Chapter 10 : Gas Dispersion and Gas Interchange in Bubbling Beds

In [2]:
%matplotlib inline

Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].
For more information, type 'help(pylab)'.

Example 1, Page 253

In [1]:
from numpy import *
%matplotlib inline
#Variable declaration
umf=[0.01,0.045];     #Velocity at minimum fluidization condition in m/s
ephsilonmf=[0.5,0.5]; #Void fraction at minimum fluidization condition
D=[2E-5,7E-5];        #Diffusion coefficient of gas in m**2/s
g=9.81;               #Acceleration due to gravity in m/s**2

#CALCULATION
db=[5.,10.,15.,20.];
n=len(umf);
m=len(db)
Kbc = zeros((n,m))
Kce = zeros((n,m))
Kbe = zeros((n,m))
    
for i in range(n):
    for j in range(m):
            Kbc[i][j]=4.5*(umf[i]/db[j])+5.85*((D[i]**0.5*g**0.25)/db[j]**(5.0/4));#Gas interchange coefficient between bubble and cloud from Eqn.(27)
            Kce[i][j]=6.77*((D[i]*ephsilonmf[i]*0.711*(g*db[j])**0.5)/db[j]**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(34)
            Kbe[i][j]=(Kbc[i][j]*Kce[i][j])/(Kbc[i][j]+Kce[i][j]);#Gas interchange coefficient between bubble and emulsion from Eqn.(14)

#OUTPUT
i=0;
j=0;
k=0;
while k<m*n:
    print '\t\tKbc for fine particles and He',
    print '\tKbc for coarse particles and ozone',
    print '\tKbe for fine particles and He',
    print '\tKbe for coarse particles and ozone'
    j = 0
    while j<m:
        print 'db=%fm'%(db[j]*10**-2);
        while i<n:
            print '\t%f'%Kbc[i][j],
            print '\t\t\t%f'%Kbe[i][j],
            i=i+1;   
            k=k+1;
            print '\t\t\t',
        i=0;
        j=j+1;
import numpy
import matplotlib.pyplot as plt
a = numpy.matrix(Kbe)
b = numpy.matrix(Kbc)
db = array(db).T
Kbe=a.T
Kbc=b.T

plt.plot(db,Kbc,db,Kbe)
#plt.plot(db,Kbe);
#Note : Python does not have plot2d function. so we can plot it 
#plt.title('Plot of Kbc,Kbe vs db','db');
plt.show()
print 'Comparing the points with the plot of Kbc,Kbe vs db in Fig.(12), we can conlcude the following:'
print 'Kbc for fine particles and helium: line 2 in Fig.(12)'
print 'Kbc for coarser particles and ozone: line 3 in Fig.(12)'
print 'Kbe for fine particles and helium: line 4 in Fig.(12)'
print 'Kbe for coarser particles and ozone: line 5 in Fig.(12)'

Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].
For more information, type 'help(pylab)'.
		Kbc for fine particles and He 	Kbc for coarse particles and ozone 	Kbe for fine particles and He 	Kbe for coarse particles and ozone
db=0.050000m
	0.015193 			0.003335 				0.052085 			0.006930 			db=0.100000m
	0.007104 			0.001434 				0.025121 			0.002964 			db=0.150000m
	0.004568 			0.000875 				0.016434 			0.001803 			db=0.200000m
	0.003345 			0.000616 				0.012173 			0.001266 			
Comparing the points with the plot of Kbc,Kbe vs db in Fig.(12), we can conlcude the following:
Kbc for fine particles and helium: line 2 in Fig.(12)
Kbc for coarser particles and ozone: line 3 in Fig.(12)
Kbe for fine particles and helium: line 4 in Fig.(12)
Kbe for coarser particles and ozone: line 5 in Fig.(12)

Example 2, Page 254

In [2]:
D=0.69;         #Diffusion coefficient of gas in cm**2/s
umf=1.0;        #Velocity at minimum fluidization condition in cm/s
ephsilonmf=0.5; #Void fraction at minimum fluidization condition
db=[5,15];      #Equilibrium bubble size in cm
g=980;          #Acceleration due to gravity in cm/s**2

#CALCULATION
n=len(db);
i=0;
Kbc = [0.,0.]
Kce = [0.,0.]
Kbe = [0.,0.]
e = [0.,0.]
while i<n:
    Kbc[i]=4.5*(umf/db[i])+5.85*((D**0.5*g**0.25)/db[i]**(5/4));#Gas interchange coefficient between bubble and cloud from Eqn.(27)
    Kce[i]=6.77*((D*ephsilonmf*0.711*(g*db[i])**0.5)/db[i]**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(34)
    Kbe[i]=(Kbc[i]*Kce[i])/(Kbc[i]+Kce[i]);#Gas interchange coefficient between bubble and emulsion from Eqn.(14)
    e[i]=(Kce[i]-Kbe[i])/Kbe[i];#Error when minor resistance is ignored
    i=i+1;

#OUTPUT
print 'db(cm)',
print '\t\tCalculated Kbc',
print '\tCalculated Kce',
print '\t\tKbe from Eqn.(14)',
print '\tErron when minor resistance is ignored (in percentage)'
i=0;
while i<n:
    print '%f'%db[i],
    print '\t%f'%Kbc[i],
    print '\t%f'%Kce[i],
    print '\t\t%f'%Kbe[i],
    print '\t\t%f'%(e[i]*100);
    i=i+1;   

db(cm) 		Calculated Kbc 	Calculated Kce 		Kbe from Eqn.(14) 	Erron when minor resistance is ignored (in percentage)
5.000000 	6.337721 	2.509152 		1.797506 		39.590766
15.000000 	2.112574 	0.635514 		0.488547 		30.082477

Example 3, Page 255

In [3]:
Kbe=[0.028,0.05];  #Reported range for gas interchange coefficient between bubble and emulsion
uo=0.30;           #Superficial gas velocity in m/s
db=0.13;           #Equilibrium bubble size in m
m=7;
ephsilonmf=0.5;    #Void fraction at minimum fluidization condition
umf=0.0018;        #Velocity at minimum fluidization condition in m/s
D=[9E-6,22E-6];    #Diffusion coefficient of gas in m**2/s
g=9.81;            #Acceleration due to gravity in m/s**2

#CALCULATION
n=len(Kbe);
i=0;
Kbem = [0,0]
Kbc = [0,0]
Kce = [0,0]
#Kbe = [0,0]
c = [0,0]

while i<n:
    Kbem[i]=(6.0/db)*Kbe[i];#Gas interchange coefficient between bubble and emulsion from Eqn.(19)
    Kbc[i]=4.5*(umf/db)+5.85*((D[i]**0.5*g**0.25)/db**(5.0/4));#Gas interchange coefficient between bubble and cloud from Eqn.(27)
    Kce[i]=6.77*((D[i]*ephsilonmf*0.711*(g*db)**0.5)/db**3)**0.5;#Gas interchange coefficient between emulsion and cloud from Eqn.(34)
    Kbe[i]=(Kbc[i]*Kce[i])/(Kbc[i]+Kce[i]);#Gas interchange coefficient between bubble and emulsion from Eqn.(14)
    c[i]=(Kbem[i]/Kbe[i]);
    i=i+1;

#OUTPUT
print 'Kbe from Eqn.(19)',
print '\tKbc from Eqn.(27)',
print '\tKce from Eqn.(34)',
print '\tKbe from Eqn.(14)',
print '\tComparison of Kbe from Eqn.(19) and that from Eqn.(14)'
i=0
while i<n:
    print '%f'%Kbem[i],
    print '\t\t%f'%Kbc[i],
    print '\t\t%f'%Kce[i],
    print '\t\t%f'%Kbe[i],
    print '\t\t%f'%c[i]
    i=i+1;   

Kbe from Eqn.(19) 	Kbc from Eqn.(27) 	Kce from Eqn.(34) 	Kbe from Eqn.(14) 	Comparison of Kbe from Eqn.(19) and that from Eqn.(14)
1.292308 		0.460200 		0.274548 		0.171959 		7.515188
2.307692 		0.684401 		0.429248 		0.263797 		8.747978
In [ ]: