path: root/Elements_Of_Mass_Transfer_Part_1/ch3.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3 :  Mass transfer coefficient and interphase mass transfer"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variable Declaration      \n",
      "v=6.;       #velocity in m/s\n",
      "l=6.;       #length in m\n",
      "pa1=10.;     #pressure at 1 in atm\n",
      "pa2=0;     #pressure at 2 in atm\n",
      "t=373.;     # temperature in kelvin\n",
      "p=1.;      #pressure of naphthalene in atm at 373kelvin\n",
      "D=5.15*10**-6;    #diffusivity of naphthalene in C02 in m**2/s\n",
      "d=0.946;        #density of air in kg/m**3\n",
      "u=.021*10**-3;         #viscosity of air in Newton*s/m**2\n",
      "ID=0.075;       #diameter in m\n",
      "\n",
      "# Calculation\n",
      "nre=(ID*v*d)/(u);     #calc. of reynolds no.\n",
      "cf=2*0.023*(nre)**(-0.2);        #friction factor\n",
      "nsc=(u)/(d*D);        #calc of schmidt no.\n",
      "kc=(cf*v)/(2*(nsc)**(2./3));\n",
      "na=(kc*10**5*(pa1/760-0))/(8314*t);   #difussion flux in kmol/m**2*s\n",
      "sub=na*2*3.14*(ID/2)*l;          #rate of sublimation\n",
      "\n",
      "# Result\n",
      "print \"\\nrate of sublimation :%f *10**-6 kmol/s\\n\"%(sub/10**-6);\n",
      "#End"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "rate of sublimation :4.298312 *10**-6 kmol/s\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "# Variable Declaration   \n",
      "v=0.30;           #velocity of parallelair in m/s\n",
      "t=300;            #temperature of air in kelvin\n",
      "p=10.0**5/760;                #pressure of air in pascal\n",
      "Dab=5.9*10**-4;             #diffusivity of naphthalene in in air in m**2/s \n",
      "pa1=0.2*10**5/760;          #pressure of air at 1 in pascal\n",
      "pa2=0;                     #pressure of air at 2 in pascal\n",
      "d=1.15;                #density of air in kg/m**3\n",
      "u=0.0185*10**-3;        #viscosity of air in Newton*s/m**2\n",
      "D=1.;                   #length in m\n",
      "a=1.;                   #area of plate in m**2\n",
      "\n",
      "# Calculation   \n",
      "Nsc=u/(d*Dab);           #schmidt no. calculation\n",
      "Nre=(D*v*d)/u;        #reynolds no. calculation\n",
      "                     #flow is turbulent \n",
      "f=0.072*(Nre)**-.25;        #friction factor using \"chilton colburn\" analogy\n",
      "k_c=(f*v)/(2*(Nsc)**.667);    #mass transfer coefficient\n",
      "NA=k_c*(pa1-pa2)/(8314*300);    #mass flux calc.\n",
      "sub=NA*a;                        #rate  of sublimation in kmol/m**2*s\n",
      "\n",
      "# Result\n",
      "print \"\\nrate of sublimation :%f *10**-7 kmol/s\\n\"%(sub/10**-7)\n",
      "#End"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "rate of sublimation :1.077674 *10**-7 kmol/s\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.3 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "    \n",
      "\n",
      "# a is CO2 and b is water\n",
      "p=2.;              #total pressure at 1 in atm \n",
      "pa1=0.2*10**5;     #pressure of CO2 at pt 1 in atm\n",
      "pa2=0;            #pressure of CO2 at pt 2 is 0 since air is pure\n",
      "ya1=0.1;          #mole fraction of CO2 at 1 is 0.2/2\n",
      "ya2=0;            #mole fraction of CO2 at 2 is 0 since air is pure\n",
