diff options
Diffstat (limited to 'Fluidization_Engineering/ch12.ipynb')
| -rw-r--r-- | Fluidization_Engineering/ch12.ipynb | 397 |
1 files changed, 397 insertions, 0 deletions
diff --git a/Fluidization_Engineering/ch12.ipynb b/Fluidization_Engineering/ch12.ipynb new file mode 100644 index 00000000..d49e64ff --- /dev/null +++ b/Fluidization_Engineering/ch12.ipynb @@ -0,0 +1,397 @@ +{ + "metadata": { + "name": "ch12" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12 : Conversion of Gas in Catalytic Reactions" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 1, Page 293\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fine Particle (Geldart A) Bubbling Bed Reactor\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Kr=10.; #rate constant in m**3 gas/m**3 cat s\n", + "D=2E-5; #Diffusion coefficient of gas in m**2/s\n", + "dpbar=68.; #Average partilce size in micrometers\n", + "ephsilonm=0.5; #Void fraction of fixed bed\n", + "gammab=0.005; #Ratio of volume of dispersed solids to that of bubble phase\n", + "ephsilonmf=0.55; #Void fraction at minimum fluidization condition\n", + "umf=0.006; #Velocity at minimum fluidization condition in m/s\n", + "db=0.04; #Equilibrium bubble size in m\n", + "Lm=0.7; #Length of the bed in m\n", + "uo=0.1; #Superficial gas velocity in m/s\n", + "dbed=0.26; #Diameter of the bed in m\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "#CALCULATION\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of bubble from Eqn.(6.7)\n", + "ub=uo-umf+ubr;#Velocity of bubbles in bubbling beds in Eqn.(6.8)\n", + "Kbc=4.5*(umf/db)+5.85*((D**0.5*g**0.25)/db**(5./4));#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", + "Kce=6.77*((D*ephsilonmf*0.711*(g*db)**0.5)/db**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(10.34)\n", + "delta=uo/ub;#Fraction of bed in bubbles from Eqn.(6.29)\n", + "fw=0.6;#Wake volume to bubble volume from Fig.(5.8)\n", + "gammac=(1-ephsilonmf)*((3/(ubr*ephsilonmf/umf-1))+fw);#Volume of solids in cloud to that of the bubble from Eqn.(6.36)\n", + "gammae=((1-ephsilonmf)*((1-delta)/delta))-gammab-gammac;#Volume of solids in emulsion to that of the bubble from Eqn.(6.35)\n", + "ephsilonf=1-(1-delta)*(1-ephsilonmf);#Void fraction of fixed bed from Eqn.(6.20)\n", + "Lf=(1-ephsilonm)*Lm/(1-ephsilonf);#Length of fixed bed from Eqn.(6.19)\n", + "Krtou=Kr*Lm*(1-ephsilonm)/uo;#Dimensionless reaction rate group from Eqn.(5)\n", + "Kf=gammab*Kr+1/((1/Kbc)+(1/(gammac*Kr+1/((1/Kce)+(1/(gammae*Kr))))));#Raction rate for fluidized bed from Eqn.(14)\n", + "XA=math.exp(-1*Kf*Lf/ub);#Conversion from Eqn.(16)\n", + "\n", + "#OUTPUT\n", + "print 'The dimnesionless reaction rate group: %f'%Krtou\n", + "print 'The reaction rate for fluidized bed: %fs**-1'%Kf\n", + "print 'Conversion: %f'%XA\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dimnesionless reaction rate group: 35.000000\n", + "The reaction rate for fluidized bed: 1.979872s**-1\n", + "Conversion: 0.030056\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 2, Page 298\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Commercial-Sized Phthalic Anhydride Reactor\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "umf=0.005; #Velocity at minimum fluidization condition in m/s\n", + "ephsilonm=0.52; #Void fraction of fixed bed\n", + "ephsilonmf=0.57; #Void fraction at minimum fluidization condition\n", + "DA=8.1E-6; #Diffusion coefficient of gas in m**2/s\n", + "DR=8.4E-6; #Diffusion coefficient of gas in m**2/s\n", + "Lm=5; #Length of the bed in m\n", + "dte=1; #Diameter of tube in m\n", + "Kr1=1.5; #rate constant in m**3 gas/m**3 cat s\n", + "Kr3=0.01; #rate constant in m**3 gas/m**3 cat s\n", + "gammab=0.005; #Ratio of volume of dispersed solids to that of bubble phase\n", + "uo=0.45; #Superficial gas velocity in m/s\n", + "db=0.05; #Equilibrium bubble size in m from Fig.