thermohub/module_7/VLE from fugacity.ipynb

{
 "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": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "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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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "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": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>P</th>\n",
       "      <th>vL</th>\n",
       "      <th>vV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>63.140000</td>\n",
       "      <td>1.283031e+04</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>0.040580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>63.171351</td>\n",
       "      <td>1.290334e+04</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>0.040369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>63.202703</td>\n",
       "      <td>1.297670e+04</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.040159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>63.234054</td>\n",
       "      <td>1.305040e+04</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.039950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>63.265406</td>\n",
       "      <td>1.312443e+04</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.039743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995</th>\n",
       "      <td>125.686024</td>\n",
       "      <td>3.319799e+06</td>\n",
       "      <td>0.000079</td>\n",
       "      <td>0.000116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>125.717376</td>\n",
       "      <td>3.324631e+06</td>\n",
       "      <td>0.000080</td>\n",
       "      <td>0.000115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>125.748727</td>\n",
       "      <td>3.329469e+06</td>\n",
       "      <td>0.000080</td>\n",
       "      <td>0.000114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>125.780079</td>\n",
       "      <td>3.334311e+06</td>\n",
       "      <td>0.000081</td>\n",
       "      <td>0.000114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>125.811430</td>\n",
       "      <td>3.339158e+06</td>\n",
       "      <td>0.000081</td>\n",
       "      <td>0.000113</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "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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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "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()"
   ]
  },
  {
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