Pergamon Carbon, Vol. 32. No. 1. pp. 51-59. 1994 Copyright 0 1994 ElsevierScienceLtd Printedin Great Britain. All rights reserved 0008-6223194 $6.00+ .OO 000%6223(93)E0052-M A FRACTAL APPROACH TO THE ANALYSIS OF LOW- TEMPERATURE COMBUSTION RATE OF A COAL CHAR. II: MODEL DEVELOPMENT P. SALATINO and F. ZIMBARDI Dipartimento di Ingegneria Chimica-UniversitB Federico II, Istituto di Ricerche sulla Combustione-C.N.R., P.le Tecchio-80125 Napoli, Italy (Received 2 February 1993; rrccepted zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM in revised form 30 June 1993) Abstract-There is increasingly large body of evidence for the existence of carbons characterized by a porous structure amenable to a topological representation based on the concepts of fractal geometry (Part I[l] and references therein). Moving from these findings, a model based on simple hypotheses is proposed for the prediction of the combustion rate of carbons characterized by a fractal pore structure. Its concern is the low temperature combustion behavior of carbons under conditions typical of chemical, kinetically controlled regime. The soundness of the model is checked satisfactorily by comparing its predictions against those obtained by a more detailed approach based on the recursive application of the Thiele analysis. The proposed model provides a useful framework for interpreting the experimental results presented in Part I[l], obtained in combustion of char from a bituminous coal. It is inferred that diffusion of oxygen within micropores is strongly activated, even at the moderately high temperature used in the combustion experiments. The formation of relatively stable oxygen-carbon complexes by dissociative oxygen chemisorption and the scarce mobility of oxygen in the chemisorbed state are indicated as possible reasons for the limited accessibility of the micropore surface. Key Words-Coal char combustion; combustion modeling, fractal geometry, micropore diffusion. 1. INTRODUCTION Modeling reaction and diffusion of gases during combustion and gasification of carbons requires the representation of the pore space topology of the fuel particles. This is relevant to establishing the diffusion paths of gaseous species, either reactants or products, through the matrix as well as the changes of the surface area available for reaction as carbon is depleted by combustion. A first level approach to this problem is that of simulating the pore space by a random dispersion of voids at different points and with different orien- tation within the solid matrix. All voids have about the same shape and size. Parallel tube bundles[2], random networks of intersecting cylindrical pores[3-51, assemblages of solid spheres[6], and regular or irregular percolating lattices[7] have been used from case to case to achieve the topological description of the pore space. The common restric- tion of these representations is that of dealing with unimodal, or nearly unimodal, pore size distribu- tions. Whatever the model, the average void size sets the characteristic length scale of the heteroge- neous structure. The structure appears homoge- neous when it is observed over length scales much larger than the void size. The existence of only one length scale of the heterogeneous structure makes the application of the classical Thiele analysis straightforward[S] through the expression ofthe par- ticle effectiveness factor as a function of the particle Thiele modulus. Modeling pore space topology of solids having broad pore size distribution is a more cumbersome problem. Simons and Finson[9] concluded, on a purely statistical ground, that the random, homoge- neous and isotropic dispersion of cylindrical pores whose radii are distributed over broad ranges within a solid matrix naturally leads to pore branching: small pores are more likely to depart from coarser ones rather than directly from the external surface of the particle. Accordingly, they suggested using treelike loopless structures to simulate the pore space when modeling pyrolysis or gasification of coal. Alternatively, modeling of a broadly distrib- uted pore space is accomplished by lumping pores into two[ 10,111 or more[ 121 pore groups, borrowing approaches developed in the framework of hetero- geneous catalysis[ 131. The concept of a hierarchical arrangement of a finite number of pore lumps smoothly leads, upon extrapolation to an infinite number of lumps, to re- cent views based on the application of the fractal geometry to the description of pore space topol- ogy[14-181. Accordingly, the internal surface of a fractal porous solid is viewed as being “rough” at any length scale, so that its area cannot be estab- lished unless the size of the “yardstick” used in the measurement is specified. The yardstick size coincides with the size of the adsorptive molecules in gas adsorption measurements, with the resolution scale in optical or electron microscopy, or with the wavelength of the radiation beam in SAXS measure- 51