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REVIEW
Thirty-Five Years of Applied Catalytic Kinetics J. M. Smith University of California, Davis, California 956 16
Progress in deducing rate equations from global measurements, for heterogeneous catalytic reactions, is reviewed. Distinctions between establishing a true kinetics model, or mechanism, and an empirical rate equation are emphasized. Considerable progress has been made in statistical analysis of intrinsic rate data for the purpose of determining optimum values of the parameters in a Langmuir-Hinshelwood, or similar form of equation. Also, laboratory reactors have been developed for obtaining global kinetics with minimal effects of transport processes. Methods of interpreting global data to eliminate transport effectsare briefly discussed for different types of reactors. However, the emphasis in this review is on rate equations for the chemical steps in catalytic reactions. At present, means are at hand to derive rate equations with empirical constants, which fit experimental data well. Progress in converting such results to true kinetics models depends upon knowledge of the nature and concentrations of the species adsorbed on the catalytic surface.
The major contributions of chemical engineering in past decades have been applications of physical and chemical sciences to the process industries. In the twenty years from 1930 to 1950 the principles of phase equilibria, as developed by Gibbs (27),have been utilized with considerable success in the burgeoning petroleum industry. Sage and Lacey (6)and Dodge ( l a ) ,and their industrial compatriots, were leaders in this endeavor, which involved primarily application of thermodynamics to separation processes. Near the end of these two decades the numerous possibilities for chemical converson of hydrocarbons to more valuable products led to the tremendous growth of the petrochemical industry and the accompanying need for rational methods for reactor design. The first book to treat this subject from a chemical engineering viewpoint is Part 111, “Kinetics and Catalysis”, of Hougen and Watson’s three-part series entitled “Chemical Process Principles” (35). Part 111was published thirty-five yers ago and included as main subjects equations for the intrinsic rate of fluid-solid catalytic reactions. Intrinsic kinetics refers to the rate expressions for the processes of adsorption, surface reaction, and desorption which occur at an activated site on the catalyst and, hence, at an intraparticle location in a porous catalyst pellet. Intrinsic rate equations are in terms of concentrations and temperatures at the intraparticle location. When combined with the effects of transport processes, intrinsic kinetics provide a global rate useful for reactor design. The global rate is expressed in terms of concentrations and temperature in the bulk fluid surrounding a catalyst pellet, and thus includes transport effects. While only fixed-bed reactors were considered in detail, this early book is remarkable in that a fundamentally sound discussion is included of four of the six transport processes (intraparticle, fluid-particle, and axial dispersion for mass and heat) that occur in nonisothermal operation. Only intraparticle heat transfer and axial dispersion of heat were omitted, and the former is normally not significant (52) and the latter is unimportant in most industrial reactors, since the velocity is relatively high and
the catalyst bed is deep (combining to give a large axial Peclet number). The chapter entitled “Catlytic Reactions” employed the concepts of Langmuir and Hinshelwood to provide a systematic procedure for deriving equations for the intrinsic rate of fluid-solid catalytic reactions. This procedure, which is widely used today, has proven valuable for correlating experimental rate data. As is often the case with important contributions, it sometimes has been given significance, especially with respect to conclusions about mechanism, that goes beyond the original intent. Sol Weller, whom we are honoring at this symposium, has provided one of the most carefully thought-out guides (5, 11, 70,71)to the usefulness and limitations, not only of the Hougen and Watson procedure, but to the concepts advanced by Langmuir and Hinshelwood. In the remarks that follow, the problems in obtaining the intrinsic rate of reactions catalyzed by solids are considered first. This is followed with a discussion of the interaction between intrinsic kinetics and transport effects.
