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Deactivation of a platinum reforming catalyst in a tubular reactor
Chemical Engineering Scknce. 1975, Vol. 30. pp. 789401.
Pcrgamon Press.
Printed in Great Britain
DEACTIVATION OF A PLATINUM REFORMING CATALYST IN A TUBULAR REACTOR R. P. DE PAUW and G. F. FROMENT Laboratorium voor Petrochemische Techniek Rijksuniversiteit, Gent, Belgium (Received 28 October 1914)
Abstract-This work concerns the methodology of characterizing the deactivation of a catalyst by coke deposition. The isomerization of npentane on a platinum reforming catalyst was studied in a tubular reactor permitting easy sampling of the gas phase at several positions in the reactor. Runs with high ratios of hydrogen to pentane did not show any deactivation and served to determine the kinetics of the main reaction and the principal side reaction, hydrocracking. At low ratios of hydrogen to pentane the catalyst was deactivated by carbonaceous deposits. At the end of the run the coke was determined in sections of the reactor and was found to be deposited according to a profile. Additional insight into the coking phenomenon was obtained from experiments on a thermohalance. A mathematical model for the performance of the tubular reactor subject to coking was set up and the parameters were determined from the experimental data. The parameters were found to be significantly determined and to obey the Arrhenius temperature dependence. The values of the parameters of the main reaction and of the hydrocracking side reaction which were derivedfrom the experimentsin the presence of coking were in agreement with those obtained from the runs in the absence of coking. 1. INTRODUCTION
Deactivation of catalysts by carbonaceous deposits is a phenomenon frequently encountered in the petroleum and petrochemical industry which has far reaching consequences. In recent years it has received increasing attention, as is evidenced by the rapidly growing number of papers dealing with this topic. A thorough review of the field has been presented by Butt [l]. The work reported here concerns the methodology of characterizing the coking of a catalyst in a tubular reactor, in view of its extrapolation to different conditions or to a different scale. It is based upon the idea that the correlation between the coke content of the catalyst and process time, often found in the literature[2-4], lacks generality. For this reason Froment and Bischoff related the coke content to the process variables such as partial pressures of the reactants and products, space time, etc. It follows from their work that even under isothermal conditions the carbon content of the bed is not uniform, but varies according to a profile which is characteristic for the mechanism giving rise to the carbon. Coke deposition by a mechanism parallel to the main reaction leads to a descending coke profile, deposition by a consecutive mechanism to an ascending profile. For two reasons the isomerization of pentane on a platinum reforming catalyst in the presence of hydrogen, lends itself particularly well to the aims of this work. First, for high ratios of hydrogen to pentane no deactivation is observed during the run lengths typical for laboratory practice, thus enabling the kinetic study of the isomerization (and of a secondary reaction: hydrocracking). #en the hydrogen/pentane ratio is lowered a rapid deactivation is observed, so that the coking can be studied in a reasonable amount of time and in a convenient way, making use of the known kinetic model for the main reaction. Without this uncoupling the problem of determining the kinetics of both the main and the coking reaction might well be inextricable and overwhelming in
its computational aspects. A second advantage of the system is the very low value of the heat of reaction, which permits isothermal operation, even with the relatively large amount of catalyst required by this type of experiments. The tubular reactor in which the experiments were performed received considerable attention and was designed to provide maximum information from one single run. For this purpose a sampling device which enabled easy sampling of the gas phase at several bed depths was built into the reactor. There is no such convenient way of following the increase of the coke content of the catalyst with time, however: the determination of the coke content requires unloading of the reactor and terminates the run. In addition, important information on the deactivation was obtained from experiments carried out in a thermobalance. 2. F.QUmMEN’r ANDEXPERIMENTAL PROCEDURE The experimental set-up, used already by Lambrecht et al. [5], is shown in Fig. 1. Figure 2 shows details of the
tubular reactor, which is made of chromium steel, free of nickel. The rings permit unloading clearly defined sections of the bed for determination of the carbon profile. Two very tightly fitting concentric tubes are axially located in the bed. The outer tube (e.d. 3.3 cm; i.d. 2.8 cm) is welded to the catalyst support ring and has six openings spaced at 10cm intervals. The inner tube can slide in the outer and has a hole near the bottom. This device permits sampling of the gas at six bed heights. In this way a conversion vs space time curve, as required for the kinetic analysis, may be determined in about half an hour and without having to vary the feed rate as is usually done. A thin thermocouple (Philips Thermocoax 21BAcl0, 1 mm dia.) is fixed to the inner sliding tube, so that its junction is located in front of the lowest opening. 789
CES Vol. 34, No. 8-B
R. P. DE PAUWand G. F. FROMENT
790
Fig. 1. The weight difference of the catalyst before and after combustion corresponds to the sum C+H t (Hz0adsorbed during manipulations). The first anhydron tube allows the determination of the sum of the amount of water adsorbed on the catalyst and that produced by the oxidation of the hydrogen. The ascarite tube adsorbs the CO*,but gives off water. This water is adsorbed in the third tube. The H/C ratio of the “coke” was found to increase from 0.65 to 4.6 as the temperature was decreased from 436 to 388°C. No dependence on the partial pressure was observed. It is hard to say whether the H/C-ratio variation really reflects the influence of the temperature at the moment of formation of the carbonaceous deposit or an effect of the prolonged stay at different temperatures, during which a gradual loss of hydrogen is possible. The coke was also extracted from the catalyst by means of acetylacetone and analyzed on a gaschromatograph with flame ionization detector. The following products were detected: naphtalene, anthracene, phenantrene and derivatives and chrysene. The experiments on the thermobalance were performed on a Cahn instrument, Type R.G. (1 pg-1 g). 3. RXPERIMENTAL PROGRAM
Fig. 2.
The gas phase was analyzed on-line for n- and i-pentane and C-C4 hydrocarbons by gaschromatography on a 2ethyl-hexylsebacate/chromosorb P column. After termination of the run, reversibly adsorbed hydrocarbons were stripped off the catalyst, at the reaction temperature and for 4Omin, by means of a hydrogen stream. After cooling and unloading, the coke content of the catalyst was determined by combustion at 500°C and with oxygen mole fractions varying from 1 to 20 per cent. The carbon monoxide in the combustion gas was oxidized into CO2on a TiO*-catalyst. The resulting gas was led through 3 U-tubes filled with resp. anhydron, ascarite and anhydron.
Experiments were performed at a total pressure ranging from I.54 atm abs. up to 2.76 atm abs. with a platinum reforming catalyst containing 0*75wt% Pt on rAl203. The hydrogenlpentane ratio in the feed, 7, was varied between 7 and 11 for the “kinetic” experiments and between 0.92 and 1.37 for the deactivation runs. The temperature range investigated was 388-436”C. The amount of catalyst was always close to 260g. The hydrocarbon flow rate was close to 1 mol/hr for the kinetic runs and to 2.5 mol/hr for the deactivation runs. The hydrocarbon feed was a mixture of n- and i-pentane containing about 90 per cent n-pentane. All the thermobalante experiments were carried out at atmospheric pressure. The temperature range investigated was 365-45O”C. The molar hydrogen/hydrocarbon ratio was varied between 0.33 and 1.6 and the i-pentane content of the hydrocarbon feed between zero and the equilibrium. Seven deactivation runs were performed, each of them
791
Deactivationof a platinum reformingcatalyst in a tubular reactor Table I. Summary of the experimental conditions for the deactivation runs Run Temperature (“C) Amount of cat. (g) Total HC flowrate % n-pentane in HC Total flow rate Molar ratio H,/HC, y Total pressure (atm abs.)
I
2
3
4
5
6
7
388 260 2607 91.1 5.434 I .08
388 261 2604 90.9 6.101 I .34 260
412 260 2644 91.3 5.078 0.92 1.54
412 262 2.548 88.3 6.045 1.37 2.49
416 260 2.615 90.3 6.071 I.32 2.76
431 263 2.613 89.3 5.785 I.21 I .79
436 261 2.579 90.1 5.956 I.31 2.46
1.63
with fresh catalyst. The experimental conditions are listed in Table 1. With fresh, untreated catalyst practically no i-pentane, but only light hydrocarbon gases were obtained. The pretreatment required to bring the catalyst to its standard activity consisted of four steps: (1) removal of adsorbed oxygen by means of hydrogen at 480°C (2) chlorination to reduce the hydrocracking activity to a low and stable level. This step increased the isomerization activity to such an extent that the isomerizationequilibrium was reached in the first centimeters of the bed already. (3) reduction of the isomerization activity without affecting the hydrocracking activity by means of a hydrogen flow containing strictly controlled amounts of water. (4) removal of water by means of a hydrogen-pentane flow until the catalyst reached a stable isomerization and hydrocracking activity for at least 48 hr. This pretreatment was always carried out at the temperature and total pressure of the deactivation run. It was followed by the “kinetic” run. This was carried out at high y and served to determine the kinetic parameters of the isomerization and hydrocracking in the absence of coking. 4. MODEL EQUATIONS
Figure 3 shows an example of the profiles of the n-pentane partial pressure through the reactor at various process-times (Run 4). Figure 4 is a cross-plot of these data, used as a basis for the calculation of the parameters. The isomerization rate is seen to decrease slowly. The effect of the coking of the A&O3sites active in isomerization is partly compensated for by the increase in driving force resulting from the reduction in hydrocracking, especially since the latter deposits coke on sites not involved in the isomerization of the intermediate olefines (viz. IV-1 and IV-2). Figure 5 shows the partial pressure of the lumped hydrocracking products (methane, ethane, propane, n- and i-butane) and Fig. 6 the corresponding crossplot. Figure 7 represents the coke profile at the end of the deactivation run, i.e. after 10 hr. The existence of a profile in the coke content, even under isothermal conditions, confirms Froment and Bischoff’s predictions[6]. According to their theory an ascending coke profile indicates coking from the reaction products, but since the carbon content is not zero at the inlet of the bed a certain amount must be deposited by a parallel mechanism, i.e. originating from the reactant.
