A Pore-Scale Model for Permeable Biofilm: Numerical Simulations and Laboratory Experiments

Abstract

In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by ±10% of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected. keywords: Biofilm · Numerical simulations · Laboratory experiments · Microbial enhanced oil recovery · Porosity 1 arXiv:1807.03400v3 [physics.flu-dyn] 31 Aug 2018• the development of a multidimensional, comprehensive pore-scale mathematical model for biofilm formation,• the inclusion of a biofilm porosity,

Numerical Simulation of Biofilm Formation in a Microchannel

“…These values are taken from [1], where the authors built a model for heterogeneous biofilm development. The dimensions of the strip and the injected nutrient concentration are also taken from [1], with values L = 600 × 10 −6 m and W = 600 × 10 −6 m. From previous studies, we set the biofilm permeability k = 1 × 10 −10 m 2 [3], the Beavers-Joseph constant α = 0.1 [2], and the stress coefficient k str = 9 × 10 −11 m/(s Pa) [8]. The initial biofilm thickness is d 0 = 30 × 10 −6 m. The volume fraction of water in the biofilm is 50%.…”

Biofilm modeling in evolving porous media with Beavers‐Joseph condition

“…This advective transport within the biomass facilitates also the “deepest” bacteria to get nutrients in an adequate time. Recently a pore‐scale model for permeable biofilm within a microchannel is derived and numerical simulations are compared with laboratory experiments in []. There the significant influence of the flow within the biofilm (in case of high flow rates) for nutritive transport and hence for biofilm growth is also emphasized.…”

“…In this sense the biomass is considered as a porous medium. For ease of presentation and contrary to the pore‐scale model of [] we do not include EPS or dead bacteria as an additional component of the biofilm. However, these components may be taken into account via the density of the biofilm.…”

“…However, these components may be taken into account via the density of the biofilm. Compared to [] this article generalizes the geometrical setting, that means we consider a two‐ or three‐dimensional porous medium with a more general microstructure instead of a pseudo one‐dimensional thin channel. For this the evolving biofilm‐liquid interface is located by a level‐set equation.…”

A pore-scale study of transport of inertial particles by water in porous media

“…We emphasise on the fact that the clogging is understood here as the result of particle accumulation, where the particles take a non-negligible part of the fluid. We do not account for other clogging mechanisms, like precipitation or dissolution/adsorption [24,25], or the growth of biofilm [26,27].…”