Chapter 8 - Chemical Reaction & Dissusion in a spherical Catalyst Pellet

Exa 8.1 Page 158

from __future__ import division
from numpy import zeros
x=[];x1=[]
for i in range(1,101):
    x.append(0)

Iter=0 ;  e1=1 ;  f=1
a=[0]
while e1>1e-6 and f>1e-6:
    Iter=Iter+1
    for i in range(1,101):
        x1.append(x[i-1])
    for i in range(2,101):
        a.append(1-(1/(i-1)))
    b=[-6.01]
    for i in range(2,101):
        b.append(-2.01)
    c=[6]
    for i in range(2,100):
        c.append(1+(1/(i-1)))
    #for i=1:99,d(i)=0, end, d(100)=-100/99,
    d=zeros(100)
    d[99]=-100/99
    i=1 ; n=100 ; Beta = [b[i-1]]
    Gamma = [d[i-1]/Beta[i-1]]
    i1=i+1
    for j in range(i1,n+1):
        Beta.append((b[j-1]-a[j-1]*c[j-2])/Beta[j-2])
        Gamma.append((d[j-1]-a[j-1]*Gamma[j-2])/Beta[j-1])
    x=zeros(n)
    x[-1]=Gamma[n-1]
    n1=n-i
    for k in range(1,n1+1):
        j=n-k
        x[j-1]=Gamma[j-1]-c[j-1]*x[j]/Beta[j-1]
    
    e1=abs(x[0]-x1[0])
    f=abs(x[99]-x1[99])

print "the solution by TDMA of node 77 to 99 by 1st order rxn. is",Iter
for i in range(78,101):
    print x[i-1]

the solution by TDMA of node 77 to 99 by 1st order rxn. is 1
2.11327608271e-05
-6.97708390547e-06
-6.19992402138e-05
2.04759969916e-05
0.000182009868277
-6.01295131167e-05
-0.000534648505839
0.000176680552708
0.0015714263084
-0.000519440824961
-0.00462125771268
0.00152798240852
0.0135974017665
-0.00449702200409
-0.0400286588926
0.0132417745751
0.117895160831
-0.0390097044184
-0.34739360391
0.114972976752
1.02409485606
-0.339006034307
-3.02025227398

Exa 8.2 Page 162

from __future__ import division
from numpy import zeros
x=zeros(100)
Iter=0 ; e1=1 ; f=1
k=.1 ; D=10**-9 ; r=.01 ; delta_r=r/10 ; t1=k*delta_r**2/D
x1=[]; a=[0] ; b=[0] ;d=[0]
while e1>1e-6 and f>1e-6:
    Iter=Iter+1
    for i in range(1,101):
        x1.append(x[i-1])
    for i in range(2,101):
        a.append(1-(1/(i-1)))
    b=[-6-t1*x1[0]]
    for i in range(2,101):
        b.append(-2-t1*x1[i-1])
    c=[6]
    for i in range(2,100):
        c.append(1+(1/(i-1)))
    for i in range(1,100):
        d.append(0)
    d.append(-100/99)
    i=1 ;  n=100 ;  Beta=[b[i-1]]
    Gamma=[d[i-1]/Beta[i-1]]
    i1=i+1
    for j in range(i1,n+1):
        Beta.append(b[j-1]-a[j-1]*c[j-2]/Beta[j-2])
        Gamma.append((d[j-1]-a[j-1]*Gamma[j-2])/Beta[j-1])
    x=zeros(n)
    x[-1]=Gamma[n-1]
    n1=n-i
    for k in range(1,n1+1):
        j=n-k
        x[j-1]=Gamma[j-1]-c[j-1]*x[j-1]/Beta[j-1]
    e1=abs(x[0]-x1[0])
    f=abs(x[99]-x1[99])

print "the solution by TDMA of node 77 to 99 by 2nd order rxn. is"
for i in range(77,101):
    print x[i-1]

the solution by TDMA of node 77 to 99 by 2nd order rxn. is
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-0.0