0 0 0 o - - - -
Experlmemal points Interpoltied profile
0.90
w/F/.
_---
c
p--_~--
__--
.a_-‘6’-Tr--
0
0.701
c
o-
_o-
-
.cF-
p_
0
I
_-
60.6
n__a--a----
B--
_
-_--
p
_--
-o---c---
_-o---o-
Q--
0.40
32.9
46s -+-a-
_s__
a--;
0
Cl.50
“‘g-4
--6--r
n--e-
0.60
t
4.5
---TJ--~--
___-A---b
66.6
.+--EL__
_a----
-b-
I
I
I
I
I
I
2
4
6
6
0
t(hr)
Fig. 3.
In addition, it was found that both n- and Cpentane (or species in equilibrium with these components) are subject to hydrocracking. The above considerations led to the following over-all reaction scheme: hydrocracking products 2 n-pentane . . i-pentane coke A
For isothermal conditions and constant density and number of moles this scheme leads to the following continuity equations: for n-pentane apA 6i-b apA
x+F,at=-
*t F,
rA
(1)
for the lumped hydrocracking products aPD
&aPD_!&hrD
az+F, at -
F,
for coke
ac
z =rc*
(2)
792
R. P. DE PAUWand G. F.
FJROMENT
o o o D *Experlmentol’polnts
DO
0
0
-----
-- - -
Interpolated profile
-
Computed profile
‘Expertmentor points Interpolated profile Computed profile
040 20
40
60
60
100
W/F,0
Fig. 4.
W/@
Fig. 6.
00030
D
,y=qq
/’ /’ 0 c, 0.0020
, 0 0 --
-
k
0 0 “Experlmentol~polnt~ -
-
hlterp&ted
protn8
Comwded profile
0~0010 t
I
I
I
I
I
20
40
00
90
I
IO0
W/F,0
Fig. 7.
----a---Q
--c--d-_cL__ 2
4
4.6
I
I
6
6
IO
Hhr)
Fig. 5. The rates rA, rD and rc are functions of the process variables, but they also have to reflect the influence of the carbonaceous deposit upon the catalyst activity. The equations for t-~ and rD were derived from the “kinetic” runs. From an investigation of rc, the rate of coking, the effect of the coke was expressed in terms of deactivation functions, &, multiplying the rates at zero coke content. rl =
?fc#+.
1. The rate of isomerization The rate r,, is the total rate of reaction of n-pentane. Since the hydrocracking produces 2 mol of gas for 1mol of n-pentane (or i-pentane) fed and the amount of npentane transformed into carbon is very small the following relation may be written between the different rates: rA= r1 + O*SrDA
(4)
rB = rI - O*Sb.
(5)
The rate of isomerization of n-pentane rJ was obtained from a curvefitting of pA, pB and pD with respect to z, followed by analytical differentiation to yield rA, rB and rB The isomerization rate equation Was based on the following well known mechanism:
193
Deactivation of a platinum reforming catalyst in a tubular reactor
the bed during the seven “kinetic” runs. The accurate determination of the adsorption constants required rates obtained at low values of y, too. Extrapolation to zero Since rr was independent of total pressure the rate time was necessary to avoid falsification of r~by deactivadetermining step is the reaction of nCJHlo on A1203[71. tion. This in itself comprises three possible rate determining None of the adsorption constants was significantly steps, between which a discrimination based upon direct temperature deendent. When the temperature dependence process observation is impossible, however: was left out of the equations the results shown in Table 2 were obtained. adsorption of nCjHlo: M + L e FL Equations (6) and (7a) were rejected because of a non-significant value for the global adsorption coefficient isomerization: ML --‘NL for the hydrocracked products (Eq. 6) and for i-pentene NL --‘N+L. desorption: (Eq. 7a). Further, K,’ and A[(k’)O] were strongly correlated in Eq. (8) so that Eq. (7b), corresponding to surface Since the hydrocracking products are also adsorbed on reaction on ALO, sites rate controlling, with K,’ = KB’ Ai203 sites they have to be accounted for in the balance of was retained. A1203 sites covered by reacting species, so that the This conclusion is in agreement with that of Sinfelt et following isomerization rate equations are possible. al.[8] but differs from that of Hosten and Froment[7], Adsorption of n-pentene rate controlling: who selected, also on the basis of the ability to fit, the adsorption of n-pentene as rate determining step. It should be noted that they operated at a total pressure of (kr)‘(%-&) (6) about 10 atm under continuous chlorine-injection, and ,+&‘&+K I&! that they did not account for the competing adsorption of DPH PH hydrocracking products. The influence of the coke on the rate of isomerization Surface reaction rate controlling: (a) different adsorpwill be discussed at a later stage. tion costants for n- and Cpentene
(b) equal adsorption constants for n- and i-pentene (k’r(c-&) rP =
m
+ KD’E Desorption of i-pentene rate controlling r/ =
(k’)‘(E-j&) I+K’&+K’& A PH
(8)
D PH
The parameters of these equations were determined by means of a non-linear least squares fit of the rates, rr, derived from the measurements at different positions in
2. 7’he rate of hydrocracking The rate of hydrocracking was found to be linearly dependent on the total pressure. The hydrocracking products were shown to originate from both n- and Cpentene and to occur on sites different from those involved in the isomerization. The latter is substantiated by the observations made during the pretreatment, but also by experiments with a catalyst in which hydrogen protons had been exchanged with lithium-ions. In these experiments the isomerization was completely suppressed, but the hydrocracking and coking were not. The composition of the hydrocracking gas was very nearly equimolar in methane, ethane, propane and butanes. This would indicate hydrocracking on platinumsites, i.e. hydrogenolysis. Several reaction paths starting from n-pentane and n-pentene are possible for the hydrocracking, as shown in Table 3. Similar schemes may be developed for i-pentane and i-pentene. Schemes 1, 2 and 6 only lead to a rate which is linearly dependent upon total pressure.
Table 2. Kinetic and adsorption parameters for the isomerization Model 6
7a 7b 8
In A NWl 17.90 ?5.%’ 16.16 -c5.38* IS.95 24.55 16.38 k 5.46
E[W’l
K.4’
27,740 ?5,540’ 24,560 f 3,500 24,350 23,240 24,810 23,300
GJ 23.32 5.65 ~2.26 7.37 22.94
*Approx. 95 per cent confidence interval.
KB’
K,’
F-test
17.28 *I364 2.47 k4.49 5.65 k 2.26
-6.11 t 10.18 50.25 f 38.65 37.98 f 18.29 60.26 *30,13
I94 322 413 406
R. P. DE PAUWand G. F. FROMENT
794
Table 3. Hydrocracking schemes For n-pentane: AtI#Al
lD,#ltD,
Altl-+lD,+lD;
AltlH~--,lD,+lD~
lDI#ltD,
lD,#ltD,
lD;#ltD;
lDz#ltDz
3
2
1
For n-pentene:
ltH,#lH,
Ml + 1 -
lD,-#ltD,
4
lD,‘t lD,’
lD,-#ltDl
lD, C-L 1+D,
lD;#ltD;
10;cltD;
5
6
Similar schemes may be developed for Cpentaneand Cpentene.
The best fit of the data was arrived at by means of the rate equation derived from reaction Scheme 6 and from an analogous scheme starting from i-pentene, with the surface reaction as rate determining step in both cases. Some of the parameters were not significantly determined and strongly correlated, however. To reduce the number of parameters the activation energies of both contributions were taken to be equal. The ratio of the corresponding
frequency factors was then found to be 0.714. Finally the rate equation for hydrocracking was as follows:
The parameter values are given in Table 4.
795
Deactivation of a platinum reforming catalyst in a tubular reactor Table 4. Kinetic and adsorption parameters for hydrocracking
In A[(kD)q El(k?‘l approx. 95% conf. int.
19.91 %2.48
31,910 ~2,!300
K%
K,”
Ftest
2.17 20.21
7.95 +144
n2
(j&, =
It is seen from Table 4 that a temperature increase favors hydrocracking more than isomerization. 3. The rate of coking The rate of coking was shown to be inversely proportional to the total pressure and to decrease as the degree of coking augments. Let the coke, for illustrative purposes be deposited only on one type of sites, namely platinum. Suppose also that it is formed from both n- and i-pentene by the following mechanism: M+l;--‘Mi
(n, - l)M + MlN+l
with K1 =&
phf Cl
Sil
$c, = f,(C,). With dual function catalysts an additional problem arises, however. It was found that coke is deposited on both Pt and A&Or-sites, but the respective amounts of each could not be determined accurately. For this reason the deactivation function was expressed in terms of the total coke content. To do so it was assumed that the distribution of the coke over the two types of sites was constant, i.e. independent of time or coke content c,=gc
PNC!
S,/
(G$):
To go any further along this approach would require hypotheses about the relation between Csr and the coke content, i.e. about the number of active sites deactivated by 1 mol of carbon. Therefore, it was preferred to express the deactivation empirically in terms of the coke content:
with KS=&
=Nl
(nz- l)N t NZ-
If two active sites of the same type were involved in the coking
Eq. (I 1) then becomes:
where Si and Si are irreversibly adsorbed components leading ultimately to “coke”. The rate of coking on these sites may be written as:
dc = f(C).
It js to be noted that Eq. (10) is also easily extended to yield the total coking rate through the relation:
or ,.c,= C,( k ;=pM”l+k :=pN”9 p can then be incorporated in the rate coefficients to give: The total number of Pt-sites is given by:
c,, = c, + Curt CL •t CL3+
,+c
kc=&.rc
and
P
B
cc
= C,(l t K,p, + KZPN+ K~PD)t c, where, for the sake of simplicity the sum of the concentrations of irreversibly covered sites is represented by Cs. It then follows that:
A convenient way to determine the relation #~c= f(C) experimentally is to make use of a thermobalance. The thermobalance is a differential reactor yielding coke contents as a function of time for fixed partial pressures of the reacting species. Several deactivation functions were tested: &=1-a& & = (1 - acC)2 & = e-4
where kLC= k Z’C,, and k f = k’%. Equation (10) expresses that the rate of coking decreases with time as a consequence of the decrease in active sites available for coke formation and may be written in the form:
1 ~C=lt+acC. The best fit of the data was obtained with the exponential
function, so that the rate of coking may be written: dC 0 -a$ rc = dt = rc e
where 4
=
9
Cl - cs Cd .
rc” represents the rate equation for coking. In a differen-
(11) tial reactor r: reduces to a constant, so that
796
R. P. DE PAUWand G. F. FROMENT EslPf z = constant along r - 7 I
C=-$ln(l+acr$t). Note that the distribution coefficient /3 is included into the deactivation coefficient (Ye,which is based on the total coke content. Many mechanisms of coke formation could be postulated, leading to a set of rate equations of the Hougen-Watson type. A couple of them only were tested, but they gave a significantly poorer fit than the three equations which follow, even when K$& and KD” were taken fom the isomerization and hydrocracking data. The following equations led to an essentially equivalent degree of fitting:
along t - 7
f
z = constant
!$z [~(!i!,‘+@$(&t>‘]e-‘&
(18)
or (‘9) along z = constant. In these equations a~, aD and a~ are either constant or function of the process variables according to:
and two equations which differed only in m: rc =
(‘3) PH PH
PH
PH
with cyc= constant with a’ temperature dependent: a;=A(a!L).exp
E(a3
[
RT
1
The second expression for aC originates from the idea that the coke precursors are polymers whose effect on the decrease of the number of active sites, responsible for the deactivation, depends upon the degree of polymerization, which in turn is determined by the process variables.
The model contains 11 parameters [(k’)‘, K!.,s, kD’, aI, (kD)“, K!&, KD~, a, (kp')',(kc)', ml when the experiments are analyzed separately, i.e. per temperature and up to 18 when they are analyzed together, so that the temperature dependence has to be included explicitly through the Arrhenius relation {A [@‘)‘I, E[(/c’)~], A@;),
4. The deactivation function So far the only rate equation in which the deactivation was accounted for was that for coking. It seemed logical to introduce the same type of deactivation function into the rate equations for isomerization and hydrocracking, so that
EW,
rl= rP41
with 4, = e-@
and rD = rDo& with $Q = e-“6
(14) (‘5)
5. Parameter estimation under fouling conditions The model Eqs. (l)-(3) can now be written more
explicitly. Along the characteristics the system of partial differential equations reduces to a system of ordinary differential equations. With rp, rDo,rc” specified by (7b), (9) and (12) or (13)and the deactivation functions by (14), (15) and (11) the system becomes:
A[UC~)~I, W=‘?l, Ab2, E(ab), A[(bC)ol, ENkp’?‘l,AE(kcC)%E[(t’%, Ata& @aLI}; and the
adsorption parameters KLB, KD’, KzB, K,” which are taken to be independent of temperature. To reduce somewhat the number of parameters and avoid too strong correlation between them, the adsorption constants were fixed at their values derived from the “kinetic” runs. The rate coefficients were left free in the model, so as to check if the values obtained under coking conditions corresponded to those derived independently. Further, it should be noted that, since only the final coke profile is available from the experiments, CYCcannot be determined, unless it is related to UI and/or (r~. It was experienced that coking and hydrocracking occur on the same sites, so that (I~ was taken to be equal to aD/2 (= aD,C).The determination of the latter was no problem since the hydrocracking profiles were measured as a function of time. Consequently, six parameters remained to be determined when the experiments were analyzed separately, 10 parameters when analyzed together and when the a’s were chosen to be constant, 12 when ar and (Y~.~where considered to depend upon the process variables. The fitting may be applied to the rate data (differential method of kinetic analysis) or directly to the partial pressure-and carbon content profiles (integral method). The former method was used here, since it is far less demanding from the computational point of view, as shown by Lambrech et a1[5].
Deactivationof a platinum reformingcatalyst in a tubular reactor The objective function involved in the parameter estimation accounted for the multi-response character of the problem. The following form was adopted: 9=
0r ~~[a(r,-il)‘+b(ro-io)’ If + c(rc - PC)‘]dz dt.
(20)
In (20) a, b and c are weighting factors, which should be inversely proportional to the variance of the responses and therefore require replicate experiments. In the absence of these, particular attention was given to an optimum selection of the weighting factors. When the runs are analyzed separately there is no parameter which is common to the first term under the double integral of (20) on one hand, and the other two terms on the other hand. The latter two have a common parameter, namely aD,=. Since the minimization of 9 was stopped when two successive sets of parameter values (not function values) differed less than a present amount, a and b may be set equal to one. c was also chosen to be one, so as to give a greater importance to the hydrocracking, which was roughly ten times faster than the coking and come to aD,c values which are independent of the initial estimate of dD,c and the coke profile. When all the runs were analyzed simultaneously the objective function (20) had to be completed to give:
191
or = -0.8t
(b)’ when(kr)03(k’)Ao, 1.8~k%;6
The same expressions were used for $r,(n) and &(‘c(n). The double integrals in (20) or (21) were calculated numerically by Lobatto numerical quadraturel91. The values of the integrand were taken in the quadrature nodes (zi, ti) discussed further, so that the terms of the objective function are approximated by: (r -
i)2 dz dt = i i wiwi(r - i):,,, ,=I ,=I
where wi and wi are the Lobatto-coefficients. The experimental rates, r, were not directly available in (4, t,). They could be obtained by a polynomial fit of the experimental partial pressure profiles followed by analytical differentiation. A more direct and simpler way was to express the experimental rates in (zi, ti) by means of collocation in terms of the mol fractions:
-1F
,
@*(Zl,f)+O*714PB(Zi, tj)) cl
$@rD(Zi,
dpD &J
tj)=z=
F
I
rch tl) =g=
*r(n) accounts for the deviation of the rate coefficient (/o)’ from the best line in the Arrhenius-diagram based on the analysis per temperature. When the experimental point (k’)’ corresponds to the value calculated from the Arrhenius line, (k’).,‘, the ratio
and +r(n) is set equal to one. For (k’)“/(k’)B = 0.5, i.e. a relative deviation as large as 50 per cent, @r(n)was chosen to be 0.1, so that @r(n)= -0.8 + lg&$
when (k’)‘=s (k’),,’
[ 2
aikPD(zk,
h)]
(23)
(24)
,
(21) For each temperature the weighting factors a(n), 6(n), c(n) were written as follows:
(22)
$,ajkc(zi,tk)
(25)
where as and ajk are given by the collocation theory. The quadrature nodes mentioned above are chosen to coincide with the collocation points. The estimates of the rates, ?, were calculated through the rate Eqs. (16)-(19). Since the objective function requires the calculation of the rates at various times the corresponding carbon profiles are required. The coke content is only measured at the end of the run, however. The intermediate coke profiles were therefore obtained by extrapolation, making use of the formula derived from the thermobalance experiments: ev.&(+
C(t, t)=&ln
,
1t [(
7)
7
-l
t > 1.
