{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# The Non Random Two Liquids (NRTL) model for *excess Gibbs energy* ($g^E$) and a case study of the Liquid-Liquid equilibria of water+acetone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy.constants import R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ethyl acetate (1) + water (2) + ethanol (3)\n",
    "\n",
    "# some identification variables\n",
    "# which integer index shall correspond to which component here\n",
    "i_EA = 0\n",
    "i_W = 1\n",
    "i_E = 2\n",
    "\n",
    "# name of the components of the system in a format suitable for labeling of the plots\n",
    "compNames = ['ethyl acetate', 'water', 'ethanol']\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitted parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 3 binary aĺpha parameters\n",
    "\n",
    "alpha12 = 0.4\n",
    "\n",
    "alpha23 = 0.3\n",
    "\n",
    "alpha13 = 0.3\n",
    "\n",
    "# 6 binary Dgij parameters\n",
    "Dg12 = 1335 * 4.184 #J/K\n",
    "Dg21 = 2510 * 4.184 #J/K\n",
    "\n",
    "Dg23 = 976 * 4.184 #J/K\n",
    "Dg32 = 88 * 4.184 #J/K\n",
    "\n",
    "Dg13 = 301 * 4.184 #J/K\n",
    "Dg31 = 322 * 4.184 #J/K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Feeding the fitted parameters to the model in matrix structure:\n",
    "we will assemble the parameters in a matrix structure so that we can access each parameter by its index, as in\n",
    "`A[0,0]` and `A[0,1]`rather than as `A11` and `A12`, so we can loop trough all of them using an iterator, see below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#assemble matrix with regressed parameters Dg_i,j, according to the model all diagonal terms are zero\n",
    "Dg3 = np.array([[0, Dg12, Dg13],\n",
    "             [Dg21, 0, Dg23],\n",
    "             [Dg31, Dg32, 0]])\n",
    "\n",
    "\n",
    "#assemble symmetric matrix alpha\n",
    "alpha3 = np.array([[0, alpha12, alpha13],\n",
    "                [alpha12, 0, alpha23],\n",
    "                [alpha13, alpha23, 0]])\n",
    "\n",
    "A3= Dg3/R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.   0.4  0.3]\n",
      " [ 0.4  0.   0.3]\n",
      " [ 0.3  0.3  0. ]]\n",
      "[[ 0.   0.3]\n",
      " [ 0.3  0. ]]\n",
      "[[    0.           671.79830492   151.46913092]\n",
      " [ 1263.0814572      0.           491.14243117]\n",
      " [  162.03674471    44.28333396     0.        ]]\n",
      "[[   0.          491.14243117]\n",
      " [  44.28333396    0.        ]]\n"
     ]
    }
   ],
   "source": [
    "#consider the binary W, E\n",
    "A = A3[np.array([1,2]),:][:,np.array([1,2])]\n",
    "alpha = alpha3[np.array([1,2]),:][:,np.array([1,2])]\n",
    "print(alpha3)\n",
    "print(alpha)\n",
    "print(A3)\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "@jit\n",
    "def Gamma(T,c_x,q_alpha, q_A):\n",
    "    #note that we used many lines for didatics\n",
    "    #we can do it in few lines:\n",
    "    #note that some expression occur more than once below\n",
    "    #so it may be useful define it as a intermediary recurrent term here\n",
    "    #and calculate it once to use it then several times\n",
    "    q_tau     = q_A/T\n",
    "    q_G       = np.exp(-(q_alpha*q_tau))\n",
    "    l_D       = ((1/((q_G.T) @ c_x)).T)\n",
    "    q_E       = (q_tau*q_G) * l_D \n",
    "    gamma     = np.exp(((q_E+(q_E.T))-(((q_G * l_D) * (c_x.T)) @ (q_E.T))) @ c_x)\n",
    "    return gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.62910219]\n",
      " [ 1.16193319]]\n"
     ]
    }
   ],
   "source": [
    "#test it to see that the results are the same\n",
    "T=78.4+273.15 #https://en.wikipedia.org/wiki/Azeotrope_tables\n",
    "x=np.array([.4,.6]) #normalized\n",
    "x_as_column = np.array([x]).T\n",
    "print(Gamma(T,x_as_column,alpha,A)) #test using those trial input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "351.54999999999995\n",
      "44733.1064386\n",
      "100741.097448\n"
     ]
    }
   ],
   "source": [
    "#Calculo de Psat com a Equação de Antoine\n",
    "#Pressões de saturação para entrar em yi.Pbol = xi*Gammai*P_sati\n",
    "print(T)\n",
    "def PantoineW(T):\n",
    "    Aw = 16.3872\n",
    "    Bw = 3885.70\n",
    "    Cw = 230.170\n",
    "    return (np.exp(Aw - Bw/(T-273 + Cw)))*1000\n",
    "PsatAw = PantoineW(T)\n",
    "print (PsatAw)\n",
    "\n",
    "def PantoineA(T): #E #http://webbook.nist.gov/cgi/cbook.cgi?ID=C64175&Mask=4&Type=ANTOINE&Plot=on\n",
    "    Aa = 5.24677\n",
    "    Ba = 1598.673\n",
    "    Ca = -46.424\n",
    "    return (np.exp(Aa - Ba/(T + Ca)))*1e5\n",
    "PsatAa = PantoineA(T)\n",
    "print (PsatAa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Pbol(x,T):\n",
    "    y_out = np.zeros(2)\n",
    "    gammas = Gamma(T,x,alpha,A)\n",
    "    Psati = ([PsatAw,PsatAa])\n",
    "    Pbol_=0\n",
    "    for i in range(0,2):\n",
    "#        print(i,Pbol_)\n",
    "        Pbol_ += x[i]*gammas[i]*Psati[i]\n",
    "    \n",
    "    #calculo das composicoes do vapor\n",
    "    for i in range(0,2):\n",
    "        y_out[i] = x[i]*gammas[i]*Psati[i]/Pbol_\n",
    "        \n",
    "        \n",
    "#    print(y_out, Gamma, x, Psati, Pbol_)\n",
    "    return [y_out, Pbol_]\n",
    "\n",
    "def Pbol_MisturaIDEAL(x,T):\n",
    "    y_out = np.zeros(2)\n",
    "    gammas = [1,1]\n",
    "    Psati = ([PsatAw,PsatAa])\n",
    "    Pbol_=0\n",
    "    for i in range(0,2):\n",
    "#        print(i,Pbol_)\n",
    "        Pbol_ += x[i]*gammas[i]*Psati[i]\n",
    "    \n",
    "    #calculo das composicoes do vapor\n",
    "    for i in range(0,2):\n",
    "        y_out[i] = x[i]*gammas[i]*Psati[i]/Pbol_\n",
    "        \n",
    "        \n",
    "#    print(y_out, Gamma, x, Psati, Pbol_)\n",
    "    return [y_out, Pbol_]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaEAAAEOCAYAAAAg4qj5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nISGEEA4jQUgIIYTDSBASQgjhMP8PwH1M9zkC4u0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa574cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xwaxis = np.linspace (0,1,100)\n",
    "P_axis = np.zeros(100)\n",
    "ywaxis = np.zeros(100)\n",
    "for i in range (0,100):\n",
    "    xa = 1-xwaxis[i]\n",
