PK1„IU¼Lå+å+"Fluidization Engineering/ch3.ipynb{
"metadata": {
"name": "",
"signature": "sha256:c2d23a740208e3823c43d8afcfc0ef305894f28fcd5f9e9793f1f1c6fe8b25f1"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3 : Fluidization and Mapping of Regimes"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, Page 68\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"weight = [0,60,150,270,330,360.0]; # Weight in grams for the oversized particles\n",
"psize = [50,75,100,125,150,175]; #PSD in micrometers\n",
"\n",
"#CALCULATION\n",
"l = len(psize); # To obtain the size of input array\n",
"# Computation of sauter mean diameter for the given PSD\n",
"i = 0;\n",
"dpi = [0,0,0,0,0,0]\n",
"weightf = [0,0,0,0,0,0]\n",
"dp = [0,0,0,0,0,0]\n",
"while i=3000:\n",
" Cd=0.60;\n",
"elif Ret>=2000:\n",
" Cd=0.61;\n",
"elif Ret>=1000:\n",
" Cd=0.64;\n",
"elif Ret>=500:\n",
" Cd=0.68;\n",
"elif Ret>=300:\n",
" Cd=0.70;\n",
"elif Ret>=100:\n",
" Cd=0.68;\n",
"\n",
"#Computation of gas velocity through orifice\n",
"uor=Cd*((2*deltapd)/rhog)**0.5; #Calculation of gas velocity through orifice by using Eqn.(12)\n",
"f=(uo/uor)*100; #Calculation of fraction of open area in the perforated plate \n",
"\n",
"\n",
"#Computation of number of orifices per unit area of distributor\n",
"dor=[0.001,0.002,0.004]; #Different orifice diameters in m\n",
"n=len(dor);\n",
"i=0;\n",
"Nor = [0.,0.,0.]\n",
"while iuf:\n",
" Dshc.append((3/16.0)*(delta[k]/(1-delta[k]))*((alpha**2*db[j]*ubr[k]*((((ubr[k]+2*uf)/(ubr[k]-uf))**(1.0/3))-1))));\n",
" #Horizontal Distribution coeff. from Eqn.(14)\n",
" else:\n",
" Dsh.append((3.0/16)*(delta/(1-delta))*(alpha**2*umf*db/ephsilonmf))\n",
" #Horizontal Distribution coeff. from Eqn.(15)\n",
" Dshc.append((3/16.0)*(delta[k]/(1-delta[k]))*((alpha**2*db[j]*ubr[k]*((((ubr[k]+2*uf)/(ubr[k]-uf))**(1/3.0))-1))));#Horizontal Distribution coeff. from Eqn.(14)\n",
" k=k+1;\n",
"i=0;\n",
"j=0;\n",
"k=0;\n",
"while k>uf=%fm/s we use Eqn.(14).'%(ub[k],uf)\n",
" print 'Gas Velocity(m/s)'\n",
" print '\\tHorizontal Drift Coefficient Calculated(m**2/s)'\n",
" print '\\tHorizontal Drift Coefficient from Experiment(m**2/s)'\n",
" while j>uf=0.404762m/s we use Eqn.(14).\n",
"Gas Velocity(m/s)\n",
"\tHorizontal Drift Coefficient Calculated(m**2/s)\n",
"\tHorizontal Drift Coefficient from Experiment(m**2/s)\n",
"db=0.100000m\n",
"0.370000 \t\t0.001283 \t\t\t\t\t0.001200\n",
"0.470000 \t\t0.001283 \t\t\t\t\t0.001800\n",
"0.570000 \t\t0.001924 \t\t\t\t\t0.002100\n",
"0.670000 \t\t0.001924 \t\t\t\t\t0.002500\n",
"db=0.140000m\n",
"0.370000 \t\t0.002566 \t\t\t\t\t0.001200\n",
"0.470000 \t\t0.002566 \t\t\t\t\t0.001800\n",
"0.570000 \t\t0.003207 \t\t\t\t\t0.002100\n",
"0.670000 \t\t0.003207 \t\t\t\t\t0.002500\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3, Page 232\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Gsup=1.5; #Solid interchange rate in kg/m**2plate s\n",
"dor=19.1; #Orifice diameter in mm\n",
"dp=210; #Particle size in micrometer\n",
"uo=0.4; #Superficial gas velocity in m/s\n",
"fopen=[0.12,0.17,0.26]; #Open area fraction \n",
"pi=3.14;\n",
"\n",
"#CALCULATION\n",
"n=len(fopen);\n",
"uor = []\n",
"ls1 = []\n",
"i=0\n",
"while i"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2, Page 267"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"#INPUT\n",
"umf=0.12 #Velocity at minimum fluidization condition in cm/s\n",
"uo=40.; #Superficial gas velocity in cm/s\n",
