEjo+XCAMSApAc44fYMG9EhyouWZgQIVWnNKCmSYeaJj3K6jQormpFa9uwznZI/UxCpA8yEgMxLDWERoPabROuFFLgrN69HJqDvwGks4t2f82Gz+ibPPVoZ8Nit+LbnBXYWLqT3o71icQjI+9ChCIUlRojPs4uo23tPA4HkywtCPv6E3CcTshiY9H/6ScgDnGbHRIKTtTTqA8xMiT1PvPvHILwKLcZZVleNjb+8AnsNiu8/YMwc9GjtP7HXK+jhc2kpZ24OIfOTYYoRI5t27YhJyeHvjYjIwMTJ4xHbfEaKKv30fsCI0ciMmkOONzOi6QxGBcLEz2XARM9XQ85Wd3y3Dp6/ed/Xw/ReVIRxHem9ou/geflh+hH3f4zDDfK3z6CLmczBH5hCL/3vz1mrhY5PBzOb8TyLcXIr3CnawgkBTV2YDhGDwijqajOiBiQzyapssIqNfLKWpBTrKSC6FRITRARPyPSQpGRGAAB/8pP4NbmGrRs+gKmsmP0Numg8598B2TJo877cx6qPYaPD34LndUAAU+AW9PnYGa/iTDZnfjmRBWyG9xRpH4iDob+uASCxgbq65Pw0IMIGD3S8z7KRh1++vIwLXAm/j7X3ZTuqfNR1lVh3bfvQtfaAoFQjCk334u41EzYNGbU/ZoHq9IIDo+DoKkJ8EoJQnZ2NrZv305fGxsbS92cNQ0HUFP0G/mG4R2QjNgBt4HHd0ecGIzugomey4CJnq6HpCluenotvf7jqzMhFZ/7P3xrSy1qPn4UXJEUMU9824Vb2bMx15Wg7sun6PXQRf+EJCoVPYGCChW+XJuLvHKVZ7jsmIHhmDUmDomRPt2SGiHF0ceKlcguaMLhgsYOaTFSGD0yPRQTB0fQNFi7ncLlQA6LxqKDaNn0FeyaJnqfODoVAVMXU9fnc6EyteKjg996ipyTAxPx0LA/IVDmT9NdP+ZVw+p0wYvPxcTsHfDb544OBU+bgtjFd3nSXWaTjUZ8inIb6e0ho6IxbU4qFUEmvRbrl32E2jJ3HRKZ3zVs0my47C40rCuEocT9+/IdGg7/sTEoKS3BunXrYLfb4efnRwucYa2h6S6X0w6JVzgSBt0JoZiNN2F0H0z0XAZM9HQ9ZPzE3CdX0+tLX54BL+m5IxSkLbjqvftozUrsMz+xegJ6cnWi7uvnYKktgjx9PIJmP9rdmwStwYqv1uZi08Eqept05l03Jg5zx8fTGp2eAkmxkQLq/SfrceBkA60NasdPIcK4QREYnxmB+HDvy97XnDYLneHVuvcXuOxWuu8qBk+D77gF57QSIIfULWW78XXOCljsFoj5Ivxp4DxkxY1Gvd6MT3PKUatzb+sIUwsSv/8MPIcD0qhI9Hvicciio9zv43Rh5+Zi7NhQRG+HRXrjpkWD4esvpfO59q77Ccf2bqKPxSYPxJSb74NAJIZqTxVU+6vp/dI4X4RclwSluhmrVq2CXq+HSCSibs4BPhxa4Gy3GcAXyhGf8SfW2cXoNpjouQyY6Ol6yO4z+wm36PnmpWnw9Tr3SZFMvK7475/o9ZinlvWYFE53ojuxHcrV71HjRuIczPfy69bt2XeiHu8vz6HChzB5aBRun9Ef/t49e6o7KZAm6bcd2TW0wFpv+mPoZ2SwF6YOj8akIZFQyC5vn7NpmqDa/DXtrCNwpQr4TVgIr4xJ56yJadQr8eHBb5CvLKG3B4ak4IGhiyAXKfBzQS22VbonrocLgFGrv4esqgJcoRAxd9+JkOlTPUKtKK8Rq5blwGS0QSTmY/YtGUge4C6wzj+yG9t//RoOux0+ASGYftuDCAiJhK5ASX18SIGzwEeM0DnJsEtBhU99fT19b1LgnJYSi7Kcr2HSk/t4iEy+AYERwy/rO2IwrgQmei4DJnq6hxv+tpqaE375/FQE+Jz75Ehs/8tfu5lej/7rl+BJFejLOC0mOhKBdAwRPx7iy9NdEC+dJatPYsP+Sno7OsQLD87LQEqsP641SAQou6AR27JrcCi3wdNdRkamjEoPxdQR0UiPD7isAmhj+THq5mxrdnvkkE7EgOn3QBze75yt7euKtmHZ8V9hc9ohE0hwd+YCjIkeimNNGnx1vBIGmwMCLgejKnIR8/sv1N/Hf+QIJDz8Z/Dl7miSRm3Cim+zUVOppreHjYmhbe18Po86Nv/+/fvQa9Tg8QUYP+d2JA8eC0ujHvWrCmDXWcDhcxE0JQHSJD96fDx50u1ETaa2Z00aj5rClWhtPE7vC4wchcik2azAmdGlMNFzGTDR0z2Qmh5S27PkuSkI9pOe97nlr99K0wSRD30EgY/bur+v0rL1W2j2/Uq9YSLv+98FTfE6i4YWA1754gAqG3TEAw83TkjAbdOTIeBf+4btBpMNO4/WYMOBSpTW/DGDKtRfhinDo2gEyFt+aUW8LocdmsO/Q73rJ7gs7oGeZLYXEa5k5MXZqNHW44P9X6NU7RaVmWHpuHfwreByZVT45DW73ZpjnGYMXf4lZK0qCP39kPDIQ/AdNJA+RoaTbvu9EHu3lbp/hghvzPtTJnz9ZTAZdNj002eoIkaGxPF50ChMmPsncO1cWudjrHAXUXtnhMB/QiyOnzxOu7vI4T8wMJCmuyytR1FX4rafkPvGIW7AIghEzA2c0TUw0XMZMNHTPdzy3G+0oPSTp7MQFnj+g2TF23fBadTSCdjCIHftQl+E1DdVf/gQXA4bguc/DVm/od2yHSdKmvHa14egM1pp6/kTCwcjo18geiMl1a1U/JAUmMli90R/xg0Kx/VjYpEYeXbBci7s+laotn0H/fFt9DZHJIXv2PnwHjKTDjs9HYfTgV/zN+DnvHX0uoQvxm0Zc5EVNwa7qlVYXlALq8MJERcYmb0L0Qd20qhPyIzpiLlzEXhi8VnTXTNuTEN6Zjj18Dmycx0ObFxJxYxfUBimL3wQvoFhUO2rgmqfu86HtLMTI8P61iasXbsWJpMJQqEQ06ZNQ5CPDeUnlsHpsNDZXXEDbmd1PowugYmey4CJnu5h4fO/05PmB09ORFTI+VNWVe//mXbDhN352jlTAn2pRV0clYLQ2//ZLUXd27Nr8L9l2bQYPSHCG8/dNfy86cneAhE8u3Nq8fu+ChRXuyMghKRoX1w/Jo624V9KlMtcW4SWDUuoJQNBEBAB/6w7IE3IPOvzqzV1+PjQdyhuKae3kwMTcP+Q28Dn+eCL45UoVbuHjyaaWpG5/CtITAaIQ0OQ+NijUPRP8qS7Vn6XjeoKd7ordWAYZt6UBolUSLu6NvzwCYy6VvAFQoybTdJdY2AsV6NhXRGcZju4Yj6CpyXCFSKkRoa1tbX0fTIzMzFscH9UnPgOZkOT2ygzYQaCY8azxgNGp8JEz2XARE/3QByZiTPzu/83gZrTnY/qT/9KBz2GLHwB0tgM9EWID0zNp3+lM5/C7ngV4oj+Xb4Nv+8tx0crj5PgAPXb+cuCQef1WOqtFFaqsHZ3OXYfq/UMzSURr+kjYjB9ZPRFF3CTLjxdzlaotn9PI5kESdxAKn7OFtF0Op1YX7Idy06sph1eAi4fN6XOxPVJU7Clohmri+upk7OUAww7sAXRR/eDw+Ui4sa5iFxwM7gCAZwOJ3ZvLcGOjcW004uYGc65dSBiEwNg1Gmw8cdPUVPqbp2PTxuCCXPvAN/OR/3qAlrvQ/AeGArfMZHYd3A/Dh06RO8LDQ3FzBlToa7ZCFX9UffzAlMQk3YL+ILzp68ZjMuFiZ7LgIme7uGuf25As8aMtx8bT91yz0ftV8/Q9uzgeX+DLKlvdok0rngThoJ9kCYORcjNT3f556/cVowv17pPhteNjsV9c9OvmqvxtYpaa6apLyIGVVq3CzTx+RmTEY65E+KREOFz0c7arbt/hubQOsBpp5ESr4GT4TvuFvDlZ76H0tCCTw8v9fj6RPtE0KiPWBBEoz7VWvccs1i9CoNXfQ+5XgtZbAyt9WkfXFpbpcYv3+dA1eyOEI0YH4dJM5LoANPsnetwcNOvcDodkCl8MHn+PYiITUbzrkq0HnZHd4QBUtrWXq2px/r162GxWCAWizF58mT4ydSoLlhF/XyEYl/EZdwOmXffTUszOg8mei4DJnq6h3te3YRGlRFvPjoWSdHnb7muX/oPmMqPI3D2o/BKH4++a0TIQcS9b3V5XdOaXWX49Fd3sev8rEQsmpHM0hanYHc4se94PdbsLuvgQJ0W74+54+IxNCXkogSiTd0A1dZvPS3uHKEEvqNvhGLY9WdYNZBD8K7Kg/jq6HLorQZwwMHk+DG4OW029tTosabEHfURwoXBh3eg35E9NOoTPnc2jfoQQ0OrxY5Na/JxZJ+7UDoo1AtzFgykxc6NNeXY9OOnaG12zwcjk9pHTrsJ5ho9GtcV0fEVpLsrYEIsECOh6a6GBvdz09LSMGJIP1Tl/QCrSUVFXFj8VITETgSHc+0XujN6Dkz0XAZM9HQP97+2GXXNBvz7oTFIjTt/i3PD8tep023A9PuoyVtfo37pP2EqPwZ5+gQEzX6kSz9725FqvLU0m15fMCUJt03v+rTatVb4vGpnKfX9IXVPhLAAGeaMj6eeP2LhmcXKp2OqyoNq81eeeh++dyDt8pKljD5DbGrMWnyTs4IKIIJCJMftGTciKWAgvjlZhZK2Wp8wowbD1iyDT2sLrfVJeOjP8E5P8xQ5r/nxGAx6KzhcDkZPise4KYk0UrNn3Y84ecBddO0fEklHWPgogtH4ezGMbbVBxMwwICsOB48fxsGD7u3w8fHB9GlZsLTshrrRPZpD7hOLmPRbIZJcWvE3g3EumOi5DJjo6R4e/M9WVDfq8OqfR2FAwvk7f5pWvUMnWvtl/Qk+I+agL0EKXuu+egbg8qgRocAnuMs++2BeA1798iA18Zs1Ng73zkljEZ5LGH2xdncZ1u+rgKFt7IWXVIAZo2JpevBCLtWk3kd/chdU276HQ9dC7xOF94P/5DshjnAXJp9KXlMRlhz5gba5E/oHxGNx5gKUaUVYUVALi8MJHlzIyD2MlH1bwXfY6RiLmDsWgS+TwaCz4PdfTiLvmPv1AcFyamgYEe2L8vwcbF3xBW1x53J5GDzxegwefx10x5rQsqsCLoeLFjkHZcVDLTPRdJdOR6wMOBg5YgQSogSoKVxFu7u4fDGik2+EX+igTvjWGX2NLCZ6Lh0merqHR97chop6Lf5530gMSjq/947y90+gy94In7E3w2/cLehLNPz4LxhLjkA+YBKCZj3UZZ9bXqfB397bBbPVQSMUf7llUJ+v4bncrq/NB6uwelcpGlqMnnlkZNwFGdFxoSJ+OtLiwBr3SAubewyFNGk4dXYWBkR0eK7dYcdvRVvxc+5vsDis4HK4mJk4EVnx07CisBEnlO5iaR+bGUM2/YqI6lII/fwQe+/d1NiQiJT84/VYt/IkFUFE3w4fF4eJ05Ngs+ixfdU3KMvN9kR9subdDW9hIBrXF8HS6I4oyRP9oRgXiW17tqOwsNBT5DxpwnC0Vv8Og8adSvMLGYTI5LmsyJlxRfRJ0fPJJ59g9+7d+PbbyxtGyURP9/DXt7ejpEaDF+8ZgSHJ549etGz5hs4y8h4+m06u7itYGspQ+/mTtCYi4v53IPQP65LP1egtePx/O9CkNtEp5P+4dyR4PFaLcSWQVNfB3Hr8sr20Q93PwMRAmvrKTAo6r6i069RQ71gGHfH3cTndxc4DJriLnRUBHZ7bbFDhq5zlOFiTQ2/7iBVYkDYHXpL++KmgFq1m97iNmPoKDNm6hhY6+wwaiLj7FkMSFgaT0YoNq/Jw/LDbQZrM7bpuXjrt8Co5cRA7VpPWdD2tEcocNxNDJ1wPzZFG9+wupws8iQCBk+NQ7VDS46rVagWPx8PIEcMREaBFQ/lW+jMQT5+o5JvgE5TSSd86o7eT1ddEz/fff49XXnkFQ4YMYaLnGuOJd3eisFKN5+4ahhFp7plA54K42Kp3/givQVMROPN+9LWOLVnqGATP/WuXjWN4/pO9yC1roQ7E/31s3HkHwjIur+V91c4y7DleR1OHhMhgOeaMi8eEwZHntQGwKquh2r6U1rgRODwBFENnwGfkjeBJvTo8N7vuJL48+hOd50WI9Y3EwgHzUKSWYktFE0i3Pd/lRMbhXUjJ2Qs+KXS+cS4i5t1IC52L8xvx2/IT0GrcEaa0QWGYMjsFfK6VCp+SE+52dWJoOOGGO+AnCUPj70WwNrc5Tvfzh3hYMLbt3Y7ycre/UHBwMCaOTYe6egMsRuUfUZ/+c8AXyjrh22b0ZrL6iuhpbGzEiy++iAMHDiAkJAQBAQFM9FxjPPX+LuSVq/D0HUOpsdv5aD2wmg5ulKeNQ9Ccv6AvQE5u1JcHri51oiZdWqRbSyLi0866CxlHMi6fJpWRdnyR2WXtbs9kuOmMkTG07sf3PHU/pNZLtfU7mKtyPc7OPiPnwnvodeAK/3idzWHD78XbsSJvHUxt6bGRkYMxOeE6rC/ToUjl9t7xNekxeNtamvISBQUh7t674TdsKMwmG7avL8ShPRXUn4m4OU+ckYQho2JQnncE21d9C5PenTZLGTIWI6bMg/GYCuqDNWTXBVfIg9/YaNQKVNi+fTttbedyuRg5YhjC/dRoqtxJ93EysT0q+Qb4Bg/o1O+c0bvI6qLzd7fHuXNzcyEQCLB69WpkZPRNs7prHWLl3z4b6EJwBe6DuNPq9h/pC7TuXUlPBqR+o6sEz8HcBip4CP+3MJMJnk4myE+KxbPT8NULU+kluU0m1f+4uQh3v7IRby/LprVVZ4M4k4fe/g+E3PIchEExdJ6XevtSOqaEzPhy2d0pLAFPgNn9p+Ddmf/A5LgxtLV9X/UR/HvHvxAuycei1DB4CflQS+TYPHMBNs9ZhAabE/mv/ht5r/wLLpUS029Iw+K/jEFYpDcsZjvW/5KLz9/ZDYl3AhY+9ipSho6jn5V3eBeWvvMcmiRViLwtg46ucFodaN5SBu/jDtw6+2bExcVRk8U9e/djy75m+MXeDLEsGHarHmXHvkVpzjewms/+MzMY3UW3R3pO5emnn6Z26CzSc23xwid7cbRIiccXZmLi4MjzPpd0sTSt+h8kMekIve0l9HZsrU305EXqHsLvfgOiULehXGfSojHhkTe309Egs8eRTq30Tv9MRkfIPwD7TzbQlvdT634GJATQup8h/YPPWvdDOr0MuXug2rEU9tYmeh/Py596/HhlZHUYSluhrsHXOcuR21REb3uLFZiVNAMmZxy2VbbA4XKRAzyS8o9i4KEdkNgsCJk5HZG3zAdPJqeePlvXFVDxQ4Z8ZQ6PooXO2pYqbPv1a6ga3eaFoTGJGD9rEfgNPGpq6LI5AC4HPkPC0ORrxI5dO+j8LkJqajL6RzvQUrOb7vNcnghhCdMQFDmKTW1nnJc+k946FSZ6rk3+sWQ/Duc34i+3DMTkYdHnfa6h6BAal/8borBEhN/1b/R2WjZ/RTt2JLEDELrwxS4psiUi9HhJM+LCvPHmX8ZCwGcnm55W9xMeKMOssfHIIn4/ojP9fsggWu3RLWjduwIOnVs08RQB8B19E7wyJtL6H/o8lwuHao/h22MrPfU+wbIAzEyajTKtH3Ia3ZEWkd2G9EM7kHzyMERSCRU+ITOmwWhyYNPafJw44hY4JOU1dnIiBo+KQO6BrTi4+VfYbcTzh4v0EZOQOWwGtHsbYCh1bxPfSwT5yFAcbcjDiRNu00vi5jxmZBpEtuMwaKrofRKvMEQn3wSZD3NzZpwdJnouAyZ6uodXvjiAA7kNeGheBqaPjDnvc00VJ1D//UsQ+Icj8oF30ZtxWoyofPc+uKwmmro41wDKq8nKbSX4cm0uREIe/vfX8YgI6lgQy+g+mtRG/La7HBv2/+H3I5cI6N8MmfJ+tjlfTrsVuqObaZu7Q98mNLwD4UPEz4AJHvFDWtw3l+3Gitx10Fh09L5Yn0iMi5uFI418zzgLhVGHgfu2ILYkF5KwUMTceQf8hg1BVbkKG1flob5G4+nymjIrBWERfOxeuwxlee72dpFEhuGTb0CMfzpadlTC3jayQxKhgD1dhp1H9kCpdIuvsLBQDBsQAF3jbjjs5PM5CIgYjvDEGay9nXEGTPRcBkz0dA+vfX0Qe4/X44EbB9CizfNhaaxA7ZL/A1eqQMxfv0RvRnNwLVo2fUmnbkfc93an2/bXNevxyBvbYLU78fD8gZg24vxRN0b3YDTbsOVQNa25qm8xeOZ8kcGvpOvrbPPr3OJnE1r3rITD4J4Mz/cOahM/4z3ix2wzY23RVqwp2AST3V3snBqYhPSwGdhba4GmrcjaT92MQfu3IKKqBN4pyYhedBu8+vfHscM1NOWl17nFTEyCP6bOSYXVUI3dvy3zpLxIl9fo6QsgV3vTQmeXnbTeA14DglEtV2HfoQOw2dy1SGmpiYgL1kKrdLs58wRShMVPQWDESJbyYnhgoucyYKKne3jj28PYmVNLXX5nj4s/73Pt2hZUvXcf9SaJfeanXusK7HI6UP3hw7BrmhAw434oMqd27ue5XPj7x+60FvHjefn+Ub32u+1dfj/uuh9iK9AOGeUye2wchqeGnOGpRAwOqfghkZ828cPz8qO+V4pBk8EVuqNFWrMOK/PXY2PJTtjJ4FMAGSEDEOU7AYcarDDZHfS+oMYaDN6/FcEN1fAdnImo2xdCEBaJPVtLsG9HGRxtYiZtYBjGTU1AfelhHNj8C8xGd6dYTP8MDBszF45cM/RFzfQ+4ugsGuSPY61FKCgooPeRZpXhmbGQcwphNjTS+8SyIET0mwXvQDYOhQEmei4HJnq6h7eWHsG2IzW46/pU3Dgx4bzPJf+xVrx+K70e/X/fgCfunX4e+oJ9aFrxJrgSL0Q98gm4AlGnft7GA5V476ccCAU8vP/ERIQG9M7vtS/N+QrwkWD6yGhMGx4DHy/RGeJHm70Bmv2r4dC752ZxJXJ4D7mOev3wJO60ZpOhBctPrqXzvJzECJEUU4cMRIhiLLIbLbC1fRaJ+Aw6tAP+zQ0IGDMaUQsXwCLxwZbfCpCbU+d+fy4HmSOiMHxMGPIObcSJfVvo9HYirpMyR2Ng8mQYDrV4vH34ChEcaVIcrDiG+nr3SAwvLzlGDgqCU38Mdps7yqXw74eIpFmQyEO66Ntm9ESY6LkMmOjpHt754Sg2H6rCn2YmY35Wvws+v/w/C+GyWRD54AcQ+PbOA13t18/CUlMIn9Hz4DfBLfI6C5XWTOefGUy2ixKejJ4L6bz7bQ+p+6mkLe/toy7GZITT1HFStG+HCB5pZ9ed2I7Wfb/CrnZPRucIxFBkToH3sFngK9wDgBt0TViR93sH8ZMenAk/+SgcV1qI+TIlsqIIGdm7EdDSiOCsSYiYfxPUNhG2/l6A0gJ3rY5AyMPwsbFISZche8cqlOUeofdzeXykD5+E5JCR0B5pgkPv3n5hoBStcS7szzsMvd4dIQoJ9sfAJAEsrSfgcjlo5DcgfChC46ZAKD7/OA9G7ySrL4qeK4WJnu7h/eU59CBNpnaT6d0XovK9++HQNiPszn9DHJ6I3oa5thh1Xz0N8PiIevhj8OWdO4n6je8OY+fRWiREeOPNR8exMRO9AKvNgd3H6rBuTzkKq9yRHEJcuDeuHx2LsYPCO0x5J+lUQ8F+mvayNrodk8Hlwyt9PLyHXw9hYNQ5xU9qUCbkkuEoVNmJByElvKqEip/g5gYEThiPiHk3oNEoxJZ1BaitdKfVxBIBRoyPQ0ysC0e2/YLasrZUlkiMQaOnI1aSDm12I/X3IQgjvVDl24qcwuN0nAUhNioA/SLNsGhL6G0Ol4+gyNEIiZ3IXJ37GFlM9Fw6TPR0Dx+vPE7/OyWChwifC1Hz2f/B2lTRZR1NXU3T6vegP7Ed8vQJCJr9SKd+Vn65Cn97fxcdKPnWY+OREHFmESzj2qa4Wk3/voiwJaNF2ru+Jg+LwsxRsR1SmeRwbirLoYaY5qo8z/2SuAwa+ZHEDaSRorOJn1jfFPh7jUZpKx27RQmtKcPAI7sR3FRL015krEWNTkiLnZWNek+b+7CxMYiMMOPItl+hrKv0dHoNGj4NEZx+0J1s9rwpN0qGcqkSJ0vy4HC4BVFyYiCi/NWwGNwzwoi/T3DMeARHjwWPf/4p9ozeQRYTPZcOEz3dw2e/nsDqXWWYn5WIP8288MDBuu9fgrniBAJnP0r/E+1NOIw6VL17L/VZCbvzNeq221kQz5cn39uJoqpWTBkWhUdvGdRpn8Xofki6a/PBSqzbW4FGlbtuhojdjMRA2qk3PDUUAv4fUT5zTQH1iDIUHnQPNiVRmIAIOt5Cnj6e1pk16JW002t7+T7Y2gqeQ73iEOI9HhVavkf8BNVXI+3YfkRWFSNg5AiEz7sJlVohdm0q9ogfoYiPoWOiERyoRs6uNWhVutNtQrEEgwZPQzgSYShU0ZEWBFeUGCXCBhSUFVGxRh5I7x+IEEUTbCa3MSNfIENw7ATa6cXjd25dHKN7YaLnMmCip3v4Yk0uftleghsmJODuWakXfH7jyjdhyN8H/yl3wXvY9ehNtM8WEwbHInzxG53aQbXtSDXeWpoNiYiHT56efN75TozeAyl0PlLQSKM/2QVucUDwlgsxaUgUpg6P6uDPZGtthObQOuhytlDPKAIpsFcMmgLFkBnge/mh1aTBuuJttNvLaHM/x0cSiijfLNToJXSgKUGhbkba8QOIKz6BgPQ0hM6ZhXpuMHZtLkZTvc5T85M5IhIhQWrkHtjgaXMnaa+BmSTykwhjkdojfhyRQhRwalBa3ZaWgwtp/bwR7KWEw6r2tLkHR4+jzs48wZl+Roxrnywmei4dJnq6h2/W5WH5luKLHnmg/P0T6LI3wmfMfPiNX4DeAhkhUPPxo7Cp6hEw8wF6UukszBY7Hnh9C1o05osuIGf0PhpaDNh0sIpGgFRtRoHtbe9Th0djdEaYZ9I7McvU5myB9tA6aqVA4XAhSxoGReY0iGPSqbfP5tLd+K1oC9SmNjdnnjdiA7KgsgTA0qZ+xEY9dXfun3cEviFBCJszCyr/fti1tQwNtVpPt1fqwFBERepRdHQzWhqq6f18gRBp6RMQLUiFuVTrET+WYC5KhQ0oqXGLHw5cSE2QIdhbBYe1rT2fL0ZQ1Bi6WM1P7yKLiZ5Lh4me7uG79fn4cVMR7S4hBoUXQrV9KVr3rIBi8HQETL8XvQVj+TE0LP0nOEIJov/ymcczpTNYtqEASzcWIshXgo+eyqKt6oy+PeuLjILZcKASR/IbPWkpmZiPCYMjqQAiRdDtRc/GokPUPNNcne95D4FfGLwyp8JrwEQ4hSLsqjyEdUVbUaVxR2oAAWL8xsGGOOjdvoPg22w06kMEUDDHgZDrZsIQl4kD+2tR2TaqghCbGICEeDOqCrZ7an5oq3vSSMTLMmGvMntqfiy+QJlUiZL6cpr2IuInKVaKMN9WOG1t7fk8IQIjRlDxI5R0bqMAo2tgoucyYKKne/hhUyG+X19A6wqIE/CFaD2wBqrNX0GWMhrBNzyO3kLDz/+BsfBAp4u5Vp0F9/xrEyxWB/62aAh18mUw2mluNWHLoSrq3dSkdqeqCDGhCkwaEonxmRHwa0uFWpsqoT2yAbqTO+Cyuh2cOXwh/dsk0R9haDzym0vwe9E2HKo71lZ7w0GAfCCkokHQWP8Q2yG1FeifexgxdRUIHjcWGDweOcUm5B+vR/tZJjjUC0nJgKbxMKqLT3peGxWVhpSg0UCNEy6bu/7ILHOiQtGCkqYKOs2dhISiQ3mIDTEB9raONg4XvsEDaOpL5n3+YceMng0TPZcBEz3dw/ItRfhmXf5FF9Pqjm+Hcs17kMRmIHThC+gN2HUqVL13Py0Yjbj3bQiDOm+w4pJVJ6mRXWKkD/77l3HMeZlxzkL3nGIlNu6vpLPx7A63mCDD3QcmBWHS4EgMTwuhre9Oiwn6kzup4SERQu0Ig2LogFN52ji0uGzYULwdW8v2wNBW9yMSRCBYMRJaq4+n3V2q1yIpLxv98o8iKCYS0vFTUWzyQ87hWtja2tclUgGSU8Xg2vNRUXAYzrYuLl+/MGREToKkRQanyV1YbebbUeenRbGmEhba6u5CiJ8LiZFO8JxuF2iC3CcWwTHj4B2Y0ukjXxjX7vn7zPG+DMYlwuO6DzDtB9ULPr/NLdZhchc+9gZ0OZup4BFHJneq4CHmdev2umsebp+RzAQP45xQB+WkILr0Rit2HavDtsPVyK9Q0QJosiQiPsZkhGHikEikDppK01uW2iIqfgx5e6m1BJkf17LlW8j6DcFNAyZh3vUzsKvqMC16rtLUoKplOTgcGQLkQwFuPIxyBY4Om4Bjg8cgqqII/dauRZRehZsmTkZ9QCpyjjVDozYh+5AN4EQgPiEJPvIq1JUehFpVh+2q7yDgizEwLgsBtgiItUBckx+i4I16Pz1KLbVoUOnQoOLCSxqI5BgOpLxm6FvLoc8ph0gaQFNf/uFD2WBTxhkw0cO4YohjLMHR3uJxAbhSt+hx9hLRQ2okSIEogaQEOhNSO0W8Wkih6qB+gZ36WYzeg1wqxIyRMXTVKfXYeqSajo5pUhlpITRZgb4SjM0Ip+nS+FmP0O5Kfe5u6I5thbWhjJofksWT+2Jw+niMH3Inqjg2Wvi8t+owlLrtAHZCLEyEj3QwTJChIj6FLpmuFYkFx5C4eROy4mNhGj4WhSoxyopbUFpMxlH4w9dvNiL7a2FQHYe6qQaHin6j2x4flol4r0Hgt/AQqfJGBBRokupQzm9Ck64FB/MAId8fCREuBCk0sBibUVO0FrUl6+EXkoHAiFGQekeyfxAYFJbeYlwxv+0uw8e/nMDoAWF4+o6hF3y+TVWH6o8eAUcoRuyT3+Nax1iWg4ZlL4MrliOKFDDzhZ3yOeQEdd9rm2nL8msPjkZafECnfA6j76S/8spbsPVwNXV/NrVNYCcQw0MifsiKDvGiKS8ifkgK7NR/VkRhiZCnjgEnYTD2q4qwqXQ3KlvbDAa5/vCWZIDLi4Xd1ZZucrkQXl2GxIIcxLbUQzp8LGoUScgt1MJidn8+h+NCVIwLUn4ZlDUnPakvhSQAaWHj4WX0Bazu05aGY0CNQoNKQz3sDjt4XCdC/W2ICbGDjz+2U+IVjsDIkfALGQReJ/19Mq4Mlt5iXDO0jz242PQW8QghkMJJYuLH4QlwLUNOBgRy8O8swUMgXkhE8AxICGCCh3FV0l9kPyLr/hsH0K6vnTm1OJTXiPpmA37aXERXZLAcYwdGYOzA+YjOWgRj8RG6zxtLj8JSV0wXNn+N9OhUDE8ZjYb0G7C99ij2VR+B2kD+NngQ8GPgLR0IG/xQGxVP116zCTFl+Yg/8RMmSYQwpIxDmVGBmmotKstJVCYBUlkcwsOaYdbkQqttxt7SFeCCh4TAwYiSpsBbL4O3RoZ+CEKdqBUV3CbUKHWoUQqhkAoQG+qEj1QLk64WVXk/o6ZwDXxDBsA/bAitAWLRn74HEz2Mq5feau+TvQBcMlmdFBq6nHAY9eB7Xbstpw6THkbieEsmSGe4/1PpDNQ6M+3GIdw8mXnyMK4uxMtn1IAwukjE52BuA534fqSgCdWNeiwlFgkbCmgH2Ii0UIwY/SCiZjphLNgPfe4uWgdkqjhBl4DHx5z4TNycPBf5MhF21hxBTn0umrWl4HIUEAmTIBGlwCqWoCglky6ZToO4kpOIK81DSkQsmkIyUNzIgUFvRXFpEIBABAUa4CWthVZZiCLlQRThILwEfkgOGQ1fWxCiLQGIgj9aoEONVIVasxLHSp0Q8IQI9TMjMsgKAcxoqT1El0jiD//wIfAPHcza3vsQTPQwrhhuWyEz8Qq5GEhnBRE+JExOQ+XXsOghNQ8kWiUMioYwJLbTPmf1zjJY7U4kRfnSSA+D0VmQ4mbS1k6WwWTD/pP1VADlFClRUa+li9hUEI+oEWmRGDH2/5DoY4OpYC8VQDZlNYxFB+kK5QtxZ/wgOPrNwVGBE7tqs1GuPgST5TB4vFCIBYkQCuJg8PLGiUGj6fJrbkBsyXGkVpdBGJuBWlkcKhtsaFLK0YQkcDixCAlSge8qh661Dger14ADLsKkCYj3zUSAWYEAowKpiEAtV4VavgpVSg2qlBJ4S6UID7QiUGGCxdSCupINqCvZCC+/eCp+fIJSmeNzL4eJHkaXR3raO7iI4LnWO7jaU1teGZM6LVSuN9noyAECmW/GQvKMrkImESBraBRdOqMVh/IasP9kA40AEQ8gMnOPLC+pEMNT4zBi1Cik+plhLSQCaDd1fibeVSg8gBQuH4Nj0tEam4UcoQv760+iXr8DBvNu8PlREAn6QcCLgCoghK4jI7Lgp2xATPkJZOjqwAtPQy0/DPXNQH1jCHEGAp+nRbC/Ek5LOWqNRXSJuTJEeqUgUtofMdYgxJiDoIMR1bwW1FhbkFdpAZcjRaC3BeEBVigkJuhUJXRx8nhQBPSnBdCk9Z3N++p9MNHDuGot65ciergS+TXfwUWKO60NpQCXD3nq2E77nN/3ltOUAykoHZpCDvYMRtdDhA2Z7UWW2WqnkZ99J+qpECKCaPOhKrqEfC7SE+IweMAIZAaZIWk4DkPhftiaa2AqOwpR2VEM53AxLjIJqpjROCYEDjQXoVG/ARyIIBDEQciPo5EgVWAIXdlkFlhLE6LL85FmrAMnMAl1vFC0aBWobVIAiIOA24IAXyXslnIUaw7RJef5IlqRilBhPFLskejviEAzNKjlqtGgVaGx1Q4xGWrqa0aonxVigRUaZS5dHK4APoHJ8CUCKCAZ3Gu89pDhhokexhXDa4v0XGwhc0evHveE5ms5yiNNHAyezG3xf7Uh7elrd7ujPDdOTKDFpwxGd0MMDWltT1ooTWvnlauw72Q9TYUp1SYaCSKLEB4YiMHJ92BopgsR5iJYig/CUl8KS1U+ZFX5GAVgrG8wVDEpOC4T4rCuGo2GfHA4YvD50bQImkSAWv2D6DpGBJhGjYiqYsS2NkEgDYeSFwK1IQD1LST1mwQBtwm+ikYYLVXIVe9GLnbDlx+CCFl/BAujEeTwgQPRaEIr6uwq1CjVqGxyQCayI8jHjGBfIoBsUDcep4vLFUARkETTX0QAsblf1y5M9DCuGD7v0mp6Tu3gulYjPaSOR3dypye11VnsOVYLldYMXy8R7aBhMHpi92Z6QgBd985JQ1WjDkfyiehpRG5ZC2qVBtQqy7CaFEwLxRiQcCOGDROgP7cCwoaTMFflwaFuhLe6ESReOlYgRmtMEgr9fHHcrkWpZgPxhoaACqBYCPgR0Hn7Ij99GPLTAb7VgvCaMoTU1ELq9IJGFIYWYwiaWklUNA0CThMUsiZonbU4odmOE+DAlx+MUEk8QsXxCHX6wQ4HGqBGnUWFqiYNyhsdkIvbBJCPGSKBDa1NJ+kiTRik84sIIJ/AVIikft39K2BcAkz0MK6Y9ujDpdX0uNNb12pNj7E4G06jFjyZD6TxFx69cTkQCy0yboJAhrkK+Mxan9GzIfVm0SEKukhk0mi20TQYGYZKIj9EwJOW+EN55Nl8+CmGIzN+Cob6qBBpLYOz+jgcejV8io9hOECXKTAcxSGhyBWYkaffCqOZAz4/HAJeJIS8KNiFUlTGJdNFfIACmuoQXFsFid4JBzcYLZZQtOhDAaSDz2mBRFAPDeqh1u1Bnm4PvPlBCBHGIFSSgAhXAOwuB5TQoMGkRo2lFWUNNiqAAhRmBHpbIRPboFeX0lVTuBoSeSitA/IOSILMJxpcLjut9mTYb4dx1QqZ7RfpyNwbIj26E8R9FpCnjweH2zkTzknKoKRGQ2skpo+M6ZTPYDA6E6lY4GmFJyKedH4RAXSsWIn8chVUWgs2H1ViM312NMIDkjEmxoF0UR18NYWwN5RCoqzFALJIHR2Xi4qIaBRLLMh35qDZuAs8bgAthBZyo8AVBKI5OJwuAokCBdfXwEvZCpFVAr3VHzprIHTWdPA4rRBy68HhK6ExHkSh8SCtAQoURCJIHIOBvDjiqgEVdFQA1ZvVqGiyQCyww19hQYDCAh+ZFSZ9PV2NFdvA5YloJ5jCP4mKIJHUv5t/A4zTYaKHcdUKmd2TkNHr529Rb55SUloJeKWP77TPaY/ykLlI3nLWRcK49qNAsWHedM3P6gerzUHngBEBdLy4GcXVatQ2G/FjM/AjiFgYhYTAcRgVpEUivx7e2lIINQ3oV1UO4lQ1k8yik0hRFqpAkaASRdbjsFmE4PMjIeCSSFAY7EIJaqPjiZ7yDEMNaKiHRG0BbF4wmlJgMpK58WYIuI2wOhuhdxWi3HwcAo4IAYJwBAgjkSSKQqorCnqY0GjVoKm5FSdadODyHPDzssBPboGflxVCWKBR5tFVTdJ50gAo/PtRIeTlG89qgXoATPQwrmIh8yVEejzzt669QmZDwT7AYaeDRYk/T2fQ3Gqik7EJs8bEdcpnMBjdiVDAQ0ZiIF3t1gwnS5vdIqikGVUNOpQo7ShRkqGh8XTFedswJlCDBH4dFUEBJh0CykowjBT9c4AKqRhlgU6UimtQbTGAw/WnqTARJxxcfggdhlqVQLq9/hBB3koVRFoHHKYo6AzR4Nid4HPUEHAbYHYpUW8tB0cPePMD4S8Ig58gHHGCJDhdLjTbtWhSa1ClbkUBx0zTYO0iSCGz0TlgSrKq99LPk8hDIG8TQF6+cUwEdQNM9DCuGP4lmhNe65EeMn+IIE8d12mfQdyXyWwkMlg0OvSPgzSD0VuRSwSejjCC1mBFfnkLcstVyCtrQUlNK8o0ApRpSIdWADhIR6xEh2H+GiQIm+BnqkaiQYtEQxV9vYnLQblEi0p/LcrExaixWMHjEW+fMIg4oYAggIogstoRmYxQNKshapXDYk4DV+cCx2WDgNMMk6MJLbZy8Dg54IEPX0EI/AXhiBWEIZ0fDYPLgmaTFs0mDfKbdLDzLPCVW+kiaTCZ2A6TvoEuZdUe+nmkHohEgWQ+MZD7REMo9ummb7/vwEQP46pFei7Np+farOmxa5S024QgT+scbx4iHjfsd4+cmDmK1fIw+iYKmRDD00LpIpgtdhRWqakAIvVuBZUqlJkUKKshoiUSQCYCuDoM8lYjVaZCmLMWKQYVUgy19Ku2uFQAABo/SURBVPVGLgcV4haUKSpQIZOi1uIClxcEPi8EElcIIAyGRSKFMlLqfjtynHI4IFdrINIIwTFGgad1gm82QsBRwuBoQqM1DzzOAQg5EvgJQqkQSuKHQM5PgN5hQrNGi2aNDpXQwsUnNUA2+HQQQe56IFTtpp8nEHlT8dMugiReYaww+irDvk3GFcPjXnp661SfHlLgeK24DBOXWYI4KhV8ReeMgziY10C7XLzlQoxMdx/wGYy+jljE75AOI75glfVaFFW3oqhSjaJqNaobOdikVmCTmqSdB8GbY0S8sAlpXhrECJrR39SIFKOaTLODhcNBtViJKnERqrzkqLLxYeH6UREkQgi4/CA4+RJoA/xIYMmDwGyGTK0ATxcLjpELkc4AkbUJGnsLqs2F4HP3Q8gRwIcfDF9BMBL5Icjkx8Fgt6BFo4Nao0Mt9LAJjPCRukWQQmqlqTGbRePxBiJwuHxIFRGQe0fRS7JIcTQZ5cO4PJjoYVw9n55LKGRud2SG0wGXxQgOGUJ6DaDP3dmpUR7Cur0V9HLKMOJL0jmdYQxGbzjuxEf40DWjrbuRtMgXExFUpfasbK0U2Rb3a3hwIIynRjS/GUmyVsTYmpFgUgFqI8jRq1nQiEpxCarEAlTKxGgWKMDjBUGIQIgQCIcoEDaxGK2hYsDz/4g/BKZgiLVmcA0AX2+DRN+MVlM9ai014HNOgM+xwYcfBG9BEML5gUjl94PLxodKo6ciqAx66Dg6yGVEANno8pZaIeDbYWitoKsdLk/YJoDC6aWMCqEAJoQuEiZ6GN3i08MViMDhC+GyW2ldD528fi2MnWiqAnh8yPqP7JTPqGvWU18TEviaNqJziqQZjN4KaZE/NRpEosgkalpaq0FZ2yqt9cJuVQB2twkhKceCKH4zInkqRIvU6GdXY6hOAyh1sHKUqBNVoVbEp6tGIoVKFAguLxBiVyD4HH84RL6wSUR0/UEAeNZ4iHQWcA0uCA0mNBpaIDHVQ+Q8Dh5HDSlPSIujyQrlB0DGj4dBb0Or3oBWGFAJPexCPS2IJiJILiF+QTZyJIJeXUZXO2RkBkmFSb1CaZ2QxCuEXvLZ8NQzYKKH0S2OzO11PQ5dC01xCa6BQevtDszS+EyPueLVZvNBdxHmoH5BCPHv+UKQwejJkLS5v7eErmGnzK3TG60oqyMiSIuy2laU1QZgS5MeTrP7Hzcxx4pwnhoRPBXCzSrECdQYyW0FFzpYOE2oJwKoTQjVicRQSYLA4QZA6vADn+sPu9gfDqEARn8BCQQRcwsAQQCSwTdZwTc4IDCYIDa2QmxshFSXA6FTBQVfCi+eP/z4fojmB0LqTITR6oBGbYASBhRDB5dYDy8igCT2tksbeLDBqKmk61R4Ai9IFe1iiAihEIhlQX16jhgTPYxuKWSmr5PIqei5FoqZXS6np55Hnt45XVvk+9t6mLh7AJOHRXXKZzAYDEAuFWJAQiBd7djsDtQ06VHZoENVg5a2zBc16LBTZSBGz+DDgRBeK0J5rQgxui9T+Br4cZWwQ4lmIQ8NQj4aRHzUC4VokATCKAyE2OkLocsHEPjBLvKCXSKEXQKYAyTQgYywcFtS8E028Ew2iIwGCE2tEJuUEBuOw9emhTffFwq+H8J5/pA6YmA386FVG9EKI6pggF2kg0hqprPDSG0QcY0WC51w2HTQtRTSdSo8gQISeRCkXiEQSQMhlpEVBIFIcc3UV14uTPQwrpo5ITkwkBN3e2HzxXdw9XyvHnNVPhzaZnBFUkgTBnfKZxB/khaNmbbuDk9l09QZjK6E1M+1myeeCpkoT8RQVZsYIqLosFKPRpWR2kqIYKNiiAoifiuiea0YwdPAh1sEE7cYjUIigvhQCnloFEnRLA6AmYoXb/C5fnAIyZLBLhHQZfEjvkREjCW6N8DpotEhockAkUkLkakBMosKvjYz/B0ChHG9IbWGQmiUw8bjQQsjamCEgRQYiXWQSGy0U0wmcl8K+C44bFro1WSVdPwSOHwIRH6QeAVD6hUMscQfQqkfRBJ/CERevaJuiIkexlUbQ9Ge4uJd5FiGa8mrx5Dn9tWQJo0Aly/slM/Y0pbaGp8ZQY3bGAxGz5gonxDhQ9ep2OxONKoMqFMaaC0eGaxaptRjl1KPllYzFUMBPC2CeFoEcnUI5WkxgNzmloDPy4NS4BZCShIdEsrQJPGHnu8LkVMBgUsBDt8HNrEPnDwB7DIRXUYaGTrFxsLlAs9ihcBsgtCshdjSAm+rCT52FwJsIvibvSHQSuHg8WHkWFELI0w8A5wiPfhiMyQiO6QiB6QiOyRCBziww2ZuokurPHHaN8EFV6CASOIHiTwQUnkg7SQTSvwgEvuCd43UDzHRw7gqU5bbuRyvnp4uelxOBwyF++l1ecqoTvkM4ka772Q9vT55KEttMRg9HTIAOCLIi67TMVnsqG8m0+X1aGgx0KjQSZURjS1GKFsNEDnNCKQCyC2KUrh6jOUp4ccth0NohUrAQwtZfB6UIgVUYn+YuD7gubzB53jDxVfALlTAyRfAIRbRZYYPtACaTt0QEiWymiGwGCG2uiCziaCw8eFt94VUy4fIwQXXCWg4NtRzjLALDYDIAL7ITEWQWOjwXHI4TjhtrTCRpS2D6rSf2QU+uHw59RoSy/wglfnTCfRCsTc1XSSLdJ51N0z0MK6YU9NZl+bK7C4G7uk1PcSM0GHQ0DZ7SUx6p3zGrqM19D/H6BAvxEd0DK8zGIxrC4mIj7hwb7pOh/xj2KIxUSFERBC5rFYZcFhlRJPKCL1SBx+uAf5cPfy4OkRyDcjgaeHPrYWEb4BJ5HSLIiqI5FCLfGDkKOCAAjyOFzhcLzgECthEXnDx+LCLJXSZ4A/iUHQGLhcEVjPEVjOkNgvkNgdkVg7EZkDkcEHgcMLpMILL0VBBxBGaIBTaTxFF7pQZiRK57K2wkmUgdoxn+SgIwOHLwRd4QShWQCz1hVTuD5HEGy6nnfoSdTZM9DCuqui5nPlbPT3SY8jfRy9l/YaBw+ucP5kth/4oYO7thYQMRl8/Xgb5SulKJyPFToP846jWWdCsMdE0Gbkks/iKWk205k+naYVDqYY3Rw8fjhFRXCO8ua3wpqLIBI7QDLPQCTURRWIvqIU+MHDlsEMOJ+TgcqQATw67UA6bSA4XlwebSEIXORI3nmfbBTYrxHYbJHYHxDYnRGYnhA4HBE4reDCCz9FBwDVAxDNAJjBDLHBARJcTfB4RRjbAroadLBNAfCLbI0ZWi5amzjobJnoYVww5SZO6HiJ4iEvqxdJe09OTIz2nprZkyZ2T2iL1AMRen2hHUs/DYDD6drlAgI+Ervbp8GeLFrXqzFQMqbQWep0IpSqd+7peq4NDqwKnXg25S49IrhkKrhJyTiWEAhMgtMLFt8IicKJFJEerwAsGrgI2jhfsHBlcHAlcXClcPCktsrYJpXBxubAJhHRdzBGb43JBaLdDaHdAaCHCyA6Bi0yiN0MAE4QcM8RcI6RcM2Q8C5yurvlnj4kexlXrfLA77DRFc8k1PUZ9H09tuWcDEUM1Xy9xp3wGg8HoXdGidv+h80HMGY1mO9RtoqhVa6HXW/UWOtBVrzfCpm+FS62BxKyFl1ULOacRXlwjBHwzOEILXHwbnAIbLAIBdEIZjRpZIIGNI4ODK6XLyZPBSQQSXwy7UExrjVwcDn0NWReDAesg6Quix+l04v3338fy5cuh0+kwdOhQvPDCC4iMbJv4xrgmEAq4MFkAq93RqyI9nZ3aIgelHUdr6PVxg1iUh8FgXN0ovEwioOtsBdenQ1rwySgPIoj+WG6B5NBbINQbwNFrIDFp4TLrwbEYwLfVgu80Qsg3gyuwgCuwwi5wwioUwCkUweQUwsIRw8aRwsERwc6RwMGTwcEnYknsFkoC4mZ9aT5v16zo+fDDD7F06VL8+9//RkhICN544w3cc889WLNmDYTC7q/0ZlwcgrYOLpvtMiI9PVT0dEVqq6Jei+pGPe0EYcNFGQxGd48UkkuFdIX94dt4QUhZg8Fko12oxO2aXAb6SBAVoqDHUafFCKfZQD3ZHGYDhIFR4Hv5wuqwwWA10rXwf9zeL3qsViu++OILPPHEE5gwYQK97+2338bYsWOxceNGXH/99d25eYxLQNDmK3Mp6a32SI/LaoLLYQOnh1mjd0Vqa0e2O8ozJDmY/jfGYDAY1+IoIm+5iK7T4XB59FhPj/enjRsS8gQQSrzhK/GGoIuO/91qr1hQUACDwYCRI/8Y3qhQKJCSkoJDhw5156YxLhEh370rXUp6iysmzqNtIyx6oCtzZ6e2SCh5Z467nocVMDMYDEYvj/Q0NDTQy9DQjmH9oKAgz2OXQlNTExwOB7Kysq7aNjIuDtJKSUKcDx0SQXQJbsJ2jZLkkcDbNLfT2sEvF8+2bWwC5+2VV/39SVSMTIAmsu/5HGmb/GMwGIy+R319PXi8znei79azjMlkopen1+6IRCJoNJpLfj/yOpIyY3Q9/t6X13XE976ExHEX09nbRup4gumcHQaDwejb8Pn8Lqnj7VbRIxa7T5REqLRfJ1gsFkgkl968dvjw4au6fQwGg8FgMHoP3VrT057WImmpUyG3g4ODu2mrGAwGg8Fg9Ea6VfT0798fcrkcBw4c8Nyn1WqRl5dH/XoYDAaDwWAwekV6i+Tvbr/9drz55pvw8/NDeHg49ekhfj1Tp07tzk1jMBgMBoPRy+j2dplHH30Udrsdf//732E2m2mE5/PPP4fgIq2rGQwGg8FgMC4Gjov44DMYDAaDwWD0crq1pofBYDAYDAajq2Cih8FgMBgMRp+AiR4Gg8FgMBh9AiZ6GAwGg8Fg9AmY6GEwGAwGg9EnYKKHwWAwGAxGn6DbfXq6iz/96U9Qq9Xgct2674svvoC/v393bxaDQb2rMjIysHjx4u7eFAaDmsdu27aNHiv//Oc/Y+bMmd29SYw+zhtvvIEdO3aAOO7ccsst9Hx+sfRJ0UO+qNraWmzevBkcDqe7N4fB8LB69Wrs37+fih4Go7sh++LJkyexZs0aOiKICJ7Jkyd3yTRsBuNsbN++HYWFhVi1ahUdTj5v3jyMHj0a8fHxuBj6ZHqrrKwMDocDd9xxB2644QZs3LixuzeJwUBjYyN++OEHLFiwoLs3hcGgjBgxAkuWLKFRHjIImogdHo/X3ZvF6MOEhobir3/9K90PpVIpoqKi6LHzYumTkR7yHwv5Y37ppZdoiuu2225DcnIyIiMju3vTGH2YF198Ec8++yxNJTAYPQU+n4/XXnsN33//PR544AEmehjdSlJSkuf6sWPHaCRywIABF/36Xi161q5di//85z8d7psxYwaeeeYZDBo0yKMaJ02aRMO4TPQwumufjImJocI7LS2NiR5GjzpWEsglqedZtGgR/YdxyJAh3bSljL7C2gvskzk5OXjkkUdofY9cLr/o9+2Ts7eOHDkCm81G/3gJr7zyClJTU2mqi8HoDu666y40NzfTNEL7JSlonj9/fndvGqMPU15eDqvV6vnv+vXXX6f/HC5cuLC7N43Rh9mzZw+eeuopKnhGjhx5Sa/tkzU9er0e//3vf+kfs0qlooVRo0aN6u7NYvRhvvzyS1osSorzSE3PnXfeyQQPo9upqqrCP//5T9jtdnrcJCebgQMHdvdmMfr4Pvm3v/0NH3300SULnl6f3joX48ePR3Z2NubOnQun04nHH38cwcHB3b1ZDAaD0SOPlbNnz6a1PLfffjtSUlK6e7MYfZglS5bQgMXf//53z31PPPEExo4d27vSW5988gl2796Nb7/91nMfESzvv/8+li9fDp1Oh6FDh+KFF15gtTmMLoHtk4yeCNsvGT2NT3rQPnlNpLdI18D//ve/M+7/8MMPsXTpUrz88su01Zd8iffccw9VgQxGZ8L2SUZPhO2XjJ7G9z1sn+zRoof03pMWSeIISrpbToV8McRFmRR7TpgwAf3798fbb7+NhoYG5rvD6DTYPsnoibD9ktHTaOyh+2SPFj25ubkQCATUpfZ0h9qCggIYDIYOhUwKhYLmmw8dOtQNW8voC7B9ktETYfslo6eR20P3yR5dyEz8c8g6G0QRtvvsnEpQUJDnMQbjasP2SUZPhO2XjJ7GpB66T/boSM/5MJlM9PL0GTAikYjO42Awuhq2TzJ6Imy/ZPQ0TN24T16zokcsFtPL04ueyBcmkUi6aasYfRm2TzJ6Imy/ZPQ0xN24T16zoqc9LEaG4J0Kuc08dxjdAdsnGT0Rtl8yehqh3bhPXrOih1R7k3kbBw4c6DBINC8vj/b7MxhdDdsnGT0Rtl8yehr9u3Gf7NGFzOeD5AKJOyhph/Pz80N4eDidwxESEoKpU6d29+Yx+iBsn2T0RNh+yehpCLtxn7xmRQ+B9PiTmTDEjtpsNlOF+Pnnn9M2OQajO2D7JKMnwvZLRk/j0W7aJ6+ZMRQMBoPBYDAYfbKmh8FgMBgMBuNSYKKHwWAwGAxGn4CJHgaDwWAwGH0CJnoYDAaDwWD0CZjoYTAYDAaD0SdgoofBYDAYDEafgIkeBoPBYDAYfQImehgMBoPBYPQJmOhhMBg9jt27d+O7777r7s1gMBi9DCZ6GIw+zF133YVhw4bBarWe8zmzZs3CbbfddsH3euCBB7B8+fIr3ian04kXX3wRL7/8MoqKis54jFjVk/k8AwYMwOzZs7F69eqzvs8rr7xCLe47m6SkJLz33nv0ellZGSZNmkSHJzIYjJ4HEz0MRh/mpptugkajwc6dO8/6eG5uLhUe8+fPP+/7rFy5Eo2NjfT9rpRNmzZBpVJhyJAh+PLLLzs89s477+Dtt9/GvHnz8Mknn2DUqFF48sknsXbt2jPeh/xM48ePR1cSFxeHrKwsKrgYDEbPg4keBqMPM2XKFHh7e58zWvLLL79ALpdj2rRp53wPMiyQTEsmkR4u98oPKV999RWNLt19991UzLS0tND7TSYTvvnmGyxatAj33XcfRo4ciaeffppGqr799tsO71FZWYm6ujr6nK6GbNtvv/1GBSODwehZMNHDYPRhRCIRrr/+emzfvh16vb7DYzabjZ68r7vuOkgkknO+x4oVK2CxWDBx4kTPfUSMLF68GD/++CMmT55MU1ELFixAeXk5tm3bRkVNRkYGjSDl5+d7Xnf8+HFkZ2fT506YMAEBAQFYunQpfUwoFGLZsmVUDJ0KmcpMPv9UduzYgczMTCrYampqaApq/fr1ePDBBzFw4EAaIfrwww/pz/zss89i8ODB9L433ngDp85g1ul0eO211+jPkJ6eTr+rn3/++bzfaWBgIEaMGEEjUQwGo2fBRA+D0cchKSkiGjZs2HBGeoikmS6U2iJRIiJQiCg5laNHj9JiZCKAiHAoLS2lURBy/f7778dbb72F+vp6PPHEE57XfP3111RcpKSkgMfj4eabb6ZCh9Qckdv9+/enooIIk+bmZnz66afYu3cvFi5ceIboOT21Rep7+vXrh48++ohGgEiqjKTJxGIx3n//fVontGTJEiqO2iNY5H3XrFmDe+65h4okIo6ee+45fPzxx+f9TqZPn46tW7fCYDBc4NtnMBhdiovBYPR55syZ47rjjjs63Pfwww+7Zs2add7X6XQ6V3JysuvLL7/scP9TTz3l6tevn6ukpMRz3wsvvEDv27t3r+e+zz//nN6n0Whc9fX1rpSUFNdPP/3keVypVLpSU1M73EdYs2YNfR1Z9913n8tkMnkeI9fT09NdxcXF9HZ1dTV93mOPPdbhfcl9Cxcu9NzndDpdmZmZrldeeYXe/v777+lzsrOzO3z2s88+S99frVbT2+Q57777bofn5Ofn0/u3b99+3u+PwWB0LSzSw2AwaLTnwIEDtBiZ0NraStNQJBJyPkikxuFwICIi4ozHSK1QfHy85zZJVRFIWqsdHx8fekm6nUJCQmgdzKmRJfKakydPnhFtIukyEkV6/vnnaTqMRGLa01L79++nr0tISOjwmkGDBp2xLeR92uFwOHSbSUqLcPDgQYSHh3d4HYF0jJHI2LFjx875vZDXEUhqjcFg9ByY6GEwGLTGhs/nY926dfQ2qeUhIoCc4M9Hu0CQSqVnPEbqac7G2Z57qURFRWHo0KG4/fbbabrp0KFDOHz4sCe1NXbs2IvanvNtC+lqI6m002kXTOdrS2+vgTq9TorBYHQvTPQwGAwacSHFuqR+hbBq1Sra2dUeiTkXvr6+9LIrfGlIfdGvv/7q6eZqh9T/EJqamq5qqzqJ+iiVyjPub7+v/Wc/G+3fx/mew2Awuh4mehgMhifFRdJLJK1DUjcXSm0RgoODaYFxQ0NDp28fKSx+6qmnzuie2rNnD70kHVqkWJqIH9I9daWQSFJtbS0tyD69cJt0jJ2aGjud9u8jLCzsireDwWBcPfhX8b0YDMY1DGnZJidpUidDanQuxuOGpIdIa/iRI0dw5513dur2kW0jwuyDDz6gqTgS4SEpLdLBRQQaqeEhZoZErFyNFNqNN95I2+UfeughPProo/Q7IR1ZpEX/4YcfhkKhOOdryfdBUlzEYJHBYPQcmOhhMBgUYix4ww03UFFBTvKkpudiIMaFZAwDKe4lvj+dyUsvvYTIyEj89NNPNAoTGhpKt5V4Al1tF2YiWojp4X//+1/a3k7qc4jj8quvvnrBKBjZDtLGT9rhGQxGz4FDWri6eyMYDMa1C3FKJvVAZBzE3Llz0dchYozUQ5E0XHu9EYPB6Bmwmh4Gg3HFEZFHHnmEDgIl7et9nS+++IKaEzLBw2D0PJjoYTAYVwwZG0F8dq7GlPVrGVJITep+Xnjhhe7eFAaDcRZYeovBYDAYDEafgEV6GAwGg8Fg9AmY6GEwGAwGg9EnYKKHwWAwGAxGn4CJHgaDwWAwGH0CJnoYDAaDwWD0CZjoYTAYDAaD0SdgoofBYDAYDEafgIkeBoPBYDAYfQImehgMBoPBYKAv8P9nXGV9SJy9YgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Critical values for Nitrogen and the acentric factor\n", + "Pc = 3.394*10**6\n", + "Tc = 126.2\n", + "omega = 0.040\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# plot several isotherms\n", + "# use the same color for IG and vdW EOS\n", + "for T in range(100, 185, 10) : \n", + " V_max = constants.R*T/(100*1000)\n", + " V_min = constants.R*T/(1000*1000)*0.03\n", + " V = np.linspace(V_min,V_max,4000)\n", + "\n", + " ax.plot(V, PR_pressure(V,T,Pc,Tc,omega), '-',label=T)\n", + "\n", + "ax.plot(V, PR_pressure(V,Tc,Pc,Tc,omega), '-',label=Tc)\n", + "\n", + "ax.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "ax.set_xscale('log')\n", + "plt.ylim([-1,8*10**6])\n", + "plt.xlim([10**-5,0.01])\n", + "plt.xlabel('V (m^3/mol)')\n", + "plt.ylabel('P (Pa)')\n", + "plt.title('PV diagram for nitrogen')" + ] + }, + { + "cell_type": "markdown", + "id": "faf1a487", + "metadata": {}, + "source": [ + "Our second example makes a prettier plot using Seaborn..." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "f387f98f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "from scipy import constants\n", + "\n", + "Pc = 3.394e6\n", + "Tc = 126.2\n", + "omega = 0.040\n", + "\n", + "rows = []\n", + "\n", + "# Make a list of temperatures for the isotherms and add Tc\n", + "temps = list(range(100, 185, 10))\n", + "temps.append(Tc)\n", + "temps = sorted(temps)\n", + "\n", + "# Generate all isotherms including Tc\n", + "for T in temps:\n", + " V_max = constants.R*T/(100*1000)\n", + " V_min = constants.R*T/(1000*1000)*0.03\n", + " V = np.linspace(V_min, V_max, 4000)\n", + " P = PR_pressure(V, T, Pc, Tc, omega)/1e6\n", + " \n", + " rows.append(pd.DataFrame({\n", + " \"V\": V,\n", + " \"P\": P,\n", + " \"T\": T\n", + " }))\n", + "\n", + "df = pd.concat(rows, ignore_index=True)\n", + "\n", + "# Convert T to string for categorical hue (fixes legend)\n", + "df[\"T\"] = df[\"T\"].astype(str)\n", + "\n", + "sns.set_theme(style=\"ticks\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "sns.lineplot(\n", + " data=df,\n", + " x=\"V\", y=\"P\",\n", + " hue=\"T\",\n", + " palette=\"viridis\",\n", + " linewidth=1.2,\n", + " ax=ax\n", + ")\n", + "\n", + "ax.set_xscale(\"log\")\n", + "ax.set_ylim([0, 10])\n", + "ax.set_xlim([1e-5, 1e-2])\n", + "\n", + "ax.set_xlabel(\"V (m$^3$/mol)\")\n", + "ax.set_ylabel(\"P (MPa)\")\n", + "ax.set_title(\"PV diagram for nitrogen\")\n", + "\n", + "# Remove legend box\n", + "leg = ax.legend(title=\"Temperature (K)\", frameon=False)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "83c296bf", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 6/pdf/PengRobinson_Et_heat_capacity_fix.pdf b/module 6/pdf/PengRobinson_Et_heat_capacity_fix.pdf new file mode 100644 index 0000000..d69b51a Binary files /dev/null and b/module 6/pdf/PengRobinson_Et_heat_capacity_fix.pdf differ diff --git a/module 6/pdf/PengRobinson_Et_throttle_problem.pdf b/module 6/pdf/PengRobinson_Et_throttle_problem.pdf new file mode 100644 index 0000000..652386d Binary files /dev/null and b/module 6/pdf/PengRobinson_Et_throttle_problem.pdf differ diff --git a/module 6/pdf/PengRobinson_Me_throttle_example.pdf b/module 6/pdf/PengRobinson_Me_throttle_example.pdf new file mode 100644 index 0000000..b2583ad Binary files /dev/null and b/module 6/pdf/PengRobinson_Me_throttle_example.pdf differ diff --git a/module 6/pdf/Peng_Robinson_EOS.pdf b/module 6/pdf/Peng_Robinson_EOS.pdf new file mode 100644 index 0000000..100c94f Binary files /dev/null and b/module 6/pdf/Peng_Robinson_EOS.pdf differ diff --git a/module 7/.DS_Store b/module 7/.DS_Store new file mode 100644 index 0000000..ba2f07a Binary files /dev/null and b/module 7/.DS_Store differ diff --git a/module 7/CO2_phases.ipynb b/module 7/CO2_phases.ipynb new file mode 100644 index 0000000..95ecaf3 --- /dev/null +++ b/module 7/CO2_phases.ipynb @@ -0,0 +1,561 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7af16f2a", + "metadata": {}, + "source": [ + "# Phase diagram calculations for carbon dioxide" + ] + }, + { + "cell_type": "markdown", + "id": "32d5dd49", + "metadata": {}, + "source": [ + "Contruct a P-T phase diagram for carbon dioxide." + ] + }, + { + "cell_type": "markdown", + "id": "bb1887c3", + "metadata": {}, + "source": [ + "## Antoine equation\n", + "\n", + "The Antoine equation is an emprical equation of the form\n", + "\n", + "$$ \\log P^\\mathrm{sub}(T) = A - \\frac{B}{T + C} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "83c296bf", + "metadata": {}, + "outputs": [], + "source": [ + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*101325" + ] + }, + { + "cell_type": "markdown", + "id": "ed693003", + "metadata": {}, + "source": [ + "## Clausius-Clapeyron equation\n", + "\n", + "Given $\\Delta^\\mathrm{sat}\\underline{H}$, $T_1$, $P_1$, and $T_2$, return $P_2$ by the equation\n", + "\n", + "$$ \\ln \\frac{P^\\mathrm{sat}(T_2)}{P^\\mathrm{sat}(T_1)} = \\frac{-\\Delta^\\mathrm{sat}\\underline{H}}{R} \\left ( \\frac{1}{T_2} - \\frac{1}{T_1} \\right ) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "4a95c76a", + "metadata": {}, + "outputs": [], + "source": [ + "# Clausius-Clapeyron equation\n", + "# Pressures in Pa, Temperatues in K\n", + "# Enthalpy in J / mol\n", + "\n", + "import numpy as np\n", + "from scipy import constants\n", + "R = constants.R\n", + "\n", + "def P_CC(delta_sat_H, T1, P1, T2):\n", + " return P1*np.exp(-delta_sat_H/R*(1/T2-1/T1))" + ] + }, + { + "cell_type": "markdown", + "id": "93580680", + "metadata": {}, + "source": [ + "## $P-T$ plot for CO2" + ] + }, + { + "cell_type": "markdown", + "id": "87fec321", + "metadata": {}, + "source": [ + "### Data for CO2 -- sublimation, VLE, critical point, and triple point\n", + "\n", + "NIST Webbook data is included below:\n", + "\n", + "https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=4#Thermo-Phase\n", + "\n", + "Full vapor-liquid properties can also be calculated in the NIST Webbook:\n", + "\n", + "https://webbook.nist.gov/cgi/fluid.cgi?TLow=217&THigh=304&TInc=&Digits=5&ID=C124389&Action=Load&Type=SatP&TUnit=K&PUnit=MPa&DUnit=mol%2Fm3&HUnit=kJ%2Fmol&WUnit=m%2Fs&VisUnit=uPa*s&STUnit=N%2Fm&RefState=DEF#Auxiliary\n", + "\n", + "We can find other thermodynamic data in:\n", + "\n", + "1. A. Jäger and R. Span, Equation of State for Solid Carbon Dioxide Based on the Gibbs Free Energy, J. Chem. Eng. Data 57, 590 (2012). https://doi.org/10.1021/je2011677\n", + "1. R. Span and W. Wagner, A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa, Journal of Physical and Chemical Reference Data 25, 1509 (1996). https://doi.org/10.1063/1.555991\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "2b4bdcfe", + "metadata": {}, + "outputs": [], + "source": [ + "# Data for CO2\n", + "# Molecular weight\n", + "MW = 44.0095 # g/mol\n", + "\n", + "# Critical parameters and acentricity\n", + "Pc = 73.8*101325 # Critical pressure in Pa\n", + "Tc = 304.18 # Critical temp in K\n", + "Vc = 0.0000919 # Critical volume in m^3/mol\n", + "omega = 0.225 # acentric factor\n", + "\n", + "# Triple point\n", + "T_triple = 216.58 # temp in K\n", + "P_triple = 5.185*101325 # pressure in Pa\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 154.26 \n", + "T_Antoine_max = 195.89\n", + "\n", + "A = 6.81228\n", + "B = 1301.679\n", + "C = -3.494\n", + "\n", + "# Enthalpy of sublimation \n", + "H_sub_1 = 26.1*1000 # J / mol, 198 to 216 K\n", + "H_sub_2 = 25.2*1000 # J / mol, 154 to 196 K\n", + "\n", + "# Enthalpy of vaporization\n", + "H_vap_1 = 16.7*1000 # J / mol, 273 to 304 K\n", + "H_vap_2 = 16.4*1000 # J / mol, 216 to 273 K\n", + "H_vap_3 = 16.7*1000 # J / mol, 267 to 303 K" + ] + }, + { + "cell_type": "markdown", + "id": "72d6aac4", + "metadata": {}, + "source": [ + "### Solid-liquid equilibrium\n", + "\n", + "Finding data for the solid-liquid equilibrium line is a little more challenging. Data for CO2 lists \n", + "\n", + "1562 kg/m3 solid at 1 atm (100 kPa) and −78.5 C \\\n", + "1101 kg/m3 liquid at saturation −37 C \\\n", + "1.977 kg/m3 gas at 1 atm (100 kPa) and 0 C\n", + "\n", + "Assuming that the solid and liquid specific (molar) volumes don't change much, we could estimate the fusion (melting) line with the Classius equation. But can we estimate the heat of fusion?\n", + "\n", + "J\\\"ager and Span (J. Chemical Eng. Data, 2006) cite the following value:\n", + "\n", + "$$\\Delta^\\mathrm{fus}\\underline{H} = 8875 \\text{ J/mol}$$\n", + "\n", + "By the Clapeyron equation, we can then find\n", + "\n", + "$$ \\left ( \\frac{\\partial P^\\mathrm{sat}}{\\partial T} \\right )_{\\underline{G}^I = \\underline{G}^{II}} = \\frac{\\Delta \\underline{H}}{T \\Delta \\underline{V} }$$\n", + "\n", + "As expected, this line should be quite steep. We can integrate the function to give\n", + "\n", + "$$ P^\\mathrm{sat}(T_2) = P^\\mathrm{sat}(T_1) + \\frac{\\Delta \\underline{H}}{\\Delta \\underline{V} } \\ln \\left ( \\frac{T_2}{T_1} \\right )$$" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cd670958", + "metadata": {}, + "outputs": [], + "source": [ + "# Integrated Clapeyron equation\n", + "def P_clapeyron(T1, P1, T2, delta_H, delta_V):\n", + " return P1 + delta_H/delta_V*np.log(T2/T1)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "1f0615ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.546529284164859e-05\n", + "92965723.30973995\n" + ] + } + ], + "source": [ + "# Calculate Delta V\n", + "delta_fus_V = 1/((1562-1101)/(MW/1000)) # Change in molar volume\n", + "\n", + "# Other data\n", + "delta_fus_H = 8875 # Heat of fusion, J/mol\n", + "\n", + "print(delta_fus_V)\n", + "print(delta_fus_H/delta_fus_V)" + ] + }, + { + "cell_type": "markdown", + "id": "3289cdae", + "metadata": {}, + "source": [ + "### Building the PT diagram plot" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "69d95f54", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'P-T diagram for carbon dioxide')" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# Make a blank plot\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Plot the triple point\n", + "plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n", + "\n", + "# Plot the critical point\n", + "plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max, 1)\n", + "ax.plot(T, P_antoine(A, B, C, T), label=r\"$P^\\mathrm{sub}$ (Antoine)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the sublimation curve\n", + "T = np.linspace(T_Antoine_max, T_triple, 300)\n", + "P = P_CC(H_sub_1,T_triple, P_triple, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{sub}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the vaporization curve\n", + "T = np.linspace(T_triple, Tc, 300)\n", + "P = P_CC(H_vap_1,T_triple, P_triple, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{vap}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use the integrated Clapeyron equation to plot the melting line\n", + "T = np.linspace(T_triple, T_triple+18, 100)\n", + "P = P_clapeyron(T_triple, P_triple, T, delta_fus_H, delta_fus_V)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{fus}$ (Clausius)\")\n", + "\n", + "# Label and axes\n", + "#plt.ylim([0,1e6])\n", + "#ax.set_yscale(\"log\")\n", + "ax.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "plt.xlabel('T (K)')\n", + "plt.ylabel('P (Pa)')\n", + "plt.title('P-T diagram for carbon dioxide')" + ] + }, + { + "cell_type": "markdown", + "id": "aa885660", + "metadata": {}, + "source": [ + "This seems reasonable. You can see that the vaporization curve calculated by the Clausius-Clapeyron equation is senstive to the heat of vaporization. The value we use overestimates the critical point slightly. A slightly lower value would bring the two into agreement.\n", + "\n", + "Let's rebuild the plot, but focus on the lower part of the phase diagram by plotting it on a log-linear scale." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "0abc0fe5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'P-T diagram for carbon dioxide')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# Make a blank plot\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Plot the triple point\n", + "plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n", + "\n", + "# Plot the critical point\n", + "plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max, 1)\n", + "ax.plot(T, P_antoine(A, B, C, T), label=r\"$P^\\mathrm{sub}$ (Antoine)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the sublimation curve\n", + "T = np.linspace(T_Antoine_max, T_triple, 300)\n", + "P = P_CC(H_sub_1,T_triple, P_triple, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{sub}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the vaporization curve\n", + "T = np.linspace(T_triple, Tc, 300)\n", + "P = P_CC(H_vap_1,T_triple, P_triple, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{vap}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use the integrated Clapeyron equation to plot the melting line\n", + "T = np.linspace(T_triple, T_triple+18, 100)\n", + "P = P_clapeyron(T_triple, P_triple, T, delta_fus_H, delta_fus_V)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{fus}$ (Clausius)\")\n", + "\n", + "# Label and axes\n", + "ax.set_yscale(\"log\")\n", + "#plt.ylim([0,4e6])\n", + "#plt.xlim([T_Antoine_min,240])\n", + "ax.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "plt.xlabel('T (K)')\n", + "plt.ylabel('P (Pa)')\n", + "plt.title('P-T diagram for carbon dioxide')" + ] + }, + { + "cell_type": "markdown", + "id": "b26ddb75", + "metadata": {}, + "source": [ + "## Answer for part C of homework problem\n", + "\n", + "In our exerpience with carbon dioxide, it is often in its gaseous state and sometimes in its solid form. The reason is clear: at atmospheric pressure, we are well below the triple point, the lowest temperature where we would observe a liquid carbon dioxide phase. \n", + "\n", + "When the gas phase is cooled (for instance, by a Joule-Thompson expansion) we expect to form the solid phase. Likewise, when handling dry ice, we observe that it sublimates directly to the gas phase without melting into a liquid first." + ] + }, + { + "cell_type": "markdown", + "id": "5ce26d98", + "metadata": {}, + "source": [ + "## Answer for part B\n", + "\n", + "Part B asks us what the state of a full gas cylinder for a home carbonation system is at room temperature (298 K) given that the cylinder volume is 0.64 L and initially contains 410 g of\n", + "carbon dioxide.