Reaction Mechanisms vs. Rate Equations The term applied kinetics can have a different meaning for chemists and engineers. In this paper the engineering viewpoint is taken so that applied kinetics refers to the reaction-rate information needed for design of chemical reactors. It is desirable that the experimentally measured rates (determined, for example, in bench-scale apparatus) include all conditions of temperature, composition, and catalyst properties that may be encountered in the design of commercial-scale reactors. Since this goal is not always reached, extrapolation (and interpolation) should be as accurate as possible. From a practical viewpoint, this is the only reason that users of applied kinetics have an interest in reaction mechanisms in lieu of wholly empirical correlations of rate data. The same distinction can be drawn between empirical and more scientifically based consideration of transport concepts necessary to convert an intrinsic rate to a global basis. As a result of this somewhat indirect interest in mech-
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anisms, the applied kineticist has followed the developments in pure kinetics. For fluids reacting on solid catalysts the concepts about mechanism start with the work of Hinshelwood and Langmuir. These researchers were interested in the actual way molecules and atoms (of the catalyst) interact to produce the chemical reaction. Other less-detailed interpretations are sometimes given to the term mechanism. Weller (71) describes this second meaning in the following words: “A convenient and reasonable representation of the reaction which, although not in general unique, is at least consistent with known data and permits both interpolation and some extrapolation.” This introduces a third, intermediate approach between the strict concept of a reaction mechanism and wholely empirical rate equation (e.g., power law formulation) mentioned in the previous paragraph. Langmuir’s important contribution (40) was to describe qualitatively and quantitatively how and at what rate a fluid molecule became attached to a solid surface; that is, he proposed a description of the adsorption process that must be associated with a catalytic reaction. Hinshelwood first summarized his ideas in the 1926 edition of a book entitled “The Kinetics of Chemical Change”. Periodic revisions appeared with a final presentation in 1940 (33). Hinshelwoods ideas of combining adsorption and surface processes are still followed in proposing mechanisms. He reasoned that chemisorbed molecules remain on the surface of the catalyst for a longer time than two molecules in close contact (close enough for reaction to occur) during collision in a homogeneous phase. Hence, the liklihood of reaction occurring, that is the probability of attaining the required activation energy, is greater for adsorbed molecules than for homogeneous molecules. Further, the surface species formed as a result of adsorption may react with a lower activation energy than in the fluid phase. From this explanation for catalyst activity it is logical to suggest that for bimolecular systems reaction it is more likely if both molecules are adsorbed on adjacent sites than if but one is adsorbed. Thus, Hinshelwood reasoned that the most likely mechanism involves surface reaction between adsorbed species. This is in contrast to the LangmuirRideal or Rideal-Eley (22, 55) concept that the surface reaction occurs as a result of the collision between a fluid-phase molecule and an adsorbed one. From these concepts a logical procedure can be proposed for formulating an equation for the rate of any catalytic reaction, and this has been systemized by Hougen and colleagues, as mentioned earlier. Before examining the suitability of this approach it is helpful to review the key assumptions made by Langmuir and Hinshelwood. The steps in developing a rate equation by the Langmuir-Hinshelwood procedure and the assumptions made in so doing have been well described by Weller (71). In general the following steps are followed. (1)Propose a series of adsorption, surface reaction, and desorption processes which, when combined, give the overall reaction. This really is a proposal for the mechanism, and, unless all intermediates are known, is a gross assumption. (2) Choose one of the processes (a surface reaction between adsorbed species according to the Hinshelwood concept, or reaction between an adsorbed species and a fluid-phase molecule according to the Rideal-Eley theory) to control the rate. This also is an assumption if only overall kinetics data are available. (3) Assume that the several processes are elemental ones to the extent that reaction order follows the stoichiometry of the process. With respect to adsorption and desorption