"ub=120; #Velocity of the bubble in cm/s\n",
"D=0.7; #Diffusion coefficient of gas in cm**2/s\n",
"abkbe1=1.; #Bubble-emuslion interchange coefficient for non absorbing particles(m=0)\n",
"abkbe2=18.; #Bubble-emuslion interchange coefficient for highly absorbing particles(m=infinity)\n",
"g=980.; #Acceleration due to gravity in square cm/s**2\n",
"\n",
"#CALCULATION\n",
"#For non absorbing particles m=0,etad=0\n",
"Kbc=(ub/uo)*(abkbe1);\n",
"dbguess=2;#Guess value of db\n",
"def solver_func(db): #Function defined for solving the system\n",
" return abkbe1-(uo/ub)*(4.5*(umf/db)+5.85*(D**0.5*g**0.25)/(db**(5/4.)));#Eqn.(10.27)\n",
"\n",
"d=fsolve(solver_func,dbguess)\n",
"#For highly absorbing particles m=infinity, etad=1\n",
"M=abkbe2-(uo/ub)*Kbc;\n",
"#For intermediate condition\n",
"alpha=100.;\n",
"m=10.;\n",
"etad=1./(1+(alpha/m));#Fitted adsorption efficiency factor from Eqn.(23)\n",
"abkbe3=M*etad+(uo/ub)*Kbc;\n",
"\n",
"#OUTPUT\n",
"print 'For non absorbing particles:\\tDiameter of bubble=%fcm\\tBubble-cloud interchange coefficient=%fs**-1'%(d,Kbc);\n",
"print 'For highly absorbing partilces:\\tM=%f'%(M);\n",
"print 'For intermediate condition:\\tFitted adsorption efficiency factor:%f\\tBubble-emuslion interchange coefficient:%fs**-1'%(etad,abkbe3);\n",
"\n",
"#====================================END OF PROGRAM ======================================================"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For non absorbing particles:\tDiameter of bubble=6.010032cm\tBubble-cloud interchange coefficient=3.000000s**-1\n",
"For highly absorbing partilces:\tM=17.000000\n",
"For intermediate condition:\tFitted adsorption efficiency factor:0.090909\tBubble-emuslion interchange coefficient:2.545455s**-1\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3, Page 273\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"rhos=1.3; #Density of solids in g/cc\n",
"phis=0.806; #Sphericity of solids\n",
"gammab=0.001; #Ratio of volume of dispersed solids to that of bubble phase\n",
"rhog=1.18E-3; #Density of air in g/cc\n",
"Pr=0.69; #Prandtl number\n",
"myu=1.8E-4; #Viscosity of gas in g/cm s\n",
"Cpg=1.00; #Specific heat capacity of gas in J/g K\n",
"ephsilonmf=0.45; #Void fraction at minimum fluidization condition\n",
"kg=2.61E-4; #Thermal concuctivity of gas in W/cm k\n",
"dp=0.036; #Particle size in cm\n",
"umf=6.5; #Velocity at minimum fluidization condition in cm/s\n",
"ut=150.; #Terminal velocity in cm/s\n",
"db=0.4; #Equilibrium bubble size in cm\n",
"etah=1; #Efficiency of heat transfer\n",
"uo=[10.,20.,30.,40.,50.];#Superficial gas velocity in cm/s\n",
"g=980.; #Acceleration due to gravity in square cm/s**2\n",
"\n",
"#CALCULATION\n",
"Nustar=2+(((dp*ut*rhog)/myu)**0.5*Pr**(1./3));#Nusselt no. from Eqn.(25)\n",
"Hbc=4.5*(umf*rhog*Cpg/db)+5.85*((kg*rhog*Cpg)**0.5*g**0.25/db**(5./4));#Total heat interchange across the bubble-cloud boundary from Eqn.(32)\n",
"ubr=0.711*(g*db)**0.5;#Rise velocity of the bubble from Eqn.(6.7)\n",
"n=len(uo);\n",
"i=0;\n",
"x = [0,0,0,0,0]\n",
"Nubed = [0,0,0,0,0]\n",
"Rep = [0,0,0,0,0]\n",
"\n",
"while i"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 4, Page 274\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"rhog=1.2; #Density of air in kg/m**3\n",
"myu=1.8E-5; #Viscosity of gas in kg/m s\n",
"kg=2.6E-2; #Thermal concuctivity of gas in W/m k\n",
"dp=1E-4; #Particle size in m\n",
