{ "cells": [ { "cell_type": "markdown", "id": "confident-curtis", "metadata": {}, "source": [ "# PeTS Equation of State - Binary Mixture (Pseudo Pure Fluid)" ] }, { "cell_type": "markdown", "id": "duplicate-hydrogen", "metadata": {}, "source": [ "Original publication of the _perturbation theory for truncated and shifted Lennard-Jones fluids_ (PeTS) of M. Heier, S. Stephan, J. Liu, W.G. Chapman, H. Hasse, K. Langenbach, Mol. Phys. **116**, 2083 (2018);\n", "https://doi.org/10.1080/00268976.2018.1447153" ] }, { "cell_type": "code", "execution_count": 1, "id": "distinguished-sessions", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from feos_pets.eos import *\n", "from feos_pets.si import *\n", "from feos_pets import *\n", "import matplotlib.pyplot as plt\n", "import pandas as pd" ] }, { "cell_type": "markdown", "id": "significant-antibody", "metadata": {}, "source": [ "## Specifying PeTS Parameters" ] }, { "cell_type": "code", "execution_count": 2, "id": "dirty-renaissance", "metadata": {}, "outputs": [], "source": [ "epsilon_k = 1.0 * KELVIN\n", "sigma = 1.0 * ANGSTROM" ] }, { "cell_type": "markdown", "id": "organized-remainder", "metadata": {}, "source": [ "## Definition of Reference Data\n", "\n", "The molecular simulation reference data is taken from J. Vrabec, G.K. Kedia, G. Fuchs, H. Hasse, Mol. Phys. **104**, 1509 (2006);\n", "https://doi.org/10.1080/00268970600556774\n", "\n", "Critical point reference data is taken from the original publication of M. Heier, S. Stephan, J. Liu, W.G. Chapman, Mol. Phys. **116**, 2083 (2018);\n", "https://doi.org/10.1080/00268976.2018.1447153" ] }, { "cell_type": "code", "execution_count": 3, "id": "western-classic", "metadata": {}, "outputs": [], "source": [ "# Dara from Vrabec et al. (2006)\n", "data = np.array([\n", " [0.64, 0.00217, 0.8176, 0.00351, 5.7118],\n", " [0.67, 0.00335, 0.8024, 0.00525, 5.5910],\n", " [0.70, 0.00479, 0.7866, 0.00727, 5.4666],\n", " [0.73, 0.00697, 0.7704, 0.01036, 5.325 ],\n", " [0.76, 0.00944, 0.7538, 0.01374, 5.179 ],\n", " [0.79, 0.01241, 0.7361, 0.01776, 5.022 ],\n", " [0.82, 0.01640, 0.7181, 0.0233, 4.844 ],\n", " [0.85, 0.0214, 0.6986, 0.0303, 4.639 ],\n", " [0.88, 0.0274, 0.6784, 0.0392, 4.413 ],\n", " [0.91, 0.0336, 0.6556, 0.0483, 4.172 ],\n", " [0.94, 0.0417, 0.6309, 0.0616, 3.87 ],\n", " [0.97, 0.0504, 0.6032, 0.0763, 3.56 ],\n", " [1.00, 0.0606, 0.5712, 0.0960, 3.18 ],\n", " [1.03, 0.0730, 0.530, 0.127, 2.63 ],\n", " [1.06, 0.0855, 0.463, 0.168, 1.88 ]]\n", ")\n", "\n", "df = pd.DataFrame(data, columns=['T*', 'p*', 'rho^L*', 'rho^V*', 'Delta^LV h*'])\n", "\n", "# Critical point data extracted from Heier et al. (2018), figure 1; unclear origin\n", "T_c = 1.0850094876660341\n", "p_c = 0.10073800738007378\n", "rho_c = 0.3194085027726432\n", "\n", "# Critical point data extracted from Vrabec et al. (2018)\n", "T_c_vrabec = 1.0779\n", "p_c_vrabec = np.exp(3.1664 - 5.9809 / T_c_vrabec + 