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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 11: Vapor-Liquid Separation Processes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.1-1 Page Number 641"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Use of Raoult's Law for Boiling Point Diagram\n",
      "import numpy as np\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "import scipy.integrate as integrate\n",
      "\n",
      "#Variable Declaration\n",
      "T = 95              #Equlibrium temperature in deg C\n",
      "P = 101.32          #Vapor pressure from table 11.1-1\n",
      "PA = 155.7          #Vapor pressure of benzene from table 11.1-1 in kPa\n",
      "PB = 63.3           #Vapor pressure of toulene from table 11.1-1 in kPa\n",
      "fPT = lambda x:PA*x + PB*(1.-x)-P\n",
      "sol = root(fPT,0.05)\n",
      "xA = sol.x[0]\n",
      "xB = 1.- xA\n",
      "yA = PA*xA/P\n",
      "yB = 1.- yA\n",
      "\n",
      "#Result\n",
      "print \"Liquid and Vapor composions of benzene at 95\u00b0C:\",round(xA,3),round(yA,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Liquid and Vapor composions of benzene at 95\u00b0C: 0.411 0.632\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.2-1 Page Number 642"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Equilibrium Contact of Vapor-Liquid Mixture\n",
      "import numpy as np\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "import matplotlib.pylab as plt\n",
      "\n",
      "#Variable Declaration\n",
      "P = 101.32                 #Presure of the vapor in kPa\n",
      "yA2 = 0.4                  #Mole fraction of benzene \n",
      "yB2 = 0.6                  #Mole fraction of toulene \n",
      "V2 = 100.                  \n",
      "L0 = 110.\n",
      "xA0 = 0.3\n",
      "xB0 = 0.7\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000])\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000])\n",
      "#Calculations\n",
      "#for equimolal overflow \n",
      "L1 = L0\n",
      "V1 = V2\n",
      "fyxe = interp1d(xe,ye, kind='cubic',bounds_error=False)\n",
      "x = np.arange(0.,1.05,0.05)\n",
      "y = fyxe(x)\n",
      "plt.plot(x,y,'r-',xe,xe,'k-')\n",
      "x1 = 0.4\n",
      "y1 = (L0*xA0 +V2*yA2 - L1*x1)/V1\n",
      "x2 = 0.2\n",
      "y2 = (L0*xA0 +V2*yA2 - L1*x2)/V1\n",
      "plt.plot([x1,x2],[y1,y2],'k-')\n",
      "f = lambda x: L0*xA0 +V2*yA2 - L1*x - V1*fyxe(x)\n",
      "sol = root(f,0.1)\n",
      "xA1 = sol.x[0]\n",
      "yA1 = fyxe(xA1)\n",
      "plt.grid(True)\n",
      "plt.xlabel('Liquid phase mole fraction, xA')\n",
      "plt.ylabel('Vapor phase mole fraction, yA')\n",
      "plt.plot(xA1,yA1,'ro')\n",
      "\n",
      "#Results\n",
      "print \"Equilibrium compositions of liquid and vapor are:\",round(xA1,4),round(yA1,4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Equilibrium compositions of liquid and vapor are: 0.254 0.4506\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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PJRBDpuq9U2GNwcHBAXfv3kXHjh3RqFEjANy4VVJSkg6aLUivpyBMooSFffti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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62e2b70>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.3-1 Page Number 645"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Relative Volatility for Benzene-Toluene System\n",
      "\n",
      "#Variable Declaration\n",
      "PA85 = 116.9              #Pressure of benzene at 85 deg C\n",
      "PB85 = 46.0               #Pressure of tuolene  at 85 deg C\n",
      "\n",
      "PA = 204.2                #Pressure of benzene at 105 deg C\n",
      "PB = 86.0                 #Pressure of toulene at 105 deg C\n",
      "\n",
      "#Calculation\n",
      "alpha85 = PA85/PB85\n",
      "alpha = PA/PB\n",
      "\n",
      "#Results\n",
      "print 'Relative Volatility for Benzene-Toluene at 85\u00b0C is %4.2f and at 105\u00b0C is %4.2f'%(alpha85,alpha)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Relative Volatility for Benzene-Toluene at 85\u00b0C is 2.54 and at 105\u00b0C is 2.37\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.3-2 Page Number 647"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Simple Differential Distillation\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt \n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "from scipy.integrate import quad, simps, romberg\n",
      "\n",
      "#Variable Declaration\n",
      "L1 = 100                 #Feed, mol\n",
      "xfnp = 0.5               #Mole fraction of n-pentane\n",
      "xfnh = 0.5               #Mole fraction of n-heptane\n",
      "P = 101.3                #Pressure in kPa\n",
      "V = 40.                  #Distilled moles\n",
      "x = np.array([0.000,0.059,0.145,0.254,0.398,0.594,0.867,1.000])\n",
      "y = np.array([0.000,0.271,0.521,0.701,0.836,0.925,0.984,1.000])\n",
      "\n",
      "#Calculations\n",
      "L2 = L1-V\n",
      "lnL1L2 = log(L1/L2)\n",
      "\n",
      "f1 = interp1d(x,y,kind = 'cubic',bounds_error=False)\n",
      "xx = np.arange(0.20,.601,0.001)\n",
      "yy = f1(xx)\n",
      "ff = 1./(yy-xx)\n",
      "f = interp1d(xx,ff,bounds_error=False)\n",
      "def Integrant(x):\n",
      "    return f(x)\n",
      "\n",
      "er = 12. \n",
      "ub = 0.5\n",
      "\n",
      "for j in range(len(xx)):\n",
      "    lb = xx[j+1]\n",
      "    zz = romberg(Integrant, lb, ub)\n",
      "    er = abs(zz-lnL1L2)\n",
      "    if er <=0.005:\n",
      "        xL = xx[j]\n",
      "        break\n",
      "yav = (L1*xfnp-L2*xL)/V\n",
      "plt.xlim(0.2,0.55)\n",
      "plt.ylim(0,3.5)\n",
      "plt.plot(xx,ff,'k-')\n",
      "xxx = np.arange(xL,xfnp+0.001,0.001)\n",
      "yyy = f1(xxx)\n",
      "fff = 1./(yyy-xxx)\n",
      "plt.fill_between(xxx,fff,0,color='0.6')\n",
      "plt.text(0.35,1.0,'Area='+str(round(lnL1L2,3)))\n",
      "plt.xlabel('$x$')\n",
      "plt.ylabel('$1/(y-x)$')\n",
      "plt.grid(True)\n",
      "#Results\n",
      "print \"Residue concentration : \", round(xL,3)\n",
      "print \"Average Distillate concentration:\", round(yav,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Residue concentration :  0.276\n",
        "Average Distillate concentration: 0.836\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vb8eOHTswe/ZsREdHy/n/+c9/WvvtC6f0nx/TyPFOJqR4rFixAjU1NaPOz83N\nxaZNmwAAiYmJaG1tRVNTEwICAhyUkCa727dvw2AwoLGxEQBgNBqhUqmwYMECTJkyZciyaWlpiI+P\nH/JcYWEhOjo68OMf/xguLi546aWX0N/fD2D8kYeHhwfa2trg5eWFtrY2eHh4jJjRy8sLAODh4QGd\nToeamhq5eBCJ5pQHRxsaGhAaGipPh4SEoL6+ftIVD71er9jRh8FgUPRfj3l5ebj77rvxxBNPyM/9\n5je/wcWLF4csFx8fjyNHjiAmJgaurq5oamqCj48Puru74eHhARcXFxgMBty8eVNeZ7yRh1arRVFR\nER566CEUFRVBp9MNW6a3txdGoxHTpk1DT08Pzp8/j4cfflieb+oZjNQTUcIZdkr/+SkqKlL02Va2\n4JTFAxj+CzDa8D49PR1hYWEAAG9vb+h0OnmHbGpIO+u0qVFqr9c3GAyQJEn+JTXtcDgdA4PBgLvu\numvITiw4OBjHjh1DSEiIvPysWbMQGBiI1157Dd3d3dBoNHjhhRewdOlSvPnmm/jxj3+ML33pS5g9\nezY+++wzXLt2bdz3f+ihh/CHP/wBBQUF8PLywtatWwEMnoJ76NAh/OhHP0JbWxvefvttAINnUS1d\nuhSurq4wGAzo7OzEhx9+iK6uLuzYsQPh4eHYsmULDAYD3n//fQwMDKC/vx9lZWXYsGGDfIjFmba/\nkqfnz58PQPz+w5JpvV6PnJwcAJD3lxMl7DqPmpoarF27dsSG+fPPP4+kpCSkpaUBAGJjY3HkyJFh\nIw9e5zE2XudBZHu8zmOQU56qu27dOuzatQsAUFxcDG9v70l3yIqISMmEFI/HH38c99xzDwwGA0JD\nQ/HBBx8gOzsb2dnZAICUlBREREQgKioKGRkZePfdd0XEtDte5yEO84ul9Py8zkNQz2P37t3jLpOV\nleWAJEREZA3e22oSY8+DyPbY8xjklD0PIiJybiweArHnIQ7zi6X0/Ox5sHgQEZEV2POYxNjzILI9\n9jwGceRBREQWY/EQiD0PcZhfLKXnZ8+DxYOIiKzAnsckxp4Hke2x5zGIIw8iIrIYi4dA7HmIw/xi\nKT0/ex4sHkREZAX2PCYx9jyIbI89j0EceRARkcVYPARiz0Mc5hdL6fnZ82DxICIiK7DnMYmx50Fk\ne+x5DOLIg4iILMbiIRB7HuIwv1hKz8+eB4sHERFZgT2PSYw9DyLbY89jEEceRERkMRYPgdjzEIf5\nxVJ6fva5ImPAAAAJcElEQVQ8BBWP/Px8xMbGIjo6Gq+//vqw+Xq9Hl5eXkhISEBCQgJeffVVASmJ\niGg0Du95DAwMICYmBocPH0ZwcDDuuusu7N69G3FxcfIyer0e27dvR25u7pivxZ7H2NjzILI99jwG\nOXzkUVJSgqioKISFhUGtViMtLQ379+8fthx3ekREzsvhxaOhoQGhoaHydEhICBoaGoYso1KpUFhY\nCK1Wi5SUFFRUVDg6pkOw5yEO84ul9PzseQBujn5DlUo17jKLFi1CXV0dNBoNDh48iNTUVFRWVo64\nbHp6OsLCwgAA3t7e0Ol0SEpKAvD/d87OOl1eXm7X1zcYDJAkCTExMfI0AE5zmtMTmJ4/fz4A8fsP\nS6b1ej1ycnIAQN5fTpTDex7FxcX42c9+hvz8fADAL3/5S7i4uOCHP/zhqOuEh4ejrKwMvr6+Q55n\nz2Ns7HkQ2R57HoMcfthqyZIluHjxImpqatDb24uPP/4Y69atG7JMU1OT/I2VlJRAkqRhhYOIiMRx\nePFwc3NDVlYWVq1ahfj4eDz22GOIi4tDdnY2srOzAQB79uzBggULoNPpsHXrVnz00UeOjukQ7HmI\nw/xiKT0/ex4Ceh4AsHr1aqxevXrIcxkZGfLXmZmZyMzMdHQsIiIyE+9tNYmx50Fke+x5DOLtSYiI\nyGIsHgKx5yEO84ul9PzsebB4EBGRFdjzmMTY8yCyPfY8BnHkQUREFmPxEIg9D3GYXyyl52fPg8WD\niIiswJ7HJMaeB5HtsecxiCMPIiKyGIuHQOx5iMP8Yik9P3seLB5ERGQF9jwmMfY8iGyPPY9BHHkQ\nEZHFWDwEYs9DHOYXS+n52fNg8SAiIiuw5zGJsedBZHvseQziyIOIiCzG4iEQex7iML9YSs/PngeL\nBxERWYE9j0mMPQ8i22PPYxBHHkREZDEhxSM/Px+xsbGIjo7G66+/PuIyW7ZsQXR0NLRaLU6ePOng\nhI7Bnoc4zC+W0vOz5yGgeAwMDOCb3/wm8vPzUVFRgd27d+P8+fNDlsnLy0NVVRUuXryIP/zhD9i8\nebOjYzpEeXm56AhWq6urEx1hQphfLKXnr6ioEB1BOIcXj5KSEkRFRSEsLAxqtRppaWnYv3//kGVy\nc3OxadMmAEBiYiJaW1vR1NTk6Kh219raKjqC1bq6ukRHmBDmF0vp+W/duiU6gnAOLx4NDQ0IDQ2V\np0NCQtDQ0DDuMvX19Q7LSEREY3Nz9BuqVCqzlvvimQDmrqckNTU1dn8PtVptl9e9efOm3V7bEZhf\nLCXnNxqN/GMWAopHcHDwkOOddXV1CAkJGXOZ+vp6BAcHD3utyMhIxReVP//5z6IjWK2wsFB0hAlh\nfrGUnl/J+57IyMgJv4bDi8eSJUtw8eJF1NTUICgoCB9//DF27949ZJl169YhKysLaWlpKC4uhre3\nNwICAoa9VlVVlaNiExHR5zi8eLi5uSErKwurVq3CwMAAnn32WcTFxSE7OxsAkJGRgZSUFOTl5SEq\nKgozZszAn/70J0fHJCKiMSj6CnMiIhLDKa8wH+8iwr/85S/QarVYuHAh7r33Xpw+fdrsdR1hIvnD\nwsKwcOFCJCQkYOnSpY6MLRsv//79+6HVapGQkIDFixfjv//9r9nrOsJE8ith+5uUlpbCzc0Ne/fu\ntXhde5pIftHbf7zser0eXl5eSEhIQEJCAl599VWz13UES/O/8sor8jyLt73kZPr7+6XIyEipurpa\n6u3tlbRarVRRUTFkmcLCQqm1tVWSJEk6ePCglJiYaPa6zpxfkiQpLCxMunHjhkMzf545+Ts6OuSv\nT58+LUVGRpq9rjPnlyRlbH/TcsnJydKaNWukPXv2WLSus+aXJLHb35zsBQUF0tq1a61a194mkl+S\nLN/2TjfyMOciwmXLlsHLywvA4EWEptPmzFnXmfObSAKPJJqTf8aMGfLXHR0d8PPzM3tdZ85v4uzb\nHwB+97vfYePGjZg1a5bF69rTRPKbiNr+5mYfKZ+Stv1Y29eSbe90xcOciwg/749//CNSUlKsWtce\nJpIfGDz97/7778eSJUuwc+dOu2Ydibn59+3bh7i4OKxevRq//e1vLVrXniaSH1DG9m9oaMD+/fvl\n2/aYThlVyvYfLb/pa1Hb35zsKpUKhYWF0Gq1SElJkW9TopRtP1p+0zxLtr3Dz7YajyXnThcUFOCD\nDz7AsWPHLF7XXiaSHwCOHTuGwMBAXLt2DQ888ABiY2OxYsUKe0Qdkbn5U1NTkZqaiqNHj+LJJ5/E\nhQsX7JzMPNbmN92oTwnbf+vWrfjVr34l31bb9NeiUn7+R8sPiN3+5mRftGgR6urqoNFocPDgQaSm\npqKystIB6cY30fyWbnunG3mYcxEhAJw+fRpf//rXkZubCx8fH4vWtaeJ5AeAwMBAAMCsWbPw1a9+\nFSUlJfYP/TmWbsMVK1agv78fN2/eREhIiGK2v4kp/40bNwAoY/uXlZUhLS0N4eHh2Lt3L77xjW8g\nNzdXMT//o+UHxG5/c7J7eHhAo9EAAFavXo2+vj5F/eyPlh+wYttb0Zexq76+PikiIkKqrq6Wenp6\nRmz61NbWSpGRkVJRUZHF69rbRPLfvn1bunXrliRJg03de+65R/rXv/7lsOySZF7+qqoqyWg0SpIk\nSWVlZVJERITZ6zpzfqVs/89LT0+X9u7da9W69jCR/KK3vznZr169Kv/sHD9+XJo7d67Z6zpzfmu2\nvdMdtjLnIsJt27ahpaVFPmaqVqtRUlIy6rpKyX/16lU88sgjAID+/n488cQTePDBB50u/969e7Fr\n1y6o1Wq4u7vjo48+GnNdpeRXyva3dF1Hmkh+0dvfnOx79uzBe++9Bzc3N2g0GsX97I+W35ptz4sE\niYjIYk7X8yAiIufH4kFERBZj8SAiIouxeBARkcVYPIiIyGIsHkREZDEWDyIishiLBxERWYzFg4iI\nLOZ0tychUrKBgQF8/PHHuHTpEkJDQ1FSUoLvfe97iIiIEB2NyKY48iCyoVOnTmHDhg2IiIiA0WjE\no48+Kt+tlGgyYfEgsqFFixZh6tSpKCoqQlJSEpKSkjB9+nTRsYhsjsWDyIZKS0tx/fp1nD17FuHh\n4Th69KjoSER2wZ4HkQ3l5+cjICAA9957L/7+978P+3x0osmCt2QnIiKL8bAVERFZjMWDiIgsxuJB\nREQWY/EgIiKLsXgQEZHFWDyIiMhiLB5ERGQxFg8iIrLY/wOgRx/AvKPogQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x64488d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.4-1 Page Number 656"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Rectification of Benzene-Toluene Mixture\n",
