MATHEMATICAL-MODELING OF GAS-SOLID REACTIONS - EFFECT OF PORE STRUCTURE

Gas-solid reactions find importance in numerous processes including conventional ones, involving gasification and ore reduction, as well as newer ones related to ceramics and VLSI production. The mathematical modelling of gas solid reactions is therefore a subject of long standing interest now receiving renewed attention. This review presents the various mathematical models in terms of a unified framework that accommodates shrinking core reactions as well as the internal reaction-diffusion formulation with an arbitrary structural model. In the former case the effect of the narrow internal reaction-diffusion zone that always accompanies the shrinking front is discussed. The error associated with the neglect of this zone is not necessarily negligible under conditions of surface reaction or product layer diffusion control. In the reaction-diffusion regime the various models differ primarily in terms of the assumed structural representation of the solid. These structural models may involve overlapping or non-overlapping populations of grains or pores of arbitrary size distribution. These models are unified by considering the motion of pore and reaction surfaces of arbitrary shape and curvature distribution. The recent percolation models emphasizing connectivity features of the structure are also accommodated in the formulation. Among the structural models the random pore models appear the most versatile because of their applicability to systems both with or without a solid product, as well as their ability to predict evolution of the pore size distribution. Percolation phenomena become important al low porosities as well as at high conversions. In the former case isolated pores are initially present which become accessible as conversion increases. In the latter case, for gasification, fragmentations can occur due to loss of connectivity of the solid matrix. Pore closure reactions also exhibit percolation effects since pore plugging can lead to open pores becoming inaccessible. The relative significance of the inaccessibility in determining ultimate conversion, however, needs to be assessed.