Ind. Eng. Chem. Res. 1993,32, 2975-2986
2975
Vaporization-Induced External Dewetting of a Catalyst during an Exothermic Multiphase Reaction Michael P. Harold' and Ka M. Ng Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
A heterogeneous model is developed to elucidate the phenomena of dewetting and hot-spot formation during a n exothermic reaction in a gas-liquid fixed-bed reactor. The model focuses on processes external to the catalyst and accounts for the mass, energy, and momentum transport, vaporization, and reaction on the gas- or liquid-covered catalytic solid surface. For a typical olefin hydrogenation reaction, model predictions indicate that the system is external heat- and mass-transfer limited and that thermokinetic coupling causes steady-state multiplicity. In addition, the effects of the heat of reaction, catalytic activity, liquid-phase volatility, and solid-phase thermal conductivity on the location of the dewetting point and conversion are assessed.
Introduction A large class of industrial processes involve as their central step an exothermic catalytic reaction between gaseous and liquid components, such as hydrogenations and oxidations. A multiphase reactor frequently used in such industrial reactions is the fixed-bed multiphase reactor, more commonly referred to as the trickle-bed reactor. The typical operational scheme is to flow the gas and liquid phases down over the bed of catalytic particles. Complex phenomena occur within the trickle-bed reactor-chemical reactions on both liquid- and gascontacted catalyst, transport of heat, mass, and momentum, and phase transition. Moreover, the spatial distribution of the two fluid phases is coupled with the transport and reaction processes. External dewetting of catalyst can be caused by an exothermic heat of reaction induced vaporization of the bulk liquid phase. The experimental data of Hanika and co-workers (1976)provide evidencefor such a phenomenon. Dewetting in turn can lead to hot-spot formation which can cause runaway in industrial reactors. Indeed, several reviews of trickle-bed reactors have emphasized the need to treat nonisothermal effects (e.g., Satterfield, 1975; Ng and Chu, 1987;Lemcoff et al., 1988;Harold, 1993). Despite this, surprisingly few models have focused on such vaporization effects coupled with reaction in the tricklebed reactor. In a pioneering study, Hanika et al. (1986) developed a model which is comprised of differential bulk gas, bulk liquid, and intraparticle mass balances, bulk liquid and solid energy balances, and phase equilibrium relations. The degree of external wetting of the catalyst is calculated using available literature correlations. The model assumes isobaric operation and local vapor-liquid and thermal equilibrium. These assumptions are questionable under conditions of intense vaporization and a high rate of reaction. Qualitative agreement of the model with a limited set of experimental data for 1,5-cyclooctadiene hydrogenation is demonstrated. Unfortunately, the degree of wetting and liquid flux profiles were not reported in the results. Such profiles could provide insight about the influence of thermal effects on the wetting distribution. Hrovat and Levec (1989)simulated an exothermic reaction with vaporization on a vertical string of three spherical pellets. Khesegi et al. (1992) recently developed a
* Author to whom inquiries should be addressed. Current address: DuPont Company, CentralResearchand Development, Experimental Station, Wilmington, DE 19880-0304. 0888-5885/93/2632-2975$04.00/0
pseudohomogeneous model which predicts some of the features of the data of Hanika et al. (1976). Their results demonstrate that a loss of liquid within the reactor can lead to significant temperature rise. However,their model does not include the catalytic kinetics, as external masstransfer processes are assumed a priori to control the overall rate. This limits the generality of the model. Moreover, given the importance of the wetting, the interphase phenomena, and the solid heat conduction, the heterogeneous approach of Hanika and co-workers is probably more prudent. In this study we consider an idealized situation involving an exothermic reaction on a solid catalyst. The catalyst is contacted by a thin liquid film containing the less volatile reactant and product, and the sparingly soluble reactant. The film is in direct contact with a flowing gas stream containing the three species. Such a situation is encountered during trickling flow with this reactor type. The combination of sufficiently volatile liquid components and sufficiently exothermic reaction can lead to vaporization of the film. This in turn can lead to complete dewetting of the catalyst and the subsequent exposure of the catalyst directly to the flowing gas stream. Our objective is to formulate a comprehensive mathematical description which relaxes many of the assumptions of previous studies. A systematic parametric sensitivity analysis helps to identify key multiphase reactiontransport interactions and different rate limiting regimes. The results are interpreted to provide fresh insight about the role of vaporization in hot-spot formation within the multiphase fixed-bed reactor. Moreover, the heterogeneous model should provide a foundation for the development of more sophisticated nonisothermal multiphase reactor models.
