大象传媒

Advisors: Florin Adrian Radu, Iuliu Sorin Pop and Kundan Kumar

Short description of project:

This dissertation addresses the applications and challenges of both聽laboratory experiments and mathematical modeling at different scales,聽where the main character is biofilm. Thus, the first part of this work聽shows biological, chemical and physical concepts for the laboratory聽experiments and mathematical terms for the modeling, upscaling and聽numerical solutions. The second part contains the research papers. In聽our research, we are interested in studying the biofilm to improve the聽oil extraction. Most of the biofilm models are based on simplifying聽assumptions, e.g. impermeability, a constant biofilm density and聽accounting for diffusion but neglecting convection for transport of聽nutrients. In this work, we propose a pore-scale model for a permeable聽multi-component biofilm including a variable biofilm density, detachment聽and transport of nutrients due to convection and diffusion. It is聽through laboratory experiments that we identify the key processes and聽variables that need to be considered. Accordingly, we use experimental聽determined parameters and compute some of the parameters through聽calibration. In addition, we study the sensitivity of the parameters in聽the mathematical models. Pore-scale models are important because they聽aim to describe physical phenomena in detail and one can derive聽core-scale models through upscaling.聽Then, we can reflect the effects of聽the pore-scale processes on the core scale. Upscaling of pore-scale聽models allows us to describe the average behavior of a system in an聽accurate manner with relatively low computational effort. Then, we聽upscale this pore-scale model in two different geometries: a thin聽channel and a thin tube, in order to derive one-dimensional effective聽equations, by investigating the limit as the ratio of the aperture to聽the length approaches to zero. In the core-scale laboratory experiments,聽biofilm is grown in cylindrical cores. Permeability and porosity changes聽over time at different flow rates and nutrient concentrations are聽studied. Numerical simulations are performed to compare with the聽experimental results. We also present how to extend the model to include聽chemotaxis and interfacial tension reduction due to surface active聽compounds. Mathematical models for biofilms are based on coupled聽non-linear partial differential equations and ordinary differential聽equations, which may be challenging to solve. Therefore, it is necessary聽to use advanced numerical methods and simulations to predict the聽behavior on time of the unknowns in these complex systems. We present聽some of the common space discretizations, time discretizations and聽numerical solvers for these models. We also discuss the difficulty of聽free boundary problems and the numerical techniques to deal with them.聽Last but not least, we discuss the challenges of parameter estimation聽and the application of sensitivity analysis.

Link to thesis at BORA-UiB:聽