      "import numpy as np\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "import matplotlib.pyplot as plt\n",
      "from math import ceil\n",
      "\n",
      "#Variable Declaration\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000])\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000])\n",
      "\n",
      "F = 100.               #Feed in kmol/hr\n",
      "xF = 0.45              #Mole fraction of benzene in feed\n",
      "xD = 0.95              #Mole fraction of benzene in distillate\n",
      "xW = 0.10              #Mole fraction of benzene at the bottom\n",
      "R = 4.0                #Reflux ratio\n",
      "lambdav = 32099.\n",
      "Cp = 159.              #Average heat capacity of feed in kJ/kmol.K\n",
      "Tb = 366.7             #Boiling point of feed (K)\n",
      "Tf = 327.6             #Temperature of feed (K)\n",
      "\n",
      "#Calculations\n",
      "\n",
      "x = np.arange(0.,1.,0.01)\n",
      "f = interp1d(xe,ye, kind='cubic')\n",
      "y = f(x)\n",
      "\n",
      "plt.text(.05, .6, 'Equilibrium Curve')\n",
      "plt.text(xF,xF-0.1, 'Feed Line')\n",
      "plt.text(xF+0.05,xF+0.1, 'q-Line')\n",
      "plt.text(xF+0.3,xF+0.3, 'UO Line')\n",
      "plt.text(xF-0.2,xF-0.2, 'LO Line')\n",
      "plt.plot(x,y,'k-')\n",
      "plt.plot(xD,xD,'ro')\n",
      "plt.plot(xW,xW,'ro')\n",
      "\n",
      "plt.annotate('$(x_D,y_D)$', xy=(xD,xD), xytext=(xD,xD-0.02))\n",
      "plt.annotate('$(x_W,y_W)$', xy=(xW,xW), xytext=(xW,xW-0.02))\n",
      "plt.xlabel('Liquid mole fraction, x')\n",
      "plt.ylabel('Vapor mole fraction, y')\n",
      "plt.plot([0,1.], [0,1.], 'ko-', lw=0.5)\n",
      "\n",
      "\n",
      "\n",
      "ff = lambda x: f(x)-(mql*x+cql)\n",
      "\n",
      "plt.plot([0,1,xF,xF],[0,1,xF,0])\n",
      "a = np.array([[1,1], [xD,xW]])\n",
      "b = np.array([F,F*xF])\n",
      "[D,W]= np.linalg.solve(a, b)\n",
      "q = 1+Cp*(Tb-Tf)/lambdav\n",
      "muol = R/(R+1)\n",
      "cuol = xD/(R+1)\n",
      "mql = q/(q-1.)\n",
      "cql = xF - mql*xF\n",
      "\n",
      "plt.plot(xD,xD,'rx')\n",
      "plt.plot(xW,xW,'rx')\n",
      "a = np.array([[1,-mql], [1,-muol]])\n",
      "b = np.array([cql,cuol])\n",
      "[yi,xi] = np.linalg.solve(a, b)\n",
      "mlol = (xW-yi)/(xW-xi)\n",
      "clol = yi - mlol*xi\n",
      "sol = root(ff,0.52)\n",
      "xq = sol.x[0]\n",
      "yq = f(xq)\n",
      "plt.plot([xF,xq],[xF,yq])\n",
      "plt.plot([xF,xi],[xF,mql*xi+cql])\n",
      "plt.plot([xD,xi],[xD,yi])\n",
      "plt.plot([xW,xi],[xW,yi])\n",
      "x1 = xD\n",
      "y1 = xD\n",
      "n = 0\n",
      "j = 0 \n",
      "while x1>xW:\n",
      "    y2 = y1\n",
      "    ff = lambda x: y1 -f(x)\n",
      "    sol = root(ff,0.2)\n",
      "    x2 = sol.x[0]\n",
      "    plt.text(x2, y2+0.02, str(n+1)) \n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    if x2 > xW:\n",
      "        n = n+1\n",
      "    else:\n",
      "        dxt = x1 - x2\n",
      "        dx = x1 - xW\n",
      "        n = n + dx/dxt\n",
      "    if x2>xW and x2<xi:\n",
      "        j = j + 1\n",
      "    x1 = x2\n",
      "    if x1 <= xi:\n",
      "        c = clol\n",
      "        m = mlol\n",
      "    else:\n",
      "        c = cuol\n",
      "        m = muol\n",
      "    ff = lambda y: x1 - (y - c)/m\n",
      "    sol = root(ff,0.5)\n",
      "    y2 = sol.x[0]   \n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "\n",
      "    x1 = x2\n",
      "    y1 = y2\n",
      "nf = n - j\n",
      "plt.title('McCabe Thiele Diagram')\n",
      "plt.grid(True)    \n",
      "#Results\n",
      "print \"Rate of distilate\",round(D,1),\"kmol/hr\\nRate of bottoms\" ,round(W,1),\"kmol/hr\" \n",
      "print 'slope of q-line: %4.2f'%mql\n",
      "print \"Number of equilibrium satges including reboiler for required separation:\",round(n,1)\n",
      "print \"Number of equilibrium satges excluding reboiler for required separation:\",round(n-1,1)\n",
      "print 'Feed is introduced on %2d'%(ceil(nf))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rate of distilate 41.2 kmol/hr\n",
        "Rate of bottoms 58.8 kmol/hr\n",
        "slope of q-line: 6.16\n",
        "Number of equilibrium satges including reboiler for required separation: 7.5\n",
        "Number of equilibrium satges excluding reboiler for required separation: 6.5\n",
        "Feed is introduced on  5\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ak5NToQwKwIH166kjytF10k980mcm6xmJYCNVYy9q6U4KTu/evQuUJiKNikQiKTXcv38f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\ndh+Fiwtht88ON0y6YYjFfeqdEEI0XoedUykuLkZQUBCOHj0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       "text": [
        "<matplotlib.figure.Figure at 0x6561ef0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.4-2 Page Number 660"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Minimum Reflux Ratio and Total Reflux in Rectification\n",
      "import numpy as np\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "import matplotlib.pylab as plt\n",
      "from math import ceil\n",
      "\n",
      "#Variable Declaration\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000])\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000])\n",
      "\n",
      "F = 100.               #Feed in kmol/hr\n",
      "xF = 0.45              #Mole fraction of benzene in feed\n",
      "xD = 0.95              #Mole fraction of benzene in distillate\n",
