{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Zuria Bauer Hartwig* ( [CAChemE](http://cacheme.org) Lightning Talk)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "25.02.2015 - Licenciado bajo Creative Commons (CC-BY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plug Flow Reactor model and simulation (with Python!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![img](PFR.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En un RFP tienen lugar las reacciones elementales en fase gas indicadas en la tabla. El reactor tiene 4 m\n",
    "de longitud y 0.3 m de diámetro interno. El alimento consiste en una mezcla de $480 kmol·min^{-1}$ de A, $270 kmol·min^{-1}$ de B y $420 kmol·min^{-1$}$ de D. La presión en el reactor es constante e igual a $130 kPa$ y la temperatura de entrada del alimento es $650ºC$. El reactor está refrigerado con agua a una Tw de $10ºC$. El coeficente global de intercambio de calor U entre el reactor y el refrigerante es igual a $25 kJ·s^{-1}·m^{-2}·K^{-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "| $\\phantom{m} Reacciones \\> Elementales$ | $\\phantom{mm} k_0 \\> \\phantom{m}(s^{-1})\\phantom{m}$  | $\\phantom{mmm} E \\> \\phantom{}(kJ·kmol^{-1})$ | $\\phantom{mm} H*_{298K} \\>\\phantom{}(kJ·kmol^{-1})$  |\n",
    "| :--------------------------: | :--------------:  | :---------------:  | :-----------------------:   |\n",
    "| $A + B \\rightarrow 2 \\; C$   | $\\:1.9·10^{12}\\:$     | $\\: 103930 \\:$           | $\\: -7100     \\:$                |\n",
    "| $C + D \\rightarrow E + F$    | $\\:6.9·10^{14}\\:$     | $\\: 176020 \\:$           | $\\:12300    \\:$                 |\n",
    "| $B + C \\rightarrow G$        | $\\:1.51·10^{14}\\:$    | $\\: 148010 \\:$           | $\\:-9200   \\:$                  |\n",
    "| $D \\rightarrow C + H$        | $\\:3.2·10^{16}\\:$     | $\\: 251020 \\:$           | $\\:13500  \\:$                   |\n",
    "| $C + H \\rightarrow D$        | $\\:7.1·10^{13}\\:$     | $\\: 129710 \\:$           | $\\:-13500\\:$                    |\n",
    "| $2 \\; A \\rightarrow E$       | $\\:7.2·10^{8} \\:$     | $\\: 42450  \\:$           | $\\:-5800\\:$                     |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Representar gráficamente los perfiles de temperatura y concentración de cada componente en el\n",
    "reactor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Otros datos__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$C_P$ : Capacidad calorífica $(kJ·kmol^{-1}·K^{-1})$\n",
    "\n",
    "|$\\phantom{mm}$ A $\\phantom{mm}$|$\\phantom{mm}$ B $\\phantom{mm}$|$\\phantom{mm}$ C $\\phantom{mm}$ |$\\phantom{mm}$ D $\\phantom{mm}$|$\\phantom{mm}$ E $\\phantom{mm}$|$\\phantom{mm}$ F $\\phantom{mm}$|$\\phantom{mm}$ G $\\phantom{mm}$|$\\phantom{mm}$ H $\\phantom{mm}$|\n",
    "|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n",
    "| 41| 74| 56| 40| 29| 22| 35| 49|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Librerías a usar\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "from __future__ import division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2a24d048>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d795cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Constante \n",
    "Rg = 8.31\n",
    "\n",
    "#Factor Pre-exponencial\n",
    "k = np.array([1.9e12, 6.9e14, 1.5e14, 3.2e16, 7.4e13, 7.2e8]) #s-1\n",
    "    \n",
    "#ENERGÍA DE ACTIVACIÓN\n",
    "Ea = np.array([103930, 176020, 148010, 251020, 129710, 42450]) #kJ/kmol\n",
    "    \n",
    "#TERMODINAMIC DATA\n",
    "    \n",
    "Tref = 298 #K\n",
    "    \n",
    "dHref = np.array([-7100, 12300, -9200, 13500, -13500, -5800]) #kJ/kmol\n",
    "    \n",
    "Cp = np.array([41, 74, 56, 40, 29, 22, 35, 49]) #kJ/kmol*K\n",
    "\n",
    "#DATOS INICIALES DE OPERACIÓN DEL REACTOR\n",
    "    \n",
    "P0 = 130 #Pa\n",
    "T0 = 650+273 #K\n",
    "    \n",
    "#DATOS REACTOR\n",
    "    \n",
    "L0 = 4 #Longitud del reactor (m)\n",
    "D = 0.3 #Diámetro (m)\n",
    "S = np.pi*((D/2)**2) #Sección del tubo (m2)\n",
    "U = 25 #Coef global de intercambio de calor (kJ/m2·s·K)\n",
    "  \n",
    "#ALIMENTO\n",
    "    \n",
    "C_A0 = 480/60\n",
    "C_B0 = 270/60\n",
    "C_D0 = 420/60\n",
    "    \n",
    "n0 = np.array([C_A0, C_B0, 0, C_D0, 0, 0, 0, 0]) #Flujo másico inicial\n",
    "nt0 = np.sum(n0) #Moles iniciales\n",
    "Qv0 = nt0 * Rg * T0 / P0 #Caudal volumétrico inicial\n",
    "\n",
    "# Matriz de coeficientes estequiométricos\n",
    "# 1    2     3     4     5     6     7     8\n",
    "# A    B     C     D     E     F     G     H\n",
    "\n",
    "alfa = np.array([\n",
    "        [-1, -1, 2, 0, 0, 0, 0, 0],\n",
    "        [ 0,  0,-1,-1, 1, 1, 0, 0],\n",
    "        [ 0, -1,-1, 0, 0, 0, 1, 0],\n",
    "        [ 0,  0, 1,-1, 0, 0, 0, 1],\n",
    "        [ 0,  0,-1, 1, 0, 0, 0,-1],\n",
    "        [-2,  0, 0, 0, 1, 0, 0, 0],\n",
    "        ], dtype=float)\n",
    "\n",
    "Nreactions, Ncomponents = alfa.shape\n",
    "\n",
    "    \n",
    "def diff_eqs(y,L):\n",
    "\n",
    "\n",
    "    n = y[:8] # mol*L-1\n",
    "    Q = y[8]\n",
    "    T = y[9]\n",
    "        \n",
    "    #Balance de materia\n",
    "        \n",
    "    Qv = Qv0 *np.sum(n)*T/sum(n0)/T0\n",
    "    C = n/Qv\n",
    "    ri = np.ones(6)\n",
    "\n",
    "\n",
    "    #Ecuaciones de velocidad\n",
    "        \n",
    "    ri[0] = k[0]*np.exp(-Ea[0]/(8.31*T))*C[0]*C[1]\n",
    "    ri[1] = k[1]*np.exp(-Ea[1]/(8.31*T))*C[2]*C[3]\n",
    "    ri[2] = k[2]*np.exp(-Ea[2]/(8.31*T))*C[1]*C[2]\n",
    "    ri[3] = k[3]*np.exp(-Ea[3]/(8.31*T))*C[3]\n",
    "    ri[4] = k[4]*np.exp(-Ea[4]/(8.31*T))*C[2]*C[7]\n",
    "    ri[5] = k[5]*np.exp(-Ea[5]/(8.31*T))*C[0]*C[0]\n",
    "\n",
    "        \n",
    "    # Ec Diferenciales\n",
    "\n",
    "    dndL = np.dot(ri, alfa)* S\n",
    "        \n",
    "    #B Energía\n",
    "        \n",
    "    q = U*2*np.pi*D/2*(10+273.15-T)\n",
    "        \n",
    "    dQdL = q\n",
    "        \n",
    "    #Entalpías\n",
    "    dCp = np.dot(alfa, Cp)\n",
    "    dH = dHref + dCp * (T-Tref)\n",