\n", + "\n", + "In this case, we have the temperature and molar volume:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "f5a1a461", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Molar volume: 6.87e-05 m^3/mol\n" + ] + } + ], + "source": [ + "T = 298\n", + "V_molar = 0.64/1000/(410/MW)\n", + "\n", + "print(f\"Molar volume: {V_molar:.2e} m^3/mol\")" + ] + }, + { + "cell_type": "markdown", + "id": "a3d34536", + "metadata": {}, + "source": [ + "From the temperature, we know that we are below the critical temperature, and the molar volume is much less than critical volume. It's reasonable to assume that the carbon dioxide is in a liquid phase at this temperature and molar volume. Looking at the PV diagram we calculated in problem 1, this is close to the saturated liquid. \n", + "\n", + "The maximum pressure on the cylinder is 250 bar, which is 25 MPa, but this is likely the limit of the cylinder pressure limit. The CO2 would be supercritical in this case.\n", + "\n", + "We can calculate the pressure using the Peng-Robinson equation of state." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c3e0db15", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the molar volume given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_volume(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " # Convert real values of Z to molar volume\n", + " V = real_roots*R*T/P\n", + "\n", + " return V\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "5e07a484", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The pressure is: 6.54e+06 Pa\n" + ] + } + ], + "source": [ + "print(f\"The pressure is: {PR_pressure(V_molar,298,Pc,Tc,omega):.2e} Pa\")" + ] + }, + { + "cell_type": "markdown", + "id": "bc8959a7", + "metadata": {}, + "source": [ + "The calculated pressure is very close to the vaporization curve.\n", + "\n", + "The pressure from the Clausius-Clapeyron equation at this temperature is a little higher:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "eecd9901", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P^vap(298K) = 6.62e+06 Pa\n" + ] + } + ], + "source": [ + "print(f\"P^vap(298K) = {P_CC(H_vap_1,T_triple, P_triple, 298):.2e} Pa\")" + ] + }, + { + "cell_type": "markdown", + "id": "6eba2f5f", + "metadata": {}, + "source": [ + "But we noted that the Clausius-Clapeyron equation might overestimate the vapor pressure curve. A more accurate calculation is necessary." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/N2_phases.ipynb b/module 7/N2_phases.ipynb new file mode 100644 index 0000000..0f1f632 --- /dev/null +++ b/module 7/N2_phases.ipynb @@ -0,0 +1,331 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7af16f2a", + "metadata": {}, + "source": [ + "# Phase diagram calculations for nitrogen" + ] + }, + { + "cell_type": "markdown", + "id": "32d5dd49", + "metadata": {}, + "source": [ + "In this example, we will construct a PT phase diagram for nitrogen using empirical relations like the Antoine equation and approximations such as the Clausius-Clapeyron equation." + ] + }, + { + "cell_type": "markdown", + "id": "bb1887c3", + "metadata": {}, + "source": [ + "## Antoine equation\n", + "\n", + "The Antoine equation is an emprical equation of the form\n", + "\n", + "$$ \\log P^\\mathrm{sub}(T) = A - \\frac{B}{T + C} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "83c296bf", + "metadata": {}, + "outputs": [], + "source": [ + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*100000" + ] + }, + { + "cell_type": "markdown", + "id": "ed693003", + "metadata": {}, + "source": [ + "## Clausius-Clapeyron equation\n", + "\n", + "Given $\\Delta^\\mathrm{sat}\\underline{H}$, $T_1$, $P_1$, and $T_2$, return $P_2$ by the equation\n", + "\n", + "$$ \\ln \\frac{P^\\mathrm{sat}(T_2)}{P^\\mathrm{sat}(T_1)} = \\frac{-\\Delta^\\mathrm{sat}\\underline{H}}{R} \\left ( \\frac{1}{T_2} - \\frac{1}{T_1} \\right ) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4a95c76a", + "metadata": {}, + "outputs": [], + "source": [ + "# Clausius-Clapeyron equation\n", + "# Pressures in Pa, Temperatues in K\n", + "# Enthalpy in J / mol\n", + "\n", + "import numpy as np\n", + "from scipy import constants\n", + "R = constants.R\n", + "\n", + "def P_CC(delta_sat_H, T1, P1, T2):\n", + " return P1*np.exp(-delta_sat_H/R*(1/T2-1/T1))" + ] + }, + { + "cell_type": "markdown", + "id": "93580680", + "metadata": {}, + "source": [ + "## $P-T$ plot for nitrogen" + ] + }, + { + "cell_type": "markdown", + "id": "87fec321", + "metadata": {}, + "source": [ + "### Data for nitrogen -- sublimation, VLE, critical point, and triple point\n", + "\n", + "NIST Webbook data is included below:\n", + "\n", + "https://webbook.nist.gov/cgi/cbook.cgi?ID=C7727379&Units=SI&Mask=4#Thermo-Phase\n", + "\n", + "We can find other thermodynamic data in:\n", + "\n", + "The solid phase of nitrogen, including estimates of the melting (fusion) line are available on wikipedia with references:\n", + "\n", + "https://en.wikipedia.org/wiki/Solid_nitrogen\n", + "\n", + "Streng (Miscibility and Compatibility of Some Liquid and Solidified Gases at Low Temperature, J. Chem. Eng. Data, 1971, 16, 357) gives the melting temperature at 1 atm as $ T^\\text{fus} = 63.3 $ K.\n", + "\n", + "The enthalpy of sublimation is measured by NIST and reported in:\n", + "\n", + "H. Shakeel, H. Wei, and J. Pomeroy, Measurements of enthalpy of sublimation of Ne, N2, O2, Ar, CO2, Kr, Xe, and H2O using a double paddle oscillator, The Journal of Chemical Thermodynamics 118, 127 (2018).\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2b4bdcfe", + "metadata": {}, + "outputs": [], + "source": [ + "# Data for nitrogen\n", + "# Molecular weight\n", + "MW = 28.0134 # g/mol\n", + "\n", + "# Critical parameters and acentricity\n", + "Pc = 33.978*100000 # Critical pressure in Pa\n", + "Tc = 126.19 # Critical temp in K\n", + "Vc = 1/(11.18*1000) # Critical volume in m^3/mol (original is 11.18 mol/l)\n", + "omega = 0.040 # acentric factor\n", + "\n", + "# Triple point\n", + "T_triple = 63.14 # temp in K\n", + "P_triple = 0.1252*100000 # pressure in Pa\n", + "\n", + "# Normal melting point\n", + "T_melt = 63.3 # in K\n", + "P_melt = 101325 # in Pa\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 63.14\n", + "T_Antoine_max = 126\n", + "\n", + "A = 3.7362\n", + "B = 264.651\n", + "C = -6.788\n", + "\n", + "# Enthalpy of sublimation is given by \n", + "H_sub_1 = 7.34*1000 # J / mol, 23 to 27.5 K\n", + "\n", + "# Enthalpy of vaporization\n", + "H_vap_1 = 6.1*1000 # J / mol, data from 63. to 126. K. (NIST)\n", + "H_vap_2 = 5.57*1000 # J / mol (data wikipedia)\n" + ] + }, + { + "cell_type": "markdown", + "id": "72d6aac4", + "metadata": {}, + "source": [ + "### Solid-liquid equilibrium\n", + "\n", + "Data for N2 lists the heat of fusion as\n", + "\n", + "$$\\Delta^\\mathrm{fus}\\underline{H} = 720 \\text{ J/mol}$$\n", + "\n", + "By the Clapeyron equation, we can then find\n", + "\n", + "$$ \\left ( \\frac{\\partial P^\\mathrm{sat}}{\\partial T} \\right )_{\\underline{G}^I = \\underline{G}^{II}} = \\frac{\\Delta \\underline{H}}{T \\Delta \\underline{V} }$$\n", + "\n", + "As expected, this line should be quite steep. We can integrate the function to give\n", + "\n", + "$$ P^\\mathrm{sat}(T_2) = P^\\mathrm{sat}(T_1) + \\frac{\\Delta \\underline{H}}{\\Delta \\underline{V} } \\ln \\left ( \\frac{T_2}{T_1} \\right )$$\n", + "\n", + "In the case for nitrogen, we have data for the triple point and normal melting point. Therefore, we can estimate the entire melting (fusion) line.\n", + "\n", + "Rearranging,\n", + "\n", + "$$ \\Delta \\underline{V} = \\frac{\\Delta \\underline{H} \\ln (T_2/T_1)}{P^\\mathrm{sat}(T_2) - P^\\mathrm{sat}(T_1)}$$\n", + "\n", + "Using the triple and normal meltint point temperature and pressures, we can find the change in molar volume and use the Clapeyron equation to plot the melting line." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cd670958", + "metadata": {}, + "outputs": [], + "source": [ + "# Integrated Clapeyron equation\n", + "def P_clapeyron(T1, P1, T2, delta_H, delta_V):\n", + " return P1 + delta_H/delta_V*np.log(T2/T1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "1f0615ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Calculated molar volume: 2.05e-05 m^3/mol\n" + ] + } + ], + "source": [ + "# Data for nitrogen\n", + "\n", + "# Other data\n", + "delta_fus_H = 0.72*1000 # Heat of fusion, J/mol (Wikipedia, 0.72 kJ/mol)\n", + "\n", + "# Calculate Delta V\n", + "delta_fus_V = delta_fus_H*np.log(T_melt/T_triple)/(P_melt-P_triple)\n", + "\n", + "print(f\"Calculated molar volume: {delta_fus_V:.2e} m^3/mol\")\n", + "#print(delta_fus_H/delta_fus_V)" + ] + }, + { + "cell_type": "markdown", + "id": "3289cdae", + "metadata": {}, + "source": [ + "### Building the PT diagram plot" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "69d95f54", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'P-T diagram for nitrogen')" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# Make a blank plot\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n", + "ax.plot(T, P_antoine(A, B, C, T), label=r\"$P^\\mathrm{vap}$ (Antoine)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the sublimation curve\n", + "T = np.linspace(24, T_triple, 300)\n", + "P = P_CC(H_sub_1,T_triple, P_triple, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{sub}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use Clausius-Clapeyron to plot the vaporization curve \n", + "# starting from the critical point down\n", + "T = np.linspace(Tc, T_Antoine_min, 300)\n", + "P = P_CC(H_vap_1,Tc, Pc, T)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{vap}$ (Clausius-Clapeyron)\")\n", + "\n", + "# Use the integrated Clapeyron equation to plot the melting line\n", + "T = np.linspace(T_triple, T_triple+18, 100)\n", + "P = P_clapeyron(T_triple, P_triple, T, delta_fus_H, delta_fus_V)\n", + "ax.plot(T, P, label=r\"$P^\\mathrm{fus}$ (Clausius)\")\n", + "\n", + "# Plot the triple point\n", + "plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n", + "\n", + "# Plot the critical point\n", + "plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n", + "\n", + "# Plot the normal melting point (from Streng)\n", + "plt.plot(T_melt, P_melt, \"co\", label=\"normal melting point\")\n", + "\n", + "# Plot the normal boiling point (from Streng)\n", + "plt.plot(77.4, 101325, \"mo\", label=\"normal boiling point\")\n", + "\n", + "# Label and axes\n", + "plt.ylim([100,Pc*2])\n", + "plt.xlim([40,Tc*1.2])\n", + "ax.set_yscale(\"log\")\n", + "ax.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "plt.xlabel('T (K)')\n", + "plt.ylabel('P (Pa)')\n", + "plt.title('P-T diagram for nitrogen')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f15f416f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/Peng_Robinson_EOS_isotherms_CO2.ipynb b/module 7/Peng_Robinson_EOS_isotherms_CO2.ipynb new file mode 100644 index 0000000..73a3dc8 --- /dev/null +++ b/module 7/Peng_Robinson_EOS_isotherms_CO2.ipynb @@ -0,0 +1,305 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7af16f2a", + "metadata": {}, + "source": [ + "# Two examples using the Peng-Robinson EOS to plot several isotherms for carbon dioxide" + ] + }, + { + "cell_type": "markdown", + "id": "3c29e0e8", + "metadata": {}, + "source": [ + "## Generalized Peng-Robinson Equation of State\n", + "\n", + "Routines to calcualte the Generalized Peng-Robinson Equation of State\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst \n", + "November 2025\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS (see SIS Table 6.4-3),\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "47da809f", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_pressure returns the pressure given V, T, Pc, Tc, omega\n", + "PR_volume returns all molar volumes (real roots of EOS) given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_pressure(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the molar volume given P, T for PR EOS in m^3/mol\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_volume(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " # Convert real values of Z to molar volume\n", + " V = real_roots*R*T/P\n", + "\n", + " return V\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2f55b187", + "metadata": {}, + "source": [ + "## Example calculation" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "fd028ebd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'PV diagram for carbon dioxide')" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Critical values for carbon dioxide and the acentric factor\n", + "Pc = 7.376*10**6 # critical pressure in Pa\n", + "Tc = 304.2 # critical temperature in K\n", + "omega = 0.225 # acentric factor\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# plot several isotherms\n", + "# use the same color for IG and vdW EOS\n", + "for T in range(250, 350, 10) : \n", + " V_max = constants.R*T/(100*1000)\n", + " V_min = constants.R*T/(1000*1000)*0.015\n", + " V = np.linspace(V_min,V_max,10000)\n", + "\n", + " ax.plot(V, PR_pressure(V,T,Pc,Tc,omega)/1e6, '-',label=T)\n", + "\n", + "ax.plot(V, PR_pressure(V,Tc,Pc,Tc,omega)/1e6, '-',label=Tc)\n", + "\n", + "ax.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "ax.set_xscale('log')\n", + "plt.ylim([-1,20])\n", + "plt.xlim([1*10**-5,0.003])\n", + "plt.xlabel('V (m$^3$/mol)')\n", + "plt.ylabel('P (MPa)')\n", + "plt.title('PV diagram for carbon dioxide')" + ] + }, + { + "cell_type": "markdown", + "id": "faf1a487", + "metadata": {}, + "source": [ + "Our second example makes a prettier plot using Seaborn..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f387f98f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "from scipy import constants\n", + "\n", + "# Critical values for carbon dioxide and the acentric factor\n", + "Pc = 7.376*10**6\n", + "Tc = 304.2\n", + "omega = 0.225\n", + "\n", + "rows = []\n", + "\n", + "# Make a list of temperatures for the isotherms and add Tc\n", + "temps = list(range(250, 350, 10))\n", + "temps.append(Tc)\n", + "temps = sorted(temps)\n", + "\n", + "# Generate all isotherms including Tc\n", + "for T in temps:\n", + " V_max = constants.R*T/(100*1000)\n", + " V_min = constants.R*T/(1000*1000)*0.015\n", + " V = np.linspace(V_min, V_max, 5000)\n", + " P = PR_pressure(V, T, Pc, Tc, omega)/1e6\n", + " \n", + " rows.append(pd.DataFrame({\n", + " \"V\": V,\n", + " \"P\": P,\n", + " \"T\": T\n", + " }))\n", + "\n", + "df = pd.concat(rows, ignore_index=True)\n", + "\n", + "# Convert T to string for categorical hue (fixes legend)\n", + "df[\"T\"] = df[\"T\"].astype(str)\n", + "\n", + "sns.set_theme(style=\"ticks\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "sns.lineplot(\n", + " data=df,\n", + " x=\"V\", y=\"P\",\n", + " hue=\"T\",\n", + " palette=\"viridis\",\n", + " linewidth=1.2,\n", + " ax=ax\n", + ")\n", + "\n", + "ax.set_xscale(\"log\")\n", + "ax.set_ylim([0, 10])\n", + "ax.set_xlim([1e-5, 1e-2])\n", + "\n", + "ax.set_xlabel(\"V (m$^3$/mol)\")\n", + "ax.set_ylabel(\"P (MPa)\")\n", + "ax.set_title(\"PV diagram for carbon dioxide\")\n", + "\n", + "# Remove legend box\n", + "leg = ax.legend(title=\"Temperature (K)\", frameon=False)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "83c296bf", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/Problem 4.ipynb b/module 7/Problem 4.ipynb new file mode 100644 index 0000000..5b105e5 --- /dev/null +++ b/module 7/Problem 4.ipynb @@ -0,0 +1,319 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "73040203-bdb6-4e2e-b631-64da6d08a77d", + "metadata": {}, + "source": [ + "## Problem 4" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "13c903f6-7b59-413c-88b3-7fa98f2c29ea", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computing PR saturation curve for CO2...\n", + "T= 220.000 K Psat= 5.93635 bar ZL= 0.0117 ZV= 0.9175\n", + "T= 222.120 K Psat= 6.47773 bar ZL= 0.0128 ZV= 0.9119\n", + "T= 224.240 K Psat= 7.05598 bar ZL= 0.0139 ZV= 0.9061\n", + "T= 226.360 K Psat= 7.67271 bar ZL= 0.0151 ZV= 0.9001\n", + "T= 228.480 K Psat= 8.32954 bar ZL= 0.0164 ZV= 0.8938\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#!/usr/bin/env python3\n", + "# -*- coding: utf-8 -*-\n", + "\"\"\"\n", + "Pure-component saturation with Peng–Robinson EOS (phi^L = phi^V)\n", + "Outputs Psat(T) *and* saturated liquid/vapor Z and molar volumes.\n", + "Units: bar, L/mol, K\n", + "\"\"\"\n", + "import math\n", + "from typing import List, Optional, Tuple\n", + "\n", + "try:\n", + " import numpy as np\n", + "except Exception:\n", + " class _NP:\n", + " @staticmethod\n", + " def linspace(a, b, n):\n", + " step = (b - a) / (n - 1)\n", + " return [a + i * step for i in range(n)]\n", + " np = _NP()\n", + "\n", + "R = 0.08314472 # bar·L/(mol·K)\n", + "\n", + "def pr_params(Tc: float, Pc: float, omega: float) -> Tuple[float, float, float]:\n", + " a = 0.45724 * R**2 * Tc**2 / Pc\n", + " b = 0.07780 * R * Tc / Pc\n", + " kappa = 0.37464 + 1.54226 * omega - 0.26992 * omega**2\n", + " return a, b, kappa\n", + "\n", + "def alpha_pr(T: float, Tc: float, kappa: float) -> float:\n", + " Tr = T / Tc\n", + " return (1 + kappa * (1 - math.sqrt(Tr))) ** 2\n", + "\n", + "def A_B(a: float, b: float, alpha: float, T: float, P: float) -> Tuple[float, float]:\n", + " A = a * alpha * P / (R**2 * T**2)\n", + " B = b * P / (R * T)\n", + " return A, B\n", + "\n", + "def _real_cubic_roots(a3: float, a2: float, a1: float, a0: float) -> List[float]:\n", + " if abs(a3) < 1e-18:\n", + " if abs(a2) < 1e-18:\n", + " if abs(a1) < 1e-18:\n", + " return []\n", + " return [-a0 / a1]\n", + " disc = a1 * a1 - 4 * a2 * a0\n", + " if disc < 0:\n", + " return []\n", + " if abs(disc) < 1e-18:\n", + " return [-a1 / (2 * a2)]\n", + " rt = math.sqrt(disc)\n", + " return [(-a1 - rt) / (2 * a2), (-a1 + rt) / (2 * a2)]\n", + " p = a2 / a3\n", + " q = a1 / a3\n", + " r = a0 / a3\n", + " shift = p / 3.0\n", + " Acoef = q - p * p / 3.0\n", + " Bcoef = (2 * p**3) / 27.0 - p * q / 3.0 + r\n", + " disc = (Bcoef / 2.0) ** 2 + (Acoef / 3.0) ** 3\n", + " roots = []\n", + " if disc > 0:\n", + " sqrt_disc = math.sqrt(disc)\n", + " u = -Bcoef / 2.0 + sqrt_disc\n", + " v = -Bcoef / 2.0 - sqrt_disc\n", + " u_c = math.copysign(abs(u) ** (1 / 3.0), u) if u != 0 else 0.0\n", + " v_c = math.copysign(abs(v) ** (1 / 3.0), v) if v != 0 else 0.0\n", + " x = u_c + v_c\n", + " roots = [x - shift]\n", + " elif abs(disc) < 1e-18:\n", + " if abs(Bcoef) < 1e-18:\n", + " x = 0.0\n", + " roots = [x - shift]\n", + " else:\n", + " u = math.copysign(abs(-Bcoef / 2.0) ** (1 / 3.0), -Bcoef / 2.0)\n", + " roots = [2 * u - shift, -u - shift]\n", + " else:\n", + " rho = math.sqrt(-Acoef**3 / 27.0)\n", + " theta = math.acos(-Bcoef / (2.0 * rho))\n", + " m = 2 * math.sqrt(-Acoef / 3.0)\n", + " x1 = m * math.cos(theta / 3.0) - shift\n", + " x2 = m * math.cos((theta + 2 * math.pi) / 3.0) - shift\n", + " x3 = m * math.cos((theta + 4 * math.pi) / 3.0) - shift\n", + " roots = [x1, x2, x3]\n", + " roots = [float(r) for r in roots]\n", + " roots.sort()\n", + " return roots\n", + "\n", + "def pr_Z_roots(A: float, B: float) -> List[float]:\n", + " a3 = 1.0\n", + " a2 = -(1.0 - B)\n", + " a1 = A - 3 * B * B - 2 * B\n", + " a0 = -(A * B - B * B - B**3)\n", + " roots = _real_cubic_roots(a3, a2, a1, a0)\n", + " roots = [z for z in roots if z > -1e-10]\n", + " return roots\n", + "\n", + "def lnphi_pure(Z: float, A: float, B: float) -> float:\n", + " sqrt2 = math.sqrt(2.0)\n", + " term1 = Z - 1.0 - math.log(max(Z - B, 1e-300))\n", + " term2 = (A / (2.0 * sqrt2 * B)) * math.log(\n", + " max((Z + (1.0 + sqrt2) * B) / (Z + (1.0 - sqrt2) * B), 1e-300)\n", + " )\n", + " return term1 - term2\n", + "\n", + "def lnphi_L_minus_V_and_roots(T: float, P: float, Tc: float, Pc: float, omega: float):\n", + " a, b, kappa = pr_params(Tc, Pc, omega)\n", + " alpha = alpha_pr(T, Tc, kappa)\n", + " A, B = A_B(a, b, alpha, T, P)\n", + " roots = pr_Z_roots(A, B)\n", + " if len(roots) < 2:\n", + " return None, None, None, None, None\n", + " Z_L = min(roots)\n", + " Z_V = max(roots)\n", + " lnphi_L = lnphi_pure(Z_L, A, B)\n", + " lnphi_V = lnphi_pure(Z_V, A, B)\n", + " return lnphi_L - lnphi_V, Z_L, Z_V, A, B\n", + "\n", + "def find_psat_at_T(T: float, Tc: float, Pc: float, omega: float,\n", + " Pmin: float = 1e-6, Pmax: Optional[float] = None, nscan: int = 200):\n", + " if Pmax is None:\n", + " Pmax = 0.999 * Pc\n", + " Ps = [Pmin * (Pmax / Pmin) ** (i / (nscan - 1)) for i in range(nscan)]\n", + " vals = []\n", + " for P in Ps:\n", + " F, ZL, ZV, A, B = lnphi_L_minus_V_and_roots(T, P, Tc, Pc, omega)\n", + " if F is not None and math.isfinite(F):\n", + " vals.append((P, F))\n", + " if len(vals) < 2:\n", + " return None\n", + " bracket = None\n", + " for (P1, F1), (P2, F2) in zip(vals[:-1], vals[1:]):\n", + " if F1 == 0.0:\n", + " P = P1\n", + " _, ZL, ZV, _, _ = lnphi_L_minus_V_and_roots(T, P, Tc, Pc, omega)\n", + " VL = ZL * R * T / P\n", + " VV = ZV * R * T / P\n", + " return P, ZL, ZV, VL, VV\n", + " if F1 * F2 < 0.0:\n", + " bracket = (P1, F1, P2, F2)\n", + " break\n", + " if bracket is None:\n", + " vals_sorted = sorted(vals, key=lambda t: abs(t[1]))\n", + " if len(vals_sorted) >= 2:\n", + " P1, F1 = vals_sorted[0]\n", + " P2, F2 = vals_sorted[1]\n", + " for _ in range(50):\n", + " if abs(F2 - F1) < 1e-14:\n", + " break\n", + " P_new = P2 - F2 * (P2 - P1) / (F2 - F1)\n", + " P_new = max(Pmin, min(P_new, Pmax))\n", + " F_new, ZL, ZV, _, _ = lnphi_L_minus_V_and_roots(T, P_new, Tc, Pc, omega)\n", + " if F_new is None:\n", + " P_new = 0.5 * (P2 + P1)\n", + " F_new, ZL, ZV, _, _ = lnphi_L_minus_V_and_roots(T, P_new, Tc, Pc, omega)\n", + " if F_new is None:\n", + " break\n", + " if abs(F_new) < 1e-10:\n", + " VL = ZL * R * T / P_new\n", + " VV = ZV * R * T / P_new\n", + " return P_new, ZL, ZV, VL, VV\n", + " P1, F1, P2, F2 = P2, F2, P_new, F_new\n", + " return None\n", + " P1, F1, P2, F2 = bracket\n", + " ZL=ZV=VL=VV=None\n", + " for _ in range(80):\n", + " Pm = 0.5 * (P1 + P2)\n", + " Fm, ZL, ZV, _, _ = lnphi_L_minus_V_and_roots(T, Pm, Tc, Pc, omega)\n", + " if Fm is None:\n", + " Pm = math.sqrt(P1 * P2)\n", + " Fm, ZL, ZV, _, _ = lnphi_L_minus_V_and_roots(T, Pm, Tc, Pc, omega)\n", + " if Fm is None:\n", + " break\n", + " if abs(Fm) < 1e-12:\n", + " VL = ZL * R * T / Pm\n", + " VV = ZV * R * T / Pm\n", + " return Pm, ZL, ZV, VL, VV\n", + " if F1 * Fm < 0:\n", + " P2, F2 = Pm, Fm\n", + " else:\n", + " P1, F1 = Pm, Fm\n", + " if ZL is None or ZV is None:\n", + " return None\n", + " Pfin = 0.5 * (P1 + P2)\n", + " VL = ZL * R * T / Pfin\n", + " VV = ZV * R * T / Pfin\n", + " return Pfin, ZL, ZV, VL, VV\n", + "\n", + "def compute_psat_curve_pr(Tc: float, Pc: float, omega: float,\n", + " T_min: Optional[float] = None,\n", + " T_max: Optional[float] = None,\n", + " nT: int = 60):\n", + " if T_max is None:\n", + " T_max = 0.999 * Tc\n", + " if T_min is None:\n", + " T_min = 0.55 * Tc\n", + " Ts = np.linspace(T_min, T_max, nT)\n", + " rows = []\n", + " for T in Ts:\n", + " out = find_psat_at_T(T, Tc, Pc, omega)\n", + " if out is None:\n", + " rows.append((float(T), None, None, None, None, None))\n", + " else:\n", + " P, ZL, ZV, VL, VV = out\n", + " rows.append((float(T), float(P), float(ZL), float(ZV), float(VL), float(VV)))\n", + " return rows\n", + "\n", + "def _maybe_plot(results):\n", + " try:\n", + " import matplotlib.pyplot as plt\n", + " except Exception:\n", + " return\n", + " # T-P plot (single line)\n", + " T = [r[0] for r in results if r[1] is not None]\n", + " P = [r[1] for r in results if r[1] is not None]\n", + " if len(T) == 0:\n", + " return\n", + " fig, ax = plt.subplots(1, 2, figsize=(11,4.2))\n", + " ax[0].plot(T, P, marker=\"o\", lw=1.5)\n", + " ax[0].set_xlabel(\"Temperature, K\")\n", + " ax[0].set_ylabel(\"Saturation Pressure, bar\")\n", + " ax[0].set_title(\"PR Saturation Curve: T–P\")\n", + "\n", + " # T–V plot (two branches)\n", + " VL = [r[4] for r in results if r[1] is not None] # L molar volume\n", + " VV = [r[5] for r in results if r[1] is not None] # L molar volume\n", + " ax[1].plot(T, VL, label=\"V_L (sat. liquid)\", lw=2)\n", + " ax[1].plot(T, VV, label=\"V_V (sat. vapor)\", lw=2)\n", + " ax[1].set_xlabel(\"Temperature, K\")\n", + " ax[1].set_ylabel(\"Molar volume, L/mol\")\n", + " ax[1].set_yscale(\"log\")\n", + " ax[1].set_title(\"Saturated Volumes\")\n", + " ax[1].legend()\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + "if __name__ == \"__main__\":\n", + " # Example: CO2\n", + " Tc = 304.2 # K\n", + " Pc = 73.8 # bar\n", + " omega = 0.225\n", + " print(\"Computing PR saturation curve for CO2...\")\n", + " table = compute_psat_curve_pr(Tc, Pc, omega, T_min=220.0, T_max=0.995*Tc, nT=40)\n", + " for row in table[:5]:\n", + " T, P, ZL, ZV, VL, VV = row\n", + " print(f\"T={T:8.3f} K Psat={P if P is not None else float('nan'):9.5f} bar \"\n", + " f\"ZL={ZL if ZL is not None else float('nan'):7.4f} \"\n", + " f\"ZV={ZV if ZV is not None else float('nan'):7.4f}\")\n", + " _maybe_plot(table)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d9f12983-dcfa-4795-91c7-11eb45aa104c", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [conda env:base] *", + "language": "python", + "name": "conda-base-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/README.md b/module 7/README.md new file mode 100644 index 0000000..db5c57c --- /dev/null +++ b/module 7/README.md @@ -0,0 +1,10 @@ +# Exporting notebooks to PDF + +The file `vdw_report.tex.j2` formats the LaTeX PDF output to use a specific filename. It makes additional changes to the format of the code blocks. + +To create the output, use the `nbeconvert` utility in `jupyter`: + +``` +% jupyter nbconvert van_der_waals_EOS.ipynb --to pdf --TemplateExporter.extra_template_paths=. --template-file vdw_report.tex.j2 --no-prompt +``` + diff --git a/module 7/VLE from fugacity final exam.ipynb b/module 7/VLE from fugacity final exam.ipynb new file mode 100644 index 0000000..4b7e713 --- /dev/null +++ b/module 7/VLE from fugacity final exam.ipynb @@ -0,0 +1,825 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "fec96515", + "metadata": {}, + "source": [ + "# VLE from fugacity calculation\n", + "\n", + "Use the Generalized Peng-Robinson equation of state to calculate the vapor-liquid equilibrium curve. We will need to evaluate the Peng-Robinson EOS and use the Peng-Robinson form of the fugacity equation.\n", + "\n", + "This notebook shows how I developed preliminary calcuations before generating the final plots. \n", + "\n", + "Eric Furst, December 2025" + ] + }, + { + "cell_type": "markdown", + "id": "84f5edf0", + "metadata": {}, + "source": [ + "## Generalized Peng-Robinson Equation of State\n", + "\n", + "Routines to calcualte the Generalized Peng-Robinson Equation of State\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst, November 2025\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS (see SIS Table 6.4-3),\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8cd6123e", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_P returns the pressure given V, T, Pc, Tc, omega\n", + "PR_Z returns the compressibility factor for all real roots of EOS given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_P(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the compressibility coefficient given P, T for PR EOS\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_Z(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots\n" + ] + }, + { + "cell_type": "markdown", + "id": "2c3f3877", + "metadata": {}, + "source": [ + "## Fugacity coefficient for the Peng-Robinson equation of state\n", + "\n", + "The fugacity coefficient $ f/P $ is written as\n", + "\n", + "$$ \\ln \\frac{f}{P} = (Z - 1) -\\ln (Z-B) - \\frac{A}{2\\sqrt{2}B}\\ln \\left [ \\frac{Z + (1+\\sqrt{2})B}{Z + (1-\\sqrt{2})B} \\right ] $$\n", + "\n", + "where\n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$\n", + "\n", + "and \n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "32f3e31d", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"Fugacity coefficient of the Peng-Robinson EOS\n", + "Returns the natural log of the fugacity coefficient\n", + "\"\"\"\n", + "import numpy as np\n", + "\n", + "def fugacity_PR(Z,A,B):\n", + " return (Z-1) - np.log(Z-B)-A/2/np.sqrt(2)/B*np.log((Z+(1+np.sqrt(2))*B)/(Z+(1-np.sqrt(2))*B))" + ] + }, + { + "cell_type": "markdown", + "id": "b9f11582", + "metadata": {}, + "source": [ + "## Example calculation - VLE for nitrogen" + ] + }, + { + "cell_type": "markdown", + "id": "ef603cb4", + "metadata": {}, + "source": [ + "Start with data for nitrogen" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "bd8d2ff0", + "metadata": {}, + "outputs": [], + "source": [ + "# Data for nitrogen\n", + "# Molecular weight\n", + "MW = 28.0134 # g/mol\n", + "\n", + "# Critical parameters and acentricity\n", + "Pc = 33.978*100000 # Critical pressure in Pa\n", + "Tc = 126.19 # Critical temp in K\n", + "Vc = 1/(11.18*1000) # Critical volume in m^3/mol (original is 11.18 mol/l)\n", + "omega = 0.040 # acentric factor\n", + "\n", + "# Triple point\n", + "T_triple = 63.14 # temp in K\n", + "P_triple = 0.1252*100000 # pressure in Pa" + ] + }, + { + "cell_type": "markdown", + "id": "49fa42eb", + "metadata": {}, + "source": [ + "The next block is a minimal calculation. We guess the pressure and check to see if the equlibrium condition is satisfied. You can iterate by hand to find the correct $P^\\mathrm{sat}$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "42d9332d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.8275367561074513 0.8344346518047008 -0.006897895697249523\n", + "Psat(101 K) = 840000 Pa\n" + ] + } + ], + "source": [ + "# This will be a manual guess and check\n", + "import numpy as np\n", + "import scipy.constants as constants\n", + "\n", + "R = constants.R\n", + "\n", + "# Specifiy the temperature\n", + "T = 0.8*Tc\n", + "\n", + "# Guess a pressure (in Pa)\n", + "P = 840000 \n", + "\n", + "# Calculate liquid and vapor fugacities\n", + "A = calc_a(T,Pc,Tc,omega)*P/R**2/T**2\n", + "B = calc_b(Pc,Tc)*P/R/T\n", + "Z = PR_Z(P,T,Pc,Tc,omega) # This returns all roots\n", + "\n", + "ln_f_L = fugacity_PR(np.min(Z),A,B) # ln of fugacity coefficient for liquid\n", + "ln_f_V = fugacity_PR(np.max(Z),A,B) # ln of fugacity coefficient for liquid\n", + "\n", + "# Are they equal (to within a tolerance?)\n", + "print(np.exp(ln_f_L), np.exp(ln_f_V), np.exp(ln_f_L)-np.exp(ln_f_V))\n", + "\n", + "print(f\"Psat({T:.0f} K) = {P:.0f} Pa\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "41f8639e", + "metadata": {}, + "source": [ + "Next, try implementing an automatic search for $P^\\mathrm{sat}(T)$ by calculating the residual of the fugacity equation\n", + "\n", + "$$\\ln \\frac{f^L}{P} - \\ln \\frac{f^V}{P} = 0$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d52a581e", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a function that returns the residual of the fugacity calculation\n", + "def residual_lnphi(P):\n", + " \"\"\"\n", + " Returns ln(phi_L) - ln(phi_V) at given P (Pa).\n", + " At Psat, this should be zero.\n", + " As written, requires globals Tc, Pc, omega, and T\n", + " \"\"\"\n", + " # EOS parameters\n", + " A = calc_a(T, Pc, Tc, omega)*P/R**2/T**2\n", + " B = calc_b(Pc, Tc)*P/R/T\n", + "\n", + " # All compressibility roots\n", + " Z_roots = np.array(PR_Z(P, T, Pc, Tc, omega))\n", + "\n", + " # Keep real roots only (in case your solver returns complex with tiny imag)\n", + " Z_real = Z_roots[np.isreal(Z_roots)].real\n", + "\n", + " ZL = np.min(Z_real) # liquid root (smallest Z)\n", + " ZV = np.max(Z_real) # vapor root (largest Z)\n", + "\n", + " ln_f_L = fugacity_PR(ZL, A, B) # ln(phi_L)\n", + " ln_f_V = fugacity_PR(ZV, A, B) # ln(phi_V)\n", + "\n", + " return ln_f_L - ln_f_V\n" + ] + }, + { + "cell_type": "markdown", + "id": "294094c3", + "metadata": {}, + "source": [ + "We'll use Newton's method in the scipy.optimize library to minimize the residual. We need a decent guess for the pressure. If it is too far away from the final value of $P^\\mathrm{sat}$, the routine will fail." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "05077a86", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Psat(101 K) = 830968 Pa\n", + "Residual at Psat = 1.3322676295501878e-15\n" + ] + } + ], + "source": [ + "# Example run\n", + "from scipy.optimize import newton\n", + "\n", + "P_guess = 200000 # Pa\n", + "T = 0.8*Tc\n", + "Psat = newton(residual_lnphi, P_guess) # or newton(residual_lnphi, P0, P1) for secant\n", + "print(f\"Psat({T:.0f} K) = {Psat:.0f} Pa\")\n", + "print(\"Residual at Psat =\", residual_lnphi(Psat))" + ] + }, + { + "cell_type": "markdown", + "id": "8b9f8dbe", + "metadata": {}, + "source": [ + "That looks like it works. Next, let's write a routine to generate a Pandas dataframe of the temperature, pressure, molar volume of the liquid and molar volume of the vapor." + ] + }, + { + "cell_type": "markdown", + "id": "d9414e99", + "metadata": {}, + "source": [ + "### Create dataframe of VLE values" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "62364367", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " T P vL vV\n", + "0 63.140000 12830.310618 0.000028 0.040580\n", + "1 63.171351 12903.335640 0.000028 0.040369\n", + "2 63.202703 12976.696886 0.000029 0.040159\n", + "3 63.234054 13050.395494 0.000029 0.039950\n", + "4 63.265406 13124.432605 0.000029 0.039743\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "# Example temperature grid (pick your own range)\n", + "T_min = T_triple\n", + "T_max = 0.997 * Tc\n", + "n_T = 2000\n", + "\n", + "T_list = np.linspace(T_min, T_max, n_T)\n", + "\n", + "rows = []\n", + "\n", + "# Initial pressure guess: something reasonable, e.g. 0.1*Pc or from your old calc\n", + "P_guess = 10000\n", + "\n", + "for T in T_list:\n", + " Psat = newton(residual_lnphi, P_guess)\n", + " \n", + " # All compressibility roots\n", + " Z_roots = np.array(PR_Z(Psat, T, Pc, Tc, omega))\n", + "\n", + " # Keep real roots only (in case your solver returns complex with tiny imag)\n", + " Z_real = Z_roots[np.isreal(Z_roots)].real\n", + "\n", + " ZL = np.min(Z_real) # liquid root of compressibility factor (smallest Z)\n", + " ZV = np.max(Z_real) # vapor root of compressibility factor (largest Z)\n", + "\n", + " vL = ZL*R*T/Psat\n", + " vV = ZV*R*T/Psat\n", + "\n", + " rows.append({\n", + " \"T\": T,\n", + " \"P\": Psat,\n", + " \"vL\": vL,\n", + " \"vV\": vV,\n", + " })\n", + "\n", + " # Use current Psat as the next initial guess (smooth VLE curve)\n", + " P_guess = Psat\n", + "\n", + "df_eq = pd.DataFrame(rows)\n", + "print(df_eq.head())" + ] + }, + { + "cell_type": "markdown", + "id": "a2d94860", + "metadata": {}, + "source": [ + "Plot the P-T diagram..." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "346d9640", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*100000\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 63.14\n", + "T_Antoine_max = 126\n", + "A = 3.7362\n", + "B = 264.651\n", + "C = -6.788\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n", + "plt.plot(T, P_antoine(A, B, C, T), \"c\", label=r\"$P^\\mathrm{vap}$ (Antoine)\")\n", + "\n", + "sns.lineplot(data=df_eq, x=\"T\", y=\"P\", label=r\"$P^\\mathrm{vap}$ (PR EOS)\")\n", + "plt.xlabel(\"T (K)\")\n", + "plt.ylabel(\"P (Pa)\")\n", + "plt.yscale(\"log\")\n", + "plt.tight_layout()\n", + "\n", + "# Plot the critical point\n", + "plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n", + "\n", + "# Plot the triple point\n", + "plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n", + "\n", + "# Plot the normal boiling point (from Streng)\n", + "plt.plot(77.4, 101325, \"mo\", label=\"normal boiling point\")\n", + "\n", + "plt.title(r\"$P-T$ diagram for nitrogen, Peng-Robinson EOS\")\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "\n", + "# Line at 1 bar\n", + "plt.plot([T_triple, Tc],[100000, 100000], linestyle = '--', color=\"gray\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c53c4fdc", + "metadata": {}, + "source": [ + "We can also create a P-V diagram using the same dataframe:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "68379299", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/vs/zb__jwqr8xj7b90059b80rzr0000gp/T/ipykernel_26142/2492820622.py:55: UserWarning: No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n", + " plt.legend(frameon=True, fancybox=True, edgecolor='none')\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# This line can cause problems in Google Colab\n", + "import matplotlib as mpl\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Plot (calculated) critical point\n", + "#Vc = PR_Z(Pc,Tc,Pc,Tc,omega)*R*Tc/Pc\n", + "#plt.plot(Vc, Pc, \"ro\", label=\"c.p.\") \n", + "\n", + "# Add the critical isotherm\n", + "V = np.linspace(Vc/3,4e-2,10000)\n", + "#plt.plot(V, PR_P(V,Tc,Pc,Tc,omega), color='gray', linestyle='-',label=f\"critical isotherm, {Tc} K\")\n", + "plt.plot(V, PR_P(V,Tc,Pc,Tc,omega), color='gray', linestyle='-')\n", + "\n", + "# Plot the t.p. tie line\n", + "row_min_T = df_eq.loc[df_eq[\"T\"].idxmin()]\n", + "vL = row_min_T[\"vL\"]\n", + "vV = row_min_T[\"vV\"]\n", + "P = row_min_T[\"P\"]\n", + "plt.plot([vL, vV], [P, P], color='gray', linestyle='-', linewidth=1)\n", + "\n", + "# Pick and plot 4 evenly spaced tie lines through the dataframe\n", + "idx = np.linspace(0, len(df_eq)/4*3, 5, dtype=int)\n", + "for i in idx:\n", + " row = df_eq.iloc[i]\n", + " vL, vV, P = row[\"vL\"], row[\"vV\"], row[\"P\"]\n", + " \n", + " # Draw tie line\n", + " plt.plot([vL, vV], [P, P], '-', linewidth=1, color='gray')\n", + "\n", + " # Plot the isotherm above the vapor line\n", + " V = np.linspace(row[\"vV\"],4e-2,1000)\n", + " plt.plot(V, PR_P(V,row[\"T\"],Pc,Tc,omega), color='gray', linestyle='-', linewidth=1)\n", + "\n", + " # Plot the isotherm below the liquid line\n", + " V = np.linspace(row[\"vL\"],2.8e-5,1000)\n", + " plt.plot(V, PR_P(V,row[\"T\"],Pc,Tc,omega), color='gray', linestyle='-', linewidth=1)\n", + " \n", + "\n", + "# Plot the vapor coexistence line\n", + "#sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"black\", linewidth=2, label=r\"$\\underbar{V}_\\mathrm{V}$\")\n", + "sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"black\", linewidth=2)\n", + "\n", + "# Plot the liquid coexistence line\n", + "#sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"black\", linewidth=2, label=r\"$\\underbar{V}_\\mathrm{L}$\")\n", + "sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"black\", linewidth=2)\n", + "\n", + "plt.grid(color='gray', linestyle='--', linewidth=0.5, alpha=0.7)\n", + "plt.ylim([6e3, 1e7])\n", + "plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(r\"$\\underbar{V}$ (m$^3$/mol)\")\n", + "plt.ylabel(r\"$P$ (Pa)\")\n", + "plt.title('$P-V$ diagram for nitrogen, Peng-Robinson EOS')\n", + "\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ad5761c", + "metadata": {}, + "source": [ + "As we approach the critical point, it becomes more difficult to calculate the binodal. I used many points, which is inefficient, but gets us to 0.99*Pc.\n", + "\n", + "Since we use a Pandas dataframe, we can easily generate a table of the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "1e8719c3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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TPvLvV
063.1400001.283031e+040.0000280.040580
163.1713511.290334e+040.0000280.040369
263.2027031.297670e+040.0000290.040159
363.2340541.305040e+040.0000290.039950
463.2654061.312443e+040.0000290.039743
...............