Exa 8.3 Page 163

from __future__ import division
from numpy import zeros,exp
x=zeros(100) ; x1=zeros(100); a=zeros(100) ;                        #initial values

e2=1 ;  f1=1 ; Iter=0                          #assumed values
k=.1*10**-2 ;  D=10**-9 ; r=.01 ; delta_r=r/100 ; t1=k*delta_r**2/D        #given data
#now solving the eqns for all the nodes and then simplifying we get the following relations
d=[]
while e2>1e-6 and f1>1e-6:
    Iter=Iter+1
    for i in range(1,101):
        x1[i-1]=x[i-1]
        
    for i in range(2,101):
        a[i-1]=1-(1/(i-1))
    b=[-6-t1*exp((1-x1[0])/(2-x1[0]))]
    for i in range(2,101):
        b.append(-2-t1*exp((1-x[i-1])/(2-x[i-1])))
    c=[6]
    for i in range(2,100):
        c.append(1+(1/(i-1)))
    for i in range(1,100):
        d.append(0)
    d.append(-100/99)
    i=1 ;  n=100 ;  Beta = [b[i-1]]
    Gamma=[d[i-1]/Beta[i-1]]
    i1=i+1
    for j in range(i1,n+1):
        Beta.append(b[j-1]-a[j-1]*c[j-2]/Beta[j-2])
        Gamma.append((d[j-1]-a[j-1]*Gamma[j-2])/Beta[j-1])
    x=zeros(n)    
    x[-1]=Gamma[n-1]
    n1=n-i
    for k in range(1,n1+1):
        j=n-k
        x[j-1]=Gamma[j-1]-c[j-1]*x[j]/Beta[j-1]
    
    e2=abs(x[0]-x1[0])
    f1=abs(x[99]-x1[99])

print "the solution by TDMA of node 77 to 100 by 1st order rxn. is"
for i in range(76,101):
    print x[i-1]

the solution by TDMA of node 77 to 100 by 1st order rxn. is
0.0604887704253
0.0678168756519
0.0760392035241
0.0852643022272
0.095613536562
0.107222479921
0.120242419314
0.134841969734
0.151208788326
0.169551370725
0.190100900502
0.213113107034
0.238870065591
0.26768184402
0.299887860369
0.335857761202
0.375991556122
0.420718642949
0.470495220437
0.525799398375
0.587123060992
0.654959197343
0.729782956961
0.812024100415
0.902027799616

Exa 8.4 Page 164

from __future__ import division
from numpy import zeros,exp
x=zeros(100);x=zeros(100)
Iter=0 ; e1=1 ; f1=1
while e1>1e-6 and f1>1e-6:
    Iter=Iter+1
    for i in range(1,101):
        x1[i-1]=x[i-1]
    for i in range(2,101):
        a[i-1]=1-(1/(i-1))
    b=[-6-.01*exp((10-10*x1[0])/(11-10*x1[0]))]
    for i in range(2,101):
        b.append(-2-.01*exp((10-10*x1[i-1])/(11-10*x1[i-1])))
    c=[6]; d= []
    for i in range(2,100):
        c.append(1+(1/(i-1)))
    for i in range(1,100):
        d.append(0)
    d.append(-100/99)
    i=1 ;  n=100 ; 
    Beta=[b[i-1]]
    Gamma=[d[i-1]/Beta[i-1]]
    i1=i+1
    for j in range(i1,n+1):
        Beta.append(b[j-1]-a[j-1]*c[j-2]/Beta[j-2])
        Gamma.append((d[j-1]-a[j-1]*Gamma[j-2])/Beta[j-1])
    x=zeros(n)
    x[-1]=Gamma[n-1]
    n1=n-i
    for k in range(1,n1+1):
        j=n-k
        x[j-1]=Gamma[j-1]-c[j-1]*x[j]/Beta[j-1]
    
    e1=abs(x[0]-x1[0])
    f1=abs(x[99]-x1[99])

print "the solution by TDMA of node 77 to 99 by 1st order rxn. is"
for i in range(76,101):
    print x[i-1]

the solution by TDMA of node 77 to 99 by 1st order rxn. is
0.0274150220283
0.0316615335985
0.0365714178414
0.0422488399165
0.0488143356681
0.0564073663768
0.0651892620654
0.0753466078611
0.087095133412
0.100684170249
0.116401745411
0.134580380148
0.155603657639
0.179913609207
0.208018937265
0.240504032341
0.278038627503
0.321387721808
0.371421006027
0.429120250921
0.495581544008
0.572005825625
0.659662934735
0.759791838019
0.873325342972