this means that the Langmuir concepts are valid. (4)Develop an intrinsic rate equation from the three prior postulates with the additional premise that the total surface coverage of all adsorbed species is less than that corresponding to a monomolecular layer. In most kinetic studies of industrially important reactions, the experimental data obtained are global rates from which transport effects are extracted to give an expression for the intrinsic rate. With only this kind of experimental information it is not surprising that the extensive and severe assumptions in the prior listing cannot be tested. Additional experiments, such as adding products to the feed, making initial rate measurements (for example in a differential reactor) over a wide range of concentrations, and dynamic studies involving periodic changes in concentrations, can improve the final rate equation and perhaps contribute to the verification of the assumptions listed. However, even with such auxiliary information it seems hazardous to claim that a mechanism has been determined. Only a knowledge of the intermediate species, which means the species existing on the catalyst surface during reaction and how these intermediates interact, can give one complete confidence about the postulates made in items (1)and (2). It is because of this that fundamental work in catalysis has been primarily a study of surface chemistry, particularly of the locations on the surface that are active for reaction [the active-center concept proposed by Taylor in 1925 (66)l. Progress in this area has been painfully slow. Over the years geometric, lattice structure, and electronic theories, among others, have been proposed (67)only to be found imperfect as additional experimental data appeared. Progress occurs as new and more sophisticated devices and methods become available for studying the surface of solid catalysts under adsorption or reaction conditions. Somorjai (62) recently has reviewed what is known about active sites and atomic structure of catalytic surfaces and discussed experimental developments. Many experimental methods of examining surfaces are operable only at high vacuum. Results at these conditions are not easily extrapolated to operating conditions of industrial reactors. Mossbauer spectroscopy does not have this disadvantage. Dumesic and Topsoe (19) have used this experimental procedure for studying adsorbed species at normal operating conditions. One of the assumptions inherent in Langmuir’s adsorption rate equations is that the catalyst surface is homogeneous; that is, all active centers have the same activity. This is not valid over a wide range of surface coverage (e) as indicated by the variation in heat of adsorption with (0) (5,B). However, special cases can occur. Pritchard and colleagues (53) analyzed rate data for the oxidation of naphthalene at two different surface coverages and found that the homogeneous surface model fit the data as well as the heterogeneous model based on the Temkin-type adsorption isotherm. In view of the numerous assumptions (refer to the foregoing list) necessary to develop a rate equation, it is difficult to be f m about any one assumption when analyzing rate data. While some pure adsorption data have been shown to fit the Langmuir isotherm, in other instances large deviations occur (29). When adsorption is combined with surface reaction, interaction between adsorbed species can cause further deviation from the Langmuir isotherm. Langmuir himself recognized deficiencies of the homogeneous-surface assumption contained in his formulation for adsorption. The major assumptions were included in his original publications (9, 40). Sinfelt (60) has reviewed the relationship between chemisorption and catalyst activity for numerous types of
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reaction: hydrogenation, hydrogenolysis, isomerization, ammonia synthesis and decomposition, oxidation, and the decomposition of alcohols and organic acids. The approach in this excellent review is not from the standpoint of quantitative adsorption rates but how adsorption data can be used to indicate solids that may be active catalysts for a given type of reaction. His conclusions are worth restating “In considering patterns of activity variation among catalysts, one can generally rationalize the results in terms of a rather broad principle relating catalytic activity to the adsorption properties of the reactants. According to this principle, maximim activity results when chemisorption of the reactant is fast but not very strong. If the adsorption bond is too strong, the catalyst will tend to be fully covered by a surface species which is too stable to undergo reaction. This represents one extreme. At the other extreme, if chemisorption of the reactant is slow, the reaction may be seriously limited by the adsorption step. Optimum catlytic activity corresponds to an intermediate degree of coverage of the surface by the adsorption complex undergoing reaction”. Qualitative conclusions of this type can be of considerable practical use in identifying catalysts, although they do not answer the problem of the validity of the assumptions employed in formulating rate equations. The Rideal-Eley mechanism and related redox approach (46) still find application as alternates to the Hinshelwood-type mechanism. For example, White and colleagues (15, 47) explain the oxidation of carbon monoixde on palladium foil as a reaction between chemisorbed oxygen atoms and carbon monoxide in the gas phase. Rate data fit this mechanism better than other postulates about how the reaction occurred. Young and Greene (73) fit overall rate data for the oxidation of benzopyrene on a commercial vanadium pentoxide-molybdenum