(26)
Consequently, the objective function, %, has been minimized, by parameter iteration by means of a Marquardt routine, on the basis of coke profiles calculated with the starting values of the parameter cr~,c.The set of parameters obtained in this minimization loop does not necessarily lead to a calculated coke protile at the end of the run that corresponds with the experimental. Therefore, the estimated coke profile c(zi, T) is compared with the experimental and a correction factor is derived from
R. P. DE PAUWand G. F. FROMEN?
798
corresponding to two successive sets of carbon profiles, agree within the desired accuracy. The procedure is illustrated in the flow diagram of Fig. 14. The time required to calculate the parameters when the data were analyzed per temperature was 1Osec on the Siemens 4004-150, when all the experiments were analyzed together 90 sec. Finally, one more remark should be made about the weighting factors. One run was also analyzed using the determinant criterion of Box and Draper [lOIinstead of
this:
azi,7)
‘(zi,. Then the carbon profiles at the “collocation times” are also corected by multiplication with this ratio. With these corrected profiles a new minimization, leading to a new set of parameter values is undertaken. The procedure is stopped when two successive sets of parameters,
Klnetk rum Deacthtkn
r”ns-per
tempemture (0)
Deactivatbn runs-all tempertires
-2.50
-
142
I 144
14.6
I 14.6
I 150
104/T
Fig. 8. I
3 5 -r
-40
---- -------
Khetkrum oeactivatbn runs-per
-
oeoctiwtlon
(0)
tempemhre
runs-on tempermures
-
-5.0 t 430 I42
420
410
I44
14.6
400 I46
390
T(V)
390
TCC)
I50
104/T
Fig. 9. \ -TO- ‘\
-_-_-.-
cteacthtbn runs-per tempemtwe (0) DectctivatlMl runs-all temperahxes
-
-9.0
-
430
420
I
I
14.2
144
400
40
I I46
104/T
Fig. 10.
I I46
I I50
Deactivation the objective excellent higher, It
function
defined
agreement.
The
in (20). The results
were in
computation
time
was
much
computations
that
the
model
however.
followed
from
the
including
Eq. (18) for the coking
because
of a poorer
therefore
consisted
was
of a platinum reforming catalyst in a tubular reactor
concluded
fit of the
that
the fit arrived
function
of the process
obtained
with constant
the validity
The
variables
at with
final
was
variables
The final parameter
concerning
turned values
and carbon
profiles,
412°C
by Figs. 4, 6 and 7, which
and aoc
superior
to that
a $-test
obey
the
evidenced
based
Cpentane,
hydrocracking
as is illustrated
pro-
for the run at
also include
upon the results
the final
of Table
Figs.
by Table
temperature
5 (all
coefficients
tion, 4,, varied from deactivation
significantly
dependence,
as
is
5 and Figs. 8-l I. This is true also for cu; and ah.=
I2 and 13. The deactivation
total pressure,
5.
also those for coking,
Arrhenius
the deactivation
on
the dependence in Table
pofiles
The rate coefficients,
model
an F-test it
out to be positive.
are given
n- and
ducts,
temperatures).
a,
al and aoc. Tn addition
of the hypothesis
on the process
data.
the experimental
computed
rate had to be discarded
of (16), (17) and (19). From
799
as illustrated
function
by
for isomeriza-
1 to 0.66 for the run at 431°C and low
which led to the highest function
coke content.
for hydrocracking,
&,
varied
The from
1 to 0.37. 6.
The model
As
DlSCUSSlON
used in this work
permits
an excellent
-_-----
I
-
already,
of the model,
rum-per
oswthuHon
runs-am kmpsmtureS
4lo
I
I
I
142
I44
146
(k’)’ rather
was
I
400
146
I
390 WC)
15.0
lO'/T
Fig. II. Table 5. Final parameter values. Results obtained with u function of the process variables Per temperature (k’)‘x a:
10’
(kD)’ x lo’ crhc
8.42 152.1 090 203.6 o-50 3.70
7.47 85.3 1.10 103.4 0.95 3.33
From “kinetic” runs
K' K,:" In A(ak)
E(a’J
12.36 115.1 246 62.6 2.93 7.21
19.69 51.4 2.49 62.0 3.83 14.87
19.17 33.0 4.73 41.4 7.69 25.33
From deactivation runs Per temperature All temperatures
15.95 24,350 564 3798
-
19.91 31,910 2.17 7.94
*Approx.
12.77 60.4 2.98 79.9 3.08 Il.07
95 per cent confidence intervals.
12.89 20,180 - 12.92 23,210 20.05 32,240 - 14.29 25,200 30.17 52,000 24.76 42,890
12.45 2 0.62’ 19,650?2,180 - 13.5126.75 23,760 -t 11,880 21.17kO.73 33,760 2 1,500 -7G1.14 16,520?4,130 23+0+3.67 43,620 ” 7,270 27.45 r 1.61 46,470 + 2,445
considered
as a
than fixing it on the basis
nmpsmtm (0)
Deactb0h
420
430
mentioned
parameter
fit of
2248 38.7 5.13 42.5 10.10 3266
R. P. DE PMJWand G. F.
142
14.4
FROMENT
14.6
146
104/T
Fig. 12.
5.0
-----_-
I
-
142
I44
olxalvatlofl
runs-per
chactm
runs-all
tempcmtw.3
I46
146
(0)
tempemhJm
15.0
104/T
Fig. 13.
of the experiments in the absence of coking. From Fig. 8 it is seen that the (k’)’ derived from the deactivation experiments are in excellent agreement with those derived from the “kinetic” experiments, also reported in Table 5. The same is true for the hydrocracking rate coefficients (kD)’ (Fig. 9). It may be concluded that a satisfactory approach has been developed and illustrated for estimating the coking characteristics of a catalyst under given process conditions. The experimental effort and the computation have been reduced to a reasonable level, permitting a rather rigorous approach. It is rewarding that such a high level of significance has been obtained from only 7 runs. The approach therefore looks promising for further work tending at establishing general correlations for catalyst coking. Acknowledgements-R. P. De Pauw is grateful to the Belgian N.F.W.O.-F.N.R.S. for a Fellowship over the years l!Vl-74. The calculations were performed at the “Centraal Digitaal Rekencentrum” of Rijksuniversiteit Gent. NOTATION
weight factors in objective function a ** differential coefficients in collocation
a, b, c
Fig. 14.
Deactivation
of a platinum reforming catalyst in a tubular reactor
mol mol frequency factor, or g cat hr g cat hr atm Or mol atm g cat hr g coke C coke content of the catalyst, g cat hr act sites concentration of active sites, g cat
A
c* E
activation energy, -$
801
W,l),j(l,h
k,n(Lti)count
variables in collocation
I isomerization M n -pentene Ml, ML adsorbed n-pentene N tpentene Nl, NL adsorbed Cpentene P parallel mechanism Cl total number of active sites Sl active sites covered by coke
9 objective function F, total flow rate, $
kc=rate coefficient for consecutive coke formation g coke ‘gcathr kc rate coefficient for parallel coke formation, id. kD rate coefficient for hydrocracking, mol g cat hr atm mol k’ rate coefficient for isomerization, g cat hr equilibrium constants K,KJG K** adsorption equilibrium constants 1 Pt-active site involved in hydrocracking and coking L A1203-active site involved in isomerization nhn2 order of the coking reaction p* partial pressure of reacting components, atm PI total pressure, atm g coke rc rate of coke formation, g cat hr mol rD rate of hydrocracking, g cat hr mol li rate of isomerization, g cat hr R
gasconstant, +&
t,t* time, hr T absolute temperature, “K w* WIF,” w,
*
integration coefficients in collocation g cat hr space time, mol axial coordinate, cm refers to subscripts or superscripts.
Subscripts A n -pentane B Cpentane
consecutive mechanism i coke D cracking products Dl adsorbed cracking products H hydrogen
Superscripts C coking D hydrocracking
I isomerization o non-fouling conditions 1 estimated values. Greek symbols
g cat g cat deactivation factor, or g coke g coke atm g coke initial rate of coke formation, g cat hr molar ratio hydrogen/hydrocarbon void fraction bed length, cm bulk density of the bed, 5 Pf
0: II* i-l
density of the gas, 2 run length deactivation function correction factor in the calculation of weight factors cross section of the bed, cm* REFERENCES
[I] Butt J. B., Chemical Reaction Engineering, Advan. Chem. Ser. 109, pp. 259-4%, Am. Chem. Sot., Washington, DC 1972. [2] Voorhies A., Ind. Eng. Chem. 1945 37 318. I31 Weekman V. W., Ind. Eng. Chem. Proc. Des. & De@. 1968790. [41 John T. M., Pachovsky R. A. and WojciechowskiB. W., in Chemical Reaction Engineering II, Adv. in Chem. Series, pp. 133-422 Advan. Chem. Sot. Washington D.C. 1974. [5] Lambrecht G. C., Nussey C. and Froment G. F., Proc. 5th Eur. Symp. on Chem. React. Eng., Amsterdam (1972), Elsevier, Amsterdam 1972. [6] Froment G. F. and Bischoff K. B., Chem. Engng Sci. I%1 16 189. [7] Hosten L. H. and Froment G. F., Ind. Eng. Chem. Proc. Des. & Devpt. 1971 10 2. [8] Sinfelt J., Hurwitz H. and Rohrer J., .I. Phys. Chem. 1960 64 892. [9] Van den Bossche B. and Hellinckx L., A.I.Ch.E. J/ 1974 24lf2) 251. [lo] Box G. and Draper N., Biometrika I%5 52 355.
