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

Abstract

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...

Simulation of Experiments for the Determination of the Thermal Stability Criteria for the “Uckron-I” Test Problem

“…Examples for use are the test of relative importance of temperature and concentration gradients in catalyst pellets as was done by Dogu and Dogu [7]. The general criterion to check for the absence of diffusion control in an isothermal catalyst pellet is another example as developed by Hudgins [8].…”

Testing the relative importance of mass and heat resistances in solid catalysts

“…Sharma 1984 . In addition, an interesting criterion on the importance of temperature and concentration gradients in Ž . catalyst pellets was given by Dogu and Dogu 1984 . These are the criteria that still are the most often applied in practice.…”

Modelling of multi gas/solid reactions – effect of structural parameters

“…A model based on the overlapping grain concepts was developed [37]. A single pellet moment technique has been presented for evaluation of reaction rate constants, diffusivities and adsorption equilibrium constants [38].…”