oxide catalyst by supposing that the oxides were reduced by the oxidation reaction and reoxidized by chemisorbed oxygen, with the latter step of the redox mechanism controlling the rate. These examples of the Rideal-Eley and redox mechanisms are illustrative of the numerous publications which propose mechanisms from overall rate data. More detailed and perhaps convincing information about mechanism is obtained when several types of measurements are employed. For example, Conner and Bennett (16) used pulse and steady-state technques in a gradientless reactor (no interphase and intrareactor transport effects) along with isotope studies with 13Cand la0to study the oxidation of carbon monoxide with a nickel oxide/ (silica gel catalyst). These authors suggested that carbon dioxide was formed by two mechanisms: (1)the conventional reaction between adsorbed oxygen atoms and CO in the gas phase, and (2) via a two-carbon intermediate, a scheme which may be represented as CO(g) + COJads)
- +
+ O(ads)
Cz03-O(ads)+ O(ads)
Cz03.0(ads)
2C02
O(ads)
Among other techniques designed to provide information about mechanism is the spectroscopic flow reactor (51). This is a continuous flow, well-stirred reactor containing a disk of catalyst and equipped with windows transmitting IR radiation so that IR transmission spectroscopy can be used to study the adsorbed species. In concluding this section on progress in reaction mechanisms two papers illustrating a novel experimental and theoretical approach should be mentioned. The first (44) consisted of rate data for the liquid-phase hydrogenaton of cyclohexene in a slurry reactor with several Pt/SiOP and Pt/A1203 catalysts and solvents. Thermodynamic considerations showed that the reaction rate
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constant was independent of the solvent (seven were used) when hydrogen concentration rather than activity was employed in the rate equation. It was also found that there were no platinum-support interactions for the nine catalysts. The second (2) is an extension of the Eyring transition-state theory for predicting preexponential factors. Order of magnitude agreement was obtained for such catalytic reactions as the oxidation of formic acid to carbon dioxide, and the production of acetylene or methane from carbon and hydrogen atoms. If further investigatons continue to show such agreement, this extension of transition state theory to surface reactions should be useful for simple reactions where the mechanism is known. With respect to the question of mechanism, the following statement made by Langmuir in 1921 (40) still is appropriate 60 years later: “With our increasing knowledge of the structure of solid bodies and of the atoms and molecules of which they are built, we should now, however, gradually (the italics have been added) begin to gain a clear insight into the mechanisms of such surface reactions”.
Parameter Evaluation in Rate Equations In addition to Weller’s helpful contributions, others have discussed how uncertain are conclusions about mechanism when based solely on reaction rate data. Edelson and AUara (21) have emphasized that the parameters appearing in the rate equations obtained by the Hougen and Watson procedure are not true rate and adsorpton-equilibrium constants. Their conclusions are illustrated by a careful study of the pyrolysis of propane. Two hundred forty reactions involving 19 radical and 20 nonradical species, with many of the rate constants determined from independent investigations,were employed. The resulting rate equations agreed well with their data (1) and with that of others (41). However, even such a detailed system failed to fit the data of Herriott (31). The conclusion was that his reaction system was more complex than even their set of numerous reactions. The need was stressed to distinguish between the correlative value of parameter fits in a rate equation as opposed to the predictive capabilities of an equation based upon a true model, that is, upon the correct reaction mechanism. Beranek (6) has also demonstrated, with the cyclohexane-cyclohexene-benzene reaction system, the uncertainty in obtaining a correct kinetics model, even with sophisticated mathematical techniques. Accepting the empirical nature of such rate equations, there remains the question of distinguishing between numerous possiblities depending upon the particular assumptons made about the reaction mechanism and controlling steps. Assuming all steps but one are fast means that the final rate equation contains equilibrium constants, particularly adsorption-equilibrium constants. For many years rate equations were eliminated if a constant turned out to be negative or did not show the expected decrease with temperature. More recently, cases of strong retardation of the rate have necessitated negative values in order to have an empirical equation that fit the data. In attempts to place such evaluations on a more fundamental basis Vannire, Boudart, and co-authors (9,68)have proposed rules for testing the suitability of numerical values in rate equations. The direct test of adsorption constants is the comparison between values determined by fitting the rate equation to observed kinetics and determined from pure adsorption measurements. Even though this ignores interaction effects on the surface, surprisingly good agreement has been observed for some reactions. Weller (71) discussed the