0.01498 / T_c_vrabec**3)\n", "rho_c_vrabec = 0.3190\n", "\n", "# Critical point data extracted from Heier et al. (2018), figure 1; critical point of original PeTS implementation\n", "T_c_pets_heier = 1.0884250474383301\n", "p_c_pets_heier = 0.10184501845018448\n", "rho_c_pets_heier = 0.3077634011090573" ] }, { "cell_type": "markdown", "id": "surface-undergraduate", "metadata": {}, "source": [ "## Definition of PeTS Equation of State" ] }, { "cell_type": "code", "execution_count": 9, "id": "regulated-sequence", "metadata": {}, "outputs": [], "source": [ "pets = Pets(PetsParameters.from_lists(epsilon_k=[epsilon_k/KELVIN]*2, sigma=[sigma/ANGSTROM]*2))" ] }, { "cell_type": "code", "execution_count": 10, "id": "cloudy-generic", "metadata": {}, "outputs": [], "source": [ "cp = State.critical_point_pure(eos=pets)\n", "\n", "T_c_pets = cp[0].temperature\n", "p_c_pets = cp[0].pressure()\n", "rho_c_pets = cp[0].density\n", "\n", "T_c_pets_red = cp[0].temperature / epsilon_k" ] }, { "cell_type": "markdown", "id": "provincial-score", "metadata": {}, "source": [ "## Phase Diagram of Pseudo Pure Fluid (Binary Mixture of the Same Component)" ] }, { "cell_type": "code", "execution_count": 11, "id": "intermediate-parallel", "metadata": {}, "outputs": [], "source": [ "temps = np.linspace(0.64, 0.99*T_c_pets_red, 101) # PhaseEquilibrium.bubble_point_tx() not converging to two phases close to critical point\n", "p_sat = np.zeros(temps.shape)\n", "rho_sat = np.zeros([temps.shape[0], 2])\n", "pressure_ic = None\n", "\n", "for i, temperature in enumerate(np.nditer(temps)):\n", " pe = PhaseEquilibrium.bubble_point(\n", " eos=pets, \n", " temperature_or_pressure=temperature * epsilon_k, \n", " liquid_molefracs=np.array([0.5, 0.5]), \n", " tp_init=pressure_ic, \n", " tol_inner=1e-7\n", " )\n", " p_sat[i] = pe.liquid.pressure() / (epsilon_k * KB / sigma**3)\n", " rho_sat[i, 0] = pe.vapor.density * (NAV * sigma**3)\n", " rho_sat[i, 1] = pe.liquid.density * (NAV * sigma**3)\n", "\n", " pressure_ic = pe.vapor.pressure() * 1.03" ] }, { "cell_type": "code", "execution_count": 12, "id": "taken-journalist", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(1,2, figsize=(14,5))\n", "\n", "ax[0].plot(temps, p_sat, color='tab:blue', label='this PeTS implementation')\n", "ax[0].scatter(df['T*'], df['p*'], marker='s', color='tab:orange', label='simulation data Vrabec et al. (2006)')\n", "ax[0].scatter(T_c_vrabec, p_c_vrabec, marker='o', color='tab:orange', label='critical point Vrabec et al. (2018)')\n", "ax[0].scatter(T_c, p_c, marker='o', color='tab:red', label='critical point Heier et al. (2018); unclear origin')\n", "ax[0].scatter(T_c_pets_heier, p_c_pets_heier, marker='o', color='tab:green', label='critical point PeTS Heier et al. (2018)')\n", "ax[0].scatter(T_c_pets/epsilon_k, p_c_pets/(epsilon_k * KB / sigma**3), marker='x', color='tab:red', label='critical point this PeTS