      "xW = 0.10              #Mole fraction of benzene at the bottom\n",
      "R = 4.0                #Reflux ratio\n",
      "lambdav = 32099.\n",
      "Cp = 159.              #Average heat capacity of feed in kJ/kmol.K\n",
      "Tb = 366.7             #Boiling point of feed (K)\n",
      "Tf = 327.6             #Temperature of feed (K)\n",
      "\n",
      "#Calculations\n",
      "x = np.arange(0.,1.,0.01)\n",
      "\n",
      "f = interp1d(xe,ye, kind='cubic')\n",
      "y = f(x)\n",
      "plt.text(.05, .6, 'Equilibrium Curve')\n",
      "plt.text(xF,xF-0.1, 'Feed Line')\n",
      "plt.text(xF+0.05,xF+0.1, 'q-Line')\n",
      "plt.grid(True)\n",
      "plt.title('McCabe Thiele Diagram')\n",
      "plt.plot(xD,xD,'ro')\n",
      "plt.plot(xW,xW,'ro')\n",
      "plt.plot(x,y,'k-')\n",
      "plt.plot([0,1.], [0,1.], 'ko-')\n",
      "plt.annotate('$(x_D,y_D)$', xy=(xD,xD), xytext=(xD,xD-0.02))\n",
      "plt.annotate('$(x_W,y_W)$', xy=(xW,xW), xytext=(xW,xW-0.02))\n",
      "plt.xlabel('Liquid mole fraction, x')\n",
      "plt.ylabel('Vapor mole fraction, y')\n",
      "\n",
      "\n",
      "ff = lambda x: f(x)-(mql*x+cql)\n",
      "plot([0,1,xF,xF],[0,1,xF,0])\n",
      "a = np.array([[1,1], [xD,xW]])\n",
      "b = np.array([F,F*xF])\n",
      "[D,W] = np.linalg.solve(a, b)\n",
      "q = 1+Cp*(Tb-Tf)/lambdav\n",
      "mql = 1./(q-1.)\n",
      "cql = xF - mql*xF\n",
      "plot(xD,xD,'rx')\n",
      "plot(xW,xW,'rx')\n",
      "sol = root(ff,0.52)\n",
      "xq = sol.x[0]\n",
      "yq = f(xq)\n",
      "plot([xF,xq],[xF,yq])\n",
      "mmin = (xD-yq)/(xD-xq)\n",
      "Rm = mmin/(1-mmin)\n",
      "x1 = xD\n",
      "y1 = xD\n",
      "n = 0\n",
      "j = 0\n",
      "while x1>xW:\n",
      "    y2 = y1\n",
      "    ff = lambda x: y1 -f(x)\n",
      "    sol = root(ff,0.2)\n",
      "    x2 = sol.x[0]\n",
      "    plt.text(x2, y2+0.02, str(n+1)) \n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    if x2 > xW:\n",
      "        n = n+1\n",
      "    else:\n",
      "        dxt = x1 - x2\n",
      "        dx = x1 - xW\n",
      "        n = n + dx/dxt\n",
      "    if x2>xW and x2<xF:\n",
      "        j = j + 1\n",
      "    x1 = x2\n",
      "    y2 = x2\n",
      "    plot([x1,x2],[y1,y2],'k-')\n",
      "    x1 = x2\n",
      "    y1 = y2\n",
      "\n",
      "#Results\n",
      "print \"A: Minimum Reflux Ratio:\", round(Rm,3)\n",
      "print \"B: Number of equilibrium satges including reboiler for required separation:\",round(n,1)\n",
      "print \"   Number of equilibrium satges excluding reboiler for required separation:\",round(n-1,1)\n",
      "print 'Feed is introduced on %2d'%(ceil(n-j))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A: Minimum Reflux Ratio: 1.104\n",
        "B: Number of equilibrium satges including reboiler for required separation: 5.8\n",
        "   Number of equilibrium satges excluding reboiler for required separation: 4.8\n",
        "Feed is introduced on  4\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vH5FN//77L9asWYO8vDxs374d48aN43ujuubyua64G6M2gMq7MdKtfcVFKhP1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\n0lw025xKWloaPDw84O/vD3V1dZGcQxT3O6H+Yh4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TEyQmJrYq8/bbbyMkJAQbNmzAoUOH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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6462910>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.4-3 Page Number 662"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Number of Trays in Stripping Tower\n",
      "import matplotlib.pylab as plt\n",
      "#Variable Declaration\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000])\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000])\n",
      "P= 101.3           #Total tower pressure in kPa\n",
      "F = 400.0          #Feed rate in kmol/hr\n",
      "xFA = 0.70         #Mole fraction of benzene in feed \n",
      "xFB = 0.30         #Mole fraction of toulene in feed\n",
      "W = 60.0           #Bottoms product rate in kmol/hr\n",
      "xWA = 0.10         #Mole fraction of benzene in bottoms\n",
      "\n",
      "#Calculations\n",
      "x = np.arange(0.,1.,0.01)\n",
      "\n",
      "f = interp1d(xe,ye, kind='cubic')\n",
      "y = f(x)\n",
      "plt.title('McCabe Thiele Diagram')\n",
      "plt.grid(True)\n",
      "plt.plot(x,y,'k-')\n",
      "plt.text(.05,0.6, 'Equilibrium Curve')\n",
      "plt.text(xFA+0.01,xFA-0.1, 'Feed Line')\n",
      "plt.text(xFA,xFA+0.2, 'q-Line')\n",
      "\n",
      "plt.plot(xW,xW,'ro')\n",
      "plt.annotate('$(x_W,y_W)$', xy=(xW,xW), xytext=(xW,xW-0.02))\n",
      "plt.xlabel('Liquid mole fraction, x')\n",
      "plt.ylabel('Vapor mole fraction, y')\n",
      "xWB = 1.- xWA\n",
      "D = F - W\n",
      "yDA = (F*xFA-W*xWA)/D\n",
      "plt.annotate('$(x_F,y_D)$', xy=(xFA,yDA), xytext=(xFA+0.02,yDA+0.02))\n",
      "plt.plot(xFA,yDA,'ro')\n",
      "plt.plot([0,1],[0,1])\n",
      "plt.plot([xFA,xFA],[0,1],'k-')\n",
      "plt.plot([xFA,xWA],[yDA,xWA],'k-')\n",
      "plt.plot(xWA,xWA,'bo')\n",
      "x1 = xFA\n",
      "y1 = yDA\n",
      "n = 0\n",
      "m = (yDA-xWA)/(xFA-xWA)\n",
      "c = yDA - m*xFA\n",
      "j = 0\n",
      "while x1>xW:\n",
      "    y2 = y1\n",
      "    ff = lambda x: y1 -f(x)\n",
      "    sol = root(ff,0.2)\n",
      "    x2 = sol.x[0]\n",
      "    plt.text(x2, y2+0.02, str(n+1)) \n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    if x2 > xW:\n",
      "        n = n+1\n",
      "    else:\n",