(6.8)\n", + "ub=1.5; #Velocity of bubbles in bubbling bed in m/s from Fig.(6.11(a))\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "#CALCULATION\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of bubble from Eqn.(6.7)\n", + "KbcA=4.5*(umf/db)+5.85*((DA**0.5*g**0.25)/db**(5.0/4));#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", + "KceA=6.77*((DA*ephsilonmf*0.711*(g*db)**0.5)/db**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(10.34)\n", + "KbcR=4.5*(umf/db)+5.85*((DR**0.5*g**0.25)/db**(5./4));#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", + "KceR=6.77*((DR*ephsilonmf*0.711*(g*db)**0.5)/db**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(10.34)\n", + "delta=uo/ub;#Fraction of bed in bubbles from Eqn.(6.29)\n", + "fw=0.6;#Wake volume to bubble volume from Fig.(5.8)\n", + "gammac=(1-ephsilonmf)*((3/(ubr*ephsilonmf/umf-1))+fw);#Volume of solids in cloud to that of the bubble from Eqn.(6.36)\n", + "gammae=((1-ephsilonmf)*((1-delta)/delta))-gammab-gammac;#Volume of solids in emulsion to that of the bubble from Eqn.(6.35)\n", + "ephsilonf=1-(1-delta)*(1-ephsilonmf);#Void fraction of fixed bed from Eqn.(6.20)\n", + "Lf=(1-ephsilonm)*Lm/(1-ephsilonf);#Length of fixed bed from Eqn.(6.19)\n", + "Krtou=Kr1*Lm*(1-ephsilonm)/uo;#Dimensionless reaction rate group from Eqn.(5)\n", + "Kr12=Kr1;#Since the reactions are a special case of Denbigh scheme\n", + "Kr34=Kr3;\n", + "Kf1=(gammab*Kr12+1/((1/KbcA)+(1/(gammac*Kr12+1/((1/KceA)+(1/(gammae*Kr12)))))))*(delta/(1-ephsilonf));#Rate of reaction 1 for fluidized bed from Eqn.(14)\n", + "Kf3=(gammab*Kr34+1/((1/KbcR)+(1/(gammac*Kr34+1/((1/KceR)+(1/(gammae*Kr34)))))))*(delta/(1-ephsilonf));#Rate of reaction 2 for fluidized bed from Eqn.(14)\n", + "Kf12=Kf1;\n", + "Kf34=Kf3;\n", + "KfA=((KbcR*KceA/gammac**2+(Kr12+KceA/gammac+KceA/gammae)* \\\n", + " (Kr34+KceR/gammac+KceR/gammae))*delta*KbcA*Kr12*Kr34/ \\\n", + " (1-ephsilonf))/(((Kr12+KbcA/gammac)*(Kr12+KceA/gammae)+Kr12*KceA/gammac) \\\n", + " *((Kr34+KbcR/gammac)*(Kr34+KceR/gammae)+Kr34*KceR/gammac));\n", + " #Rate of raection with respect to A from Eqn.(35)\n", + "KfAR=Kr1/Kr12*Kf12-KfA;#Rate of reaction from Eqn.(34)\n", + "tou=Lf*(1-ephsilonf)/uo;#Residence time from Eqn.(5)\n", + "XA=1-math.exp(-Kf1*tou);#Conversion of A from Eqn.(26)\n", + "XR=1-((KfAR/(Kf12-Kf34))*(math.exp(-Kf34*tou)-math.exp(-Kf12*tou)));#Conversion of R from Eqn.(27)\n", + "SR=(1-XR)/XA;#Selectivity of R\n", + "\n", + "#OUTPUT\n", + "\n", + "print 'Rate of reaction 1 for fluidized bed:%.4f'%Kf1\n", + "print 'Rate of reaction 2 for fluidized bed:%.4f'%Kf3\n", + "print 'Rate of reaction 1 with respect to A:%.4f'%KfA\n", + "print 'The Conversion of Napthalene:%.0f percentage'%(XA*100);\n", + "print 'The selectivity of Phthalic anhydride:%.0f percentage'%(SR*100);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rate of reaction 1 for fluidized bed:0.6007\n", + "Rate of reaction 2 for fluidized bed:0.0099\n", + "Rate of reaction 1 with respect to A:0.0058\n", + "The Conversion of Napthalene:96 percentage\n", + "The selectivity of Phthalic anhydride:95 percentage\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3, Page 302\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Bubbling Bed Reactor for Intermediate Sized Reactor\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Kr=3.; #rate constant in m**3 gas/m**3 cat s\n", + "db=0.12; #Equilibrium bubble size in m\n", + "D=9E-5; #Diffusion coefficient of gas in m**2/s\n", + "dpbar=68; #Average partilce size in micrometers\n", + "ephsilonm=0.42; #Void fraction of fixed bed\n", + "uo=0.4; #Superficial gas velocity in m/s\n", + "Lm=0.8; #Length of the bed in m\n", + "ephsilonmf=0.45; #Void fraction at minimum fluidization condition\n", + "umf=0.21; #Velocity at minimum fluidization condition in m/s\n", + "gammab=0; #Ratio of volume of dispersed solids to that of bubble phase\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "#CALCULATION\n", + "ubr=0.711*(g*db)**0.5; #Rise velocity of bubble from Eqn.(6.7)\n", + "ub=uo-umf+ubr; #Velocity of bubbles in bubbling beds in Eqn.(6.8)\n", + "ubstar=ub+3*umf; #Rise velocity of the bubble gas from Eqn.(45)\n", + "delta=(uo-umf)/(ub+umf);#Fraction of bed in bubbles from Eqn.(6.46)\n", + "Kbe=4.5*(umf/db); #Interchange coefficient between bubble and emulsion from Eqn.(47)\n", + "Lf=Lm*(1-ephsilonm)/((1-delta)*(1-ephsilonmf));#Length of fixed bed\n", + "phi=((Kr/Kbe)**2*((1-ephsilonmf)-gammab*(umf/ubstar))**2+ \\\n", + " ((delta/(1-delta))+umf/ubstar)**2+2*(Kr/Kbe)*((1-ephsilonmf) \\\n", + " -gammab*(umf/ubstar))*((delta/(1-delta))-umf/ubstar))**0.5;\n", + " #From Eqn.(52)\n", + " \n", + "q1=0.5*Kr/umf*((1-ephsilonmf)+gammab*(umf/ubstar))+0.5*Kbe/umf* \\\n", + " (((delta/(1-delta))+umf/ubstar)-phi);#From Eqn.(50)\n", + "q2=0.5*Kr/umf*((1-ephsilonmf)+gammab*(umf/ubstar))+0.5*Kbe/umf* \\\n", + " (((delta/(1-delta))+umf/ubstar)+phi);#From Eqn.(50)\n", + " \n", + "si1=0.5-0.5*((1-delta)/delta)*(umf/ubstar-Kr/Kbe*((1-ephsilonmf)- \\\n", + " gammab*(umf/ubstar))-phi);#From Eqn.(51)\n", + "si2=0.5-0.5*((1-delta)/delta)*(umf/ubstar-Kr/Kbe*((1-ephsilonmf)- \\\n", + " gammab*(umf/ubstar))+phi);#From Eqn.(51)\n", + "XA=1-(delta/(1-delta))*(1/(uo*phi))*((1-si2)*(si1*delta*ubstar+ \\\n", + " (1-delta)*umf)*math.exp(-q1*Lf)+(si1-1)* \\\n", + " (si2*delta*ubstar+(1-delta)*umf)*math.exp(-q2*Lf));\n", + " #Conversion from Eqn.(49)\n", + " \n", + "Krtou=Kr*Lm*(1-ephsilonm)/uo;#Dimensionless reaction rate group from Eqn.(5)\n", + "\n", + "#OUTPUT\n", + "print 'COmparing the values of 1-XA = %f and Krtou = %f with Fig.(6), \\\n", + "we can conlcude that this operating condition is shown as point \\\n", + "A in Fig.(3)'%(1-XA,Krtou);\n", + "print 'Line 2 gives the locus of conversions for different values of the \\\n", + "reaction rate group for this fluidized contacting'\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "COmparing the values of 1-XA = 0.113843 and Krtou = 3.480000 with Fig.(6), we can conlcude that this operating condition is shown as point A in Fig.(3)\n", + "Line 2 gives the locus of conversions for different values of the reaction rate group for this fluidized contacting\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4, Page 305\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Reaction in the Slow Bubble Regime\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "uo=0.25; #Superficial gas velocity in m/s\n", + "db=0.025; #Equilibrium bubble size in m\n", + "Kr=1.5; #rate constant in m**3 gas/m**3 cat s\n", + "umf=0.21; #Velocity at minimum fluidization condition in m/s\n", + "Lm=0.8; #Length of the bed in m\n", + "ephsilonm=0.42; #Void fraction of fixed bed\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "#CALCULATION\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of bubble from Eqn.(6.7)\n", + "ub=uo-umf+ubr;#Velocity of bubbles in bubbling beds in Eqn.(6.8)\n", + "delta=(uo-umf)/(ub+2*umf);#Fraction of bed in bubbles from Eqn.(55) since ub/umf<<1 \n", + "XA=1-math.exp(-Kr*Lm*((1-ephsilonm)/uo)*(umf/uo)*(1-delta));#Conversion from Eqn.