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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 16 : Design for Physical Operations"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, Page 404\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"T=1000.; #Operating temperature of calciner in degree celcius\n",
"deltaHr=1795.; #Heat of reaction in kJ/kg\n",
"M1=0.1; #Molecular weight of Calcium carbonate in kg/mol\n",
"M2=0.056; #Molecular weight of CaO in kg/mol\n",
"M3=0.044; #Molecular weight of Carbon dioxide in kg/mol\n",
"M4=0.029; #Molecular weight of Air in kg/mol\n",
"M5=0.029; #Molecular weight of Combustion gas in kg/mol\n",
"Cp1=1.13; #Specific heat of Calcium carbonate in kJ/kg K\n",
"Cp2=0.88; #Specific heat of CaO in kJ/kg K\n",
"Cp3=1.13; #Specific heat of Carbon dioxide in kJ/kg K\n",
"Cp4=1.00; #Specific heat of Air in kJ/kg K\n",
"Cp5=1.13; #Specific heat of Calcium carbonate in kJ/kg K\n",
"Tf=20.; #Temperature of feed in degree celcius\n",
"ma=15.; #Air required per kg of fuel in kg\n",
"Hc=41800.; #Net combustion heat of fuel in kJ/kg\n",
"Tpi=20.; #Initial temperature of solids in degree C\n",
"Tgi=1000.; #Initial temperature of gas in degree C\n",
"\n",
"#CALCULATION\n",
"mc=1;#Based on 1 kg of Calcium carbonate\n",
"B=(1/(Hc-(ma+mc)*Cp5*(T-Tpi)))*(M3*Cp3*(T-Tf)+M2*Cp2*(T-Tf)+deltaHr)#Fuel consumption(kg fuel/kg calcium carbonate)\n",
"B1=B*M3/M2;#Fuel consumption(kg fuel/kg Cao)\n",
"H=Hc*B1;#Heat required for calcination\n",
"eta=deltaHr/(B*Hc);#Thermal efficiency\n",
"\n",
"#OUTPUT\n",
"print 'Fuel consumption:%f kg fuel/kg Cao'%B1\n",
"print 'Heat requirement for calcination:%f kJ/kg Cao'%H\n",
"print 'Thermal efficiency:%f percentage'%(eta*100)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Fuel consumption:0.061731 kg fuel/kg Cao\n",
"Heat requirement for calcination:2580.366029 kJ/kg Cao\n",
"Thermal efficiency:54.657251 percentage\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2, Page 405\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from scipy.optimize import fsolve\n",
"import math\n",
"\n",
"#INPUT\n",
"F = 400. #Feed rate of Calcium carbonate in tons/day\n",
"T = 1000. #Operating temperature of calciner in degree celcius\n",
"deltaHr = 1795.#Heat of reaction in kJ/kg\n",
"M1 = 0.1 #Molecular weight of Calcium carbonate in kg/mol\n",
"M2 = 0.056 #Molecular weight of CaO in kg/mol\n",
"M3 = 0.044 #Molecular weight of Carbon dioxide in kg/mol\n",
"M4 = 0.029 #Molecular weight of Air in kg/mol\n",
"M5 = 0.029 #Molecular weight of Combustion gas in kg/mol\n",
"Cp1 = 1.13 #Specific heat of Calcium carbonate in kJ/kg K\n",
"Cp2 = 0.88 #Specific heat of CaO in kJ/kg K\n",
"Cp3 = 1.13 #Specific heat of Carbon dioxide in kJ/kg K\n",
"Cp4 = 1.00 #Specific heat of Air in kJ/kg K\n",
"Cp5 = 1.17 #Specific heat of Combustion gas in kJ/kg K\n",
"Tf = 20. #Temperature of feed in degree celcius\n",
"ma = 15. #Air required per kg of fuel in kg\n",
"uo = 0.8 #Superficial gas velocity in m/s\n",
"Hc = 41800. #Net combustion heat of fuel in kJ/kg\n",
"Tpi = 20. #Initial temperature of solids in degree C\n",
"Tgi = 1000. #Initial temperature of gas in degree C\n",
"rhoa = 1.293 #Density of air in kg/m**3\n",
"pi = 3.14\n",
"\n",
"#CALCULATION\n",
"mc = 1. #Based on 1 kg of Calcium carbonate\n",
"Bguess = 2. #Guess value of B\n",