    "    x_ = np.array([[xwaxis[i],xa]]).T\n",
    "    y_, P_axis[i] = Pbol(x_,T)\n",
    "    ywaxis[i] = y_[0]\n",
    "\n",
    "plt.figure(1)\n",
    "plt.plot(xwaxis,P_axis)\n",
    "plt.plot(ywaxis,P_axis)\n",
    "\n",
    "pmax = np.max(P_axis)\n",
    "\n",
    "xwaxis = np.linspace (0,1,100)\n",
    "P_axis = np.zeros(100)\n",
    "ywaxis = np.zeros(100)\n",
    "for i in range (0,100):\n",
    "    xa = 1-xwaxis[i]\n",
    "    x_ = [xwaxis[i],xa]\n",
    "    y_, P_axis[i] = Pbol_MisturaIDEAL(x_,T)\n",
    "    ywaxis[i] = y_[0]\n",
    "\n",
    "plt.plot(xwaxis,P_axis)\n",
    "plt.plot(ywaxis,P_axis)\n",
    "\n",
    "labels = [r'$P_{bub}(x_W)$', r'$P_{dew}(y_W),$,',r'$P^{ideal}_{bub}(x_W)$', r'$P^{ideal}_{dew}(y_W),$']\n",
    "plt.legend(labels, loc=0)\n",
    "\n",
    "plt.ylabel(r'$Pressure$')\n",
    "plt.xlabel(r'$mole fraction$')\n",
    "\n",
    "plt.scatter([0],[PsatAa])\n",
    "plt.scatter([1],[PsatAw])\n",
    "\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(PsatAw,1.01*pmax)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#min em T aqui: http://www.ddbst.com/en/EED/VLE/VLE%20Acetone%3BWater.php\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\iuri\\Anaconda3\\lib\\site-packages\\matplotlib\\figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAEJCAYAAABSX1EAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa79d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# GRAPHICAL ABSTRACT\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams as rc\n",
    "\n",
    "fig_width = 9 / 2.54 #in inches\n",
    "fig_height = 9 / 2.54 #in inches\n",
    "fig_size =  [fig_width,fig_height]\n",
    "\n",
    "#FONTS & TICKS\\n\",\n",
    "params = {'backend': 'ps',\n",
    "'axes.labelsize': 12,  #in pts\n",
    "'font.size': 8, #in pts\n",
    "'legend.fontsize': 8, #in pts\n",
    "'xtick.labelsize': 10, #in pts\n",
    "'ytick.labelsize': 10, #in pts\n",
    "'text.usetex': False,\n",
    "'figure.figsize': fig_size}\n",
    "rc.update(params)\n",
    "\n",
    "GAfig, GAax1 = plt.subplots(1,1)\n",
    "xwaxis = np.linspace (0,1,100)\n",
    "P_axis = np.zeros(100)\n",
    "ywaxis = np.zeros(100)\n",
    "for i in range (0,100):\n",
    "    xa = 1-xwaxis[i]\n",
    "    x_ = np.array([[xwaxis[i],xa]]).T\n",
    "    y_, P_axis[i] = Pbol(x_,T)\n",
    "    ywaxis[i] = y_[0]\n",
    "\n",
    "GAax1.plot(xwaxis,P_axis)\n",
    "GAax1.plot(ywaxis,P_axis)\n",
    "\n",
    "pmax = np.max(P_axis)\n",
    "\n",
    "xwaxis = np.linspace (0,1,100)\n",
    "P_axis = np.zeros(100)\n",
    "ywaxis = np.zeros(100)\n",
    "for i in range (0,100):\n",
    "    xa = 1-xwaxis[i]\n",
    "    x_ = np.array([[xwaxis[i],xa]]).T\n",
    "    y_, P_axis[i] = Pbol_MisturaIDEAL(x_,T)\n",
    "    ywaxis[i] = y_[0]\n",
    "\n",
    "GAax1.plot(xwaxis,P_axis, ls='--')\n",
    "GAax1.plot(ywaxis,P_axis, ls='--')\n",
    "\n",
    "\n",
    "#GAax1.plot([0,.2],[PsatAa,PsatAa],color='k',ls=':')\n",
    "#GAax1.plot([0,.2],[pmax+.1*(pmax-PsatAa),pmax+.1*(pmax-PsatAa)],color='k',ls=':')\n",
    "#GAax1.plot([.0,.0],[PsatAa,pmax+.1*(pmax-PsatAa)],color='k',ls=':')\n",