"rhos=8920; #Density of solids in kg/m**3\n",
"Cps=390; #Specific heat capacity of the solid in J/kg K\n",
"ephsilonf=0.5; #Void fraction of the fluidized bed\n",
"umf=0.1; #Velocity at minimum fluidization condition in m/s\n",
"uo=0.1; #Superficial gas velocity in m/s\n",
"pi=3.14\n",
"\n",
"#CALCULATION\n",
"to=0; #Initial temperature of the bed\n",
"T=100; #Temperature of the bed\n",
"t=0.99*T; #Particle temperature i.e. when it approaches 1% of the bed temperature\n",
"mp=(pi/6)*dp**3*rhos; #Mass of the particle\n",
"A=pi*dp**2; #Surface area of the particle\n",
"Rep=(dp*uo*rhog)/myu; #Reynold's no. of the particle\n",
"Nubed=0.0178; #Nusselt no. from Fig.(6)\n",
"hbed1=(Nubed*kg)/dp; #Heat transfer coefficient of the bed\n",
"t1=(mp*Cps/(hbed1*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(a)\n",
"hbed2=140*hbed1;#Since from Fig.(6) Nup is 140 times Nubed\n",
"t2=(mp*Cps/(hbed2*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(b)\n",
"\n",
"#OUTPUT\n",
"print 'Case(a):Using the whole bed coefficient from Fig.(6)'\n",
"print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.0fs'%t1\n",
"print 'Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)'\n",
"print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.2fs'%t2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a):Using the whole bed coefficient from Fig.(6)\n",
"\tTime needed for the particle approach 1 percentage of the bed temperature is 58s\n",
"Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)\n",
"\tTime needed for the particle approach 1 percentage of the bed temperature is 0.41s\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}PK1„IMÂC¤hDhD#Fluidization Engineering/ch12.ipynb{
"metadata": {
"name": "",
"signature": "sha256:3cabb972e9b40cc3c2621280c95233b4046eb8d671e52d74d499a7e149a3d9aa"
},
"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": [
"\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": [
"\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": [
"\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": [
"\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": [
"\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": {}
}
]
}PK1„INÌ¹Ã×(×(#Fluidization Engineering/ch13.ipynb{
"metadata": {
"name": "",
"signature": "sha256:a97460b196d7b42e945dcfefc11684cc1c39c5847f8b0bdc9e3f6cdcd94bfcc3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Chapter 13 : Heat Transfer between Fluidized Beds and Surfaces"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1, Page 331\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"dp=57.0; #Particle size in micrometer\n",
"rhos=940.0; #Density of solids in kg/m**3\n",
"Cps=828.0; #Specific heat capacity of the solid in J/kg K\n",
"ks=0.20; #Thermal conductivity of solids in W/m k\n",
"kg=0.035; #Thermal concuctivity of gas in W/m k\n",
"umf=0.006; #Velocity at minimum fluidization condition in m/s\n",
"ephsilonmf=0.476;#Void fraction at minimum fluidization condition\n",
"do1=0.0254; #Outside diameter of tube in m\n",
"L=1;\n",
"uo=[0.05,0.1,0.2,0.35];#Superficial gas velocity in m/s\n",
"nw=[2.,3.1,3.4,3.5]; #Bubble frequency in s**-1\n",
"g=9.81; #Acceleration due to gravity in square m/s**2\n",
"\n",
"\n",
"#CALCULATION\n",
"dte=4.*do1*L/2.*L; #Hydraulic diameter from Eqn.(6.13)\n",
"db=(1+1.5)*0.5*dte; #Rise velocity of the bubble\n",
"ubr=0.711*(g*db)**0.5; #Rise velocity of bubble from Eqn.(6.7)\n",