      "        dxt = x1 - x2\n",
      "        dx = x1 - xW\n",
      "        n = n + dx/dxt\n",
      "    if x2>xW and x2<xF:\n",
      "        j = j + 1\n",
      "\n",
      "    x1 = x2\n",
      "    ff = lambda y: x1 - (y - c)/m\n",
      "    sol = root(ff,0.5)\n",
      "    y2 = sol.x[0]\n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    x1 = x2\n",
      "    y1 = y2\n",
      "#Results\n",
      "print \"Overhead product rate is\", round(D,2),\"kmol/hr\"\n",
      "print \"Number of equilibrium satges including reboiler for required separation:\",round(n,1)\n",
      "print \"Number of equilibrium satges excluding reboiler for required separation:\",round(n-1,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overhead product rate is 340.0 kmol/hr\n",
        "Number of equilibrium satges including reboiler for required separation: 5.3\n",
        "Number of equilibrium satges excluding reboiler for required separation: 4.3\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h/v372LRpE7y9vYXyZl5JRUUFtmzZgr///hv+/v7Q0dERuAzUSxAxmj6Fgv+I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\nhqCgIAwcOBD9+vXD3r17a513d3fH8OHDoaGhgXH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       "text": [
        "<matplotlib.figure.Figure at 0x5faf190>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.6-1 Page Number 670"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Enthalpy Concentration Plot for Benzene-Toluene\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "#Variable Declaration\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000]) #Equillibrium liquid phase composition benzene toulene\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000]) #Equillibrium vapor phase composition\n",
      "T = np.array([110.6,105.0,100.0,95.0,90.0,85.0,80.1])      #Saturation temperatures corresponding to equillibrium points\n",
      "Tb = np.array([80.1,110.6])      #Boiling point of benzene toulene resp in \u00b0C\n",
      "Cpl = np.array([138.0,167.5])    #Liquid heat capacity of benzene toulene resp kJ/kmol.K\n",
      "Cpg = np.array([96.3,138.2])     #Vapor heat capacity of benzene toulene resp kJ/kmol.K\n",
      "Lbd = np.array([30820,33330])    #Latent heat of benzene toulene resp kJ/kmol\n",
      "h = np.zeros(len(xe))            #Enthalpy of liquid in KJ/kmol\n",
      "H = np.zeros(len(xe))            #Enthalpy of vapor in KJ/kmol\n",
      "Tref = 80.1                      #Reference   temperature in \u00b0C\n",
      "#Calculations\n",
      "\n",
      "LbdA = Cpl[0]*(Tb[0]-Tref) + Lbd[0] - Cpg[0]*(Tb[0]-Tref)\n",
      "LbdB = Cpl[1]*(Tb[1]-Tref) + Lbd[1] - Cpg[1]*(Tb[1]-Tref)\n",
      "h = xe*Cpl[0]*(T-Tref)+(1.-xe)*Cpl[1]*(T-Tref)\n",
      "H = ye*(LbdA + Cpg[0]*(T-Tref)) + (1-ye)*(LbdB + Cpg[1]*(T-Tref))\n",
      "\n",
      "#Results\n",
      "print ' Enthalpy (kJ/kgmol) of      '\n",
      "print '   Liquid     Vapor '\n",
      "print '     h         H  '\n",
      "for i in range(len(h)):\n",
      "    print '   %4.0f      %5.0f'%(h[i],H[i])\n",
      "\n",
      "plt.plot(xe,h,'bo-',ye,H,'ro-')\n",
      "plt.ylabel('Enthalpy, kJ/kgmol')\n",
      "plt.xlabel('x, y')\n",
      "plt.title('Enthalpy concentration Diagram')\n",
      "plt.grid(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Enthalpy (kJ/kgmol) of      \n",
        "   Liquid     Vapor \n",
        "     h         H  \n",
        "   5109      38439\n",
        "   4075      36504\n",
        "   3182      35042\n",
        "   2315      33737\n",
        "   1489      32625\n",
        "    708      31653\n",
        "      0      30820\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DBxQYGEgKhYKCgoIoLy9POGbLli3k6upKbm5uFB8fL2y/dOkSeXh4kKurKy1b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\nJzsbuHq15vaiIqB/f90Jp/a2nj2bdj4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       "text": [
        "<matplotlib.figure.Figure at 0xe7f1d90>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.6-2 Page Number 674"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Distillation Using Enthalpy-Concentration Method\n",
      "import matplotlib.pylab as plt\n",
      "import numpy as np\n",
      "from scipy.interpolate import interp1d\n",
      "from scipy.optimize import root\n",
      "\n",
      "#Variable Declaration\n",
      "    #Equillibrium liquid phase composition benzene toulene\n",
      "xe = np.array([0.000,0.130,0.258,0.411,0.581,0.780,1.000]) \n",
      "    #Equillibrium vapor phase composition\n",
      "ye = np.array([0.000,0.261,0.456,0.632,0.777,0.900,1.000]) \n",
      "    #Saturation temperatures corresponding to equillibrium points\n",
      "T = np.array([110.6,105.0,100.0,95.0,90.0,85.0,80.1])      \n",
      "Tb = np.array([80.1,110.6])      #Boiling point of benzene toulene resp in \u00b0C\n",
      "Cpl = np.array([138.0,167.5])    #Liquid heat capacity of benzene toulene resp kJ/kmol.K\n",
      "Cpg = np.array([96.3,138.2])     #Vapor heat capacity of benzene toulene resp kJ/kmol.K\n",
      "Lbd = np.array([30820,33330])    #Latent heat of benzene toulene resp kJ/kmolF = 100.\n",
      "xF = 0.45           #Feed mole fraction for benzene\n",
      "xD = 0.95           #Distillate mole fraction for benzene\n",
      "xW = 0.10           #Bottoms mole fraction for benzene\n",
      "Rm = 1.17           #Minimum reflux ratio\n",
      "lambdav = 32099.    #Average Latent heat of vaporiztion kJ/kmol\n",
      "Cp = 159.           #Average  heat capacity kJ/kmol.K\n",
      "Tbb = 366.7         #Boiling point of feed in K\n",