Physical Picture Figure 1shows a schematic of the catalyst, a nonporous slab of thickness 269, length L, and width W. It is contacted by a flowing liquid film, the thickness (6) of which is a function of the distance ( z ) down the slab. The width of the channel between adjacent slabs is 26,. The gas which flows cocurrently with the liquid occupies the remaining interstitial space. The dashed lines denote lines of symmetry which bound the region actually modeled. An exothermic reaction given by
-
AGL) + VBB(G,L)VPP(GU + heat is considered. In this study the reaction is assumed to 0 1993 American Chemical Society
2976 Ind. Eng. Chem. Res., Vol. 32,No. 12,1993
justified for a dilute solution but may lead to an underprediction of the flux in a concentrated solution (Cuealer, 1984). Given the intent of the current model, the linear driving force term is deemed adequate. The first term in each balance accounts for a change in the molar flux VAL, FBL,FL) through the liquid film. The reference area for the liquid flux is W6. The thickness of the film is approximated by the expression derived from the integrated momentum balance for laminar film flow down a vertical wall: (4) Figure 1. Schematic of model consisting of a nonporous catnlytic dab, and a flow channel for gas and liquid.
occur only on the surface of the slab. Thus, our model sidesteps any complexities due to intraparticle processes, such as imbibition and capillary condensation,and focuses on external phase transition and transport-reaction interactions. The reader is referred to recent studies which primarily dealt with intraparticle processes (Jaguste and Bhatia, 1991; Harold and Watson, 1993). The three components A, B, and P are distributed between the two fluid phases. Without loss in generality, species A is considered to he a highly volatile component which is sparingly soluble in the liquid phase. The combination of sufficientlyvolatile liquid components and large rate of heat generation results in the formation of a dewetting point at a distance Z* from the top of the slab which demarcates the wetted and nonwetted sections. The slab can be visualized as a vertical line of catalytic pellets in the multiphase fixed-bed reactor and thus serves as an idealized yet realistic model for studying phase transition and hot-spot formation.
Model Development The model consistsof differentialhalancesfor the liquidcontacted section (0 < z < z*) and gas-contacted section (z* < z 0) and activated ( Y ~ G= y r =~ 25). The catalyst is fairly active (Du'G= 1). Finally, the geometry corresponds to a system which has a channel width narrower than the slab thickness 5; 6,lL = and much shorter than the slab length (6s/6, 0.01). The model was solved numerically using an IMSL b-spline collocation code (COLSYS)appropriately modified to handle the two sections (wet and dry). In addition, multiple solutions were obtained by using parameter continuation. The reader is referred to Appendix C of Harold and Watson (1993)for details. The dewetting point is formally defined as the point a t which the liquid flow rate vanishes (eq 46). This condition had to be approximated to avoid numerical difficulties. In all the simulations reported below we used the criterion
-
u
= 42
1.75
That is, dewetting is taken to occur when the film thickness is less than 1%of the gap width. A sensitivity analysis of the value used for e revealed negligible outcome on the results.