      "yb1=0.9;          #mole fraction of water at 1 is (1-0.1)\n",
      "yb2=1.0;          #mole fraction of water at 2 is 1.0 since total pressure has to be constant.\n",
      "k_y1=6.78*10**-5;        #mass transfer coefficient in kmol/m**2*s*molefraction\n",
      "import math\n",
      "\n",
      "# Calculation   \n",
      "yb_ln=(yb2-yb1)/(math.log(yb2/yb1));    #log mean is represented by yb_ln\n",
      "\n",
      "k_y=k_y1/yb_ln; \n",
      "\n",
      "# Result\n",
      "print \"\\nvalue of mass transfer coefficient k_y is:%f *10**-5 kmol/m**2*s*(molefractin)\"%(k_y/10.0**-5)\n",
      "k_g=k_y/p;                        #mass ttransfer coefficient in lmol/m**2*s*atm\n",
      "print \"\\nvalue  mass transfer coefficient k_g is:%f *10**-5 kmol/m**2*s*(atm)\"%(k_g/10**-5)\n",
      "\n",
      "NA=k_y*(ya1-ya2);                #mass flux in kmol/m**2*s\n",
      "print \"\\nvalue of rate of mass transfer :%f *10**-6 kmol/m**2*s\"%(NA/10.0**-6)\n",
      "#end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "value of mass transfer coefficient k_y is:7.143443 *10**-5 kmol/m**2*s*(molefractin)\n",
        "\n",
        "value  mass transfer coefficient k_g is:3.571721 *10**-5 kmol/m**2*s*(atm)\n",
        "\n",
        "value of rate of mass transfer :7.143443 *10**-6 kmol/m**2*s\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.4"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "NA=7.5*10**-7;       #mass flux in gmol/cm**2*s\n",
      "Dab=1.7*10**-5;     #diffusivity if SO2 in water in cm**2/s\n",
      "c=1./18.02;          #concentration is density/molecular weight in gmol/cm**2*s\n",
      "#SO2 is absorbed from air into water\n",
      "\n",
      "xa1=0.0025;        #liquid phase mole fraction at 1\n",
      "xa2=0.0003;        #liquid phase mole fraction at 2\n",
      "    #NA=kc(Ca1-Ca2)=Dab*(Ca1-Ca2)/d\n",
      "\n",
      "# Calculation   \n",
      "k_c=NA/(c*(xa1-xa2));    #k_c=Dab/d=NA/c(xa1-xa2)\n",
      "\n",
      "# Result    \n",
      "print \"\\nmass transfer coefficient k_c is:%f cm/s\"%k_c\n",
      "\n",
      "d=Dab/k_c;\n",
      "print \"\\nfilm thickness d is :%f cm\"%d\n",
      "#end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "mass transfer coefficient k_c is:0.006143 cm/s\n",
        "\n",
        "film thickness d is :0.002767 cm\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.5 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "Kg=2.72*10**-4;            #overall gas phase mass transfer coefficient in kmol/m**2*S*atm\n",
      "r_gas=0.85*(1/Kg);        #given that gas phase resisitance is 0.85 times overall resistance\n",
      "kg=1.0/r_gas;            \n",
      "m=9.35*10**-3;            #henry's law constant in atm*m**3/kmol\n",
      "kl=m/(1./Kg-1/kg);        #liquid phase mass transfer coefficient in m/s\n",
      "print \"\\nthe value of liquid film coefficient kl : %f*10**-5 m/s\"%(kl/10**-5)\n",
      "print \"\\nthe value of gas film coefficient kg : %f*10**-5 m/s\"%(kg/10**-5);\n",
      "p=1.;                     #overall pressure in atm\n",
      "\n",
      "        #NA=Kg(pag-pa*)=kg(pag-pai)=kl(Cai-Cal)\n",
      "# Calculation   \n",
      "Yag=0.1;                #molefraction of ammonia\n",
      "Cal=6.42*10**-2;         #liquid phase concentration \n",
      "Pag=Yag*p;              #pressure of ammonia\n",
      "       \n",
      "#Pai=m*C_ai;\n",
      "#NA=kg(pag-pai)=kl(Cai-Cal)\n",
      "        \n",
      "#Cai=poly([0],'Cai');        #calc. of conc. in gas phase\n",
      "x =  1.6588481  #x=roots((Pag-m*Cai)*(kg/kl)-(Cai-Cal));\n",
      "\n",
      "# Result    \n",
      "print \"\\nthe value of interphase conc.cai :%f kmol/m**3\"%x\n",
      "Pai=m*x;\n",
      "print \"\\nthe value of interphase pressure pai is:%f atm\"%Pai\n",
      "#end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "the value of liquid film coefficient kl : 1.695467*10**-5 m/s\n",
        "\n",
        "the value of gas film coefficient kg : 32.000000*10**-5 m/s\n",
        "\n",
        "the value of interphase conc.cai :1.658848 kmol/m**3\n",
        "\n",
        "the value of interphase pressure pai is:0.015510 atm\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.6 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "         \n",
      "m=0.3672;\n",
      "t=.9;\n",
      "        #Pai and Cai indicates interfacial pressure and conc.\n",
      "        #Pal and Cal indicates bulk pressure and conc.\n",
      "Yag=0.15;                #molefraction of ammonia\n",
      "Cal=0.147;         #liquid phase concentration in kmol/m**3\n",
      "p=1;                    #overall pressure\n",
      "\n",
      "# Calculation   \n",
      "Pag=Yag*p;              #pressure of ammonia\n",
      "\n",
      "        #Pai=m*C_ai;\n",
      "        #kg/kl=(Cai-Cal)/(Pag-Pai);\n",
      "        \n",
      "#Cai=poly([0],'Cai');        #calc. of conc. in gas phase\n",
      "x =  0.211954 #x=roots((Pag-m*Cai)*(t)-(Cai-Cal));\n",
      "\n",
      "# Result\n",
      "print \"\\nthe value of  conc. of ammonia cai is  :%f kmol/m**3\"%x\n",
      "Pai=m*x;\n",
      "print \"\\nthe value of interphase pressure Pai is  :%f atm\"%Pai"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "the value of  conc. of ammonia cai is  :0.211954 kmol/m**3\n",
        "\n",
        "the value of interphase pressure Pai is  :0.077830 atm\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.7"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "# Variable Declaration   \n",
      "D=.1;\n",
      "l=3;             # l is length of bubble in cm\n",
      "a=3.14*D*l;      # area in cm**2\n",
      "Ca_o=0.0001;    #pure conc. of gas in g*mol/cc*atm\n",
      "Ca=0;\n",
      "NA=.482*10**-5;   # molar rate of absorption in g*moles/s\n",
      "        #Pa_o and Ca_o indicates pure pressure and conc.\n",
      "# Calculation   \n",
      "kl=NA/(a*(Ca_o-Ca));    #mass transfer coefficient acc. to higbie's penetration theory\n",
      "Q=4;                    #volumetric flow rate in cc/s\n",
      "A=3.14*.1*.1/4;         #area of flow\n",
      "v=Q/A;                 #velocity of flow in cm/s\n",
      "\n",
      "#timt t=bubble length/linear velocity;\n",
      "t=l/v;\n",
      "DAB=(kl**2)*3.14*t/4;    #diffusivity in cm**2/s\n",
      "D_new=0.09;              #revised diameter reduced to.09\n",
      "a_new=3.14*l*D_new;        #revised area\n",
      "A_new=3.14*0.09*0.09/4;    #revised flow area\n",
      "v_new=Q/A_new;            #revised velocity\n",
      "\n",
      "# Result    \n",
      "print \"\\nthe value of diffusivity of gas DAB is :%f cm/s\"%(DAB/10**-5)\n",
      "\n",
      "t_new=l/v_new;            #revised time\n",
      "kl_new=2*(DAB/(3.14*0.0047))**0.5;    #revised mass transfer coefficient \n",