      "Tf = 327.6          #Feed temperature in K\n",
      "Rmul = 1.5          #Number of times minimum reflux\n",
      "F = 100.            #Feed rate to distillation, khmol/h\n",
      "\n",
      "#Calculations\n",
      "Tref = Tb[0]\n",
      "LbdA = Cpl[0]*(Tb[0]-Tref) + Lbd[0] - Cpg[0]*(Tb[0]-Tref)\n",
      "LbdB = Cpl[1]*(Tb[1]-Tref) + Lbd[1] - Cpg[1]*(Tb[1]-Tref)\n",
      "h = xe*Cpl[0]*(T-Tref)+(1.-xe)*Cpl[1]*(T-Tref)\n",
      "H = ye*(LbdA + Cpg[0]*(T-Tref)) + (1-ye)*(LbdB + Cpg[1]*(T-Tref))\n",
      "Hi = interp1d(ye,H,kind='cubic')\n",
      "hi = interp1d(xe,h,kind='cubic')\n",
      "yei = interp1d(xe,ye,kind='cubic')\n",
      "\n",
      "def LiquidH(T,x):\n",
      "    return x*Cpl[0]*(T-Tref)+(1.-x)*Cpl[1]*(T-Tref)\n",
      "\n",
      "def VaporH(T,y):\n",
      "    return y*(LbdA + Cpg[0]*(T-Tref)) + (1-y)*(LbdB + Cpg[1]*(T-Tref))\n",
      "\n",
      "R = Rm*Rmul\n",
      "\n",
      "x = np.arange(0.,1.,0.01)\n",
      "f = interp1d(xe,ye, kind='cubic')\n",
      "y = f(x)\n",
      "plt.title('McCabe Thiele Diagram')\n",
      "plt.grid(True)\n",
      "plt.plot(x,y,'k-')\n",
      "plt.text(.05, .6, 'Equilibrium Curve')\n",
      "plt.text(xF,xF-0.1, 'Feed Line')\n",
      "plt.text(xF+0.05,xF+0.1, 'q-Line')\n",
      "plt.text(xF+0.3,xF+0.3, 'UO Line')\n",
      "plt.text(xF-0.2,xF-0.2, 'LO Line')\n",
      "plt.plot(xD,xD,'ro')\n",
      "plt.plot(xW,xW,'ro')\n",
      "plt.annotate('$(x_D,y_D)$', xy=(xD,xD), xytext=(xD,xD-0.02))\n",
      "\n",
      "plt.annotate('$(x_W,y_W)$', xy=(xW,xW), xytext=(xW,xW-0.02))\n",
      "plt.xlabel('Liquid mole fraction, x')\n",
      "plt.ylabel('Vapor mole fraction, y')\n",
      "\n",
      "plt.plot([0,1,xF,xF],[0,1,xF,0])\n",
      "a = np.array([[1,1], [xD,xW]])\n",
      "b = np.array([F,F*xF])\n",
      "[D,W]= np.linalg.solve(a, b)\n",
      "L = R*D\n",
      "q = 1+ Cp*(Tbb-Tf)/lambdav\n",
      "V1 = L + D\n",
      "H1 = VaporH(82.3,xD)\n",
      "hD = LiquidH(81.1,xD)\n",
      "muol = R/(R+1)\n",
      "cuol = xD/(R+1)\n",
      "mql = q/(q - 1.)\n",
      "cql = xF - mql*xF\n",
      "plt.plot(xD,xD,'ro')\n",
      "plt.plot(xW,xW,'ro')\n",
      "a = np.array([[1,-mql], [1,-muol]])\n",
      "b = np.array([cql,cuol])\n",
      "[yi,xi] = np.linalg.solve(a, b)\n",
      "plt.plot([xF,xi],[xF,yi])\n",
      "xuol = np.arange(0.40,0.96,0.01)\n",
      "yuol = np.zeros(len(xuol))\n",
      "\n",
      "m = muol\n",
      "c = cuol\n",
      "for j in  range(len(xuol)):\n",
      "    xn = xuol[j]\n",
      "    yn1 = m*xn + c\n",
      "    er = 1.\n",
      "    while er >=0.001:\n",
      "        hn = hi(xn)\n",
      "        Hn1 = Hi(yn1)\n",
      "        Vn1 = (V1*H1-D*hi(xn)+L*hD)/(Hi(yn1)-hi(xn))\n",
      "        Ln = Vn1 - D \n",
      "        yn1c = Ln/Vn1*xn+D*xD/Vn1\n",
      "        er = abs(yn1-yn1c)\n",
      "        yn1 = yn1c\n",
      "    yuol[j] = yn1\n",
      "plt.plot(xuol,yuol)    \n",
      "Qc = V1*H1-L*hD-D*hD\n",
      "\n",
      "hF = LiquidH(54.5,xF)\n",
      "hW = hi(xW)\n",
      "Qr = D*hD+W*hW+Qc-F*hF\n",
      "\n",
      "mlol = (xW-yi)/(xW-xi)\n",
      "clol = yi - mlol*xi\n",
      "xlol = np.arange(0.1,0.52,0.02)\n",
      "ylol = np.zeros(len(xlol))\n",
      "m = mlol\n",
      "c = clol\n",
      "yW = yei(xW)\n",
      "HW = Hi(yW)\n",
      "hW = hi(xW)\n",
      "ym1 = yW\n",
      "Lm = Ln + q*F \n",
      "Vm1 = Vn1 - (1.-q)*F\n",
      "for j in  range(len(ylol)):\n",
      "    xm = xlol[j]\n",
      "    ym1 = m*xm - c \n",
      "    er = 1.\n",
      "    while er >=0.001:\n",
      "        hm = hi(xm)\n",
      "        Hm1 = Hi(ym1)\n",
      "        Vm1 = (W*(hm-hW)+Qr)/(Hm1-hm)\n",
      "        Lm = Vm1 + W\n",
      "        ym1c = Lm*xm/Vm1 - W*xW/Vm1\n",
      "        er = abs(ym1-ym1c)\n",
      "        ym1 = ym1c\n",
      "    ylol[j] = ym1c\n",
      "plt.plot(xlol,ylol)\n",
      "\n",
      "fl = interp1d(xlol,ylol)\n",
      "fu = interp1d(xuol,yuol)\n",
      "\n",
      "ff = lambda x: f(x)-(mql*x+cql)\n",
      "sol = root(ff,0.52)\n",
      "xq = sol.x[0]\n",
      "yq = f(xq)\n",
      "\n",
      "x1 = xD\n",
      "y1 = xD\n",
      "n = 0\n",
      "j = 0\n",
      "while x1>xW:\n",
      "    y2 = y1\n",
      "    ff = lambda x: y1 -f(x)\n",
      "    sol = root(ff,0.2)\n",
      "    x2 = sol.x[0]\n",
      "    plt.text(x2-0.02, y2+0.02, str(n+1))\n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    if x2 > xW:\n",
      "        n = n+1\n",
      "    else:\n",
      "        dxt = x1 - x2\n",
      "        dx = x1 - xW\n",
      "        n = n + dx/dxt\n",
      "\n",
      "    if x2>xW and x2<xi:\n",
      "        j = j + 1\n",
      "\n",
      "    x1 = x2\n",
      "    if x1 >= xi:\n",
      "        ff = lambda y: y - fu(x1)\n",
      "        sol = root(ff,0.65)\n",
      "        y2 = sol.x[0]\n",
      "    elif x1 <= xi and x1 >=xW:\n",
      "        ff = lambda y: y - fl(x1)\n",
      "        sol = root(ff,0.2)\n",
      "        y2 = sol.x[0]\n",
      "    else:\n",
      "        y2 = x1   \n",
      "\n",
      "    plt.plot([x1,x2],[y1,y2],'k-')\n",
      "    x1 = x2\n",
      "    y1 = y2\n",
      "\n",
      "#Results\n",
      "print 'Vapor rate from reboiler %4.1f kmol/h'%Vm1\n",
      "print 'Bottoms product rate %4.1f kJ/h'%W\n",
      "print 'Distillate rate %4.1f kJ/h'%D\n",
      "print 'Condeser duty %8.2f kJ/h'%Qc\n",
      "print 'Reboiler duty %8.2f kJ/h'%Qr\n",