    "    rH = np.dot(ri, dH)\n",
    "        \n",
    "    #Ec dif\n",
    "    nCp = np.dot(n, Cp)\n",
    "    dTdL = (dQdL-S*rH)/ nCp\n",
    "\n",
    "\n",
    "        \n",
    "    dTP = np.array([dQdL, dTdL])\n",
    "    \n",
    "    dy = np.concatenate((dndL, dTP), axis=0)\n",
    "    dy = np.transpose(dy)\n",
    "    \n",
    "    return (dy)\n",
    "\n",
    "   \n",
    "\n",
    "Q_0 = 0 # Initial\n",
    "\n",
    "y0 = [C_A0, C_B0, 0, C_D0, 0, 0, 0, 0, Q_0, T0]\n",
    "L  =  np.linspace(0, L0, 100000)   # length of the reactor gride\n",
    "\n",
    "# SOLVER\n",
    "soln = odeint(diff_eqs, y0, L)\n",
    "\n",
    "C_A  = soln[:, 0] # mol*L-1\n",
    "C_B  = soln[:, 1] # mol*L-1\n",
    "C_C  = soln[:, 2] # mol*L-1\n",
    "C_D  = soln[:, 3] # mol*L-1\n",
    "C_E  = soln[:, 4] # mol*L-1\n",
    "C_F  = soln[:, 5] # mol*L-1\n",
    "C_G  = soln[:, 6] # mol*L-1\n",
    "C_H  = soln[:, 7] # mol*L-1\n",
    "\n",
    "Q = soln[:, 8] # heat\n",
    "T = soln[:,9] # K\n",
    "    \n",
    "# Plot\n",
    "\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(nrows=2, ncols=1,  figsize=(15,7))\n",
    "\n",
    "ax1.plot(L, C_A,\n",
    "         L, C_B,\n",
    "         L, C_C,\n",
    "         L, C_D,\n",
    "         L, C_E,\n",
    "         L, C_F,\n",
    "         L, C_G,\n",
    "         L, C_H)\n",
    "ax1.set_xlabel('Long (m)',)\n",
    "\n",
    "ax1.set_ylabel('$C_{i}$ (kmol/m3)')\n",
    "\n",
    "ax1.legend(['$C_A$','$C_B$','$C_C$','$C_D$','$C_E$','$C_F$','$C_G$','$C_H$'],\n",
    "           loc=4, fontsize = 10)\n",
    "\n",
    "ax1.set_title('Gas-Phase Plug Flow Reactor')\n",
    "    \n",
    "ax1.set_xlim([0,4])\n",
    "ax1.set_ylim([0,16])\n",
    "font = {'family' : 'serif',\n",
    "        'color'  : 'black',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 16,\n",
    "        }\n",
    "ax1.text(3,7.5, r''' Reactions:\n",
    "A + B $\\rightarrow$ 2C\n",
    "C + D $\\rightarrow$ E + F\n",
    "B + C $\\rightarrow$ G\n",
    "D $\\rightarrow$ C + H\n",
    "C + H $\\rightarrow$ D\n",
    "2A $\\rightarrow$ E''')\n",
    "\n",
    "ax2.plot(L,T)\n",
    "ax2.set_xlabel('Long (m)')\n",
    "ax2.set_ylabel('Temperatura (K)' )\n",
    "ax2.legend(['Temperatura (K)'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"
     ]
    }
   ],
   "source": [
    "#Importamos la librería para los widgets\n",
    "from IPython.html.widgets import interact\n",
    "from IPython.display import clear_output, display, HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gasPFR(C_A0, C_B0, C_D0):\n",
    "\n",
    "    #Constante \n",
    "    Rg = 8.31\n",
    "\n",
    "    #Factor Pre-exponencial\n",
    "    k = np.array([1.9e12, 6.9e14, 1.5e14, 3.2e16, 7.4e13, 7.2e8]) #s-1\n",
    "\n",
    "    #ENERGÍA DE ACTIVACIÓN\n",
    "    Ea = np.array([103930, 176020, 148010, 251020, 129710, 42450]) #kJ/kmol\n",
    "\n",
    "    #TERMODINAMIC DATA\n",
    "\n",
    "    Tref = 298 #K\n",
    "\n",
    "    dHref = np.array([-7100, 12300, -9200, 13500, -13500, -5800]) #kJ/kmol\n",
    "\n",
    "    Cp = np.array([41, 74, 56, 40, 29, 22, 35, 49]) #kJ/kmol*K\n",
    "\n",
    "    #DATOS INICIALES DE OPERACIÓN DEL REACTOR\n",
    "\n",
    "    P0 = 130 #Pa\n",
    "    T0 = 650+273 #K\n",
    "\n",
    "    #DATOS Reactor\n",
    "\n",
    "    L0 = 4 #Longitud del reactor (m)\n",
    "    D = 0.3 #Diámetro (m)\n",
    "    S = np.pi*((D/2)**2) #Sección del tubo (m2)\n",
    "    U = 25 #Coef global de intercambio de calor (kJ/m2·s·K)\n",
    "\n",
    "    #Alimento\n",
    "\n",
    "    #C_A0 = 480/60\n",
    "    #C_B0 = 270/60\n",
    "    #C_D0 = 420/60\n",
    "\n",
    "    n0 = np.array([C_A0, C_B0, 0, C_D0, 0, 0, 0, 0]) #Flujo másico inicial\n",
    "    nt0 = np.sum(n0) #Moles iniciales\n",
    "    Qv0 = nt0 * Rg * T0 / P0 #Caudal volumétrico inicial\n",
    "\n",
    "    # Matriz de coeficientes estequiométricos\n",
    "    # 1    2     3     4     5     6     7     8\n",
    "    # A    B     C     D     E     F     G     H\n",
    "\n",
    "    alfa = np.array([\n",
    "            [-1, -1, 2, 0, 0, 0, 0, 0],\n",
    "            [ 0,  0,-1,-1, 1, 1, 0, 0],\n",
    "            [ 0, -1,-1, 0, 0, 0, 1, 0],\n",
    "            [ 0,  0, 1,-1, 0, 0, 0, 1],\n",
    "            [ 0,  0,-1, 1, 0, 0, 0,-1],\n",
    "            [-2,  0, 0, 0, 1, 0, 0, 0],\n",
    "            ], dtype=float)\n",
    "\n",
    "    Nreactions, Ncomponents = alfa.shape\n",
    "\n",
    "\n",
    "    def diff_eqs(y,L):\n",
    "\n",
    "\n",
    "        n = y[:8] # mol*L-1\n",
    "        Q = y[8]\n",
    "        T = y[9]\n",
    "\n",
    "        #Balance de materia\n",
    "\n",
    "        Qv = Qv0 *np.sum(n)*T/sum(n0)/T0\n",
    "        C = n/Qv\n",
    "        ri = np.ones(6)\n",
    "\n",
    "\n",
    "        #Ecuaciones de velocidad\n",
    "\n",
    "        ri[0] = k[0]*np.exp(-Ea[0]/(8.31*T))*C[0]*C[1]\n",
    "        ri[1] = k[1]*np.exp(-Ea[1]/(8.31*T))*C[2]*C[3]\n",
    "        ri[2] = k[2]*np.exp(-Ea[2]/(8.31*T))*C[1]*C[2]\n",
    "        ri[3] = k[3]*np.exp(-Ea[3]/(8.31*T))*C[3]\n",
    "        ri[4] = k[4]*np.exp(-Ea[4]/(8.31*T))*C[2]*C[7]\n",
    "        ri[5] = k[5]*np.exp(-Ea[5]/(8.31*T))*C[0]*C[0]\n",
    "\n",
    "\n",
    "        # Ec Diferenciales\n",
    "\n",
    "        dndL = np.dot(ri, alfa)* S\n",
    "\n",
    "        #B Energía\n",
    "\n",
    "        q = U*2*np.pi*D/2*(10+273.15-T)\n",
    "\n",
    "        dQdL = q\n",
    "\n",
    "        #Entalpías\n",
    "        dCp = np.dot(alfa, Cp)\n",
    "        dH = dHref + dCp * (T-Tref)\n",
    "        rH = np.dot(ri, dH)\n",
    "\n",
    "        #Ec dif\n",
    "        nCp = np.dot(n, Cp)\n",
    "        dTdL = (dQdL-S*rH)/ nCp\n",
    "\n",
    "\n",
    "\n",
    "        dTP = np.array([dQdL, dTdL])\n",
    "\n",
    "        dy = np.concatenate((dndL, dTP), axis=0)\n",
    "        dy = np.transpose(dy)\n",
    "\n",
    "        # Intento 1 = si le pido que me devuelva dndL, dQdL y dTdl = ERROR\n",
    "        # Intento 2 = si dejo el código como esta pero le pido solo que devuelva dndL = GRÁFICO\n",
