{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4aa3c832",
   "metadata": {},
   "source": [
    "# UNIQUAC\n",
    "\n",
    "UNIQUAC (**uni**versal **qua**si**c**hemical) Excess Gibbs free energy model.\n",
    "\n",
    "$$ \n",
    "\\frac{G^E}{RT} = \\sum_k n_k \\ln\\frac{\\phi_k}{x_k}\n",
    "+ \\frac{z}{2}\\sum_k q_k n_k \\ln\\frac{\\theta_k}{\\phi_k}\n",
    "- \\sum_k q_k n_k \\ln\\left(\\sum_l \\theta_l \\tau_{lk} \\right)\n",
    "$$\n",
    "\n",
    "With:\n",
    "\n",
    "$$x_k = \\frac{n_k}{\\sum_l n_l}$$\n",
    "\n",
    "$$ \\phi_k = \\frac{r_k n_k}{\\sum_l r_l n_l} $$\n",
    "\n",
    "$$ \\theta_k = \\frac{q_k n_k}{\\sum_l q_l n_l} $$\n",
    "\n",
    "$$ \\tau_{lk} = \\exp \\left[\\frac{-\\Delta U_{lk}}{R T} \\right] $$\n",
    "\n",
    "$$\n",
    "\\frac{-\\Delta U_{lk}}{R T} = a_{lk}+\\frac{b_{lk}}{T}+c_{lk}\\ln T + d_{lk}T +\n",
    "e_{lk}{T^2}\n",
    "$$\n",
    "\n",
    "An example of having a mixture of Water-Ethanol-Bezene at 298.15 K with \n",
    "constant $\\frac{\\Delta U}{R}$ [K]:\n",
    "\n",
    "|Water|Ethanol|Benzene|\n",
    "|---------|--------|---------|\n",
    "| 0       | 526.02 | 309.64  |\n",
    "| −318.06 | 0      | −91.532 |\n",
    "| 1325.1  | 302.57 | 0       |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "48ae7daa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.18109416, -0.15137624,  0.35449467])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import yaeos\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "rs = [0.92, 2.1055, 3.1878]\n",
    "qs = [1.4, 1.972, 2.4]\n",
    "\n",
    "# Calculate bij from DUij. We need -DU/R to get bij\n",
    "bij = [\n",
    "    [0.0, -526.02, -309.64],\n",
    "    [318.06, 0.0, 91.532],\n",
    "    [-1325.1, -302.57, 0.0],\n",
    "]\n",
    "\n",
    "model = yaeos.UNIQUAC(qs, rs, bij=bij)\n",
    "\n",
    "\n",
    "n = [2.0, 2.0, 8.0] # number of moles [mol]\n",
    "T = 298.15          # Temperature [K]\n",
    "\n",
    "\n",
    "model.ln_gamma(n, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d38e9779",
   "metadata": {},
   "source": [
    "The complete docstring of the UNIQUAC model is the following:\n",
    "\n",
    "\n",
    "```\n",
    "Init signature: yaeos.UNIQUAC(qs, rs, aij=None, bij=None, cij=None, dij=None, eij=None) -> None\n",
    "Docstring:     \n",
    "UNIQUAC (UNIversal QUAsiChemical) Excess Gibbs free energy model.\n",
    "\n",
    "Please refer to the `yaeos` user documentation for an in-depth look at the\n",
    "model's information: https://ipqa-research.github.io/yaeos/page/index.html\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "qs : array_like\n",
    "    Molecule's relative areas :math:`Q_i`\n",
    "rs : array_like\n",
    "    Molecule's relative volumes :math:`R_i`\n",
    "aij : array_like\n",
    "    Interaction parameters matrix :math:`a_{ij}` zero matrix if no\n",
    "    provided, by default None\n",
    "bij : array_like\n",
    "    Interaction parameters matrix :math:`b_{ij}` zero matrix if no\n",
    "    provided, by default None\n",
    "cij : array_like\n",
    "    Interaction parameters matrix :math:`c_{ij}` zero matrix if no\n",
    "    provided, by default None\n",
    "dij : array_like\n",
    "    Interaction parameters matrix :math:`d_{ij}` zero matrix if no\n",
    "    provided, by default None\n",
    "eij : array_like\n",
    "    Interaction parameters matrix :math:`e_{ij}` zero matrix if no\n",
    "    provided, by default None\n",
    "```"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "yaeos",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}