Effect of internal diffusion on catalytic reactions

Schneider, P.; Mitschka, P.

doi:10.1016/0009-2509(66)85056-x

Cited by 26 publications

(7 citation statements)

References 5 publications

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“…A problem equivalent to the one of interest here but cast in terms of analogous Langmuir-Hinshelwood kinetics was first treated numerically by Prater and Lago (1956) and by Chu and Hougen (1962), and subsequently in more general fashion by Roberts and Satterfield (1965), Krasuk and Smith (1965), and Schneider and Mitschka (1965). Atkinson and Daoud ( 1968) fitted these numerical results with high accuracy to a single empirical function by use of a least squares procedure.…”

Section: Conclusion a N D Sign If Icancementioning

confidence: 99%

Effect of diffusional limitations on lineweaver‐burk plots for immobilized enzymes

1974

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EnzymesLineweaver-Burk plats of reaction rate data obtained with immobilized enzymes need not be liqear even when intrinsic enzyme kinetics follow the simple Michaelis-Menten rate expression. Theoretical calculations show that mass transfer effects mqy cause curvature which is concave or convex to the abscissa, depending upon experimental conditions. Consequently, graphical procedures commonly employed for analysis of soluble enzyme kinetics may yield misleading regults when applied to immobilized enzymes. Three approaches which follow from the behavior of numerical and asymptotic solutions to the problem are proposed for extraction of intrinsic kinetic information. Practical application of enzymatic catalysis often requires that enzymes be immobilized, thereby permitting recovery and continuops use. It is important that the kinetics of immobilized enzymes be well understood to facilitate their economic utilization. In particular, it is necessary to account for the effect of diffusional limitations and to develop procedures which permit extraction of intrinsic kinetic parameters from observed reaction rates. BRUCENative enzymes in sdution typically follow hyperbolic Michaelis-Menten kinetics, Equation (l), which are formally analogous to Langmuir-Hinshelwood kinetics in heterogeneous catalysis. Graphical analysis of kinetic data is commonly carried out on transformed coordinates such as a Lineweaver-Burk plot of reciprocal reaction rate versus reciprocal substrate concentration. This serves to linearize the data so that the maximum reaction rate and the Michaelis constant qan be evaluated directly from the intercept and slope. The same approach is often used with immobilized enzymes, but little attention has been paid to the precise physical meaning of the parameters so determined. Nonlinear Lineweaver-Burk plots have been reported in several experimental studies with enzymes immobilized in porous supports (Lilly and Sharp, 1968;Kay and Lilly, 1970;Bunting and Laidler, 1972); in all cases, the enzymes in solution gave Michaelis-Menten kinetics. It is unclear whether the curvature observed with immobilized enzymes stems from diffusional limitations, from changes in intrinsic enzyme kinetics after immobilization, or from other factors.In this paper we examine through theoretical analysis the effect of diffusional limitations on the observed kinetics of immobilized enzymes. Of particular interest i s the behavior of Lineweaver-Burk plots and the extraction of intrinsic kinetic parameters when diffusional effects are large. The problem considered is substrate diffusion in a homogeneous porous support in the form of a one-dimensional slab or membrane in which an enzyme that catalyzes a reaction following irreversible Michaelis-Menten kinetics is uniformly immobilized. Both internal and external diflusional resistances are considered, and emphasis is placed upon the asymptotic solution which is valid when diffusional effects are important and the modified Thiele modulus is large. CONCLUSIONS A N D SIGN IF ICANCELinewea...

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Section: Conclusion a N D Sign If Icancementioning

confidence: 99%

Effect of diffusional limitations on lineweaver‐burk plots for immobilized enzymes

1974

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“…Weisz and Prater (1954) proposed a criterion to test the importance of diffusional limitations on the observed rates for isothermal pellets. This criterion is later generalized by Petersen (1965), Hutchings and Carberry (1966), Schneider and Mitschka (1966), Bischof (1967), Hudgins (1968), and Narshimhan and Guha (1972).…”

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Testing the relative importance of temperature and concentration gradients in catalyst pellets

Doğu

1984

AIChE Journal

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The intrapellet concentration and temperature gradients within a catalyst pellet cause the reaction rate to vary with position. To predict the average rates, simultaneous solution of the differential equations for the temperature and concentrations is required. The temperature and the concentration dependence of the rate expressions are generally nonlinear. Also, for many systems more than one chemical reaction has to be considered. For such systems, it is difficult to predict the observed rates by the solution of the energy and species conservation equations. The mathematical theory of diffusion and reaction in porous catalysts is discussed in detail by Ark (1975). Treatment of nonisothermal conditions within a pellet is also reviewed by Petersen (1965a), Smith (1970), Froment and Bischoff (1979), and Carberry (1979).When the activation energy of the rate constants is not small, the impact of thermal gradients on the activity and selectivity of catalysts is much more important than the concentration gradients. For an exothermic reaction, the increase of the rate due to temperature rise within the pellet can more than offset the decrease in rate due to drop in reactant concentration. From the practical point of view it is quite important to know the relative importance of diffusion and heat transfer on the observed rates and the conditions under which the effects of temperature and concentration gradients can be neglected.Anderson (1963) derived a criterion to test the isothermal behavior of a catalyst pellet. The Anderson criterion assumes that the rate of reaction depends on temperature in the Arrhenius fashion and does not consider the effect of temperature rise on the concentration gradients and diffusion limitations. Weisz and Hicks (1962) also considered the nonisothermal behavior of the catalyst pellet, and a set of computations were reported for the prediction of effectiveness factors under nonisothermal conditions. Weisz and Prater (1954) proposed a criterion to test the importance of diffusional limitations on the observed rates for isothermal pellets. This criterion is later generalized by Petersen (1965), Hutchings and Carberry (1966), Schneider and Mitschka (1966), Bischof (1967), Hudgins (1968), and Narshimhan and Guha (1972).The criterion developed by Hudgins is also applicable for reactions having other than power-type rate expressions. Dozu and Dozu (1980, 1982) generalized the Hudgins criterion to bidisperse porous catalysts and to multiple reaction systems. In this work, a general criterion is developed to test the relative importance of diffusion and heat transfer limitations on the observed rates of reactions catalyzed by porous solids. The criterion is applicable to reactions conforming to any rate law. It can be used even if there are more than one temperature-dependent parameters in the rate expression, and it is derived for the general case of a multiple reaction system. For a multiple reaction system with n-independent reactions and rn species, the intrinsic rate of reaction i can be gi...

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“…Analytical solutions are also possible for reversible reactions (e.g. Schneider and Mitschka, 1966;Xu and Chuang, 1997), where the Thiele modulus,^, depends on the equilibrium concentration. Effects of temperature gradients have also been considered in this relationship (Copelowitz and Aris, 1970;Hlavacek and Kubicek, 1970;Bischoff, 1968).…”

Section: Theoretical Backgroundmentioning

confidence: 99%