implementation')\n", "ax[0].set_title('Vapor-Liquid Coexistence - Vapor Pressure')\n", "ax[0].set_xlabel(r'$T* = \\frac{T}{\\frac{\\epsilon}{k_\\mathrm{B}}}$')\n", "ax[0].set_ylabel(r'$p* = \\frac{p}{\\frac{\\epsilon}{\\sigma^3}}$')\n", "ax[0].set_xlim(0.6, 1.2)\n", "ax[0].set_ylim(0.0, 0.11)\n", "ax[0].legend(loc='upper left')\n", "ax[0].grid()\n", "\n", "ax[1].plot(temps, rho_sat[:,0], color='tab:blue', label='this PeTS implementation')\n", "ax[1].plot(temps, rho_sat[:,1], color='tab:blue')\n", "ax[1].scatter(df['T*'], df['rho^L*'], marker='s', color='tab:orange', label='simulation data Vrabec et al. (2006)')\n", "ax[1].scatter(df['T*'], df['rho^V*'], marker='s', color='tab:orange')\n", "ax[1].scatter(T_c, rho_c, marker='o', color='tab:red', label='critical point Heier et al. (2018); unclear origin')\n", "ax[1].scatter(T_c_vrabec, rho_c_vrabec, marker='o', color='tab:orange', label='critical point Vrabec et al. (2018)')\n", "ax[1].scatter(T_c_pets_heier, rho_c_pets_heier, marker='o', color='tab:green', label='critical point PeTS Heier et al. (2018)')\n", "ax[1].scatter(T_c_pets/epsilon_k, rho_c_pets*NAV*sigma**3, marker='x', color='tab:red', label='critical point this PeTS implementation')\n", "ax[1].set_title('Vapor-Liquid Coexistence - Saturated Densities')\n", "ax[1].set_xlabel(r'$T* = \\frac{T}{\\frac{\\epsilon}{k_\\mathrm{B}}}$')\n", "ax[1].set_ylabel(r'$\\rho* = \\rho \\sigma^3$')\n", "ax[1].set_xlim(0.6, 1.1)\n", "ax[1].set_ylim(0.0, 0.9)\n", "ax[1].legend(loc='center left')\n", "ax[1].grid()" ] }, { "cell_type": "markdown", "id": "surface-implement", "metadata": {}, "source": [ "## Binary Phase Diagram - Pressure-Composition of Pseudo Pure Fluid (Binary Mixture of the Same Component)" ] }, { "cell_type": "code", "execution_count": 15, "id": "marine-background", "metadata": {}, "outputs": [], "source": [ "dia_p = PhaseDiagram.binary_vle(eos=pets, temperature_or_pressure=1*epsilon_k)" ] }, { "cell_type": "code", "execution_count": 19, "id": "still-twelve", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(1, 2, figsize=(20,5))\n", "ax[0].scatter(dia_p.liquid.molefracs[:, 0], dia_p.liquid.pressure/(epsilon_k * KB / sigma**3), color='tab:red', marker='s')\n", "ax[0].scatter(dia_p.vapor.molefracs[:, 0], dia_p.liquid.pressure/(epsilon_k * KB / sigma**3), color='tab:blue', marker='x')\n", "ax[0].set_xlim(0, 1)\n", "ax[0].set_ylim(0, 0.15)\n", "ax[0].set_xlabel(r'$x_1, x_2$')\n", "ax[0].set_ylabel(r'$p* = \\frac{p}{\\frac{\\epsilon}{\\sigma^3}}$')\n", "\n", "\n", "ax[1].plot([0, 1], [0, 1], color='black')\n", "ax[1].scatter(dia_p.liquid.molefracs[:, 0], dia_p.vapor.molefracs[:, 0], color='tab:orange', marker='s')\n", "ax[1].set_xlim(0, 1)\n", "ax[1].set_ylim(0, 1)\n", "ax[1].set_xlabel(r'$x_1$')\n", "ax[1].set_ylabel(r'$y_1$');" ] } ], "metadata": { "kernelspec": { "display_name": "feos-pets", "language": "python", "name": "feos-pets" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }