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+//Kunii D., Levenspiel O., 1991. Fluidization Engineering(II Edition). Butterworth-Heinemann, MA, pp 491

+

+//Chapter-12, Example 5, Page 307

+//Title: Conversion in the Freeboard of a Reactor

+//==========================================================================================================

+

+clear

+clc

+

+//INPUT

+uo=0.3;//Superficial gas velocity in m/s

+Lf=1.1;//Length of fixed bed in m

+Hf=1.2;//Length of freeboard in m

+db=0.04;//Equilibrium bubble size in m

+umf=0.006;//Velocity at minimum fluidization condition in m/s

+ephsilonmf=0.55;//Void fraction at minimum fluidization condition

+gammab=0.005;//Ratio of volume of dispersed solids to that of bubble phase

+Kr=10;//rate constant in m^3 gas/m^3 cat s

+D=2E-5;//Diffusion coefficient of gas in m^2/s

+g=9.81;//Acceleration due to gravity in square m/s^2

+

+//CALCULATION

+ubr=0.711*(g*db)^0.5;//Rise velocity of bubble from Eqn.(6.7)

+ub=uo-umf+ubr;//Velocity of bubbles in bubbling beds in Eqn.(6.8)

+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)

+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)

+delta=uo/ub;//Fraction of bed in bubbles from Eqn.(6.29)

+ephsilonf=1-(1-delta)*(1-ephsilonmf);//Void fraction of fixed bed from Eqn.(6.20)

+fw=0.6;//Wake volume to bubble volume from Fig.(5.8)

+gammac=(1-ephsilonmf)*((3/(ubr*ephsilonmf/umf-1))+fw);//Volume of solids in cloud to that of the bubble from Eqn.(6.36)

+gammae=((1-ephsilonmf)*((1-delta)/delta))-gammab-gammac;//Volume of solids in emulsion to that of the bubble from Eqn.(6.35)

+Kf=(gammab*Kr)+1/((1/Kbc)+(1/(gammac*Kr+1/((1/Kce)+(1/(gammae*Kr))))));//Raction rate for fluidized bed from Eqn.(14)

+XA=1-exp(-1*Kf*Lf/ub);//Conversion at the top of dense bed from Eqn.(16)

+etabed=(Kf*delta)/(Kr*(1-ephsilonf));//Reactor efficiency from Eqn.(22)

+a=0.6/uo//Since uoa = 0.6s^-1 from Fig.(5)

+adash=6.62;//From Fig.(5)

+XA1=1-1/(exp(((1-ephsilonf)*Kr/(uo*a))*[(1-exp(-a*Hf))-((1-etabed)/(1+(adash/a)))*(1-exp(-(a+adash)*Hf))]));//Conversion from Eqn.(64)

+XA2=1-(1-XA1)*(1-XA);//Conversion at the exit from Eqn.(64)

+

+//OUTPUT

+printf('\nThe conversion:');

+mprintf('\n\tAt the top pf the dense bed: %f percentage',XA*100);

+mprintf('\n\tAt the reactor exit: %f percentage',XA2*100);

+

+//Disclaimer: The value of kf deviate from the one given in textbook, where as it is close to the value obtained by manual calculation. 

+//====================================END OF PROGRAM ======================================================
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