acethylene fixed bed reactor reaction constants are not clear

Pergamon Chemical Engineerin 9 Science, Vol. 53, No. 1, pp. 149 155, 1998 I 1997 Elsevier Science Ltd. All rights reserved

Printed in Great Britain P I I : S0009-2509(97)00282-0 ooo9 2509/98 $19.00 + 0.00

Modelling of fixed-bed reactor: two models of industrial reactor for selective

hydrogenation of acetylene

M. Szukiewicz, K. Kaczmarski and R. Petrus* Department of Chemical Engineering and Process Control, Rzesz6w University of Technology,

A1 Powstafic6w Warszawy 6, 35-959 Rzeszdw, Poland

(Received 5 August 1996; accepted in revised form 2 May 1997)

Abstract--Modelling and simulation of operation conditions for a heterogeneous fixed-bed reactor are investigated on the basis of the industrial reactor for selective hydrogenation of acetylene on palladium catalyst (in ethylene production). Heterogeneous and pseudohomogeneous models of the above-mentioned reactor with their advantages and drawbacks are presented. It is shown, that the proper formulation of a pseudohomogeneous model allows for its use even in process with complex reaction routes and in which, intraparticle mass transfer resistances plays a major role. © 1997 Elsevier Science Ltd

Keywords: Heterogeneous catalysis; selective hydrogenation of acetylene; simulation.

I N T R O D U C T I O N

Modelling and simulation have become more and more the usually applied methods of design and operation condition analysis of chemical apparatus. Un- fortunately, in many chemical engineering branches using such convenient methods is difficult, especially sophisticated are cases, when we try to describe a real industrial process. If, additionally, the solid phase takes part in the process, e.g. heterogeneous catalysis, the task becomes very complex. The models commonly applied in simulation of heterogeneous fixed-bed reactor performance are widely described in literature (e.g. Froment and Bischoff, 1979; Doraiswamy and Sharma, 1984; Szarawara et al., 1991), but often there appears a problem of choice between two types of models: heterogeneous and pseudohomogeneous ones. The first type of model usually gives results with quite good accuracy, but solving the model equation set is rather difficult, because of a large set of highly non-linear and coupled equations (the usual case in industrial practice). Apart from that, even finding a solution method does not mean fully successful simulation since the time of solving can be unaccep- tably long. Therefore such models can be used only in a limited range, i.e. for preliminary calculation of reactor operation conditions. Solving pseudohomogeneous model is simple, but most often their accuracy is low, which limits their application. There- fore, it seems purposeful to make such a model, which

* Corresponding author.

would have the combined advantages of the two mentioned models it should be as precise as a heterogeneous one and as easy for solving and fast as a pseudohomogeneous one.

The selective hydrogenation of acetylene on palladium catalyst (in ethylene production) is an example of a process, where intraparticle mass transfer resistances play a major role. Because of that, a prognosis for using typical pseudohomogeneous models is rather poor. The confirmation of this fact one can find even in the recently published paper by Schbib et al. (1996). In spite of good agreement between computed and experimental results in case of kinetic equations, the simulation of the behaviour of a commercial hydrogenation unit rather failed.

In this work two models of industrial fixed-bed reactor for the selective hydrogenation of acetylene are presented. Both models were used for successful simulation of performance of industrial fixed-bed reactor for selective hydrogenation of acetylene (Szukiewicz et al., 1994; Szukiewicz, 1995). The process kinetics and reactor operation conditions were proposed by Fertilizers Research Institute, Pulawy, Poland. The first proposed model-- the heterogeneous one--is very universal. Calculations based on it is acceptable for a wide range of changeable process operation conditions, but it has a great drawback--a quite long time of computations. The second--the pseudohomogeneous model is significantly faster than the heterogeneous one, at the cost of time necessary for carrying out the preliminary calculations and universality (it can be used only for such catalyst pellet for which preliminary computations were

149

150 M. Szukiewicz et al.

performed). These models can be used even for acom- Heterogeneous model plex reaction set with sophisticated kinetic. Mass and heat balances for fluid:

M O D E L S

Assumptions for both the models given below are the same:

dFi 3(1 - - ~) ko. i -4-- - - (Pi,b - - Pi,s) = 0

dV Ro RgT

i = A , B , C , D {6)

1. Inside the tubular reactor, on catalyst pellet two exothermic reactions take place:

C 2 H 2 + H 2 ~ C 2 H 4 (1)

] dV cpkldV + dV {-AH2) ]

with initial conditions

(7)

C 2 H 4 + H 2 -~ C 2 H 6 . (2) for V = 0

The kinetic of these reactions are expressed in the following form:

kl exp( -E /Rg T)pA PB rc~n~ = 1 + K PA (3)

PA = PA.O; PB = PB,0;

PD = Po,o; T = To.

