{ "cells": [ { "cell_type": "markdown", "id": "bdb38ce8", "metadata": {}, "source": [ "# SAFT-VR-Mie\n", "\n", "The SAFT-VR-Mie EOS of Lafitte et al. (https://doi.org/10.1063/1.4819786) is based on the use of a Mie potential of the form\n", "\n", "$$\n", "u(r) = C\\epsilon \\left((\\sigma/r)^{\\lambda_r}-(\\sigma/r)^{\\lambda_a}\\right)\n", "$$\n", "with \n", "$$\n", "C = \\frac{\\lambda_r}{\\lambda_r-\\lambda_a}\\left(\\frac{\\lambda_r}{\\lambda_a}\\right)^{\\lambda_a/(\\lambda_r-\\lambda_a)}\n", "$$\n", "\n", "which allows for a better representation of thermodynamic properties in general, but not always." ] }, { "cell_type": "code", "execution_count": 1, "id": "d1842386", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:24.264062Z", "iopub.status.busy": "2025-10-15T23:09:24.263958Z", "iopub.status.idle": "2025-10-15T23:09:24.281296Z", "shell.execute_reply": "2025-10-15T23:09:24.280862Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.23.1'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import teqp\n", "teqp.__version__" ] }, { "cell_type": "code", "execution_count": 2, "id": "16f05ec8", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:24.282871Z", "iopub.status.busy": "2025-10-15T23:09:24.282740Z", "iopub.status.idle": "2025-10-15T23:09:25.554518Z", "shell.execute_reply": "2025-10-15T23:09:25.553602Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas\n", "import matplotlib.pyplot as plt\n", "import CoolProp.CoolProp as CP\n", "import scipy.integrate" ] }, { "cell_type": "code", "execution_count": 3, "id": "be8268a7", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:25.556013Z", "iopub.status.busy": "2025-10-15T23:09:25.555786Z", "iopub.status.idle": "2025-10-15T23:09:25.562775Z", "shell.execute_reply": "2025-10-15T23:09:25.562323Z" } }, "outputs": [ { "data": { "text/plain": [ "-0.04926724350863725" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "-0.04926724350863725" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show two ways to instantiate a SAFT-VR-Mie model, the\n", "# first by providing the coefficients, and the second\n", "# by providing the name of the species. Only a very small\n", "# number of molecules are provided for testing, you should\n", "# plan on providing your own parameters.\n", "# \n", "# Show that both give the same result for the residual pressure\n", "\n", "z = np.array([1.0])\n", "model = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": {\n", " \"coeffs\": [{\n", " \"name\": \"Ethane\",\n", " \"BibTeXKey\": \"Lafitte\",\n", " \"m\": 1.4373,\n", " \"epsilon_over_k\": 206.12, # [K]\n", " \"sigma_m\": 3.7257e-10,\n", " \"lambda_r\": 12.4,\n", " \"lambda_a\": 6.0\n", " }]\n", " }\n", "})\n", "display(model.get_Ar01(300, 300, z))\n", "\n", "model = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": {\n", " \"names\": [\"Ethane\"]\n", " }\n", "})\n", "display(model.get_Ar01(300, 300, z))" ] }, { "cell_type": "code", "execution_count": 4, "id": "d3d42d81", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:25.564013Z", "iopub.status.busy": "2025-10-15T23:09:25.563892Z", "iopub.status.idle": "2025-10-15T23:09:26.628989Z", "shell.execute_reply": "2025-10-15T23:09:26.628398Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here is an example of using teqp to trace VLE for propane\n", "# with the default parameters of PC-SAFT and SAFT-VR-Mie\n", "# models\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " model = teqp.make_model(j)\n", "\n", " z = np.array([1.0])\n", " Tc, rhoc = model.solve_pure_critical(300, 10000)\n", "\n", " # Extrapolate away from the critical point\n", " Ti = Tc*0.9997\n", " rhoL, rhoV = model.extrapolate_from_critical(Tc, rhoc, Ti)\n", "\n", " o = []\n", " T = Ti\n", " while T > 88:\n", " rhoL, rhoV = model.pure_VLE_T(T, rhoL, rhoV, 10)\n", " T -= 0.1\n", " o.append({'rhoL': rhoL, 'rhoV': rhoV, 'T': T})\n", "\n", " df = pandas.DataFrame(o)\n", " line, = plt.plot(df['rhoL'], df['T'], label=kind)\n", " plt.plot(df['rhoV'], df['T'], color=line.get_color())\n", "\n", "# From the reference EOS of Lemmon et al. via CoolProp\n", "name = 'Propane'\n", "Tc = CP.PropsSI(name, 'Tcrit')\n", "Ts = np.linspace(88, Tc, 1000)\n", "rhoL = CP.PropsSI('Dmolar','T',Ts,'Q',0,name)\n", "rhoV = CP.PropsSI('Dmolar','T',Ts,'Q',1,name)\n", "line, = plt.plot(rhoL, Ts, label='Reference