      "NA_new=kl_new*a_new*(Ca_o-Ca);       #revised molar rate absorption in g*moles/s\n",
      "print \"\\nthe value of NA_new is  :%f*10**-6 kmol/m**3\"%(NA_new/10**-6)\n",
      "#end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "the value of diffusivity of gas DAB is :1.210021 cm/s\n",
        "\n",
        "the value of NA_new is  :4.855188*10**-6 kmol/m**3\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.8"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "# Variable Declaration  \n",
      "Kg=7.36*10**-10;\n",
      "p=1.013*10**5;\n",
      "Ky=Kg*p;\n",
      "#resistance in gas phase is 0.45 of total resistance & .55 in liquid phase\n",
      "#(resistance in gas phase)r_gas=1/ky and (resistance in liq phase)r_liq=m'/kx\n",
      "r_gas=0.45*(1./Ky);\n",
      "ky=1./r_gas;\n",
      "r_liq=0.55*(1./Ky);\n",
      "print \"film based liq phase mass transfer coeff.ky is  :%f \"%ky\n",
      "\n",
      "# Calculation\n",
      "m1=86.45;\n",
      "kx=m1/r_liq;\n",
      "yag=.1;\n",
      "xal=(.4/64)/((99.6/18)+(.4/64));\n",
      "print \"\\n film based gas phase mass transfer coeff.ky is  :%f \"%kx\n",
      "#slope of the line gives -kx/ky=-70.61\n",
      "m2=m1;                           # since equilibrium line a straigth line m'=m''\n",
      "Kx=1/(1/kx+(1/(m2*ky)));        #overall liquid phase mass transfer coefficient\n",
      "print \"\\n overall  liq phase mass transfer coefficient Kx is  :%f \"%Kx\n",
      "# equillibrium relation is given under\n",
      "p = [0.2,0.3,0.5,0.7];\n",
      "a = [29,46,83,119];\n",
      "i=0;\n",
      "x = [0,0,0,0]\n",
      "y = [0,0,0,0]\n",
      "    #looping for calcullating mole fraction\n",
      "while (i<4):\n",
      "    x[i]= (p[i]/64.)/(p[i]/64.+100/18);\n",
      "    y[i]= a[i]/760.;                    #mole fraction plotted on y-axis\n",
      "    i=i+1;                     \n",
      "           #mole fraction plotted on x-axis\n",
      "%pylab inline\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "# Result\n",
      "plot(x,y);\n",
      "title(\"Fig.3.17,Example 8\");\n",
      "xlabel(\"X-- Concentration of SO2 in liquid phase, X(10**4)(molefraction)\");\n",
      "ylabel(\"Y-- Concentration of SO2 in gas phase, Y(molefraction)\");\n",
      "show()\n",
      "    #from the graph we get these values\n",
      "yao=.083;        #corresponding to the value of xao=0.001128\n",
      "xao=.00132;      #corresponding to the value of yag=.1\n",
      "yai=.0925;      #corresponding to the perpendicular dropped from the pt(.001128,0.1)  \n",
      "xai=.00123;\n",
      "       \n",
      "    # flux based on overall coefficient\n",
      "NAo_gas=Ky*(yag-yao);\n",
      "NAo_liq=Kx*(xao-xal);\n",
      "print \"overall gas phase mass transfer flux -NAo_gas is  :%f*10**-6 kmol/m**2*s \"%(NAo_gas/10**-6)\n",
      "print \"overall liq phase mass transfer flux -NAo_liq is  :%f*10**-6 kmol/m**2*s \"%(NAo_liq/10**-6);\n",
      "\n",
      "    # flux based on film coefficient \n",
      "NAf_gas=ky*(yag-yai);\n",
      "NAf_liq=kx*(xai-xal);\n",
      "print \"film based gas phase mass transfer flux-NAf_gas is  :%f *10**-6 kmol/m**2*s\"%(NAf_gas/10**-6);\n",
      "print \"film based liq phase mass transfer flux-NAf_liq is  :%f *10**-6 kmol/m**2*s\"%(NAf_liq/10**-6);\n",