Mass balances for catalyst pellet:

PC = PC,O;

(8)

FC2H 6 k 2 exp ( - E/Rg T ) PB

1 + K p A exp (~-~E~ ~ pn. (4) + k~ ~:g ~ /

2. Activity distribution function can be described as follows: where:

Def,i R 21 ~0 11~2 ~Pi'~ ~ ) -- a{R)r~ = 0 RgT

i = A , B , C , D (9)

{~dla 0 ~ < R < R , a(R) = dla R, ~< R ~< Ro.

(active material in outer part of catalyst pellet only)

(5) 3. The flow is of a plug type. 4. Axial mixing is ignored. 5. External and internal heat transfer resistances

are negligible.

Remarks • Kinetic expressions are proposed by Fertilizers

Research Institute, Putawy, Poland (manufac- turer of industrial catalyst) so as to fit in the best way to the experimental results. In our opinion, the success of a simulation of reactor operation conditions depends on the 'quality' of the kinetic equations. They, first of all, should fit as well as possible the experimental results and pos- sibly have a simple form. Therefore, the kinetic equations proposed above should be regarded rather as empirical correlations which predict the rates of reactions within the range of experimental conditions. The complex mechanism of the selective hydrogenation of acetylene process, still partially speculative, induces that the equations presented here are as good as others, derived by using different possible reaction schemes.

• Assumptions 4 and 5 were accepted after checking them by using the well-known criteria (Fogler, 1992; Doraiswamy and Sharma, 1984) adapted to investigate the process (described in detail in Szukiewicz, 1995).

r A = rC2H2

r B = rC2H2 + rC2H 6 (lO)

r C = --rC2H2 -/- FC2H6

r D = _ rC2H~

with boundary conditions

~?pi - - = 0 for R = 0 ( l la ) dR

~3pi Def.i~--~ = kg , i (Pi ,o - P i . s ) for R = Ro. ( l lb)

The model equations were solved using the Euler method for reactor mass and heat balances (6), (7) and orthogonal collocation method for pellet mass balances (9).

Pseudohomogeneous model Mass and heat balances:

dF~ d---~ + r* = 0 i = A , B , C , D (12)

d,o ] dT 1 ( -AH1) + (--AH2) (13) dV cp dV

with initial conditions

for V = 0

PA = PA,O; Pn = PB.O; PC = PC.O;

Po=PD,o; T = T o (14)

where

Effectiveness reactions:

r* = rll rC2H2,b

r~ = ~1 rc:H:,b + ?/2 rC2H~,b

rE = - q l rc2H2,b + r/2 rC2H~.b

r* = --q2 rC2H~,b.

factors were defined for both main

Modelling of fixed-bed reactor 151

is most often very long. It is the largest drawback of the heterogeneous model presented above; therefore, the pseudohomogeneous model was developed. As it will be shown in the following, the pseudohomo-

(15) geneous model proposed here is as precise as the heterogeneous one, but significantly easier for solving and many times faster. In this case, the main problem is the proper assumption about the functional dependence of the effectiveness factors. This assumption decides about good or poor effect of simulation. A next step (problem) is the base building. It should ensure an acceptable precision of calculations, which means finding the proper way of discretization of space (T, YA, YB). Of course, the more points in the base the better, because approximation of functions eq. (17) is more precise, but it also means more time lost on preliminary calculations of the effectiveness factor values. For the process under consideration, the proper discretization of space (T, YA, YB) was found by trial-and-error method; a dimension (amount of points) of the base was enlarged until differences between the computed results using both models were not more than 1% (for both the criteria described below) for the chosen reactor operation conditions.

A comparison of the agreement between the two proposed models were done on the basis of the following parameters:

• Acetylene conversion:

PA.O -- PA ~ a - - - - ( 1 9 )

Pmo

• Selectivity:

S = (hydrogen consumption in acetylene hydrogen-

ation reaction/total hydrogen consumption). (20)

Comparison of the results of simulation, in a wide range of reactor operation conditions are presented in Figs 1-4. Tables 1 and 2 present the relative errors between the computed results using both models for the chosen reactor operation conditions. All of the figures and tables show that compatibility of the results obtained for both models is very high. For many

