In this research, we investigate the large-time solution behavior of a representative bioreactive transport model under the conditions that the mixing of two required substrates occurs only in the directions transverse to groundwater flow. The transport physics is governed by the commonly used advection-dispersion equations at a steady uniform flow field. The microbial population dynamics are described by double Monod kinetics and a linear decay term. Through mathematical analyses we developed useful formulations to estimate the size of reaction zones and the level of microbial concentrations with the model parameters. The results show that microbial reaction rates are always limited by the transverse transport of the substrates at steady state, providing the substrate concentrations far away from the reaction zone are much larger than a characteristic concentration determined only by microbial kinetic parameters. Thus the reaction rates can be considered to be instantaneous. This greatly simplifies the governing equations and allows us to efficiently solve the steady state solutions for large-scale problems. The method was applied to a large-scale steady contaminant source problem, in which a dissolved contaminant was assumed to be biodegraded only at its plume fringe because of transverse mixing but not inside the plume. The results indicate that the transverse mixing at the plume fringe may successfully constrain the spread of a plume of high total organic carbon (TOC) concentrations (TOC = 500 mg/L) generated from a passive bioreactive barrier. However, the TOC reduction along the plume center line is insignificant even after the plume has traveled 10 km.