1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
|
{
"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": {}
}
]
}
|
