Study of the mechanism and kinetics of poisoning phenomena in a diffusion-influenced single catalyst pellet

Chemical Engineering Science, 1973, Vol. 28, pp. 69-82.

Pergmon

Press.

Printed in Great Britain

Study of the mechanism and kinetics of poisoning phenomena in a diffusion-influenced single catalyst pellet L. L. HEGEDUSt and E. E. PETERSEN Department of Chemical Engineering, University of California, Berkeley, California 94720, U.S.A. (Received 6 December 1971; accepted 9 March 1972) Abstract-The decay of catalyst activity in a diffusion-influenced isothermal single catalyst pellet is characterized by idealized mathematical models. Impurity poisoning, parallel self-poisoning, series self-poisoning, and triangular self-poisoning mechanisms are considered with general nonlinear kinetics in the first three cases and with fust order kinetics in the latter one. For first order main reactions, numerical solutions of the arising conservation equations were carried out, revealing that relative reaction rates plotted vs. a normalized center-plane concenttation allow qualitative discrimination among the postulated poisoning mechanisms. A maximum of three experiments are necessary for this purpose. For the selected mechanism, plots of the dimensionless center-plane concentration vs. a time variable allow quantitative evaluation of the. model parameters.

INTRODUCTION

of intraparticle mass transfer resistance on impurity (independent) poisoning and parallelself-poisoning mechanisms. and series-type Effectiveness factors were developed by those authors for single isothermal catalyst pellets with first-order main reaction and first-order poisoning reaction kinetics. Balder and Petersen[S] expressed the relative rate of a fist-order simple isothermal reaction in a single catalyst pellet in terms of the dimensionless center-plane concentration, which eliminated time as a primary variable. The dimensionless center-plane concentration was directly measured using a single-pellet diffusion reactor. This technique allowed the experimental discrimination between uniform and pore-mouth poisoning in a diffusion-influenced catalyst pellet. Chu[6] has extended the series, parallel and impurity (independent) poisoning mechanisms to Langmuir-Hinshelwood rate expressions. Although such rate equations are inherently more flexible than simple power-law kinetic equations, they are often impractical due to the difficulty of evaluating their numerous parameters. Parallel and series fist-order self-poisoning mechanisms in the diffusion-influenced region were considered by Murakami et al. [7]. Their

TIMEscale of the decay of catalyst activity is a dominant variable in the design and operation of industrial reactors. To provide design data on this variable, empirical catalyst aging studies are required. Such studies are expensive, particularly when they span many months, and accordingly, there is a significant interest in mathematical models combined with suitable experimental techniques which could predict accurately the long-term activity behavior of a catalyst. The importance of diffusion effects on catalyst poisoning was recognized some time ago. Wheeler[i, 21 considered the influence of intraparticle mass transfer on the rate of a chemical reaction at various poisoning mechanisms. He presented analytical solutions for the limiting cases of uniform poisoning (non-selective or homogeneous poisoning) and pore-mouth poisoning (selective poisoning) of a first-order reaction. Wheeler eliminated time as the reaction variable and replaced it by the fraction of surface poisoned, The dynamics of the fraction of surface poisoned by a pore-mouth type mechanism was treated mathematically by Carberry and Got-ring

THE

r31. Masamune and Smith [4] investigated the effect

tPresent address: Research Laboratories, General Motors Technical Center, Warren, Michigan, 48090, U.S.A.

