examples/1. Computing 1st and 2nd order derivative properties with the FE-ANN EoS.ipynb

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  {
   "cell_type": "markdown",
   "id": "448d4768",
   "metadata": {},
   "source": [
    "# 1. Computing 1st and 2nd order derivative properties using the FE-ANN EoS\n",
    "\n",
    "This notebook exemplifies how to use the FE-ANN EoS to compute derivate properties of the Helmholtz free energy.\n",
    "\n",
    "The FE-ANN EoS model systems interacting throgh the Mie Potential:\n",
    "\n",
    "$$ U^{Mie} = \\mathcal{C}_{Mie} \\epsilon \\left[ \\left(\\frac{\\sigma}{r}\\right)^{\\lambda_r} -  \\left(\\frac{\\sigma}{r}\\right)^{\\lambda_a} \\right], \\quad \\mathcal{C}_{Mie} = \\frac{\\lambda_r}{\\lambda_r- \\lambda_a} \\left( \\frac{\\lambda_r}{\\lambda_a}\\right)^{\\frac{\\lambda_a}{\\lambda_r - \\lambda_a}} $$ \n",
    "\n",
    "Here, $\\epsilon$ represents the potential well depth, $\\sigma$ is the effective monomer diameter, $r$ is the centre-to-centre distance between two Mie monomers, and $\\lambda_r$ and $\\lambda_a$ are the repulsive and attractive exponent, respectively. The FE-ANN EoS uses dimensionless Lennard-Jones units (equivalently to setting $\\epsilon$, $\\sigma$, the Boltzmann constant $k_b$ and the monomer mass $m$ to 1).\n",
    "\n",
    "The FE-ANN EoS describes the residual Helmholtz free energy as follows.\n",
    "\n",
    "$$ A^{res} = ANN(\\alpha_{vdw}, \\rho, 1/T) - ANN(\\alpha_{vdw}, \\rho=0.0, 1/T) $$\n",
    "\n",
    "Where, $A^{res}$ is the dimensionless residual Helmholtz free energy, $\\rho$ is the dimensionless density, $T$ is the dimensionless temperature and $\\alpha_{vdw}$ is defined a the Mie fluid as follows:\n",
    "\n",
    "$$ \\alpha_{vdw} = \\mathcal{C}_{Mie} \\left[ \\left(\\frac{1}{\\lambda_a-3} \\right) - \\left(\\frac{1}{\\lambda_r-3} \\right) \\right]$$\n",
    "\n",
    "**Note: all expressions and quantities in this notebook assume dimensionless units ( $\\epsilon = \\sigma = k_b = m = 1.$)**\n",
    "\n",
    "To start using the FE-ANN EoS, firstly, we import the required packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "313aaf98",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "# HelmholtzModel_Tinv is the custom TensorFlow model class, only needed if creating a new model from scratch\n",
    "from helmholtz_model_Tinv import HelmholtzModel_Tinv\n",
    "\n",
    "# Setting up tensorflow for float64\n",
    "PRECISSION = 'float64'\n",
    "type_np = np.float64\n",
    "type_tf = tf.float64\n",
    "tf.keras.backend.set_floatx(PRECISSION)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4a6b547",
   "metadata": {},
   "source": [
    "The pre-saved model is loaded using the `tf.keras.models.load_model` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "513ebf4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading saved model using tensorflow\n",
    "model_path = '../fe-ann-eos'\n",
    "model = tf.keras.models.load_model(model_path, compile=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c344d6b",
   "metadata": {},
   "source": [
    "The EoS is ready to be used. This notebook will exemplify calculations for the Lennard-Jones fluid ($\\lambda_r=12$ and $\\lambda_a=6$). First, the $\\alpha_{vdw}$ parameter is computed. Then, the inputs arrays that contains $\\alpha_{vdw}$, $\\rho$ and $T$ are set up. For this example, all calculations will be made at a constant temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7dbc82cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computing α for the Lennard-Jones fluid\n",
    "lr = 12.\n",
    "la = 6.\n",
    "c_alpha = (lr / (lr-la)) * (lr/la)**(la/(lr-la))\n",
    "alpha_aux = c_alpha*(1./(la-3) - 1./(lr-3))\n",
    "\n",
    "# Setting up arrays to perform the calculations\n",
    "n = 50 # number of data points to compute\n",
    "T = 1.2\n",
    "alpha = alpha_aux * np.ones(n, dtype=type_np)\n",
    "density = np.linspace(1e-3, 1.2, n, dtype=type_np)\n",
    "temperature = T * np.ones(n, dtype=type_np)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f155ac1",
   "metadata": {},
   "source": [
    "## Helmholtz free energy calculations \n",
    "The Helmholtz free energy and its derivatives can be easily accessed using the model's method. The ``model.helmholtz`` method computes the residual Helmholtz free energy. \n",
    "\n",
    "``model.helmholtz`` method.\n",
    "\n",
    "Inputs\n",
    "- $\\alpha_{vdw}$: van der Waals $\\alpha$ parameter\n",
    "- $\\rho$: dimensionless density\n",
    "- $T$: dimensionless temperature\n",
    "\n",
    "Outputs:\n",
    "- `helmholtz`: dimensionless residual Helmholtz free energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0f19176d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-02-14 08:21:48.373757: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(50,), dtype=float64, numpy=\n",
       "array([-0.00475626, -0.11932764, -0.23044083, -0.33815134, -0.44253595,\n",
       "       -0.5436838 , -0.64168945, -0.73664751, -0.82864851, -0.91777563,\n",
       "       -1.0041021 , -1.08768896, -1.16858306, -1.246815  , -1.32239711,\n",
       "       -1.39532102, -1.46555478, -1.5330391 , -1.59768242, -1.65935427,\n",
       "       -1.71787654, -1.77301256, -1.82445406, -1.87180693, -1.91457736,\n",
       "       -1.95216062, -1.98383525, -2.00876491, -2.02600939, -2.03454413,\n",
       "       -2.03328566, -2.02111871, -1.99691993, -1.95957384, -1.90797819,\n",
       "       -1.84103841, -1.7576527 , -1.65669121, -1.53697356, -1.39724925,\n",
       "       -1.23618583, -1.05236914, -0.84431997, -0.61053106, -0.34952722,\n",
       "       -0.05994934,  0.25934005,  0.60913704,  0.98977555,  1.40102376])>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "helmholtz = model.helmholtz(alpha, density, temperature)\n",
    "helmholtz"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be3c8a5a",
   "metadata": {},
   "source": [
    "The ``model.dhelmholtz`` computes the Helmholtz free energy and its first derivatives (both density and temperature derivatives).  This function returns a tuple that contains ``(helmholtz, dhelmholtz_drho, dhelmholtz_dT)``.\n",
    "\n",
    "``model.dhelmholtz`` method.\n",
    "\n",
    "Inputs\n",
    "- $\\alpha_{vdw}$: van der Waals $\\alpha$ parameter\n",
    "- $\\rho$: dimensionless density\n",
    "- $T$: dimensionless temperature\n",
    "\n",
    "Outputs:\n",
    "- ``helmholtz``: residual dimensionless Helmholtz free energy\n",
    "- ``dhelmholtz_drho``: first derivative of dimensionless residual Helmholtz free energy with respect to density.\n",
    "- ``dhelmholtz_dT``: first derivative of dimensionless residual Helmholtz free energy with respect to temperature.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "575c349e",
   "metadata": {},
   "outputs": [],
   "source": [
    "out = model.dhelmholtz(alpha, density, temperature)\n",
    "helmholtz = out[0]\n",
    "dhelmholtz_drho = out[1] \n",
    "dhelmholtz_dT = out[2] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5d34ccb",
   "metadata": {},
   "source": [
    "Lastly, the ``model.d2helmholtz`` computes the Helmholtz free energy and its first and second order derivatives (density, temperature and cross-derivative). This function returns a tuple that contains ``(helmholtz, dhelmholtz_drho, dhelmholtz_dT, d2helmholtz_drho2, d2helmholtz_dT2, d2helmholtz_drho_dT)``.\n",
    "\n",
    "\n",
    "``model.d2helmholtz`` method.\n",
    "\n",
    "Inputs\n",
    "- $\\alpha_{vdw}$: van der Waals $\\alpha$ parameter\n",
    "- $\\rho$: dimensionless density\n",
    "- $T$: dimensionless temperature\n",
    "\n",
    "Outputs\n",
    "- ``helmholtz``: dimensionless residual Helmholtz free energy\n",
    "- ``dhelmholtz_drho``: first derivative of dimensionless residual Helmholtz free energy with respect to density.\n",
    "- ``dhelmholtz_dT``: first derivative of dimensionless residual Helmholtz free energy with respect to temperature.\n",
    "- ``d2helmholtz_drho2``: second derivative of dimensionless residual Helmholtz free energy with respect to density.\n",
    "- ``d2helmholtz_dT2``: second derivative of dimensionless residual Helmholtz free energy with respect to temperature.\n",
    "- ``d2helmholtz_drho_dT``: cross derivative of dimensionless residual Helmholtz free energy with respect to density and temperature.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "07a15184",
   "metadata": {},
   "outputs": [],
   "source": [
    "out = model.d2helmholtz(alpha, density, temperature)\n",
    "\n",
    "helmholtz = out[0]\n",
    "dhelmholtz_drho = out[1] \n",
    "dhelmholtz_dT = out[2] \n",
    "d2helmholtz_drho2 = out[3] \n",
    "d2helmholtz_dT2 = out[4] \n",
    "d2helmholtz_drho_dT = out[5] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "202d91b1",
   "metadata": {},
   "source": [
    "## First-order derivative properties calculation\n",
    "\n",
    "Once the Helmholtz free energy and its derivatives are available other thermophysical properties can be easily computed.\n",
    "\n",
    "### Pressure calculation\n",
    "\n",
    "The pressure of the system is computed as the sum of the ideal and residual contribution.\n",
    "\n",
    "$$P = P^{id} + P^{res}; \\quad P^{id} = \\rho T; \\quad P^{res} = \\rho^2 \\left( \\frac{\\partial A^{res}}{\\partial \\rho }\\right)_{T}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aee4493e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$P$')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# computing the ideal contribution\n",
    "pressure_ideal = density*temperature\n",
    "# computing the residual contribution\n",
    "pressure_residual = density**2 * dhelmholtz_drho\n",
    "\n",
    "# computing the total pressure\n",
    "pressure = pressure_ideal + pressure_residual\n",
    "\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(density, pressure)\n",
    "ax.set_xlim([0, 1.2])\n",
    "ax.set_xlabel(r\"$\\rho$\")\n",
    "ax.set_ylabel(r\"$P$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "824ef271",
   "metadata": {},
   "source": [
    "### Internal Energy calculation\n",
    "\n",
    "Similarly, the internal energy can also be computed from an ideal and a residual contribution.\n",
    "\n",
    "$$U = U^{id} + U^{res}; \\quad U^{id} = 1.5 T; \\quad U^{res} = A^{res} - T \\left( \\frac{\\partial A^{res}}{\\partial T }\\right)_{\\rho}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f482af71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$U$')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eZ1dfBEHAB0M647HOXiguFfGPVQdw4NwVqWMRQRBl8p13VFQUVq5cecf87du3o0+fPtVah8lkgl6vh9FohIuLi4UT2q6ikjKMWbkfu0/lwUWnwtrxEQhsxvePLKsm22e1iys0NBQhISEVU1BQENRqtUUCWwuLq/auF5XghS/24WB6Ppo4axE3vidaujtKHYtsSE22z2p/VIyIiMDhw4cxadIkhIWFwdnZGSEhIZgwYQL27NlT59DUsDlqVIiNCkdgM2dcLDDjhWX7kGsqlDoW2akaf1QsLS3F0aNHkZiYiMTERPzyyy9IS0tDZGQkYmNjIQhCfWWtM+5x1V2uqRDPLPkD6ZevI8DTGWvG9YCro0bqWGQD6uWjYlW2bduG559/HjNnzsTYsWPrurp6w+KyjPRL1/HMkr3ILTAjuKUrvh7bHY4aSb+gJhtQLx8Vq/LII4/ggw8+wNKlSy2xOmrgWro74ssx3aF3UMOQzhElyPosdjpEjx49kJqaaqnVUQMX0MwZsaPKR5TYfSoPk9cc4ogSZDXVLq6FCxciISEBZrP5rv9+8eJF2X3LSHXTrWVjLI0MgVopYNPhbPx7wxGOKEFWUe1jXI0bN4bJZIJKpUKHDh0QGhqK0NBQtG/fHtevX0d0dDRat26NdevW1XfmWuMxrvqxKTkbr60+CFEEXunTGlMGBkodiWSoJttntY+oXrlyBWlpaThw4EDFFBcXh/z8fABAYGAg5syZU6fgJE+PBXnBVNgZ0esPY9GONDR21OClB1tJHYtsWJ2/VczMzERxcTH8/f0tlanecI+rfi3akYr/3hzD679PB+HZMA4jRNVXL3tc99KiRYu6roJsxMs3R5T4bNdpTF2fDL2jGgM6NpM6Ftkg2VxkTQ2fIAiIHhSIZ0NboEwEJqw24I+0S1LHIhvE4iKLEgQBM5/sjP4dPFFUUoaXViXiyHmj1LHIxrC4yOJUSgXmjwhGd383XDWXICo2AWfyrkkdi2wIi4vqhU6txOcjQ9HBywV5V4sQuWwfLvCibLIQFhfVGxedGitHh8PX3RGZV25g5PIEGG8USx2LbACLi+pVE2ctvhrTHU2ctTieU4CXViaisJjXNVLdsLio3vm4OWLlqHA4a1VIOHsZE1YbUFJaJnUskjEWF1lFB28XfDEyFBqVAttSLmBaPK9rpNpjcZHVdG/ljgUjgqEQgDWJGZizlXfKptphcZFVDejYDB/evFP2wu1piN1zRuJEJEcsLrK6EeEt8c9H2gEA3vsxBT8mZ0mciOSGxUWSeO1vbfBihC9EEZi85hD2puVJHYlkhMVFkhAEAdMHd8SgTs1QVFqGcasOICXLJHUskglZFNfZs2cxZswY+Pv7w8HBAa1bt8b06dNRVFQkdTSqA6VCwNxhXRHu74aCm5cGZVy+LnUskgFZFNfx48dRVlaGpUuX4ujRo5g7dy6WLFmCt99+W+poVEc6tRKfvxiKAE9n5BaYMXJ5Ai5f4x8kqppFbk8mhY8++giLFy/G6dOnq/0YDiTYcOUYC/HUoj3IMhaiW0tXfD22Bxw0SqljkRVZ/fZkUjAajXBzc6tyGbPZDJPJVGmihqmZXodVY8Khd1DjYHo+Xv/WwLsG0T3JsrjS0tKwYMECjB8/vsrlYmJioNfrKyYfHw4l3JC1aepc6ez66Rt5dj3dnaTFNWPGDAiCUOWUmJhY6TFZWVkYOHAghg4det+7ZkdHR8NoNFZMGRkZ9flyyALC/Nzwv2FdIQjAV3+mY9GONKkjUQMk6TGuvLw85OVVff6On58fdDodgPLS6tu3L7p3744VK1ZAoahZ7/IYl3zE7jmDd39IAQB8PLQLng7hvQ1snVVvllEXHh4e8PDwqNay58+fR9++fRESEoLY2NgalxbJy6he/sg2FuKzXafxVlwyPF106N22ev+vkO2TxdaflZWFPn36wMfHB3PmzMHFixeRk5ODnJwcqaNRPZo6MBCDu3ijpEzE+K8O4Fg2v1yhcpLucVXX1q1bkZqaitTU1Dtuh8aDt7ZLoRAwZ2gQck2F2HfmMkbF7kf8qz3hpXeQOhpJTBZ7XFFRURBF8a4T2TatSonPIkPRtmkj5JgKEbV8P0yFHP7Z3smiuMi+6R3ViB0VhibOWpy4UICXvzqAohKOoGrPWFwkCy0aOyI2KgyOGiX2pF7C1Lhk7nHbMRYXyUan5noser4blAoB6w3nMfeXU1JHIomwuEhW+gQ0xQdDOgEA5v96CmsTeVKxPWJxkeyMCG+JV/q0BgC8vf4wfj/FQQjtDYuLZOlf/QPwxM1zvF7+6gCO5/AcL3vC4iJZUigEfDQ0qGIQwlGx+5FjLJQ6FlkJi4tkq/wcrxC0auKEbGMhRq/Yj6vmEqljkRWwuEjWXB01WDkqHB6NNEjJNmHCNwd5l2w7wOIi2fNxc8QXI8OgUyuw/cRFTN94lOd42TgWF9mErj6umDcsGIIAfL0vHZ/vrv6Q3iQ/LC6yGQM7NcO0R9sDAGZuPo7Nh7MlTkT1hcVFNmVMb3+MjPAFAExak4QD565InIjqA4uLbIogCHhncEc83L4pzCVleGlVIs5duiZ1LLIwFhfZHKVCwPwRwejcXI/L14owKnY/rvBejTaFxUU2yVGjwrKRoWju6oDTedcw7ssDMJeUSh2LLITFRTarqYsOsaPC4KxVIeHsZbz5XTLKeK9Gm8DiIpvWztMZSyJDoFII2HgoCx9vOyF1JLIAFhfZvF5tPBDzVGcAwMLtafg2IV3iRFRXLC6yC0NDffB6v7YAgGkbjmDHiVyJE1FdsLjIbkx6uC2e6tYcpWUiXv36II5mGaWORLXE4iK7IQgCZj0VhJ6t3XGtqBSjYvfjfP4NqWNRLbC4yK5oVAosiQxBgKczcgvMGB3L253JkWyK64knnkDLli2h0+ng5eWFyMhIZGVlSR2LZMhFV367s6Y3b3c2/kve7kxuZFNcffv2xdq1a3HixAnExcUhLS0NzzzzjNSxSKa8XR0QOyoMThol9qZdwpR1h3iOl4wIokwHLtq4cSOGDBkCs9kMtVpdrceYTCbo9XoYjUa4uLjUc0KSg10nL2L0iv0oKRMx/qHWmDooUOpIdqsm26ds9rj+6vLly/j666/Rs2fPKkvLbDbDZDJVmoj+6sF2TTDr6SAAwJKdaVj1x1lpA1G1yKq43nrrLTg5OcHd3R3p6en4/vvvq1w+JiYGer2+YvLx8bFSUpKTZ0Ja4F/92wEApm88ip+O5EiciO5H0uKaMWMGBEGockpMTKxY/s0334TBYMDWrVuhVCrx4osvVjlEb3R0NIxGY8WUkcGbh9Ldvdq3DUaEt4QoAhO/NSDx7GWpI1EVJD3GlZeXh7y8qm/m6efnB51Od8f8zMxM+Pj4YO/evYiIiKjW8/EYF1WlpLQM4786gF+O5cJFp8K6l3uinaez1LHsRk22T5WVMt2Vh4cHPDw8avXYW31rNpstGYnsmEqpwIIR3fD8F3/iYHo+XlyWgLhXeqK5q4PU0eg2sjjGlZCQgE8//RRJSUk4d+4ctm/fjueeew6tW7eu9t4WUXU4aJRYHhWGNk0bIcdUiMhl+3CZgxA2OLIoLgcHB6xfvx79+vVDQEAARo8ejU6dOmHnzp3QarVSxyMb4+qowarR4fDS63D64jWMWrEf14t4o9mGRLbncdUGj3FRTaTmFuCZJX8g/3oxHmrXBJ+/GAqNShZ/62XJ5s/jIrKGNk2dsTyq/EazO09exOS1SSjl2fUNAouLqArdWjbGkhdCoFYK+DE5G9PiD/Mu2Q0Ai4voPvoENMX/hgdDIQDf7s/AzM3HWF4SY3ERVcOjnb0w66nyS4M+330Gn/6WKnEi+8biIqqmZ8N88J/HOwAAPt52ErF7zkicyH6xuIhqYExvf7zxcPnY9e/+kIKv952TOJF9YnER1dDEfm3xjwdbAQCmxR/Bmv28a5C1sbiIakgQBEQPCsToXv4AgKnrD+O7RF7Ab00sLqJaEAQB/3m8PUZG+EIUgSlxyYg3ZEody26wuIhqSRAEzHiiI57vXj4czj/XHsL3SeeljmUXWFxEdSAIAt7/eycMD/NBmQi8sSYJa/fzY2N9Y3ER1ZFCIWDmk53x3M09rylxyRwCup6xuIgsQKEQ8OGQThUH7N/5/iiW7kyTOJXtYnERWcitA/av9W0DAIjZchzzfjnJy4PqAYuLyIIEQcC/BgTgzQEBAIB5v5zC+z8e4z0bLYzFRVQPXu3bBu/cvDxo+Z4zmLgmCeaSUolT2Q4WF1E9Gd3bH/OGdYVaKeCHQ1kYFbsfBYXFUseyCSwuono0JLg5lkeFwUmjxN60Sxi29E/kmgqljiV7LC6ievZA2yZYMy4CHo00SMk24anFe3HyQoHUsWSNxUVkBZ2a67H+5V7wc3dE5pUbeHLhHvx67ILUsWSLxUVkJS3dHRH/Si/0aOWGa0WlGLsqEUt2pvF0iVpgcRFZUWMnDb4c073i+sZZW47jn2sPobCY3zjWBIuLyMrUSgU+fLIz3v97RygVAtYbzmPY0j+Qcfm61NFkQ3bFZTab0bVrVwiCgKSkJKnjENVaZIQfVo0Oh95BjUOZRjw2fze2Hs2ROpYsyK64pkyZAm9vb6ljEFlErzYe+HFCb3TxcYWpsAT/+PIA3v8xBUUlZVJHa9BkVVxbtmzB1q1bMWfOHKmjEFmMj5sjvhsXgbG9yy/QXvb7GTzLj45Vkk1xXbhwAS+99BK+/PJLODo6VusxZrMZJpOp0kTUEGlUCvz78Q74LDIELjoVkjLyMXDeLny975xdfOsoiiJi95yu9vKyKC5RFBEVFYXx48cjNDS02o+LiYmBXq+vmHx8fOoxJVHd9e/YDJtefwBhfo1xragU0+KPIHJZAjKv2O7el6mwGOO/OoCPt56q9mMkLa4ZM2ZAEIQqp8TERCxYsAAmkwnR0dE1Wn90dDSMRmPFlJHBkSmp4fNxc8Saf0TgP493gE6twO+peRg4bzdWJ6Tb3N7XsWwTnljwO34+egFqpVDtxwmihO9EXl4e8vLyqlzGz88Pw4cPxw8//ABB+P8XVlpaCqVSieeffx4rV66s1vOZTCbo9XoYjUa4uLjUKTuRNZy+eBVvrkvGgXNXAAAhvo0xY3BHdG6hlzhZ3a0/mIm34w+jsLgMzV0d8N8n2qB3R99qbZ+SFld1paenVzo+lZWVhQEDBmDdunXo3r07WrRoUa31sLhIjkrLRMTuOYNPtp3E9aJSCALwbIgP3hwYAI9GWqnj1djFAjPe+zEFPxzKAgA81K4J5g3rCmVpYbW3T1kU1+3Onj0Lf39/GAwGdO3atdqPY3GRnOUYCzFryzFsSCrf4J21Krzery0iI3yhUyslTnd/oijiu8RMfLj5GIw3iqEQgNf7tcXrf2sLhUKo0fapslJmIqqjZnod5g0PRmSEL2ZsTMHh80Z8uPkYlu46jXEPtsLzPVrCUdMwN+kzedcQvT4Zf56+DADo6O2CWU8F1fojryz3uGqLe1xkK8rKRKw7mIn5v55C5pUbAAA3Jw3GPuCPyB6+cNapJU5YLvPKdSzekYbvEjNRVFoGnVqByY+0w+he/lApK383WJPtk8VFJGPFpWWIN5zHwu2pOHep/JQJJ40Sg7t4Y3h4S3Rpoa/0pZa1pF+6jkU7UrHuQCZKbo63/2C7Jvjg753Q0v3u52GyuO6BxUW2qqS0DD8kZ2Hh9jSk5l6tmB/YzBnDw3zwaJAXmjrr6jVDUUkZdp28iA1J57HlSA5KbxZW7zYemPC3Nujeyr3Kx7O47oHFRbZOFEUknLmMb/dnYPPhbJj/cs1jp+Yu6BvQFH0CmqKrjyuUirrviRWXlmH/mcvYeCgLW47kwHjj/8fU7xPQBBP+1hYhvo2rtS4W1z2wuMieGK8XI96QifWG80jONFb6NxedCh28XRDYzAWBzZwR0MwZfu5OcNap7jj2BJTv0RlvFOPiVTOOnjchOTMfhzKNSMk2VbogvKmzFo8FeeHpbi3QqXnNDryzuO6BxUX26mKBGTtPXsT2E7nYffIiTIUl91zWQa2Es06FRjoVikrKYLxejALzvZdv7KjGwE7NMLiLN7r7u9d6T47FdQ8sLqLyvafjOQXlU7YJJy6U//fFAvN9H6t3UCPA0xmdW+gR1EKPLi1c4evuaJEvAHgeFxHdk0qpQKfm+js+yhWXluFqYQmumktgKixGQWEJNCoFXB3UaOyogYuD2iLHxSyBxUVEAMqHlG7spEFjJ43UUe5LFsPaEBH9FYuLiGSHxUVEssPiIiLZYXERkeywuIhIdlhcRCQ7dnUe162LBHibMqKG59Z2WZ2LeeyquC5dugQAvE0ZUQNWUFAAvb7qC7Ttqrjc3NwAlN98435vTENkMpng4+ODjIwM2V5rKffXIPf8QMN9DaIooqCgAN7e3vdd1q6KS6EoP6Sn1+sb1C+splxcXGSdH5D/a5B7fqBhvobq7lDw4DwRyQ6Li4hkx66KS6vVYvr06dBq5XcTTUD++QH5vwa55wds4zXY1UCCRGQb7GqPi4hsA4uLiGSHxUVEssPiIiLZkXVxLVq0CP7+/tDpdAgJCcHu3burXH7nzp0ICQmBTqdDq1atsGTJkjuWiYuLQ4cOHaDVatGhQwfEx8fXV3wANXsN69evxyOPPIImTZrAxcUFERER+Pnnnysts2LFCgiCcMdUWFgoef4dO3bcNdvx48crLWfN30FN8kdFRd01f8eOHSuWsfb7v2vXLgwePBje3t4QBAEbNmy472Ma4nZQY6JMffvtt6JarRY///xzMSUlRZw4caLo5OQknjt37q7Lnz59WnR0dBQnTpwopqSkiJ9//rmoVqvFdevWVSyzd+9eUalUijNnzhSPHTsmzpw5U1SpVOKff/7ZIF7DxIkTxdmzZ4sJCQniyZMnxejoaFGtVosHDx6sWCY2NlZ0cXERs7OzK00NIf/27dtFAOKJEycqZSspKalYxpq/g5rmz8/Pr5Q7IyNDdHNzE6dPn16xjDXff1EUxc2bN4vTpk0T4+LiRABifHx8lcs3xO2gNmRbXOHh4eL48eMrzQsMDBSnTp161+WnTJkiBgYGVpo3btw4sUePHhU/P/vss+LAgQMrLTNgwABx+PDhFkpdWU1fw9106NBBfPfddyt+jo2NFfV6vaUiVqmm+W8V15UrV+65Tmv+Dur6/sfHx4uCIIhnz56tmGfN9/921Smuhrgd1IYsPyoWFRXhwIED6N+/f6X5/fv3x969e+/6mD/++OOO5QcMGIDExEQUFxdXucy91lkXtXkNtysrK0NBQUHFxeO3XL16Fb6+vmjRogUef/xxGAwGi+W+pS75g4OD4eXlhX79+mH79u2V/s1avwNLvP/Lli3Dww8/DF9f30rzrfH+11ZD2w5qS5bFlZeXh9LSUnh6elaa7+npiZycnLs+Jicn567Ll5SUIC8vr8pl7rXOuqjNa7jdxx9/jGvXruHZZ5+tmBcYGIgVK1Zg48aNWL16NXQ6HXr16oVTp05Jnt/LywufffYZ4uLisH79egQEBKBfv37YtWtXxTLW+h3U9f3Pzs7Gli1bMHbs2ErzrfX+11ZD2w5qS9ajQ9x+229RFKu8Ffjdlr99fk3XWVe1fb7Vq1djxowZ+P7779G0adOK+T169ECPHj0qfu7Vqxe6deuGBQsWYP78+ZYLflNN8gcEBCAgIKDi54iICGRkZGDOnDl48MEHa7XOuqrtc61YsQKurq4YMmRIpfnWfv9royFuBzUlyz0uDw8PKJXKO/4C5Obm3vGX4pZmzZrddXmVSgV3d/cql7nXOuuiNq/hljVr1mDMmDFYu3YtHn744SqXVSgUCAsLs/hf/Lrk/6sePXpUymat30Fd8ouiiOXLlyMyMhIaTdV3fa6v97+2Gtp2UFuyLC6NRoOQkBBs27at0vxt27ahZ8+ed31MRETEHctv3boVoaGhUKvVVS5zr3XWRW1eA1C+pxUVFYVvvvkGjz322H2fRxRFJCUlwcvLq86Z/6q2+W9nMBgqZbPW76Au+Xfu3InU1FSMGTPmvs9TX+9/bTW07aDWpPlOoO5ufZW9bNkyMSUlRXzjjTdEJyenim94pk6dKkZGRlYsf+tr4EmTJokpKSnismXL7vgaeM+ePaJSqRRnzZolHjt2TJw1a5ZVToeo7mv45ptvRJVKJS5cuLDSV+35+fkVy8yYMUP86aefxLS0NNFgMIijRo0SVSqVuG/fPsnzz507V4yPjxdPnjwpHjlyRJw6daoIQIyLi6tYxpq/g5rmv+WFF14Qu3fvftd1WvP9F0VRLCgoEA0Gg2gwGEQA4ieffCIaDIaKUzrksB3UhmyLSxRFceHChaKvr6+o0WjEbt26iTt37qz4t5EjR4oPPfRQpeV37NghBgcHixqNRvTz8xMXL158xzq/++47MSAgQFSr1WJgYGCljUrq1/DQQw+JAO6YRo4cWbHMG2+8IbZs2VLUaDRikyZNxP79+4t79+5tEPlnz54ttm7dWtTpdGLjxo3F3r17i5s2bbpjndb8HdT0/6H8/HzRwcFB/Oyzz+66Pmu//7dOMbnX/xNy2Q5qisPaEJHsyPIYFxHZNxYXEckOi4uIZIfFRUSyw+IiItlhcRGR7LC4iEh2WFxEJDssLiKSHRYXydbvv/+O8PBw6HQ6eHh4YO7cuVJHIithcZEsbd68GU8++SReeeUVJCcnY9y4cZg8eTLS0tKkjkZWwGsVSXYKCwvRtm1bzJ49G8899xwAoLS0FI0bN8a8efMwevRoiRNSfeMeF8nOb7/9hhs3bmDYsGEV85RKJVQqFbRarYTJyFpYXCQ727dvR5cuXaBUKivmnTlzBleuXEG3bt0kTEbWwuIi2TEYDCgqKqo0b8GCBejWrRvat28vUSqyJlnfLIPsU1JSEsrKyrBy5UpERERg7dq1WLx4Mfbs2SN1NLISFhfJSnp6Oi5duoRNmzbhrbfewsmTJxEUFISffvqJHxPtCL9VJFnZuHEjRo0ahUuXLkkdhSTEY1wkKwaDAZ07d5Y6BkmMxUWyYjAYEBQUJHUMkhg/KhKR7HCPi4hkh8VFRLLD4iIi2WFxEZHssLiISHZYXEQkOywuIpIdFhcRyQ6Li4hkh8VFRLLD4iIi2fk/6aZDEVyxtXUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# computing the ideal contribution\n",
    "internal_energy_ideal = 1.5 * temperature\n",
    "# computing the residual contribution\n",
    "internal_energy_residual = helmholtz - temperature * dhelmholtz_dT\n",
    "\n",
    "# computing the total internal energy\n",
    "internal_energy = internal_energy_ideal + internal_energy_residual\n",
    "\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(density, internal_energy)\n",
    "ax.set_xlim([0, 1.2])\n",
    "ax.set_xlabel(r\"$\\rho$\")\n",
    "ax.set_ylabel(r\"$U$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8e27642",
   "metadata": {},
   "source": [
    "## Second-order derivative properties calculation\n",
    "\n",
    "Similarly, second-order derivatives properties, such as heat capacities, the isothermal compressibility and can be computed from the Helmholtz free energy derivatives.\n",
    "\n",
    "### Isobaric Heat Capacity\n",
    "\n",
    "The isobaric heat capacity is defined as follows:\n",
    "\n",
    "$$ C_V = \\left( \\frac{\\partial U}{\\partial T}\\right)_{\\rho} = \\underbrace{\\left( \\frac{\\partial U^{id}}{\\partial T}\\right)_{\\rho}}_{C_V^{id}} + \\underbrace{ \\left( \\frac{\\partial U^{res}}{\\partial T}\\right)_{\\rho}}_{C_V^{res}}  $$\n",
    "\n",
    "Where,\n",
    "\n",
    "$$ C_V^{id} =  \\left( \\frac{\\partial U^{id}}{\\partial T}\\right)_{\\rho} = 1.5$$ \n",
    "\n",
    "$$ C_V^{res} =  \\left( \\frac{\\partial U^{res}}{\\partial T}\\right)_{\\rho} = -T \\left( \\frac{\\partial^2 A^{res}}{\\partial T^{2}}\\right)_{\\rho}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0fc2e134",
   "metadata": {},
   "outputs": [],
   "source": [
    "# computing the ideal contribution\n",
    "cv_ideal = 1.5\n",
    "# computing the residual contribution\n",
    "cv_residual = - temperature * d2helmholtz_dT2\n",
    "\n",
    "# computing the total isobaric heat capacity\n",
    "cv = cv_ideal + cv_residual"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68739032",
   "metadata": {},
   "source": [
    "Other second-order derivative properties can be defined using the density and temperature derivatives of the total pressure. The density derivative is computed as follows:\n",
    "\n",
    "$$ \\left( \\frac{\\partial P}{\\partial \\rho} \\right)_{T} = \\left( \\frac{\\partial P^{id}}{\\partial \\rho} \\right)_{T} + \\left( \\frac{\\partial P^{res}}{\\partial \\rho} \\right)_{T} $$\n",
    "\n",
    "Where: \n",
    "$$ \\left( \\frac{\\partial P^{id}}{\\partial \\rho} \\right)_{T} = T;  \\quad  \\left( \\frac{\\partial P^{res}}{\\partial \\rho} \\right)_{T} = 2 \\rho \\left( \\frac{\\partial A^{res}}{\\partial \\rho }\\right)_{T} + \\rho^2 \\left( \\frac{\\partial^2 A^{res}}{\\partial \\rho^2 }\\right)_{T} $$ \n",
    "\n",
    "Similarly, the temperature derivative is computed as follows:\n",
    "\n",
    "$$ \\left( \\frac{\\partial P}{\\partial T} \\right)_{\\rho} = \\left( \\frac{\\partial P^{id}}{\\partial T} \\right)_{\\rho} + \\left( \\frac{\\partial P^{res}}{\\partial T} \\right)_{\\rho} $$\n",
    "\n",
    "Where: \n",
    "$$ \\left( \\frac{\\partial P^{id}}{\\partial T} \\right)_{\\rho} = \\rho;  \\quad  \\left( \\frac{\\partial P^{res}}{\\partial T} \\right)_{\\rho} =\\rho^2 \\left( \\frac{\\partial^2 A^{res}}{\\partial T \\partial \\rho}\\right) $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d5828b7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "dpressure_drho_resisual = 2*density*dhelmholtz_drho + density**2*d2helmholtz_drho2\n",
    "dpressure_drho_ideal = 1.*temperature\n",
    "dpressure_drho = dpressure_drho_ideal + dpressure_drho_resisual\n",
    "\n",
    "dpressure_dT_resisual = density**2 * d2helmholtz_drho_dT\n",
    "dpressure_dT_ideal = 1.*density\n",
    "dpressure_dT = dpressure_dT_ideal + dpressure_dT_resisual"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12aaa997",
   "metadata": {},
   "source": [
    "Then the other derivative properties are computed as follows:\n",
    "\n",
    "\n",
    "### Thermal Pressure Coefficient\n",
    "\n",
    "$$ \\gamma_V = \\left(\\frac{\\partial P}{\\partial T} \\right)_\\rho $$\n",
    "\n",
    "### Thermal  Expansion Coefficient\n",
    "\n",
    "$$ \\alpha_P = \\frac{-1}{\\rho} \\left(\\frac{\\partial \\rho}{\\partial T} \\right)_{P} = \\left( \\frac{\\partial P}{\\partial T} \\right)_{\\rho} \\bigg/ \\rho \\left(\\frac{\\partial P}{\\partial \\rho} \\right)_{T}  $$ \n",
    "\n",
    "### Isothermal Compressibility\n",
    "\n",
    "$$ \\kappa_T = \\frac{1}{\\rho} \\left( \\frac{\\partial \\rho}{\\partial P} \\right)_{T} = \\left[ \\rho \\left( \\frac{\\partial P}{\\partial \\rho} \\right)_{T} \\right]^{-1} $$ \n",
    "\n",
    "### Isobaric Heat Capacity\n",
    "\n",
    "$$ C_P = \\left( \\frac{\\partial H}{\\partial T} \\right)_{P} = C_V + \\frac{T \\alpha_P^2}{\\rho \\kappa_T} $$\n",
    "\n",
    "### Joule Thompson Coefficient\n",
    "\n",
