{ "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": "2024-03-15T22:40:32.511034Z", "iopub.status.busy": "2024-03-15T22:40:32.510710Z", "iopub.status.idle": "2024-03-15T22:40:33.336347Z", "shell.execute_reply": "2024-03-15T22:40:33.335805Z" } }, "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": "2024-03-15T22:40:33.338883Z", "iopub.status.busy": "2024-03-15T22:40:33.338424Z", "iopub.status.idle": "2024-03-15T22:40:33.964387Z", "shell.execute_reply": "2024-03-15T22:40:33.963874Z" } }, "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": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 5 }