I
R. B. ANDERSON and A. M. WHITEHOUSE Pittsburgh Coal Research Center, U. S. Bureau of Mines, Pittsburgh, Pa.
Poisoning in Fixed Beds of Catalysts The effect of distribution of poison along the catalyst bed is examined for a number of poisoning equations phenomena relating to A poisoning within a given particle of catalyst has been considered extenLTHOUGH
sively in the literature (3, 5-70), the net effect of poisoning in fixed beds where the concentration of poison is not uniform has not been given much consideration (3, 8 ) . Pertinent early work on poisoning has been reviewed by Taylor (9). The article considers poisoning in fixed catalyst beds for several types of poison concentration gradients along bed length and several functions relating activity to poison concentration. Poison concentration in all cases refers to quantity of poison adsorbed on catalyst per unit weight or unit surface area of catalyst, and not to poison concentrations in the reactant-product stream. This article is not concerned with phenomena within the catalyst particle but with the integrated effect of poisoning in a given increment of the bed a n d the distribution of poison along the bed on the average activity of a fixed bed of catalyst. Relative activity, F, the ratio of the activity of the poisoned to the corresponding unpoisoned catalyst, is a useful quantity for expressing activity. Activity should be expressed as a rate constant of a fundamental or empirical kinetic equation, or other rational expressions, such as space velocity or spacetime yield a t constant conversion with feed composition, temperature, and pressure held constant. With the exception of zero order processes and systems in which the conversion is maintained very low, conversion a t constant operating conditions is unsatisfactory as a linear measure of activity. A number of equations for expressing activity as a function of poison concentration have been derived for individual particles or uniformly poisoned catalysts. For prepoisoned metal catalysts in liquid phase hydrogenations, the activity decreased linearly with increasing poison concentration, until most of the activity was lost (6). Russian workers have predicted an exponential decrease in activity with increasing poison concentration ( 5 ) , and this relationship was observed for nickel oxide-asbestos prepoisoned with boric acid in the
oxidation of octane (7). Wheeler developed fundamental rate equations for poisoning of porous catalysts (70). Three of his equations are considered: F = 1 aS; F = (1 as)-];and F = (1 US)'/^, where S is the concentration of poison on the catalyst and a is a constant. Wheeler’s equations were expressed in terms of fraction of surface covered by poison, which differs from the present form by a constant.
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Distribution Effect of Activity
Poison
on
In most poisoning studies the poison is introduced with the feed, and the average activity of the catalyst bed is determined as a function of average poison concentration. The average relative activity, F,is given by
S S S
= [&(I
+f’)l/z (forf’
0)
- ff)!/ln(l/ff) = solf’/(l- f’)! In ( l / f f ) =
(10)
(11) (12)
Nine combinations of poisoning and distribution equations were evaluated, and a qualitative characterization of each case is given below:
Case
I I1 I11 IV V VI VI1 VI11
IX
PYf
Effectiveness of Poison in an Increment of Bed Moderate t o very strong Moderatea Stron& Stron$ Very stronge Very .stronge Very strongE Strongb Weak0
Tendency of Poison t o Accumulate near Inlet Very strong Independent of distribution Very strongC Strongd Very strongc Strongd Very strong’ Very strong’ Very strongn
and the average poison concentration, by
s,
where x is the distance from inlet of bed, x’ is the bed length, and Fz and S, are the relative activity and poison concentration, respectively, at position x in the bed. In subsequent equations the prime will be omitted as all integrations are made over the entire length of bed. Usually, S, is expressed as S, = Sof, where SO is the concentration of poison on the catalyst a t the inlet, andfis a constant, 0 5 f 5 1. The variation of average relative activity with average poison concentration is examined for combinations of four poisoning equations with three concentration distribution equations. The relative activity equations are: Fz = 1 - US, (for QS, 6 1) (3) F,
=
exp( -as,)
Case I. Poison Is Strongly a n d Rapidly Adsorbed. In Figure l A , a t some point in the bed, the poison concentration decreases stepwise to zero, and F increases stepwise from 0 to 1. In Figure l B , the poison concentration decreases and the relative activity in-
I
A.
