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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6 : Bubbling Fluidized Beds"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 1, Page 150"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "z=0.5;     #Height of bed in m\n",
      "dt=0.5;    #ID of tube in m\n",
      "rhos=1.6;  #Density of catalyst in g/cm**3\n",
      "dpbar=60.;  #Averge catalyst diameter in micrometer\n",
      "umf=0.002; #Velocity at minimum fluidization condition in m/s\n",
      "uo=0.2;    #Superficial velocity in m/s\n",
      "dor=2.;     #Diameter of orifice in mm\n",
      "lor=20.;    #Pitch of perforated plate in mm\n",
      "g=9.80;    #g=980;#Acceleration due to gravity in m/s**2\n",
      "\n",
      "#CALCULATION\n",
      "#Method 1. Procedure using Eqn.(10) & Eqn.(11)\n",
      "db=(0.035+0.040)/2.;#Bubble size at z=0.5m from Fig.7(a) & Fig.7(b)\n",
      "ub1=1+1.55*((uo-umf)+14.1*(db+0.005))*(dt**0.32)*0.711*(g*db)**0.5;#Bubble velocity using Eqn.(10) & Eqn.(11)\n",
      "\n",
      "#Method 2. Werther's procedure\n",
      "si=0.8;#From Fig.6 for Geldart A solids \n",
      "ub2=si*(uo-umf)+(3.2*(dt**(1./3)))*(0.711*(g*db)**0.5);#Bubble velocity using Eqn.(9)\n",
      "\n",
      "#OUTPUT\n",
      "print 'Method 1. Procedure using Eqn.(10) & Eqn.(11)'\n",
      "print '\\tDiameter of the bubble=%.4fm'%db\n",
      "print '\\tRise velocity of the bubble=%.4fm/s'%ub1\n",
      "print 'Method 2. Werthers procedure'\n",
      "print '\\tDiameter of the bubble=%fm'%db\n",
      "print '\\tRise velocity of the bubble=%fm/s'%ub2\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Method 1. Procedure using Eqn.(10) & Eqn.(11)\n",
        "\tDiameter of the bubble=0.0375m\n",
        "\tRise velocity of the bubble=1.4267m/s\n",
        "Method 2. Werthers procedure\n",
        "\tDiameter of the bubble=0.037500m\n",
        "\tRise velocity of the bubble=1.253125m/s\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 2, Page 151\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "z=0.5;      #Height of bed in m\n",
      "dt=0.5;     #ID of tube in m\n",
      "rhos=2.6;   #Density of catalyst in g/cm**3\n",
      "dpbar=100.; #Averge catalyst diameter in micrometer\n",
      "umf=0.01;   #Velocity at minimum fluidization condition in m/s\n",
      "uo=0.45;    #Superficial velocity in m/s\n",
      "dor=2.;     #Diameter of orifice in mm\n",
      "lor=30.;    #Pitch of perforated plate in mm\n",
      "g=9.80;     #Acceleration due to gravity in m/s**2\n",
      "pi=3.142857;\n",
      "\n",
      "#CALCULATION\n",
      "#Part(a).Bubble Size\n",
      "Nor=(2/math.sqrt(3))*(1/lor**2);\n",
      "dbo=5.5;\n",
      "\n",
      "#Method 1.Werther's procedure for finding bubble size\n",
      "z1=[0,5,10,20,30,50,70]\n",
      "db = [0.,0.,0.,0.,0.,0.,0.]\n",
      "n=len(z1);\n",
      "i=0; \n",
      "while i<n:\n",
      "    db[i]=0.853*((1+0.272*(uo-umf)*100)**(1/3.0))*(1+0.0684*z1[i])**1.21;\n",
      "    i=i+1;    \n",
      "\n",
      "db1=0.163;#Since bubble size starts at dbo=5.5cm at z=0, we shift the curve accordingly to z=0.5m\n",
      "\n",
      "#Method 2.Mori and Wen's procedure for finding bubble size\n",
      "dbm=0.65*((math.pi/4.0)*((dt*100)**2)*(uo-umf)*100)**0.4;\n",
      "db2=dbm-(dbm-dbo)*math.exp(-0.3**(z/dt));\n",
      "\n",
      "#Part(b).Bubble Velocity\n",
      "#Method 1.Procedure using Eqn.(12)\n",