69

L. L. HEGEDUS

and E. E. PETERSEN

treatment is an extension of the work of Masamune and Smith in the sense that they allowed for a rapid deterioration of the catalyst activity, so that the time scale of the poisoning became comparable to the time scale of the main reaction and of the transport processes in the pellet. In addition, Murakami et al. present an experimental demonstration of the predicted poison distribution (coking) in the catalyst pellet. Hahn and Petersen[8] used a modification of the single-pellet reactor to experimentally demonstrate the breakthrough of a poisoning wave across a single catalyst pellet. Using a valve arrangement which permitted reactants to pass by either face of the catalyst pellet, they were able to show that poisoning took place nonuniformly through the pellet. Balder and Petersen’s experimental data in the single-pellet reactor were used more recently by Dougharty[9] to evaluate the parameters of a parallel self-poisoning model. Dougharty reemphasized that time as a primary variable can be conveniently eliminated using the singlepellet reactor. This method was, however, not sensitive enough to discriminate unequivocally among some of the parameters he postulated and so he resorted to bulk rate vs. time plots in an attempt to differentiate between two kinetic poisoning situations. It is the aim of this paper to show that the single-pellet reactor is ideally suited to discriminate among impurity poisoning, parallel self-poisoning, series self-poisoning and .triangular self-poisoning, and to quantitatively evaluate the model parameters involved. Only a limited number of experiments is required for this purpose. DEVELOPMENT AND NUMERICAL SOLUTION OF THE POISONING MODELS

In this paper catalyst poisoning phenomena will be considered to involve the irreversible chemisorption of some species on the active sites of the catalyst, thus rendering it inactive. The chemical species which causes the loss of catalyst activity can be either an impurity contained by the feed, or side reactions with the

reactants or products themselves can form a poisonous structure on the catalytic surface. Accordingly, two basic classes will be distinguished: impurity-poisoning and selfpoisoning. If one or more of the reactants act as poison precursors, the poisoning reaction is parallel to the main reaction and will be referred to as parallel self-poisoning. Similarly, if one or more of the reaction products act as precursors of the poisonous reaction is sequential to the main reaction and will be called series self-poisoning. The simultaneous occurrence of parahel and series self-poisoning will be designated as triangular self-poisoning. The main reaction considered is a simple, isothermal, first-order reaction, occurring in the pores of an infinite flat porous slab of finite thickness. This geometry corresponds closely to the geometry of the single-pellet reactor which is suited for the center-plane concentration measurements[5,10,12,13]. Modifications of this study to include nonlinear main reactions and other pellet geometries involve minor changes, leaving the essential features of the poisoning behavior unaltered. The consumption of reactants and products by the poisoning reaction is generally very small compared to the amount processed by the main reaction. For this work the consumption will be assumed to be identically zero. Furthermore, the time scale of the poisoning process is frequently very much larger than the time scale of the main reaction. To the extent that this observation is true, then, the main reaction is at quasisteady state. Lastly, it is assumed that the effective diffusivity is uniform throughout the pellet and remains unaffected by the poisoning processing process and that the initial activity is uniformly distributed in the pellet. Impurity poisoning

The chemically reactive system is characterized by A-B 7'0

Study of the mechanism and kinetics of poisoning phenomena

PAW.

+=z,

Here A is the reactant, B is the product, P is the poison precursor and W is the poisonous structure blocking the catalyst’s surface. If only one type of catalytically active site is present, the conservation of species A, P and W can be described by the following set of equations. The geometry of the pellet is depicted in Fig. 1. 52

a-k,(a,-ap)c,= ot

A ai8

where Aw is the surface area rendered inactive by 1 mole of the poison W. The fraction of the originally active surface which remains unpoisoned at time t is (4) Equations (l)-(3) can now be made dimension-

(1) less by

Here LStis the effective diffisivity of species i in porous solid (cm%ec), C~is its concentration (gmole/cm3), x is a distance variable (cm) from the outer surface of the pellet towards its center, k is a heterogeneous rate constant [ l/(cm2 set)], (Yand 6 are the kinetic orders characterizing the poisoning reaction, t is the time, and a, is the initial active surface area (cm2/cm3of pellet). The kinetic reaction orders are assumed to be independent of temperature. CAand cp are interpreted as moles/(cm3 pore volume), while cw has the dimension of moles/(cm3 pellet volume), since it describes the concentration of the adsorbed species on the surface. cw can be related to the originally active surface area rendered inactive by W:

$A(T,r))

=$+,7

JIP(T,r))

=*

the

Fig. 1. Geometry of a flat catalyst slab in tbe singe-pellet reactor.

dimensionless reactant concentration , dimensionless poison precursor concentration

,

r) = f, dimensionless distance variable. For CA@,

0) =

CA0

CP(O, 0) = CPO we

have initial Thiele parameter of the main reaction

h, = LJT,

initial Thiele parameter of the poisoning reaction,

With these dimensionless variables and the corresponding dimensionless boundary conditions the problem becomes

?SticaY speaking, the area term in Eq. (1) should be raised to the mth power, to read (~,-a~)~. For simplicity, we assume m equal to unity in this treatment.

