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diff --git a/Fluidization_Engineering/ch6.ipynb b/Fluidization_Engineering/ch6.ipynb new file mode 100644 index 00000000..39b1fc56 --- /dev/null +++ b/Fluidization_Engineering/ch6.ipynb @@ -0,0 +1,504 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "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": [ + "#Bubble Size and Rise Velocity in Geldart A Beds\n", + "\n", + "#Variable declaration\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": [ + "#Bubble Size and Rise Velocity in Geldart B Beds\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": [ + "#Scale-down of a Commercial Chlorinator\n", + "\n", + "#Variable declaration\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": [ + "#Reactor Scale-up for Geldart A Catalyst\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": [ + "#Reactor Scale-up for Geldart B Catalyst\n", + "\n", + "#Variable declaration\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": {} + } + ] +}
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