STOCHASTIC-CONVECTIVE TRANSPORT WITH NONLINEAR REACTION - BIODEGRADATION WITH MICROBIAL-GROWTH

The representation of subsurface flow and reactive transport as an ens emble of one-dimensional stream tubes is extended to account for nonli near biodegradation with coupled microbial growth. The stochastic-conv ective reaction (SCR) model is derived for bioreaction of a single sol ute by a single class of microorganisms coupled with dynamic microbial growth. A new global variable, the integral of the solute degraded pe r unit length of system traversed, accounts for degradation. Dimension less scaling and the method of characteristics are used to reduce the model, written for a single convecting reactor (stream tube), to a pai r of coupled nonlinear functional equations for solute concentration a nd microbial biomass. Existence of a solution to the stream tube syste m is shown, both numerical and approximate analytical approaches to th e solution are given, and example computations using both methods are presented. Conditions under which the stream tube solution is ''canoni cal,'' or scalable to fit any permissible stream tube travel time func tion, arise from requirements for invariance (over the stream tube ens emble) of effective one-dimensional stream tubes used to represent tra nsport along real stream tubes in three-dimensional space. Averaging o f the stream tube solution over travel time and reaction properties re presentative of physical and chemical heterogeneities is described as a way to separate and upscale the processes of macrodispersion and mic robiological reaction. The approach is exercised to simulate Monte Car lo average behavior of bioreactive transport in physically heterogeneo us two-dimensional media. Results show that the method captures the en semble average large-scale effects of the nonlinear reactions more acc urately than done in the classical reactive convection-dispersion equa tion (CDR), even when the appropriate scale dependent dispersion coeff icient is afforded to the CDR.