Biofilm Growth in Porous Media Well Approximated by Fractal Multirate Mass Transfer With Advective-Diffusive Solute Exchange

Abstract

Biofilm growth in porous media changes not only the hydrodynamic properties of the medium (reduction in porosity and permeability, and increase in dispersivity), but also the transport itself (breakthrough curves display increasingly fast first arrivals and long tails). These features are well reproduced by multicontinuum models (Multi-Rate Mass Transfer, MRMT) which can be used to describe reactive transport in heterogeneous porous media and facilitate the simulation of reactions that are localized within biofilms. Here, we present a conceptual and numerical model of biochemical reactive transport with dynamic biofilm growth based on MRMT formulations. Mass exchange between mobile water and immobile biofilm aggregates is represented by a memory function, which simplifies definition of MRMT parameters. We successfully tested this model on two sets of laboratory data and found that (a) a basic model based on the growth of uniformly sized biofilm aggregates fails to reproduce laboratory tracer tests and rate of biofilm growth, while a fractal growth model, which we obtain by integrating the memory functions of biofilm aggregates with a power law distribution, does; (b) the biofilm memory function evolves as the biofilm grows; and (c) the early time portion of eluted volume tracer breakthrough curves are independent of flow rate, whereas the tail becomes heavier when the flow rate is decreased, which implies that both advection controlled and diffusion controlled mass exchange coexist in biofilms. These findings imply that porous media biofilms are essentially different from those developing in human tissues or open spaces.