Estimation of effectiveness factor for arbitrary particle shape and non-linear kinetics

NESTOR JAVIER MARIANI; CLARISA MOCCIARO; OSVALDO MIGUEL MARTÍNEZ; GUILLERMO FERNANDO BARRETO

Ixtapa-Zihuatanejo, México

Congreso; Mexican Congress on Chemical Reaction Engineering (MCCRE 2008); 2008

Instituto Mexicano del Petróleo

The analysis of catalytic reactions coupled with transport processes in real catalytic pelletsfrequently involves solving conservation balances in two (2D) or three (3D) spatialcoordinates. The computational task is readily affordable when a single set of conditions isundertaken. However, it is clear that even for the simplest practical case (e.g. simulation of acatalytic reactor with a single reaction) such evaluation have to be performed hundreds orthousands of times. Moreover, for applications that require recurrent simulation, as foroptimization, the number of evaluations will increase by orders of magnitude. The occurrenceof multiple reactions will further increase the amount of numerical calculations. It is thenhighly desirable, or even necessary, to avoid the use of 2D or 3D computations.An very simple approach to reduce 2D or 3D problems into a 1D problem was provided manyyears ago by several authors (e.g. Aris, 1965) who showed that at large values of the Thielemodulus, the effectiveness factor for a single reaction does not depend on the pellet shape, butjust on the ratio of pellet volume to external surface area, l . To perform approximateevaluations at low and intermediate values of Thiele modulus, any geometry satisfying theactual value of l could be adopted, as a simple slab of half-width l . The expected precisionwith this approximation is of the order of 20% for relatively simple kinetics.A more convenient 1D model was formerly proposed by Burghardt and Kubaczka (1996).For this model, hereafter called Generalized Cylinder (GC) model, it is supposed thatdiffusion takes place along a distance L of a hypothetical body of variable cross sectionaccording to zs, being z the non-dimensional coordinate. Values of the two modelparameters, L (effective diffusion length) and s (shape factor), can be obtained by matchingthe value l of the actual pellet and one additional property related with the shape of the actualpellet.Mariani et al. (2007) proposed a criterion to estimate the shape factor s by stating that theCG model should mimic the behavior of the actual particle at high reaction rates. Thisapproach allows obtaining the effective reaction rate with a high precision: errors less than3% arose for a variety of particles with isothermal linear kinetics. The estimation of theparameter s demands a minimum effort provided that a geometrical characterization of thepellet is available.The objective of this contribution is to validate the GC model predictions, employing thecriterion of Mariani et al. (2007), for different particles shapes with non-linear kineticsexpressions.