EOS')\n", "plt.plot(rhoV, Ts, line.get_color())\n", "\n", "plt.gca().set(xlabel=r'$\\rho$ / mol/m$^3$', ylabel=r'$T$ / K')\n", "plt.legend()\n", "plt.tight_layout(pad=0.2)\n", "plt.savefig('SAFTVRMIE_PCSAFT.pdf')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "5c617489", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:26.630662Z", "iopub.status.busy": "2025-10-15T23:09:26.630512Z", "iopub.status.idle": "2025-10-15T23:09:47.787409Z", "shell.execute_reply": "2025-10-15T23:09:47.786810Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "998 μs ± 626 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "161 μs ± 98.3 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n" ] } ], "source": [ "# Time calculation of critical points\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " model = teqp.make_model(j)\n", "\n", " z = np.array([1.0])\n", " %timeit model.solve_pure_critical(300, 10000)" ] }, { "cell_type": "code", "execution_count": 6, "id": "c34aaf8b", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:47.789287Z", "iopub.status.busy": "2025-10-15T23:09:47.789107Z", "iopub.status.idle": "2025-10-15T23:09:48.259050Z", "shell.execute_reply": "2025-10-15T23:09:48.258254Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Checking the effective hardness of interaction,\n", "# the neff parameter defined in https://doi.org/10.1063/5.0007583\n", "# SAFT-VR-Mie comes closest to the right behavior\n", "modelVR = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": { \"names\": [\"Methane\"] }\n", "})\n", "modelPCSAFT = teqp.make_model({\n", " \"kind\": 'PCSAFT',\n", " \"model\": { \"names\": [\"Methane\"] }\n", "})\n", "modelMF = teqp.build_multifluid_model([\"Methane\"], teqp.get_datapath())\n", "\n", "for model, label in [(modelVR, 'SAFT-VR-Mie'), \n", " (modelPCSAFT, 'PC-SAFT'), \n", " (modelMF, 'reference EOS')]:\n", " z = np.array([1.0])\n", " rho = 1e-5\n", " T = np.geomspace(8, 10000, 10000)\n", " neff = []\n", " for T_ in T:\n", " neff.append(model.get_neff(T_, rho, z))\n", " plt.plot(T, neff, label=label)\n", "plt.xscale('log')\n", "plt.ylim(0, 30)\n", "plt.gca().set(xlabel=r'$T$ / K', ylabel=r'$n_{\\rm eff}$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "ab669adc", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:48.260415Z", "iopub.status.busy": "2025-10-15T23:09:48.260276Z", "iopub.status.idle": "2025-10-15T23:09:48.804131Z", "shell.execute_reply": "2025-10-15T23:09:48.803309Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Checking the temperature derivative of the virial coefficient\n", "name = 'Methane'\n", "modelVR = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": { \"names\": [name] }\n", "})\n", "modelPCSAFT = teqp.make_model({\n", " \"kind\": 'PCSAFT',\n", " \"model\": { \"names\": [name] }\n", "})\n", "modelMF = teqp.build_multifluid_model([name], teqp.get_datapath())\n", "\n", "for model, label in [(modelVR, 'SAFT-VR-Mie'), \n", " (modelPCSAFT, 'PC-SAFT'), \n", " (modelMF, 'reference EOS')]:\n", " z = np.array([1.0])\n", " T = np.geomspace(8, 10000, 10000)\n", " n = 2\n", " B, TdBdT, thetan = [],[],[]\n", " for T_ in T:\n", " TdBdT.append(model.get_dmBnvirdTm(n, 1, T_, z)*T_)\n", " B.append(model.get_dmBnvirdTm(n, 0, T_, z))\n", " thetan.append(B[-1]+TdBdT[-1])\n", " plt.plot(T, thetan, label=label)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.gca().set(xlabel=r'$T$ / K', ylabel=r'$B+T\\times$d$B$/d$T$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "f89b0433", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:48.805456Z", "iopub.status.busy": "2025-10-15T23:09:48.805309Z", "iopub.status.idle": "2025-10-15T23:09:56.286746Z", "shell.execute_reply": "2025-10-15T23:09:56.285965Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "627 μs ± 5.68 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "281 μs ± 2.87 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] } ], "source": [ "# Time model instantiation\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " %timeit teqp.make_model(j)" ] }, { "cell_type": "markdown", "id": "95237e68", "metadata": {}, "source": [ "## Calculation of diameter\n", "\n", "The calculation of the diameter is based upon\n", "$$\n", "d_{ii} = \\int_0^{\\sigma_{ii}}(1-\\exp(-\\beta u_{ii}^{\\rm Mie}(r)){\\rm d}r\n", "$$\n", "but the integrand is basically constant from 0 to some cutoff value of $r$, which we'll call $r_{\\rm cut}$. So first we need to find the value of $r_{\\rm cut}$ that makes the integrand take its constant value, which is explained well in the paper from Aasen (https://github.com/ClapeyronThermo/Clapeyron.jl/issues/152#issuecomment-1480324192). Finding the cutoff value is obtained when \n", "$$\n", "\\exp(-\\beta u_{ii}^{\\rm Mie}(r)) = EPS\n", "$$\n", "where EPS is the numerical precision of the floating point type. Taking the logs of both sides, \n", "$$\n", "-\\beta u_{ii}^{\\rm Mie} = \\ln(EPS)\n", "$$\n", "\n", "To get a starting value, it is first assumed that only the repulsive contribution contributes to the potential, yielding $u^{\\rm rep} = C\\epsilon(\\sigma/r)^{\\lambda_r}$ which yields\n", "$$\n", "-\\beta C\\epsilon(\\sigma/r)^{\\lambda_r} = \\ln(EPS)\n", "$$\n", "and \n", "$$\n", "(\\sigma/r)_{\\rm guess} = (-\\ln(EPS)/(\\beta C \\epsilon))^{1/\\lambda_r}\n", "$$\n", "\n", "Then we solve for the residual $R(r)=0$, where $R_0=\\exp(-u/T)-EPS$. Equivalently we can write the residual in logarithmic terms as $R=-u/T-\\ln(EPS)$. This simplifies the rootfinding as you need $R$, $R'$ and $R''$ to apply Halley's method, which are themselves quite straightforward to obtain because $R'=-u'/T$, $R''=-u''/T$, where the primes are derivatives taken with respect to $\\sigma/r$." ] }, { "cell_type": "code", "execution_count": 9, "id": "79563001", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:56.289058Z", "iopub.status.busy": "2025-10-15T23:09:56.288923Z", "iopub.status.idle": "2025-10-15T23:09:56.643895Z", "shell.execute_reply": "2025-10-15T23:09:56.643392Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\kappa \\left(- \\frac{j^{\\lambda_{a}} \\lambda_{a}}{j} + \\frac{j^{\\lambda_{r}} \\lambda_{r}}{j}\\right)$" ], "text/plain": [ "kappa*(-j**lambda_a*lambda_a/j + j**lambda_r*lambda_r/j)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\frac{\\kappa \\left(- j^{\\lambda_{a}} \\lambda_{a}^{2} + j^{\\lambda_{a}} \\lambda_{a} + j^{\\lambda_{r}} \\lambda_{r}^{2} - j^{\\lambda_{r}} \\lambda_{r}\\right)}{j^{2}}$" ], "text/plain": [ "kappa*(-j**lambda_a*lambda_a**2 + j**lambda_a*lambda_a + j**lambda_r*lambda_r**2 - j**lambda_r*lambda_r)/j**2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculation of the residual function (needed for Halley's method)\n", "import sympy as sy\n", "kappa, j, lambda_r, lambda_a = sy.symbols('kappa, j, lambda_r, lambda_a')\n", "u = kappa*(j**lambda_r - j**lambda_a)\n", "display(sy.diff(u, j))\n", "display(sy.simplify(sy.diff(u, j, 2)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "8e1e5746", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:09:56.645564Z", "iopub.status.busy": "2025-10-15T23:09:56.645318Z", "iopub.status.idle": "2025-10-15T23:09:56.651030Z", "shell.execute_reply": "2025-10-15T23:09:56.650447Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "quasi-exact; (value, error estimate):\n", "3.597838592720949 3.228005612223332e-12\n", "teqp; (value, error from quasi-exact in %)\n", "3.597838640613809 1.331156429529301e-06\n" ] } ], "source": [ "# Here is a small example of using adaptive quadrature \n", "# to obtain the quasi-exact value of d for ethane\n", "# according to the pure-fluid parameters given in \n", "# Lafitte et al.\n", "\n", "epskB = 206.12 # [K]\n", "sigma_m = 3.7257e-10 # [m]\n", "lambda_r = 12.4 \n", "lambda_a = 6.0\n", "C = lambda_r/(lambda_r-lambda_a)*(lambda_r/lambda_a)**(lambda_a/(lambda_r-lambda_a))\n", "T = 300.0 # [K]\n", "\n", "# The classical method based on adaptive quadrature\n", "def integrand(r_m):\n", " u = C*epskB*((sigma_m/r_m)**(lambda_r) - (sigma_m/r_m)**(lambda_a))\n", " return 1.0 - np.exp(-u/T)\n", "\n", "print('quasi-exact; (value, error estimate):')\n", "exact, exact_error = scipy.integrate.quad(integrand, 0.0, sigma_m, epsrel=1e-16, epsabs=1e-16)\n", "print(exact*1e10, exact_error*1e10)\n", "\n", "j = {\"kind\": 'SAFT-VR-Mie', \"model\": {\"names\": [\"Ethane\"]}}\n", "model = teqp.make_model(j)\n", "d = model.get_core_calcs(T, -1, z)[\"dmat\"][0][0]\n", "print('teqp; (value, error from quasi-exact in %)')\n", "print(d, abs(d/(exact*1e10)-1)*100)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.14" } }, "nbformat": 4, "nbformat_minor": 5 }