(18) cases results of the simulations are exactly the same (curves on figures overlaps at least partially) or differences are significantly smaller than the assumed 1% of relative error (Tables 1 and 2). This error was ex- ceeded only near the higher limit of the temperature range of reactor operation conditions (Figs 3 and 4, Table 2), which was accepted as tolerable. It could be corrected by changing the base discretization (which practically means that the base will grow) but at the cost of computational time. Higher differences for higher temperatures, in our opinion, come from the fact that an influence of temperature is strongly non- linear, while method used for the calculation of effectiveness factor is simply a multidimensional linear approximation. Comparison of Figs 1 and 3 with Figs 2 and 4, respectively, shows that compatibility

ql - ~v'rc2n2 dVp (16a)

Vp FC2Hz,b

r12 - ~vf C:H~ d Vp (16b) Vp FC2H~,,b

In order to minimize time of calculation with the use of this model, the values of the effectiveness factors in eqs (15) were computed on the basis of the following scheme:

• it was assumed that the functional dependence of effectiveness factors has a form

qj = f j ( r , yA,y,) j = 1, 2. (17)

• For chosen points of space (T, YA, YB) effectiveness factor values were calculated; these points were chosen in such a way as to contain each possible operation conditions of the modelling reactor. Such set of points together with the effectiveness factors values calculated for them will be called, 'the base' in the following. The calculations of the effectiveness factor values were performed using the model of a single catalyst pellet eq. (9).

• Expanding the function (17) in Taylor series (limited to the first derivatives only)

qj(T + AT, y~, + AyA, y~ + Ayn) = tlj(T, ya, y~)

• -I c3~IJ(T"ya'YB) A T + &lj(T, YA, Yn) AyA OT ~YA

~qj(T, yA,yB) -t Ays, j = 1,2

OYB

and using an interpolation method, it is possible to calculate the effectiveness factor values in eqs (15).

The model equations (12) and (13) were solved using the Euler method.

RESULTS AND DISCUSSION

Heterogeneous models of fixed-bed reactors give results of quite good precision, but especially in case of complex reaction with many reaction components and sophisticated kinetics their solution is very difficult. Finding a method of solution is a very difficult task (see Szukiewicz, 1995). Apart from that, the time of solution of the heterogeneous model equations set

152 M. S z u k i e w i c z et al.

1.0

' 7 <

E .o

ID ;>

O O ID

¢,..)

4.0

O

0,8

0.6

0.4

0.2

0,0 0.0

Eo=1.4

H E T

] . . . . . . P S H j E0=1.2 t

= .

0.2 0.4 0.6 0.8 1.0

r e ac to r lenght , z[-]

Fig. 1. Calculated conversion for heterogeneous and pseudohomogeneous models for chosen values of parameter E0 = Ps,o/PA,o.

"7" c#3

" 3

o,3

1.0

0.9

0.8

. ~ = - . . . . . . . . . . E0=1.1

E°=1'4 " ; ' " 2 - "

- - H E T " " ~ , \

P S H

i I i I i I L I i

0.0 0.2 0.4 0.6 0.8

r eac to r lenght , z[-]

.0

Fig. 2. Calculated selectivity for heterogeneous and pseudohomogeneous models for chosen values of parameter E0 = PB,o/PA,O.

between the computed results in the case of acetylene conversion is much better than in the case of selectivity. Precision of the pseudohomogeneous model for conversion is practically the same as the heterogeneous one. Accuracy of selectivity calculation is in most cases worse. In the authors' opinion, the difference in precision of calculation for conversion and selectivity values is caused by the fact that the first parameter depends on acetylene hydrogenation reaction only, while the second depends on both the reactions con- sidered here.

As it was shown, results of calculation using both models are much the same, but differences can be

larger or smaller in dependence on the way of discretization, the interpolating method used and, finally, the calculated parameter. The difference can be reduced by enlarging the base dimension, but at the cost of computational time. The evaluation, whether accuracy of the obtained results (for determined process operation conditions) is sufficient or not, is up to the model builder.

Times of calculation using the heterogeneous and the pseudohomogeneous models and times needed for the base preparation and simulation are presented in Table 3. They show that calculations using the second model are more than 10,000 times faster.

Modelling of fixed-bed reactor 153

1.0

0.8 HET " ' . . . . . . . . . . . . . . - - - - - -

0.6

0.4

0.2

"7" <

o o,,,~

cD

o o

I1) O

0 . 0 , I ~ I ~ I ~ 1 ~ I

290 300 310 320 330 340

front-end temperature, T0[K ]

Fig. 3. Calculated conversion for heterogeneous and pseudohomogeneous models; Eo = 1.2.

1.0

,-p

r/l

- - HET

~ ' ' - . - . . . . . P S H

0.9

0.8

I , I ~ I J I , I

290 300 310 320 330 340

front-end temperature, T0[K ]

Fig. 4. Calculated selectivity for heterogeneous and pseudohomogeneous models; Eo = 1.2.