%-

71

h12wA = 0

(5)

L. L. HEGEDUS

q) = (/&IA(() 7

and E. E. PETERSEN

These will be discussed in more detail later in the paper. As poisoning progresses, the reactant and poison will be more and more evenly distributed in the pellet. Close to complete poisoning, a kinetically limited main reaction with uniform poisoning is predicted by the equations.

cosh[(1-71)hl cash (h,)

Parallel self-poisoning

The simplest case of such a process might be depicted as Ak’-B A kn

w.

With similar assumptions as in the previous case, the process can be characterized by a set of partial differential equations containing dimensionless variables:

For various values of hl, he, (Yand S, the above system was solved numerically on a CDC 6400 computer. The numerical technique applied Newman’s method [ 1 l] to treat simultaneous nonlinear ordinary differential equations by linearization around a trial solution, matrix inversion and iteration. The partial differential equations were treated by stepwise progression and trapezoidal integration in the time domain. The technique is flexible to the nonlinearity parameters (Yand 6 in the applied range. For a first-order main reaction, the interaction between the kinetic and diffusion rate processes is most important for the Thiele parameter region between 1 and 5. Accordingly, the equations were solved for h, = 2.5. hz G 1 represents the situation when the poisoning process is controlled by its kinetic rate, corresponding to Wheeler’s ideal case of uniform poisoning. If h, S 5, a poisoning wave progresses through the pellet, from its outer surface toward its center. This situation approximates Wheeler’s ideal case of pore-mouth poisoning. The numerical solutions also reveal that h, = 0.1 approximates uniform poisoning fairly closely, while h = 10 is not large enough for the poisoning to be essentially pore-mouth (all for h, = 2.5).

(9)

For constant bulk reactant concentration the dimensionless time becomes 7 = t{/G_ao~-lcff~w}.

cAo, (10)

Deleting &, the initial and boundary conditions are the same as for the impurity poisoning model. The problem was solved numerically in a way similar to the impurity poisoning model, and again, h, = 2.5 was selected for the illustration. For the case of impurity poisoning the poisoning process was independent of the main reaction, whereas for self-poisoning models the poisoning processes are strongly coupled to the main reaction. In fact, if h, is very small, one observes uniform poisoning. If h, is very large, the poison will initially progress in a sharp wave. For intermediate values of h, (such as 2*5), the poisoning mechanism will be initially between the two extreme cases. 72

Study of the mechanism and kinetics of poisoning phenomena

Series self-poisoning

product B has a tendency to accumulate close to the center of the pellet. Reacting there with the surface, it builds a poisoning front which moves from the pellet’s core towards its outer surface. For first-order mechanisms, this was first predicted by Masamune and Smith[4], and was experimentally demonstrated by Murakami et al. [7] on a consecutively coked catalyst pellet. The idealization of this process results in the limiting case of core poisoning (Appendix).

The simplest example of the situation where the reaction product acts as the poison precursor can be represented by the mechanism AK’-B B -%

W.

