Mathematical modeling of biofilm formation: from the pore-scale to the core-scale

The main objective of the IMMENS project (improving microbial selective plugging technology through experimentally based modelling and simulation) is to develop a core scale bio-plug MEOR (microbial enhanced oil recovery) simulator to be used for understanding and optimizing adaptive bio-plug technology. This mechanism consists in growing the bacteria in the high permeable zones in the reservoir. Therefore, we can reach and recover the oil in the less permeable zones. This is our motivation for developing mathematical models that better describe the biofilm mechanisms. To study the impact on the numerical results due to model simplifications, we must build more complex mathematical models. In the laboratory, biofilm is growth in a T-shape micro-channel. We build a mathematical model for biofilm formation, including the notions of porosity, permeability, and different biofilm components: extracellular polymeric substances (EPS), water, active bacteria, and dead bacteria. A segregated finite element algorithm is used to solve the mathematical model equations. Using the best estimate of physical parameters from the existing experiments, we perform numerical simulations. The stress coefficient is selected to match the experimental results. To identify the critical model parameters, a sensitivity analysis is performed. In the numerical simulations, we observe a reduction of the biofilm height as the water flux velocity increases. We apply homogenization techniques in order to obtain the upscaled model. Numerical computations are presented to compare the outcome of the effective (upscaled) model with two different geometries: a thin strip and a micro-tube.