0
BED LENGTH
(4)
F, = (1 $-a&)-’
(5)
F, = (1 - Q S , ) ~ ’ ~ (for US, 5 1 ) ( 6 )
The poison concentration equations are: f = ( & / S O )= (1
f f
- bx)
= (&/SO) = e x p ( - b x ) = (S,/So)
=
(1
+ bx)-’
(for bx
1)
(7)
I
I
/
(8)
IIr//
(9)
where a and b are constants. The average poison concentrations in terms off’, the value off at the outlet of the bed, are then as follows for Equations 7, 8, and 9.
’9.
EED LENGTH
Figure 1 . Relative activity and poison Concentration as a function of bed length for Case I VOL. 53,
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DECEMBER 1961
101 1
b of the distribution equation) with SO constant. Condition ( 2 ) should approach the result obtained when a catalyst is poisoned by small constant concentrations of poison in the feed. Plots of 1 P as a function of USare useful, because they usually aeproach straight lines a t small values of as. The integral for P is usually simplified
-
by expressing it as ( l / x )
s1”‘
[F,/(df/dx)]
df,and for the present case,
1 - {In[(1
+ a S o ) / ( l + ~ S o f ’ )}]/In Vf‘ (16)
For small values off’, F = 1 - akS, where k = (l/uSo)ln(l u s o ) . Log-log plots of 1 - F as a function of USare shown in Figure 2A. Also plotted on this curve is Case 11, P = 1-aS. For condition ( y ) (f‘ = constant) the shape and position of the curves do not change appreciably over the range f = 1 to 0.09, but the curves move down and to the right a t a more rapid rate asf’ is decreased further. For condition ( z ) , f’ varied a t constant a&, the curves first increase linearly with a slope of 1 with increasing aSo according to the equation above, and finally flatten and traverse the zone given by condition (y) whenf exceeds 0.09. These curves terminate at US = a&, (f’= 1). Case 1V. Equations 5 and 9. Here the average relative activity is given by
+
a5
Figure 2.
Loss in average relative activity as a function of a$
- - -,Constant vaIues of f’. -,Constant values of aSo. creases, both linearly with bed length, over a distance 6. Both of these cases lead to
P=l-CcS
(13)
where a is the reciprocal of the concentration of poison required to decrease the activity to zero. I n Figure ll?, if 6 is small relative to the length of the bed, Equation 13 applies accurately for any equations for S, and F,. Case 11. Equation 3. Here,
F
( l / x ) K(1- aS,)dx =
=
1
+, End of solid curves
- (u/x)
1
S,dx = 1
- US
(14)
for distribution of poison concentration. Case 111. Equations 5 a n d 8 . For this and most other cases to be considered the average relative activity is not a unique function of average poison concentration except a t certain limiting conditions, such as f’ being small. I n general, P is a function of both S and f’. Two limiting cases are consideredaverage poison concentration varied by (y) varying $0 withf’ constant; or ( z ) varying f’ (by changing the value of constant
which, as f’ decreases to small values, slowly approaches F = 1 - a s . Again for condition (y), f’ constant, the curves vary little in position or shape as f’ is varied from 1 to 0.09 as shown in Figure 2B. For condition ( z ) , aSo constant, the curves increase almost linearly with low values of a& but with a slightly lower slope than unity. When values of f’ exceed 0.09 the curves traverse the zone shown for condition (y), and the curves terminate when a 3 = uSo, (f = 1). When the poison is distributed according tof = (1 b x ) - l , (Case IV), the poison for a given value of US is more effective than when distributed according to f = exp(-bx), (Case 111). Case V. Equations 4 a n d 8. The integral for average relative activity is
+
e x p l -OS,)
CasoXI F, = erpl-a S, .I -
0.2
0.1
0.4
0.6 0.8
1.0
2
aS
Figure 3.
f =
4
I
I
6
8
IO
-
Loss in average relative activity as a function of S
- - -,
V
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Case
.
), f =
with constant values of f.
