A Versatile Lattice Simulator for Fluid-Solid Noncatalytic Reactions in Complex Media Alessandra Adrover* ,†,§ and Massimiliano Giona ‡,§ Dipartimento di Ingegneria Chimica, Universita ` di Roma “La Sapienza”, Via Eudossiana 18, 00184 Roma, Italy, Dipartimento di Ingegneria Chimica, Universita ` di Cagliari, and Piazza d’Armi, 09123 Cagliari, Italy, and Centro Interuniversitario sui Sistemi Disordinati e sui Frattali nell’Ingegneria Chimica, Universita ´ di Roma, Via Eudossiana 18, 00184 Roma, Italy A versatile lattice simulator for fluid-solid noncatalytic reactions is developed in detail in order to study linear, nonlinear, and nonisothermal kinetics in complex media, in the presence of multicomponent diffusion and n-solid reactant species. The simulator is based on a time-splitting algorithm for the diffusion and for the reaction steps. The simulator is quantitatively checked in many different cases involving initially nonporous particles constituted by a solid reactant dispersed in an inert matrix. The influence of spatial correlation properties in the case of uniform and nonuniform solid reactant distribution is analyzed in detail. 1. Introduction Fluid-solid reactions represent a basic mechanism in many industrial processes, from coal gasification to ore leaching. Over the last 20 years, many authors have studied the application of percolation models and of other concepts derived from the theory of disordered systems to interpret the relationship between the macroscopic overall kinetics and structural properties of the solid matrices, especially in regard to porous solids (Sahimi, 1994). The first attempt to apply percolation models was performed by Mohanty et al. (1982). Subsequently, Reyes and Jensen (1986a,b, 1987) modeled different gas-solid reaction (char gasification, sulfation of cal- cined limestones) in both reaction-controlled and diffu- sion-controlled regimes. The estimate of the structural properties and of effective transport parameters comes from the assumption of a Cayley-tree topology in the pore network (Yortsos and Sharma, 1986; Kerstein and Bug, 1986). These models are effective continuum models, in which the balance equations for the fluid reactant are written for continua, and the effective transport param- eters and the macroscopic description (and temporal evolution) of the pore network (accessible porosity, accessible surface area) are obtained from percolation models or from other models of disorder. There are several drawbacks to continuum models for disordered media. The first is that they may not be valid in the presence of structures possessing infinite- correlation length. This occurs, for example, in gas- solid reactions in the proximity of the fragmentation threshold (since fragmentation can be regarded as a critical phenomenon). Moreover, all the parameters (transport and struc- tural) entering into hybrid models are based on a priori assumptions about the pore-network structure and/or distribution of the solid reactant within an inert matrix. In particular, transport and structural parameters are generally obtained starting from simple (and uncorre- lated) models of disorder (the classical site and/or bond percolation models) or from unrealistic topologies (such as Cayley trees, which are loopless and nonfinite in dimension; see Aharony and Stauffer (1992)). The limitation of these assumptions is that both the pore- network structure of real materials and/or the distribu- tion of solid reactants within the pore-network matrix are spatially correlated in real materials. Although the spatial correlations are usually short-range (and the universality class is therefore the same as the corre- sponding uncorrelated structures), the structural prop- erties, for noncritical structures (i.e., not at the perco- lation threshold), may be different, as shown by Adrover and Giona (1996) for permeability. A detailed discus- sion of this issue is developed in Section 5. Over the last 10 years, the growth of interest in the influence of the structural features of porous and granular materials on global transport and reaction properties together with the availability of fast comput- ers possessing large memory capacity has stimulated the development of lattice models of porous structures. Lattice models for noncatalytic fluid-solid reactions were developed by Kerstein and Edwards (1987) and by Sahimi and Tsotsis (1987, 1988). Kerstein and Edwards (1987) modeled the char oxidation process as the ignition and burnout (i.e., removal) of solid bonds. Upon ignition, a solid bond is assigned a randomly selected burning time drawn from a distribution func- tion depending on the mass of the fragment. The distinguishing features of the film-diffusion-limited regime of char oxidation are incorporated into the solid- bond ignition criterion and into the dependence of the particle-burning rate per unit surface area on the mass (i.e., the number of solid bonds) of a given subcluster. In the model developed by Sahimi and Tsotsis (1987, 1988), diffusion is simulated by means of a random walk of the fluid reactant, which is controlled by the local bond conductances (diffusivities), and reaction is a random event occurring with a probability depending on the rate of reaction (and on temperature). The simulation refers, however, to isothermal conditions. This kind of model takes advantage of the basic analogy between transport (diffusion) and random walk, as widely applied in the literature on elementary reactions in disordered (fractal) media. Lattice models can be classified in terms of two major * Author to whom correspondence should be addressed. Phone: +39-6-44585892. Fax: +39-6-44585339. E-mail: alex@ giona2.ing.uniroma1.it. † Universita ` di Roma “La Sapienza”. ‡ Universita ` di Cagliari. § Centro Interuniveristario sui Sistemi Disordinati e sui Frattali nell’Ingegneria Chimica. 4993 Ind. Eng. Chem. Res. 1997, 36, 4993-5009 S0888-5885(97)00164-4 CCC: $14.00 © 1997 American Chemical Society