Mathematical Modelling And Scaling Up Of Microbial Enhanced Oil Recovery
Authors: Islam M.R. , Gianetto A. 
Published: March 2010

Abstract
A complete mathematical model for describing microbial transport, nutrient propagation, and microbial growth in porous media is presented in this paper. Also presented is the scaling up criteria for conducting meaningful experiments in the laboratory. Microbial Enhanced Oil Recovery (MEOR) is one of the fastest growing EOR schemes in the world. This is due to low cost of MEOR as compared to other EOR schemes, such as chemical flooding, thermal methods, etc. Micro-organisms are able to travel relatively easily in an oil reservoir with preferential access into the wafer-bearing channels. In situ bio-generation of chemicals has the unique advantage of minimizing chemical loss by adsorption. If properly designed, microbial species can be used for selective plugging of high permeability water-bearing channels, leading to improved oil recovery.
Even though there has been considerable experimental and field work done on MEOR, very little effort has been devoted to mathematical simulation as well as studies of scale-up procedures of MEOR. The lack of reliable numerical prediction techniques or proper scaling criteria often leads to inaccurate evaluation of a field project. This paper presents a new approach for modelling microbial plugging of water channels which are often present in oil reservoirs. Combination of the bacterial and nutrient transport models are coupled with a kinetic model of bacterial growth. A detailed parametric study of the MEOR simulator is presented. This model accurately redicts bacteria entrainment and deposition in a laboratory core. The numerical simulation results compared favourably with published experimental data. This model provides an insight into bacterial transport laboratory and field and may be used to define new targets for bacterial plugging. Based on the numerical model, scaling criteria/or conducting experiments using MEOR arederived. These scaling criteria are essential for scaling up laboratory experimental results to the field.

Introduction
Many field trials have been conducted using microbes for mainly two applications: selective plugging of undesirable channels(1), and reduction of oil-water interfacial tension and oil viscosity for oil mobilization(2). Only a few field trials have been successful even though most field trials preceeded by laboratory experimentations.
In the past, laboratory experiments have been poorly extrapolated to design a field project. This is mainly due to the lack of scaling criteria or a proper mathematical simulator which could be used for modelling field perfomance under realistic field conditions. Even though there have been several studies reporting transport of bacteria through porous media(1–4), very little has been conductedin the areas of mathematical modelling of microbial transport and metabolism. A simplified model was proposed by Knapp et al.(5).
This model used a fundamental conservation laws along with growth and retention kinetics of biomass in order to predict porosity reduction as a function of distance and time. Updesraff(6) used a filtration model in order to express bacteria transport as a function of pore entrance size. A similar model was used by Lang el al.(1) as well. In a recent work, Jenneman el al.(7) modified the filtration theory to relate permeability, with the rate of bacteria penetration.