"def solver_func(B): #Function defined for solving the system\n",
" phi = ((ma+mc)*Cp5*B+(M3*Cp3))/Cp1\n",
" T3 = (Tpi+(phi+phi**2+phi**3)*Tgi)/(1+phi+phi**2+phi**3)\n",
" phiplus = 30.6*B\n",
" Tr = (T+Tpi*phiplus)/(1+phiplus)\n",
" return Hc*B+Cp3*(T3-Tpi)+ma*B*Cp4*(Tr-20)-(ma+mc)*Cp5*(T-Tpi)-M3*Cp3*(T-Tpi)-M2*Cp2*(T-Tpi)-deltaHr\n",
" #fn = (1/20800)*(2470-T3-13.34*(Tr-20))\n",
"\n",
"B = fsolve(solver_func,1E-6)#Using inbuilt function fsolve for solving Eqn.(23) for tou\n",
"phi = ((ma+mc)*Cp5*B+(M3*Cp3))/Cp1\n",
"#Temperature of various stages\n",
"T1 = (Tpi+(phi)*Tgi)/(1+phi)\n",
"T2 = (Tpi+(phi+phi**2)*Tgi)/(1+phi+phi**2)\n",
"T3 = (Tpi+(phi+phi**2+phi**3)*Tgi)/(1+phi+phi**2+phi**3)\n",
"phiplus = 30.6*B\n",
"Tr = (T+Tpi*phiplus)/(1+phiplus)\n",
"eta = deltaHr/(B*Hc) #Thermal efficiency\n",
"H = B*Hc/M2 #Heat requirement\n",
"#For lower heat recovery section\n",
"Ql = (F*10**3/(24*3600))*B*ma/(rhoa*(273/(Tr+273)))#Volumetric flow rate of gas in the lower heat recovery section\n",
"dtl = math.sqrt(4/pi*Ql/uo)#Diameter of lower bed\n",
"#For calcination section\n",
"Qc = (F*10**3/(24*3600))*B*ma/(rhoa*(273/(T+273)))#Volumetric flow rate of gas in the calcination section\n",
"dtc = math.sqrt(4/pi*Qc/uo)#Diameter of calcination section\n",
"#For I stage\n",
"Q1 = (F*10**3/(24*3600))*B*ma/(rhoa*(273/(T1+273)))#Volumetric flow rate of gas in the I stage\n",
"dt1 = math.sqrt(4/pi*Q1/uo)#Diameter of I stage\n",
"#For II stage\n",
"Q2 = (F*10**3/(24*3600))*B*ma/(rhoa*(273/(T2+273)))#Volumetric flow rate of gas in the II stage\n",
"dt2 = math.sqrt(4/pi*Q2/uo)#Diameter of II stage\n",
"#For III stage\n",
"Q3 = (F*10**3/(24*3600))*B*ma/(rhoa*(273/(T3+273)))#Volumetric flow rate of gas in the III stage\n",
"dt3 = math.sqrt(4/pi*Q3/uo)#Diameter of III stage\n",
"\n",
"#OUTPUT\n",
"print '\\nDiameter of lower bed:%fm'%(dtl)\n",
"print '\\nDiameter of calcination section:%fm'%(dtc)\n",
"print '\\nBed no.\\t\\t1\\t2\\t\\t3'\n",
"print '\\nDiameter(m)%f\\t%f\\t%f'%(dt1,dt2,dt3)\n",
"\n",
"#The value of diameter of each section is largely deviating from the values in the textbook. This is because the fuel consumption B have not been included in the energy balance equation. And the value of molecular weight is wrong by one decimal point.\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Diameter of lower bed:7.097814m\n",
"\n",
"Diameter of calcination section:13.351483m\n",
"\n",
"Bed no.\t\t1\t2\t\t3\n",
"\n",
"Diameter(m)12.728715\t13.270865\t13.340712\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, Page 413\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"T=20; #Temeprature in degree C\n",
"M=0.018; #Molecular weight of water in kg/mol\n",
"Q=10; #Flow rate of dry air in m**3/s\n",
"R=82.06E-6; #Universal gas constant\n",
"pi=0.0001; #Initial moisture content in atm\n",
"pj=0.01; #Final moisture content in atm\n",
"\n",
"#CALCULATION\n",
"a=Q*(273+T)/273; #Term At*uo\n",
"b=a*M/(R*(T+273));#Term C*At*uo\n",
"#The value of slope can be found only by graphical mehtod. Hence it has been taken directly from the book(Page no.414,Fig.E3)\n",
"m=10.2;\n",
"Fo=b/m; #Flow rate of solids\n",
"Q3=(b/Fo)*(pj-pi);#Moisture content of leaving solids\n",
"\n",
"#OUTPUT\n",