-, Case V with aSo constant. -.-,
Case V I with as0 = 10
where Ei is the exponential integral, which must be evaluated numerically from tables ( 4 ) .
r l lh
Again for condition ( y ) (f’ constant) as shown in Figure 3, the values of (1 - F ) do not change greatly asf’ is decreased from 1 to 0.1. For condition ( z ) ,(aSo constant) and low values of a S , the curves have a slope of 1 but are displaced to the right from the curve for F = 1 - a S (Case 11). The curves flatten at higher values of US, eventually traverse the zone defined byf’ = 0.1 andf’ = 1 of condition (y), and terminate at US = aSo (f’ = 1 ) . Case VI. Equations 4 and 9. The integral for average relative activity is
- f’)l {(l/f’)exp( - Q S O ~ ’-) exp( -a&) aSo [Ez( -a&) - Ei( -aSaf’)] 1
uniform distribution of poison. The integral for average relative activity is nf’
In this case F can be expressed as a function of 3 F = 1 - UkS (25) where k = (2/aSo) X (1 - [I - exp( -QSo)l/USof (26) For bx < 1, 0 5 f’ Equation 9, and
F
= [I/aSo( 1
s
F
(22)
where Ei is the exponential integral. Only condition ( z ) with aSo = 10 was evaluated, and these values are plotted on Figure 3. Poisoning for Case V I a t given values of a 3 and a& is more severe than for Case V. see also previous comparison of Cases I11 and IV. Thus, the more gradual decline in poison conbx)-I discentration in the f = (1 tribution results in a greater loss in activity than when the poison is distributed exponentially. Case VII. Equations 4 a n d 7. For this and the next case the integrals must be arranged so that negative values of f are not permitted. When br exceeds L, that is when S, decreases to zero at some point in the catalyst bed, the integrals are evaluated as
+
- f’)][exp( -asof) -
F = 1 - QkS where k = ( ~ / Q SX J) [ 1 - ( l / U s O ) In (1 Forbx 1 is then given as
Lf’/(l
-( 1/ b x ) J ’ 1
1 , S is given by
exp( -aSo)]
=
Q S O ~ ’ )( 3 0 )
and 3 is given by Equation 9. The plots of these functions (Figure 4B) have similar characteristics to those of Case VII. Case IX. Equations 6 and 8. Only one case was evaluated using poisoning Equation 6, because the results do not differ very much from the case for
I
\, \
.6
4
-
Figure 4. Loss in average relative activity as a function of
-
IU
as
- - -,Constant values of f. -, Constant values of Case pm
Fx =(
ado. curves
t + a q P ; f= I.bx
+,
End of solid
Case
X
f = exp ( - b x )
b Figure 5. Average relative activity as a function of as
0.1
0.2
0.4
0.6 0.8 1.0
2
4
6
8 I C
Fx=(l-aS,I
.2
0
02
06
04
a9
08
10
9:
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increases with a&. The effectiveness of the poison increases with U S 0 for both cases. Again, poison distributed according to f = (1 b x ) - l is more effective than that distributed according to f = exp(-bx) at lower average concentrations of poison. At high concentrations the curves are identical. The activity remaining at S/S0 = 1 is the amount that persists after the poison concentration has reached So throughout the bed, where So is the concentration in equilibrium with the poison concentration of the feed. Figures 2 to 4 were plotted on log-log scales so that experimental plots of 1 F against S c a n be superimposed on them for determining the type of curves that are most appropriate and the values of constant a. With accurate experimental data it should be possible to find appropriate poisoning and distribution equations; however, if the experimental uncertainties are moderately large, as catalytic data frequently are, the selection of the most appropriate equations may be difficult. Distinguishing features are the point at which the decrease in F with increasing S deviates from linearity and the values of F a t high values of 3. A poisoning law of the type F, = (1 --aSz)’/2 changes only slightly with distribution of poison and could be recognized without difficulty. The nature of the relative activity function can be determined most directly by using uniformly prepoisoned catalysts. However, the prepoisoning must closely approximate poisoning that occurs during the catalytic reaction. In many cases this simulation may prove difficult.