1995125.6860243.319799e+060.0000790.000116
1996125.7173763.324631e+060.0000800.000115
1997125.7487273.329469e+060.0000800.000114
1998125.7800793.334311e+060.0000810.000114
1999125.8114303.339158e+060.0000810.000113
\n", + "

2000 rows × 4 columns

\n", + "
" + ], + "text/plain": [ + " T P vL vV\n", + "0 63.140000 1.283031e+04 0.000028 0.040580\n", + "1 63.171351 1.290334e+04 0.000028 0.040369\n", + "2 63.202703 1.297670e+04 0.000029 0.040159\n", + "3 63.234054 1.305040e+04 0.000029 0.039950\n", + "4 63.265406 1.312443e+04 0.000029 0.039743\n", + "... ... ... ... ...\n", + "1995 125.686024 3.319799e+06 0.000079 0.000116\n", + "1996 125.717376 3.324631e+06 0.000080 0.000115\n", + "1997 125.748727 3.329469e+06 0.000080 0.000114\n", + "1998 125.780079 3.334311e+06 0.000081 0.000114\n", + "1999 125.811430 3.339158e+06 0.000081 0.000113\n", + "\n", + "[2000 rows x 4 columns]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_eq" + ] + }, + { + "cell_type": "markdown", + "id": "36bc4abe", + "metadata": {}, + "source": [ + "Some additional things we can do include \n", + "\n", + "1. Plot the triple point isotherm \n", + "1. Plotting tie lines on the VLE phase envelope and plotting isotherms around the binodal\n", + "2. Plotting $\\ln P^\\mathrm{vap}(T)$ versus $1/T$ and fitting the Antoine equation." + ] + }, + { + "cell_type": "markdown", + "id": "f4076545", + "metadata": {}, + "source": [ + "Plot $\\ln P^\\mathrm{vap}$ versus $1/T$:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "373ca4aa", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Add 1/T to the dataframe:\n", + "df_eq['1_over_T'] = 1 / df_eq[\"T\"]\n", + "\n", + "# Plot the result\n", + "sns.lineplot(data=df_eq, x=\"1_over_T\", y=\"P\", color=\"b\", linewidth=2, label=\"PR EOS\")\n", + "\n", + "# Add the Antoine equation to the plot\n", + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*100000\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 63.14\n", + "T_Antoine_max = 126\n", + "A = 3.7362\n", + "B = 264.651\n", + "C = -6.788\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n", + "plt.plot(1/T, P_antoine(A, B, C, T), \"c\", label=\"Antoine eqn\")\n", + "\n", + "#plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(r\"$1/T$ (K$^{-1}$)\")\n", + "plt.ylabel(r\"$P^\\mathrm{vap}$ (Pa)\")\n", + "plt.title(r'$P^\\mathrm{vap}$ diagram for nitrogen, Peng-Robinson EOS')\n", + "\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8d34c490", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/VLE from fugacity.ipynb b/module 7/VLE from fugacity.ipynb new file mode 100644 index 0000000..ebb8c99 --- /dev/null +++ b/module 7/VLE from fugacity.ipynb @@ -0,0 +1,813 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "fec96515", + "metadata": {}, + "source": [ + "# VLE from fugacity calculation\n", + "\n", + "Use the Generalized Peng-Robinson equation of state to calculate the vapor-liquid equilibrium curve. We will need to evaluate the Peng-Robinson EOS and use the Peng-Robinson form of the fugacity equation.\n", + "\n", + "This notebook shows how I developed preliminary calcuations before generating the final plots. \n", + "\n", + "Eric Furst, December 2025" + ] + }, + { + "cell_type": "markdown", + "id": "84f5edf0", + "metadata": {}, + "source": [ + "## Generalized Peng-Robinson Equation of State\n", + "\n", + "Routines to calcualte the Generalized Peng-Robinson Equation of State\n", + "\n", + "SIS is Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed.\n", + "\n", + "Eric Furst, November 2025\n", + "\n", + "The Generalized Peng-Robinson equation of state is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a(T)}{\\underline{V}(\\underline{V}+b) + b(\\underline{V}-b)} \\tag{Eq. 6.4-2}$$\n", + "\n", + "with\n", + "\n", + "$$ b = 0.07780 \\frac{RT_c}{P_c} \\tag{Eq. 6.7-2}$$\n", + "$$ a(T) = a(T_c)\\alpha(T) = 0.45724 \\frac{R^2T_c^2}{P_c}\\alpha(T) \\tag{Eq. 6.7-1}$$\n", + "$$ \\sqrt{\\alpha} = 1 + \\kappa \\left ( 1- \\sqrt{\\frac{T}{T_c}} \\right ) \\tag{Eq. 6.7-3}$$\n", + "$$ \\kappa = 0.37464 + 1.54226\\omega − 0.26992\\omega^2 \\tag{Eq. 6.7-4}$$\n", + "\n", + "The acentric factor $\\omega$ and the crticial temperatures and pressures are given in SIS table 6.6-1.\n", + "\n", + "Calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve the cubic equation of state of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the Peng-Robinson EOS (see SIS Table 6.4-3),\n", + "\n", + "$$ \\alpha = -1 + B $$\n", + "$$ \\beta = A - 3B^2 -2B $$\n", + "$$ \\gamma = -AB + B^2 + B^3 $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "id": "8cd6123e", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Generalized Peng-Robinson EOS \n", + "PR_P returns the pressure given V, T, Pc, Tc, omega\n", + "PR_Z returns the compressibility factor for all real roots of EOS given P, T, Pc, Tc, omega\n", + "\"\"\"\n", + "import numpy as np\n", + "from scipy import constants\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "R = constants.R # Set the gas constant to R\n", + "\n", + "def calc_b(Pc,Tc):\n", + " return 0.07780*R*Tc/Pc\n", + "\n", + "def calc_a(T,Pc,Tc,omega):\n", + " kappa = 0.37464 + 1.54226*omega - 0.26992*omega**2\n", + " sqrtalpha = 1 + kappa*(1-np.sqrt(T/Tc))\n", + " return 0.45724*R**2*Tc**2/Pc*sqrtalpha**2\n", + "\n", + "# Calculate the presure given V, T for PR EOS\n", + "def PR_P(V,T,Pc,Tc,omega):\n", + " a = calc_a(T,Pc,Tc,omega)\n", + " b = calc_b(Pc,Tc)\n", + "\n", + " P = R*T/(V-b) - a/(V*(V+b)+b*(V-b))\n", + " return P\n", + "\n", + "# Calculate the compressibility coefficient given P, T for PR EOS\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def PR_Z(P, T, Pc, Tc, omega):\n", + " # Calculate a, b, A, and B\n", + " a = calc_a(T, Pc, Tc, omega)\n", + " b = calc_b(Pc, Tc)\n", + " A = a*P/R**2/T**2\n", + " B = b*P/R/T\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -1 + B\n", + " beta = A - 3*B**2 -2*B\n", + " gamma = -A*B + B**2 + B**3\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots\n" + ] + }, + { + "cell_type": "markdown", + "id": "2c3f3877", + "metadata": {}, + "source": [ + "## Fugacity coefficient for the Peng-Robinson equation of state\n", + "\n", + "The fugacity coefficient $ f/P $ is written as\n", + "\n", + "$$ \\ln \\frac{f}{P} = (Z - 1) -\\ln (Z-B) - \\frac{A}{2\\sqrt{2}B}\\ln \\left [ \\frac{Z + (1+\\sqrt{2})B}{Z + (1-\\sqrt{2})B} \\right ] $$\n", + "\n", + "where\n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$\n", + "\n", + "and \n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "id": "32f3e31d", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"Fugacity coefficient of the Peng-Robinson EOS\n", + "Returns the natural log of the fugacity coefficient\n", + "\"\"\"\n", + "import numpy as np\n", + "\n", + "def fugacity_PR(Z,A,B):\n", + " return (Z-1) - np.log(Z-B)-A/2/np.sqrt(2)/B*np.log((Z+(1+np.sqrt(2))*B)/(Z+(1-np.sqrt(2))*B))" + ] + }, + { + "cell_type": "markdown", + "id": "b9f11582", + "metadata": {}, + "source": [ + "## Example calculation - VLE for nitrogen" + ] + }, + { + "cell_type": "markdown", + "id": "ef603cb4", + "metadata": {}, + "source": [ + "Start with data for nitrogen" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "bd8d2ff0", + "metadata": {}, + "outputs": [], + "source": [ + "# Data for nitrogen\n", + "# Molecular weight\n", + "MW = 28.0134 # g/mol\n", + "\n", + "# Critical parameters and acentricity\n", + "Pc = 33.978*100000 # Critical pressure in Pa\n", + "Tc = 126.19 # Critical temp in K\n", + "Vc = 1/(11.18*1000) # Critical volume in m^3/mol (original is 11.18 mol/l)\n", + "omega = 0.040 # acentric factor\n", + "\n", + "# Triple point\n", + "T_triple = 63.14 # temp in K\n", + "P_triple = 0.1252*100000 # pressure in Pa" + ] + }, + { + "cell_type": "markdown", + "id": "49fa42eb", + "metadata": {}, + "source": [ + "The next block is a minimal calculation. We guess the pressure and check to see if the equlibrium condition is satisfied. You can iterate by hand to find the correct $P^\\mathrm{sat}$." + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "id": "42d9332d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.8275367561074513 0.8344346518047008 -0.006897895697249523\n", + "Psat(101 K) = 840000 Pa\n" + ] + } + ], + "source": [ + "# This will be a manual guess and check\n", + "import numpy as np\n", + "import scipy.constants as constants\n", + "\n", + "R = constants.R\n", + "\n", + "# Specifiy the temperature\n", + "T = 0.8*Tc\n", + "\n", + "# Guess a pressure (in Pa)\n", + "P = 840000 \n", + "\n", + "# Calculate liquid and vapor fugacities\n", + "A = calc_a(T,Pc,Tc,omega)*P/R**2/T**2\n", + "B = calc_b(Pc,Tc)*P/R/T\n", + "Z = PR_Z(P,T,Pc,Tc,omega) # This returns all roots\n", + "\n", + "ln_f_L = fugacity_PR(np.min(Z),A,B) # ln of fugacity coefficient for liquid\n", + "ln_f_V = fugacity_PR(np.max(Z),A,B) # ln of fugacity coefficient for liquid\n", + "\n", + "# Are they equal (to within a tolerance?)\n", + "print(np.exp(ln_f_L), np.exp(ln_f_V), np.exp(ln_f_L)-np.exp(ln_f_V))\n", + "\n", + "print(f\"Psat({T:.0f} K) = {P:.0f} Pa\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "41f8639e", + "metadata": {}, + "source": [ + "Next, try implementing an automatic search for $P^\\mathrm{sat}(T)$ by calculating the residual of the fugacity equation\n", + "\n", + "$$\\ln \\frac{f^L}{P} - \\ln \\frac{f^V}{P} = 0$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d52a581e", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a function that returns the residual of the fugacity calculation\n", + "def residual_lnphi(P):\n", + " \"\"\"\n", + " Returns ln(phi_L) - ln(phi_V) at given P (Pa).\n", + " At Psat, this should be zero.\n", + " As written, requires globals Tc, Pc, omega\n", + " \"\"\"\n", + " # EOS parameters\n", + " A = calc_a(T, Pc, Tc, omega)*P/R**2/T**2\n", + " B = calc_b(Pc, Tc)*P/R/T\n", + "\n", + " # All compressibility roots\n", + " Z_roots = np.array(PR_Z(P, T, Pc, Tc, omega))\n", + "\n", + " # Keep real roots only (in case your solver returns complex with tiny imag)\n", + " Z_real = Z_roots[np.isreal(Z_roots)].real\n", + "\n", + " ZL = np.min(Z_real) # liquid root (smallest Z)\n", + " ZV = np.max(Z_real) # vapor root (largest Z)\n", + "\n", + " ln_f_L = fugacity_PR(ZL, A, B) # ln(phi_L)\n", + " ln_f_V = fugacity_PR(ZV, A, B) # ln(phi_V)\n", + "\n", + " return ln_f_L - ln_f_V\n" + ] + }, + { + "cell_type": "markdown", + "id": "294094c3", + "metadata": {}, + "source": [ + "We'll use Newton's method in the scipy.optimize library to minimize the residual. We need a decent guess for the pressure. If it is too far away from the final value of $P^\\mathrm{sat}$, the routine will fail." + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "id": "05077a86", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Psat(101 K) = 830968 Pa\n", + "Residual at Psat = 1.3322676295501878e-15\n" + ] + } + ], + "source": [ + "# Example run\n", + "from scipy.optimize import newton\n", + "\n", + "P_guess = 200000 # Pa\n", + "T = 0.8*Tc\n", + "Psat = newton(residual_lnphi, P_guess) # or newton(residual_lnphi, P0, P1) for secant\n", + "print(f\"Psat({T:.0f} K) = {Psat:.0f} Pa\")\n", + "print(\"Residual at Psat =\", residual_lnphi(Psat))" + ] + }, + { + "cell_type": "markdown", + "id": "8b9f8dbe", + "metadata": {}, + "source": [ + "That looks like it works. Next, let's write a routine to generate a Pandas dataframe of the temperature, pressure, molar volume of the liquid and molar volume of the vapor." + ] + }, + { + "cell_type": "markdown", + "id": "d9414e99", + "metadata": {}, + "source": [ + "### Create dataframe of VLE values" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "62364367", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " T P vL vV\n", + "0 63.140000 12830.310618 0.000028 0.040580\n", + "1 63.171351 12903.335640 0.000028 0.040369\n", + "2 63.202703 12976.696886 0.000029 0.040159\n", + "3 63.234054 13050.395494 0.000029 0.039950\n", + "4 63.265406 13124.432605 0.000029 0.039743\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "# Example temperature grid (pick your own range)\n", + "T_min = T_triple\n", + "T_max = 0.997 * Tc\n", + "n_T = 2000\n", + "\n", + "T_list = np.linspace(T_min, T_max, n_T)\n", + "\n", + "rows = []\n", + "\n", + "# Initial pressure guess: something reasonable, e.g. 0.1*Pc or from your old calc\n", + "P_guess = 10000\n", + "\n", + "for T in T_list:\n", + " Psat = newton(residual_lnphi, P_guess)\n", + " \n", + " # All compressibility roots\n", + " Z_roots = np.array(PR_Z(Psat, T, Pc, Tc, omega))\n", + "\n", + " # Keep real roots only (in case your solver returns complex with tiny imag)\n", + " Z_real = Z_roots[np.isreal(Z_roots)].real\n", + "\n", + " ZL = np.min(Z_real) # liquid root of compressibility factor (smallest Z)\n", + " ZV = np.max(Z_real) # vapor root of compressibility factor (largest Z)\n", + "\n", + " vL = ZL*R*T/Psat\n", + " vV = ZV*R*T/Psat\n", + "\n", + " rows.append({\n", + " \"T\": T,\n", + " \"P\": Psat,\n", + " \"vL\": vL,\n", + " \"vV\": vV,\n", + " })\n", + "\n", + " # Use current Psat as the next initial guess (smooth VLE curve)\n", + " P_guess = Psat\n", + "\n", + "df_eq = pd.DataFrame(rows)\n", + "print(df_eq.head())" + ] + }, + { + "cell_type": "markdown", + "id": "a2d94860", + "metadata": {}, + "source": [ + "Plot the P-T diagram..." + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "346d9640", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*100000\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 63.14\n", + "T_Antoine_max = 126\n", + "A = 3.7362\n", + "B = 264.651\n", + "C = -6.788\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n", + "plt.plot(T, P_antoine(A, B, C, T), \"c\", label=r\"$P^\\mathrm{vap}$ (Antoine)\")\n", + "\n", + "sns.lineplot(data=df_eq, x=\"T\", y=\"P\", label=r\"$P^\\mathrm{vap}$ (PR EOS)\")\n", + "plt.xlabel(\"T (K)\")\n", + "plt.ylabel(\"P (Pa)\")\n", + "plt.yscale(\"log\")\n", + "plt.tight_layout()\n", + "\n", + "# Plot the critical point\n", + "plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n", + "\n", + "# Plot the triple point\n", + "plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n", + "\n", + "# Plot the normal boiling point (from Streng)\n", + "plt.plot(77.4, 101325, \"mo\", label=\"normal boiling point\")\n", + "\n", + "plt.title(r\"$P-T$ diagram for nitrogen, Peng-Robinson EOS\")\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "\n", + "# Line at 1 bar\n", + "plt.plot([T_triple, Tc],[100000, 100000], linestyle = '--', color=\"gray\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c53c4fdc", + "metadata": {}, + "source": [ + "We can also create a P-V diagram using the same dataframe:" + ] + }, + { + "cell_type": "code", + "execution_count": 168, + "id": "68379299", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# This line can cause problems in Google Colab\n", + "import matplotlib as mpl\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Plot (calculated) critical point\n", + "Vc = PR_Z(Pc,Tc,Pc,Tc,omega)*R*Tc/Pc\n", + "plt.plot(Vc, Pc, \"ro\", label=\"c.p.\") \n", + "\n", + "# Add the critical isotherm\n", + "V = np.linspace(Vc/3,4e-2,10000)\n", + "plt.plot(V, PR_P(V,Tc,Pc,Tc,omega), color='red', linestyle='-',label=f\"critical isotherm, {Tc} K\")\n", + "\n", + "# Plot the t.p. tie line\n", + "row_min_T = df_eq.loc[df_eq[\"T\"].idxmin()]\n", + "vL = row_min_T[\"vL\"]\n", + "vV = row_min_T[\"vV\"]\n", + "P = row_min_T[\"P\"]\n", + "plt.plot([vL, vV], [P, P], color='gray', linestyle='-')\n", + "\n", + "# Pick and plot 4 evenly spaced tie lines through the dataframe\n", + "idx = np.linspace(0, len(df_eq)/4*3, 5, dtype=int)\n", + "for i in idx:\n", + " row = df_eq.iloc[i]\n", + " vL, vV, P = row[\"vL\"], row[\"vV\"], row[\"P\"]\n", + " \n", + " # Draw tie line\n", + " plt.plot([vL, vV], [P, P], '-', linewidth=1, color='gray')\n", + "\n", + " # Plot the isotherm above the vapor line\n", + " V = np.linspace(row[\"vV\"],4e-2,1000)\n", + " plt.plot(V, PR_P(V,row[\"T\"],Pc,Tc,omega), color='gray', linestyle='-', linewidth=1)\n", + "\n", + " # Plot the isotherm below the liquid line\n", + " V = np.linspace(row[\"vL\"],2.8e-5,1000)\n", + " plt.plot(V, PR_P(V,row[\"T\"],Pc,Tc,omega), color='gray', linestyle='-', linewidth=1)\n", + " \n", + "\n", + "# Plot the vapor coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"c\", linewidth=2, label=r\"$\\underbar{V}_\\mathrm{V}$\")\n", + "\n", + "# Plot the liquid coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"b\", linewidth=2, label=r\"$\\underbar{V}_\\mathrm{L}$\")\n", + "\n", + "plt.ylim([1e4, 1e7])\n", + "plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(r\"$\\underbar{V}$ (m$^3$/mol)\")\n", + "plt.ylabel(r\"$P$ (Pa)\")\n", + "plt.title('$P-V$ diagram for nitrogen, Peng-Robinson EOS')\n", + "\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ad5761c", + "metadata": {}, + "source": [ + "As we approach the critical point, it becomes more difficult to calculate the binodal. I used many points, which is inefficient, but gets us to 0.99*Pc.\n", + "\n", + "Since we use a Pandas dataframe, we can easily generate a table of the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "id": "1e8719c3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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TPvLvV
063.1400001.283031e+040.0000280.040580
163.1713511.290334e+040.0000280.040369
263.2027031.297670e+040.0000290.040159
363.2340541.305040e+040.0000290.039950
463.2654061.312443e+040.0000290.039743
...............
1995125.6860243.319799e+060.0000790.000116
1996125.7173763.324631e+060.0000800.000115
1997125.7487273.329469e+060.0000800.000114
1998125.7800793.334311e+060.0000810.000114
1999125.8114303.339158e+060.0000810.000113
\n", + "

2000 rows × 4 columns

\n", + "
" + ], + "text/plain": [ + " T P vL vV\n", + "0 63.140000 1.283031e+04 0.000028 0.040580\n", + "1 63.171351 1.290334e+04 0.000028 0.040369\n", + "2 63.202703 1.297670e+04 0.000029 0.040159\n", + "3 63.234054 1.305040e+04 0.000029 0.039950\n", + "4 63.265406 1.312443e+04 0.000029 0.039743\n", + "... ... ... ... ...\n", + "1995 125.686024 3.319799e+06 0.000079 0.000116\n", + "1996 125.717376 3.324631e+06 0.000080 0.000115\n", + "1997 125.748727 3.329469e+06 0.000080 0.000114\n", + "1998 125.780079 3.334311e+06 0.000081 0.000114\n", + "1999 125.811430 3.339158e+06 0.000081 0.000113\n", + "\n", + "[2000 rows x 4 columns]" + ] + }, + "execution_count": 145, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_eq" + ] + }, + { + "cell_type": "markdown", + "id": "36bc4abe", + "metadata": {}, + "source": [ + "Some additional things we can do include \n", + "\n", + "1. Plot the triple point isotherm \n", + "1. Plotting tie lines on the VLE phase envelope and plotting isotherms around the binodal\n", + "2. Plotting $\\ln P^\\mathrm{vap}(T)$ versus $1/T$ and fitting the Antoine equation." + ] + }, + { + "cell_type": "markdown", + "id": "f4076545", + "metadata": {}, + "source": [ + "Plot $\\ln P^\\mathrm{vap}$ versus $1/T$:" + ] + }, + { + "cell_type": "code", + "execution_count": 165, + "id": "373ca4aa", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Add 1/T to the dataframe:\n", + "df_eq['1_over_T'] = 1 / df_eq[\"T\"]\n", + "\n", + "# Plot the result\n", + "sns.lineplot(data=df_eq, x=\"1_over_T\", y=\"P\", color=\"b\", linewidth=2, label=\"PR EOS\")\n", + "\n", + "# Add the Antoine equation to the plot\n", + "# Antoine equation given parameters A, B, and C\n", + "# Pressure is returned in Pa\n", + "def P_antoine(A, B, C, T):\n", + " return 10**(A - B/(T + C))*100000\n", + "\n", + "# Antoine equation parameters\n", + "# Valid temperature range in K\n", + "T_Antoine_min = 63.14\n", + "T_Antoine_max = 126\n", + "A = 3.7362\n", + "B = 264.651\n", + "C = -6.788\n", + "\n", + "# Plot the Antoine equation\n", + "T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n", + "plt.plot(1/T, P_antoine(A, B, C, T), \"c\", label=\"Antoine eqn\")\n", + "\n", + "#plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(r\"$1/T$ (K$^{-1}$)\")\n", + "plt.ylabel(r\"$P^\\mathrm{vap}$ (Pa)\")\n", + "plt.title(r'$P^\\mathrm{vap}$ diagram for nitrogen, Peng-Robinson EOS')\n", + "\n", + "plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8d34c490", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/pdf/.DS_Store b/module 7/pdf/.DS_Store new file mode 100644 index 0000000..5008ddf Binary files /dev/null and b/module 7/pdf/.DS_Store differ diff --git a/module 7/pdf/CO2_phases.pdf b/module 7/pdf/CO2_phases.pdf new file mode 100644 index 0000000..ae7cbdb Binary files /dev/null and b/module 7/pdf/CO2_phases.pdf differ diff --git a/module 7/pdf/Fig_6.6-1.pdf b/module 7/pdf/Fig_6.6-1.pdf new file mode 100644 index 0000000..b00b86f Binary files /dev/null and b/module 7/pdf/Fig_6.6-1.pdf differ diff --git a/module 7/pdf/Fig_7.3-1.pdf b/module 7/pdf/Fig_7.3-1.pdf new file mode 100644 index 0000000..ddd3e97 Binary files /dev/null and b/module 7/pdf/Fig_7.3-1.pdf differ diff --git a/module 7/pdf/Fig_7.3-2.pdf b/module 7/pdf/Fig_7.3-2.pdf new file mode 100644 index 0000000..536a65e Binary files /dev/null and b/module 7/pdf/Fig_7.3-2.pdf differ diff --git a/module 7/pdf/Fig_7.3-3.pdf b/module 7/pdf/Fig_7.3-3.pdf new file mode 100644 index 0000000..06f86f1 Binary files /dev/null and b/module 7/pdf/Fig_7.3-3.pdf differ diff --git a/module 7/pdf/Fig_7.3-4.pdf b/module 7/pdf/Fig_7.3-4.pdf new file mode 100644 index 0000000..79bd457 Binary files /dev/null and b/module 7/pdf/Fig_7.3-4.pdf differ diff --git a/module 7/pdf/N2_phases.pdf b/module 7/pdf/N2_phases.pdf new file mode 100644 index 0000000..6cee4af Binary files /dev/null and b/module 7/pdf/N2_phases.pdf differ diff --git a/module 7/pdf/Peng_Robinson_EOS_isotherms_CO2.pdf b/module 7/pdf/Peng_Robinson_EOS_isotherms_CO2.pdf new file mode 100644 index 0000000..a1e19e0 Binary files /dev/null and b/module 7/pdf/Peng_Robinson_EOS_isotherms_CO2.pdf differ diff --git a/module 7/pdf/VLE from fugacity.pdf b/module 7/pdf/VLE from fugacity.pdf new file mode 100644 index 0000000..1ed757e Binary files /dev/null and b/module 7/pdf/VLE from fugacity.pdf differ diff --git a/module 7/pdf/van_der_waals_EOS.pdf b/module 7/pdf/van_der_waals_EOS.pdf new file mode 100644 index 0000000..a7c37d3 Binary files /dev/null and b/module 7/pdf/van_der_waals_EOS.pdf differ diff --git a/module 7/van_der_waals_EOS.ipynb b/module 7/van_der_waals_EOS.ipynb new file mode 100644 index 0000000..c23497e --- /dev/null +++ b/module 7/van_der_waals_EOS.ipynb @@ -0,0 +1,1472 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7af16f2a", + "metadata": {}, + "source": [ + "# Goal of this notebook\n", + "\n", + "The goal of this notebook is to reproduce the following figures in chapters 6 and 7 of Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed. These illustrations are based on the van der Waals equation of state.