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research of Kabel and Johanson (37) on the dehydraton of ethanol to ether. A more recent illustration is the gas-phase isomerization of n-butane (54). First, steadystate rate data were correlated by the Langmuir-Hinshelwood model, based upon adsorption of n-butene as the controlling process. This led to a rate equation of the form
where subscripts n and i designate normal and isobutene. Then the moment method was used to analyze pulserepsonse data in a fixed bed of catalyst particles to determine, indiependently, a value for the adsorption equilibrium constant Ki. These dynamic data were obtained at reaction conditions but with flow rates such that the resisdence time of the pulse was very low. At these conditions the extent of reaction was negligible. In this way it was possible to analyze the response curve for isobutene without interferecence from n-butane. The adsorption equilibrium constant can be calculated from the first moment, or retention time, of the pulse in the bed. These dynamic results for Kiagreed within 12% of the values obtained by fitting rate data with eq 1. What are we to conclude from such examples as these? There are other examples where agreement between adsorption and reaction data do not agree, and, or course, many examples where pure adsorption data were not obtained at reaction conditions. In view of the assumptions listed at the beginning of this paper, it seems unusual that agreement of the Kadsvalues would be obtained. Can the agreement be used as a test of the validity of the mechanism? For the simple isomerization of n-butane, it may be reasonable to assume that most of the surface is covered by isobutene so that the kinetics are, indeed, controlled by the rate of adsorption of n-butane on the few unoccupied sites. Under these circumstances the only component appreciably adsorbed is isobutene. Hence, there is no problem in comparing adsorption under reaction conditions, where interaction might be expected, with adsorption of a pure component. On the other hand, the dehydration study of Kabel and Johanson (37) involved adsorption of ethanol, water, and ether. Yet the Kadsvalues determined from adsorption experiments on each pure component agreed with the values obtained by fitting rate data to a Langmuir-Hinshelwood model based upon a surface reaction between adsorbed molecules. To evaluate better the equality of Kadsvalues as a test of the kinetic model, more investigations of reaction and adsorption, at reaction conditions, are needed. By interconnecting a chromatographic column with a multipole mass spectrometer it is possible to determine, essentially simultaneously, the composition of many components in the effluent from the column. By feeding the reaction mixture to a column containing the catalyst particles, the apparatus offers the possiblity of simultaneous measuring adsorption equilibrium constants and reaction rates. By varying operting conditions the possiblity also exists for separately establihsing rates of adsorption and surface reaction (63). The judicious utilization of dynamic experiments may provide a means of identifying the controlling step in a sequence of processes in heterogeneous catalysis-an opportunity not available with steady-state rate data.
Statistical Analysis of Rate Data In this section cocern about the validity of the Langmuir-Hinshelwood postulates is set aside. Our interest is in what form of the equation is best and how we evaluate the constants in it. Such equations for the steady-state
rate normally contain one rate constant and one or more adsorption-equilibrium constants. The expression for the dehydration of ethanol (37) included three of the latter for a total of four arbitarary constants to be evaluated from rate data. With four adjustable parameters it is possible to obtain a good fit with a variety of different equations. Further, there is considerable flexiblity in statistical analysis of the data. Froment (25)has extensively reviewed both aspects of this problem and also suggested desirable experimental procedures for obtaining the intrinsic-rate data. In particular this review relates the method of analysis to the experiments, pointing out how the number of experiments can be reduced by thinking about the method to be used for parameter estimation. It is shown that nonlinear analysis, in contrast to linear regression procedures, can provide a better fit to the experimental data, particularly if there is some uncertainty about the accuracy of the experiments, Detailed descriptions of the nonlinear procedures proposed by Seinfeld (55)and Bard and Lapidus (4) are given. Froment also includes a description of sequential methods for reducing the number of experiments needed for parameter estimation. The procedure is illustrated with experimental data (20)for the dehydrogenation of n-butene to butadiene obtained with a chromium-aluminum oxide catalyst in a differential reactor. Fifteen possible equations (all of the LangmuirHinshelwood type) were evaluated. The maximum number of parameters in the