{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f406bbb5",
   "metadata": {},
   "source": [
    "# PC-SAFT\n",
    "\n",
    "The PC-SAFT implementation in teqp is based on the implementation of Gross and Sadowski (https://doi.org/10.1021/ie0003887), with the typo from their paper fixed.  It does NOT include the association contribution, only the dispersive contributions.\n",
    "\n",
    "The model in teqp requires the user to specify the values of ``sigma``, ``epsilon/kB``, and ``m`` for each substance.  A very few substances are hardcoded in teqp, for testing purposes.  "
   ]
  },
  {
   "cell_type": "raw",
   "id": "d9efd027",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The Python class is here: :py:class:`PCSAFTEOS <teqp.teqp.PCSAFTEOS>`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "984925ce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:08:52.431028Z",
     "iopub.status.busy": "2025-10-15T23:08:52.430911Z",
     "iopub.status.idle": "2025-10-15T23:08:52.482173Z",
     "shell.execute_reply": "2025-10-15T23:08:52.481716Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.23.1'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import teqp\n",
    "import numpy as np\n",
    "teqp.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7bbd7129",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:08:52.483669Z",
     "iopub.status.busy": "2025-10-15T23:08:52.483485Z",
     "iopub.status.idle": "2025-10-15T23:08:52.487872Z",
     "shell.execute_reply": "2025-10-15T23:08:52.487240Z"
    }
   },
   "outputs": [],
   "source": [
    "TeXkey = 'Gross-IECR-2001'\n",
    "ms = [1.0, 1.6069, 2.0020]\n",
    "eoverk = [150.03, 191.42, 208.11]\n",
    "sigmas = [3.7039, 3.5206, 3.6184]\n",
    "\n",
    "coeffs = []\n",
    "for i in range(len(ms)):\n",
    "    c = teqp.SAFTCoeffs()\n",
    "    c.m = ms[i]\n",
    "    c.epsilon_over_k = eoverk[i]\n",
    "    c.sigma_Angstrom = sigmas[i]\n",
    "    coeffs.append(c)\n",
    "    \n",
    "model = teqp.PCSAFTEOS(coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "19ec9bfb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:08:52.489386Z",
     "iopub.status.busy": "2025-10-15T23:08:52.488909Z",
     "iopub.status.idle": "2025-10-15T23:09:07.885476Z",
     "shell.execute_reply": "2025-10-15T23:09:07.884904Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.82 μs ± 5.34 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.37 μs ± 4.39 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.8 μs ± 29.4 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Here are some rudimentary timing results\n",
    "T = 300.0\n",
    "rhovec = np.array([3.0, 4.0, 5.0])\n",
    "rho = rhovec.sum()\n",
    "x = rhovec/np.sum(rhovec)\n",
    "%timeit model.get_fugacity_coefficients(T,rhovec)\n",
    "%timeit (-1.0)*model.get_Ar20(T, rho, x)\n",
    "%timeit model.get_partial_molar_volumes(T, rhovec)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "578630c8",
   "metadata": {},
   "source": [
    "The model parameters can be queried:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d4e47e54",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.887053Z",
     "iopub.status.busy": "2025-10-15T23:09:07.886896Z",
     "iopub.status.idle": "2025-10-15T23:09:07.890611Z",
     "shell.execute_reply": "2025-10-15T23:09:07.890256Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.    , 1.6069, 2.002 ]),\n",
       " array([150.03, 191.42, 208.11]),\n",
       " array([3.7039, 3.5206, 3.6184]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_m(), model.get_epsilon_over_k_K(), model.get_sigma_Angstrom()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cbb382d",
   "metadata": {},
   "source": [
    "## Adjusting k_ij\n",
    "\n",
    "Fine-tuned values of $k_{ij}$ can be provided when instantiating the model.  A complete matrix of all the $k_{ij}$ values must be provided. This allows for asymmetric mixing models in which $k_{ij}\\neq k_{ji}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a32c41b5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.891939Z",
     "iopub.status.busy": "2025-10-15T23:09:07.891806Z",
     "iopub.status.idle": "2025-10-15T23:09:07.895008Z",
     "shell.execute_reply": "2025-10-15T23:09:07.894569Z"
    }
   },
   "outputs": [],
   "source": [
    "k_01 = 0.01; k_10 = k_01\n",
    "kmat = [[0,k_01,0],[k_10,0,0],[0,0,0]]\n",
    "model = teqp.PCSAFTEOS(coeffs, kmat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "536fac81",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.896161Z",
     "iopub.status.busy": "2025-10-15T23:09:07.896036Z",
     "iopub.status.idle": "2025-10-15T23:09:07.899531Z",
     "shell.execute_reply": "2025-10-15T23:09:07.899149Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.01, 0.  ],\n",
       "       [0.01, 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and the matrix of parameters can be printed back out\n",
    "model.get_kmat()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc5519d8",
   "metadata": {},
   "source": [
    "## Alternative a and b matrices\n",
    "\n",
    "In the PC-SAFT implementation of Gross and Sadowski, they have specified coefficients for the approximations used for the integrals in the perturbation theory (Eqs. A.16 to A.19) \n",
    "\n",
    "$$\n",
    "I_1 = \\sum_{i=0}^6a_i(\\bar m)\\eta^i\n",
    "$$\n",
    "$$\n",
    "I_2 = \\sum_{i=0}^6b_i(\\bar m)\\eta^i\n",
    "$$\n",
    "\n",
    "$$\n",
    "a_i(\\bar m) = a_{0i} + \\frac{\\bar m-1}{\\bar m}a_{1i} + \\frac{\\bar m-1}{\\bar m}\\frac{\\bar m-2}{\\bar m}a_{2i}\n",
    "$$\n",
    "$$\n",
    "b_i(\\bar m) = b_{0i} + \\frac{\\bar m-1}{\\bar m}b_{1i} + \\frac{\\bar m-1}{\\bar m}\\frac{\\bar m-2}{\\bar m}b_{2i}\n",
    "$$\n",
    "\n",
    "and they provide tabulated values in Table 1 in their paper, but other works have identified that some of the limitations of PC-SAFT can be traced back to these universal parameters. Thus, as of version 0.21, two additional options for these parameter matrices are available from the works of Liang et al:\n",
    "\n",
    "* \"Liang-IECR-2012\": [Approach to Improve Speed of Sound Calculation within PC-SAFT Framework](https://pubs.acs.org/doi/10.1021/ie3018127)\n",
    "* \"Liang-IECR-2014\": [New Variant of the Universal Constants in the Perturbed Chain-Statistical Associating Fluid Theory Equation of State](https://pubs.acs.org/doi/10.1021/ie503925h)\n",
    "\n",
    "and they can be selected by providing the \"ab\" field in the JSON data structure. Something like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3c62c695",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.900764Z",
     "iopub.status.busy": "2025-10-15T23:09:07.900631Z",
     "iopub.status.idle": "2025-10-15T23:09:07.904616Z",
     "shell.execute_reply": "2025-10-15T23:09:07.903985Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<teqp.teqp.AbstractModel at 0x7ff0fc196210>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec = {\n",
    "  \"kind\": \"PCSAFT\", \n",
    "  \"model\": {\n",
    "    \"names\": [\"Methane\", \"Ethane\"], \n",
    "    \"ab\": \"Liang-IECR-2014\"\n",
    "  }\n",
    "}\n",
    "teqp.make_model(spec, validate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca52e844",
   "metadata": {},
   "source": [
    "## Superancillary\n",
    "\n",
    "The superancillary equation for PC-SAFT has been developed, and is much more involved than that of the cubic EOS. As a consequence, the superancillary equation has been provided as a separate package rather than integrating it into to teqp to minimize the binary size of teqp. It can be installed from PYPI with: ``pip install PCSAFTsuperanc``\n",
    "\n",
    "The scaling in the superancillaries uses reduced variables:\n",
    "\n",
    "$$ \\tilde T = T/(\\epsilon/k_{\\rm B}) $$\n",
    "$$ \\tilde\\rho = \\rho_{\\rm N}\\sigma^3 $$\n",
    "\n",
    "where $\\rho_{\\rm N}$ is the number density, and the other parameters are from the PC-SAFT model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f6e3b8d2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.905760Z",
     "iopub.status.busy": "2025-10-15T23:09:07.905624Z",
     "iopub.status.idle": "2025-10-15T23:09:07.921169Z",
     "shell.execute_reply": "2025-10-15T23:09:07.920585Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ttilde crit: 2.648680568587752\n",
      "Pressures are: 227809.1231446739 227809.12314409122 Pa\n"
     ]
    }
   ],
   "source": [
    "import PCSAFTsuperanc\n",
    "\n",
    "sigma_m = 3e-10 # [meter]\n",
    "e_over_k = 150.0 # [K]\n",
    "m = 5\n",
    "\n",
    "# The saturation temperature\n",
    "T = 300\n",
    "\n",
    "[Ttilde_crit, Ttilde_min] = PCSAFTsuperanc.get_Ttilde_crit_min(m=m)\n",
    "print('Ttilde crit:', Ttilde_crit)\n",
    "\n",
    "# Get the scaled densities for liquid and vapor phases\n",
    "[tilderhoL, tilderhoV] = PCSAFTsuperanc.PCSAFTsuperanc_rhoLV(Ttilde=T/e_over_k, m=m)\n",
    "# Convert back to molar densities\n",
    "N_A = PCSAFTsuperanc.N_A # The value of Avogadro's constant used in superancillaries\n",
    "rhoL, rhoV = [tilderho/(N_A*sigma_m**3) for tilderho in [tilderhoL, tilderhoV]]\n",
    "\n",
    "# As a sanity check, confirm that we got the same pressure in both phases\n",
    "c = teqp.SAFTCoeffs()\n",
    "c.sigma_Angstrom = sigma_m*1e10\n",
    "c.epsilon_over_k = e_over_k \n",
    "c.m = m\n",
    "model = teqp.PCSAFTEOS([c])\n",
    "z = np.array([1.0])\n",
    "pL = rhoL*model.get_R(z)*T*(1+model.get_Ar01(T, rhoL, z))\n",
    "pV = rhoV*model.get_R(z)*T*(1+model.get_Ar01(T, rhoV, z))\n",
    "print('Pressures are:', pL, pV, 'Pa')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bdf568f",
   "metadata": {},
   "source": [
    "## Maximum density\n",
    "\n",
    "The maximum number density allowed by the EOS is defined based on the packing fraction. To get a molar density, divide by Avogadro's number. The function is conveniently exposed in Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3c8491a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:07.922792Z",
     "iopub.status.busy": "2025-10-15T23:09:07.922618Z",
     "iopub.status.idle": "2025-10-15T23:09:07.927758Z",
     "shell.execute_reply": "2025-10-15T23:09:07.927127Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9139171771761775e+28"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "31782.085306811314"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_rhoN = teqp.PCSAFTEOS(coeffs).max_rhoN(130.0, np.array([0.3, 0.3, 0.4]))\n",
    "display(max_rhoN)\n",
    "max_rhoN/6.022e23 # the maximum molar density in mol/m^3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b310ef6",
   "metadata": {},
   "source": [
    "## Polar contributions\n",
    "\n",
    "As of teqp version 0.15, quadrupolar and dipolar contributions have been added to the hard chain plus dispersion model which is referred to conventionally as PC-SAFT. The definitions of the reduced dipolar and quadrupolar parameters are not well documented, so they are given here. The work of Stoll, Vrabec, and Hasse (https://doi.org/10.1063/1.1623475) clearly describes the formulation of the star-scaling. \n",
    "\n",
    "In SI units, the reduced squared dipole moment is defined by\n",
    "$$\n",
    "\t(\\mu^*)^2_{\\rm conventional} = \\frac{(\\mu[Cm])^2}{4\\pi\\epsilon_0(\\varepsilon[J])(\\sigma[m])^3}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\t(Q^*)^2_{\\rm conventional} = \\frac{(Q[Cm^2])^2}{4\\pi\\epsilon_0(\\varepsilon[J])(\\sigma[m])^5}\n",
    "$$\n",
    "\n",
    "In the PC-SAFT formulation, the only difference is the addition of dividing the denominator by the number of segments $m$\n",
    "\n",
    "$$\n",
    "\t(\\mu^*)^2 = \\frac{(\\mu[Cm])^2}{4\\pi\\epsilon_0m(\\varepsilon/k_{\\rm B}[K])k_B(\\sigma[m])^3}\n",
    "$$\n",
    "$$\n",
    "(Q^*)^2 = \\frac{(Q[Cm^2])^2}{4\\pi\\epsilon_0m(\\varepsilon/k_B[K])k_B(\\sigma[m])^5}\n",
    "$$\n",
    "\n",
    "The unit conversions are obtained from\n",
    "$$\n",
    "(\\sigma[m]) = (10^{-10}m/A)(\\sigma[A])\n",
    "$$\n",
    "$$\n",
    "(\\mu[Cm]) = (3.33564 \\times 10^{-30}  Cm/D)(\\mu[D])\n",
    "$$\n",
    "and $\\epsilon_0=8.85419e-12$ C$^2$  N$^{-1}$ m$^{-2}$ is the permittivity of vacuum. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "01a3552d",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-10-15T23:09:09.475389Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CO2 with quadrupolar contributions\n",
    "j = {\n",
    "    'kind': 'PCSAFT',\n",
    "    'model': {\n",
    "        'coeffs': [{\n",
    "            'name': 'CO2',\n",
    "             'BibTeXKey': 'Gross-AICHEJ',\n",
    "             'm': 1.5131,\n",
    "             'sigma_Angstrom': 3.1869,\n",
    "             'epsilon_over_k': 169.33,\n",
    "             '(Q^*)^2': 1.26, # modified from the values in Gross and Vrabec since the base model is different\n",
    "             'nQ': 1\n",
    "        }]\n",
    "    }\n",
    "}\n",
    "\n",
    "model = teqp.make_model(j)\n",
    "Tc, rhoc = model.solve_pure_critical(300, 11000)\n",
    "\n",
    "T = Tc*0.999\n",
    "rhoL_, rhoV_ = model.extrapolate_from_critical(Tc, rhoc, T)\n",
    "rhoL, rhoV = model.pure_VLE_T(T, rhoL_, rhoV_, 10)\n",
    "\n",
    "import CoolProp.CoolProp as CP\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "o = []\n",
    "for T_ in np.linspace(T, 215, 1000):\n",
    "    rhoL, rhoV = model.pure_VLE_T(T_, rhoL, rhoV, 10)\n",
    "    try:\n",
    "        o.append({\n",
    "          'T': T_, 'rhoL': rhoL, 'rhoV': rhoV, \n",
    "          'rhoLSW': CP.PropsSI('Dmolar','T',T_,'Q',0,'CO2'), \n",
    "          'rhoVSW': CP.PropsSI('Dmolar','T',T_,'Q',1,'CO2')\n",
    "        })\n",
    "    except:\n",
    "        pass\n",
    "df = pandas.DataFrame(o)\n",
    "plt.plot(df['rhoL'], df['T'], 'r', label='PCSAFT+Q')\n",
    "plt.plot(df['rhoV'], df['T'], 'r')\n",
    "plt.plot(df['rhoLSW'], df['T'], 'k', label='S&W')\n",
    "plt.plot(df['rhoVSW'], df['T'], 'k')\n",
    "plt.legend()\n",
    "plt.gca().set(xlabel=r'$\\rho$ / mol/m$^3$', ylabel='$T$ / K')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "00312a15",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-10-15T23:09:09.477611Z",
     "iopub.status.busy": "2025-10-15T23:09:09.477363Z",
     "iopub.status.idle": "2025-10-15T23:09:09.833009Z",
     "shell.execute_reply": "2025-10-15T23:09:09.832256Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Acetone with dipolar contributions\n",
    "j = {\n",
    "    'kind': 'PCSAFT',\n",
    "    'model': {\n",
    "        'coeffs': [{\n",
    "            'name': 'acetone',\n",
    "             'BibTeXKey': 'Gross-IECR',\n",
    "             'm': 2.7447,\n",
    "             'sigma_Angstrom': 3.2742,\n",
    "             'epsilon_over_k': 232.99,\n",
    "             '(mu^*)^2': 1.9, # modified from the values in Gross and Vrabec since the base model is different\n",
    "             'nmu': 1\n",
    "        }]\n",
    "    }\n",
    "}\n",
    "\n",
    "model = teqp.make_model(j)\n",
    "Tc, rhoc = model.solve_pure_critical(300, 11000)\n",
    "\n",
    "T = Tc*0.999\n",
    "rhoL_, rhoV_ = model.extrapolate_from_critical(Tc, rhoc, T)\n",
    "rhoL, rhoV = model.pure_VLE_T(T, rhoL_, rhoV_, 10)\n",
    "\n",
    "import CoolProp.CoolProp as CP\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "o = []\n",
    "for T_ in np.linspace(T, 215, 1000):\n",
    "    rhoL, rhoV = model.pure_VLE_T(T_, rhoL, rhoV, 10)\n",
    "    try:\n",
    "        o.append({\n",
    "          'T': T_, 'rhoL': rhoL, 'rhoV': rhoV, \n",
    "          'rhoLSW': CP.PropsSI('Dmolar','T',T_,'Q',0,'acetone'), \n",
    "          'rhoVSW': CP.PropsSI('Dmolar','T',T_,'Q',1,'acetone')\n",
    "        })\n",
    "    except:\n",
    "        pass\n",
    "df = pandas.DataFrame(o)\n",
    "plt.plot(df['rhoL'], df['T'], 'r', label='PCSAFT+D')\n",
    "plt.plot(df['rhoV'], df['T'], 'r')\n",
    "plt.plot(df['rhoLSW'], df['T'], 'k', label='S&W')\n",
    "plt.plot(df['rhoVSW'], df['T'], 'k')\n",
    "plt.legend()\n",
    "plt.gca().set(xlabel=r'$\\rho$ / mol/m$^3$', ylabel='$T$ / K')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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
}