Figure 11.11
Solution: For the zero-order reaction,
(CAkt?1?0.3t,t?3.3min )element?1???CAoCAo?0,t?3.3min?0.3t,t?3.3minCA )element??CAo?1,t?3.3minE(t)dt (liquid macrofluid reacts)
So (XA)element?1?(XA??(XA)0?elementFrom Fig11.11, we know
?0,0?t?4min?0.1(t?4),4?t?6min?E(t)??
?0.025(14?t),6?t?14??0,t?14minXA??1?E(t)dt?1
414Thus, the conversion of A is 100%.
11.12—11.14 Hydrogen sulfide is removed form coal gas by contact with a moving bed of
iron oxide
particles which convert to the sulfide as follows: Fe2O3 → FeS
In our reactor the fraction of oxide converted in any particle is any particle is
determined by its residence time t and the time needed for complete conversion of the particle ? and this is given by t 1 – X = (1- )3 when t < 1 hr, and with ?= 1 hr
?and X = 1 when t ? 1 hr
Find the conversion of iron oxide to sulfide if the RTD of solides in the contactor is approximated by the curve of Fig.P11.12,P11.13,P11.14.
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11.12
Figure 11.12
Solution: From Fig.11.12, we know
E(t)???1,0?t?1hr?0,t?1hr When t<1hr, 1?(XA)3element?(1?t)
So X?A??(XA)elementE(t)dt??1001?[1?(1?t)3]dt?0.75
11.13
Figure 11.13
Solution: From Fig.11.13, we know
E(t)????,t?0.5hr?0,t?0.5hr When t<1hr, 1?(XA)element?(1?t)3
also (XA)element?1?(1?t)3
So X?A??(XA)?30elementE(t)dt??0[1?(1?t)]??(t?0.5)dt?0.875Thus, the conversion of A is 87.5%.
11.14
41
Figure 11.14
From Fig.11.13, we know
?0,t?0.5hrE(t)???1,0.5?t?1.5hr
??0,t?1.5hr
When t<1hr, 1?(XA)element?(1?t)3
also (XA)element?1?(1?t)3
When t>1hr, (XA)element?1
So X?A??(XA)elementE(t)dt??1[1?(1?t)3]?1dt??1.500.511?1dt?0.9844Thus, the conversion of A is 98.44%.
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Chapter 18 Solid Catalyzed Reactions
18.22 In the absence of pore diffusion resistance a particular first-order gasphase reaction
proceeds as reported below.
??? = 10-6 mol/cm3cat·-rAs
at
CA = 10-5 mol/cm3, at 1 atm and 400℃
what size of spherical catalyst pellets (?e = 10-3 cm-3/cm cat·s) would ensure that
pore resistance effects do not intrude to slow the rate of reaction? Solution:
?The rate expression of first-order reaction is ?rA?k???CA
???, CA replaced by numerical values, we obtain And with ?rA10?6k?????5?0.1s?1
10To judge what type of the pore resistance, we need to calculate the Thiele modulus
k???dp10?15MT?L??dp ?3De6103When MT, the pore resistance effects could be neglected.
3Thus, dp?0.4, also dp?2.4mm
5So the diameter of spherical catalyst pellets should be less than 2.4mm.
18.24 The first-order decomposition of A is run in an experimental mixed flow reactor. Find the role played by pore diffusion in these runs; in effect determine whether the runs were made under diffusion-free, strong resistance, or intermediate conditions.
dp 4 8
W 1 3
CA0 300 100
?
60 160
XA
0.8 0.6
A→R
??Solution: ?rAoutCAo?XAout W?1?For the first run, ?rAout
300?60?0.8?14400
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?2?For the second run, ?rAout100?160?0.6?3200
3?114400?rAout??4.5 ?2?rAout3200While
R2dP2??2, R1dP1Thus, the runs were running under intermediate pore resistance.
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