      "ub1=1.6*((uo-umf)+1.13*db1**0.5)*(dt**1.35)+(0.711*(g*db1)**0.5);\n",
      "\n",
      "#Method 2.Werther's Procedure\n",
      "si=0.65;\n",
      "ub2=si*(uo-umf)+2*(dt**0.5)*(0.711*(g*db1)**0.5);\n",
      "\n",
      "#Using Eqn.(7) & Eqn.(8)\n",
      "ubr1=0.711*(g*db1)**0.5;\n",
      "ubr2=0.711*(g*db2/100.0)**0.5\n",
      "ub3=uo-umf+ubr1;\n",
      "ub4=uo-umf+ubr2;\n",
      "\n",
      "#OUTPUT\n",
      "print 'Bubble Size'\n",
      "print 'Initial bubble size from Fig.5.14 for %.2fm/s = %.2fcm'%(uo-umf,dbo)\n",
      "print '\\tMethod 1.Werthers procedure for finding bubble size'\n",
      "print '\\t\\tHeight of bed(cm)'\n",
      "print '\\t\\t\\tBubble size(cm)'\n",
      "m=len(z1);\n",
      "j=0;\n",
      "while j<m:\n",
      "    print '\\t\\t%d'%z1[j],\n",
      "    print '\\t\\t\\t\\t%.2f'%db[j]\n",
      "    j=j+1;\n",
      "\n",
      "print '\\tMethod 2.Mori and Wens procedure for finding bubble size'\n",
      "print '\\t\\tMaximum expected bubble size=%.2fcm'%dbm\n",
      "print '\\t\\tBubble size=%.0fcm'%db2\n",
      "print 'Bubble Velocity'\n",
      "print '\\tMethod 1.Procedure using Eqn.(12)'\n",
      "print '\\t\\tBubble velocity=%.2fm/s'%ub1\n",
      "print '\\tMethod 2.Werthers procedure'\n",
      "print '\\t\\tBubble velocity=%.2fm/s'%ub2\n",
      "print 'Comparing the above results with the expressions of the simple two-phase theory'\n",
      "print '\\tWerthers bubble size'\n",
      "print '\\tBubble rise velocity=%.2fm/s\\tBubble velocity=%.2fm/s'%(ubr1,ub3)\n",
      "print '\\tMori & Wens bubble size'\n",
      "print '\\tBubble rise velocity=%.1fm/s\\tBubble velocity=%.2fm/s'%(ubr2,ub4)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Bubble Size\n",
        "Initial bubble size from Fig.5.14 for 0.44m/s = 5.50cm\n",
        "\tMethod 1.Werthers procedure for finding bubble size\n",
        "\t\tHeight of bed(cm)\n",
        "\t\t\tBubble size(cm)\n",
        "\t\t0 \t\t\t\t2.00\n",
        "\t\t5 \t\t\t\t2.86\n",
        "\t\t10 \t\t\t\t3.77\n",
        "\t\t20 \t\t\t\t5.69\n",
        "\t\t30 \t\t\t\t7.73\n",
        "\t\t50 \t\t\t\t12.10\n",
        "\t\t70 \t\t\t\t16.77\n",
        "\tMethod 2.Mori and Wens procedure for finding bubble size\n",
        "\t\tMaximum expected bubble size=61.31cm\n",
        "\t\tBubble size=20cm\n",
        "Bubble Velocity\n",
        "\tMethod 1.Procedure using Eqn.(12)\n",
        "\t\tBubble velocity=1.46m/s\n",
        "\tMethod 2.Werthers procedure\n",
        "\t\tBubble velocity=1.56m/s\n",
        "Comparing the above results with the expressions of the simple two-phase theory\n",
        "\tWerthers bubble size\n",
        "\tBubble rise velocity=0.90m/s\tBubble velocity=1.34m/s\n",
        "\tMori & Wens bubble size\n",
        "\tBubble rise velocity=1.0m/s\tBubble velocity=1.43m/s\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3, Page 153\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "dpbar=53.;      #Average particle size in micrometer\n",
      "s=[1,2];        #Size of Bermuda rock in cm \n",
      "rhosbar=3200.;  #Average solid density of the coke-zircon mixture in kg/m**3\n",
      "ephsilonm=0.5;  #Void fraction for fixed bed\n",
      "ephsilonf=0.75; #Void fraction for bubbling bed\n",
      "rhogbar=0.64;   #Average density of gas in kg/m**3\n",
      "uo=14.;         #Superficial gas velocity in cm/s\n",
      "myu=5E-5;       #Viscosity of gas in kg/m s\n",