\n", + "\n", + "- Fig 6.6-1 -- five isotherms illustrated around the critical isotherm\n", + "- Fig 7.3-1 -- five isotherms labeled with local maxima and minima\n", + "- Fig 7.3-2 -- a diagram showing the isotherm construction for a sub-critical temperature\n", + "- Fig 7.3-3 -- the resulting isotherm for a sub-critical temperature\n", + "- Fig 7.3-4 -- the van der Waals EOS PV diagram with multiple isotherms and two phase region\n", + "\n", + "\n", + "Copyright (c) 2025 Eric M. Furst\n" + ] + }, + { + "cell_type": "markdown", + "id": "3c29e0e8", + "metadata": {}, + "source": [ + "## van der Waals equation of state\n", + "\n", + "Below are routines to calculate the van der Waals equation of state.\n", + "\n", + "The van der Waals equation of state (vdW EOS) is\n", + "\n", + "$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a}{\\underline{V}^2} \\tag{Eq. 6.2-38b}$$\n", + "\n", + "Like other cubic equations of state, calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve a cubic equation of the form\n", + "\n", + "$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n", + "\n", + "where $Z$ is the compressibility factor\n", + "\n", + "$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n", + "\n", + "For the van der Waals EOS (see SIS **Table 6.4-3**),\n", + "\n", + "$$ \\alpha = -1 - B $$\n", + "$$ \\beta = A $$\n", + "$$ \\gamma = -AB $$\n", + "\n", + "and \n", + "\n", + "$$ A = \\frac{aP}{(RT)^2} $$\n", + "$$ B = \\frac{bP}{RT} $$\n", + "\n", + "Here, we will use the reduced van der Waals equation of state\n", + "\n", + "$$ \\left ( P_r + \\frac{3}{\\underline{V}_r} \\right )(3\\underline{V}_r - 1) = 8T_r \\tag{Eq. 6.6-6}$$\n", + "\n", + "This can be written in the form \n", + "\n", + "$$ \\underline{V}_r^3 + \\alpha \\underline{V}_r^2 + \\beta \\underline{V}_r + \\gamma = 0 $$\n", + "\n", + "with\n", + "\n", + "$$\\alpha = -\\frac{P_r+8T_r}{3P_r}$$\n", + "$$\\beta = \\frac{3}{P_r}$$\n", + "$$\\gamma = -\\frac{1}{P_r}$$\n", + "\n", + "which is left as an exercise for the reader." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "47da809f", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "Reduced van der Waals equation of state \n", + "rvdw_P returns the pressure given Vr, Tr\n", + "rvdw_V returns all reduced molar volumes (real roots of EOS) given Pr and Tr\n", + "\"\"\"\n", + "import numpy as np\n", + "from numpy.polynomial import Polynomial\n", + "\n", + "\n", + "# Calculate the reduced presure given Vr, Tr for reduced vdw EOS\n", + "def rvdw_P(Vr,Tr):\n", + "\n", + " return 8*Tr/(3*Vr-1) - 3/Vr**2\n", + "\n", + "# Calculate the reduced molar volume given Pr, Tr\n", + "# Note that we can return multiple real roots (up to three)\n", + "# The largest and smallest will be the vapor and liquid, respectively\n", + "def rvdw_V(Pr, Tr):\n", + "\n", + " # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n", + " alpha = -(Pr+8*Tr)/3/Pr\n", + " beta = 3/Pr\n", + " gamma = -1/Pr\n", + "\n", + " # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n", + " p = Polynomial([ gamma, beta, alpha, 1 ]) \n", + "\n", + " roots = p.roots() # returns all (possibly complex) roots of Z\n", + " real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n", + "\n", + " return real_roots\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2f55b187", + "metadata": {}, + "source": [ + "# Figure 6.6-1 -- The pressure-volume behavior of the van der Waals equation of state\n", + "\n", + "We begin by plotting isotherms on the reduced scale. We'll plot a few above and below the critical isotherm." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "fd028ebd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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UCr2mLwJRNqJSFCS9++67asqUKapp06bP/bsQLVTS+lpNi9YYRJFRiag3zwMBxVkr0Cv9i4gUP9+uXbuq69evy0i7QIwuCCHOhmLqZ2TqESFfxBSR6f79+5UViRcvnvRatmvXTopwkF4dOHBg0CIytMYEC1QDI8qFqCKChaAGKzKNSJcuXcTgAVN38DwzZszwyqCDEOI+KKaRgOgTla/POzP1pHp9jUzR12hV8FqRTs2SJYu4Df3xxx8ydQZCayUgnD179jTkuZo3by7PB19jOCYtXLjQcteDEGI+rOaNAkQiwYpMUUSDPlMjh4T7CiLR3r17y1klhB8FSW4dLu6hRo0a4uG7ZcsWOVd287AAQsjzoZh6cW4aLDFFxAdCQ0OV1UGxz86dO6UABwVDhw4dUm4GqWQY5GMWKibOXLp0yewlEUIsBMXUCzF9UZrXVzFFTydA+tQO5MmTR+3Zs0emquDXaBvBpBy3UqRIEbV582b1zz//qOLFi1uymIwQYg62EVNEh0iPRnzYLTKFSQEKWuwQmXrAeeHixYulXaR79+6qWLFittkM6MEbb7yhtm7dqp48eSLX4tixY2YviRBiAWwjpuj1gxB5HunTp7fdmSnOIxGd2k2MUIiFgiT4+OLMN1++fOr777833bTfLHD2DUFNnDixKlmyZNDmtxJC7IttxBQ385s3b4Y/zp07Z7vI1HNuaqfI9Nk0J1p70PuJKleYw1+5ckW5kTRp0qhNmzbJzxNj3DZu3Gj2kgghJmIbMYWowf4u4sNuZ6YAkaldxdTzmjELFdW+6PPMlSuX19NfnAbS9rgG2GTA7IIzUQlxL7YRU7PQIzI9f/68un//vrIzqPZFZStaZ+rUqSO/R2GO2/AMGcf0HbTQcIQbIe6EYhrgmSlaR3w5O4SY4u+fOnVK2Z1UqVKpn376Sf34449q/fr1EqUiYnXbWSo2XHjdnhFuI0aMcN01IMTtUEwDTPPipuntTFM7tsd4U1QFdyBEqTg7xK8RoRl1pm0VMBMVvsP9+/cXH+KPP/5YPX361OxlEUIMgmIaYJoX+JLqTZ06tYxiO3nypHISKVKkUPPmzZPz0127dqmcOXO6ri8VG4vBgwer8ePHqy+//FI1btz4hRsxQoizoJgaLKZoM3nttdfU8ePHlROpVauW9F5i6gyiMxTnuK11pH379pL2hY8vRtv5eq5OCLEfFNMAz0yBrzfL119/3bFiCtAHjOgMdoQwNyhcuLDq3LmzpT2Jgw2KslatWiXXAIPX3VicRYiboJgGeGbqr5i6wTkHIgo7wpEjR8qMVKR+YZ7vluIcnCGjFxXnx3BLckLRGSHk+VBMDU7zesQUZgduMDxAYQ7SvShQgnMSBpBjlJlbfG3xmrdv3y4bCLQR/fbbb2YviRCiAxRTk9K8wA3RacRZrkuXLpVzRAz2RpQ6atQo9ejRI+UG+0FYMcI1qVSpUnRLIsSBUEwDSPNiSDQKinwV02zZssm/c5OYeqpdEZnidbdu3VpaSDDeDZGb00mZMqWIKFLfFStWdK1rFCFOhWIaQJoX4gAHHF/FFN8T0YrbxDRiRD927Fi1e/duuRY4T2zTpo26du2acvrrxpBxbCjgGPX111+bvSRCSJCgmAYgpv5aCrqhotcb8ufPL9WuqPydM2eOypEjh5oxY4ajC5RwbDBr1izVqVMn1aFDB9W7d2+aOxDiACimAZyZBiqmKMpxOzFixJC+TGwsypYtqz744AP5euLECeVUkOKHocWYMWNUSEiImDtE9h4jhFgfimkAZ6aBiCmGTJ89e1bGyZH/7wwFj1/0ZuK65MmTR3366ae2HwgQGV27dhXXKPgbY+rMjRs3zF4SIcRPKKZepnlflHr0V0zz5s0rXw8ePBjwGp0EinMOHTqkevbsqT7//HOVO3dutWbNGuVkcweMccP7AGfH2EgQQuwHxdQLMYWQvshj1l8xxflgrFixKKbPAd7Fn332mVybdOnSqQoVKqiGDRuqixcvKidSvHhxqWi+e/euKlq0KHtRCbEhFFMvzkzBi860MKTcH5s8fF/0Wh44cCDgNToVbDgw2g0zQhGd4vcTJkwQi0KnkT17drVjxw7pRS1RooT65ZdfzF4SIcQHKKZeRKbgReem8KH199wTqV6KaeSg/QhFSShIQjsJipXgJLR//37lNDAfFr2oJUuWlGHj33//vdlLIoR4CcXUSzF9UWQaqJjifNCJkVawSZIkifr222/V1q1bJR1asGBBKeBx2kQW9C0vWbJEBo03b95cDRo0yNGtQoQ4BYppgGKaKFGigMT03r17jhkUbgQo0oEd4fDhw2UYN1qMUA3rJMGBn/HEiRPV0KFD1cCBA1XLli1dYbtIiJ2hmHp5ZhpZmhdnpv403nsqepnq9Q0UbqHa12Oejxmq77//vjp9+rRyUnq7T58+YmKBR9WqVV01wo4Qu0ExDUKaF1GRP+nGZMmSqfTp07tueHawyJQpk5jnIzJFBSwKumCC4KQoDoYO6L1FcRKqftk6Q4g1oZgGQUyBv6leGJ//+uuvAazQ3SCCq1GjhkSpH330kURznrFnTgHDxSGm2LAVKVJEZsQSQqwFxTQIZ6aBiilujixCCgz0+8KeD9cyfvz4EsV17NjRMQVKiLrhY4xoHNW+GLJOCLEOFNMgnJkCf63gIKZ37txx7QSZYOOJSiGsU6dOVbly5VI///yzcsoYN/Td4vwU58QjR450VOEVIXaGYhoFcePGla8v8ogNNM2LFg8YnzPVG1zz/C5duqjDhw+L0UOlSpXk7PHKlSvKCe5Q8DBGOhtFWBhd56QzYkLsCsXUSzHVK82LvkKk8Hbt2hXAKsnzePXVV9Xq1avF/GDlypXSRgMhsns0h83XkCFD5HXhgc0CTfIJMReKaYCRKf4/WjUCuZmxCEnfAqWmTZtKGr106dLi8Ys06blz55TdweuC7SCqweEKderUKbOXRIhroZh6WYAEc4UX3awDcUECb731ljghcRybvueNGHe2ePFisSLEWSp8fu0+mPudd96RwiSkelHpi6pfQojxUEy9cKPBI7K5moG4IAFUZ+Km7qR2DqtSrVo1deTIEdWgQQPx+S1VqpQMJrczr732mogozocRfc+dO9fsJRHiOiimXoBUbmRiGmhkmi1bNjE537Rpk9/fg3gPNj+wItywYYOMdYMTFaz77FzIAwMQTNbBfNT69eurwYMH2/5smBA7QTENkpgGcmaKVDEiJIqp8SlSzExF5e+AAQMkTWrn+bI4kvjhhx9kFixeD0QVQwEIIfpDMQ2CmAaa5vWkemE4gJ5TYmyrCSwIPeeOBQoUkEktL+ortjrYmPXr108tXLhQLV++XN5X58+fN3tZhDgeiqkF0rwAkenjx49ZQGIS6PfFZqZ3794S2aHCGn6/dqVmzZpq27Zt6p9//lGFChVitTghOkMx9TJ60TPNC9BrmiJFCrV27dqAvg8JLE0KIYXwoCAMIoR0qV2j1DfffFPt3r1bZc6cWTZrs2bNMntJhDgWiqlF0rxIz1WoUEFMBoi5INWLKBUuQ8OGDRNRRTuNnS0IUb0MF6hPPvnE9u1AhFgRiqlF0rzgvffek9Ti33//HfD3IoF7MuPsFM5U2OhAUPv37/9CJyyrR9zwKR41apScD2PKjlMGABBiFSimQRJTFA7hzDMQypcvLzduRqfWMs6HoEJIP//88/CzVbuB91W3bt2kKGnjxo10TCIkyFBMg5TmBYFGp8mTJ5ebNYZBE2tFqTg7hYjCwKNo0aKqb9++toxS4eOLIjc4eqHIavPmzWYviRBHQDH1UkxfZCcYjMkxz6Z6EZnatejFycDcAVHqwIEDZfwZzlZR4GM3UOyGIqvcuXOrcuXKqcmTJ5u9JEJsD8U0SGneYIkpzrNQGQx3HmI9MNQAfZwwl8dZJKJUFPVE9v6wIkmTJpVNW6tWrVTr1q3VRx99xA0cIQFAMQ2CmCZOnFi+Xr9+PSjRT5YsWaTpnlgXRHUwekArzejRo20ZpWJj8PXXX0tkOm3aNPH1ZfEbIf5BMQ2CmCZJkiRoYopCkdq1a6tFixYFXNBE9BcjtM/s27dPepE9UardzlJbtmwpVpYoSMKZPTYJhBDfoJgGQUwTJkwoA5uvXbsWlOeDmF65coVevTbhjTfekKIemMsjSs2fP7/tolRsBJC6zpQpkxg8fPfdd2YviRBbQTENgphCSJHqDZaYImUI15qZM2cG5fsRY6JUVPhCkPB+wYxau1X8pk6dWs7qW7RoIdFqu3bteI5KiJdQTIMgpp5U79WrV4PyfEj1NmvWTM2fP1/dvn07KN+TGHuW6qn4RdoUAmunNqBvvvlGffvtt2rKlCmqTJkyMqaOEBI5FNMgimmwIlPQtGlTGZ8FQSX2rPj19KVitBtMH+wU5aHKF8cMf/75p2wIaJRPSORQTC0qphkyZFBly5bl2ZWNyZMnj/Slfvrpp+HuSShWsgtIVWNDgPciRrnBkpAQ8nwopl6KKWZdPnnyxDAxBej/wxgtO48CczuIUiGmKEjC2TqiVDtNokmTJo2co+LY4cMPP+Q5KiEvgGLqBWh7AJEVk+ghpjBwQFTwxRdfBPX7EnPGoSFKRVESJtHYaV4qzCkmTZokD2RKEKWeO3fO7GURYikopl5GpiAyS0E9xBTnbR07dlQ//vgji0AcAIp7UJgEUdU0TSbRYDINsh52AJmSrVu3irED2n84e5eQ/4Ni6oOYRmXcEGwxBWhRwE14zJgxQf/exLxJNEj7wuABDkqIUg8cOKDsADYAqE6GmGL+7tChQzkflRCKaXDFFJFrZNGrP2AiTZcuXdT48eMZnToIbJBg8oAqWThdoTgJv7dDlJosWTK1cuVKqVBG1XL16tWD4v5FiJ2JpiHfZENu3boVPpQbDkR6AncbzH88fPiwypUr13P/Dm4ulStXVn/99ZcUbQQT3KheffVVKQKxwvkp5q7iAaH3tO7UqVNHDPrnzp0btL5Ko57HbHAWjwgVFb+oAJ4+fbr0q9oBvO8bN24spiXwk8bZMCFOwSed0WzKzZs3sQmQr3qzb98+ea49e/a88O/s2LFD/s6hQ4d0WcOQIUO0WLFiaSdOnNDMZM2aNdrevXvDf58/f35t/vz54b8PCQmx1fNYid27d2u5cuWSn/Nnn32mPXz4ULMDf/75p5YvXz4tbty42rRp08xeDiGm6AzTvEFM8wI9zk3Bxx9/rNKlSycFSWYmExAV4rzMA/omMRPTA2wQ7fQ8VsLjltS9e3dpn4FfLrIhVgdZk+3bt6tGjRqp5s2bS6GS3UbSERIwmk0xMjLFzhvPtXbt2hf+ncuXL8vfWbRokW7rWLp0qTzHnDlzNCuAyDFz5syOeR4rsWvXLi1nzpwSpQ4dOlR79OiRZgemTJmixYkTRytQoIB26tQps5dDiGE6EzNwOXY+3kSmONfTMzIFVatWlYkybdu2VcWLF1dp06ZVZoLWiIjRYmRR5vDhwyP9OyEhIQE/j5PwVM2ilQaFPhjJ9/3337/wzN4qwNgB1cp4n+Irzn/ff/99s5dFiP5oNsXIyPTatWvyXAsWLIj0773yyivayJEjdV3LlStXtDRp0mhlypQxPVopV66cNmnSJMc8j1XZuXOnliNHDi127NjasGHDTP+5e/uZqV69unxuPv74Y+3BgwdmL4kQn+GZqQmRqZ69phFJmjSpjGaDCXnPnj2VmRgVMboxMo0ILAj3798vLVJoRUFl+dGjR5WVQXXvTz/9JNXn48aNE9ekM2fOmL0sQnSDaV4v7dSAkWPYIqN06dJyk0IxEoo/8NVoME0EqW1vCoECSfO+6HlQkIT2GGwuUPDiSbM7eUOHawSLSbRIoTgL7kndunUTpywrglGCnTt3FsP8unXrhqd9cVxBiOPQbIqRaV6AFNu4ceMi/Tvly5fXateubch6nj59qvXo0UOuwfjx4zWjuH79urSo4HUmSpRI0q/4M6OfB60ynhaa0NBQzU3cvXtX6969uxYtWjStSJEi2rFjxzQ7pH2rVasm79du3brZpu2HuJubPugMxdRLEiZMGOV5aL169bTSpUtrRgFBxXkUrsOAAQO0J0+eaG4AAurmM1QP27Zt01577TWpnh0xYoT2+PFjzcrg/Tp27FgtZsyYWtGiRbXTp0+bvSRCIoVnpibNNE2ePLm6fPmyoWm0UaNGiT8qrOhq1qyprly5opwO+jGROsZZ6oIFC+TXbgRnp5g80759e9WrVy9VokQJdeLECWVV8H7Fua/HLB9p32XLlpm9LEKCAsXUhzFsVhNTzw2qT58+aunSpWrz5s0qZ86cMmXGpi6RXoHzURRfoSgJLRhOPy+N6n05evRotWXLFtlIwc4Pv49s9q4VCqpw5g3xR9sMTCrs4ElMSGRQTIMcmeKGZsYUjSpVqkiFJ6omGzZsqAoUKCC9iTBRJ86nWLFiEqWiB7lHjx7yPvj999+VVUGx3uLFi2Ua0pdffil906GhoWYvixC/oZgGUUxTpEghEYFZEzRSpUolac+NGzeql19+WdK+GC6OUV8w67dytEICJ168eCJOaJv6559/VN68edXYsWMt+3NHVqVr165q27ZtsglF2nfWrFlmL4sQv6CYBjkyBUanep+lVKlSkvJFKg2tFJMmTZLzNazv3XfflbTwnDlz1M6dO9WFCxc4j9JhIH2K+aht2rSR1hm8H06ePKmsCua5oo8WKV9MoGnatKkKCwsze1mEOHMEG8ZU4RFxNE769OkNGcEG3nnnHTGah2HCizh27JicWULIcEOzCkj1Yhj1L7/8ovbs2SMiCxGNGCHgGmLUEL7iHA69izFixPjP1+jRo8vXiI9n/wy/R28uvleCBAnkq+cBQUcEnTJlSomkiL7gvQjzeRT8oNcXPcn4+ViVGTNmqHbt2sl7BGf/KDYjxA4j2KzZ7f0ccCNAk7rV07xWiEyfBUKIxnk8PCAVfe7cOXGlwY0WbxbPA68TqUGIsOcrHohg8XsUi2Bjg1/j4fnziL/H90B0gQe+5/PObvHmhKhiU5QlSxYxZsBXPLJmzWrIJsnp4Oz04MGDkupHJS1mjk6dOlWurxVp0qSJTMtp0KCBZFOGDRsmE5OsvAEgBDAy9ZLq1auLICxfvvyFfwciEjt2bDV+/Hj10Ucf6b4mu4C3GH52+Jlho3Hx4sXwB4T87NmzUnyCB36eHjJmzChDsj0PnAHmyJGDN1Y/wVl6ixYt5LpjEHmHDh0sey0fPnwo1okjR45UFSpUEOckRKuEGIkjI1OkDT22fmZFplH1cOLGBHs7q0WmZoM0Mq4fHojeI5t8Am9jiCr6JQ8dOiRR1Q8//KD++usv+f94Q+OMDdELHmizSJYsmYGvxr7gqALXs3fv3mLzhyh12rRplpwNi03piBEjpP3pgw8+kI0Upua89957Zi+NkOdizW2pBYEQ3L17N8q/B7GgmAbWMoHxYyhEgRftzz//rM6fPy+ex+vWrRMhwFkriqrQDoQz2Ndff12MC2CsrvegAbuDKm9kTtavXy8ZAUT8+L1Vi9AQlWIDAC/iSpUqSco3YoaKEKtAMfUS3MDv3bsX5d8zw7jBLSJbpkwZOftbsmSJunTpkpjgo5UC54IorqpVq5ZEqeixhanDhg0baAYQybAERP6onEVRUtmyZeV6WhFsUFesWCFtPxB+ZCMOHz5s9rII+RcUUy9Bhau3YooeP6J/6hgTc2BQgSgVrR+nT59W3333nUSqqAqF+OJGjGIWiC6j1v9GqRMmTBBbxlOnTqk8efLI760YpeIIBT2pu3btkg0SqnwxOcmKayXuhGLqQ2TqTZqXkal5oGAJbSBoX8IZK9qBcDYIJyCkjSGs6Ln86quv/tUa5HYQlSJKxTVCuhznlNiYWBHYJaK9CwV+EFekgXEMQIjZUEyDLKY8M7VOJIPoZeDAgWrv3r1yw0XUhWgMXrDoGUZ6GGlDVBS7HfQDT5w4Ua1Zs0YKwN544w31zTffWDLyQ5YIUSlS++jtRkQ9b948s5dFXA7FVIczU7P8ecmLSZs2rQwRx9kb0vCoYoWAILrB/0OlK9LFbp1A4wFRKaJUpM9hnoDID73IVqR8+fKyVqy5Xr160qMasbWKECOhmPqwG0ZkGlVbLsQU/ahuvylbGUyZQeENhBWFTDhnRbW2x3kHN+aVK1e6dkgA2o++/fZbtXr1akmRI0rFRsOKLekoTJs7d660T6EwDVEqXJ8IMRqKqZd4rO/s6oJEXnwzxjnrqlWrJBU8ZMgQmb5TuXJlSQXD2xatGW4EUSkiv/r168sZZcWKFaWdxorFaIhK8XPCuTmyDGihgvEDIUZBMfVRTKNK9XrElBW99iN16tRynoqbMvyLISKoCoZhAIwiEMHeuXNHuQm4v0yePFn6fXE+aeWz1EyZMkk7FKxH0UaDFpojR46YvSziEiimPqR5QVRFSB7LMxa12BdEOhgHhiIXVAVj7ibS961atVJp0qSRile3RauYNoTeTqTAkQ5H8RbE1Wpg0EKvXr3Ur7/+KpEpzB7gpGTVMXTEOVBMfYxMoxJT7ORx/kYxdQaxYsVS1apVk/NVmBrA4ABOS4hWMTgAFnfeVHk7KUpF9IfMC9pUPvvsM0umU7EZQhU3WqOQ8sUUJysPSyf2h2Ia5DQvohqkC9nH6DyQRsSZKs4N4WuLQh2ct+JsFdGQVategw3OJDEvFSnxwYMHS/SH4fNWA5taRKVbt26VGgaI/5dffmnJFDWxPxTTIEemAKlARqbOjlZr1qwp1a7oycQkFlS7wjC+du3aUk1qxcrXYB97DB06VAwU8OtixYqpTp06WXKoN0a5QfyRpscYOjhjWdU6kdgXimmQz0wBIlOKqTuAgI4aNUoqgWEAgYIXuCwhWkMKOKrqb7uDdPfOnTvV6NGjpUALE4GQErfiZhhRKQz+kUFACw1MKpy+6SHGQTENcpoXUEzdB5yV2rZtK2KKiBXZCaSAM2TIoPr37y/9rE4FRT8wv0CBEnyRMc0Hpg9WrGiHwT+Kxxo1aiQ/L7T7nDt3zuxlEQdAMdUhzUsxdbeNIfozEZ2h4AXtNWPHjpX+RzgwYU6rU8HgAfTrop0IVn8QVgz1tlr0B+crpOWxVvQUo90HjlhWWyexFxRTndK8mFDCuYvuJlu2bGKqj8hnwIABatmyZSIw1atXV9u2bVNOBAV4MMxH2wwGeTdr1kw2F1Y8o0RUimi6Ro0acu6NiJpRKvEXiqkPRScxY8b0WkzBxYsXDVgZsTqJEyeWOayYxILWEkSnxYsXl8KYRYsWObK6FH25mN4DW0aPJSHOlq1m0QhrSZxtL126VO3fv1/OfBG1OvFnQvSFYqqD2b1HTNkeQyISJ04c9eGHH8q5Km7e2JyhKjhHjhxyA3disRKiU7zeNm3ayMD2QoUKyUxSq1G1alVJ+datW1esEzGWDpXahHgLxVSHMWweMeW5KXnRuSpu3mihQSUsKktRDIPKYFTF3r59WzmtOAvnxnAlQhq4aNGi4iJltQkviFKnTJkiw9JR8Zs7d26xJaR7EtFNTNEIjQ8FdpuYLoHf16lTR37thskxUZE0aVKJOiimJCrgH7tgwQJ1/PhxieLg1oNiJZghXL9+XTkJT1QKgcKUF0TkmPhitcIfz7B0FIzBmAI9tPT4JVGi+cH169fx7v/Pn+PP9u7dqxnBzZs35fnw1Shy5cqlde7c2au/mz59eq1v3766r4k4izNnzmgdOnTQ4saNqyVIkEDr1auXdvHiRc1pnDt3TqtRo4Z8ht99910tNDRUsyLbtm3TcuTIocWKFUsbPHiw9uDBA7OXRAzEF53xKzKF6wlSUs/DilV7Rqd5AdtjiD+gL3XcuHFSrITU79dffy02hnAXclKlKSwY4XGMs2OcVaLwZ9iwYZbz+UWRGAqTcN47aNAgia7h+UvIs/glpmvWrJHp9hHBOQPOHGCn5vY0L6A/LwmElClTqpCQEDm7Q+oXlbFZsmRRLVu2VH/88YdyCjg7Rgq1Q4cO6tNPPxWDenjpWs3jF57Mu3fvlvNupObhxeyWAQdERzGFcJYvX/5fv8cH3+k7Nm+reUH69OkdFUkQ84aXo0cVogov3OXLl6vs2bOLgw/OWZ1SoDRy5Ei5f8BQARNesGm4evWqshIQepz5YlIOrAnR7gNzCkL8FlMMTkY6F4UTeOADj2j1RalfN6Z5ka7DdBFCggFEpkePHurUqVNiBIFK4Jw5c4ptnxXnivrr87t9+3YZPo77CgqUUKhkpQIl9JujZxgFSnB8gvEDNjZWtE4kBuPrgeyaNWu0RIkSaWZjRgFS48aNtZIlS3r1d+fMmSPru3Hjhu7rIu7j/v372oQJE6TQLVq0aFr9+vW1I0eOaE7h77//1ho0aCCfodKlS1vytT19+lSbPn26ljRpUi1x4sTalClT5M+Ic9C1AAlRacGCBZUbwZmpt2leRKaA0SnRywACBUonT55UEyZMEHtCpB3hBeyENo5UqVKp2bNny9AAHJcgasU5pZV6cNEe+MEHH0i6/f3335fUNGa9OiX9TnzDZzFFOjfieamb8DXNCyimRG9RhWMPRBXpUQzphtlAvXr1HCGq8PVFShXnxkhvI/U7f/58S6V+kyVLJpaE69atk6JDCP/AgQPpze0yvBZTnJHCnAHFRqhqQ4TqNnwRU+ysYdxAMSVGiSpMVCCqmNMJtyGIKuzxYOZuZ1BN269fPzkbRlYMrwkia7UJPBg6DuFHGw3afCCqmzZtMntZxGpiiuIivEmwI8TOEMOP3YYvrTGY8Zg2bVqKKTGU2LFji3MPzOXh94vqU4gqHMpwo7cz6LddvHixVDRjc4/XhWKgO3fuKCsJP6p90ZuKiBVpX0ykuXLlitlLIzpDb16dWmMAK3qJmaLaqlUrEVVMqoHRCjyA0Qdu90i1cuXKksJGtPrFF1/IWLuFCxdaKvULEwpUXGNDg8lAaGfCz4HTaJwLxVSnNK9HTNlrSswWVRTGQFRh4o5eTogqCpXsXCiDCBAmDxBVpFOxSYC3MdLcVgEGD56B8DCnwK/hqOTGIzI3QDH1UUwxj/HRo0de/X1GpsRK/ZEY/4YbO85U0c+J6KlJkya2dlTC8ROGrsOWEK8NFc2IWK3kTpQiRQopUEKkinXBkhCOTzdu3DB7aSSIUEx9PDMFvrggnT9/niOciOXOVBHBoTp2/fr1UiGLcz0YQtgVzzxSWC9iCDkMLeD9a6XUL5ydkBnA+qZPny6pX6uZUhD/oZj6GJkCX9pjIKQ0vCdWrP7FTFFEpZihunLlSvXaa69JRbBdsynY7MKMHmfCiLpr1aolHuJWOiNGhqBr166SYi9durRq2rSpKlWqlKXWSPyDYqqjmGIuJcAEECeBPmO0SWF+LX6Nh2eubYECBWz3PG4GAtS5c2cVGhqqhg8fLtFctmzZJA35119/KTuSNWtWtWLFCnmgZuHNN99UHTt2VNeuXVNWAZX+c+bMkb59WBFijZidGhYWZvbSiL9oNsUMO8Ht27fLcx4+fNirv3/79m35+7Accwqwk4w4szZ//vza/Pnzw38fEhJiq+ch/+bWrVvasGHDxB4vTpw4Mr8X1n52BfNHR44cKbNhYfsHC8bHjx9rVrOGxDV/6aWXtDRp0ogVKW0JXTLP1K34GpnGjx9fRrHZucDjWVA0EbHHGJWJEcfx+TrsAFEmHno/D/HeUB+9mzg/7dOnjxTOeHrML1++rOx4RoyID9XMOFdt166dvK+sZKaAlDuuOc58UZyESmv0px44cMDspRFf0GyKGZHp77//Ls+5ceNGr/9N8eLFtYYNG2pOBJFj5syZ/fq3iCxbt26thYaG6vo8JDCuXbum9evXT3v55Ze1+PHja3369NGuXr2q2ZVff/1VK1KkiHyO69Spo50+fVqzGqtXr9Zy5MihRY8eXWvbtq125coVs5fkWm4yMtUHRJrAF8cVnN84KTKNCKwlnx0SHxU480SRC/oC0dDuTYTpz/OQ4JA4cWJx9EGkinNUmCTAiQheuXZs7ShcuLC0BaGadsuWLVLJjKIlK7XSwCrx4MGDUhg2a9YsOcMeP368tOUR60Ix1VlMs2TJIsUdTgTFE94WAmE+JUQU3qreiqg/z0P0AdZ4n3/+uYgqnJWQmsc8zyFDhqhbt24pOwEzBUx7QeoXxVfw0YWLkpUM9FH126VLF2lhqlmzpurUqZMMJ9+wYYPZSyMvgGLqh5j6MgYKkenVq1dtuYsPZsQYSCUlI1NlKQMCREzwxoUgIWqFqIaEhFjKI9fb82FsEDwuSjDQR5sKrBetdL3hXIXhIlgvzPThs3zmzBmzl0aeRbMpZpyZgrhx42pfffWV139/165dss49e/ZoTgJnnf4MifflrDSy58E5as+ePeX7Xb9+3ed1kOBw7tw5OdeLFSuWljx5cm306NHa3bt3NTuyatUqLVeuXPJ5/eCDD+S1WQlU+M6cOVMqfnEfGjBggHbnzh2zl+VobvqgMxRTH0F5/fDhw30q4MA6586dqzkBCBdaVGrXri0iN2nSJL/ELCpRjep50CrjaaHxVpiJfpw6dUpr2bKlFiNGDC1VqlSy4bx3755mNx49eqRNnDhRNgZoVfn000+1sLAwzUpgPZ988okWO3ZsLUOGDNqPP/7IVhqdoJjqSMaMGbW+ffv69G/Qszd06FDd1mRnIKoQSl+AgPr6b4gx/PHHH1rTpk2lEjVt2rTS14k+SruB+0rv3r2l1zZ16tTa1KlTLdefimtdrVo1uQ8WLVpU+uBJcGE1r468/PLLPp2Zes5NnVqEFCjoX4RXrC+giAln0DhLRWGTE8+j7QoK7tCbikHeOH+EZSGqUVHF/fDhQ2UXEiZMKI5QsP3D64B3Md53VioAwrXGfFes6cGDBzKRBj2qTnNcswsUUz+KkHwttMDNBBMtSHBIlCiRiDCKktBig98TawGfX7R1wHMWN/mPPvpI/gzFNN5OXbICaAP68ccfpZ0G5gooAKpWrZpUAlsFGDygaAqbGE+7Dwz/b968afbSXAXF1IDIFBMs4G5ilbJ7QowC73140B46dEh6PNFWg2kp06ZNs1Xf5FtvvaV27Nghwvrbb7+JkT5aV6zi94t2H5jmQ+ThpjRu3DjJiH3zzTe2us52hmLqR2Tqj5hev35dXbp0Sbd1EWJlID7z5s0TMwLY+SFtiggK5gl2udlHixYtfKg6WoKmTp0qgjVmzBhJs1rl/gRDDYhqlSpVJM2OYfA///wzN/M6QzH1IzL1Nc2LGwlAdEqIm8mdO7eccyO6w6+bNWsmm82ZM2faZu4vJu0gjQpDBfSm4sgB0TZew9OnT5VVptIg+kf6N2XKlKpSpUrq3XfflQwB0QeKqQFpXrj9wHAbzeHEOHBjQxoOo8RQAIbNDAzzMaAZJuL4PW6IKNi4cuWKrc7y7A5MEhYtWiQ/D7gPNWnSRDads2fPto2oQqQmTpwo58JwJ8JrgFMXHLusArIAGACPQiW4V2HU24cffqjOnz9v9tIcRzSU9CobAguzV155RQ7ZUXlnFBjsu3r1ap+jTNw8UIiBMwwSHJA2R2EX3HgglvgK4cR0EzzgPOVrpIA0GQqa4EmbKlUq2eGnS5cu/CsKUpDaQ3RCggciqIEDB8oMUogrUpVw+sFZoF3Ytm2bRKkoVsLsXbhCQWStAqqpYeU5ePBgCQhgpYgImwV8wdEZiqmP9O/fX/3www8+23k1aNBAXbhwwVKjn+wEBihv3rxZokqkCPfv3/+vM2iIHTIAELzkyZOHP5ImTSqj8+LGjSsPVGTiBo0oFGd1+IoHbi4410abDR6IaP/++28RZzzw64hnexkyZJAqbVSo4oFzKWyY8HzEf3bt2iWiijM+RKoQ1Vq1atlGVHE7XbJkiYgUNnqNGjUS/2Jswqx07xw1apTYQuLz0LdvXzlbxeeDBKAzmk0xy7Th888/15IkSeLzvxs8eLCWLFkyXdbkRG7cuCGuUR999JH2+uuvy88aj3Tp0mlVqlTR+vfvry1cuFA7evSoIU47T5480S5cuKBt27ZNmzZtmjjQ1KpVS8udO7dYuz27PowtW7BggeUs6ezCjh07tAoVKsg1xTXGzxo/Azs5KcFYBG5QcCrq2rWr5UapYeg7Pl9wrYKT0vTp0y1nTGE2dEDSkXHjxokriq/gZoD1Xrp0SZd1OYGzZ8+KDV25cuW0mDFjyvXKnj271qZNG2327NnaX3/9pVkR3ICOHTsmtm5wzXn33XfFNSeiwGJ2Jnxr4VJjR0cgs8DmBe8HXMe8efNqixYtspV13u3bt7XPPvtM5sG+8sorYkVqNe/iEydOyMbQs3FZsWKFra6xnlBMdQRRCZ734cOHPr9h8e9ghUf+D/z8YNVWunRpLVq0aGKYjohk/Pjx2pkzZzQ7g0j2p59+0nr06CFD4j0RLCIV/B6+rxs2bLClh63RbN68Wd4juH7wZV66dKmtbvjYRHfs2FE2ibBZnDJlikSvVssGlCxZUq7xO++8I4PU3c5Niql+wHwdz+uruTtSVAkSJJA0MdFkig48XCEwENEyZcrIRgXpXaeCDdju3bu1L7/8UqtZs6YcF+C9hGuA1z9kyBCJxHzdqLmJjRs3ht/wCxYsqC1fvtxWogo/3Xr16sn6X3vtNTnKsFL6GtcS1/SNN96QNSKjcvz4cc2t3KSY6sfKlSvlec+fP+/zv8VNAG9Ot4KdOFKhb731llxDnNMMGzbMteeKuInu379fGzNmjJyzJkyYUK4LviLt9t1331k2tW32DX/dunUS3XtE1W6R6r59+7RKlSrJ+t98803LpVZxdIHNbfr06WVoQbNmzWQykNu4STHVN92E5/Vnt9alSxctc+bMmtt48OCBNnnyZHntuHaIwnD2xWKH/242du7cKcVq2HAgYvfcbFHwhPee1VKDZgLxwbFJiRIl5Drly5dP0upWivSiYsuWLeHrL1asmLZp0ybNSuAIApmUFClSyBFM+/bt5fjCLdykmOq7o/R32PeMGTPk32LGqRtAuvKbb76RCBSvG9EWIjHiHaj+ROFV48aNpRIc1xCzXRs0aCDpwVu3bpm9REulf7FJ8xTR4PrYZbOGTQEGk+MsGOuvWLGiX/cXvQupkEXC+w9zXlEHYLXqZD2gmOqIp5DInx0k2jjwb5GicjK4OSDyxJkQoivc/A8fPmz2smwNoq1du3ZpAwYMkEjVU8iEVCGi/osXL5q9REuwdetWESNcH7RUzZo1y1aiinaqHDlyhG8+cc+wEqgVQdtX/PjxpQZk4MCBht+DjYRiqiM4w8Lz4ozDV/ChxptwxIgRmlNBgY3nLAtVub/99pvZS3Ikf/75pzZ27Fg5h8eZFjYtuO6jRo3SQkNDNbeDdHnlypXlfZgtWzbt+++/t02KHOvEejNmzCg/WxTqWe288p9//tE+/vhjaRNMmjSp3NPu3LmjOQ2KqY6g2hTPizSSP+BcpG7duprTwHXBeQpu6kizIW1FjLuxoVipatWqcnPD+7NAgQJygzt9+rTmZpAurVatmlwTnNmjJQVn+HYA/choEUuZMmX4eaU/hY96guJB9IHHjBlTequxXrtcX2+gmOq8a8TzojfSH3DWgD4zK1XuBQJex5w5c8TpBVE3KlPtEgE4kbCwMNnoofXG09datGhRiWKtdiM2EmRIateuHV5FjrN8u5hn4LwSZg9opcJmCf2qVqvy/uOPP7QmTZrIZhrXF+5PThBViqnO4CYFpx5/QAk/1u2EVBxuzu+99568nho1aoiDEbEOKFCaOXOmRKyIbHCjQ+Uooge3nrEeOnRIq1+/vlwLbGrxObaaI9GLwL0ObkooAsI9qHPnzmIJaCWOHDkSfn2dIKoUU53BGQEq2/zh6tWrsm6cidg5GkWVaeLEiSW1s2TJErOXRLwoHEHfIKwOkZLDWVzZsmXlz5xcQPIiYP+ISArXAVkVZFTscuaHI5VBgwaJPSFEFWeXVtscHT58WMwp7C6qFFOdQWFA3759/f73OFP88MMPNTty+fJlMZ7AtceHxQ3l8U4DP7Nvv/1WLOPwc0SrA6IJON+4zX3p5MmTWvPmzcXsPXny5NrQoUN9djczC6wTlpQw+cDPsHv37nJ+biUO21xUHSmmON/AC/I8cPBtlpjmypVLUiz+0q5dO6kwtBvwkUUkiogUTkbE/sD/GBaXeE/j8wRBwZkcfFmdcq7vbXV027Zt5UwS4gSTDLsMpUC2C+0qaFVB3UKvXr1k02slDttUVB0ppuiv80zhiPgwQ0wLFy6stWzZ0u9/DyHC2q123hFZjyPOapASQzRjteIHEjgQThhqIGWItKfHOxZuTBAatwB3HxQJYsoLor1OnTrZphYAGQdsAiCoWD9+bbXM0WGbiaojxdRKkSmcVpAW8xecb2DtmB9odbA7L1++vLz5kVKySwM88R/8jH/55Rc5U8SN2WN1h9SwW85XEe3hXBIVtDhjbtGihRi22AFEpYhO48WLJ6Las2dPy0XZhw4dkhZBj6hOmDDBktOTHCmmVjozff/998WYPBBgzm31flO4PCGti9Qfbq7EfaAtAy5CcBVCZgLRGuwN4eJlJw/cQFqNMIcWnwPc+PGZtYslJgQU83U9UTa8wa3WHnXo0KHwSBXXGKYjuOZWgWKqM7DHQ7oz0LQ1qvGsWPCBlN/XX38tO/JSpUoxrUsE3IhRxY7zfnz2UIiHbIUb0sDIjCEl6RnWABtHWBfaJcrG/QYtNbCg/Oijjyxn5nHixAkpBMM9B9kAHC9YoRCMYqozcPyAw0wgwGcV64dBt5XA+UXr1q1lbTgvogEDed5mC0KCinREPZ5h0ji2QCTrZPB5QKTumfcJO0e4fdmhWAstNdgMYWgCRAvi9fvvv2tW4vTp0+L0hEIwFFQhsjYzRU0x1RkUKARajYsUGWzC8L2sAt608HdFgz/s6QiJCojnDz/8oJUuXVo+j7gBQmQhtnYQmEA+v+ivLlKkiLxuTHyZP3++LWoK8DND6hqFZkjdN2zYUMwWrMTff//9n0IwM+YeU0x1BpWtEMJAadWqlZYpUyZL3HQwWg6DgPG6tm3bZvZyiA1BuhfpRKR/PQbz6Nu02jldMMFnd/369Vq5cuXCXzPSwVYspnkWrBFuWPjc48zSiiMSr0ZIUWOTj3smrAuNgmKqMxiWi91SMAp88BowINhM4K2L14PUtV3aAIi1ozYUKKFQCe8rRD8o2Fu8eLElawSCBY5uYGiC14th2thI2GF2MY52MMbPcx6Mn5XVNtQ3b96UfmhcV1zfRo0aaQcOHDDkeSmmOgILNjx3oDcG3HRQFo4zWDPA8/fp00deC1I9dvEoJfYB53QTJ06U6nW8z5BaxDkYnIecCl4bDCBg9YfWoq5du4o5hh3Og2fMmCFzYPGzgo8zRk1aIXPmAfco+Cnjvok1whscdSd6rZFiqjMLFy6U50YKIlDQWA1HIaMnWOC6wQAd6Z2QkBBLfWCIM0EKsUOHDpKyw+cH56wo5rFDStTfGgQ4E+HzjYIf9O0ePHhQszrYZCOL4DkPhv0pBiZYqRjx4cOHclbvKQTDWn/66aegt2tRTHVmzZo18tzBGNgLw218L7xZjQIVfNh9wjbNnyHnhAQaXeD97vEGhtjAwtCItJ0ZoG/yiy+++Fc0BWtOq29gsT5EfRiOgHWjvgNnrFYaCPD06VPxlEYUjTXmyJFDiieDFZxQTHUGvqV47mB9+CtUqCBpMCM+XKtXr5bIAFZxEHJCzAQbO7j1oPANn6lChQpJAY8TnZYQTWETkSdPnvDXapcKYGQV0F+P80q01qAI02rnwdu3bw8fBJ8mTRqZbBUoFFOd8USTmzdvDsr3+/nnn3XvOYVQoxweHwbsjK3QEE1IRKFZtGiRVrlyZXmPwgoPfZC4QVo9gvMVvB70psKWFJ/7LFmyyLByO9QsYA4zBnXgPBhtK/ByNqNlJTKOHj0q7x0cxwUKxVRn4AiE50Z6IRggz48+NfR46nHjwJkUzmuwZvh02mEnTNwLbs6IfJBWxHs2Z86cMm/UapNQgsHu3bvFotAT8cFRymqzSZ8H1ojiRbi4oWWlRYsWImJOg2JqQNMznjsYaYRno9OlS5dqwa4shFBjJ2nkuSwhwdhkoj4BYoMbNh74NXyineYLjN5JFGchIof7D4wvMGHF6uD+O3LkSPHVxf0LmQX03Tolm0Ax1Rm8UbCTRMl/ML8nprOg4T1YRs9z584VRxqkkWDKQIhdQVSK6BRRqqcYBtGr1VKMgYJzSPRT4swPrxMDBlDnYHVxun//vrQMeqprsYFHpbbd+4oppgaAIp4RI0YEfXeKJnd44wYCxBi9q7g+mMjgxGIO4k4gKjAUwJkYojinGkLASAGZpHz58snnGMPbUaVq9Taip/87D0ZRJdadLl06iVzRb2xHKKYGgDJ39JAFG8yMxOuCI4k/IC2GXTtEGUUNVt/REuIv+Ow/awiBvm0j7eaMak/B2Ef0hMMBCHNW//nnH83qHDhwQGvatKmk55Ehg3mF1abVRAXF1ACQzoD5sh5gRBJ23GhK9sUXFS5GnmZ4J91QCPGmdQPTRlAQg88AKmVR02D1SM7XMWWopMVGGeeq8Km1mkH9iwo2PeY0MWLE0OrXry+FV3aAYmoAb7/9ttasWTNdvjeKK1CAgNeHG0RkbSz4MMG6DLs/FAFMmTKF0ShxLWgvwSYUo9Hw+cFszM6dO8sQaqdw5coVGaXmKfpBqxsyUlb/3N++fVsbN25cuAcwfkaYvGPlYjKKqQHAFaRmzZq6fX98MPDGw7kQdtstW7aUMxP04uFmgZ0ejOlxDTym2k6fJUmILxw/flzGeCVPnlw+J0WLFpXNZrAK/Kxwrop7Qd68ecNbiJD2tvp94PHjx9IDioAE686aNasMD7FibQfF1ABQoo+xS0akSNDPlT17dnm9ngd2pUiXoGIXHypCyPPB52PBggWyAca5I8wGkCKFk5nVozlfxsDVqFFDjodQHNm9e/eg2J3qzY4dO+Q+Bu9inKvi6MxKQxAopgaASLFw4cKGp7CQ4nHKzpoQo0EBDOZjYoYn7h+w9sMUkmAMrbACEFBE4xBUCGv16tVt0fd5/vx5rW/fvmJcgQ0PKrTRT2z2un3RmeiK+EXChAnVrVu3DH3Ol156SSVNmlS9/PLLhj4vIU4hY8aMauDAgerUqVNq5cqVKmvWrOrjjz9WadKkUY0bN1YbN25EgKHsSqZMmdSIESPU+fPn1TfffKNOnjypypQpo/LkyaMmT56s7t69q6xI2rRp1ZAhQ9S5c+fUd999J18rVKigcuXKpSZOnKju3LmjrA7F1EZiSggJDjFixFDvvfeeWrhwody4Bw8erHbt2qVKly6tsmfPrkJCQtSlS5eUXYkfP75q3bq1OnTokFq3bp3KkiWLatOmjUqXLp3q1auXOnPmjLIicePGVc2bN1f79++Xjc3rr7+u2rdvL+vu2bOnZdctaDbF7DQv3Fhw9kIIcVZPZ+PGjaX1BOd4OIfEmEIn+FnDpL5bt25S0IgUMAoo9RysHczUNc6APalrrHvTpk2GrNsXnYmG/ygbgqjwlVdeUTdv3pQo0WiQimjZsqV6/Pix7HKJu3ny5Im6du2aunr1qrp9+7a6f/++evDggXzFw/M+ifiIFSuWpOwTJEgQ/hWPOHHimP1yXM/169fVrFmzJDV68OBBiYxatGghD6SK7QzenzNnzlRfffWVOnbsmMqdO7fq0KGDatiwoaWPkO7cuaNmzJjxr3Ujam3UqJFu6/ZFZyimfjJ//nxVt25ddePGDVkHcS74iFy8eFEdPXpUnT59Wh5IN+Er/vzKlSvyPgjWRylevHgqRYoUKmXKlPLV82uc6+FG7nmY8b53G/iZ7tmzR02ZMkXNnj1bbug4y2vVqpWqWrWqih07trLza0MKGOK0fPly2cg1bdpUtWvXTuXIkUNZed1r165VX3/9tVq2bJkIabNmzWTdSNEHE4qpAaxevVq9++67clPNkCGD4c9P9OHp06ey692xY4ec2xw+fFgeiDpBtGjRwkUNxR74dbJkyaQwzPMVNyWc/UR8IBJF9Brx8ejRI4kSwsLC/vXAc/3zzz9yZoevnl9fuHBB/o2HRIkSyTpeffVVuYl4HrgRJkmSxMSr6Ezws5o3b55Eqzt37lTJkycX8UGGKtg3caPBxvDbb7+VTcPly5fl7BjiVK1aNcmgWJUzZ86oSZMmyc8Em9ry5ctLtFqlSpWgZAwppgaAm+3bb78tB/xvvPGG4c9Pgiee+/btk83Rli1b5CaJ91T06NFFlJBKws8Xj5w5c4qAmhWNQIARCeMGEvERGhqqTpw4oc6ePRv+dyHsuMGjgAOVnHnz5pWvEGASONhgQXiQdsTmp0SJEhKt1qpVSzILdgVHEyjKmjBhgtq2bZtKnTq1FDLhtaHi1qrcv39fsoWIVn/99VcJcIYPHy6p60CgmBrAkSNH5Aa7detWVaxYMcOfnwT23kF6aMWKFWrNmjWyo0WqCDdEbJDeeustVbhwYYkw7QTaHtAKAWE9fvy4fEVqGo+HDx/K30EkC2H1PPLlyyeRLSJu4t9NfPHixRIZrV+/Xu5JaLFBtPrmm28qO3PgwAFpr8H5Kl5n9erVJVpF1Grl98uePXtEVBGdYnMTCBRTA/jrr7+kKAE35EqVKhn+/MQ3kD6FgCJNt2rVKtmB58+fX1L1FStWFAG1cjorEJAahrji5hjxgfSxJ4rF5sHzKFSokPwZ8Q1kCFCYOG3aNMkgFChQQCK6Bg0a2Pp8G/dYROCIVnEEgoxN27Zt1QcffOD4TMctiqkxUQB6ubBrQzUZsR54ayNti7OguXPnqnv37qmiRYtK4Vjt2rVV+vTplZvBDX/v3r1q9+7d0mOJB6qRQebMmVWRIkVEXBGtI4J16mYj2KByG4YQiFbxFWfmeM9BWLFps3JUF9XnadOmTSKqixYtkuMO3PsgrPny5VNOhGJqALhsaGEYM2aMlJUT64CNzvfffy8feqTjcc6JtBvSb3Zva9D7Pf3nn3+GCyvOnnCejCge54DYiBQvXlzS4fi1ldsorAIyWIhUEbGiyAdRHSpPmzRpIsVrduXvv/+WM2MU/+A1FixYUM5W69evb7vjkaDpjGZTzDZtAJjWMnjwYNOen/wbDEz+9NNPtaRJk0pzd61atbTVq1dbesSTHUzid+7cqY0cOVIGVGOkGT53mEuJodxdunSRCSB2GFZtJngPwmu2QYMGWty4ceX9WalSJW3+/Pna/fv3Nbvy6NEjbfHixfJaPEMEWrdure3Zs0dzAjS6NwhMcsH0eGIuuJHj54CbFAYnd+jQQYalE31EATN0J02aJE5BmTJlCp9klDt3bpkdihmVkc3gdTu4Nt98840MysB1w+YP01Iw4NzOnDlzRjazadOmldeVP39+GQlnxdFq3kIxNQjMR9RrQDiJGvzs8eHFbhjjm/Dry5cvm70s13Hu3Dlt5syZWosWLbSMGTPK5xKRV6FChbRevXpJdsDqMzbNAhsTWOWlTJlSrtubb74psz3t/D5GtLps2TKtatWq8j6IHz++TNnatWuX5a0Ln4ViahCYcF+tWjXTnt+twCcVO17s6OGhCr9RO998nAayApMnT5aUpkckYsWKpZUoUULGn23ZskV7+PCh2cu0FLgeS5cuFS9geALjeuGYYvny5SJOdt5oDRo0KHzkHQaZf/3119qNGzc0O0AxNYiGDRtqJUuWNO353QjO7woUKCA/+w8++EA+rMS6IBJB9DVu3DgRCpiV42eXMGFC+T02RXYYYm30scXYsWNl1iquVerUqbWePXtqx44d0+y8AV6xYoUEHzhvjxcvnta8eXMZDm7laJViahDt27eXcyKiP9jJtmrVKjwVtm3bNrOXRPy8qf76669SuFesWDG5seJn+tprr2kdO3aUSIwp4f8PRGbv3r1SA+Ap/MLREs6r7RLZvWgQ+GeffaZlyJBBXlPOnDm1UaNGaRcvXtSsBsXUIPr16yfpC6IvqILEdca56Pjx4x0xDov8XzEOqoFRAeo5b40dO7ZWpkwZLSQkRPvtt98sHbkYBSp+582bJ0dLOIdEoV2jRo20tWvX2rZa/fHjx9qqVau0unXrys8c6e3q1atLutsqqW2KqUGMHj2aM0115NatW1qbNm3k51y2bFnt9OnTZi+J6AhE8/jx41KAg1YLpALxs0+VKpUU+qGNxM6VocGM7IYPHy7RPK4PNpqffPKJrdPAV65ckaOAfPnyhf/MrZDappgaxNSpU2UNLKYIPmgTyJo1q1QCTpgwgdGJS6OxdevWaT169JBUID5riF5Kly4taUHcaN38vsBrx3HHRx99FH4WjQpqiJKdC/L27dsnKf/EiRPLa3r77be1KVOmyObaaCimBrFo0SJZAxvWg3uDQFEKqnSxS/3999/NXhKxCChUQpofqU70FOOzlzlzZrnxIl147949zc0bjwULFoixBjYceODX+DO7mkLcu3dPmzt3rlaxYkUxhECmAhmKzZs3G7aJopgaxMaNG2UNJ06cMG0NTuLOnTvSToFr2rZtW1ffHEnU7xUUK+F94ilkwc0WvY3YjLm5yhube0SniFJxXRDhIXrdvn27bSP5s2fPStESNk94TdmyZdOGDRsmKW89oZgaxIEDB2QNaNcggYGbHxxTcEOcM2eO2cshNgICcejQIe3zzz+XXlZPhTBaS3CWuHXrVtcWrR09elSuQbp06eSa4OgEfZ+hoaGaHXny5Im2YcMGrUmTJlKEhWIsRK6zZ8/W7t69G/Tno5gaaJ+FNfz888+mrcEJYDOCggMUUqB6k5BAuHbtmvbjjz+K3SGMPfAZTZYsmaQIf/rpJy0sLExzGxAhnD/jGqBoEtcEGw+Ya9i1zebGjRuy/uLFi4f3LsNpCaYgwYrAKaYGgQNxrAG7IuIfqNDE+ehbb71lyT4zYm8QkaJIp3fv3uFFTHi/oVoY/rh6pwmtCPp4Yf9YoUIFiexwPdCegrS5XYspT548qfXv3z+8vSpLlizarFmzAv6+FFODwO4HKSXYYxHfQZUuCgtwTmrXIgliv5vumDFjtHfeeSc8HQxHLaQ+UUFu1zNFf8FmYsSIEVquXLnCI/h27drJBsSO1+LJ/9LAnlaqQKGYGgjefEOGDDF1DXYDH9KBAwfKzw9TRuzadE7snw5G9FKvXj1JEXp6NiEmqA520wYPn0m0pMB03zP1BROB+vTpI3aQbuWmDzrD4eAB8tprr6n3339fjRo1yrQ12Am83Tp37qzGjRunhg0bpnr37q2iRYtm9rKIy3n48KHavHmzWrp0qTzOnDkjw8/fffdd+XxXqlRJJU2aVLmBJ0+eqC1btqhZs2apBQsWqBs3bqi8efOqRo0ayfDv9OnTK7dwywedoZgGSJEiRdQbb7yhvvvuO9PWYBfwVuvQoYOaMGGCmjRpkmrdurXZSyLkue/Tw4cPhwvrrl27VPTo0VWxYsVEWPHAJtoNPHjwQP38889q9uzZatmyZfL7kiVLirDWqlVLJUmSRDmZWxRT48DONV68eOqnn34ybQ12E9IpU6aoDz/80OwlEeIVf//9t1qxYoUI65o1a9T9+/dV9uzZVdWqVUVY3377bRUjRgzldHDPxX0Owrpu3Tp5zYjYIaxVqlRRL730knIaFFMDadiwobpw4YLauHGjaWuwi5B+8803avLkyRRSYlvu3r2r1q5dK1EaHpcuXZL0L8QEwlqhQgVJD7thgzFv3jxJBe/evVslSJBA1axZU+6HZcqUUTFjxlROgGJqIJ06dVIbNmxQhw4dMm0NVgfnoiEhIYxIiaN4+vSppIA96eAjR46oOHHiqLJly4qwInJNkyaNcjonT56UaBXCil+nTJlS1a1bV85XixYtKilyu0IxNZDBgwdL6vLixYumrcHKjBw5UvXs2VN98cUXUnhEiFMJDQ0NF1YU8KCQp2DBgqpatWoirrlz53Z0sZ2maWrv3r0iqohakbFDsRKEtV69enIt7Pb6KaYGgtRlx44d1aNHj2z3RtGbadOmqRYtWqi+ffuqIUOGmL0cQgzj2rVrUrizZMkStWrVKhUWFqYyZcoUXsCEIp5YsWIpJ0ftW7duVXPnzpWK4H/++UdlzpxZRBWPPHny2OJ+STE1kPnz58vOCx+exIkTm7YOq4HzpOrVq6tWrVrJhsMOHxxC9AAVsJs2bQqPWs+dOyf3rvfee0+iVhQxJkqUSDmVx48fy+ufM2eOFDDhXokCLo+w5syZU1kViqmBoPCodOnS6vfff1fZsmUzbR1W4rffflPFixeXYgxsNtxQ6UiIN+B2i8+HR1j37dsnxTqlSpUKj1oRwTqVR48eSQEXItZFixbJfRzpb4+wZs2aVVkJiqmBoOgAfabbtm2TEnm3g3OSwoULq1SpUsluNH78+GYviRDLgigVWRwI6/r160VskAL1CGuBAgVsXcATGWgxWr16tQgrXv+dO3fk9UJUke3LmDGjMhuKqYGgNB7CsXjxYknZuL1tADtslM2jytENlYyEBPOeBnGBsKCv9fr16/IZ8vSzouUkbty4yqn3jpUrV0oqGK8dQotKYIhq7dq1TXNdopgafB6AQgK3t33gbYQ3Pj4QKDzIly+f2UsixLbgvoJsFwqY8Pjzzz8ly1OxYkUR1sqVK6tkyZIpJxIWFibROiJWFG/B6hFOcxBVuC69+uqrhq2FYmowsNRC+wf6Kd3eAoMCgxo1api9HEIcA27Rx44dk4gVwvrrr79KQR+OlTxtN061N7x165Zavny5VASjOhoRK1LBderUEWHV+4yVYmowHmsxt5rdw7SiXLlyIqbDhw83ezmEOBr0tCMVCmGNaG/oOWd96623HFn0FxYWJpkvCCte/71799Sbb74pESvEVY8NBcXUYGCAjR3S9OnTldv466+/VP78+aUIC+c9TrERI8RO9oaIWpEaRT8n0r8R7Q2dWAR4584dSQFDWPG68XtUBUNY8QhWuw3F1GDQT4kqPOyW3ATOMt555x2pSITzSYoUKcxeEiGuBY5LEe0Njx49KvaGyBpBWCGwTiwKvHfvnmzkIax43YhgX3/9ddW/f3/VoEEDw3TGmTXXBpM8eXJ1+fJl5TZ69eql9uzZI29iCikh5oLULlK8OGpByx563zEz+Pbt26pt27Yqbdq00rY2dOhQ8RK3aRz1HzCtBgHNzJkzJTKHoBYqVMjwLBkj0yDwySefSOUZKu7cAooBMH5p7NixqkuXLmYvhxASCVevXpXzRggN0qMQWFTFes5ZS5Qo4Wh7Q39hZGowbotM0VvbrFkzsUOjeT0h1gdj4po0aSKOZFeuXBFBhY0hskqYcoN7GManoc8TwkF8h2IaBHDgj50equqcDgysIaQeI3t67hJiL3COin5VTLvy1Dsgu4T2G5wx4n5Wvnx5NW7cOHXmzBmzl2sbKKZBALs6gB2f08EHDLtaVC5jbiEhxL5gM4xq/IEDB6r9+/eLeGJcIiwMu3XrJj7BaD/p16+f2rFjhxQ5EZufmWLyAh4Rc9mwmLLCmSkmzeNgH6bVTnb+OXjwoBzst2/fXo0ZM8bs5RBCdAT3Vo+9IWokMO0FUSvSw3BgQnTr9ElZjmyNwc5p0KBB//lzK4jp2bNnxZQZbzi80ZwIWn9g6YWvqOBFqogQ4g4Qke7cuVPa//DAxhrVw3BhQstN5cqVpbfTacc+jhRTK0emWBcMqKdOnaqaN2+unMhnn30mmxlYmcHOixDiXnDWiupgCCtMI+7duycBBUQVD4ylRMuK3XFkNS8iIbyYiA8rrQ3VcpiW4kSwC4WYwnuYQkoIQSDTpk0bSQF72m6qVKkiXyGmuB/CYnXixIkivG7ANpGplftMAays4AaEAh0nwfQuIcRXU/4VK1aIQT0m3yBFjPujJx2M0Wp28Q52ZGRqdVKnTu3IyPTzzz+XyPT777+nkBJCIiVatGhydtqjRw+1adMm6b9H7yoqgidPnqyKFy8ubmmNGjVSs2fPlqImp0BX8iCK6R9//KGcBLw9kd6FbSDTu4QQX0mcOLGqV6+ePBChovMBESsiV4gpWnBggQgDGDwguvgzO8I0b5DAeeK8efMcYykIcwakrTHuCZEpCqwIISSYE6dW/q+Iad26dWJ8g951tNxAWGEcgbNXu+gMI9Mgp3mxN3FCeTjSulu2bJE3OYWUEBJs0qZNq1q1aiUPTKDC+SoMYdBi+MMPP0iEiv59tBtCXJEds/JZKyPTIIGoFKmM69evq0SJEik7g3OOHDlyiJH9jBkzzF4OIcSFUeuqVavkgQHouM8jSkXUCnHFVyMmVTmyz9TqYooormTJknLOiFl6dgbeuyh5P378OEerEUJM5fHjx2IYgYgV4gqnOYBIFRErxBUdB3qMXGM1r0lpXmD3it6NGzeK725ISAiFlBBiOjFjxpQqYMxhhSk/7rG4R2XLlk3M+vH/4I9et25dGb5x4cIFU9bJyDRI3LlzR7388ssyoBZl33YE5xZ58uQR/83NmzfbtqqOEOIOnvyvQthz1opfQ9Ly5s2revbsKWPlAoEFSCYQP358lSBBAltHpl9++aW092DmIYWUEGJ1YsSIISYQeMC/HZO7cMYKYdUj7RsZFNMgYmfjBrTAoKe0Xbt24lZCCCF2I1myZDKTFQ+jYfgRRNKkSWNbMf3kk09U7NixZXdHCCHENxiZBllMz58/r+wGzhnQV4rD/CRJkpi9HEIIsR2MTINIhgwZZLap3ZyOOnXqJIVHrVu3Nns5hBBiSxiZBhHM80NkigozKzt1RGTWrFnSw7VhwwbbrJkQQqwGI9MgiykajM3qc/KVsLAwMbGvXbu2+PASQgjxD4ppkNO84MyZM8ou49Vgfzhy5Eizl0IIIbaGYhrkyNQuYgrvy7Fjx6quXbuqTJkymb0cQgixNRTTIAIHJFTD2qEIadCgQeqll16SNC8hhJDAYAGSDtGp1SNTGNh/9913atSoUWKVRQghJDAYmbpQTGHQkD59enE7IoQQEjgUUx2KkKwsptu3b1eLFy9WQ4YMUXHixDF7OYQQ4ggopjpFplYcxoM14YwUExUCnaZACCHk/+CZqQ5ievfuXXXt2jWZDG8lli9frrZu3SoTFTgVhhBCggfvqDq1x5w+fVpZCbgy9e7dW5UpU0ZVrFjR7OUQQoijoJgGmcyZM8vX0NBQZSUwmf7o0aNi1BAtWjSzl0MIIY6CYhpk0GeK9O7JkyeVVbh375769NNPVd26dVWhQoXMXg4hhDgOiqkOZMuWTf3+++/KKowbN05dunRJDR061OylEEKII6GY6iSmVolMUQg1fPhw1aZNG5U1a1azl0MIIY6EYupwMcUZ6aNHj1T//v3NXgohhDgWiqlOYnrlyhV148YNU9dx7tw59dVXX6nu3burlClTmroWQghxMhRTncQUmB2dougI3rvdunUzdR2EEOJ0KKY6iumJEydMW8OhQ4ekHQaCmiBBAtPWQQghboBiqgMJEyYUI/kjR46YtoY+ffpIz2urVq1MWwMhhLgF2gnqRO7cudXhw4dNee7NmzeLdeCcOXNU7NixTVkDIYS4CUamOvHGG2+YIqYeM/sCBQqoOnXqGP78hBDiRiimOoop/HnDwsIMfd5FixapnTt3qpCQEJrZE0KIQfBuq6OYAvjhGsXjx49l8DeM7MuWLWvY8xJCiNuhmOpEjhw5JDJEVa1RfPfdd9KOA6MGQgghxkEx1YmXXnpJZc+eXe3fv9+Q57t9+7YaMGCAaty4sXrzzTcNeU5CCCH/H4qpjmBCy+7duw15rtGjR4vj0meffWbI8xFCCPk/KKY6UrBgQXXgwAH18OFDXZ/n4sWLauTIkapTp07hw8kJIYQYB8VU58gUQqr3uenAgQOlnxTFR4QQQoyHYqojefPmVTFjxtQ11Xvs2DE1ZcoU1a9fP5U4cWLdnocQQsiLoZjqXIQEJyT0feoFolFYF7Zv31635yCEEBI5tBPUmRIlSqhly5bpZhu4ZMkSNWvWLBUnThxdnoMQQkjUMDLVmXfeeUedOnVKnT17NugGDR07dlSFCxdW9evXD+r3JoQQ4hsUU50pWbKkfN20aVNQv+/kyZPVwYMH1bhx42gbSAghJsO7sM4kTZpUzk03btwYtO959epVKThq0aKFRKaEEELMhWJqAOXLl1erVq1ST58+Dcr369+/v6R5hw0bFpTvRwghJDAopgbw/vvvqwsXLqh9+/YF/L3wPSZNmiS9pSlTpgzK+gghhAQGxdQAihUrJj2gS5cuDej7PHr0SH344YcykaZDhw5BWx8hhJDAoJgaAIwbKleurBYuXCjDu/1l1KhRUnSE6TCxYsUK6hoJIYT4D8XUIBo1aiSzTffu3evXvz9+/LgaNGiQ6tatm3j+EkIIsQ4UUwOLkNKmTaumTp3q87+Fvy9Gq8HpCGelhBBCrAXF1CBixIihmjZtKm5FN2/e9NkyEOndOXPmqHjx4um2RkIIIf5BMTUQ+Oc+ePBAjR8/3ut/s3jxYjVmzBg1YsQIVaBAAV3XRwghxD8opgaSJk0a1bJlSxHHa9euedUGg7PWWrVqqc6dOxuyRkIIIb5DMTWYvn37qidPnqiPP/440r935MgRValSJZUrVy71ww8/qGjRohm2RkIIIb5BMTWY1KlTq7Fjx6rp06fLHNLnsWPHDjHIhynD8uXLeU5KCCEWh2JqAs2aNZPz09atW4sl4L179+TPL1++rPr06SPm+NmzZ1cbNmxQKVKkMHu5hBBCoiCaFoiLgIncunVLvfLKK1IZmzBhQmU34NMLs/qQkBAVN25clSxZMnXu3DkZKN69e3f5fzRmIIQQe+gMxdRkQkNDpWL3xo0b6tVXX1VVq1ZVyZMnN3tZhBDiem5RTAkhhBDjdIZnpoQQQkiAUEwJIYSQAKGYEkIIIQFCMSWEEEICJKayCfC0xcODxyweB8SEEEJIsPHoizd1urYR0+HDh8s8z2fBWDJCCCFEL8LCwqSq1xGtMc9GpjA9gFl80qRJA/atxe4DogzTBLbZvBheJ+/htfIeXivv4HUy/lpBHiGkGFISPXp0Z0SmceLEkUdEEiVKFNTnwEXnmzRqeJ28h9fKe3itvIPXydhrFVVE6oEFSIQQQkiAUEwJIYSQAKGY/i+FPGDAgP+kkcm/4XXyHl4r7+G18g5eJ2tfK9sUIBFCCCFWhZEpIYQQEiAUU0IIISRAKKaEEEJIgFBMCSGEkAChmBJCCCEBQjElhBBCAoRiSgghhAQIxZQQQggJEIopIYQQEiAUU0IIISRAKKaEEEJIgFBMCSGEkAChmBJCCCEBQjElhBBCAoRiSgghhAQIxZQQQggJEIopIYQQEiAUU0IIISRAKKaEOJhevXqpaNGiqTZt2qg///wz/M9v3LihChQooMqXL6/Wrl1r6hoJcQLRNE3TzF4EIUQ/IKZ79+5V+fPn/9efjxgxQvXs2dO0dRHiJBiZEuJwMmfO/K+oFCAarV27tmlrIsRpUEwJcaGY4vf4c0JIcKCYEuJwIJqhoaHhv//2229V69atTV0TIU6DYkqIw8mSJUt4ZMqIlBB9oJgS4qI074IFC1S5cuXMXhIhjoNiSohLxBRCyqIjQvSBYkqIw/Gkda9du8YULyE6wT5TQlwADBrQa0oI0QeKKSGEEBIgTPMSQgghARIz0G9ACLGujaAvMElFiP9QTAlxKBRHQoyDaV5CCCEkQCimhBBCSIBQTAkhhJAAoZgSQgghAUIxJYQQQgKEYkoIIYQECMWUEEIICRCKKSGEEBIgFFNCCCFEBcb/A302W9O0cFbwAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "from matplotlib.transforms import offset_copy\n", + "\n", + "# May cause problems in Colab or installations without LaTeX\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Good PDF defaults\n", + "mpl.rcParams.update({\n", + " \"pdf.fonttype\": 42, # keep text as text in PDF\n", + " \"ps.fonttype\": 42,\n", + "})\n", + "\n", + "# Function to make plot labels\n", + "def label_curve(\n", + " ax,\n", + " x, y, text,\n", + " *,\n", + " dx=0, dy=3, # offset in points\n", + " ha=\"left\", va=\"bottom\",\n", + " fontsize=9,\n", + " bbox=True\n", + "):\n", + " \"\"\"\n", + " Place a text label in data coordinates with a point offset.\n", + " \"\"\"\n", + " transform = offset_copy(ax.transData, fig=ax.figure, x=dx, y=dy, units=\"points\")\n", + "\n", + " bbox_kw = None\n", + " if bbox:\n", + " bbox_kw = dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\")\n", + "\n", + " ax.text(float(x), float(y), text, ha=ha, va=va, fontsize=fontsize, transform=transform,\n", + " bbox=bbox_kw)\n", + "\n", + "# Make the plot\n", + "fig, ax = plt.subplots(figsize=(5.0, 4.5)) # choose size you like\n", + "\n", + "# Range of reduced molar volumes\n", + "Vr_max = 3\n", + "Vr_min = 0.5\n", + "Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + "# plot the labeled lines, 0.95, 1.0, 1.05\n", + "Tr = 0.95\n", + "ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n", + "label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T < T_c$\", dy=15)\n", + "\n", + "Tr = 1.0\n", + "ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n", + "label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T = T_c$\")\n", + "\n", + "Tr = 1.05\n", + "ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n", + "label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T > T_c$\")\n", + "\n", + "# plot several isotherms above the critical temperature\n", + "for Tr in np.array([0.9, 1.1]): \n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n", + "\n", + "plt.ylim([0.4,1.4])\n", + "plt.xlabel(r\"$\\underline{V}$\", labelpad=15)\n", + "plt.ylabel(r'$P$', rotation=0, labelpad=20)\n", + "\n", + "fig.tight_layout()\n", + "\n", + "ax.tick_params(\n", + " labelbottom=False,\n", + " labelleft=False\n", + ")\n", + "\n", + "# ---- SAVE HIGH-QUALITY PDF ----\n", + "fig.savefig(\"pdf/Fig_6.6-1.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ce9572ad", + "metadata": {}, + "source": [ + "# Figure 7.3-1 Isotherms of the van der Waals equation in the pressure-volume plane\n", + "\n", + "This figure is similar to figure 6.6-1, but it labels the curves differently." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b3546598", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "from matplotlib.transforms import offset_copy\n", + "\n", + "# May cause problems in Colab or installations without LaTeX\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Good PDF defaults\n", + "mpl.rcParams.update({\n", + " \"pdf.fonttype\": 42, # keep text as text in PDF\n", + " \"ps.fonttype\": 42,\n", + "})\n", + "\n", + "# Function to make plot labels\n", + "def label_curve(ax, x, y, text, *, dx=2, dy=3, ha=\"left\", va=\"bottom\", fontsize=9, bbox=False):\n", + " # Place a text label in data coordinates with a point offset.\n", + " transform = offset_copy(ax.transData, fig=ax.figure, x=dx, y=dy, units=\"points\")\n", + "\n", + " bbox_kw = None\n", + " if bbox:\n", + " bbox_kw = dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\")\n", + "\n", + " ax.text(float(x), float(y), text, ha=ha, va=va, fontsize=fontsize, transform=transform,\n", + " bbox=bbox_kw)\n", + "\n", + "# Function to label local minimum and maximum for isotherms below Tc\n", + "def label_loop_extrema(ax, Vr, P, *, label_min=\"A\", label_max=\"B\",\n", + " dy_min=-8, dy_max=6, marker=True):\n", + " # numerical derivative\n", + " dP = np.gradient(P, Vr)\n", + " s = np.sign(dP)\n", + "\n", + " # sign flips\n", + " imax = np.where((s[:-1] > 0) & (s[1:] < 0))[0] + 1 # + to - : local max\n", + " imin = np.where((s[:-1] < 0) & (s[1:] > 0))[0] + 1 # - to + : local min\n", + "\n", + " if len(imax) == 0 or len(imin) == 0:\n", + " return None # no loop/extrema found (near/above critical)\n", + "\n", + " iB = imax[0] # local maximum\n", + " iA = imin[0] # local minimum\n", + "\n", + " if marker:\n", + " ax.plot(Vr[iA], P[iA], \"o\", ms=4, color=\"black\")\n", + " ax.plot(Vr[iB], P[iB], \"o\", ms=4, color=\"black\")\n", + "\n", + " label_curve(ax, Vr[iA], float(P[iA]), label_min, dx=-2, dy=dy_min, \n", + " ha=\"left\", va=\"top\", bbox=False)\n", + " label_curve(ax, Vr[iB], float(P[iB]), label_max, dx =-2, dy=dy_max, \n", + " ha=\"left\", va=\"bottom\", bbox=False)\n", + "\n", + " return (Vr[iA], P[iA], Vr[iB], P[iB])\n", + "\n", + "# Make the plot\n", + "fig, ax = plt.subplots(figsize=(5.0, 4.5)) # choose size you like\n", + "\n", + "# Range of reduced molar volumes\n", + "Vr_max = 3\n", + "Vr_min = 0.5\n", + "Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + "\"\"\"\n", + "Plot five isotherms\n", + "\"\"\"\n", + "label_horiz_Vr = 2\n", + "\n", + "# These are the labels for the sub-critical isotherm minima and maxima\n", + "extrema_labels = {\n", + " 0.9: (r\"$A$\", r\"$B$\"),\n", + " 0.95: (r\"$A'$\", r\"$B'$\"),\n", + "}\n", + "\n", + "for k, Tr in enumerate([0.9, 0.95, 1.0, 1.1, 1.2], start=1):\n", + " P = rvdw_P(Vr, Tr)\n", + " ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n", + "\n", + " # label the isotherm itself\n", + " i = np.argmin(np.abs(Vr - label_horiz_Vr))\n", + " label_curve(ax, Vr[i], float(P[i]), rf\"$T_{k}$\", dy=2)\n", + "\n", + " # label loop extrema for the subcritical ones\n", + " labels = extrema_labels.get(Tr)\n", + " if labels is not None:\n", + " label_loop_extrema(\n", + " ax, Vr, P,\n", + " label_min=labels[0],\n", + " label_max=labels[1],\n", + " dy_min=15,\n", + " dy_max=5\n", + " )\n", + "\n", + "# Mark and label the critical point\n", + "plt.plot(1, 1, \"o\", ms=4, color=\"black\")\n", + "label_curve(ax, 1.0, float(np.asarray(rvdw_P(1.0, 1.0)).squeeze()), \n", + " \"C\", dx = -2, dy=6, bbox=True)\n", + "\n", + "# Plot scaling and axes labels\n", + "plt.ylim([0.4,1.4])\n", + "plt.xlabel(r\"$\\underline{V}$\", labelpad=15)\n", + "plt.ylabel(r'$P$', rotation=0, labelpad=20)\n", + "\n", + "fig.tight_layout()\n", + "\n", + "# Hide the tick labels\n", + "ax.tick_params(\n", + " labelbottom=False,\n", + " labelleft=False\n", + ")\n", + "\n", + "# ---- SAVE HIGH-QUALITY PDF ----\n", + "fig.savefig(\"pdf/Fig_7.3-1.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0acfc455", + "metadata": {}, + "source": [ + "# Fugacity calculation for VLE\n", + "\n", + "Next, we will build the vapor-liquid equilibrium line using a fugacity calculation. This will give us the vapor and liquid molar volumes at the vapor pressure. We use this to draw tie lines through the vapor-liquid equlibrium." + ] + }, + { + "cell_type": "markdown", + "id": "cbffc9d7", + "metadata": {}, + "source": [ + "## Fugacity calculation for the van der Waals equation of state\n", + "\n", + "The fugacity of the van der Waals equation of state is\n", + "\n", + "$$ \\ln \\frac{f}{P} = (Z-1) -\\ln (Z-B) - \\frac{A}{Z} $$\n", + "\n", + "First we define a function that evaluates the equation. Then we define a function to calculate the residual of the vapor and liquid fugacities." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "38cd8c8e", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"Fugacity coefficient of the van der Waals EOS\n", + "Returns the natural log of the fugacity coefficient\n", + "\"\"\"\n", + "import numpy as np\n", + "\n", + "def fugacity_vdw(Z,A,B):\n", + " return (Z-1) - np.log(Z-B)-A/Z" + ] + }, + { + "cell_type": "markdown", + "id": "fa8878ef", + "metadata": {}, + "source": [ + "### Residual calculation\n", + "\n", + "The following function calculates the residual between the liquid and vapor fugacities from the EOS. We will use this and Newton's method to solve\n", + "\n", + "$$ \\ln \\frac{f^V}{P} - \\ln \\frac{f^L}{P} = 0$$\n", + "\n", + "After defining the function, we test it with a calculation.\n", + "\n", + "Newton's method will fail if the the reduced pressure guess is too far off. In this case, the pressure will be outside of the van der Waals loops of the isotherm. We can see this using the calculation above and noting the local maximum and minimum (reduced) pressures from the isotherms we plotted earlier.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a8782881", + "metadata": {}, + "outputs": [], + "source": [ + "# Function that returns the residual of the fugacity calculation\n", + "def residual_lnphi(Pr):\n", + " \"\"\"\n", + " Returns ln(phi_L) - ln(phi_V) at given the reduced pressure Pr.\n", + " At P_r^sat, this should be zero.\n", + " As written, requires globals Tr\n", + " \"\"\"\n", + " \n", + " A = 27*Pr/64/Tr**2\n", + " B = Pr/8/Tr\n", + "\n", + " # All compressibility roots\n", + " V_real = rvdw_V(Pr,Tr)\n", + " Z_real = V_real*Pr/Tr*3/8\n", + "\n", + " ZL = np.min(Z_real) # liquid root (smallest Z)\n", + " ZV = np.max(Z_real) # vapor root (largest Z)\n", + "\n", + " ln_f_L = fugacity_vdw(ZL, A, B) # ln(phi_L)\n", + " ln_f_V = fugacity_vdw(ZV, A, B) # ln(phi_V)\n", + "\n", + " return ln_f_L - ln_f_V" + ] + }, + { + "cell_type": "markdown", + "id": "b02b7331", + "metadata": {}, + "source": [ + "## Create a dataframe of the resulting VLE\n", + "\n", + "With a method for calculating the vapor-liquid equilibrium line using fugacity, we construct a dataframe of the values. The dataframe will be a table that gives the equilibrium temperature, pressure, and molar volumes of the liquid and vapor in reduced values. We also include the vapor and liquid compressibility factors.\n", + "\n", + "We use a large number of points to get close to the critical point. Each guess of the vapor pressure for a higher isotherm is the previous vapor pressure. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3f46e5d9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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10000 rows × 6 columns