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I.c
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1
I
1
I
I
I
0
2
4
6 os
8
10
Figure 6. Effectiveness of poison varies widely with i t s distribution of catalyst bed
-.-
--.f
= 1 - bx;--f = exp [ - b x ) ;
f = (1
-f
= 1
+ bx)-’i
and 5 from preferential poisoning of the most effective parts, and Equation 6 from preferential poisoning of the less effective parts. The average relative activity as a function of average poison concentration in a fixed bed of catalyst was evaluated for two limiting conditions-where the ratio of poison concentrations on the catalyst a t the outlet to the inlet of the bed, f’,remains constant, and the average concentration is increased by increasing the inlet concentration; and where the inlet concentration is constant and the average concentration is increased by increasing the value of constant f’. Condition (y) is probably encountered only infrequently; for example, when the rate of adsorption of poison is slow. The limiting case of f’ = 1 is approached by systems in which the concentration of poison approaches the equilibrium value throughout the bed in a short time, for example, when the poison is reversibly and weakly adsorbed, or when the poisoning results from a reversible reaction that is near equilibrium. An example of the latter is the poisoning of iron catalysts in ammonia synthesis by water vapor (I, 2 ) . For condition ( y ) whenf’ > 0.1, the curves are not greatly different from that for f’ = 1 except a t high values of aS. Forf’ = 1 the poisoning equation for the bed is identical with the equation for a n increment of the bed.
101 4
Figure 7. Relative activity i s dependent upon both the poisoning equation and the distribution of poison
Condition (2) approximates the phenomena usually encountered in poisoning by contaminants in the feed, where the poison is adsorbed, a t least moderately, strongly and rapidly. For low values of aS the equations often have the form F = 1 - ka3, where k is a function of aSo. I n all cases except IX, concentration of the poison near the inlet of the bed causes the plot of average activity against average poison content to approach a linear relationship more closely than the poisoning law operative in individual portions of the bed. Figure G compares linear plots of F against S for several cases under condition ( z ) for aSo = 10, with condition (y) for f’ = 1. For a given poison distribution function, the curves for F, = exp( r a S , ) decrease more rapidly with US than for F, = (1 For a given relative activity function, the poison increases in effectiveness with distribution function in the following order: f = 1 - bx, f = exp(-bbx), f = (1 and f = 1. This order is the reverse of the tendency of the poison to accumulate a t the inlet of the bed for these distribution functions. The length of the linear portions of the curves of Figure 6 also varies in the same manner, Figures 2, 3, 4, and 7 show that the length of the linear portion of the curves increases with increasing values of aSo. Figure 7 is a linear plot of P as a function of S/& for Cases I11 and IV and condition (2) using different values of a&. The effectiveness of the poison
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Literature Cited (1) Almquist, J. A., Black, C. A,, J. Am. Chem. Soc. 48, 2814 (1926). (2) Brunauer. S.. Emmett. P. H.. Zbid..
Rideal, E. K., 44).
les of Functions,” p. 5, Dover’ Publications, New York, 1945. (5) Kobozev, N. I., Acta Physicochim. >
,
U.R.S.S. 13, 469 (1940). (6) Maxted, E. B., “Advances in Catalysis.” Vol. 111, pp. 129-79, Academic Press, New York, 1951. f7\ Rozinskii. S. 2.. Element. N. I.. Izvest, Akud. Nauk S.S.S.R., Otdd. Khim: Nuuk 1951, p. 350. \
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(8) Russell, W. W., Gehring, L. G., J . Am. Chem. Soc. 57, 2544 (1935). (9) Taylor, H. S., in “Twelfth Catalysis
Report,” Chap. IV, Wiley, New York,
1940. ~. .. (10) Wheeler, A., “Advances in Catalysis,” Vol. 111, PF. 307-13, Academic Press, New York, 1951; “Catalysis,” Vol. 11, P. H. Emmett, editor,. pp. 151-58, Reinhold, New York, 1955.
RECEIVED for review January 5, 1961 ACCEPTED July 12, 1961 Present study is part of Federal Bureau of Mines’ research on coal-to-oil processes and is related to current studies of poisoning by sulfur compounds of Fischer-Tropsch catalvs ts.