Pcrgamon Press.
Printed in Great Britain
DEACTIVATION OF A PLATINUM REFORMING CATALYST IN A TUBULAR REACTOR R. P. DE PAUW and G. F. FROMENT Laboratorium voor Petrochemische Techniek Rijksuniversiteit, Gent, Belgium (Received 28 October 1914)
Abstract-This work concerns the methodology of characterizing the deactivation of a catalyst by coke deposition. The isomerization of npentane on a platinum reforming catalyst was studied in a tubular reactor permitting easy sampling of the gas phase at several positions in the reactor. Runs with high ratios of hydrogen to pentane did not show any deactivation and served to determine the kinetics of the main reaction and the principal side reaction, hydrocracking. At low ratios of hydrogen to pentane the catalyst was deactivated by carbonaceous deposits. At the end of the run the coke was determined in sections of the reactor and was found to be deposited according to a profile. Additional insight into the coking phenomenon was obtained from experiments on a thermohalance. A mathematical model for the performance of the tubular reactor subject to coking was set up and the parameters were determined from the experimental data. The parameters were found to be significantly determined and to obey the Arrhenius temperature dependence. The values of the parameters of the main reaction and of the hydrocracking side reaction which were derivedfrom the experimentsin the presence of coking were in agreement with those obtained from the runs in the absence of coking. 1. INTRODUCTION
Deactivation of catalysts by carbonaceous deposits is a phenomenon frequently encountered in the petroleum and petrochemical industry which has far reaching consequences. In recent years it has received increasing attention, as is evidenced by the rapidly growing number of papers dealing with this topic. A thorough review of the field has been presented by Butt [l]. The work reported here concerns the methodology of characterizing the coking of a catalyst in a tubular reactor, in view of its extrapolation to different conditions or to a different scale. It is based upon the idea that the correlation between the coke content of the catalyst and process time, often found in the literature[2-4], lacks generality. For this reason Froment and Bischoff related the coke content to the process variables such as partial pressures of the reactants and products, space time, etc. It follows from their work that even under isothermal conditions the carbon content of the bed is not uniform, but varies according to a profile which is characteristic for the mechanism giving rise to the carbon. Coke deposition by a mechanism parallel to the main reaction leads to a descending coke profile, deposition by a consecutive mechanism to an ascending profile. For two reasons the isomerization of pentane on a platinum reforming catalyst in the presence of hydrogen, lends itself particularly well to the aims of this work. First, for high ratios of hydrogen to pentane no deactivation is observed during the run lengths typical for laboratory practice, thus enabling the kinetic study of the isomerization (and of a secondary reaction: hydrocracking). #en the hydrogen/pentane ratio is lowered a rapid deactivation is observed, so that the coking can be studied in a reasonable amount of time and in a convenient way, making use of the known kinetic model for the main reaction. Without this uncoupling the problem of determining the kinetics of both the main and the coking reaction might well be inextricable and overwhelming in
its computational aspects. A second advantage of the system is the very low value of the heat of reaction, which permits isothermal operation, even with the relatively large amount of catalyst required by this type of experiments. The tubular reactor in which the experiments were performed received considerable attention and was designed to provide maximum information from one single run. For this purpose a sampling device which enabled easy sampling of the gas phase at several bed depths was built into the reactor. There is no such convenient way of following the increase of the coke content of the catalyst with time, however: the determination of the coke content requires unloading of the reactor and terminates the run. In addition, important information on the deactivation was obtained from experiments carried out in a thermobalance. 2. F.QUmMEN’r ANDEXPERIMENTAL PROCEDURE The experimental set-up, used already by Lambrecht et al. [5], is shown in Fig. 1. Figure 2 shows details of the
tubular reactor, which is made of chromium steel, free of nickel. The rings permit unloading clearly defined sections of the bed for determination of the carbon profile. Two very tightly fitting concentric tubes are axially located in the bed. The outer tube (e.d. 3.3 cm; i.d. 2.8 cm) is welded to the catalyst support ring and has six openings spaced at 10cm intervals. The inner tube can slide in the outer and has a hole near the bottom. This device permits sampling of the gas at six bed heights. In this way a conversion vs space time curve, as required for the kinetic analysis, may be determined in about half an hour and without having to vary the feed rate as is usually done. A thin thermocouple (Philips Thermocoax 21BAcl0, 1 mm dia.) is fixed to the inner sliding tube, so that its junction is located in front of the lowest opening. 789
CES Vol. 34, No. 8-B
R. P. DE PAUWand G. F. FROMENT
790
Fig. 1. The weight difference of the catalyst before and after combustion corresponds to the sum C+H t (Hz0adsorbed during manipulations). The first anhydron tube allows the determination of the sum of the amount of water adsorbed on the catalyst and that produced by the oxidation of the hydrogen. The ascarite tube adsorbs the CO*,but gives off water. This water is adsorbed in the third tube. The H/C ratio of the “coke” was found to increase from 0.65 to 4.6 as the temperature was decreased from 436 to 388°C. No dependence on the partial pressure was observed. It is hard to say whether the H/C-ratio variation really reflects the influence of the temperature at the moment of formation of the carbonaceous deposit or an effect of the prolonged stay at different temperatures, during which a gradual loss of hydrogen is possible. The coke was also extracted from the catalyst by means of acetylacetone and analyzed on a gaschromatograph with flame ionization detector. The following products were detected: naphtalene, anthracene, phenantrene and derivatives and chrysene. The experiments on the thermobalance were performed on a Cahn instrument, Type R.G. (1 pg-1 g). 3. RXPERIMENTAL PROGRAM
Fig. 2.
The gas phase was analyzed on-line for n- and i-pentane and C-C4 hydrocarbons by gaschromatography on a 2ethyl-hexylsebacate/chromosorb P column. After termination of the run, reversibly adsorbed hydrocarbons were stripped off the catalyst, at the reaction temperature and for 4Omin, by means of a hydrogen stream. After cooling and unloading, the coke content of the catalyst was determined by combustion at 500°C and with oxygen mole fractions varying from 1 to 20 per cent. The carbon monoxide in the combustion gas was oxidized into CO2on a TiO*-catalyst. The resulting gas was led through 3 U-tubes filled with resp. anhydron, ascarite and anhydron.
Experiments were performed at a total pressure ranging from I.54 atm abs. up to 2.76 atm abs. with a platinum reforming catalyst containing 0*75wt% Pt on rAl203. The hydrogenlpentane ratio in the feed, 7, was varied between 7 and 11 for the “kinetic” experiments and between 0.92 and 1.37 for the deactivation runs. The temperature range investigated was 388-436”C. The amount of catalyst was always close to 260g. The hydrocarbon flow rate was close to 1 mol/hr for the kinetic runs and to 2.5 mol/hr for the deactivation runs. The hydrocarbon feed was a mixture of n- and i-pentane containing about 90 per cent n-pentane. All the thermobalante experiments were carried out at atmospheric pressure. The temperature range investigated was 365-45O”C. The molar hydrogen/hydrocarbon ratio was varied between 0.33 and 1.6 and the i-pentane content of the hydrocarbon feed between zero and the equilibrium. Seven deactivation runs were performed, each of them
791
Deactivationof a platinum reformingcatalyst in a tubular reactor Table I. Summary of the experimental conditions for the deactivation runs Run Temperature (“C) Amount of cat. (g) Total HC flowrate % n-pentane in HC Total flow rate Molar ratio H,/HC, y Total pressure (atm abs.)
I
2
3
4
5
6
7
388 260 2607 91.1 5.434 I .08
388 261 2604 90.9 6.101 I .34 260
412 260 2644 91.3 5.078 0.92 1.54
412 262 2.548 88.3 6.045 1.37 2.49
416 260 2.615 90.3 6.071 I.32 2.76
431 263 2.613 89.3 5.785 I.21 I .79
436 261 2.579 90.1 5.956 I.31 2.46
1.63
with fresh catalyst. The experimental conditions are listed in Table 1. With fresh, untreated catalyst practically no i-pentane, but only light hydrocarbon gases were obtained. The pretreatment required to bring the catalyst to its standard activity consisted of four steps: (1) removal of adsorbed oxygen by means of hydrogen at 480°C (2) chlorination to reduce the hydrocracking activity to a low and stable level. This step increased the isomerization activity to such an extent that the isomerizationequilibrium was reached in the first centimeters of the bed already. (3) reduction of the isomerization activity without affecting the hydrocracking activity by means of a hydrogen flow containing strictly controlled amounts of water. (4) removal of water by means of a hydrogen-pentane flow until the catalyst reached a stable isomerization and hydrocracking activity for at least 48 hr. This pretreatment was always carried out at the temperature and total pressure of the deactivation run. It was followed by the “kinetic” run. This was carried out at high y and served to determine the kinetic parameters of the isomerization and hydrocracking in the absence of coking. 4. MODEL EQUATIONS
Figure 3 shows an example of the profiles of the n-pentane partial pressure through the reactor at various process-times (Run 4). Figure 4 is a cross-plot of these data, used as a basis for the calculation of the parameters. The isomerization rate is seen to decrease slowly. The effect of the coking of the A&O3sites active in isomerization is partly compensated for by the increase in driving force resulting from the reduction in hydrocracking, especially since the latter deposits coke on sites not involved in the isomerization of the intermediate olefines (viz. IV-1 and IV-2). Figure 5 shows the partial pressure of the lumped hydrocracking products (methane, ethane, propane, n- and i-butane) and Fig. 6 the corresponding crossplot. Figure 7 represents the coke profile at the end of the deactivation run, i.e. after 10 hr. The existence of a profile in the coke content, even under isothermal conditions, confirms Froment and Bischoff’s predictions[6]. According to their theory an ascending coke profile indicates coking from the reaction products, but since the carbon content is not zero at the inlet of the bed a certain amount must be deposited by a parallel mechanism, i.e. originating from the reactant.
0 0 0 o - - - -
Experlmemal points Interpoltied profile
0.90
w/F/.
_---
c
p--_~--
__--
.a_-‘6’-Tr--
0
0.701
c
o-
_o-
-
.cF-
p_
0
I
_-
60.6
n__a--a----
B--
_
-_--
p
_--
-o---c---
_-o---o-
Q--
0.40
32.9
46s -+-a-
_s__
a--;
0
Cl.50
“‘g-4
--6--r
n--e-
0.60
t
4.5
---TJ--~--
___-A---b
66.6
.+--EL__
_a----
-b-
I
I
I
I
I
I
2
4
6
6
0
t(hr)
Fig. 3.
In addition, it was found that both n- and Cpentane (or species in equilibrium with these components) are subject to hydrocracking. The above considerations led to the following over-all reaction scheme: hydrocracking products 2 n-pentane . . i-pentane coke A
For isothermal conditions and constant density and number of moles this scheme leads to the following continuity equations: for n-pentane apA 6i-b apA
x+F,at=-
*t F,
rA
(1)
for the lumped hydrocracking products aPD
&aPD_!&hrD
az+F, at -
F,
for coke
ac
z =rc*
(2)
792
R. P. DE PAUWand G. F.
FJROMENT
o o o D *Experlmentol’polnts
DO
0
0
-----
-- - -
Interpolated profile
-
Computed profile
‘Expertmentor points Interpolated profile Computed profile
040 20
40
60
60
100
W/F,0
Fig. 4.
W/@
Fig. 6.
00030
D
,y=qq
/’ /’ 0 c, 0.0020
, 0 0 --
-
k
0 0 “Experlmentol~polnt~ -
-
hlterp&ted
protn8
Comwded profile
0~0010 t
I
I
I
I
I
20
40
00
90
I
IO0
W/F,0
Fig. 7.
----a---Q
--c--d-_cL__ 2
4
4.6
I
I
6
6
IO
Hhr)
Fig. 5. The rates rA, rD and rc are functions of the process variables, but they also have to reflect the influence of the carbonaceous deposit upon the catalyst activity. The equations for t-~ and rD were derived from the “kinetic” runs. From an investigation of rc, the rate of coking, the effect of the coke was expressed in terms of deactivation functions, &, multiplying the rates at zero coke content. rl =
?fc#+.
1. The rate of isomerization The rate r,, is the total rate of reaction of n-pentane. Since the hydrocracking produces 2 mol of gas for 1mol of n-pentane (or i-pentane) fed and the amount of npentane transformed into carbon is very small the following relation may be written between the different rates: rA= r1 + O*SrDA
(4)
rB = rI - O*Sb.
(5)
The rate of isomerization of n-pentane rJ was obtained from a curvefitting of pA, pB and pD with respect to z, followed by analytical differentiation to yield rA, rB and rB The isomerization rate equation Was based on the following well known mechanism:
193
Deactivation of a platinum reforming catalyst in a tubular reactor
the bed during the seven “kinetic” runs. The accurate determination of the adsorption constants required rates obtained at low values of y, too. Extrapolation to zero Since rr was independent of total pressure the rate time was necessary to avoid falsification of r~by deactivadetermining step is the reaction of nCJHlo on A1203[71. tion. This in itself comprises three possible rate determining None of the adsorption constants was significantly steps, between which a discrimination based upon direct temperature deendent. When the temperature dependence process observation is impossible, however: was left out of the equations the results shown in Table 2 were obtained. adsorption of nCjHlo: M + L e FL Equations (6) and (7a) were rejected because of a non-significant value for the global adsorption coefficient isomerization: ML --‘NL for the hydrocracked products (Eq. 6) and for i-pentene NL --‘N+L. desorption: (Eq. 7a). Further, K,’ and A[(k’)O] were strongly correlated in Eq. (8) so that Eq. (7b), corresponding to surface Since the hydrocracking products are also adsorbed on reaction on ALO, sites rate controlling, with K,’ = KB’ Ai203 sites they have to be accounted for in the balance of was retained. A1203 sites covered by reacting species, so that the This conclusion is in agreement with that of Sinfelt et following isomerization rate equations are possible. al.[8] but differs from that of Hosten and Froment[7], Adsorption of n-pentene rate controlling: who selected, also on the basis of the ability to fit, the adsorption of n-pentene as rate determining step. It should be noted that they operated at a total pressure of (kr)‘(%-&) (6) about 10 atm under continuous chlorine-injection, and ,+&‘&+K I&! that they did not account for the competing adsorption of DPH PH hydrocracking products. The influence of the coke on the rate of isomerization Surface reaction rate controlling: (a) different adsorpwill be discussed at a later stage. tion costants for n- and Cpentene
(b) equal adsorption constants for n- and i-pentene (k’r(c-&) rP =
m
+ KD’E Desorption of i-pentene rate controlling r/ =
(k’)‘(E-j&) I+K’&+K’& A PH
(8)
D PH
The parameters of these equations were determined by means of a non-linear least squares fit of the rates, rr, derived from the measurements at different positions in
2. 7’he rate of hydrocracking The rate of hydrocracking was found to be linearly dependent on the total pressure. The hydrocracking products were shown to originate from both n- and Cpentene and to occur on sites different from those involved in the isomerization. The latter is substantiated by the observations made during the pretreatment, but also by experiments with a catalyst in which hydrogen protons had been exchanged with lithium-ions. In these experiments the isomerization was completely suppressed, but the hydrocracking and coking were not. The composition of the hydrocracking gas was very nearly equimolar in methane, ethane, propane and butanes. This would indicate hydrocracking on platinumsites, i.e. hydrogenolysis. Several reaction paths starting from n-pentane and n-pentene are possible for the hydrocracking, as shown in Table 3. Similar schemes may be developed for i-pentane and i-pentene. Schemes 1, 2 and 6 only lead to a rate which is linearly dependent upon total pressure.
Table 2. Kinetic and adsorption parameters for the isomerization Model 6
7a 7b 8
In A NWl 17.90 ?5.%’ 16.16 -c5.38* IS.95 24.55 16.38 k 5.46
E[W’l
K.4’
27,740 ?5,540’ 24,560 f 3,500 24,350 23,240 24,810 23,300
GJ 23.32 5.65 ~2.26 7.37 22.94
*Approx. 95 per cent confidence interval.
KB’
K,’
F-test
17.28 *I364 2.47 k4.49 5.65 k 2.26
-6.11 t 10.18 50.25 f 38.65 37.98 f 18.29 60.26 *30,13
I94 322 413 406
R. P. DE PAUWand G. F. FROMENT
794
Table 3. Hydrocracking schemes For n-pentane: AtI#Al
lD,#ltD,
Altl-+lD,+lD;
AltlH~--,lD,+lD~
lDI#ltD,
lD,#ltD,
lD;#ltD;
lDz#ltDz
3
2
1
For n-pentene:
ltH,#lH,
Ml + 1 -
lD,-#ltD,
4
lD,‘t lD,’
lD,-#ltDl
lD, C-L 1+D,
lD;#ltD;
10;cltD;
5
6
Similar schemes may be developed for Cpentaneand Cpentene.
The best fit of the data was arrived at by means of the rate equation derived from reaction Scheme 6 and from an analogous scheme starting from i-pentene, with the surface reaction as rate determining step in both cases. Some of the parameters were not significantly determined and strongly correlated, however. To reduce the number of parameters the activation energies of both contributions were taken to be equal. The ratio of the corresponding
frequency factors was then found to be 0.714. Finally the rate equation for hydrocracking was as follows:
The parameter values are given in Table 4.
795
Deactivation of a platinum reforming catalyst in a tubular reactor Table 4. Kinetic and adsorption parameters for hydrocracking
In A[(kD)q El(k?‘l approx. 95% conf. int.
19.91 %2.48
31,910 ~2,!300
K%
K,”
Ftest
2.17 20.21
7.95 +144
n2
(j&, =
It is seen from Table 4 that a temperature increase favors hydrocracking more than isomerization. 3. The rate of coking The rate of coking was shown to be inversely proportional to the total pressure and to decrease as the degree of coking augments. Let the coke, for illustrative purposes be deposited only on one type of sites, namely platinum. Suppose also that it is formed from both n- and i-pentene by the following mechanism: M+l;--‘Mi
(n, - l)M + MlN+l
with K1 =&
phf Cl
Sil
$c, = f,(C,). With dual function catalysts an additional problem arises, however. It was found that coke is deposited on both Pt and A&Or-sites, but the respective amounts of each could not be determined accurately. For this reason the deactivation function was expressed in terms of the total coke content. To do so it was assumed that the distribution of the coke over the two types of sites was constant, i.e. independent of time or coke content c,=gc
PNC!