"print '\\nMoisture content of leaving solids:%.3f kg H2O/kg dry solids'%Q3\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Moisture content of leaving solids:0.101 kg H2O/kg dry solids\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 4, Page 422\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"\n",
"\n",
"#INPUT\n",
"Qfi = 0.20 #Initial moisture fraction\n",
"Qfbar = 0.04 #Average final moisture fraction\n",
"rhos = 2000. #Density of solid in kg/m**3\n",
"Cps = 0.84 #Specific heat of solids in kJ/kg K\n",
"Fo = 7.6E-4 #Flow rate of solids in kg/m**3\n",
"Tsi = 20. #Inital temperature of solids in degree C\n",
"rhog = 1. #Density of gas in kg/m**3\n",
"Cpg = 1 #Specific heat of gas in kJ/kg K\n",
"uo = 0.3 #Superficial gas velocity in m/s\n",
"Tgi = 200 #Initial temperature of gas in degee C\n",
"L = 2370 #Enthalpy of liquid in kJ/kg\n",
"Cpl = 4.2 #Specific heat of liquid in kJ/kg K\n",
"dt = 0.1 #Diameter of reactor in m\n",
"Lm = 0.1 #Length of fixed bed in m\n",
"ephsilonm = 0.45 #Void fraction of fixed bed\n",
"pi = 3.14\n",
"Fo1 = 1 #Feed rate for commercial-scale reactor in kg/s\n",
"\n",
"#CALCULATION\n",
"#(a)Bed temperature\n",
"Teguess = 50#Guess value of Te\n",
"def solver_func(Te):#Function defined for solving the system\n",
" return (pi/4.)*dt**2*uo*rhog*Cpg*(Tgi-Te)-Fo*(Qfi-Qfbar)*(L+Cpl*(Te-Tsi))-Fo*Cps*(Te-Tsi)\n",
"\n",
"Te = fsolve(solver_func,Teguess)\n",
"\n",
"#(b)Drying time for a particle\n",
"xguess = 2#Guess value of x, ie term tou/tbar\n",
"def solver_func1(x): #Function defined for solving the system\n",
" return 1-(Qfbar/Qfi)-(1-math.exp(-x))/x\n",
"\n",
"\n",
"x = fsolve(solver_func1,xguess)\n",
"W = (pi/4.)*dt**2*Lm*(1-ephsilonm)*rhos#Weight of soilds in bed\n",
"tbar = W/Fo#Mean residence time of solids from Eqn.(59)\n",
"tou = tbar*x#Time for complete drying of a particle\n",
"\n",
"#(c)Commercial-scale dryer\n",
"W1 = Fo1*tbar\n",
"Atguess = 5#Guess value of area\n",
"def solver_func3(At): #Function defined for solving the system\n",
" return At*uo*rhog*Cpg*(Tgi-Te)-Fo1*(Qfi-Qfbar)*(L+Cpl*(Te-Tsi))-Fo1*Cps*(Te-Tsi)\n",
"\n",
"At = fsolve(solver_func3,Atguess)\n",
"dt1 = math.sqrt(4/pi*At)#Diameter of commercial-scale dryer\n",
"Q1 = At*uo*rhog#Flow rate necessary for the operation\n",
"\n",
"#OUTPUT\n",
"print 'Bed temperature:%f degree C'%(Te)\n",
"print 'Time for complete drying of particle:%fs'%(tou)\n",
"print 'Flow rate of gas necessary for Commercial-scale dryer:%fkg/s'%(Q1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bed temperature:58.728126 degree C\n",
"Time for complete drying of particle:527.431202s\n",
"Flow rate of gas necessary for Commercial-scale dryer:3.098684kg/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, Page 425\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable Declaration\n",
"rhos=1600.; #Density of solid in kg/m**3\n",
"Cps=1.25; #Specific heat of solids in kJ/kg K\n",
"Fo=0.5; #Flow rate of solids in kg/s\n",
"Tsi=20.; #Inital temperature of solids in degree C\n",
"Qwi=1.; #Initial moisture fraction in water\n",
"Qwf=0.2; #Final moisture fraction in water\n",
"Qhi=1.1; #Initial moisture fraction in heptane\n",
"Qhf=0.1; #Final moisture fraction in heptane\n",
"Tgi=240.; #Initial temperature of gas in degee C\n",
"Te=110.; #Bed temperature in degree C\n",
"ephsilonm=0.45; #Void fraction of fixed bed\n",
"ephsilonf=0.75; #Void fraction of fluidized bed\n",
"uo=0.6; #Superficial gas velocity in m/s\n",
"di=0.08; #Diameter of tubes in m\n",
"li=0.2; #Pitch for square arrangement\n",
"hw=400.; #Heat transfer coefficient in W/m**2 K\n",
"Tc=238.; #Temperature at which steam condenses in degree C\n",
"#Specific heats in kJ/kg K\n",
"Cwl=4.18; #Water liquid\n",
"Cwv=1.92; #Water vapor\n",
"Chl=2.05; #Heptane liquid\n",
"Chv=1.67; #Heptane vapor\n",
"#Latent heat of vaporization in kJ/kg\n",
"Lw=2260.; #Water\n",
"Lh=326.; #Heptane\n",
"#Density of vapor in kg/m**3 at operating conditions\n",
"rhow=0.56; #Water\n",
"rhoh=3.1; #Heptane\n",
"Lf=1.5; #Length of fixed bed in m\n",
"t=140.; #Half-life of heptane in s\n",
"L=1.5; #Length of tubes in heat exchanger\n",
"pi=3.14;\n",
"\n",
"#CALCULATION\n",
"#(a) Dryer without Internals\n",
"xw=(Qwi-Qwf)/(Qhi-Qhf); #Water-heptane weight ratio\n",
"xv=((Qwi-Qwf)/18.)/((Qhi-Qhf)/100.); #Water-heptane volume ratio\n",
"T=(Qwi-Qwf)/18.+(Qhi-Qhf)/100.; #Total volume\n",
"rhogbar=((Qwi-Qwf)/18.)/T*rhow+((Qhi-Qhf)/100.)/T*rhoh; #Mean density of the vapor mixture\n",
"Cpgbar=(((Qwi-Qwf)/18.)/T)*rhow*Cwv+(((Qhi-Qhf)/100.)/T)*rhoh*Cwv;#Mean specific heat of vapor mixture\n",
"#Volumetric flow of recycle gas to the dryer in m**3/s from Eqn.(53)\n",
"x=(Cpgbar*(Tgi-Te))**-1*(Fo*(Qwi-Qwf)*(Lw+Cwl*(Te-Tsi))+Fo*(Qhi-Qhf)*(Lh+Chl*(Te-Tsi))+Fo*(Cps*(Te-Tsi)));\n",
"r=Fo*((Qwi-Qwf)/rhow+(Qhi-Qhf)/rhoh); #Rate of formation of vapor in bed\n",
"uo1=uo*(x/(x+r)); #Superficial velocity just above the distributor\n",
"At=x/uo1; #Cross-sectional area of bed\n",
"dt=math.sqrt(4./pi*At); #Diameter of bed\n",
"B=-math.log(Qwf/Qwi)/t; #Bed height from Eqn.(63)\n",
"tbar=((Qhi/Qhf)-1)/B; #Mean residence time of solids\n",
"W=Fo*tbar; #Weight of bed\n",
"Lm=W/(At*(1-ephsilonm)*rhos); #Static bed height\n",
"Lf=(Lm*(1-ephsilonm))/(1-ephsilonf); #Height of fluidized bed\n",
"\n",
"#(b) Dryer with internal heaters\n",
"f=1/8.0; #Flow rate is 1/8th the flow rate of recirculation gas as in part (a)\n",
"x1=f*x; #Volumetric flow of recycle gas to the dryer in m**3/s from Eqn.(53)\n",
"uo2=uo*(x1/float(x1+r)); #Superficial velocity just above the distributor\n",
"Abed=x1/uo2; #Cross-sectional area of bed\n",
"q=(Fo*(Qwi-Qwf)*(Lw+Cwl*(Te-Tsi))+Fo*(Qhi-Qhf)*(Lh+Chl*(Te-Tsi))+Fo*(Cps*(Te-Tsi)))-Abed*uo2*Cpgbar*(Tgi-Te);#Heat to be added from energy balance of Eqn.(53)\n",
"Aw=q*10**3/(hw*(Tc-Te));#Total surface area of heat exchanger tubes\n",
"Lt=Aw/(pi*di); #Total length of tubes\n",
"Nt=Lt/L; #Total number of tubes\n",
"Atubes=Nt*(pi/4*di**2); #Total cross-sectional area of tubes\n",
"Atotal=Abed+Atubes; #Total cross-sectional area of tube filled dryer\n",
"d=math.sqrt(Atotal*pi/4.);#Diameter of vessel\n",
"li=math.sqrt(Atotal/Nt); #Pitch for square array of tubes\n",
"\n",
"#OUTPUT\n",
"print '\\t\\t\\tBed diameter(m)\\tRecycle vapor flow(m**3/s)'\n",
"print 'Without internal heater\\t%f\\t%f'%(dt,x)\n",
"print 'With heating tubes\\t%f\\t%f'%(d,x1)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\t\t\tBed diameter(m)\tRecycle vapor flow(m**3/s)\n",
"Without internal heater\t3.630144\t5.331235\n",
"With heating tubes\t1.503916\t0.666404\n"
]
}
],
"prompt_number": 3
},
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"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
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}