{ "cells": [ { "cell_type": "markdown", "id": "e86a8de0", "metadata": {}, "source": [ "# RK-PR\n", "\n", "The EOS can be given as \n", "\n", "$$ \\alpha^{\\rm r} = \\psi^{(-)} - \\dfrac{a_m}{RT } \\psi^{(+)} $$\n", "\n", "$$ \\psi^{(-)} =-\\ln(1-b_m\\rho ) $$\n", "\n", "$$ \\psi^{(+)} = \\dfrac{\\ln\\left(\\dfrac{\\Delta_1 b_m\\rho+1}{\\Delta_2b_m\\rho+1}\\right)}{b_m(\\Delta_1-\\Delta_2)} $$\n", "\n", "with the EOS fixed constants of\n", "$$\n", "\\Delta_1 = \\sum_i x_i \\delta_{1,i}\n", "$$\n", "$$\n", "\\Delta_2 = \\frac{1-\\Delta_1}{1+\\Delta_1}\n", "$$\n", "\n", "The attractive term goes like\n", "$$\n", "a_{i} = a_{c,i}\\left(\\frac{2}{3+T/T_{c,i}}\\right)^{k_i}\n", "$$\n", "with quadratic mixing rules\n", "$$\n", "a_m = \\sum_i\\sum_jx_ix_j(1-k_{ij})\\sqrt{a_{i}(T)a_{j}(T)}\n", "$$\n", "And the covolume also gets quadratic mixing rules\n", "$$\n", "b_m = \\sum_i\\sum_jx_ix_j(1-l_{ij})(b_{i}+b_{j})/2\n", "$$\n", "\n", "Thus, to implement the RK-PR model in predictive mode, the following steps are required:\n", "\n", "1. Obtain the critical parameters Tc, pc\n", "2. Solve for delta_1 from the experimental critical compressibility factor, begin with the values from the correlation\n", "3. Solve for k by fixing the pressure at the T=0.7*Tc. In the case (e.g, CO$_2$) that Tt < 0.7*Tc, use instead Tr=Tt/Tc \n", "\n", "It may be necessary to adjust the values of $\\delta_{1,i}$ and $k_i$ for an individual component to better match the behavior of more polar components." ] }, { "cell_type": "code", "execution_count": 1, "id": "e1aa4062", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:10:06.416995Z", "iopub.status.busy": "2025-10-15T23:10:06.416817Z", "iopub.status.idle": "2025-10-15T23:10:07.863336Z", "shell.execute_reply": "2025-10-15T23:10:07.862906Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np \n", "import scipy.optimize \n", "import matplotlib.pyplot as plt \n", "import teqp, numpy as np\n", "import CoolProp.CoolProp as CP \n", "import pandas\n", "\n", "def delta1_correlation(Zc):\n", " # Eq. B.4 of Cismondi FPE 2005\n", " d1 = 0.428363\n", " d2 = 18.496215\n", " d3 = 0.338426\n", " d4 = 0.660000\n", " d5 = 789.723105\n", " d6 = 2.512392\n", " return d1 + d2*(d3-Zc)**d4 + d5*(d3-Zc)**d6 \n", "\n", "def Zc_delta1(delta1):\n", " # Eqs. B.1 to B.3 of Cismondi FPE 2005\n", " d1 = (1+delta1**2)/(1+delta1)\n", " y = 1 + (2*(1+delta1))**(1/3) + (4/(1+delta1))**(1/3)\n", " return y/(3*y + d1 - 1)\n", "\n", "DELTA1 = np.linspace(np.sqrt(2)-1, 25, 1000)\n", "ZZ = Zc_delta1(DELTA1)\n", "plt.plot(DELTA1, ZZ, label='values')\n", "DELTA1back = delta1_correlation(ZZ)\n", "plt.axvline(np.sqrt(2)-1)\n", "plt.plot(DELTA1back, ZZ, dashes=[2,2], label='correlation')\n", "plt.gca().set(ylabel='$Z_c$', xlabel='$\\delta_1$')\n", "plt.legend(loc='best')\n", "plt.show()\n", "\n", "# for Zc in np.linspace(0.2, 0.3383, 1000):\n", "# resid = lambda x: Zc_delta1(x)-Zc\n", "# # print(resid(delta1_correlation(Zc)))\n", "# print(Zc, scipy.optimize.newton(resid, delta1_correlation(Zc)), delta1_correlation(Zc))" ] }, { "cell_type": "code", "execution_count": 2, "id": "8fb5d777", "metadata": { "execution": { "iopub.execute_input": "2025-10-15T23:10:07.864822Z", "iopub.status.busy": "2025-10-15T23:10:07.864595Z", "iopub.status.idle": "2025-10-15T23:10:08.357766Z", "shell.execute_reply": "2025-10-15T23:10:08.357303Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "names = ['CO2', 'n-Decane']\n", "\n", "R = 8.31446261815324\n", "Tc = np.array([CP.PropsSI(k,\"Tcrit\") for k in names])\n", "pc = np.array([CP.PropsSI(k,\"pcrit\") for k in names])\n", "rhoc = np.array([CP.PropsSI(k,\"rhomolar_critical\") for k in names])\n", "Zcexp = pc/(rhoc*R*Tc)\n", "\n", "# Use a rescaled Zc to obtain delta_1\n", "Zc = 1.168*Zcexp\n", "\n", "delta_1 = [scipy.optimize.newton(lambda x: Zc_delta1(x)-Zc_, delta1_correlation(Zc_)) for Zc_ in Zc]\n", "\n", "def solve_for_k(i, p_target, Tr):\n", " \"\"\" \n", " The value of k for the i-th component is based on getting \n", " the right vapor pressure, so a rootfinding routing is\n", " used to obtain these values\n", " \"\"\"\n", " def objective(k):\n", " j = {\n", " \"kind\": \"RKPRCismondi2005\",\n", " \"model\": {\n", " \"delta_1\": [delta_1[i]],\n", " \"Tcrit / K\": [Tc[i]],\n", " \"pcrit / Pa\": [pc[i]],\n", " \"k\": [k],\n", " \"kmat\": [[0.0]],\n", " \"lmat\": [[0.0]],\n", " }\n", " }\n", " model = teqp.make_model(j)\n", " T = Tr*Tc[i]\n", " z = np.array([1.0])\n", " a, b = model.get_ab(T, z)\n", "\n", " anc = teqp.build_ancillaries(model, Tc[i], rhoc[i], 150)\n", " rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)\n", " p = T*R*rhoL*(1+model.get_Ar01(T, rhoL, z))\n", " \n", " return p-p_target\n", " return scipy.optimize.newton(objective, 2.1)\n", "\n", "Tr = 0.7\n", "i = 1\n", "k_C10 = solve_for_k(i, CP.PropsSI('P','T',Tr*Tc[i],'Q',0,names[i]), Tr)\n", "\n", "model = teqp.make_model({\n", " \"kind\": \"RKPRCismondi2005\",\n", " \"model\": {\n", " \"delta_1\": delta_1,\n", " \"Tcrit / K\": Tc.tolist(),\n", " \"pcrit / Pa\": pc.tolist(),\n", " \"k\": [2.23854, k_C10],\n", " \"kmat\": [[0,0],[0,0]],\n", " \"lmat\": [[0,0],[0,0]],\n", " }\n", "})\n", "\n", "# Start at both pures\n", "for ipure in [0, 1]:\n", " Tc, rhoc = model.solve_pure_critical(300, 5000, {\"alternative_pure_index\":ipure, \"alternative_length\": 2})\n", " z = np.array([0.0, 0.0]); z[ipure] = 1.0\n", " pc = Tc*R*rhoc*(1+model.get_Ar01(Tc, rhoc, z))\n", " plt.plot(Tc, pc/1e5, 'o')\n", " \n", " opt = teqp.TCABOptions(); opt.polish=True; opt.verbosity=100; opt.integration_order=5; opt.rel_err=1e-10; opt.abs_err=1e-10\n", " trace = model.trace_critical_arclength_binary(Tc, z*rhoc, options=opt)\n", " df = pandas.DataFrame(trace)\n", " plt.plot(df['T / K'], df['p / Pa']/1e5)\n", " \n", "# Overlay the data from Reamer and Sage, Cismondi additional data points not present in Reamer and Sage\n", "Tc_K = [310.928, 344.261, 377.594, 410.928, 444.261, 477.594, 510.928]\n", "pc_kPa = np.array([7997.92, 12824.25, 16492.26, 18560.69, 18836.48, 17836.74, 15333.94])\n", "plt.plot(Tc_K, pc_kPa/1e2, 'o')\n", "\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / bar');" ] } ], "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 }