Porous media research at the University of Bergen is a major cross-disciplinary effort, involving scientists from mathematics, physics, geophysics, geology, chemistry, biology and medicine. Several long-term research topics are actively pursued within this collaboration, broadly based around either processes in geophysical porous materials (as applied to geothermal energy, CO2 and energy storage, and oil and gas recovery) and image processing (as applied to seismic data and medical imaging). For more details on the individual projects connected to the applications described below, see the Projects page.

Subsurface Energy Storage

Intermittent renewable energy (IRE) such as wind and solar are among the fastest growing energy sources and are critical for the transition to a low carbon emission society. A characteristic feature of these IRE sources is their great variability on both short (sub-daily) and long (seasonal) time-scales. In contrast, the majority of industrial demand, as well as seasonal household consumption such as heating and cooling, remain fixed or seasonal in nature.

A portfolio of scalable solutions must be deployed to mitigate the production-consumption gap. Today, conventional energy resources such as hydroelectric and fossil fuels are used to buffer the comparatively small output from IRE sources, however this strategy becomes less viable as the market share of IRE increases. Furthermore, transmission bottlenecks in the power grid and inertia in the implementation of smart grids and local-scale batteries also calls for additional storage solutions.

Fig 1: Illustration of subsurface energy storage systems in the context of intermittent renewable energy

We are interested in subsurface energy storage in the context of energy storage in geological permeable layers such as saline aquifers or depleted oil and gas reservoirs. These geological features are found globally, and as such provide an attractive venue for energy storage. Our particular interest lies in thermo-mechanical storage: hot fluids at temperatures above 50 °C are injected at elevated pressure, and both thermal and mechanical energy can be recovered during extraction.

To date, large-scale thermo-mechanical subsurface energy storage has not been applied in the context of IRE. Some experience has been gained over the last decades with high-temperature aquifer thermal energy storage (HT-ATES), and research needs related to fracturing of the confining layers and dissolution and precipitation due to water chemistry and temperatures have been identified. Our research is initiated around the following topics:

  1. Cyclical thermo-mechanical weakening of the rock leading to continuous development of fracture networks during operation.
  2. High fluid pressure fluctuations and high thermal fluctuations leading to coupled flow-mechanical-chemical systems.
  3. Extreme flow-rates needed to accommodate rapid oscillations in the production-demand gap leading to non-equilibrium flow conditions.

Geothermal Energy

Unlocking the world’s vast geothermal energy resources depends on our ability to engineer profitable geothermal reservoirs, characterized by sufficient permeability corresponding to distributed contact area between mobile fluids and reservoir rock. The Enhanced Geothermal System is a technology for producing geothermal energy from regions where the permeability and/or fluid content of the reservoir initially is too low for commercial production.

Fig 2: Simulated temperature distribution during production from highly fractured rock

The reservoir performance of an enhanced geothermal system depends on the presence of open interconnected fracture networks, or the ability to create such networks. In geothermal reservoirs, fractures increase not only permeability, but also the contact surface between the rock and the fluid, which facilitates the heat transport. Distributed and connected networks of fractures enable production from large reservoir volumes, but fractures may also result in significant water losses and decrease of sweep efficiency due to water short-circuiting between injectors and producers. Thus, the reservoir stimulation process has crucial importance for achieving the best possible conditions for geothermal energy production.

The PMG at the University of Bergen has had a sustained effort on developing mathematical models and numerical tools for the stimulation and production of geothermal reservoirs. Research activities involve mathematical modeling, upscaling and development of simulation tools for processes in fractured geothermal reservoirs, including coupled THCM processes. Several of the group’s ongoing research projects supporting this activity include strong inter-disciplinary and inter-sectoral collaboration.

Enhanced Oil Recovery (EOR)

Efficient recovery is essential for optimal exploitation of existing and new oilfields. In spite of technological advances, between 25 and 50 % of the oil is left in reservoirs after conventional recovery. EOR refers to the techniques used to recover the rest of the oil in the reservoir. The success and optimization of an EOR technique is crucially dependent on mathematical models and numerical simulations.

Our group is currently involved in four interdisciplinary projects involving EOR. The projects focus on microbial EOR (MEOR), nano-particle EOR (NANO-EOR), CO2-EOR and polymer EOR. The challenges behind all these projects are in dealing with the multi-phase, multi-scale, multi-physics character of the problems and to design reliable and efficient simulators. To exemplify, we present below more details of the MEOR project.