Unfortunately, this model also needs a time-consuming preliminary calculations and it is less universal (it can be used only for such catalyst pellet, for which the preliminary computations were performed). These calculations need the model, which can simulate behaviour of a single catalyst pellet for the investigating process.

Our investigations on modelling of the selective hydrogenation of acetylene process allows for listing the following drawbacks and advantages of both the models presented:

• The heterogeneous model: Advantages--accuracy of computations is very high, the model is very universal, which

means that it is possible to change practically all parameters without rebuilding of the model. Drawbacks difficulties in solving model equations set and a long time of calculations. The pseudohomogeneous model: Advantages--very short time of computation; therefore, this model can be used for optimization of reactor operation conditions and even for on- line control. Drawbacks--an acceptable precision of calculations needs a large size base, it is very time consuming, apart from being less universal; the pseudohomogeneous model can be used only for

154 M. Szukiewicz et al.

such type of catalyst pellet for which the preliminary computa t ions were performed.

Because of the advantages and drawbacks ment ioned above, the presented models were used for hydro- genat ion unit s imulat ion s u p p l e m e n t a r y - - t h e heterogeneous one for pre l iminary calculations, and the pseudohomogeneous one for finding of opt imal opera t ion condit ions. It is worthwhile to add that

any computa t ions of op t imal opera t ion condi t ions would be practically impossible (even when having many times faster calculat ing compute r than ours) by using the heterogeneous model only. M a t h e m a t - ical opt imizat ion needs many repeated s imulat ions of the invest igated uni t opera t ion condit ions, and only a fast model ensures its usefulness. In the invest igated process, opt imizat ion were performed on a compute r which is not very fast IBM PC 486DX-33 MHz.

Table 1. Relative errors for acetylene conversion and process selectivity for heterogeneous and pseudohomogeneous

models for chosen points along the reactor, Eo = 1.2

2 ~A,IHET) 0~A,(PSH) ~ (%) S(HET) S(PSH) ~ (%)

0 0.000 0.000 0.960 0.1 0.065 0.065 0 0.958 0.2 0.135 0.135 0 0.956 0.3 0.211 0.211 0 0.953 0.4 0.291 0.291 0 0.950 0.5 0.371 0.371 0 0.947 0.6 0.452 0.452 0 0.943 0.7 0.536 0.536 0 0.938 0.8 0.619 0.619 0 0.931 0.9 0.701 0.701 0 0.924 1 0.780 0.780 0 0.915

Relative errors were calculated as 6 = (~a.(nET) -- eaaPSH))/ ~A,(HET) or 6 = (S(HET) -- S(PSH))/S(HET ),

Table 2. Relative errors for acetylene conversion and process selectivity for heterogeneous and pseudohomogeneous

models for chosen front-end temperatures, Eo = 1.2

Z ~A,(HET) ~A,(PSH) 6 (%) S(HET ) S(PSH ) ~ (%)

293 0.190 0.190 0 0.954 303 0.434 0.434 0 0.943 313 0.778 0.773 0.6 0.905 323 0.964 0.96 0.4 0.820 333 0.960 0.950 1.0 0.802 343 0.941 0.920 2.2 0.786

Relative errors were calculated as 6 = (ea.~UEV) -- C~A.~PSH))/ ~A,(HET) or 6 = (S(HET) -- S(PSH))/S(HET ).

Table 3. The comparison of times of calculation

Pseudohomogeneous model The calculation of r/1 and r/2 an average time 8 min using single catalyst pellet model 20 s Preliminary calculations of the base total time about 78 h

30 min A single reactor work simulation an average time 1 s

Heterogeneous model A single reactor work simulation an average time 6 h

20 rain

The results presented in the table were performed using computer IBM PC 486DX-33 MHz.

CONCLUSIONS

O n the basis of the invest igat ions performed for selective hydrogena t ion of acetylene process some no tewor thy conclusions regarding heterogeneous

0.955 0.5 fixed-bed reactor model l ing can be drawn. Each of the two models presented has its own drawbacks and 0.954 0.4

0.952 0.4 advantages and therefore it is no t possible to present 0.949 0.4 a universal methodology which will be correct in 0.945 0.5 every case. We are able to ,present only some direc- 0.942 0.5 tions, which in our op in ion can help to do successful 0.937 0.6 s imulat ion of opera t ion of any industr ial hetero- 0.930 0.9 geneous reactor. 0.923 0.9 The heterogeneous model is very convenient for 0.916 0.9 invest igat ions in case of a wide range of process para- 0.908 0.8

meters changes, but finding its solut ion is usually a ra ther difficult task. The pseudohomogeneous model suggested in this paper is easy to solve and very fast, but at the cost of t ime necessary for carrying out the prel iminary calculat ions and less universali ty (universality of the model depends on the investigated process).

In our opinion, in many processes (e.g., the selective hydrogena t ion of acetylene process presented here) the models ment ioned above are supplementary and it is purposeful to build up bo th of them: First, a hetero-

0.951 0.3 geneous one to approximate ly determine reactor 0.938 0.5 opera t ion condi t ions and, then, the pseudohomo- 0.898 0.8 geneous to opt imize these condit ions. P repara t ion of 0.821 -0.1 the heterogeneous model of reactor first means, in 0.795 0.9 practice, tha t a model for calculat ing the effectiveness 0.765 2.7 factor (model of a single catalyst pellet) is ready,

too. This strategy is correct, especially in case when universali ty of bo th models is no t the same. If a pseudohomogeneous model is as universal as the heterogeneous one or the t ime needed for proper base calculat ion is significantly shor ter than the time of a single reactor work s imulat ion using the heterogeneous model, it seems tha t it is bet ter to build it at once. The model of a single catalyst pellet is significantly easier for solving than the heterogeneous model of reactor and, therefore, calculat ing even a large size base is better, because we obta in immediately a very useful calculat ing tool; a very fast and precise model can be used, e.g. for process opera t ion opt imizat ion or on-line control.

The influence of different (especially larger) n u m b e r of react ion componen t s and /o r the n u m b e r of reactions, which is to say ' ano the r process', on the t ime of computa t ion using bo th the heterogeneous and the

Modelling of fixed-bed reactor

pseudohomogeneous model is difficult to precisely Ayi foresee, when details of the process are unknown. Of z = 1/L course, apart from the simplest cases (e.g., one sub- strate, linear kinetic, etc.) where the profit of using the pseudohomogeneous model will be too small to build Greek letters such a model. In our opinion, the final evaluation of ~A computational expense of both models or only one of 6 them is up to the model builder, e,

th, q2

a(R) Cp

Def,i

E Eo = PB,o/PA,o Fi

AH1, AH2 kl, k2, k~ k0,i

K l L Pi P ri

r*

rCzH z

rCzH 6 R Ra

R o

Ro S T AT V Vp Yi

NOTATION

activity profile function heat capacity of reacting gas effective diffusion coefficient of component i activation energy front-end hydrogen-acetylene ratio molar flow rate of component i heat of reaction reaction rate constants mass transfer coefficient of component i adsorption equilibrium coefficient position in reactor length of reactor partial pressure of component i total pressure reaction rate of component i for heterogeneous model reaction rate of component i for pseudohomogeneous model reaction rate defined by eq. (3) reaction rate defined by eq. (4) radial position in catalyst particle radius of pellet on board inactive core-active shell gas constant radius of catalyst pellet selectivity temperature change of temperature reactor volume catalyst pellet volume mole fraction of component i

155

change of mole fraction of component i dimensionless distance along the reactor

conversion of acetylene relative error porosity effectiveness factors

Subscripts 0 reactor inlet 1 hydrogenation of acetylene reaction 2 hydrogenation of ethylene reaction b bulk p pellet s pellet surface A acetylene B hydrogen C ethylene D ethane

REFERENCES

Doraiswamy, L. K. and Sharma, M. M. (1984) Hetero- geneous Reactions: Analysis, Examples and Reactor Design. Wiley, New York.

Fogler, H. (1992) Elements of Chemical Reaction Engineering, Prentice-Hall International, Inc. Englewood Cliffs, NJ.

Froment, G. F. and Bischoff, K. B. (1979) Chemical Reactor Analysis and Design. Wiley, New York.

Schbib, N. S., Garcia, M. A., Gigola, C. A. and Errazu, A. F. (1996) Kinetics of front-end acetylene hydrogenation in ethylene production. Ind. Engng Chem. Res. 35, 1496 1505.

Szarawara, J., Skrzypek J. and Gawdzik, A. (1991) Podstawy In~ynierii Reaktorbw Chemicznych. WNT.

Szukiewicz, M. (1995) Ph. D. thesis. Cracow Technical University, Poland.

Szukiewicz, M., Kaczmarski, K., Petrus, R. and Got~biowski, A. (1994) Selective hydrogenation of acetylene. Mathematical analysis. In~. Chem. I Procesowa 3, 481-489.

acethylene fixed bed reactor reaction constants are not clear

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