    "#GAax1.plot([.2,.2],[PsatAa,pmax+.1*(pmax-PsatAa)],color='k',ls=':')\n",
    "\n",
    "GAax1.plot([0,1],[PsatAa,PsatAa],color='k',ls=':',alpha=.5)\n",
    "GAax1.plot([0,1],[pmax+.05*(pmax-PsatAa),pmax+.05*(pmax-PsatAa)],color='k',ls=':',alpha=.5)\n",
    "GAax1.plot([.05,.05],[0,2*pmax],color='k',ls=':',alpha=.5)\n",
    "GAax1.plot([.2,.2],[0,2*pmax],color='k',ls=':',alpha=.5)\n",
    "\n",
    "'''\n",
    "import matplotlib.patches as patches\n",
    "GAax1.add_patch(\n",
    "    patches.Rectangle(\n",
    "        (0, PsatAa),   # (x,y)\n",
    "        0.2,          # width\n",
    "        pmax+.1*(pmax-PsatAa) - PsatAa, # height\n",
    "        alpha=0.25,\n",
    "        edgecolor=\"none\",\n",
    "        facecolor=\"#000000\"\n",
    "    ))\n",
    "'''\n",
    "\n",
    "\n",
    "labels = [r'$P_{bub}(x_W)$', r'$P_{dew}(y_W),$,',r'$P^{ideal}_{bub}(x_W)$', r'$P^{ideal}_{dew}(y_W),$']\n",
    "\n",
    "plt.legend(labels, loc=1)\n",
    "\n",
    "GAax1.set_title('[water; ethanol] \\n LVE at ' + '351.55' + ' K')\n",
    "\n",
    "GAax1.set_ylabel(r'$P(\\mathrm{Pa})$')\n",
    "GAax1.set_xlabel(r'$\\mathrm{mol. frac. water}$')\n",
    "\n",
    "GAax1.scatter([0],[PsatAa])\n",
    "GAax1.scatter([1],[PsatAw])\n",
    "\n",
    "GAax1.set_xlim(0,1)\n",
    "GAax1.set_ylim(PsatAw,1.01*pmax)\n",
    "\n",
    "GAfig.subplots_adjust(left=0.17, right=0.9, top=0.9, bottom=0.14)\n",
    "\n",
    "\n",
    "###\n",
    "\n",
    "left, bottom, width, height = [0.18, 0.15, 0.25, 0.25]\n",
    "ax2 = GAfig.add_axes([left, bottom, width, height])\n",
    "\n",
    "xwaxis = np.linspace (0,1,100)\n",
    "P_axis = np.zeros(100)\n",
    "ywaxis = np.zeros(100)\n",
    "for i in range (0,100):\n",
    "    xa = 1-xwaxis[i]\n",
    "    x_ = np.array([[xwaxis[i],xa]]).T\n",
    "    y_, P_axis[i] = Pbol(x_,T)\n",
    "    ywaxis[i] = y_[0]\n",
    "\n",
    "ax2.plot(xwaxis,P_axis)\n",
    "ax2.plot(ywaxis,P_axis)\n",
    "ax2.set_ylim((PsatAa+pmax)/2,pmax+.05*(pmax-PsatAa))\n",
    "ax2.set_xlim(0.05,.2)\n",
    "\n",
    "ax2.set_title('max.-in-P \\n azeotropy')\n",
    "ax2.tick_params(\n",
    "    axis='x',          # changes apply to the x-axis\n",
    "    which='both',      # both major and minor ticks are affected\n",
    "    top='off',         # ticks along the top edge are off\n",
    "    labelbottom='off') # labels along the bottom edge are off\n",
    "\n",
    "ax2.tick_params(\n",
    "    axis='y',          # changes apply to the x-axis\n",
    "    which='both',      # both major and minor ticks are affected\n",
    "    right='off',         # ticks along the top edge are off\n",
    "    labelleft='off') # labels along the bottom edge are off\n",
    "\n",
    "plt.setp(ax2.get_yaxis().get_offset_text(), visible=False)\n",
    "\n",
    "\n",
    "###\n",
    "\n",
    "\n",
    "GAax1.ticklabel_format(style = 'sci', axis='y', scilimits=(0,0))\n",
    "\n",
    "GAfig.savefig('fig2.png', dpi=1000)\n",
    "\n",
    "GAfig.show()\n",
    "\n",
    "#min em T aqui: http://www.ddbst.com/en/EED/VLE/VLE%20Acetone%3BWater.php\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}