"phib=0.19;#From Fig.(15) for ks/kg=5.7\n",
"ke=ephsilonmf*kg+(1-ephsilonmf)*ks*(1/((phib*(ks/kg))+(2/3.0)))\n",
" #Effective thermal conductivity of bed from Eqn.(3) \n",
" \n",
"n=len(uo);\n",
"i=0;\n",
"ub = [0,0,0,0]\n",
"delta = [0,0,0,0]\n",
"h = [0,0,0,0]\n",
"while ix2min:\n",
" excess_air[i]=(x2[i]-x2min)/x2min; #Excess air used\n",
" else:\n",
" excess_air[i]=0;\n",
" i=i+1;\n",
"\n",
"#OUTPUT \n",
"print 'T4(degree celcius)',\n",
"print '\\tFs/F1',\n",
"print '\\t\\tF2/F1',\n",
"print '\\t\\tExcess air(percentage)'\n",
"i=0;\n",
"while idte:\n",
" li=(pi/4*dte*do1+pi/4*do1**2)**0.5;#Pitch if we add dummy tubes\n",
"import math\n",
"f=li**2-pi/4*do1**2;#Fraction of bed cross section taken up by tubes\n",
"dt1=math.sqrt(4/pi*At/(1-f));#Reactor diameter including all its tubes\n",
"\n",
"#OUTPUT\n",
"print 'Superficial gas velocity=%fm/s'%uo\n",
"print 'No. of %1.0fm tubes required=%1.0f'%(L,Nt);\n",
"print 'Reactor diameter=%fm'%dt1\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Superficial gas velocity=0.460000m/s\n",
"No. of 7m tubes required=295\n",
"Reactor diameter=7.173176m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, Page 444\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"db=0.08; #Estimated bubble size in m\n",
"dte=2; #Equivalent diameter in m\n",
"F1=55.6; #Feed rate of oil in kg/s\n",
"XA=0.63; #Conversion\n",
"uo=0.6; #Superficial gas velocity in m/s\n",
"T1=500.0; #Temperature of reactor in degree C\n",
"T2=580.0; #Temperature of regenerator in degree C\n",
"Fs=F1*23.3; #Solid circulation rate from Ex.(15.2)\n",
"rhos=1200.0; #Density of catalyst in kg/m**3\n",
"dpbar=60.0; #Average particle size in micrometer\n",
"ephsilonm=0.50;#Void fraction of fixed bed\n",
"ephsilonmf=0.55;#Void fraction at minimum fluidized condition\n",
"umf=0.006; #Velocity at minimum fluidization condition in m/s\n",
"dt=8.0; #Diameter of reactor in m\n",
"D=2E-5; #Diffusion coefficient of gas in m**2/s\n",
"Kr=8.6; #Rate constant for reaction at 500 degree C in s**-1\n",
"Ka1=0.06; #Rate constant for deactivatiion at 500 degree C in s**-1\n",
"Ka2=0.012; #Rate constant for regeneration at 580 degree C in s**-1\n",
"gammab=0.005; #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",
"pi=3.14;\n",
"\n",
"#CALCULATION\n",
"#Parameters for the fluidized reactor\n",
"ubr=0.711*(g*db)**0.5;#Rise velocity of bubble from Eqn.(6.7)\n",
"ub=1.55*((uo-umf)+14.1*(db+0.005))*dte**0.32+ubr;#Bubble velocity for Geldart A particles from Equation from Eqn.(6.11)\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/(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",
"Kbc=4.5*(umf/db)+5.85*((D**0.5*g**0.25)/db**(5.0/4));#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",
"import math\n",
"#Bed height versus catalyst activity in reactor\n",
"a1bar=0.07;#Guess value for average activity in reactor\n",
"x=Kr*a1bar;#Value of Kra1 to be used in the following equation\n",
"Kf=(gammab*x+1/((1/Kbc)+(1/(gammac*x+1/((1/Kce)+(1/(gammae*x)))))))*(delta/(1-ephsilonf));#Effective rate constant from Eqn.(12.14)\n",
"tou=-math.log(1-XA)/Kf;#Space time from Eqn.(12.16)\n",
"Lm=tou*uo/(1-ephsilonm);#Length of fixed bed for guess value of a1bar\n",
"a1bar1=[0.0233,0.0465,0.0698,0.0930,0.116,0.140];#Various activity values to find Lm\n",
"x1 = [0,0,0,0,0,0]\n",
"Kf1 = [0,0,0,0,0,0]\n",
"tou1 = [0,0,0,0,0,0]\n",
"Lm1 = [0,0,0,0,0,0]\n",
"\n",
"n=len(a1bar1);\n",
"i=0;\n",
"while i