Results and Discussion Base Case: Identification of Key Trends and RateControllingRegimes. It is instructive to examine in some detail the results of a typical case that corresponds to the base set of parameters (see Table I). Figures 2a, 2b, and 3a show the impact of the liquid to gas feed flux ratio f OLG (=F "IJF O G ) on the species B conversion (XB), dewetting point position (E*), and end slab temperature ( r s ( f = l ) ) , respectively. Figures 3b, 4a, and 4b show selected profiles of slab temperature ( T S ( [ ) ) , liquid composition (xi(.!)), and gas composition (yi([)), respectively. A t sufficiently high liquid flow rate cf OLG) the catalyst is completely wetted by the liquid film ( f * = l)), as shown in Figure 2b. In addition, as f OLG is decreased a transition from a completelywetted to partially contacted slab occurs. These trends are not unexpected because recall that the feed gas is not saturated with the main liquid components B and P. However, as the simulations show, the existence of the exothermicreaction enhances the drying-out process.
Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 2981
INLET LIQUID FLUXIINLET GAS FLUX
0.0'
" 0.1 0.2 0.3 0.4 0.5 0.6 INLET LIQUID FLUXIINLET GAS FLUX "
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Figure 2. Dependenciesof (a)species B conversionand (b) dewetting position on the ratio of liquid flux and gas flux at the reactor inlet.
E w &
the f OLGvalueat which the ignition point of the conversion hysteresis loop is encountered. An inspection of the species B conversion plot (Figure 2a) reveals that the bounding states are quite different in extent of reaction. Along the "low" branch in the conversion plot for f OLG > 0.35 the conversion is very low (XB< le2). Along the "high" branch, encountered for f O L G < 0.39, the conversion increases monotonically with decreasing f OLG from approximately 0.02 to close to 0.4. Correspondingly, the dewetting point decreases monotonically from 0.98 to 0 as f OLG is decreased from 0.39. The differences in the extent of reaction are underscored in the dependence of the temperature at the end of the slab (q([=l)) on f OLG (Figure 3a). It is interesting to note that since the system is adiabatic the end slab temperature is lower (higher) than the bulk gas temperature along the low (high) rate state. In the low rate state the heat effects are dominated by the endothermic vaporization process and thus a temperature decrease is encountered. On the other hand, in the high rate state the heat effects are dominated by the exothermic reaction. Thus, the end slab temperature is less than unity along the low-conversion branch but greater than unity along the high-conversion branch. Slab temperature profiles that are encountered at the three labeled points in the T s ( t = l ) versus f oLGplOt(Figure 3a) are shown in Figure 3b. When the slab is completely wetted ( ~ O L G = 0.38, point 11, the slab temperature decreases monotonically from the top of the slab. Again, this is due to the energy consumed by the steady-state vaporization process. At the same liquid flow rate but along the high conversion branch cf OLG = 0.38, point 21, the slab temperature profile exhibits a local minimum and maximum. The minimum occurs just before the dewetting point ([* = 0.68);the maximum occurs at the end of the slab. A sharp temperature increase is predicted in the vicinity of the dewetting point. A t a lower liquid flow rate ( ~ O L G = 0.24, point 3) the same qualitative features are evident; however, the temperature increase occurs closer to the top of the slab (t* = 0.05) and is more pronounced. A close examination of Figure 3b reveals that the temperature decreases below its feed value along the liquid-contacted section. This indicates that the heat generated by the downstream catalytic reaction is not conducted upstream effectively. The primary cause for the large increase in the conversion along the two bounding states is readily identified by inspecting some representative composition profiles in the direction of flow. For the completelywetted slab, the overall rate is limited by the supply of the sparingly soluble reactant A. This is also true locally along the liquid contacted section of the partially wetted slab. Figure 4a compares the liquidphase mole fractions of reactants A and B for the partially contacted slab cf OLG = 0.24; point 3 in Figure 3a). Also shown is the mole fraction of species A at the surface of the catalyst. An increase in the species B concentration occurs along the length of the liquid film. Recall that the entering gas contains 75% A, 20% B, and 5 % P. The entering liquid contains 50% B, a trace of A (0.01%), and the remainder B. Species P, being more volatile than species B, vaporizes. This leads to a concentration of B in the film. The relatively small change in the gas composition during its contact with the liquid film indicates that the gas is flowing at a much more rapid rate (Figure 4b). Most significantly, there is a large difference in the species A bulk and surface mole fractions along the length of the wettedpart (Figure 4a). This clearlyindicates that the limiting reactant A cannot be supplied at a sufficient rate, and thus the reaction is external mass
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Figure 3. (a) Dependence of the temperature at the end of the slab on the ratio of liquid flux and gas flux at the reactor inlet. (b) Temperature profiles of the slab at a ratio of liquid flux to gas flux atthe reactorinlet of0.38. Alsoshownare the slab and gastemperature profiles at a ratio of 0.24.