      "print \"Number of equilibrium stages including reboiler for required separation:\",round(n,1)\n",
      "print \"Number of equilibrium stages excluding reboiler for required separation:\",round(n-1,1)\n",
      "print 'Feed is introduced on %2d'%(ceil(n-j))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Vapor rate from reboiler 128.2 kmol/h\n",
        "Bottoms product rate 58.8 kJ/h\n",
        "Distillate rate 41.2 kJ/h\n",
        "Condeser duty 3524297.05 kJ/h\n",
        "Reboiler duty 4178128.14 kJ/h\n",
        "Number of equilibrium stages including reboiler for required separation: 10.9\n",
        "Number of equilibrium stages excluding reboiler for required separation: 9.9\n",
        "Feed is introduced on  6\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3HDt2jDFjxhAZGcm+ffvYt2+f/oTy9s7VZenSd5KHyfWxUTbIJ2JKPlKqVq0q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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x63fda10>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.7-1 Page Number 682"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Boiling Point of Multi-Component Liquid\n",
      "import numpy as np\n",
      "\n",
      "#Variable Declaration\n",
      "x = np.array([0.40,0.25,0.20,0.15])       #Feed composition in molfrac\n",
      "K1 = np.array([1.68,0.630,0.245,0.093])   #Values at 65 \u00b0C are taken from Fig 11.7-2\n",
      "K2 = np.array([1.86,0.710,0.2815,0.110])  #Values at 70 \u00b0C are taken from Fig 11.7-2\n",
      "\n",
      "#Calcualtion\n",
      "k = 2\n",
      "alpha = K1/K1[k]\n",
      "alpx = alpha*x\n",
      "s1 = s2 = 0.0\n",
      "for j in range(len(x)):\n",
      "    s1 = s1 + alpx[j]\n",
      "\n",
      "Kc = 1./s1\n",
      "print \"Kc:\", round(Kc,4), \"This value corresponds to 69\u00b0C \"\n",
      "\n",
      "alpha = K2/K2[k]\n",
      "alpx = alpha*x\n",
      "print \"At 69\u00b0C the value calculated is not shown and corresponds to 70\u00b0C\"\n",
      "for j in range(len(x)):\n",
      "    s2 = s2 + alpx[j]\n",
      "\n",
      "Kc = 1./s2\n",
      "\n",
      "#Results\n",
      "print \"Kc:\", round(Kc,4), \"This value corresponds to 70\u00b0C Hence converged\"\n",
      "print \"Bubble temperature is equal to 70 \u00b0C \""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Kc: 0.2745 This value corresponds to 69\u00b0C \n",
        "At 69\u00b0C the value calculated is not shown and corresponds to 70\u00b0C\n",
        "Kc: 0.2831 This value corresponds to 70\u00b0C Hence converged\n",
        "Bubble temperature is equal to 70 \u00b0C \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.7-2 Page Number 684"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Calculation of Top and Bottom Temeperature and Total Reflux\n",
      "import numpy as np\n",
      "from scipy.optimize import root\n",
      "\n",
      "#Variable Declaration\n",
      "Name = np.array(['A','B','C','D'])              #Component Nomenclature C4,C5,C6,C7\n",
      "xF = np.array([0.40,0.25,0.20,0.15])            #Feed composition in molfrac\n",
      "\n",
      "xW = np.array([0.0011,0.0704,0.5068,0.4217])    #Bottoms composition in molfrac\n",
      "K993 = np.array([3.12,1.38,0.60,0.28])          #Values of K at 99.3 \u00b0C\n",
      "K670 = np.array([1.75,0.65,0.26,0.10])          #Values of K at 67.0 \u00b0C for first trial\n",
      "K132 = np.array([5.00,2.35,1.15,0.61])          #Values of K at 132.0 \u00b0C for first trial\n",
      "yD = np.zeros(4)\n",
      "xW = np.zeros(4)\n",
      "\n",
      "F = 100.            #Molar feed rate to column, mol/h\n",
      "xBD = 0.90          #Fraction of B in Distillate\n",
      "xCW = 0.90          #Fraction of C in Bottoms\n",
      "hk = 2              #Heavy key index\n",
      "lk = 1              #Light key index \n",
      "q = 1.0             #Value of q as feed is saturated \n",
      "\n",
      "#Calculations\n",
      "mBD = F*xF[lk]*xBD\n",
      "mBW = F*xF[lk]-mBD\n",
      "mCW = F*xF[hk]*xCW\n",
      "mCD = F*xF[hk]-mCW\n",
      "\n",
      "#With assumption of no moles of D in Distillate and no moles of A in Bottoms\n",
      "mAD = F*xF[0]\n",
      "mDW = F*xF[3]\n",
      "\n",
      "#Calculate Flow rate of Distillate and Bottoms\n",
      "D = mAD+mBD+mCD\n",
      "W = mBW+mCW+mDW\n",
      "yD[0] = mAD/D\n",
      "yD[1] = mBD/D\n",
      "yD[2] = mCD/D\n",
      "xW[1] = mBW/W\n",
      "xW[2] = mCW/W\n",
      "xW[3] = mDW/W\n",
      "\n",
      "#Dew Point Calculations for Distillate with initial guess of 67\u00b0C\n",
      "alp67 = K670/K670[hk]\n",
      "alphalkD = alp67[lk]\n",
      "\n",
      "ybyalp = yD/alp67\n",
      "Syba = 0.0\n",
      "\n",
      "for j in range(len(yD)):\n",
      "    Syba = Syba + ybyalp[j]\n",
      "    \n",
      "\n",
      "x = ybyalp/Syba\n",
      "Sx = 0.0\n",
      "for j in range(len(xW)):\n",
      "    Sx = Sx + x[j]\n",
      "\n",
      "#Bubble Point Calculations for Bottoms with initial guess of 132\u00b0C\n",
      "alp132 = K132/K132[hk]\n",
      "alpixi = xW*alp132\n",
      "Sxa = 0.0\n",
      "for j in range(len(yD)):\n",
      "    Sxa = Sxa + alpixi[j]\n",
      "\n",
      "y = alpixi/Sxa\n",
      "Sy = 0.0\n",
      "for j in range(len(yD)):\n",
      "    Sy = Sy + y[j]\n",
      "\n",
      "alphalkW = alp132[lk]\n",
      "\n",
      "alpavg = sqrt(alphalkD*alphalkW)\n",
      "\n",
      "Nm = log((yD[lk]/yD[hk])*(xW[hk]/xW[lk]))/log(alpavg)\n",
      "alpavA = sqrt(alp67[0]*alp132[0])           #Average relative volatility of Butane\n",
