Macrotransport of a biologically reacting solute through porous media

A physically based model is developed to study the transport of a solute utilized by microorganisms forming a biofilm coating on sail grains in a porous medium. A wavy-walled channel is used as a geometrical model of a porous medium and a biofilm is attached to the channel wall. Within the biofilm the solute is consumed according to a first-order volumetric rate. A numerical study is performed to obtain the dependence of the macrotransport coefficients on the Peclet number and Damkohler number. It is found that in some cases of practical importance the pore fluid is not well mixed, and mass transport limitations can control macroreaction rates. For diffusion-limited cases (large Damkohler numbers) increased solvent velocity can enhance the macroreaction rate by a factor of almost 3. Mean solute and mean solvent velocities are, in general, not equal, and mean solute velocities can exceed mean solvent velocities by 60% at high Damkohler numbers. These results agree qualitatively with those of a previous numerical study by Edwards et al. [1993]. The results also suggest that due to the spatially variable pore geometry, the biomass nearest the pore throat is more effective at consuming the solute than biomass in the pore chamber. A comparison is made between mass transfer correlations and the results determined for the macroreaction rate coefficient, We find that over a limited range of Peclet numbers a macroscale Sherwood number follows the Pe(1/3) behavior determined from experimental mass transfer correlations and predicted by boundary layer theory.