Biofilm Growth in Porous Media well approximated by Fractal Multirate Mass Transfer with Advective-Diffusive Solute Exchange

Biofilm growth in porous media changes the hydrodynamic properties of the medium: porosity and permeability decrease, and dispersivity increases. However, the first arrival of breakthrough curves (BTCs) is more reduced than derived from the reduction in porosity, and the BTC tail becomes heavier. These observations suggest the need for multicontinuum models (Multi-Rate Mass Transfer, MRMT) which describe reactive transport in heterogeneous porous media and facilitate the simulation of localized reactions often observed within biofilms. Here, we present a conceptual model of biochemical reactive transport with dynamic biofilm growth based on MRMT formulations. The model incorporates microbial growth by updating the porosity, dispersivity, and local mass exchange between mobile water and the immobile biofilm according to the stoichiometry and kinetic rate laws of biochemical reactions. This model has been successfully tested using two sets of laboratory data. We found that (1) the basic model based on the growth of uniformly sized biofilm aggregates (memory function with 1/2 slope), fails to reproduce laboratory tracer tests and rate of biofilm growth, while the fractal growth model, which we obtain by integrating the memory functions of biofilm aggregates with a power law distribution, does; (2) The biofilm memory function evolves as the biofilm grows in response to the varying aggregate size distribution; and (3) the early time portion of eluted volume BTCs are independent of flow rate, whereas the tail becomes heavier when the flow rate is decreased, that both advection controlled and diffusion controlled mass exchange coexist in biofilms.