{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a6e6ebc7",
   "metadata": {},
   "source": [
    "# GERG \n",
    "\n",
    "In the GERG-2004 and GERG-2008 models, the pure fluids are modeled with high-accuracy multiparameter EOS. The model is covered exhaustively in the GERG-2004 monograph: https://www.gerg.eu/wp-content/uploads/2019/10/TM15.pdf  and in the GERG-2008 paper: https://doi.org/10.1021/je300655b\n",
    "\n",
    "The following components are supported (case-sensitive) in GERG-2004:\n",
    "\n",
    "* methane\n",
    "* nitrogen\n",
    "* carbondioxide\n",
    "* ethane\n",
    "* propane\n",
    "* n-butane\n",
    "* isobutane\n",
    "* n-pentane\n",
    "* isopentane\n",
    "* n-hexane\n",
    "* n-heptane\n",
    "* n-octane\n",
    "* hydrogen\n",
    "* oxygen\n",
    "* carbonmonoxide\n",
    "* water\n",
    "* helium\n",
    "* argon\n",
    "\n",
    "and GERG-2008 adds the components:\n",
    "\n",
    "* hydrogensulfide\n",
    "* n-nonane\n",
    "* n-decane\n",
    "\n",
    "(as well as modifying the pure component EOS for carbon monoxide and isopentane). \n",
    "\n",
    "The interaction parameters and departure functions are not editable (by design) and the EOS parameters are hard-coded. No ancillary equations are available along with the GERG-2004 model, but you can use the on-the-fly ancillary generator of teqp.\n",
    "\n",
    "The residual portions of these models were added in version 0.18.0, and it is planned to add the ideal-gas portions as well at a later date. The residual portion is enough for many applications like phase equilibria and critical locus tracing.\n",
    "\n",
    "The kind is 'GERG2004resid' for the GERG-2004 residual model and 'GERG2008resid' for the GERG-2008 residual model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0789f562",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.089680Z",
     "iopub.status.busy": "2025-10-15T23:12:25.089554Z",
     "iopub.status.idle": "2025-10-15T23:12:25.559315Z",
     "shell.execute_reply": "2025-10-15T23:12:25.558877Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.23.1'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import teqp\n",
    "import numpy as np\n",
    "import pandas\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "teqp.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dcaa96c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.560640Z",
     "iopub.status.busy": "2025-10-15T23:12:25.560436Z",
     "iopub.status.idle": "2025-10-15T23:12:25.563380Z",
     "shell.execute_reply": "2025-10-15T23:12:25.562981Z"
    }
   },
   "outputs": [],
   "source": [
    "model = teqp.make_model({'kind':\"GERG2004resid\", 'model':{\"names\": ['methane','ethane']}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "90cd0540",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.564616Z",
     "iopub.status.busy": "2025-10-15T23:12:25.564490Z",
     "iopub.status.idle": "2025-10-15T23:12:25.766022Z",
     "shell.execute_reply": "2025-10-15T23:12:25.765577Z"
    },
    "tags": [
     "raises-exception"
    ]
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Unable to load pure info for MeThAnE",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m      1\u001b[39m \u001b[38;5;66;03m# Note that names are case-sensitive; this doesn't work\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m model = \u001b[43mteqp\u001b[49m\u001b[43m.\u001b[49m\u001b[43mmake_model\u001b[49m\u001b[43m(\u001b[49m\u001b[43m{\u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mkind\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m:\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mGERG2004resid\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mmodel\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m:\u001b[49m\u001b[43m{\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mnames\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mMeThAnE\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43methane\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m}\u001b[49m\u001b[43m}\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[36mFile \u001b[39m\u001b[32m~/checkouts/readthedocs.org/user_builds/teqp/conda/latest/lib/python3.11/site-packages/teqp/__init__.py:47\u001b[39m, in \u001b[36mmake_model\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m     42\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mmake_model\u001b[39m(*args, **kwargs):\n\u001b[32m     43\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m     44\u001b[39m \u001b[33;03m    This function is in two parts; first the make_model function (renamed to _make_model in the Python interface)\u001b[39;00m\n\u001b[32m     45\u001b[39m \u001b[33;03m    is used to make the model and then the model-specific methods are attached to the instance\u001b[39;00m\n\u001b[32m     46\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m47\u001b[39m     AS = \u001b[43m_make_model\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m     48\u001b[39m     attach_model_specific_methods(AS)\n\u001b[32m     49\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m AS\n",
      "\u001b[31mValueError\u001b[39m: Unable to load pure info for MeThAnE"
     ]
    }
   ],
   "source": [
    "# Note that names are case-sensitive; this doesn't work\n",
    "model = teqp.make_model({'kind':\"GERG2004resid\", 'model':{\"names\": ['MeThAnE','ethane']}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c99900a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.767519Z",
     "iopub.status.busy": "2025-10-15T23:12:25.767401Z",
     "iopub.status.idle": "2025-10-15T23:12:25.947880Z",
     "shell.execute_reply": "2025-10-15T23:12:25.947316Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we trace the critical locus for methane+ethane\n",
    "rhovec0 = np.array([0.0, 0.0])\n",
    "ifluid = 0\n",
    "T0 = model.get_Tcvec()[0]\n",
    "rhovec0[ifluid] = 1/model.get_vcvec()[0]\n",
    "trace = model.trace_critical_arclength_binary(T0=T0, rhovec0=rhovec0)\n",
    "df = pandas.DataFrame(trace)\n",
    "plt.plot(df['T / K'], df['p / Pa'])\n",
    "plt.gca().set(xlabel='$T$ / K', ylabel='$p$ / Pa');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "78b8faf7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.949260Z",
     "iopub.status.busy": "2025-10-15T23:12:25.949126Z",
     "iopub.status.idle": "2025-10-15T23:12:25.952145Z",
     "shell.execute_reply": "2025-10-15T23:12:25.951448Z"
    }
   },
   "outputs": [],
   "source": [
    "model = teqp.make_model({'kind':\"GERG2004resid\", 'model':{\"names\": ['methane']}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c8c11235",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:12:25.953373Z",
     "iopub.status.busy": "2025-10-15T23:12:25.953234Z",
     "iopub.status.idle": "2025-10-15T23:12:25.978869Z",
     "shell.execute_reply": "2025-10-15T23:12:25.978178Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(27361.12577999801),\n",
       " np.float64(42.046298502526746),\n",
       " 'mol/m^3 for liquid and vapor')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build an on-the-fly ancillary equation \n",
    "# (not as accurate as the specialized ones, but works acceptably in many cases)\n",
    "anc = teqp.build_ancillaries(model, Tc=model.get_Tcvec()[0], rhoc = 1/model.get_vcvec()[0], Tmin=60)\n",
    "\n",
    "# And then use the dynamic ancillary to calculate VLE at 100 K\n",
    "T = 100 # K\n",
    "rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)\n",
    "rhoL, rhoV, 'mol/m^3 for liquid and vapor'"
   ]
  }
 ],
 "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
}