Making similar assumptions as in the two previous cases, the following set of partial differential equations will describe the problem:

Triangular self-poisoning series self-poisoning)

(11)

(combinedparallel

and

One can simultaneously allow for parallel and series self-poisoning, resulting in

(12) The normalization of c, was carried out with respect to c,:

dJB(T, rl) =

$+$. 1

For the case of series self-poisoning with constant bulk reactant concentration [C, (t, 0) = cAO= constant], the dimensionless time has the same expression as for parallel self-poisoning. 1, which is equivalent to no mole If $A++B = number change upon conversion and zero product concentration in the feed, I,!J~can be replaced by (1 - $A) in the conservation equations. This results in Eq. (11) and

Taking the case of simple irreversible first-order reactions and neglecting the amount of A and-B consumed by the poisoning proces,ses results in

k2(ao-ap)cA+

k3(ao-ap)cB =

2,

(15)

with initial and boundary conditions similar to the previous models. Introducing the nondimensional variables discussed earlier and $A++B=%

(16)

one obtains

The initial and boundary conditions are the same as for the parallel self-poisoning model. The numerical problem was solved for h, = 2.5. Along with the solutions of the previous models, the numerical results will be discussed later on. The series self-poisoning model bears some interesting qualitative features, which result from the coupling of the poisoning process to the main reaction. If the main reaction is affected by diffusion,

$$- h12tqA = 0

initial and boundary conditions as for the other two self-poisoning models. It is now interesting to show that the triangular with

73

the same

L. L. HEGEDUS

and E. E. PETERSEN

poisoning model contains the parallel and series self-poisoning models as special cases. If k,/k, -G 1, parallel self-poisoning prevails, while if k,/ k2 S 1, series self-poisoning prevails. For k3 = k2, both mechanisms can be equally important in the poisoning of the catalyst pellet. Using the same approach as for the previous models, numerical solutions were carried out for h, = 2.5 and for various values of k,/k,. The results and implications of these solutions will be discussed later in this paper. Impurity poisoning, parallel, series, and triangular self-poisoning are idealized poisoning schemes. In practice more complicated schemes are of course possible. Quite frequently, however, they can be represented by idealized schemes such as those discussed here.

SELF-POISONING h,=2.5

s\ 0.5 a

Fig. 3. Relative rate vs. normalized center-plane concentration for parallel self-poisoning.

QUALITATIVE DISCRIMINATION AMONG THE POISONING MODELS

Before attempting to evaluate any of the model parameters, the qualitative identification of the poisoning mechanism is of primary importance. With the help of the numerical solutions to the individual models, it will be shown that the discrimination is possible using the single-pellet reactor. Figures 2-5 display the dependence of the IMPURITY

PARALLEL

SERIES SELF-POISONING h, =2.5

POISONING

ItAc~,Ibqo,l) I-

*A(o,l)

Fig. 4. Relative rate vs. normalized center-plane concentration for series self-poisoning.

relative reaction rate R/R0 on the normalized center-plane concentration 0.5 ~*(T,I,-y&o,I,

JIA(T,1) -+A@, 1) l-qh(O, 1) -

I.0

I-Jl,to,l,

For the limiting cases of pore-mouth poisoning, uniform poisoning and core poisoning with

Fig. 2. Relative rate vs. normalized center-plane concentration for impurity poisoning.

74

Study of the mechanism and kinetics of poisoning phenomena TRIANGULAR

0

0

OUALITATIVE DlSCRlYlNATlON BETWEEN POISONING MODELS II,= 2.5

SELF- POISONING h, =2.S

0.5 JIA(r,I,-J;ro.l)

I.0

I-eA(o,l,

Fig. 5. Relative rate vs. normalized center-plane concentration for triangular self-poisoning (first order kinetics). o = 1.

Fig. 6. Qualitative discrimination between poisoning models.

first-order reactions, simple analytical solutions are obtainable. The first two cases were calculated by Balder and Petersen[S]. The remaining case of a sharp poisoning front moving backwards, from the center of the catalyst pellet towards its outer surface (core poisoning), is developed in the Appendix of this paper. The numerical solutions for the individual poisoning models with various poisoning kinetics fall between the boundaries of the limiting curves. Figures 3 and 4 reveal that the solutions for the parallel and series self-poisoning models are confined to relatively narrow bands, designated by numbers 2 and 5 in Fig. 6. Figure 2 shows that regions 1, 2 and 3 (in Fig. 6) are available for impurity poisoning, and Fig. 5 reveals that the triangular self-poisoning curves are confined to regions 2-5 (o = 1). Region 6 is not accessible in any practical situation, except the hypothetical case of an impurity poisoning front progressing Corn the pellet’s center plane towards its outside boundary. Regions 6, 5 and 4 would be available for the dam resulting from such cases. The exact regions displayed on Fig. 6 depend upon a value of h, = 2.5. Decreasing h1 will