equations was six. By an optimal discrimination method (34) it was possible with but fourteen runs to reduce the viable rate equations to two. The discrimination procedure does not necessarily provide the optimum values of the parameters. Froment’s review also discusses this separate question: sequential design of experiments for optimal parameter estimation, particularly the procedure of Box and Lucas (10). A combined approach involving a sequence of experiments gradually switching from model discrimination to parameter estimation also has been proposed (32). The data of Froment and Mezaki (24)for the isomerization of n-pentane were reanalyzed in the review (25) to illustrate a parameterestimation procedure; Froment and his colleagues have been careful to characterize their methods correctly as parameter evaluation rather than determination of true kinetic models. The references given in the preceding paragraphs on parameter estimation represent a small fraction of the efforts that have been devoted to this subject during the past twenty years. It seems that this subject is well developed in relation to experimental techniques designed to discriminate between rate equations. Perhaps it is not too harsh to state that the most important contributions to be made in improving kinetic models will come from experiments which provide information about surface intermediates. Spectroscopic analysis of the surface during reaction, dynamic operation of reactors, and experiments involving isotopic labeling are examples of useful techniques, but new experimental ideas are needed to ensure rapid progress. Langmuir-Hinshelwood rate equatons are accumulating for a growing number of catalytici.eactions; for example, the hydrogenation of styrene and phenyl acetylene (50), carbon monoxide oxidation (30),butane hydrogenolysis (36),and for the reaction of thiophene (desulfurization) and of butene on Co0-Mo03/A1203 (42). External and internal transport effects can complicate the task of obtaining an expression for the intrinsic rate. Studies of desulfurization of gas oil (72) and hydrogenation of ethylene (23) are examples where extensive transport ef-
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fects had to be accounted for before intrinsic rate equatons could be obtained. Transport Effects Before laboratory kinetics data can be analyzed for an intrinsic rate equation, all transport effects must be eliminated. In recent years “gradientless reactors” have been designed to avoid the influence of all mass and energy transport except those within the catalyst particle. Examples are the Carberry (64),the Berty (7,12),and other types of recycle reactors (61). The review of Froment (25) and ref 61 provide summaries about how laboratory data should be analyzed to eliminate transport effects. Here only a few general comments will be made. For most fluid-solid catalytic reactions in a fixed-bed, intraparticle temperature gradients are of lesser significance (13,52). (However, when catalyst deactivation occurs, intraparticle temperature differences can increase (43).) Similarly, interphase concentration differences are usually unimportant. Hence, in interpreting integral fixed-bed data, intrareactor (axial and radial) gradients along with interphase heat transfer and intraparticle mass transfer should be considered. In differential reactors the intrareactor effects can be simplified, if not eliminated, although care must be taken that axial dispersion is not important (48). By recycling the fluid at high recycle ratios, all of the interphase and intrareactor transport effects can be greatly reduced so that stirred-tank behavior is approached. Then only intraparticle diffusion is possibly significant and this depends upon the ratio of the intraparticle diffusion to reaction resistances, that is, upon the Thiele modulus. The usual procedure for evaluating the retardation of the rate due to intraparticle diffusion is to carry out experiments with at least two different sizes of catalyst particles. However, when there is a nonuniform distribution of catalyst activity within the particles, the usual conclusion-that there is no intraparticle retardation when the rate does not change with reduction in particle size-is not necessarily valid (17). To provide a more fundamental insight into the intraparticle problem, Merrill (49) has shown that the Thiele modulus can be expressed as the product WR, where W is the number of random walks a molecule must make to penetrate the particle and R is the probability that a molecule will react when it strikes the pore wall. Transport effects have been investigated more fully in fixed-bed catalytic reactors than for other types. However, some semiqualitative comments for other types may be helpful. In three-phase reactors the solid catalyst particles are slurried in the liquid or held in a fixed-bed with cocurrent down-flow (trickle-bed), of gas and liquid, cocurrent up-flow, or countercurrent flow. Due to the small size of particles in a slurry reactor intraparticle, mass-transport resistance might be unexpected. However, diffusivities in liquid-filled pores are about three orders of magnitude less than in the gas phase. Hence, effectiveness factors less than unity have been measured (26) for particles of 100 bm size. The small particles tend to move with the liquid so that the relative velocity between particle and liquid can be low, resulting in a significant mass-transfer resistance between bulk liquid and outer surface of the particles. The importance of gas bubble-to-bulk liquid mass transport depends primarily upon the ratio of the number concentrations of bubbles and particles and their diameters. Results have been reported in the literature (57) for either interphase mass transport or for the intrinsic reaction controlling the rate. Coalescence of bubbles, and their residence-time distribution, along with uncertainty about mixing in the reactor (particularly when there are
internals in the reactor), can render uncertain the analysis of rate data. Due to the large heat capacity of the liquid and small catalyst particles, temperature gradients in slurry reactors are negligible. Transport effects are different in trickle-bed reactors (widely used for hydrogenation and desulfurization), the other common form for three-phase systems. Here the pores of the catalyst particles are filled with liquid and they are large enough that it is particularly important to consider intraparticle mass transfer. The problem is complicated because all of the outer surface of the particles may not be covered with flowing liquid. This results in nonuniform concentrations on the outer surface and renders invalid the conventional developments for treating intraparticle transport. Recent reviews (28 57, 59, 65) discuss this “wetting efficiency” question. In principle three interphase transport effects may exist in trickle-beds when at least one reactant is in the gas phase. These are gas-to-particle gas-to-liquid, and liquid-to-particle. When the liquid rate is sufficiently large that the wetting efficiency is 10070,only the latter two are involved. Also, the gas-to-solid transport coefficient may be large enough that equilibrium may be assumed at this interface, particularly when the catalyst activity is not especially high. The problem is further complicated by the existence of different flow regimes, depending upon the gas and liquid flow rates (14). These complications suggest that intrinsic kinetics may best be determined in a liquid-full apparatus so that the interphase effects due to the gas can be eliminated. This is possible for a system with a gaseous reactant if a sufficient quantity of this reactant can be dissolved in the liquid. The role of transport processes in gaseous fluidized-bed reactors presents yet another set of problems. Interphase and intraparticle transfer rates of energy and mass are normally large due to the small particle size (large external surface are a per unit mass of catalyst) and turbulence in the gas phase. Proper accounting for intrareactor transport is essential to successful analysis of rate measurements. Again the question of flow regimes is important (38). In the usual condition of a bubbling fluidized bed, “bubbles” of gas containing relatively few catalyst particles rise through a “dense”,high-particle concentration region. This introduces the possiblity of gaseous reactants bypassing catalyst particles and transport of reactants between bubbles and the dense phase. Separation of the intrinsic rate from global data is of uncertain accuracy. In laboratory reactors it is sometimes possible to choose a mass and size distribution of particles such that well-mixed (stirred-tank) performance is attained. Finally, we mention the advantages of single-pellet reactors. By careful design of operating conditions it is possible to reduce the significance to negligible levels for all transport effects except intraparticle ones. Petersen (3) and Wakao (69),among others, have described applications of the single-pellet reactor. With respect to transport effects, the single-pellet type accomplishes the same result as the recycle, fixed-bed form mentioned earlier. However, commercial catalyst pellets can be used in recycle reactors, while larger, specially made pellets are normally required in the single-pellet type. Such special pellets may not have the same pore structure (and, therefore, transport characteristics) and intrinsic activity as the commerical catalyst. Conclusions In view of the substantial problems in resolving transport effects to obtain intrinsic kinetics, and the severe assumptions of the Langmuir-Hinshelwood and related
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procedures, establishing true kinetic models from global kinetics for all but the most simple reactions seems unattainable. Most practioneers of applied kinetics now properly describe the adjustable quantities in the final rate equations as parameters rather than as true rate and equilibrium constants. This pronouncement does not differ significantly from the one given in the conclusion of Weller’s 1975 paper (71), and that, in turn, does not differ greatly from the evaluation he offered much earlier (22).
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Received for review January 15, 1982 Accepted July 30, 1982 Presented as part of the Murphree Symposium in honor of Sol Weller, 183rd National Meeting of the American Chemical Society, Los Vegas, NV, Mar 28-31, 1982.