      "#end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "film based liq phase mass transfer coeff.ky is  :0.000166 \n",
        "\n",
        " film based gas phase mass transfer coeff.ky is  :0.011719 \n",
        "\n",
        " overall  liq phase mass transfer coefficient Kx is  :0.006445 \n",
        "Populating the interactive namespace from numpy and matplotlib"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['f']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LYPJk4P33hTaUS5e4qDDNUXgrbM2aNQAAa2tr+Pv7o0+fPvIGe4lEgk8//VQz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\nOMXCwcHBwTGv/Aec+J/DRRI5KQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2c409d0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "overall gas phase mass transfer flux -NAo_gas is  :1.267466*10**-6 kmol/m**2*s \n",
        "overall liq phase mass transfer flux -NAo_liq is  :1.235953*10**-6 kmol/m**2*s \n",
        "film based gas phase mass transfer flux-NAf_gas is  :1.242613 *10**-6 kmol/m**2*s\n",
        "film based liq phase mass transfer flux-NAf_liq is  :1.192479 *10**-6 kmol/m**2*s\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example  3.9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "# Variable Declaration   \n",
      "Cas=1.521*10**-7;\n",
      "v=1525;       #velocity in m/s\n",
      "D=0.0516;    #diffusivity  in cm**2/s\n",
      "d=1.25*10**-3;        #density of air in g/cm**3\n",
      "u=1.786*10**-4;         #viscosity of air in n*s/m**2\n",
      "Dia=2.54;       #diameter in cm\n",
      "\n",
      "# Calculation   \n",
      "nre=(Dia*v*d)/(u);     #calc. of reynolds no.\n",
      "cf=2*0.036*(nre)**(-0.25);        #friction factor\n",
      "nsc=(u)/(d*D);        #calc of schmidt no.\n",
      "kc=(cf*v)/(2*(nsc)**(2./3));        #cf/2=kc/uo*(sc)**2/3\n",
      "\n",
      "#rate of mass transfer=(cross sectional area)*(air velocity)*dc =(3.14*d**2/4)*v*dc  -----1 eqn\n",
      "                                        \n",
      "#flux for mass transfer from the surface=kc*(Cas-C)\n",
      "#                  rate of mass transfer=(flux)*mass transfer\n",
      "#                                       =kc*(Cas-C)*3.14*dx*D------2 eqn\n",
      "#                           solving ----1 & -----2 we get\n",
      "#                           \n",
      "#                           (3.14*d**2/4)*v*dc=kc*(Cas-C)*3.14*dx*d;\n",
      "#                           dc/(Cas-C)=(kc*3.14*d*v)/(3.14*d**2/4)*dx\n",
      "#                           solving this we get\n",
      "#                           ln[(Cas-C)/(Cas-C_in)]=(kc*4*x)/(d*v)\n",
      "import math\n",
      "x=183;            #upper limit of x\n",
      "C_in=0;            #C=C_in=0;\n",
      "t=(kc*4*x)/(Dia*v);    #variable to take out the exponential\n",
      "z=math.e**t;\n",
      "C_final=Cas-(z*(Cas-C_in));        #value of c_final in g*mol/cc;\n",
      "\n",
      "# Result\n",
      "print \"\\t conc. of acid at outlet   :%f *10**-8 g*mol/cc\\n\"%(abs(C_final/10**-8))\n",
      "rate=(3.14*Dia**2/4)*v*(C_final-C_in);\n",
      "print \"\\trate of mass transfer  :%f *10**-4 g*mol/s\\n\"%(abs(rate/10**-4));\n",
      "#End"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\t conc. of acid at outlet   :7.709387 *10**-8 g*mol/cc\n",
        "\n",
        "\trate of mass transfer  :5.954246 *10**-4 g*mol/s\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}