      "alpavD = sqrt(alp67[3]*alp132[3])           #Average relative volatility of Butane\n",
      "\n",
      "#Distribution of Componenet in Distillate and Bottoms\n",
      "\n",
      "DbyWA = alpavA**Nm*yD[hk]*D/(xW[hk]*W)\n",
      "DbyWD = alpavD**Nm*yD[hk]*D/(xW[hk]*W)\n",
      "\n",
      "mAW = xF[0]*F/(1.0+DbyWA)\n",
      "mAD = mAW*DbyWA\n",
      "mDW = xF[3]*F/(1.0+DbyWD)\n",
      "mDD = mDW*DbyWD\n",
      "\n",
      "#Revised Distillate and Bottoms Compositions\n",
      "D = mAD+mBD+mCD+mDD\n",
      "W = mAW+mBW+mCW+mDW\n",
      "yD[0] = mAD/D\n",
      "yD[1] = mBD/D\n",
      "yD[2] = mCD/D\n",
      "yD[3] = mDD/D\n",
      "\n",
      "xW[0] = mAW/W\n",
      "xW[1] = mBW/W\n",
      "xW[2] = mCW/W\n",
      "xW[3] = mDW/W\n",
      "\n",
      "#Dew Point Calculations for Distillate with revised compositions\n",
      "alphalkD = alp67[lk]\n",
      "\n",
      "ybyalp = yD/alp67\n",
      "Syba = 0.0\n",
      "\n",
      "for j in range(len(yD)):\n",
      "    Syba = Syba + ybyalp[j]\n",
      "    \n",
      "x = ybyalp/Syba\n",
      "Sx = 0.0\n",
      "for j in range(len(xW)):\n",
      "    Sx = Sx + x[j]\n",
      "\n",
      "#Bubble Point Calculations for Bottoms with revised compositions \n",
      "alpixi = xW*alp132\n",
      "Sxa = 0.0\n",
      "for j in range(len(yD)):\n",
      "    Sxa = Sxa + alpixi[j]\n",
      "    \n",
      "y = alpixi/Sxa\n",
      "Sy = 0.0\n",
      "for j in range(len(yD)):\n",
      "    Sy = Sy + y[j]\n",
      "\n",
      "#Results\n",
      "print \"For Part A\"\n",
      "print \"Distillate Compositions are:\"\n",
      "for i in range(len(yD)):\n",
      "    print Name[i],\":\",round(yD[i],4)\n",
      "print \"Bottoms Compositions are:\"\n",
      "for i in range(len(xW)):\n",
      "    print Name[i],\":\",round(xW[i],4)\n",
      "print \"Distillate and Bottoms rate are\", round(D,3), \"and\",round(W,3)\n",
      "\n",
      "print \"For Part B\"\n",
      "print \"Dew temperature for top product and Bubble temperature for Bottoms are:\\nguess values of 67 and 132 \u00b0C\"\n",
      "\n",
      "print \"For Part C\"\n",
      "print \"Minimum number of stages including reboiler are:\", round(Nm,3)\n",
      "print \"Minimum number of stages excluding reboiler are:\", round(Nm-1,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For Part A\n",
        "Distillate Compositions are:\n",
        "A : 0.6197\n",
        "B : 0.3489\n",
        "C : 0.031\n",
        "D : 0.0004\n",
        "Bottoms Compositions are:\n",
        "A : 0.0011\n",
        "B : 0.0704\n",
        "C : 0.5068\n",
        "D : 0.4217\n",
        "Distillate and Bottoms rate are 64.483 and 35.517\n",
        "For Part B\n",
        "Dew temperature for top product and Bubble temperature for Bottoms are:\n",
        "guess values of 67 and 132 \u00b0C\n",
        "For Part C\n",
        "Minimum number of stages including reboiler are: 5.389\n",
        "Minimum number of stages excluding reboiler are: 4.389\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.7-3 Page Number 687"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Minimum Reflux and Number of Stages at Operating Reflux\n",
      "import numpy as np\n",
      "from scipy.optimize import root\n",
      "\n",
      "#Variable Declaration\n",
      "xF = np.array([0.40,0.25,0.20,0.15])            #Feed composition in molfrac\n",
      "xD = np.array([0.6197,0.3489,0.0310,0.0004])    #Distillate composition in molfrac\n",
      "xW = np.array([0.0011,0.0704,0.5068,0.4217])    #Bottoms composition in molfrac\n",
      "K = np.array([3.12,1.38,0.60,0.28])             #Values of K at 99.3 \u00b0C\n",
      "\n",
      "hk = 2                              #Heavy key index\n",
      "lk = 1                              #Light key index \n",
      "q = 1.0                             #Value of q as feed is saturated \n",
      "alavlk,D,W = 2.258,64.484,35.516    #From Example 11.7-2\n",
      "#Calculation\n",
      "al = K/K[hk]\n",
      "alxF = al*xF\n",
      "alxD = al*xD\n",
      "f = lambda x: alxF[0]/(al[0]-x)+ alxF[1]/(al[1]-x)+ alxF[2]/(al[2]-x)+ alxF[3]/(al[3]-x)\n",
      "sol = root(f,1.1)\n",
      "theta = sol.x[0]\n",
      "Rm = alxD[0]/(al[0]-theta)+ alxD[1]/(al[1]-theta)+ alxD[2]/(al[2]-theta)+ alxD[3]/(al[3]-theta) - 1.0\n",
      "R = 1.5*Rm\n",
      "ordiR = R/(1+R)\n",
      "Param = Rm/(1+Rm)\n",
      "#From Fig 11.7-3\n",
      "Nm = log((xD[lk]/xD[hk])*(xW[hk]/xW[lk]))/log(alavlk)\n",
      "NmbyN = 0.49             \n",
      "N = Nm/NmbyN\n",
      "ff = lambda Ne:log(Ne/(N-Ne))-0.206*log((xF[hk]/xF[lk])*(W/D)*(xW[lk]/xD[hk]))\n",
      "sol = root(ff,5)\n",
      "Ne = sol.x[0]\n",
      "#Results\n",
      "print \"For Part A \"\n",
      "print \"Minimum reflux is\",round(Rm,3)\n",
      "print \"For Part B\"\n",
      "print \"Number of Theoretical Stages including reboiler are\", round(N,1)\n",
      "print \"Number of Theoretical Stages excluding reboiler are\", round(N-1,1)\n",
      "print \"For Part C\"\n",
      "print \"Feed is introduce on tray number\", round(Ne,0),\"from top\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For Part A \n",
        "Minimum reflux is 0.395\n",
        "For Part B\n",
        "Number of Theoretical Stages including reboiler are 11.0\n",
        "Number of Theoretical Stages excluding reboiler are 10.0\n",
        "For Part C\n",
        "Feed is introduce on tray number 6.0 from top\n"
       ]
      }
     ],
     "prompt_number": 39
    }
   ],
   "metadata": {}
  }
 ]
}