Small particles (50-200 micrometer) of catalysts/adsorbents were entrapped in sinter-locked networks of micron diameter fibers to form novel microstructred heterogeneous contacting systems called Microfibrous Entrapped Catalysts/Sorbents (MFECS). MFECS have shown excellent benefits in terms of reduced pressure drops and improved reaction rates in many heterogeneous catalytic and adsorption processes. This study was specifically aimed at understanding the effect of fibers on the mass transfer rates these microstructured geometries. Computational fluid dynamics (CFD) simulations were employed to analyze the effect of fibers on flow patterns and associated mass transfer rates inside these materials. The fibers present in MFECS can act as static mixers and also help create conditions closer to plug-flow. In this preliminary analysis, comparisons of logs of reductions in simplified 2D geometries with and with out fibers was made. These comparisons were used to understand the influence of fibers. A detailed dimensionless analysis was made to study the effects of various parameters like diffusivity, inlet velocity, viscosity , fiber diameter, fiber volume, channel diameter, etc. on the mass transfer rates in the microstructured geometries. In this analysis, reduction in axial dispersion due to elimination of parabolic velocity profiles in reactors was found to have significant effect in high velocity and/or low diffusivity applications.