S,/
(G$):
To go any further along this approach would require hypotheses about the relation between Csr and the coke content, i.e. about the number of active sites deactivated by 1 mol of carbon. Therefore, it was preferred to express the deactivation empirically in terms of the coke content:
with KS=&
=Nl
(nz- l)N t NZ-
If two active sites of the same type were involved in the coking
Eq. (I 1) then becomes:
where Si and Si are irreversibly adsorbed components leading ultimately to “coke”. The rate of coking on these sites may be written as:
dc = f(C).
It js to be noted that Eq. (10) is also easily extended to yield the total coking rate through the relation:
or ,.c,= C,( k ;=pM”l+k :=pN”9 p can then be incorporated in the rate coefficients to give: The total number of Pt-sites is given by:
c,, = c, + Curt CL •t CL3+
,+c
kc=&.rc
and
P
B
cc
= C,(l t K,p, + KZPN+ K~PD)t c, where, for the sake of simplicity the sum of the concentrations of irreversibly covered sites is represented by Cs. It then follows that:
A convenient way to determine the relation #~c= f(C) experimentally is to make use of a thermobalance. The thermobalance is a differential reactor yielding coke contents as a function of time for fixed partial pressures of the reacting species. Several deactivation functions were tested: &=1-a& & = (1 - acC)2 & = e-4
where kLC= k Z’C,, and k f = k’%. Equation (10) expresses that the rate of coking decreases with time as a consequence of the decrease in active sites available for coke formation and may be written in the form:
1 ~C=lt+acC. The best fit of the data was obtained with the exponential
function, so that the rate of coking may be written: dC 0 -a$ rc = dt = rc e
where 4
=
9
Cl - cs Cd .
rc” represents the rate equation for coking. In a differen-
(11) tial reactor r: reduces to a constant, so that
796
R. P. DE PAUWand G. F. FROMENT EslPf z = constant along r - 7 I
C=-$ln(l+acr$t). Note that the distribution coefficient /3 is included into the deactivation coefficient (Ye,which is based on the total coke content. Many mechanisms of coke formation could be postulated, leading to a set of rate equations of the Hougen-Watson type. A couple of them only were tested, but they gave a significantly poorer fit than the three equations which follow, even when K$& and KD” were taken fom the isomerization and hydrocracking data. The following equations led to an essentially equivalent degree of fitting:
along t - 7
f
z = constant
!$z [~(!i!,‘+@$(&t>‘]e-‘&
(18)
or (‘9) along z = constant. In these equations a~, aD and a~ are either constant or function of the process variables according to:
and two equations which differed only in m: rc =
(‘3) PH PH
PH
PH
with cyc= constant with a’ temperature dependent: a;=A(a!L).exp
E(a3
[
RT
1
The second expression for aC originates from the idea that the coke precursors are polymers whose effect on the decrease of the number of active sites, responsible for the deactivation, depends upon the degree of polymerization, which in turn is determined by the process variables.
The model contains 11 parameters [(k’)‘, K!.,s, kD’, aI, (kD)“, K!&, KD~, a, (kp')',(kc)', ml when the experiments are analyzed separately, i.e. per temperature and up to 18 when they are analyzed together, so that the temperature dependence has to be included explicitly through the Arrhenius relation {A [@‘)‘I, E[(/c’)~], A@;),
4. The deactivation function So far the only rate equation in which the deactivation was accounted for was that for coking. It seemed logical to introduce the same type of deactivation function into the rate equations for isomerization and hydrocracking, so that
EW,
rl= rP41
with 4, = e-@
and rD = rDo& with $Q = e-“6
(14) (‘5)
5. Parameter estimation under fouling conditions The model Eqs. (l)-(3) can now be written more
explicitly. Along the characteristics the system of partial differential equations reduces to a system of ordinary differential equations. With rp, rDo,rc” specified by (7b), (9) and (12) or (13)and the deactivation functions by (14), (15) and (11) the system becomes:
A[UC~)~I, W=‘?l, Ab2, E(ab), A[(bC)ol, ENkp’?‘l,AE(kcC)%E[(t’%, Ata& @aLI}; and the
adsorption parameters KLB, KD’, KzB, K,” which are taken to be independent of temperature. To reduce somewhat the number of parameters and avoid too strong correlation between them, the adsorption constants were fixed at their values derived from the “kinetic” runs. The rate coefficients were left free in the model, so as to check if the values obtained under coking conditions corresponded to those derived independently. Further, it should be noted that, since only the final coke profile is available from the experiments, CYCcannot be determined, unless it is related to UI and/or (r~. It was experienced that coking and hydrocracking occur on the same sites, so that (I~ was taken to be equal to aD/2 (= aD,C).The determination of the latter was no problem since the hydrocracking profiles were measured as a function of time. Consequently, six parameters remained to be determined when the experiments were analyzed separately, 10 parameters when analyzed together and when the a’s were chosen to be constant, 12 when ar and (Y~.~where considered to depend upon the process variables. The fitting may be applied to the rate data (differential method of kinetic analysis) or directly to the partial pressure-and carbon content profiles (integral method). The former method was used here, since it is far less demanding from the computational point of view, as shown by Lambrech et a1[5].
Deactivationof a platinum reformingcatalyst in a tubular reactor The objective function involved in the parameter estimation accounted for the multi-response character of the problem. The following form was adopted: 9=
0r ~~[a(r,-il)‘+b(ro-io)’ If + c(rc - PC)‘]dz dt.
(20)
In (20) a, b and c are weighting factors, which should be inversely proportional to the variance of the responses and therefore require replicate experiments. In the absence of these, particular attention was given to an optimum selection of the weighting factors. When the runs are analyzed separately there is no parameter which is common to the first term under the double integral of (20) on one hand, and the other two terms on the other hand. The latter two have a common parameter, namely aD,=. Since the minimization of 9 was stopped when two successive sets of parameter values (not function values) differed less than a present amount, a and b may be set equal to one. c was also chosen to be one, so as to give a greater importance to the hydrocracking, which was roughly ten times faster than the coking and come to aD,c values which are independent of the initial estimate of dD,c and the coke profile. When all the runs were analyzed simultaneously the objective function (20) had to be completed to give:
191
or = -0.8t
(b)’ when(kr)03(k’)Ao, 1.8~k%;6
The same expressions were used for $r,(n) and &(‘c(n). The double integrals in (20) or (21) were calculated numerically by Lobatto numerical quadraturel91. The values of the integrand were taken in the quadrature nodes (zi, ti) discussed further, so that the terms of the objective function are approximated by: (r -
i)2 dz dt = i i wiwi(r - i):,,, ,=I ,=I
where wi and wi are the Lobatto-coefficients. The experimental rates, r, were not directly available in (4, t,). They could be obtained by a polynomial fit of the experimental partial pressure profiles followed by analytical differentiation. A more direct and simpler way was to express the experimental rates in (zi, ti) by means of collocation in terms of the mol fractions:
-1F
,
@*(Zl,f)+O*714PB(Zi, tj)) cl
$@rD(Zi,
dpD &J
tj)=z=
F
I
rch tl) =g=
*r(n) accounts for the deviation of the rate coefficient (/o)’ from the best line in the Arrhenius-diagram based on the analysis per temperature. When the experimental point (k’)’ corresponds to the value calculated from the Arrhenius line, (k’).,‘, the ratio
and +r(n) is set equal to one. For (k’)“/(k’)B = 0.5, i.e. a relative deviation as large as 50 per cent, @r(n)was chosen to be 0.1, so that @r(n)= -0.8 + lg&$
when (k’)‘=s (k’),,’
[ 2
aikPD(zk,
h)]
(23)
(24)
,
(21) For each temperature the weighting factors a(n), 6(n), c(n) were written as follows:
(22)
$,ajkc(zi,tk)
(25)
where as and ajk are given by the collocation theory. The quadrature nodes mentioned above are chosen to coincide with the collocation points. The estimates of the rates, ?, were calculated through the rate Eqs. (16)-(19). Since the objective function requires the calculation of the rates at various times the corresponding carbon profiles are required. The coke content is only measured at the end of the run, however. The intermediate coke profiles were therefore obtained by extrapolation, making use of the formula derived from the thermobalance experiments: ev.&(+
C(t, t)=&ln
,
1t [(
7)
7
-l
t > 1.