cause the regions to move toward the diagonal and as h, + 0 the regions will degenerate to a single line - the diagonal, Analogously, increasing h, causes the uniform poisoning curve to move downward and away from the diagonal. The pore-mouth and core poisoning curves also move away from the diagonal to coincide with boundaries of the plot as h1 + a~. In principle, then, the range of usefulness of the technique depends upon the accuracy with which the center-plane concentrations can be measured. As a practical guide, values of h, between 1 and 5 are useful. This restriction does not limit the applicability of this technique as much as one might think at first because one can vary the activity of the catalyst by dilution with inert solid, vary the effective ditl?usivity by the pelleting pressure, vary the thickness of the pellet, in addition to varying the temperature in order to adjust the numerical magnitude of the Thiele parameter. The authors have been able to design numerous experiments wherein the values of the Thiele parameter were in the range of l-5. These experiments, using the reaction of hydrogen and cyclopropane on platinum-~-alumina catalyst, will be described in a forthcoming paper on the application of this technique. 75

L. L. HEGEDUS

and E. E. PETERSEN

The qualitative discrimination between the postulated poisoning mechanisms will now be discussed in terms of Fig. 6 and the numerical solutions for the individual mechanisms (Figs. 2-5). Data in region 1 can be clearly identified as impurity poisoning. Similarly, data in region 4 can be due to triangular self-poisoning. Coincidence is observed in region 2 between parallel self-poisoning, triangular self-poisoning, and impurity poisoning; in region 3 between triangular self-poisoning and impurity poisoning; and in region 5 between series self-poisoning and triangular self-poisoning models. Fortunately, these coincidences can be resolved by a maximum of two additional experiments as described below. Before the second experiment, data from the first experiment are fitted to a parallel self-poisoning model (region 2) or a series selfpoisoning model (region S), and the corresponding values of (Yand 6 are evaluated. The second experiment will be carried out at a different (say, higher) temperature, whereby the Thiele parameters for the main reaction and the poisoning reaction increase. An attempt is then made to fit the data of the second experiment using the same self-poisoning mechanism as previously, changing only h1 to its new value, while maintaining the previous values of (Yand 6. If the fit is unsuccessful, the possibility of parallel selfpoisoning in region 2, or analogously, the possibility of series self-poisoning in region 5, is eliminated. The remaining possibilities are impurity poisoning or triangular self-poisoning in regions 2 and 3, or triangular self-poisoning in region 5. The existence of a triangular selfpoisoning mechanism can now be verified or eliminated by a third experiment. The third experiment should be carried out at a bulk product concentration which is different (say, higher) from what was applied for the previous two experiments. The temperature and the reactant bulk concentration should remain unchanged. If triangular self-poisoning prevails, upon increasing the bulk product concentration the data should shift into the direction of series

self-poisoning (upwards). The third experiment discriminates between impurity and triangular self-poisoning mechanisms in regions 2 and 3, and verifies triangular self-poisoning in region 5. This third experiment is also helpful to distinguish parallel and series self-poisoning from triangular self-poisoning in cases where E3 = E,, so that temperature changes don’t affect the position of the data with respect to the reference line. In summary, a maximum of three experiments with the single-pellet reactor are expected to result in the qualitative discrimination among impurity poisoning, parallel self-poisoning, series self-poisoning, and triangular self-poisoning mechanisms. One interesting implication of Fig. 6 is that while h, and h, are completely independent for impurity poisoning, the distribution of the poisoned surface is a strong function of the reactant distribution (h,) in the case of the selfpoisoning models. For example, it is not possible to obtain either uniform or pore-mouth poisoning in a self-poisoning process with intermediate values of hl, such as 2.5 in our example. Another interesting observation is that it is not always necessary to have uniform poison precursor distribution in the catalyst pellet in order to achieve uniform poisoning. For the triangular model, kJk, = 1 results in uniform poisoning for any value of hl, as shown in Fig. 5. QUANTITATIVE MODEL

