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   "source": [
    "# NRTL\n",
    "\n",
    "The Non-Random-Two-Liquid model presented by Renon and Prausnitz.\n",
    "This model uses local compositions to represent the excess Gibbs energy.\n",
    "\n",
    "$$\n",
    "   G^E = nRT \\cdot \\sum_i x_i \\frac{\\sum_j x_j \\tau_{ji} G_{ji}}{\\sum_j x_j G_{ji}}\n",
    "$$\n",
    "\n",
    "with:\n",
    "\n",
    "$$\\tau_{ij} = A_{ij} + \\frac{B_{ij}}{T}$$\n",
    "\n",
    "$$G_{ij} = exp(-C\\tau_{ij})$$\n",
    "\n",
    "Where $A_{ij}, B_{ij}, \\text{ and } C$ are fittable parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3922ec11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.08590952, -0.94469266,  0.1460286 ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import yaeos\n",
    "\n",
    "\n",
    "aij = [\n",
    "    [0.0, -0.801, -0.351],\n",
    "    [-0.523, 0.0, 0.214],\n",
    "    [0.127, 0.211, 0.0],\n",
    "]\n",
    "\n",
    "bij = [\n",
    "    [0.0, -586.1, 246.2],\n",
    "    [301.2, 0.0, -104.2],\n",
    "    [150.23, -114.78, 0.0],\n",
    "]\n",
    "\n",
    "cij = [\n",
    "    [0.0, 0.3, 0.3],\n",
    "    [0.3, 0.0, 0.3],\n",
    "    [0.3, 0.3, 0.0],\n",
    "]\n",
    "\n",
    "model = yaeos.NRTL(aij, bij, cij)\n",
    "\n",
    "n = [2.0, 2.0, 8.0] # number of moles [mol]\n",
    "T = 298.15          # Temperature [K]\n",
    "\n",
    "model.ln_gamma(n, T)"
   ]
  }
 ],
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