{ "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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", 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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 }