New publication in microbial enhanced oil recovery

The paper A Pore-Scale Model for Permeable Biofilm: Numerical Simulations and Laboratory Experiments was published online on 08 December 2018 in the Journal Transport in Porous Media.

In this paper, we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided into two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substance (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 biofilm–water 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/death 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 which is a beautiful tragedy confirming the difficulty of this problem.

This work is part of the project IMMENS. In this project we aim to develop a numerical simulator for bio-plugging technology based on experiments from the pore to the core scale. In this publication we developed a pore-scale model for biofilm formation. A second publication is under review, where we upscaled this pore-scale model in two different pore geometries. Finally, a third paper is in preparation, where we aim to calibrate a core-scale model with laboratory results.


Water flux

Visiting Tufts University

This fall semester I had a chance to visit Computational and Applied Math group at Tufts University in Medford, USA. Together with Xiaozhe Hu, I have been studying preconditioning techniques for applications in fractured porous media to allow for efficient simulation of subsurface processes. For simulation, we combined the softwares of each research group – PorePy toolbox of PMG in Bergen and HAZMATH solver library developed by Xiaozhe Hu with James Alder (Tufts) and Ludmil Zikatanov (Penn State).


Our main focus was to develop robust solvers and preconditioners for single-phase flow problems in fractured porous media based on the mixed-dimensional modeling of the phenomenon. We investigated two approaches to the problem: one specifically designed for the flow model, and another more general approach resulting from the mathematical structure of related partial differential equations. It was very inspiring to learn and implement new solving strategies that may also be used in different applications, but also very exciting to see our research producing valuable results.


Apart from research, living in greater Boston area was a great new experience. Having many excellent universities close by, I had a lot of fun hanging out with students and academics from all over the US and the world. But, the highlights of my visit were definitely being there in time to enjoy the most of American culture, such as trick-or-treating on Halloween and having a big family dinner on Thanksgiving.


Ana Budiša


Four of the group members went to last week’s European Geothermal Workshop in Strasbourg, along with our good friend and collaborator Luisa Zuluaga, from the UiB geology department. The workshop attracted a diverse range of participants from working on all aspects of geothermal exploitation, from monitoring and characterisation to risk management and modelling. We congratulate Luisa most warmly with the workshop’s poster prize, awarded for her poster on studies of outcrops from Sotra.

Benchmark study

Members of the group have contributed to a paper with the title Call for participation: Verification benchmarks for single-phase flow in three-dimensional fractured porous media, which is now available at arXive. We strongly encourage interested researchers to participate. The UiB simulations are already available in the PorePy collection of published results, here.

Simulated matrix and fracture pressure from the fourth test case.

Associate professor position

We would like to draw attention to a call for applications to an associate professor position in applied and computational mathematics at UiB with deadline 15 September. For further details, please follow this link.

Visiting Imperial College

Since the middle of April, I have had the great pleasure of visiting the Rock Mechanics group at Imperial College. Here, I have studied the simulation of fracture propagation under the excellent supervision of Dr. Adriana Paluszny. One main objective is to transfer the insights gained from using the Imperial College Geomechanics Toolkit (watch example videos here!) to the PorePy toolbox being developed in Bergen.

The work I’m currently doing with Adriana is about verifying the thermo-mechanical coupling and fracture growth part of the code by comparison to a classical quenching experiment where the contraction of a pre-heated specimen immersed into cold water causes fracturing. I am really excited to see how well we will be able to reproduce the experimental results. It is also inspiring to recognize the physical processes in everyday occurrences such as the cooling of a brownie (Adriana’s observation) or putting ice in a drink (my observation, see picture in slideshow!); perhaps our research can actually have a somewhat broader application!

For a running enthusiast like myself, Imperial College’s situation just to the south of Hyde Park allows for physical recreation in beautiful surroundings and is much appreciated, especially with all the nice weather we have had. If the office becomes too warm, London’s parks also offer an excellently relaxed atmosphere for reading a paper or writing a blog post!

Ivar Stefansson

Watson forum interview with Eren Ucar

The Watson Forum is a series of (informal) interviews that seek to highlight contributions of women in the areas of numerical modelling, simulation, and programming in the context of Maths, Physics, Earth Sciences and Engineering. The interviews are performed by Dr. Adriana Paluszny of Imperial College, and we encourage you to watch the interview with Eren Ucar here. For a more detailed description of the project, refer to its home page.

Letter from CMWR 2018 in Saint Malo

This week seven members of the PMG went to France to attend the conference Computational Methods in Water Resources XXII (CMWR). Optimistic as I am, I showed up with swimming suit and sunglasses, and the rain coat was left in Bergen. Of course, I never thought of checking the weather report, and my dreams of sun, swimming, and long beaches were harshly crushed already when we landed. As the plane parked we were not allowed out of the airplane for twenty minutes because it rained too much. However, despite striking French railroad workers we managed to arrive in the small city Saint-Malo at the north-west coast of France. The longing for sun was temporarily forgotten as the conference started on Monday and I had to use all my concentration trying to follow the arguments of a talk trying to fit in 50 slides and the scientific work of the last ten years in a 15 minutes talk. Phew, I got through that, and after a long first day, I managed to do a short sightseeing of the city the following night.

Sightseeing in Saint-Malo

Wednesday I held a talk on fracture stimulation in enhanced geothermal systems. I was a bit nervous, but can now enjoy the remaining talks. It is truly inspiring to see so many great presentations! Today is the last day of the conference and then it is back to the normal life in Bergen.

Presentation at CMWR


Meltzer prize to Kundan Kumar

Kundan Kumar has been awarded the Meltzer prize for young researchers. The PMG congratulates warmly!

Finse workshop on efficient solvers for fractured porous media

This January we have hosted a workshop in solvers for materials with high-aspect-ratio inclusions. The event was located in beautiful snowy Finse, known as the highest point of the Oslo-Bergen railway. Several international experts in the field have given interesting talks that sat the ground for focused and fruitful discussions. We are grateful to all the participants and presenters for their contributions to the workshop and hopefully start of exciting new collaborations. Special thanks to Jan Martin Nordbotten, Eirik Keilegavlen and Ana Budiša for organizing and Finse 1222 for hosting, but also to The Norwegian Research Council and University of Bergen for financial support.