EVALUATION PARAMETERS

OF THE

While in principle obtaining the kinetic parameters should be possible from any of the plots, in practice these plots are not equally sensitive to the kinetic parameters. For example, it has been shown herein that plots of R/R0 vs. the normalized center-plane concentration have unique advantages to discriminate among postulated poisoning mechanisms. However, they are less suitable for quantitiative purposes than the more traditional R/R0 vs. time plots. As Figs. 7-10 demonstrate, the time behavior of the center-plane concentration is quite sensi-

76

Study of the mechanism and kinetics of poisoning phenomena IMPURITY

I

Oo

PARALLEL

POISONING

I

I

I

I

I

I

I

I

2

3

4 T

5

6

7

0

Fig. 7. Dimensionless center-plane concentration vs. dimensionless time for impurity poisoning, h, = 0.1 and 2.5.

1

'0

,MPURlTY h,s2,5; I

I

Oo

I

I

I

I

I

I

I

I

2

3

4

5

6

7

8

z

Fig. 9. Dimensionless center-plane concentration vs. dimensionless time for parallel self-poisoning.

POISONING h2-IO0 I

I

I

I

SELF-POISONING h, =2.5

1

I

I

I

I

I

I

10

20

30

40 r

50

60

70

00

Fig. 8. Dimensionless center-plane concentration vs. dimensionless time for impurity poisoning, h, = 10.

tive to LYto 6 and so it allows their quantitative evaluation. Similarly, Fig. 11 demonstrates the sensitivity of the time behavior of the centerplane concentration to kJk, in the case of triangular poisoning with first order kinetics. These plots also appear to be sensitive to the functional form of the poisoning kinetics. In this case parameter evaluation depends upon how well the real system can be approximated by the simple kinetic expressions such as those of Eqs. (6), (9), (13) or (18). Before the evaluation of (Yand 6 is attempted, however, the value of h1 has to be determined from the initial bulk rate and center-plane concentration measurements (10,12,13) of any poisoning experiment. The reader is reminded at this point that the kinetic order of the main reaction has to be known (for this paper, it was assumed to be one). The kinetic reaction order can be determined using the single-pellet reactor, as explained by Balder [ 121. The numerical 77

L. L. HEGEDUS SERIES

and E. E. PETERSEN TRIANGULAR

S~L~~~OISONING

SELF-POISONING

‘.“l--+---

Oo

I

2

3

4

5

6

7

00 I

6

3

4

5

6

7

8

T

Fig. 11. Dimensionless center-plane concentration vs. dimensionless time for triangular self-poisoning (first order kinetics) 0J= 1.

Fig. 10. Dimensionless center-plane concentration vs. dimensionless time for series self-poisoning.

solutions will then be carried out for this measured value of hl, to compare the calculated results with the measured data. The comparison yields in the values of the model parameters. In the case of impurity poisoning, preliminary knowledge of h, is also necessary, in addition to hl. However, as with hl, h, can also be determined from the initial section of the data taken during the poisoning experiment in the singlepellet reactor, if 6 is known and if the poison’s concentration is measured in the bulk and at the pellet’s center plane. If 6 is unknown, it can be determined in two experiments, carried out at two distinct bulk poison concentrations, by the same method as described by Balder to determine the order of the main reaction [ 121. Numerical solutions with hl, h2 and S at various values of (Ycan now be compared with the experimentally measured data to find the time constant