      "T=1000.;        #Temperature in degree C\n",
      "P=1.;           #Pressure in atm\n",
      "dt=91.5;        #ID of bed in cm\n",
      "sh=150.;        #Slumped height in cm\n",
      "\n",
      "#CALCULATION\n",
      "rhog2=1.2;      #Density of ambient air\n",
      "myu2=1.8E-5;    #Viscosity of ambient air\n",
      "rhos2=rhog2*(rhosbar/rhogbar);#For the requirement of constant density ratio\n",
      "m=((rhogbar*myu2)/(rhog2*myu))**(2./3);#Scale factor by usin Eqn.(16)\n",
      "u2=(m**0.5)*uo;  #Superficial gas velocity by using Eqn.(17)\n",
      "#OUTPUT\n",
      "print 'For the model use'\n",
      "print '\\tBed of ID %.2fcm\\tSlumped bed height of %.2fcm\\tPacked bed distributor consisting of %.2f-%.2fmm rock'%(m*dt,m*sh,m*s[0],m*s[1])\n",
      "print 'Fluidizing gas: ambient air at %.2fatm'%P\n",
      "print 'Solids: \\tzirconia, Average particle size=%.2fmicrometers'%(m*dpbar)\n",
      "print 'Entering gas:\\tSuperficial velocity=%.2fcm/s'%u2\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For the model use\n",
        "\tBed of ID 30.45cm\tSlumped bed height of 49.92cm\tPacked bed distributor consisting of 0.33-0.67mm rock\n",
        "Fluidizing gas: ambient air at 1.00atm\n",
        "Solids: \tzirconia, Average particle size=17.64micrometers\n",
        "Entering gas:\tSuperficial velocity=8.08cm/s\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 4, Page 159\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "dtb=20;          #ID of bench-scale reactor\n",
      "dtp=1;           #ID of pilot reactor\n",
      "dpbar=52;        #Average particle size in micrometer\n",
      "ephsilonm=0.45;  #Void fraction for fixed bed\n",
      "ephsilonmf=0.50; #Void fraction at minimum fluidization condition\n",
      "ephsilonmb=0.60; #Void fraction \n",
      "uo=30;           #Superficial gas velocity in cm/s\n",
      "Lmb=2;           #Length of fixed bed in m\n",
      "umf=0.33;        #Velocity at minimum fluidization condition in cm/s\n",
      "umb=1;           #Velocity at in cm/s\n",
      "db=3;            #Equilibrium bubble size in cm\n",
      "g=9.80;          #Acceleration due to gravity in m/s**2\n",
      "pi=3.142857;\n",
      "\n",
      "#CALCULATION\n",
      "ubr=0.711*(g*db/100)**0.5;#Rise velocity of bubble using Eqn.(7)\n",
      "\n",
      "#Bubble velocity for the bench unit\n",
      "ubb1=1.55*(((uo-umf)/100.0)+14.1*((db/100.0)+0.005))*((dtb/100.0)**0.32)+ubr;#Bubble velocity using Eqn.(11)\n",
      "si=1;\n",
      "ubb2=si*((uo-umf)/100.0)+(3.2*((dtb/100.0)**(1/3.0)))*ubr;#Bubble velocity using Eqn.(9)\n",
      "ubb=(ubb1+ubb2)/2;#Average bubble velocity\n",
      "\n",
      "#Bubble velocity for the pilot unit\n",
      "ubp1=1.55*(((uo-umf)/100.0)+14.1*((db/100.0)+0.005))*(dtp**0.32)+ubr;#Bubble velocity using Eqn.(11)\n",
      "si=1;\n",
      "ubp2=si*((uo-umf)/100)+(3.2*(dtp**(1/3)))*ubr;#Bubble velocity using Eqn.(9)\n",
      "ubp=(ubp1+ubp2)/2;#Average bubble velocity\n",
      "\n",
      "#Rise velocity of upflowing emulsion\n",
      "ueb=ubb-ubr;#For the bench unit\n",
      "uep=ubp-ubr;#For the pilot unit\n",
      "\n",
      "#Scale-Up Alternative 1.\n",
      "dteb=20;#Effective bubble diameter\n",
      "dib=[5,10,15,20];#Different outside diameters\n",
      "n=len(dib);\n",
      "li = [0.,0.,0.,0.]\n",
      "i=0;\n",
      "while i<n:\n",
      "    li[i]=math.sqrt(((pi*dib[i]*dteb)/4)+((pi/4)*(dib[i])**2));#Pitch using Eqn.(13)\n",