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" + ], + "text/plain": [ + " T P vL vV zL zV\n", + "0 0.620000 0.104701 0.438683 14.146629 0.027781 0.895866\n", + "1 0.620038 0.104737 0.438695 14.142255 0.027789 0.895842\n", + "2 0.620076 0.104773 0.438707 14.137883 0.027798 0.895818\n", + "3 0.620114 0.104809 0.438719 14.133512 0.027806 0.895794\n", + "4 0.620152 0.104845 0.438731 14.129143 0.027815 0.895770\n", + "... ... ... ... ... ... ...\n", + "9995 0.998848 0.995400 0.936057 1.072259 0.349809 0.400709\n", + "9996 0.998886 0.995551 0.937057 1.070984 0.350223 0.400278\n", + "9997 0.998924 0.995702 0.938076 1.069691 0.350644 0.399840\n", + "9998 0.998962 0.995854 0.939116 1.068376 0.351073 0.399394\n", + "9999 0.999000 0.996005 0.940177 1.067041 0.351509 0.398941\n", + "\n", + "[10000 rows x 6 columns]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "from scipy.optimize import newton\n", + "\n", + "# Temperature, pressure, and volume are in reduced units\n", + "\n", + "# Example temperature grid\n", + "# Many points are used to keep the solver working near the c.p.\n", + "T_min = 0.62\n", + "T_max = 0.999\n", + "n_T = 10000\n", + "\n", + "T_list = np.linspace(T_min, T_max, n_T)\n", + "\n", + "rows = []\n", + "P_guess = 0.2 # A good guess for Tr close to 0.7\n", + "\n", + "for Tr in T_list:\n", + " Psat = newton(residual_lnphi, P_guess)\n", + "\n", + " V_roots = np.array(rvdw_V(Psat, Tr), dtype=complex)\n", + " V_real = V_roots[np.isreal(V_roots)].real\n", + " V_real = V_real[np.isfinite(V_real)]\n", + "\n", + " if V_real.size == 0:\n", + " rows.append({\"T\": Tr, \"P\": Psat, \"vL\": np.nan, \"vV\": np.nan})\n", + " continue\n", + "\n", + " vL = V_real.min()\n", + " vV = V_real.max()\n", + "\n", + " zL = vL*Psat/Tr*3/8\n", + " zV = vV*Psat/Tr*3/8\n", + "\n", + " rows.append({\"T\": Tr, \"P\": Psat, \"vL\": vL, \"vV\": vV, \"zL\": zL, \"zV\": zV})\n", + " P_guess = Psat\n", + "\n", + "df_eq = pd.DataFrame(rows)\n", + "df_eq" + ] + }, + { + "cell_type": "markdown", + "id": "a7184f6c", + "metadata": {}, + "source": [ + "# Figure 7.3-2 A low-temperature isotherm of the van der Waals equation\n", + "\n", + "Here we reconstruct Figure 7.3-2, which shows an isotherm below $T_c$.\n", + "\n", + "This is a busy plot. We have to identify and label points on the curve. Several helper functions are defined in order to create the labels." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1fa98126", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\" \n", + "These are helper functions for generating plot 7.3-2\n", + "\n", + "find_loop_extrema -- finds the local min and max of the isotherm\n", + "draw_loop_extrema -- labels the local min and max\n", + "root_between_extrema_bisect -- finds the unstable solution molar volume\n", + "label_bottom_axis -- routine for adding bottom axis labels\n", + "label_left_axis -- routine for adding left axis labels\n", + "\"\"\"\n", + "\n", + "\n", + "# --- Find the local maximum and minimum along a van der Waals loop\n", + "def find_loop_extrema(Vr, P):\n", + " \"\"\"\n", + " Find local minimum (A) and local maximum (B) on a vdW loop.\n", + "\n", + " Returns a dict with:\n", + " - iA, VA, PA : index/coords of local minimum\n", + " - iB, VB, PB : index/coords of local maximum\n", + " or None if no extrema are found.\n", + " \"\"\"\n", + " Vr = np.asarray(Vr)\n", + " P = np.asarray(P)\n", + "\n", + " dP = np.gradient(P, Vr)\n", + " s = np.sign(dP)\n", + "\n", + " imax = np.where((s[:-1] > 0) & (s[1:] < 0))[0] + 1 # + -> - : max\n", + " imin = np.where((s[:-1] < 0) & (s[1:] > 0))[0] + 1 # - -> + : min\n", + "\n", + " if len(imax) == 0 or len(imin) == 0:\n", + " return None\n", + "\n", + " iB = int(imax[0])\n", + " iA = int(imin[0])\n", + "\n", + " return {\n", + " \"iA\": iA, \"VA\": float(Vr[iA]), \"PA\": float(P[iA]),\n", + " \"iB\": iB, \"VB\": float(Vr[iB]), \"PB\": float(P[iB]),\n", + " }\n", + "\n", + "# --- Given a minimum or maximum, label the point on the curve\n", + "def draw_loop_extrema(ax, extrema, *, label_min=\"A\", label_max=\"B\",\n", + " dx=-2, dy_min=-8, dy_max=6, marker=True, bbox=False):\n", + " \"\"\"\n", + " Given the output of find_loop_extrema, draw markers + labels on ax.\n", + " \"\"\"\n", + " if extrema is None:\n", + " return None\n", + "\n", + " VA, PA = extrema[\"VA\"], extrema[\"PA\"]\n", + " VB, PB = extrema[\"VB\"], extrema[\"PB\"]\n", + "\n", + " if marker:\n", + " ax.plot(VA, PA, \"o\", ms=4, color=\"black\")\n", + " ax.plot(VB, PB, \"o\", ms=4, color=\"black\")\n", + "\n", + " label_curve(ax, VA, PA, label_min, dx=dx, dy=dy_min,\n", + " ha=\"left\", va=\"top\", bbox=bbox)\n", + " label_curve(ax, VB, PB, label_max, dx=dx, dy=dy_max,\n", + " ha=\"left\", va=\"bottom\", bbox=bbox)\n", + "\n", + " return extrema\n", + "\n", + "# --- Routine to find the unstable molar volume where P = Pvap\n", + "def root_between_extrema_bisect(Tr, Pvap, VA, VB, *, tol=1e-10, max_iter=200):\n", + " lo, hi = (VB, VA) if VB < VA else (VA, VB)\n", + "\n", + " def f(V):\n", + " return float(np.asarray(rvdw_P(V, Tr)).squeeze()) - Pvap\n", + "\n", + " flo, fhi = f(lo), f(hi)\n", + " if flo == 0.0: return lo\n", + " if fhi == 0.0: return hi\n", + " if flo * fhi > 0:\n", + " return None # not bracketed\n", + "\n", + " for _ in range(max_iter):\n", + " mid = 0.5 * (lo + hi)\n", + " fmid = f(mid)\n", + "\n", + " if abs(fmid) < tol or (hi - lo) < tol:\n", + " return mid\n", + "\n", + " if flo * fmid < 0:\n", + " hi, fhi = mid, fmid\n", + " else:\n", + " lo, flo = mid, fmid\n", + "\n", + " return 0.5 * (lo + hi)\n", + "\n", + "from matplotlib.transforms import blended_transform_factory\n", + "\n", + "# --- Routine to label x-axis\n", + "def label_bottom_axis(ax, x, text, *, dy=-10, fontsize=9):\n", + " trans = blended_transform_factory(ax.transData, ax.transAxes)\n", + " text_trans = offset_copy(trans, fig=ax.figure, y=dy, units=\"points\")\n", + "\n", + " ax.text(\n", + " x, 0.0, text,\n", + " transform=text_trans,\n", + " ha=\"center\",\n", + " va=\"top\",\n", + " fontsize=fontsize\n", + " )\n", + "\n", + "# -- Routine to label y-axis\n", + "def label_left_axis(ax, y, text, *, dx=-5, fontsize=9):\n", + " trans = blended_transform_factory(ax.transAxes, ax.transData)\n", + " text_trans = offset_copy(trans, fig=ax.figure, x=dx, units=\"points\")\n", + "\n", + " ax.text(\n", + " 0.0, y, text,\n", + " transform=text_trans,\n", + " ha=\"right\",\n", + " va=\"center\",\n", + " fontsize=fontsize\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "ce25198f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "\n", + "# May cause problems in Colab or installations without LaTeX\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Good PDF defaults\n", + "mpl.rcParams.update({\n", + " \"pdf.fonttype\": 42, # keep text as text in PDF\n", + " \"ps.fonttype\": 42,\n", + "})\n", + "\n", + "# Make the plot\n", + "fig, ax = plt.subplots(figsize=(5.0, 2.5)) # choose size you like\n", + "\n", + "\"\"\"\n", + "Plot one isotherm and add plot annotations\n", + "\"\"\"\n", + "# Range of reduced molar volumes\n", + "Vr_min = 0.5\n", + "Vr_max = 2.1\n", + "Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + "# Plot the isotherm and label it\n", + "Tr = 0.95\n", + "P = rvdw_P(Vr, Tr)\n", + "ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n", + "\n", + "i = np.argmin(np.abs(Vr - label_horiz_Vr))\n", + "label_curve(ax, 0.8*Vr_max, rvdw_P(0.8*Vr_max, Tr), rf\"$T" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "\n", + "# May cause problems in Colab or installations without LaTeX\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Good PDF defaults\n", + "mpl.rcParams.update({\n", + " \"pdf.fonttype\": 42, # keep text as text in PDF\n", + " \"ps.fonttype\": 42,\n", + "})\n", + "\n", + "# Make the plot\n", + "fig, ax = plt.subplots(figsize=(5.0, 2.5)) # choose size you like\n", + "\n", + "\"\"\"\n", + "Plot one isotherm and add plot annotations\n", + "\"\"\"\n", + "# Range of reduced molar volumes\n", + "Vr_min = 0.5\n", + "Vr_max = 2.1\n", + "Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + "# Plot the isotherm and label it\n", + "# Plot from Vr_min to vL\n", + "# at Pvap from vL to vV\n", + "# from vV to Vr_max\n", + "\n", + "Tr = 0.95\n", + "P = rvdw_P(Vr, Tr)\n", + "\n", + "i = np.argmin(np.abs(Vr - label_horiz_Vr))\n", + "label_curve(ax, 0.8*Vr_max, rvdw_P(0.8*Vr_max, Tr), rf\"$T" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib as mpl\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.transforms import offset_copy\n", + "import numpy as np\n", + "\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "# Good PDF defaults\n", + "mpl.rcParams.update({\n", + " \"pdf.fonttype\": 42, # keep text as text in PDF\n", + " \"ps.fonttype\": 42,\n", + "})\n", + "\n", + "fig, ax = plt.subplots(figsize=(6.0, 4.5)) # choose size you like\n", + "\n", + "# plot several isotherms above the critical temperature\n", + "for Tr in np.arange(1, 3.5, 0.5):\n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min, Vr_max, 1000)\n", + "\n", + " P = rvdw_P(Vr, Tr)\n", + " ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n", + "\n", + " # Label at Vr=8.5 using the already-computed curve (scalar-safe)\n", + " Vlab = 8.5\n", + " i = np.argmin(np.abs(Vr - Vlab))\n", + " Plab = float(np.asarray(P[i]).squeeze())\n", + "\n", + " text_transform = offset_copy(ax.transData, fig=ax.figure, y=3, units='points')\n", + " ax.text(\n", + " float(Vr[i]),\n", + " Plab,\n", + " rf\"$T/T_c = {Tr:.1f}$\",\n", + " ha=\"left\",\n", + " va=\"bottom\",\n", + " fontsize=9,\n", + " transform=text_transform,\n", + " bbox=dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\"),\n", + " )\n", + "\n", + "# plot several isotherms below the critical temperature\n", + "for Tr in np.array([0.7, 0.8, 0.9]):\n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min, Vr_max, 1000)\n", + "\n", + " row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n", + " P = row[\"P\"]\n", + " vL = row[\"vL\"]\n", + " vV = row[\"vV\"]\n", + "\n", + " ax.plot([vL, vV], [P, P], color=\"black\", linewidth=1)\n", + "\n", + " text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n", + " ax.text(\n", + " 0.5 * (vL + vV),\n", + " P,\n", + " rf\"$T/T_c = {Tr:.1f}$\",\n", + " color=\"black\",\n", + " ha=\"center\",\n", + " va=\"top\",\n", + " transform=text_transform,\n", + " )\n", + "\n", + " # Above vapor line\n", + " V = np.linspace(row[\"vV\"], Vr_max, 1000)\n", + " ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n", + "\n", + " # Below liquid line\n", + " V = np.linspace(row[\"vL\"], Vr_min, 1000)\n", + " ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n", + "\n", + "# coexistence lines behind\n", + "sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"gray\", linewidth=1,\n", + " ax=ax, linestyle=\"--\", zorder=0, legend=False)\n", + "sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"gray\", linewidth=1,\n", + " ax=ax, linestyle=\"--\", zorder=0, legend=False)\n", + "\n", + "ax.set_xlim(.01, 10)\n", + "ax.set_ylim(0, 1.4)\n", + "ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n", + "ax.set_ylabel(r\"$P/P_c$\")\n", + "\n", + "fig.tight_layout()\n", + "\n", + "# ---- SAVE HIGH-QUALITY PDF ----\n", + "fig.savefig(\"pdf/Fig_7.3-4.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2b4181bf", + "metadata": {}, + "source": [ + "# Exercises\n", + "\n", + "1. Plot the van der Waals PV diagram on a log-log scale.\n", + "2. Locate and plot the spinodal in addition to the binodal." + ] + }, + { + "cell_type": "markdown", + "id": "ec213591", + "metadata": {}, + "source": [ + "# Extra figures\n", + "\n", + "Here we build plots of the van der Waals EOS vapor-liquid equilibrium using different scales and incorporating the isotherms with the van der Waals loops. We draw tie lines for several reduced temperatures below the critical temperature in color and grayscale." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8a37ffca", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib as mpl\n", + "\n", + "# This line can cause problems in Google Colab\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "\n", + "# plot several isotherms above the critical temperature\n", + "for Tr in np.arange(1, 3.5, 0.5) : \n", + " Vr_max = 10\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n", + "\n", + "# plot several isotherms below the critical temperature\n", + "for Tr in np.array([0.7, 0.8, 0.9]) : \n", + " Vr_max = 10\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n", + "\n", + " # tie lines given Tr\n", + " # This finds the closest tie line in the dataframe\n", + " row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n", + " P = row[\"P\"]\n", + " vL = row[\"vL\"]\n", + " vV = row[\"vV\"]\n", + " ax.plot([vL, vV], [P, P], color=\"magenta\", linewidth=2) \n", + "\n", + "# Plot the vapor coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"blue\", linewidth=2, ax=ax, legend=False)\n", + "\n", + "# Plot the liquid coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"red\", linewidth=2, ax=ax, legend=False)\n", + "\n", + "#ax.grid(color='gray', linestyle='--', linewidth=0.5, alpha=0.7)\n", + "ax.set_xlim(.01, 10)\n", + "ax.set_ylim(0, 1.4)\n", + "ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n", + "ax.set_ylabel(r\"$P/P_c$\")\n", + "ax.set_title(r\"$P-V$ diagram for van der Waals EOS\")\n", + "\n", + "#ax.set_xscale(\"log\")\n", + "\n", + "#plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "18b7a6d0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib as mpl\n", + "\n", + "# For label spacing on tie lines\n", + "from matplotlib.transforms import offset_copy\n", + "\n", + "# This line can cause problems in Google Colab\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# plot several isotherms above the critical temperature\n", + "for Tr in np.arange(1, 3.5, 0.5) : \n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n", + "\n", + "# plot several isotherms below the critical temperature\n", + "for Tr in np.array([0.65, 0.8, 0.9]) : \n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n", + "\n", + " # tie lines given Tr\n", + " # This finds the closest tie line in the dataframe\n", + " row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n", + " P = row[\"P\"]\n", + " vL = row[\"vL\"]\n", + " vV = row[\"vV\"]\n", + " ax.plot([vL, vV], [P, P], color=\"magenta\", linewidth=2) \n", + "\n", + " text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n", + "\n", + " ax.text(\n", + " 0.5 * (vL + vV),\n", + " P,\n", + " rf\"$T_r = {Tr:.2f}$\",\n", + " color=\"black\",\n", + " ha=\"center\",\n", + " va=\"top\",\n", + " transform=text_transform\n", + " )\n", + "\n", + "# Plot the vapor coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"blue\", linewidth=2, ax=ax, legend=False)\n", + "\n", + "# Plot the liquid coexistence line\n", + "sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"red\", linewidth=2, ax=ax, legend=False)\n", + "\n", + "ax.set_xlim(.4, 14)\n", + "ax.set_ylim(0.1, 2)\n", + "ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n", + "ax.set_ylabel(r\"$P/P_c$\")\n", + "#ax.set_title(r\"$P-V$ diagram for van der Waals EOS\")\n", + "ax.plot(1,1,\"mo\")\n", + "\n", + "\n", + "#ax.set_xscale(\"log\")\n", + "\n", + "#plt.legend(frameon=True, fancybox=True, edgecolor='none')\n", + "#plt.tight_layout()\n", + "\n", + "ax.set_xscale(\"log\")\n", + "ax.set_yscale(\"log\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b1cb7c4f", + "metadata": {}, + "source": [ + "## Grayscale, log-log scale\n", + "\n", + "Notice that the \"equal areas\" of the van der Waals loop is more difficult to see on this scale. One of the interesting things about this plot is the shape of the binodal along the vapor curve and the fact that, far from the critical point, the vapor isotherms as they approach the binodal behave nearly ideally. That is an assumption made deriving the Clausius-Clapeyron equation." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c50cde2b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import seaborn as sns\n", + "import matplotlib as mpl\n", + "\n", + "# For label spacing on tie lines\n", + "from matplotlib.transforms import offset_copy\n", + "\n", + "# This line can cause problems in Google Colab\n", + "mpl.rcParams[\"text.usetex\"] = True\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# plot several isotherms above the critical temperature\n", + "for Tr in np.arange(1, 3.5, 0.5) : \n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n", + "\n", + "# plot several isotherms below the critical temperature\n", + "for Tr in np.array([0.65, 0.8, 0.9]) : \n", + " Vr_max = 14\n", + " Vr_min = 0.4\n", + " Vr = np.linspace(Vr_min,Vr_max,1000)\n", + "\n", + " ax.plot(Vr, rvdw_P(Vr,Tr), '',label=Tr, color=\"gray\", linewidth=0.5)\n", + "\n", + " # tie lines given Tr\n", + " # This finds the closest tie line in the dataframe\n", + " row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n", + " P = row[\"P\"]\n", + " vL = row[\"vL\"]\n", + " vV = row[\"vV\"]\n", + " ax.plot([vL, vV], [P, P], color=\"black\", linewidth=1) \n", + "\n", + " text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n", + "\n", + " ax.text(\n", + " 0.5 * (vL + vV),\n", + " P,\n", + " rf\"$T_r = {Tr:.2f}$\",\n", + " color=\"black\",\n", + " ha=\"center\",\n", + " va=\"top\",\n", + " transform=text_transform\n", + " )\n", + "\n", + " # Plot the isotherm above the vapor line\n", + " V = np.linspace(row[\"vV\"],Vr_max,1000)\n", + " plt.plot(V, rvdw_P(V,row[\"T\"]), color='black', linestyle='-', linewidth=1)\n", + "\n", + " # Plot the isotherm below the liquid line\n", + " V = np.linspace(row[\"vL\"],Vr_min,1000)\n", + " plt.plot(V, rvdw_P(V,row[\"T\"]), color='black', linestyle='-', linewidth=1)\n", + "\n", + "# Plot the vapor coexistence line\n", + "sns.lineplot(data=df_eq, \n", + " x=\"vV\", y=\"P\", \n", + " color=\"gray\", \n", + " linewidth=1, \n", + " ax=ax, \n", + " linestyle=\"--\",\n", + " zorder=0,\n", + " legend=False)\n", + "\n", + "# Plot the liquid coexistence line\n", + "sns.lineplot(data=df_eq, \n", + " x=\"vL\", y=\"P\", \n", + " color=\"gray\", \n", + " linewidth=1, \n", + " ax=ax, \n", + " linestyle=\"--\",\n", + " zorder=0,\n", + " legend=False)\n", + "\n", + "ax.set_xlim(.4, 14)\n", + "ax.set_ylim(0.1, 2)\n", + "ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n", + "ax.set_ylabel(r\"$P/P_c$\")\n", + "\n", + "ax.set_xscale(\"log\")\n", + "ax.set_yscale(\"log\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/module 7/vdw_report.tex.j2 b/module 7/vdw_report.tex.j2 new file mode 100644 index 0000000..d06f7d0 --- /dev/null +++ b/module 7/vdw_report.tex.j2 @@ -0,0 +1,25 @@ +((*- extends 'latex/index.tex.j2' -*)) + +% ---------- Remove code cell prompts ---------- +((* block input_prompt *))((* endblock input_prompt *)) +((* block output_prompt *))((* endblock output_prompt *)) + +% ---------- Document metadata ---------- +((* block title *)) +\title{Van der Waals Equation of State} +((* endblock title *)) + +((* block author *)) +\author{Eric Furst} +((* endblock author *)) + +((* block date *)) +\date{\today} +((* endblock date *)) + +% ---------- Code font size ---------- +((* block packages *)) +((( super() ))) +\usepackage{fancyvrb} +\fvset{fontsize=\footnotesize} +((* endblock packages *)) diff --git a/test code/Ternary Diagram Practice.py b/test code/Ternary Diagram Practice.py new file mode 100644 index 0000000..cbd2809 --- /dev/null +++ b/test code/Ternary Diagram Practice.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Tue Apr 29 12:12:56 2025 + + +Plots the water, acetone and n-octane ternary diagram at 25 °C as calculated +by Aspen Plus. + + +@author: lobo +""" + +import numpy as np +import matplotlib.pyplot as plt +import mpltern + + +data_set = np.loadtxt("WaterAcetoneOctaneEquil.csv", delimiter = ',', skiprows=2) + +water = data_set[:,1] +acetone = data_set[:,2] +octane = data_set[:,3] + +ax = plt.subplot(projection='ternary') + +ax.plot(acetone, octane, water) + +#Tie Lines +ax.plot([0,0],[0.9989768, 2.43E-06], [0.00102325, 0.9999976], 'b') +ax.plot([0.1248013,0.1403329],[0.8706273,0.000389155],[0.00457142,0.8592779], 'r') +ax.plot([0.2102607,0.3371009],[0.7798967,0.00720065],[0.00984261,0.6556985], 'k') +ax.plot([0.2552231,0.5722035],[0.731291,0.055398],[0.0134858,0.3723985], 'g') +ax.plot([0.4018703,0.6527512],[0.5729588,0.2466414],[0.0251709,0.1006074], 'c') + +ax.grid() + +ax.set_tlabel("Acetone") +ax.set_llabel("n-Octane") +ax.set_rlabel("Water") + + +plt.show() diff --git a/test code/WaterAcetoneOctaneEquil.csv b/test code/WaterAcetoneOctaneEquil.csv new file mode 100644 index 0000000..b12e6f8 --- /dev/null +++ b/test code/WaterAcetoneOctaneEquil.csv @@ -0,0 +1 @@ +NUMBER,MOLEFRAC WATER,MOLEFRAC ACETO-01,MOLEFRAC N-OCT-01 ,,, 1,0.00102325,0,0.9989768 1,0.00313195,0.0887932,0.9080748 1,0.00581823,0.1496758,0.844506 1,0.00844799,0.1915717,0.7999803 1,0.0102965,0.2160187,0.7736848 1,0.0114953,0.2308099,0.7576948 1,0.0126262,0.2446168,0.7427569 1,0.0141047,0.2629019,0.7229934 1,0.016268,0.2900783,0.6936536 1,0.0195717,0.3322021,0.6482261 1,0.0251668,0.4018477,0.5729855 1,0.0273743,0.4267799,0.5458458 1,0.031737,0.4666277,0.5016353 1,0.0689948,0.6182799,0.3127253 1,0.0849716,0.639267,0.2757613 1,0.1006058,0.6527549,0.2466392 1,0.1713427,0.6670415,0.1616157 1,0.2516352,0.6426541,0.1057108 1,0.3384626,0.5947338,0.0668036 1,0.4302309,0.5301969,0.0395722 1,0.5263484,0.4525658,0.0210858 1,0.626094,0.3644045,0.00950154 1,0.7256479,0.2709878,0.00336432 1,0.8196334,0.1795186,0.000847999 1,0.9070264,0.0928556,0.000117929 1,0.9999976,0,2.43E-06 \ No newline at end of file diff --git a/test code/ternary.ipynb b/test code/ternary.ipynb new file mode 100644 index 0000000..42584d9 --- /dev/null +++ b/test code/ternary.ipynb @@ -0,0 +1,104 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "044f4353", + "metadata": {}, + "source": [ + "# Ternary plot practice" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a252c3cc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#!/usr/bin/env python3\n", + "# -*- coding: utf-8 -*-\n", + "\"\"\"\n", + "Created on Tue Apr 29 12:12:56 2025\n", + "\n", + "\n", + "Plots the water, acetone and n-octane ternary diagram at 25 °C as calculated\n", + "by Aspen Plus.\n", + "\n", + "\n", + "@author: lobo\n", + "\"\"\"\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import mpltern\n", + "\n", + "\n", + "data_set = np.loadtxt(\"WaterAcetoneOctaneEquil.csv\", delimiter = ',', skiprows=2)\n", + "\n", + "water = data_set[:,1]\n", + "acetone = data_set[:,2]\n", + "octane = data_set[:,3]\n", + "\n", + "ax = plt.subplot(projection='ternary')\n", + "\n", + "ax.plot(acetone, octane, water)\n", + "\n", + "#Tie Lines\n", + "ax.plot([0,0],[0.9989768, 2.43E-06], [0.00102325, 0.9999976], 'b')\n", + "ax.plot([0.1248013,0.1403329],[0.8706273,0.000389155],[0.00457142,0.8592779], 'r')\n", + "ax.plot([0.2102607,0.3371009],[0.7798967,0.00720065],[0.00984261,0.6556985], 'k')\n", + "ax.plot([0.2552231,0.5722035],[0.731291,0.055398],[0.0134858,0.3723985], 'g')\n", + "ax.plot([0.4018703,0.6527512],[0.5729588,0.2466414],[0.0251709,0.1006074], 'c')\n", + "\n", + "ax.grid()\n", + "\n", + "ax.set_tlabel(\"Acetone\")\n", + "ax.set_llabel(\"n-Octane\")\n", + "ax.set_rlabel(\"Water\")\n", + "\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0f57f830", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}