    "        # Intento 3 = si borro el código de dQdL y dTdL y represento = ERROR\n",
    "\n",
    "        return (dy)\n",
    "\n",
    "\n",
    "    #Parámetros, los primeros 8 son de C, el 9 de Q y el 10 es T\n",
    "\n",
    "    Q_0 = 0 # ?initial \n",
    "\n",
    "    y0 = [C_A0, C_B0, 0, C_D0, 0, 0, 0, 0, Q_0, T0]\n",
    "    L  =  np.linspace(0, L0, 100000)   # length of the reactor gride\n",
    "\n",
    "    # SOLVER\n",
    "    soln = odeint(diff_eqs, y0, L)\n",
    "\n",
    "    C_A  = soln[:, 0] # mol*L-1\n",
    "    C_B  = soln[:, 1] # mol*L-1\n",
    "    C_C  = soln[:, 2] # mol*L-1\n",
    "    C_D  = soln[:, 3] # mol*L-1\n",
    "    C_E  = soln[:, 4] # mol*L-1\n",
    "    C_F  = soln[:, 5] # mol*L-1\n",
    "    C_G  = soln[:, 6] # mol*L-1\n",
    "    C_H  = soln[:, 7] # mol*L-1\n",
    "\n",
    "    Q = soln[:, 8] # heat\n",
    "    T = soln[:,9] # K\n",
    "\n",
    "    # Representación\n",
    "\n",
    "\n",
    "    fig, (ax1, ax2) = plt.subplots(nrows=2, ncols=1,  figsize=(15,7))\n",
    "\n",
    "    ax1.plot(L, C_A,\n",
    "             L, C_B,\n",
    "             L, C_C,\n",
    "             L, C_D,\n",
    "             L, C_E,\n",
    "             L, C_F,\n",
    "             L, C_G,\n",
    "             L, C_H)\n",
    "    ax1.set_xlabel('Long (m)',)\n",
    "\n",
    "    ax1.set_ylabel('$C_{i}$ (kmol/m3)')\n",
    "\n",
    "    ax1.legend(['$C_A$','$C_B$','$C_C$','$C_D$','$C_E$','$C_F$','$C_G$','$C_H$'],\n",
    "           loc=4, fontsize = 10)\n",
    "\n",
    "    ax1.set_title('Gas-Phase Plug Flow Reactor')\n",
    "\n",
    "    ax1.set_xlim([0,4])\n",
    "    ax1.set_ylim([0,16])\n",
    "    font = {'family' : 'serif',\n",
    "            'color'  : 'black',\n",
    "            'weight' : 'normal',\n",
    "            'size'   : 16,\n",
    "            }\n",
    "    ax1.text(3,7.5, r''' Reactions:\n",
    "    A + B $\\rightarrow$ 2C\n",
    "    C + D $\\rightarrow$ E + F\n",
    "    B + C $\\rightarrow$ G\n",
    "    D $\\rightarrow$ C + H\n",
    "    C + H $\\rightarrow$ D\n",
    "    2A $\\rightarrow$ E''')\n",
    "\n",
    "    ax2.plot(L,T)\n",
    "    ax2.set_xlabel('Long (m)')\n",
    "    ax2.set_ylabel('Temperatura (K)' )\n",
    "    ax2.legend(['Temperatura (K)'])\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3166f6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.gasPFR>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Widgets Interactivos\n",
    "\n",
    "interact(gasPFR,\n",
    "         C_A0=(0/60, 800/60, 0.1), C_B0=(0/60, 800/60, 0.1),\n",
    "         C_D0 = (0/60, 800/60, 0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Bibliografía:__\n",
    "\n",
    "Apuntes de __\"Diseño de Reactores 1\"__ de Ingeniería Química - *Examen. Convocatoria de enero de 2014*"
   ]
  }
 ],
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   "language": "python",
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.1"
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 },
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}