2

{k.$pc&&7}

=

1BptzGdw}

(19)

and CX. According to this treatment, for complete characterization of the impurity poisoning process, the poison’s identity and its concentration at the pellet’s center surface and at its center plane must be known. For the cases h, 4 1 and h, + 5, however, the limiting models of uniform poisoning and pore-mouth poisoning apply. For those cases, which can be recognized from center-plane concentration data [5, 101, it is not necessary to know the poison or to measure its concentration. Figures 7 and 8 show numerical solutions for I/J~(T,1) vs. 7, depending on various values of h2, a and S. h, is kept constant at 2.5. The dimensionless time on these figures can be converted into real time by observing that 7 - th,‘. 78

Study of the mechanism and kinetics of poisoning phenomena

The evaluation of the model parameters is main reaction was plotted vs. the dimensionless simpler for parallel and series self-poisoning time in Figs. 12-16. These plots represent the mechanisms, because hi does not appear. A information available from conventional poisoncomparison of the measured center-plane con- ing studies, where only the bulk concentration centrations in real time against the calculated is measured as a function of time at the bulk gas curves for various values of (Yand 8 in dimension- phase, and where the overall reaction rate is less time (Figs. 9 and 10) results in the straight- then evaluated from the first time derivative of forward evaluation of (Y,6 and [~+z,,“-~A WciJ. the bulk concentrations. In the case of triangular self-poisoning, if all As it was explained earlier, relative rate vs. reactions involved are of first order, only two time plots are less useful than plots involving parameters (h, and kJk,) appear. center-plane concentrations, when the mechanComparing the numerical solutions (Fig. 11) ism and kinetics of the poisoning process is to be for the dimensionless center-plane concentra- elucidated. However, these plots give a simple tion vs. the dimensionless time with the measured visualization of the deactivation process and are center-plane concentrations vs. real time enables often of value for design purposes and to study one to evaluate k,/k,,and [ kzcA,J w]. the kinetics of simple deactivation phenomena with known mechanism. EFFECT OF MECHANISM AND KINETICS OF POISONING PROCESS ON OVERALL RATE OF MAIN REACTION

CONCLUSIONS

The effect of the mechanism and kinetics of the poisoning process on the overall rate of the

The mechanism and kinetics of poisoning reactions in heterogeneous catalyst pellets can

IMPURITY POISONING h,=2.5; h2=010nd2.5 I

I

I

I

I

I

I.01

I

Fig. 12. Relative overall rate vs. dimensionless time for impurity poisoning, h2 = 0.1 and 25.

IMPURITY FOISONING h,*2.5;~*00 I

I

I

I

I

I

I

Fig. 13. Relative overall rate k. dimensionless time for impurity poisoning, hz = 10.

79

L. L. HEGEDUS

PARALLEL SELF-POISONING h, -2.5 1 I 1 ,

1

and E. E. PETERSEN

TRIANGULA; I

,

,

\

\

2

3

S;E&F-POISONING aI 1 \

,

I

I

Fig. 14. Relative overall rate vs. dimensionless time for parallel self-poisoning.

I

‘0

I

I

I

2.3

I

I

I

I

I

I

4 T

5

6

7

0

4 z

5

6

7

3

Fig. 16. Relative rate vs. dimensionless time for triangular self-poisoning (first order kinetics). o = 1.

be sensitively studied in the diffusion-influenced region, where they have a pronounced effect on the center-plane concentration. For first order main reactions, this range is between about h, = 1 and 5. Mathematical models were constructed describing the poisoning of a single catalyst pellet by four different poisoning mechanisms. Numerical solutions indicate that the models can be discriminated using dimensionless plots of overall reaction rates vs. a normalized centerplane concentration. The formulation of the models also allows qualitative insight into the poisoning process. For the quantitative evaluation of the kinetic exponents and of the time scale of the poisoning process, dimensionless center-plane concentration vs. time plots are useful. Center-plane concentrations, in addition to concentrations at the catalyst pellet’s outer surface, can be measured in a single-pellet diffusion reactor. The results of the numerical solutions pre-

Fig. 15. Relative rate vs. dimensionless time for series selfpoisoning.

