{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "d88bffed", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:05.408064Z", "iopub.status.busy": "2024-10-29T15:20:05.407572Z", "iopub.status.idle": "2024-10-29T15:20:08.940671Z", "shell.execute_reply": "2024-10-29T15:20:08.939978Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.21.0'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.interpolate\n", "import teqp\n", "import numpy as np\n", "import pandas\n", "import matplotlib.pyplot as plt\n", "teqp.__version__" ] }, { "cell_type": "markdown", "id": "8218498b", "metadata": {}, "source": [ "# Critical curves & points\n", "\n", "\n", "## Pure Fluids\n", "\n", "Solving for the critical point involves finding the temperature and density that make\n", "$$\n", "\\left(\\frac{\\partial p}{\\partial \\rho}\\right)_T = \\left(\\frac{\\partial^2 p}{\\partial \\rho^2}\\right)_T = 0\n", "$$\n", "by 2D non-linear rootfinding. Newton steps are taken, and the analytic Jacobian is used (thanks to the ability to do derivatives with automatic differentiation). This is all handily wrapped up in the\n", "``solve_pure_critical`` method which requires the user to provide guess values for temperature and density" ] }, { "cell_type": "code", "execution_count": 2, "id": "46657a96", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:08.943046Z", "iopub.status.busy": "2024-10-29T15:20:08.942736Z", "iopub.status.idle": "2024-10-29T15:20:08.948161Z", "shell.execute_reply": "2024-10-29T15:20:08.947612Z" } }, "outputs": [ { "data": { "text/plain": [ "(190.564, 9442.816240022832)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Values taken from http://dx.doi.org/10.6028/jres.121.011\n", "modelPR = teqp.canonical_PR([190.564], [4599200], [0.011])\n", "\n", "# Solve for the critical point from a point close to the critical point\n", "T0 = 192.0\n", "# Critical compressibility factor of P-R is 0.307401308698.. (see https://doi.org/10.1021/acs.iecr.1c00847)\n", "rhoc = (4599200/(8.31446261815324*190.564))/0.3074\n", "rho0 = rhoc*1.2345 # Perturb to make sure we are doing something in the solver\n", "modelPR.solve_pure_critical(T0, rho0)" ] }, { "cell_type": "markdown", "id": "9141858c", "metadata": {}, "source": [ "If you have a mixture, but want to obtain the critical point of a pure fluid of this mixture, you can specify the index of the component in the mixture, as well as the number of componnts in the mixture with something like:\n", "\n", "``\n", "model.solve_pure_critical(T0, rho0, {\"alternative_pure_index\": 1, \"alternative_length\": 2})\n", "``\n", "so here, for the second fluid, with 0-based index of 1, in a two-component mixture" ] }, { "cell_type": "markdown", "id": "e15eeded", "metadata": {}, "source": [ "## Mixtures\n", "\n", "A pure fluid has a single vapor-liquid critical point, but mixtures are different:\n", "\n", "* They may have multiple (or zero!) critical points for a given mixture composition\n", "* The critical curves may not emanate from the pure fluid endpoints\n", "\n", "When it comes to critical points, intuition from pure fluids is not helpful, or sometimes even counter-productive. \n", "\n", "teqp has methods for working with the critical loci of binary mixtures (only binary mixtures, for now) and especially, methods for tracing the critical curves emanating from the pure fluid endpoints.\n", "\n", "The tracing method in teqp is based explicitly on the isochoric thermodynamics formalism introduced by Ulrich Deiters and Sergio Quinones-Cisneros. It uses the Helmholtz energy density as the fundamental potential and all other properties are derived from it. For critical curves it is based upon the integration of sets of ordinary differential equations; the differential equations are in the form of derivatives of the molar concentrations of each component in the mixture with respect to an integration variable. The set of ODE is then integrated.\n", "\n", "Here is an example of the construction of the critical curves emanating from the pure fluid endpoints for the mixture nitrogen + ethane." ] }, { "cell_type": "code", "execution_count": 3, "id": "81619ae2", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:08.950270Z", "iopub.status.busy": "2024-10-29T15:20:08.950038Z", "iopub.status.idle": "2024-10-29T15:20:11.072013Z", "shell.execute_reply": "2024-10-29T15:20:11.071369Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import timeit\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import pandas\n", "import teqp\n", "\n", "def get_critical_curve(ipure):\n", " \"\"\" Return curve as pandas DataFrame \"\"\"\n", " names = ['Nitrogen', 'Ethane']\n", " model = teqp.build_multifluid_model(names, teqp.get_datapath())\n", " T0 = model.get_Tcvec()[ipure]\n", " rho0 = np.array([1.0/model.get_vcvec()[ipure]]*2)\n", " rho0[1-ipure] = 0\n", " o = teqp.TCABOptions() \n", " o.init_dt = 1.0 # step in the arclength tracing parameter\n", " o.rel_err = 1e-8\n", " o.abs_err = 1e-5\n", " o.integration_order = 5\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rho0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(7, 6))\n", "tic = timeit.default_timer()\n", "for ipure in [1,0]:\n", " df = get_critical_curve(ipure)\n", " first_unstable = np.argmax(~df['locally stable'])\n", " df = df.iloc[0:(first_unstable if first_unstable else len(df))]\n", " line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '.')\n", " \n", " # And interpolate to smooth out the curve using the arclength\n", " # parameter (which must be monotonically increasing) as \n", " # the interpolation variable\n", " tinterp = np.linspace(df['t'].min(), df['t'].max(), 10000)\n", " Tinterp = scipy.interpolate.interp1d(df['t'], df['T / K'], kind='cubic')(tinterp)\n", " pinterp = scipy.interpolate.interp1d(df['t'], df['p / Pa'], kind='cubic')(tinterp)\n", " plt.plot(Tinterp, pinterp/1e6, color=line.get_color())\n", " \n", " plt.plot(df['T / K'].iloc[0], df['p / Pa'].iloc[0]/1e6, 'd', \n", " color=line.get_color())\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa',\n", " xlim=(100, 350), ylim=(1, 1e3))\n", "plt.yscale('log')\n", "plt.tight_layout(pad=0.2)\n", "plt.gcf().text(0,0,f'time: {elap:0.1f} s', ha='left', va='bottom', fontsize=7)\n", "plt.gcf().text(1,0,f'teqp: {teqp.__version__}', ha='right', va='bottom', fontsize=7);" ] }, { "cell_type": "markdown", "id": "6120531f", "metadata": {}, "source": [ "And now for something a bit more interesting: ethane + alkane critical curves" ] }, { "cell_type": "code", "execution_count": 4, "id": "92020440", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:11.074220Z", "iopub.status.busy": "2024-10-29T15:20:11.073975Z", "iopub.status.idle": "2024-10-29T15:20:12.069842Z", "shell.execute_reply": "2024-10-29T15:20:12.069109Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import timeit\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import pandas\n", "import teqp\n", "\n", "def get_critical_curve(names, ipure):\n", " \"\"\" Return curve as pandas DataFrame \"\"\"\n", " model = teqp.build_multifluid_model(names, teqp.get_datapath())\n", " T0 = model.get_Tcvec()[ipure]\n", " rho0 = np.array([1.0/model.get_vcvec()[ipure]]*2)\n", " rho0[1-ipure] = 0\n", " o = teqp.TCABOptions() \n", "# print(dir(o))\n", " o.init_dt = 1.0 # step in the parameter\n", " o.rel_err = 1e-6 # relative error on the step\n", " o.abs_err = 1e-6 # absolute error on the step\n", " o.max_dt = 100 # cap the size of the allowed step\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rho0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(7, 6))\n", "tic = timeit.default_timer()\n", "name0 = 'ETHANE'\n", "for othername in ['METHANE','PROPANE','BUTANE','PENTANE','HEXANE']:\n", " for ipure in [1]:\n", " df = get_critical_curve([name0, othername], ipure)\n", " line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '-')\n", " plt.plot(df['T / K'].iloc[0], df['p / Pa'].iloc[0]/1e6, 'd', \n", " color=line.get_color())\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')#,xlim=(100, 350), ylim=(1, 1e3))\n", "plt.tight_layout(pad=0.2)\n", "plt.gcf().text(0,0,f'time: {elap:0.1f} s', ha='left', va='bottom', fontsize=7)\n", "plt.gcf().text(1,0,f'teqp: {teqp.__version__}', ha='right', va='bottom', fontsize=7);" ] }, { "cell_type": "markdown", "id": "b664c012", "metadata": {}, "source": [ "## Pure fluid EOS with nonanalytic terms\n", "\n", "For the highest accuracy EOS for normal water and carbon dioxide, there are non-analytic terms that prevent the initialization of the critical tracing at the pure fluid critical point. Instead, one can start close to, but not *AT*, the pure fluid endpoint. After deciding on that starting composition, one solves for the critical point and then traces away from it.\n", "\n", "You might need to either do tracing in two parts, one with init_c=+1 and then init_c=-1, or one tracing might be good enough.\n", "\n", "Here is an example:" ] }, { "cell_type": "code", "execution_count": 5, "id": "afe71d81", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:12.072186Z", "iopub.status.busy": "2024-10-29T15:20:12.071920Z", "iopub.status.idle": "2024-10-29T15:20:14.860299Z", "shell.execute_reply": "2024-10-29T15:20:14.859622Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def get_critical_curve_composition(names, T0, rhovec0, init_c=-1):\n", " \"\"\" Trace the critical curve from a fixed point along it \"\"\"\n", " o = teqp.TCABOptions() \n", "# print(dir(o))\n", " o.init_dt = 1.0 # step in the parameter\n", " o.rel_err = 1e-6 # relative error on the step\n", " o.abs_err = 1e-6 # absolute error on the step\n", " o.max_dt = 100 # cap the size of the allowed step\n", " o.calc_stability = True\n", " o.polish = True\n", " o.init_c = init_c # You might need to swap the initial tracing direction by making this +1.0\n", " curveJSON = model.trace_critical_arclength_binary(T0, rhovec0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "# Tracing with multi-fluid from an endpoint with non-analytic terms\n", "model = teqp.build_multifluid_model([\"Water\", \"Methane\"], teqp.get_datapath())\n", "\n", "x0 = 1-1e-6 # ever so slightly away from the pure fluid\n", "molefrac = np.array([x0, 1-x0])\n", "\n", "# Solve for the actual critical point at this mole fraction with scipy\n", "y0 = [model.get_Tcvec()[0], 1/model.get_vcvec()[0]]\n", "residual = lambda y: model.get_criticality_conditions(y[0], y[1]*molefrac)\n", "res = scipy.optimize.fsolve(residual, y0)\n", "T = res[0]\n", "rho0 = res[1]\n", "rhovec0 = rho0*molefrac\n", "\n", "# Now trace from this point\n", "curve = get_critical_curve_composition(model, T0=T, rhovec0=rhovec0)\n", "plt.plot(curve['T / K'], curve['p / Pa']/1e6, label='multifluid')\n", "\n", "# With GERG-2008, things are much more straightforward...\n", "model = teqp.make_model({'kind': 'GERG2008resid', 'model': {'names': ['water','methane']}})\n", "\n", "def get_critical_curve_simple(model, ipure, T0, rho0):\n", " \"\"\" Trace from a pure fluid... \"\"\"\n", " rhovec0 = np.array([0, 0])\n", " rhovec0[ipure] = rho0\n", " o = teqp.TCABOptions()\n", " o.init_dt = 1.0 # step in the arclength tracing parameter\n", " o.rel_err = 1e-8\n", " o.abs_err = 1e-5\n", " o.integration_order = 5\n", " o.calc_stability = True\n", " o.polish = True\n", " curveJSON = model.trace_critical_arclength_binary(T0, rhovec0, '', o)\n", " df = pandas.DataFrame(curveJSON)\n", " rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", " df['z0 / mole frac.'] = df['rho0 / mol/m^3']/rhotot\n", " return df\n", "\n", "for ifluid in [0]:\n", " Tci = model.get_Tcvec()[ifluid]\n", " vci = model.get_vcvec()[ifluid]\n", " df = get_critical_curve_simple(model, ipure=ifluid, T0=Tci, rho0 = 1.0/vci)\n", " plt.plot(df['T / K'], df['p / Pa']/1e6, label='GERG-2008')\n", "\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')\n", "plt.yscale('log')\n", "plt.xlim(600, 950)\n", "plt.ylim(20, 300)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "id": "933a88ef", "metadata": {}, "source": [ "## Critical points\n", "\n", "If you have a relatively simple critical curve for a binary mixture and you would like to obtain the critical point at a given composition, you can obtain it reliably in a multi-step process:\n", "\n", "1. Trace the binary curve \n", "2. Interpolate to find the approximate value for critical temperature and density\n", "3. Use Newton's method to solve the criticality conditions from estimated critical point\n", "4. Calculate whatever else you want" ] }, { "cell_type": "code", "execution_count": 6, "id": "4618df2a", "metadata": { "execution": { "iopub.execute_input": "2024-10-29T15:20:14.862516Z", "iopub.status.busy": "2024-10-29T15:20:14.862272Z", "iopub.status.idle": "2024-10-29T15:20:15.222385Z", "shell.execute_reply": "2024-10-29T15:20:15.221693Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = get_critical_curve([name0, othername], ipure)\n", "model = teqp.build_multifluid_model([name0, othername], teqp.get_datapath())\n", "line, = plt.plot(df['T / K'], df['p / Pa']/1e6, '-')\n", "rhotot = df['rho0 / mol/m^3']+df['rho1 / mol/m^3']\n", "\n", "# Build cubic interpolators between the variables\n", "tinterp = scipy.interpolate.interp1d(df['z0 / mole frac.'], df['t'], kind='cubic') # interpolator from mole fraction to tracing parameter\n", "Tinterp = scipy.interpolate.interp1d(df['t'], df['T / K'], kind='cubic')\n", "rhointerp = scipy.interpolate.interp1d(df['t'], rhotot, kind='cubic')\n", "\n", "# Iterate over composition\n", "for x0 in np.arange(0.1, 1, 0.05):\n", "\n", " molefracs = np.array([x0, 1-x0])\n", " \n", " # Initial guess for critical point from interpolation\n", " t = tinterp(x0)\n", " T0 = Tinterp(t)\n", " rho0 = rhointerp(t)\n", " p0 = rho0*model.get_R(molefracs)*T0*(1+model.get_Ar01(T0, rho0, molefracs))\n", " plt.plot(T0, p0/1e6, 'o')\n", " \n", " # Newton iteration for the correct critical point\n", " def resid(x):\n", " return model.get_criticality_conditions(T=x[0], rhovec=x[1]*molefracs)\n", " soln = scipy.optimize.fsolve(resid, x0=[T0, rho0])\n", " T, rho = soln\n", " p = rho*model.get_R(molefracs)*T*(1+model.get_Ar01(T, rho, molefracs))\n", " plt.plot(T, p/1e6, '+')\n", "# print(x0, T0, rho0, p0, resid([T0, rho0]), T, rho, resid([T, rho]))\n", "\n", "elap = timeit.default_timer()-tic\n", "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / MPa')\n", "plt.tight_layout(pad=0.2)" ] } ], "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 5 }