MEOR technologies are environmentally sound and cost-efficient tertiary recovery methods for water-injected oil reservoirs. Norway has a leading position in MEOR, with Statoil taking a first use position through the offshore development at Norne and later at the Statfjord field.

Fig 3: Two-phase flow through smooth and fluvial layers from the SPE 10 benchmark

MEOR is a complex process, where flow of multiple phases and their interaction with the rock surface are affected by bacterial growth and activity, metabolic components and structural changes. The project aims at studying MEOR mechanisms involved in adaptive bio-plugging of highly permeable structures in heterogeneous reservoir formations. The processes involved in MEOR are encountered at various scales, but is initiated at pore scale. Our approach is to develop a pore scale and core model where the mathematical modelling is based on experimental data from both scales.

The objective of the MEOR project is to develop accurate mathematical models and numerical approaches for MEOR, capable of describing the relevant biological, physical and chemical processes occurring at various scales. Given the complexity of MEOR, this can only be gained by combining the practical insights from the laboratory experiments with a consistent treatment of the pore scale and transition to a heterogeneous porous system at Darcy scale, from both analytical and numerical point of view. This challenging task requires a tight, interdisciplinary collaboration.

Discretisation Techniques and Solvers

Typical mathematical models for the applications above are systems of non-linear, fully coupled partial differential equations, with coefficients ranging over many order of magnitudes, which are very challenging to be solved. A special focus of our group is on mass conservative discretisation methods (FV, MPFA, MFEM), on higher-order space-time elements (continuous or discontinuous Galerkin in time), on non-linear solvers (Newton method, L-scheme or combination of them) and linear solvers which adequately incorporate the geometrical properties of the domain. We particularly emphasise our recent works on multi-phase flow, poromechanics and upscaling.

Regarding multi-phase flow: we recently developed a new, very robust iterative scheme for solving two-phase flow in porous media or for the Richards equation. The scheme, called L-scheme, is only first order convergent but does not employ the computation of any derivatives and, moreover, the linear systems to be solved within each iteration are typically much better conditioned than the corresponding systems in the Newton method. One can also combine the robust L-scheme with the quadratic convergent Newton method by performing a few iterations using the L-scheme and then switching to Newton (based on a posteriori indicators).

Fig 4: Flow as predicted by a new hierarchical mixed finite element discretization for fractured media

Our newest results on linear or non-linear poromechanics concern the development of a new finite volume scheme (MPSA), extension of the fixed stress method to heterogeneous media and the development of robust iterative schemes for non-linear poromechanics and of higher-order space-time schemes. A special focus is also on developing new solvers for coupled multi-phase flow and mechanics. These challenges must always be seen in context with the need to handle the presence of fractures in the material.

Another core area of our research is the development of multiscale simulators by homogenisation or numerical multiscale methods. We apply homogenisation to develop new models, which adequately describe the evolving geometry at the micro-scale (due to e.g. precipitation/dissolution processes or biofilm formation). These models are capable of describing features like clogging or structure damage in a rational manner. Multigrid methods can be obtained by defining projectors and restriction operators based on homogenisation.

Interpretation of Dynamic Contrast Images in Medicine

The measurement of perfusion and filtration are important clinical parameters used in diagnosis, follow-up, and therapy. By utilising complementary and well documented research skills, the aim is to investigate a novel approach towards interpretation of dynamic medical imaging with emphasis on blood distribution and flow. Typical applications include characterisation of strokes and planning and evaluation of cancer treatment procedures.

Fig 5: Segmentation of MRI data for computational assessment and parameter estimation related to kidneys

Medical image acquisition techniques like computerised tomography (CT), magnetic resonance imaging (MRI), or positron emission tomography (PET), can all be applied in a dynamic setting where the evolving distribution of an injected contrast agent is gathered together as a temporal sequence of images. Quantitative tissue characterisation (e.g., blood perfusion) from such data is currently performed locally by applying tracer-kinetic methodology to a single region of interest (ROI) or a voxel at a time.

Our research will formulate and investigate an alternative interpretation strategy where the tracer concentration for an individual voxel will be considered in the context of a global flow problem that connects all voxels in the image domain. By modelling the flow between voxels from first principles and calibrate the models to observations via systematic assimilation techniques that include rigorous error estimates, our goal is to advance understanding and clinical utility of dynamic imaging interpretation.