Indeed, for the particular choice of parameters the transition from a completely liquid-contacted to partially contacted state is complicated by the existence of three solutions for an intermediate range off OLG. That is, the critical flow rate for which a dry spot forms at the bottom of the slab, f OLG[fL(E=l) = 01 = 0.35, does not correspond to the highest flow rate which results in a partially wetted slab. Rather, the highest flow rate corresponds to the f OLG value at the extinction point of the clockwise conversion hysteresis loop (Le., f O~~[f~([=0.98) = 01 = 0.39). The critical liquid flow rate at which dry-out is initiated at the bottom of the slab corresponds closely to
2982 Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 1.0
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transfer limited. Combined with the very low solubility of A, the extent of reaction along the wetted part is negligible. If a fraction of the slab surface is exposed directly to the gas, the rate increases dramatically. This is due in part to the much higher supply rate of species A to the catalyst surface with the absence of the liquid film. Also contributing to the higher rate is the less effective heat removal and the absence locally of an endothermic vaporization process. The model predicts for this particular case that there is an adequate supply of A to the catalyst surface along the high-conversion branch. However, as Figure 4b indicates, the surface concentration of B vanishes. This is a species B supply limited state; i.e., the local rate is given by eq 31. These results lend support to the model developed by Khesegi et al. (1992) in which external mass transport is assumed to be rate limiting. The external heat transport limitations are equally severe. This is confirmed in Figure 3a, which compares the exit gas temperature to the exit slab temperature along the high branch. A large temperature difference between the solid and flowing gas is apparent. The existence of steady-atate multiplicity can be attributed to a thermokinetic coupling mechanism as encountered, say, when an exothermic reaction is carried out in a fixed-bed catalytic reactor (Froment and Bischoff, 1979). Thermal feedback is provided by conduction primarily through the solid. Heat generated by the gasphase catalysis raises the local temperature and supplies the needed latent energy for vaporization of the flowing film. That is, even in the absence of gradients in the main flow direction (downward) the interaction between the exothermic reaction and boundary layer transport processes can cause multiplicity. Below we provide more insight into which mechanism causes the predicted multiplicity in this system. Catalytic Activity. Earlier it was pointed out that, even in the absence of reaction, dewetting should occur because the gas and liquid feeds are not in thermodynamic equilibrium. To evaluate the contribution of reaction on dewetting, it is useful to check the impact of the catalytic activity on the overall performance of the catalytic slab.
Figure 5. Influence of catalytic activity on system behavior: caee a Da'G = 1 (base case); case c Da'G =
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Figure 6. Influence of catalytic activity on system behavior: case b DU'G 0.003.
The catalytic activity is varied by adjusting the value of the gas phase Damkohler number, Da'G (=ks(T,,)).The corresponding rate constant for the liquid phase reaction is adjusted using eq 32. The following values Of Da'G are considered in Figures 5 and 6: base case a:
DatG = 1
case b:
D d G = 0.003
case c:
Da'G = lo3
Case c mimics the situation of negligible reaction. The results in Figures 5 and 6 help to differentiate between simple vaporization and vaporization-induced conversion increases. At a sufficiently low activity (case
Ind. Eng. Chem. Res., Vol. 32, No. 12,1993 2983 5
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