    "$$ \\mu_{JT} = \\left( \\frac{\\partial T}{\\partial P} \\right)_{H} = \\frac{1}{\\rho C_P} \\left[T \\alpha_P - 1 \\right]$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ff96e731",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computing thermal pressure coefficient\n",
    "thermal_pressure_coefficient = 1. * dpressure_dT\n",
    "\n",
    "# Computing thermal expansion coefficient\n",
    "thermal_expansion_coefficient = dpressure_dT/(density*dpressure_drho)\n",
    "\n",
    "# Computing isothermal compressibility\n",
    "isothermal_compressibility = 1/(density*dpressure_drho)\n",
    "\n",
    "# Computing isobaric heat capacity\n",
    "cp = temperature*thermal_expansion_coefficient**2/(density*isothermal_compressibility)\n",
    "cp += cv\n",
    "\n",
    "# Computing Joule-Thomson Coefficient\n",
    "joule_thomson = temperature*thermal_expansion_coefficient - 1.\n",
    "joule_thomson /= (density*cp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5676bb20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\mu_{JT}$')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9,6), constrained_layout=True)\n",
    "ax1 = fig.add_subplot(231)\n",
    "ax1.plot(density, cv)\n",
    "ax1.set_xlim([0, 1.2])\n",
    "ax1.set_xlabel(r\"$\\rho$\")\n",
    "ax1.set_ylabel(r\"$C_V$\")\n",
    "\n",
    "ax2 = fig.add_subplot(232)\n",
    "ax2.plot(density, thermal_pressure_coefficient)\n",
    "ax2.set_xlim([0, 1.2])\n",
    "ax2.set_xlabel(r\"$\\rho$\")\n",
    "ax2.set_ylabel(r\"$\\gamma_V$\")\n",
    "\n",
    "ax3 = fig.add_subplot(233)\n",
    "ax3.plot(density, thermal_expansion_coefficient)\n",
    "ax3.set_xlim([0, 1.2])\n",
    "ax3.set_xlabel(r\"$\\rho$\")\n",
    "ax3.set_ylabel(r\"$\\alpha_P$\")\n",
    "\n",
    "ax4 = fig.add_subplot(234)\n",
    "ax4.plot(density, density*isothermal_compressibility)\n",
    "ax4.set_xlim([0, 1.2])\n",
    "ax4.set_xlabel(r\"$\\rho$\")\n",
    "ax4.set_ylabel(r\"$\\rho \\cdot \\kappa_T$\")\n",
    "\n",
    "ax5 = fig.add_subplot(235)\n",
    "ax5.plot(density, cp)\n",
    "ax5.set_xlim([0, 1.2])\n",
    "ax5.set_xlabel(r\"$\\rho$\")\n",
    "ax5.set_ylabel(r\"$C_P$\")\n",
    "\n",
    "ax6 = fig.add_subplot(236)\n",
    "ax6.plot(density, joule_thomson)\n",
    "ax6.set_xlim([0, 1.2])\n",
    "ax6.set_xlabel(r\"$\\rho$\")\n",
    "ax6.set_ylabel(r\"$\\mu_{JT}$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22d338b0",
   "metadata": {},
   "source": [
    "The `model` object also includes other handy functions to compute some properties directly. **These methods include the calculation of only residual contributions**. All of these methods use ($\\alpha_{vdw}$, $\\rho$ and $T$) as inputs.\n",
    "\n",
    "- `model.pressure`: computes the pressure of the fluid\n",
    "- `model.dpressure_drho`: computes the pressure of the fluid and its first density derivative\n",
    "- `model.d2pressure_drho2`: computes the pressure of the fluid and its first and second-order density derivatives\n",
    "- `model.dpressure_dT:` computes the pressure of the fluid and its first temperature derivative\n",
    "- `model.internal_energy`: computes the internal energy of the fluid\n",
    "- `model.enthalpy`: computes the enthalpy of the fluid\n",
    "- `model.cv_residual`: computes the isochoric heat capacity of the fluid\n",
    "- `model.chemical_potential`: computes the chemical potential of the fluid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d7829904",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tf-cpu",
   "language": "python",
   "name": "tf-cpu"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}