(57)\n", + "Krtou=Kr*Lm*(1-ephsilonm)/uo;#Dimensionless reaction rate group from Eqn.(5)\n", + "\n", + "\n", + "#OUTPUT\n", + "print 'Comparing the values of 1-XA = %f and Krtou = %f with Fig.(6), \\\n", + "we can conlcude that this operating condition is shown \\\n", + "as point B in Fig.(3)'%(1-XA,Krtou);\n", + "print 'Line 3 gives the locus of conversions for different values \\\n", + "of the reaction rate group for this fluidized contacting'\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Comparing the values of 1-XA = 0.108243 and Krtou = 2.784000 with Fig.(6), we can conlcude that this operating condition is shown as point B in Fig.(3)\n", + "Line 3 gives the locus of conversions for different values of the reaction rate group for this fluidized contacting\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5, Page 307\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Conversion in the Freeboard of a Reactor\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "uo=0.3; #Superficial gas velocity in m/s\n", + "Lf=1.1; #Length of fixed bed in m\n", + "Hf=1.2; #Length of freeboard in m\n", + "db=0.04; #Equilibrium bubble size in m\n", + "umf=0.006; #Velocity at minimum fluidization condition in m/s\n", + "ephsilonmf=0.55; #Void fraction at minimum fluidization condition\n", + "gammab=0.005; #Ratio of volume of dispersed solids to that of bubble phase\n", + "Kr=10.; #rate constant in m**3 gas/m**3 cat s\n", + "D=2E-5; #Diffusion coefficient of gas in m**2/s\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "#CALCULATION\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of bubble from Eqn.(6.7)\n", + "ub=uo-umf+ubr;#Velocity of bubbles in bubbling beds in Eqn.(6.8)\n", + "Kbc=4.5*(umf/db)+5.85*((D**0.5*g**0.25)/db**(5./4));\n", + "#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", + "\n", + "Kce=6.77*((D*ephsilonmf*0.711*(g*db)**0.5)/db**3)**0.5;\n", + "#Gas interchange coefficient between emulsion and cloud from Eqn.(10.34)\n", + "\n", + "delta=uo/ub;#Fraction of bed in bubbles from Eqn.(6.29)\n", + "ephsilonf=1-(1-delta)*(1-ephsilonmf);#Void fraction of fixed bed from Eqn.(6.20)\n", + "fw=0.6;#Wake volume to bubble volume from Fig.(5.8)\n", + "gammac=(1-ephsilonmf)*((3.0/(ubr*ephsilonmf/umf-1))+fw);\n", + "#Volume of solids in cloud to that of the bubble from Eqn.(6.36)\n", + "\n", + "gammae=((1-ephsilonmf)*((1-delta)/delta))-gammab-gammac;\n", + "#Volume of solids in emulsion to that of the bubble from Eqn.(6.35)\n", + "\n", + "Kf=(gammab*Kr)+1.0/((1.0/Kbc)+(1.0/(gammac*Kr+1.0/((1.0/Kce)+(1.0/(gammae*Kr))))));\n", + "#Raction rate for fluidized bed from Eqn.(14)\n", + "\n", + "XA=1-math.exp(-1*Kf*Lf/ub);#Conversion at the top of dense bed from Eqn.(16)\n", + "etabed=(Kf*delta)/(Kr*(1-ephsilonf));#Reactor efficiency from Eqn.(22)\n", + "a=0.6/uo #Since uoa = 0.6s**-1 from Fig.(5)\n", + "adash=6.62; #From Fig.(5)\n", + "XA1=1-1.0/(math.exp(((1-ephsilonf)*Kr/(uo*a))*((1-math.exp(-a*Hf))- \\\n", + " ((1-etabed)/(1+(adash/a)))*(1-math.exp(-(a+adash)*Hf)))));#Conversion from Eqn.(64)\n", + "XA2=1-(1.0-XA1)*(1.0-XA);#Conversion at the exit from Eqn.(64)\n", + "\n", + "#OUTPUT\n", + "print 'The conversion:'\n", + "print '\\tAt the top pf the dense bed: %d percentage'%(XA1*100)\n", + "print '\\tAt the reactor exit: %d percentage'%(XA2*100);\n", + "\n", + "#Disclaimer: The value of kf deviate from the one given in textbook, where as it is close to the value obtained by manual calculation. \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The conversion:\n", + "\tAt the top pf the dense bed: 96 percentage\n", + "\tAt the reactor exit: 99 percentage\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |