A THEORY OF DIFFUSION AND REACTION IN POROUS MEDIA The process of diffusion and heterogeneous reaction is analyzed using the method of volume-averaging. Closure is obtained in terms of the solution of two associated transport equations used to predict the spatial deviation of the concentration. For a first order, irreversible reaction the theory yields a diffusion equation of the form D. RYAN R. G. CARBONELL and S. WHITAKER a<c>' E-- = - ka.<c>' + at - provided the temperature and pressure are constant and the dilute solution constraint applies to the reacting species. The last term in this result represents a convective-like transport mechanism caused by the heterogeneous reaction. The vector depends only on the geometry of the porous medium, and one can show that > Is always small compared to a, <c> Y and must, of course, be zero for isotropic porous media. Department of Chemical Engineering University af Califomia Davis. Califomia 95616 The process of diffusion in porous media is a II\3.tter of oonstant interest in chanical reac- tor design where mass transport in catalyst pellets plays a crucial role in the design of heterogeneous reactors. '!be mass transport process is canplicated by the poorly charac- terized geanetry, the transition between Knudsen and bulk. diffusion, additional trans- port owing to surface diffusion and the inter- action between the heterogenealS reaction ani the diffusion process. A central assumption made in the analysis of diffusicn in porous catalysts is that the foDtl of the transport equation is identical to that for a harogen- eous system ani that the effective diffusivity is a II\3.terial coefficient rather than a pro- ,cess parameter. '!he first suggestion that this asSUItption might be incorrect was awar- enUy made by Otani ani Smith (!.). '!bey cx::m- pared diffusivities ootained fran exper:ilren- tally neasured effectiveness factors with those calculated using the II\3.cropore--micro- pore nodel of Wakao and Smith (ll and foorrl that the calculated values were 4 to' 5 0065-S812-81-4330-0202-$2.00 " Tht> American Institute of Chemical Engineers, 1981 times greater than those deteI:mined experiIren- tally in a reacting system. other II\3.cropore--micropore nodels are available, such as the Foster-Butt convergent-divergent pore nodel, and Steisel and Butt (!) used this m::xiel to calculate the effective diffusivities neasured by Otani ani Sm.ith. Quite oontrary to Otani and Smith, they found excellent m:mt between neasured and calculated effective diffusivities. Balder and Petersen (2) recognized the difficulty of canparing experiIrental results for reacting systems with specialized gec:rre..- tric nodels ani they speculated as to "whe<- ther there really is a difference between the diffusion coefficients for diffusion alone and for diffusicn with chemical reaction." '!bey referred to these o...u parameters as the "physical" diffusivity and the "kinetic" dif- fusi vi ty and set up an exper:ilrental program to rreasure the o...u quantities in the same porous catalyst. '!beir exper:ilrents were carried out in the transition region where the Knudsen diffusion coefficient is canparable to the 46