Modeling Biofilm-Induced Hydraulic Changes In 3-Dimensional Prefractal Porous Media

Biofilm-induced clogging is the significant phenomenon in subsurface hydrology that may affect aquifer recharge and solute transport. Modeling biofilm impact on flow and transport at pore scale should include characterization of the heterogeneity of both biofilm and medium. In this study, a numerical model of biofilm- induced hydraulic changes in porous media was developed based on the individual-based model (IbM) for the biofilm growth according to the Monod equation, and the Lattice Boltzmann model (LBM) for the water flow. The LBM was modified to consider biofilm growth in each grid cell, and IbM was synchronized with the LBM. The model behavior was first investigated for simple geometry of the prismatic void space with constant flow and concentration boundary conditions at the inflow boundary, no-gradient condition on the outflow side, and periodic boundary condition on the other sides. The mass conservation was tested by varying Peclet number and computing the solute breakthrough. The breakthrough was retarded when a solid sphere was placed in the prism, and the retardation was increasing as flow velocity was increasing. Increase in the biofilm volume surrounding solid sphere increased pressure at the windward side of sphere, and the flow velocity in the narrow passage between biofilms was increased. The biofilm grew more vigorously on the windward side compared with the leeward side of the sphere because the biofilm growth interrupted the supply of the dissolved substrate to the leeward side. Darcy relation was better to estimate hydraulic conductivity than Kozeny-Carman relation which assumes that biofilms are uniformly distributed on the surface. Finally, 3- dimensional mass and pore-solid prefractal lattices as models of heterogeneous porous media were generated by iterated function system and used as the simulation domain. The flow in these domains reached the steady state at threshold porosities (hydrostatic threshold) that were estimated to be about 0.6 and 0.4 in 3-dimensional mass prefractal and pore-solid prefractal porous media, respectively. At porosities below the hydrostatic threshold, the biofilm growth was insignificant because the flow was clogged early, and thus the substrate supply was restricted. On the contrary, the biofilm growth depended on the substrate concentration and biofilm-induced clogging rate was independent on the initial porosity at porosities above the hydrostatic threshold.