80

Study of the mechanism and kinetics of poisoning phenomena

E 8 F

sented in this paper indicate that fewer experiments are required to determine the mechanism and kinetics of poisoning using this method than traditional methods. This could be advantageous especially in long-term deactivation studies.

h k L P

Acknowledgements-Financial support for this work was provided in part by a grant Born the National Science Foundation. Discussions with Professor J. Newman about the computer technique used in this paper are gratefully acknowledged.

g go

t NOTATION a0

ap A

AW B Ci#W

CW CiO

x

catalytically active initial surface area, cm2/cm3pellet poisoned surface area, cm2/cm3pellet reactant surface area rendered inactive by 1 mole of W, cm2 product concentration of species i, mole/cm3 concentration of W, mole/cm3 pellet concentration of species i at the pellet’s surface at zero time effective diffisivity of species i, cm2/sec

W

energy of activation, kcal/mole effectiveness factor total pellet cross section, cm2 Thiele parameter, see text rate constant, heterogeneous thickness of the catalyst pellet poison precursor overall reaction rate, = E(t) k(a, - up) cA (t, O)FL, molelsec overall reaction rate at zero time time, set distance coordinate, cm poison

Greek symbols

a, 6 exponents of the poisoning rate expression 7) dimensionless distance e fraction of catalytic surface area remaining unpoisoned dimensionless time ; fraction of catalytic surface area poisoned & dimensionless concentration of species i w = $A+& - proportionality

REFERENCES [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll]

WHEELER A., Adu. Cad. 1950 III 250. WHEELER A., Catalysis II, p. 105. Reinhold 1955. CARBERRY J. J. and GORRING R. L.,J. Catul. 1966 5 529. MASAMUNE S. and SMITH J. M., A.I.Ch.E. Jl1%6 12 384. BALDER J. R. and PETERSEN E. E., Chem. Engng Sci. 1968 23 1287. CHU C., Ind. Engng Chem. Fundls 1968 7 509. MURAKAMI Y., KOBAYASHI T., HATTORI T. and MASUDA M., Ind. Engng Gem. Fund/s 1968 7 599. HAHN J. L. and PETERSEN E. E., CunJ. Gem. Engng 197048 147. DOUGHARTY N. A., Chem. Engng Sci. 1970 25 489. HEGEDUS L. L. and PETERSEN E. E., Ind. Engng Chem. Fundls in press, 1972. NEWMAN J., Ind. Engng Chem. Fund& 1968 7 514; UC Berekeley, Lawrence Radiation Laboratory Report No. UCRL-17739 1967. [ 121 BALDER J. R., Thesis, University of California, Berkeley 1967. [13] BALDER J. R. and PETERSEN E. E., J. Cutul. 1968 11202.

APPENDIX

as a(O) = Fa&,c,(O, O)$(O)L

CORE POISONING OF A FIRST-ORDER REACTION IN A FLAT CATALYST SLAB The limiting case of a sharp poisoning wave progressing Born the center of a catalyst pellet towards its outer surface (core poisoning) is considered here for the first-order, irreversible, isothermal, simple chemical reaction

s’(t) = Fu&,(t,

(A-2)

(A-3) and (A-4)

natedby

81

CES Vol. 28, No. 1-F

0)$(t) (1 -+)L.

The corresponding Thiele parameters become

A + B. If the 6-action of the catalyst’s surface poisoned is desig$J, the rate of the overall reaction can be expressed

(A-l)

and

L. L. HEGEDUS and E. E. PETERSEN The effectiveness factors are, then: “(” 8(O) = tanh h,(O) IP(t)

=

(A-5)

tanh [(l--dh(O)l

(A-6)

Cl-4hW The relative rate becomes

‘) =cosh [lb,(O),’

r,nd

JIA(fr ‘) =cash [(l&z,(O)]* Plotting %?(r)/MO) vs.

Wd -=

tanh [(I-+)h,(O)l

a(o)

ti[h,(O)l

’

(A-7)

The center plane concentration is

hk

1)-&(O, 1) 1-JIA(O,1)

results in the limiting curve for core poisoning (Fig. 6).

82

(A-g)

(A-9)