{ "cells": [ { "cell_type": "markdown", "id": "763029ee", "metadata": {}, "source": [ "# Gerg2008\n", "\n", "In `yaeos` the multifluid equation $GERG2008$ residual term is implemented." ] }, { "cell_type": "code", "execution_count": 1, "id": "9c00035a", "metadata": {}, "outputs": [], "source": [ "import yaeos\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "6b862e7c", "metadata": {}, "source": [ "The `GERG2008` object is instantiated by providing a list of the components\n", "desired to include. The available components are:\n", "\n", "- `methane`\n", "- `nitrogen`\n", "- `carbon dioxide`\n", "- `ethane`\n", "- `propane`\n", "- `n-butane`\n", "- `isobutane`\n", "- `n-pentane`\n", "- `isopentane`\n", "- `n-hexane`\n", "- `n-heptane`\n", "- `n-octane`\n", "- `nonane`\n", "- `decane`\n", "- `hydrogen`\n", "- `oxygen`\n", "- `carbon monoxide`\n", "- `water`\n", "- `hydrogen sulfide`\n", "- `helium`\n", "- `argon`\n", "\n", "\n", "For example, we will calculate the phase envelope for the ternary system of \n", "methane, n-butane and decane." ] }, { "cell_type": "code", "execution_count": 14, "id": "2f571eac", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the model to use\n", "model = yaeos.GERG2008([\"methane\", \"n-butane\", \"decane\"])\n", "\n", "# Calculate the phase envelope at a specific composition\n", "z = [0.4, 0.2, 0.4]\n", "env = model.phase_envelope_pt(z, kind=\"dew\", max_points=800, t0=400, p0=2)\n", "env.plot()" ] }, { "cell_type": "markdown", "id": "e7e08196", "metadata": {}, "source": [ "## Things to be careful about\n" ] }, { "cell_type": "markdown", "id": "906a5dab", "metadata": {}, "source": [ "### Multiple volume roots\n", "\n", "Due to it's multiparametric nature, the GERG2008 can also be the source of\n", "unexpected and undesired errors in modelling. One of the most common cases is\n", "the precense of multiple unrealistic volume roots. In this example we show \n", "how the isotherm of pure n-Heptane can present an unrealistic root.\n", "\n", "When we draw the isotherm at $350~K$ we can see that there are three possible\n", "volume roots for pressures from $0 bar$ to near $250 bar$. The middle root does\n", "not satisfy the mechanically stability criteria ($dP/dV$ should be negative) but\n", "the other two roots do. But, if we pay attention to the root at higher molar\n", "volumes, we can see that it is an unrealistic vapor root that's just an artifact\n", "of the complexity of the GERG2008 equation, and it should not be taken into\n", "account.\n", "\n", "In `yaeos`, we use the $SRK$ equation of state to initialize liquid and vapor\n", "volumes, so in most cases we should not end on those unrealisic roots. This is\n", "shown in this example, where both the (initialized as) liquid and vapor roots\n", "end up in the realistic liquid root. But extra care should be taken when\n", "calculating these kind of roots, because this method is not perfect.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "6deea540", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import yaeos\n", "\n", "model = yaeos.GERG2008([\"n-heptane\"])\n", "\n", "Tc = [540.2]\n", "Pc = [27.4]\n", "w = [0.349469]\n", "\n", "srk = yaeos.SoaveRedlichKwong(Tc, Pc, w)\n", "\n", "T = 350 # Temperature in Kelvin\n", "P = 100 # Pressure in bar\n", "\n", "# Define a range of molar volumes to calculate pressures\n", "vs = np.linspace(1e-3, 2, 10000)\n", "\n", "# Calculate pressures for the specified molar volumes using the GERG2008 model\n", "ps = [model.pressure([1], v, T) for v in vs]\n", "\n", "# Calculate pressures using the SRK EoS for comparison\n", "ps_srk = [srk.pressure([1], v, T) for v in vs]\n", "\n", "# Calculate the liquid and vapor roots at the specified pressure and temperature\n", "v_liq = model.volume([1], P, T, root=\"liquid\")\n", "v_vap = model.volume([1], P, T, root=\"vapor\")\n", "\n", "# Plotting the results\n", "plt.ylim(-300, 400)\n", "plt.plot(vs, ps, color=\"black\", label=\"GERG2008 EoS\")\n", "plt.plot(vs, ps_srk, linestyle=\"--\", color=\"gray\", label=\"SRK EoS\")\n", "\n", "plt.scatter(v_liq, P, color=\"blue\", label=\"Initialized Liquid root\", zorder=10)\n", "plt.scatter(v_vap, P, color=\"red\", label=\"Initialized Vapor root\", zorder=10)\n", "\n", "plt.axhline(P, color=\"lightgray\", linestyle=\"-\", label=\"Specified pressure\")\n", "plt.xlabel(\"Molar volume (L/mol)\")\n", "plt.ylabel(\"Pressure (bar)\")\n", "plt.title(\"Pressure vs Molar Volume for n-Heptane at {T} K\".format(T=T))\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "c9fef026", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "thermo", "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": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 5 }