      "    i=i+1;\n",
      "\n",
      "#Scale-Up Alternative 2.\n",
      "Lmp=Lmb*(ubp/ubb);#Static bed height of commercial unit\n",
      "dtep=100.0;#Effective bubble diameter\n",
      "dip=[10,15,20,25];#Different outside diameters\n",
      "m=len(dip);\n",
      "i=0;\n",
      "lip = [0.,0.,0.,0.]\n",
      "while i<m:\n",
      "    lip[i]=math.sqrt(((math.pi*dip[i]*dtep)/4.0)+(math.pi/4.0)*dip[i]);#Pitch using Eqn.(13)\n",
      "    i=i+1;\n",
      "\n",
      "#Height of Bubbling beds\n",
      "#For bench unit\n",
      "deltab=((uo/100.0)-(umb/100.0))/(ubb-(umb/100.0));#Fraction of bed in bubbles using Eqn.(28)\n",
      "ephsilonfb=deltab+(1-deltab)*ephsilonmb;#Void fraction of bubbling bed using Eqn.(20)\n",
      "Lfb=Lmb*(1-ephsilonm)/(1-ephsilonfb);#Hieght of bubbling bed usnig Eqn.(19)\n",
      "#For pilot unit\n",
      "deltap=((uo/100.0)-(umb/100.0))/(ubp-(umb/100.0));#Fraction of bed in bubbles using Eqn.(28)\n",
      "ephsilonfp=deltap+(1-deltap)*ephsilonmb;#Void fraction of bubbling bed using Eqn.(20)\n",
      "Lfp=Lmp*(1-ephsilonm)/(1-ephsilonfp);#Hieght of bubbling bed usnig Eqn.(19)\n",
      "\n",
      "#OUTPUT\n",
      "print 'Rise velocity of bubble=%.3fm/s'%ubr\n",
      "print 'For the bench unit'\n",
      "print '\\tWith Eqn.(11), Rise velocity=%.3fm/s'%ubb1\n",
      "print '\\tWith Werthers procedure, Rise velocity=%.2fm/s'%ubb2\n",
      "print '\\tAverage rise velocity=%.2fm/s'%ubb\n",
      "print '\\tRise velocity of upflowing emulsion=%.2fm/s'%ueb\n",
      "print 'For the pilot unit'\n",
      "print '\\tWith Eqn.(11), Rise velocity=%.2fm/s'%ubp1\n",
      "print '\\tWith Werthers procedure, Rise velocity=%.2fm/s'%ubp2\n",
      "print '\\tAverage rise velocity=%.2fm/s'%ubp\n",
      "print '\\tRise velocity of upflowing emulsion=%.2fm/s'%uep\n",
      "print 'Scale-Up Alternative 1.'\n",
      "print '\\tOuter diameter of tube(cm)'\n",
      "print '\\tPitch(cm)'\n",
      "n=len(dib);\n",
      "j=0;\n",
      "while j<n:\n",
      "    print '\\t\\t%d'%dib[j],\n",
      "    print '\\t\\t\\t%.2f'%li[j]\n",
      "    j=j+1;\n",
      "\n",
      "print '\\tSuitable arrangement'\n",
      "print '\\t\\tOuter Diameter=%dcm\\tPitch:Diameter ratio=%.2f'%(dib[1],(li[1]/dib[1]))\n",
      "print 'Scale-Up Alternative 2.'\n",
      "print '\\tStatic bed height for commercial unit=%fm'%Lmp\n",
      "print '\\tOuter diameter of tube(cm)'\n",
      "print '\\tPitch(cm)'\n",
      "n=len(dip);\n",
      "j=0;\n",
      "\n",
      "while j<n:\n",
      "    print '\\t\\t%d'%dip[j],\n",
      "    print '\\t\\t\\t%.2f'%lip[j]\n",
      "    j=j+1;\n",
      "\n",
      "print '\\tSuitable arrangement'\n",
      "print '\\t\\tOuter Diameter=%dcm\\tPitch:Diameter ratio=%.2f'%(dip[2],(lip[2]/dip[2]))\n",
      "print '\\t\\t\\t\\tFraction of bed in bubbles\\tVoid fraction of bed\\tStatic bed height(m)\\tHeight of bubbling bed(m)'\n",
      "print '\\t\\t\\t\\t---------------------------------------------------------------------------------------------------------'\n",
      "print 'Bench unit\\tID=%fm\\t%f\\t\\t\\t%f\\t\\t%f\\t\\t%f'%(dtb/100.,deltab,ephsilonfb,Lmb,Lfb)\n",
      "print 'Commercial unit\\tID=%fm\\t%f\\t\\t\\t%f\\t\\t%f\\t\\t%f'%(dtp,deltap,ephsilonfp,Lmp,Lfp)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rise velocity of bubble=0.386m/s\n",
        "For the bench unit\n",
        "\tWith Eqn.(11), Rise velocity=1.117m/s\n",
        "\tWith Werthers procedure, Rise velocity=1.02m/s\n",
        "\tAverage rise velocity=1.07m/s\n",
        "\tRise velocity of upflowing emulsion=0.68m/s\n",
        "For the pilot unit\n",
        "\tWith Eqn.(11), Rise velocity=1.61m/s\n",
        "\tWith Werthers procedure, Rise velocity=1.53m/s\n",
        "\tAverage rise velocity=1.57m/s\n",
        "\tRise velocity of upflowing emulsion=1.18m/s\n",
        "Scale-Up Alternative 1.\n",
        "\tOuter diameter of tube(cm)\n",
        "\tPitch(cm)\n",
        "\t\t5 \t\t\t9.91\n",
        "\t\t10 \t\t\t15.35\n",
        "\t\t15 \t\t\t20.31\n",
        "\t\t20 \t\t\t25.07\n",
        "\tSuitable arrangement\n",
        "\t\tOuter Diameter=10cm\tPitch:Diameter ratio=1.54\n",
        "Scale-Up Alternative 2.\n",
        "\tStatic bed height for commercial unit=2.941439m\n",
        "\tOuter diameter of tube(cm)\n",
        "\tPitch(cm)\n",
        "\t\t10 \t\t\t28.16\n",
        "\t\t15 \t\t\t34.49\n",
        "\t\t20 \t\t\t39.83\n",
        "\t\t25 \t\t\t44.53\n",
        "\tSuitable arrangement\n",
        "\t\tOuter Diameter=20cm\tPitch:Diameter ratio=1.99\n",
        "\t\t\t\tFraction of bed in bubbles\tVoid fraction of bed\tStatic bed height(m)\tHeight of bubbling bed(m)\n",
        "\t\t\t\t---------------------------------------------------------------------------------------------------------\n",
        "Bench unit\tID=0.200000m\t0.274171\t\t\t0.709668\t\t2.000000\t\t3.788769\n",
        "Commercial unit\tID=1.000000m\t0.185857\t\t\t0.674343\t\t2.941439\t\t4.967774\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5, Page 161\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "dtb=20;          #ID of bench-scale reactor\n",
      "dtp=1;           #ID of pilot reactor\n",
      "dpbar=200;       #Average particle size in micrometer\n",
      "ephsilonmf=0.50; #Void fraction at minimum fluidization condition\n",
      "ephsilonmb=0.50; #Void fraction \n",
      "uo=30;           #Superficial gas velocity in cm/s\n",
      "Lmb=2;           #Length of fixed bed in m\n",
      "umf=3;           #Velocity at minimum fluidization condition in cm/s\n",
      "umb=3;           #Velocity at in cm/s\n",
      "g=9.80;          #Acceleration due to gravity in m/s**2\n",
      "pi=3.142857;\n",
      "\n",
      "#CALCULATION\n",
      "#In the small bench unit\n",
      "c=1;\n",
      "ubb=c*((uo-umf)/100.0)+0.35*(g*(dtb/100.0))**0.5;#Velocity using Eqn.(5.22)\n",
      "zsb=60*(dtb)**0.175;#Height using Eqn.(5.24)\n",
      "\n",
      "#In the large pilot unit\n",
      "ubp=c*((uo-umf)/100.0)+0.35*(g*dtp)**0.5;#Velocity using Eqn.(5.22)\n",
      "zsp=60*(dtp*100)**0.175;#Height using Eqn.(5.24)\n",
      "\n",
      "#OUTPUT\n",
      "print 'Condition at which bubbles transform into slugs'\n",
      "print 'For tha small bench unit\\t\\tVelocity=%fm/s\\t\\tHeight above distributor plate=%fm'%(ubb,zsb/100.)\n",
      "print 'For tha large pilot unit\\t\\tVelocity=%fm/s\\t\\tHeight above distributor plate=%fm'%(ubp,zsp/100.);\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Condition at which bubbles transform into slugs\n",
        "For tha small bench unit\t\tVelocity=0.760000m/s\t\tHeight above distributor plate=1.013518m\n",
        "For tha large pilot unit\t\tVelocity=1.365673m/s\t\tHeight above distributor plate=1.343233m\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}