(26)
Consequently, the objective function, %, has been minimized, by parameter iteration by means of a Marquardt routine, on the basis of coke profiles calculated with the starting values of the parameter cr~,c.The set of parameters obtained in this minimization loop does not necessarily lead to a calculated coke protile at the end of the run that corresponds with the experimental. Therefore, the estimated coke profile c(zi, T) is compared with the experimental and a correction factor is derived from
R. P. DE PAUWand G. F. FROMEN?
798
corresponding to two successive sets of carbon profiles, agree within the desired accuracy. The procedure is illustrated in the flow diagram of Fig. 14. The time required to calculate the parameters when the data were analyzed per temperature was 1Osec on the Siemens 4004-150, when all the experiments were analyzed together 90 sec. Finally, one more remark should be made about the weighting factors. One run was also analyzed using the determinant criterion of Box and Draper [lOIinstead of
this:
azi,7)
‘(zi,. Then the carbon profiles at the “collocation times” are also corected by multiplication with this ratio. With these corrected profiles a new minimization, leading to a new set of parameter values is undertaken. The procedure is stopped when two successive sets of parameters,
Klnetk rum Deacthtkn
r”ns-per
tempemture (0)
Deactivatbn runs-all tempertires
-2.50
-
142
I 144
14.6
I 14.6
I 150
104/T
Fig. 8. I
3 5 -r
-40
---- -------
Khetkrum oeactivatbn runs-per
-
oeoctiwtlon
(0)
tempemhre
runs-on tempermures
-
-5.0 t 430 I42
420
410
I44
14.6
400 I46
390
T(V)
390
TCC)
I50
104/T
Fig. 9. \ -TO- ‘\
-_-_-.-
cteacthtbn runs-per tempemtwe (0) DectctivatlMl runs-all temperahxes
-
-9.0
-
430
420
I
I
14.2
144
400
40
I I46
104/T
Fig. 10.
I I46
I I50
Deactivation the objective excellent higher, It
function
defined
agreement.
The
in (20). The results
were in
computation
time
was
much
computations
that
the
model
however.
followed
from
the
including
Eq. (18) for the coking
because
of a poorer
therefore
consisted
was
of a platinum reforming catalyst in a tubular reactor
concluded
fit of the
that
the fit arrived
function
of the process
obtained
with constant
the validity
The
variables
at with
final
was
variables
The final parameter
concerning
turned values
and carbon
profiles,
412°C
by Figs. 4, 6 and 7, which
and aoc
superior
to that
a $-test
obey
the
evidenced
based
Cpentane,
hydrocracking
as is illustrated
pro-
for the run at
also include
upon the results
the final
of Table
Figs.
by Table
temperature
5 (all
coefficients
tion, 4,, varied from deactivation
significantly
dependence,
as
is
5 and Figs. 8-l I. This is true also for cu; and ah.=
I2 and 13. The deactivation
total pressure,
5.
also those for coking,
Arrhenius
the deactivation
on
the dependence in Table
pofiles
The rate coefficients,
model
an F-test it
out to be positive.
are given
n- and
ducts,
temperatures).
a,
al and aoc. Tn addition
of the hypothesis
on the process
data.
the experimental
computed
rate had to be discarded
of (16), (17) and (19). From
799
as illustrated
function
by
for isomeriza-
1 to 0.66 for the run at 431°C and low
which led to the highest function
coke content.
for hydrocracking,
&,
varied
The from
1 to 0.37. 6.
The model
As
DlSCUSSlON
used in this work
permits
an excellent
-_-----
I
-
already,
of the model,
rum-per
oswthuHon
runs-am kmpsmtureS
4lo
I
I
I
142
I44
146
(k’)’ rather
was
I
400
146
I
390 WC)
15.0
lO'/T
Fig. II. Table 5. Final parameter values. Results obtained with u function of the process variables Per temperature (k’)‘x a:
10’
(kD)’ x lo’ crhc
8.42 152.1 090 203.6 o-50 3.70
7.47 85.3 1.10 103.4 0.95 3.33
From “kinetic” runs
K' K,:" In A(ak)
E(a’J
12.36 115.1 246 62.6 2.93 7.21
19.69 51.4 2.49 62.0 3.83 14.87
19.17 33.0 4.73 41.4 7.69 25.33
From deactivation runs Per temperature All temperatures
15.95 24,350 564 3798
-
19.91 31,910 2.17 7.94
*Approx.
12.77 60.4 2.98 79.9 3.08 Il.07
95 per cent confidence intervals.
12.89 20,180 - 12.92 23,210 20.05 32,240 - 14.29 25,200 30.17 52,000 24.76 42,890
12.45 2 0.62’ 19,650?2,180 - 13.5126.75 23,760 -t 11,880 21.17kO.73 33,760 2 1,500 -7G1.14 16,520?4,130 23+0+3.67 43,620 ” 7,270 27.45 r 1.61 46,470 + 2,445
considered
as a
than fixing it on the basis
nmpsmtm (0)
Deactb0h
420
430
mentioned
parameter
fit of
2248 38.7 5.13 42.5 10.10 3266
R. P. DE PMJWand G. F.
142
14.4
FROMENT
14.6
146
104/T
Fig. 12.
5.0
-----_-
I
-
142
I44
olxalvatlofl
runs-per
chactm
runs-all
tempcmtw.3
I46
146
(0)
tempemhJm
15.0
104/T
Fig. 13.
of the experiments in the absence of coking. From Fig. 8 it is seen that the (k’)’ derived from the deactivation experiments are in excellent agreement with those derived from the “kinetic” experiments, also reported in Table 5. The same is true for the hydrocracking rate coefficients (kD)’ (Fig. 9). It may be concluded that a satisfactory approach has been developed and illustrated for estimating the coking characteristics of a catalyst under given process conditions. The experimental effort and the computation have been reduced to a reasonable level, permitting a rather rigorous approach. It is rewarding that such a high level of significance has been obtained from only 7 runs. The approach therefore looks promising for further work tending at establishing general correlations for catalyst coking. Acknowledgements-R. P. De Pauw is grateful to the Belgian N.F.W.O.-F.N.R.S. for a Fellowship over the years l!Vl-74. The calculations were performed at the “Centraal Digitaal Rekencentrum” of Rijksuniversiteit Gent. NOTATION
weight factors in objective function a ** differential coefficients in collocation
a, b, c
Fig. 14.
Deactivation
of a platinum reforming catalyst in a tubular reactor
mol mol frequency factor, or g cat hr g cat hr atm Or mol atm g cat hr g coke C coke content of the catalyst, g cat hr act sites concentration of active sites, g cat
A
c* E
activation energy, -$
801
W,l),j(l,h
k,n(Lti)count
variables in collocation
I isomerization M n -pentene Ml, ML adsorbed n-pentene N tpentene Nl, NL adsorbed Cpentene P parallel mechanism Cl total number of active sites Sl active sites covered by coke
9 objective function F, total flow rate, $
kc=rate coefficient for consecutive coke formation g coke ‘gcathr kc rate coefficient for parallel coke formation, id. kD rate coefficient for hydrocracking, mol g cat hr atm mol k’ rate coefficient for isomerization, g cat hr equilibrium constants K,KJG K** adsorption equilibrium constants 1 Pt-active site involved in hydrocracking and coking L A1203-active site involved in isomerization nhn2 order of the coking reaction p* partial pressure of reacting components, atm PI total pressure, atm g coke rc rate of coke formation, g cat hr mol rD rate of hydrocracking, g cat hr mol li rate of isomerization, g cat hr R
gasconstant, +&
t,t* time, hr T absolute temperature, “K w* WIF,” w,
*
integration coefficients in collocation g cat hr space time, mol axial coordinate, cm refers to subscripts or superscripts.
Subscripts A n -pentane B Cpentane
consecutive mechanism i coke D cracking products Dl adsorbed cracking products H hydrogen
Superscripts C coking D hydrocracking
I isomerization o non-fouling conditions 1 estimated values. Greek symbols
g cat g cat deactivation factor, or g coke g coke atm g coke initial rate of coke formation, g cat hr molar ratio hydrogen/hydrocarbon void fraction bed length, cm bulk density of the bed, 5 Pf
0: II* i-l
density of the gas, 2 run length deactivation function correction factor in the calculation of weight factors cross section of the bed, cm* REFERENCES
[I] Butt J. B., Chemical Reaction Engineering, Advan. Chem. Ser. 109, pp. 259-4%, Am. Chem. Sot., Washington, DC 1972. [2] Voorhies A., Ind. Eng. Chem. 1945 37 318. I31 Weekman V. W., Ind. Eng. Chem. Proc. Des. & De@. 1968790. [41 John T. M., Pachovsky R. A. and WojciechowskiB. W., in Chemical Reaction Engineering II, Adv. in Chem. Series, pp. 133-422 Advan. Chem. Sot. Washington D.C. 1974. [5] Lambrecht G. C., Nussey C. and Froment G. F., Proc. 5th Eur. Symp. on Chem. React. Eng., Amsterdam (1972), Elsevier, Amsterdam 1972. [6] Froment G. F. and Bischoff K. B., Chem. Engng Sci. I%1 16 189. [7] Hosten L. H. and Froment G. F., Ind. Eng. Chem. Proc. Des. & Devpt. 1971 10 2. [8] Sinfelt J., Hurwitz H. and Rohrer J., .I. Phys. Chem. 1960 64 892. [9] Van den Bossche B. and Hellinckx L., A.I.Ch.E. J/ 1974 24lf2) 251. [lo] Box G. and Draper N., Biometrika I%5 52 355.