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Eirik Keilegavlen's picture

Eirik Keilegavlen

Researcher
  • E-mailEirik.Keilegavlen@uib.no
  • Phone+47 55 58 28 31
  • Visitor Address
    Realfagbygget, Allégt. 41
  • Postal Address
    Postboks 7803
    5020 Bergen

As an applied mathematician, my main research interest is to facilitate enhanced understanding of nature by the development mathematical models for physical phenomena, analysis of the resulting equations, and the construction of numerical solution algorithms for the problems. My main focus is on porous media, as this contains problems of high societal importance such as subsurface processes (energy extraction and waste disposal) and biological flow, and also lead to interesting and challenging mathematical problems. However, my research interest also includes elasticity, geo- and hydro-mechanics. 

Specific research fields that I am involved in include:

 

  • Geothermal energy, including both fluid flow and coupling of flow and geo-mechanics.
  • Multiscale approaches to porous media flow, including both modeling and numerical methods.
  • Design of linear and non-linear solvers, with focus on exploiting physical properties of the underlying equations to improve the numerical methods.

 

 

Academic article
  • 2019. Reactivation of fractures in subsurface reservoirs - A numerical approach using a static-dynamic friction model. Lecture Notes in Computational Science and Engineering. 653-660.
  • 2019. Implementation of mixed-dimensional models for flow in fractured porous media. Lecture Notes in Computational Science and Engineering. 573-580.
  • 2019. Finite volume discretization for poroelastic media with fractures modeled by contact mechanics. International Journal for Numerical Methods in Engineering. 644-663.
  • 2019. Dual virtual element methods for discrete fracture matrix models. Oil & gas science and technology. 1-17.
  • 2019. Consistent MPFA Discretization for Flow in the Presence of Gravity. Water Resources Research. 1-14.
  • 2019. Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations. Journal of Computational Physics. 694-712.
  • 2019. A pore-scale study of transport of inertial particles by water in porous media. Chemical Engineering Science (CES). 397-409.
  • 2018. Unified approach to discretization of flow in fractured porous media. Computational Geosciences. 1-13.
  • 2018. Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. Transport in Porous Media. 1-19.
  • 2018. Three-Dimensional Numerical Modeling of Shear Stimulation of Fractured Reservoirs. Journal of Geophysical Research (JGR): Solid Earth. 3891-3908.
  • 2018. Input and benchmarking data for flow simulations in discrete fracture networks. Data in Brief. 1135-1139.
  • 2018. In vivo detection of chronic kidney disease using tissue deformation fields from dynamic MR imaging. IEEE Transactions on Biomedical Engineering. 1779-1790.
  • 2018. Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches. Transport in Porous Media. 215-236.
  • 2018. Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media. 439-462.
  • 2018. Dual virtual element method for discrete fractures networks. SIAM Journal on Scientific Computing. 228-258.
  • 2018. A heterogeneous multiscale MPFA method for single-phase flows in porous media with inertial effects. Computational Geosciences. 107-126.
  • 2018. A finite-volume discretization for deformation of fractured media. Computational Geosciences. 993-1007.
  • 2017. Postinjection normal closure of fractures as a mechanism for induced seismicity. Geophysical Research Letters. 9598-9606.
  • 2017. High-accuracy phase-field models for brittle fracture based on a new family of degradation functions. Journal of the mechanics and physics of solids. 458-489.
  • 2017. Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs. Computational Geosciences. 451-467.
  • 2017. Fractal structures in freezing brine. Journal of Fluid Mechanics. 975-995.
  • 2017. Finite volume methods for elasticity with weak symmetry. International Journal for Numerical Methods in Engineering. 939-962.
  • 2016. The effect of deformation bands on simulated fluid flow within fault-propagation fold trap types: Lessons from the San Rafael monocline, Utah. American Association of Petroleum Geologists Bulletin. 1523-1540.
  • 2016. A multiscale multilayer vertically integrated model with vertical dynamics for CO2 sequestration in layered geological formations. Water Resources Research. 6490-6505.
  • 2015. Two-scale preconditioning for two-phase nonlinear flows in porous media. Transport in Porous Media. 485-503.
  • 2015. Inexact linear solvers for control volume discretizations in porous media. Computational Geosciences. 159-176.
  • 2014. Physics-based preconditioners for flow in fractured porous media. Water Resources Research. 1357-1373.
  • 2014. Conservative inexact solvers for porous media flow. Lecture Notes in Computational Science and Engineering. 333-340.
  • 2014. Application of Vertically-Integrated Models with Subscale Vertical Dynamics to Field Sites for CO2 Sequestration. Energy Procedia. 3523-3531.
  • 2014. Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media. Multiscale Modeling & simulation. 335-363.
  • 2013. Domain decomposition strategies for nonlinear flow problems in porous media. Journal of Computational Physics. 439-451.
  • 2013. Deformation bands and their impact on fluid flow in sandstone reservoirs: the role of natural thickness variations. Geofluids. 359-371.
  • 2013. Auxiliary variables for 3D multiscale simulations in heterogeneous porous media. Journal of Computational Physics. 141-153.
  • 2012. Tensor relative permeabilities: Origin, modeling and numerical discretization. International Journal of Numerical Analysis & Modeling. 701-724.
  • 2012. Multidimensional upstream weighting for multiphase transport on general grids. Computational Geosciences. 1021-1042.
  • 2011. Monotonicity for MPFA methods on triangular grids. Computational Geosciences. 3-16.
  • 2011. Field-case simulation of CO2-plume migration using vertical-equilibrium models. Energy Procedia. 3801-3808.
  • 2010. Simulation of anisotropic heterogeneous near-well flow using MPFA methods on flexible grids. Computational Geosciences. 509-525.
  • 2009. Sufficient criteria are necessary for monotone control volume methods. Applied Mathematics Letters. 1178-1180.
  • 2009. Non-hydrostatic pressure in sigma-coordinate ocean models. Ocean Modelling. 240-249.
Lecture
  • 2019. Numerical investigation of wing crack initiation and propagation due to shear slip.
  • 2018. Domain Decomposition Preconditioner for Mixed-dimensional Flow Problems in Fractured Porous Media.
  • 2017. Understanding the stimulation of deep geothermal reservoirs through modeling and simulation.
  • 2017. Simulation of geothermal energy extraction on realistic geologies using the dual virtual element method.
  • 2017. Fractal structures in freezing brine.
  • 2017. Coupled processes in geothermal systems.
  • 2017. BDDC Preconditioner for Robust Discretization of Flow in Fractured Porous Media.
  • 2017. A robust control volume heterogeneous multiscale method for non-linear flows in porous media.
  • 2017. A BDDC Method for Robust Discretization of Flow in Fractured Porous Media.
  • 2016. Improving the Accuracy of Phase-Field Models for Brittle Fracture.
  • 2016. Impact of Degradation Functions on the Accuracy of Phase-Field Models for Brittle Fracture.
  • 2015. Simulation of Slip-Induced Permeability Enhancement Accounting For Multiscale Fractures.
  • 2015. Phase-field modelling of fluid pressure-induced fractures.
  • 2015. Fracture propagation in Enhanced Geothermal Systems.
Popular scientific lecture
  • 2017. Structural impact of fractures on dynamic processes in geothermal reservoirs.
Academic lecture
  • 2019. Numerical investigation of wing crack initiation and propagation due to shear slip .
  • 2019. Numerical Modeling of Fracture Reactivation in a Three-dimensional Domain Based on a Coulomb Friction Law.
  • 2019. Numerical Methods for Flow in Fractured Porous Media in a Unified Implementation.
  • 2019. Mixed-dimensional discrete fracture matrix models with heterogeneous discretization and non-matching grids.
  • 2019. Induced seismicity in the Reykjanes geothermal reservoir, Iceland: seismic event monitoring, characterization and clustering.
  • 2019. Fracture mechanics of brittle materials: fracture criteria and numerical approach.
  • 2019. Enhancing Geothermal Reservoirs – Modelling and Analysis of Hydraulic and Thermal Stimulation.
  • 2019. Enhanced fluid convection and heat transfer near the bottom of the IDDP-1 well in Krafla, NE Iceland.
  • 2019. Consistent discretization of flow for inhomogeneous gravitational fields.
  • 2019. Challenges in Modelling the Anisotropic Poroelastoplastic Behaviour of Fractured Rocks as Homogenized Media.
  • 2018. Viscous fingering in fractured porous media.
  • 2018. Unified modeling and discretization of flow in fractured porous media.
  • 2018. Three-dimensional numerical modelling of hydraulic stimulation of geothermal reservoirs: permeability enhancement and induced seismicity.
  • 2018. PorePy: A Python Simulation Tool for Fractured and Deformable Porous Media​.
  • 2018. Multi-fracture propagation in porous medium under shear stimulation of fluid flow.
  • 2018. Modelling of thermal shock induced fracture growth.
  • 2018. Modelling of conditions close to geothermal heat sources.
  • 2018. Modeling fracture reactivation in a mixed dimensional setting​: Friction models and numerical challenges​.
  • 2018. Modeling fracture reactivation in a mixed dimensional setting​: Friction models and numerical challenges​.
  • 2018. Fracture propagation in porous medium under shear stimulation of fluid flow.
  • 2018. A general framework for heterogeneous discretizations in mixed-dimensional single-phase flow.
  • 2017. Simulation of hydraulic stimulation of fractured geothermal reservoirs.
  • 2017. PorePy: A Python Simulation Tool for Fractured and Deformable Porous Media.
  • 2017. Hydraulic stimulation and friction laws for fracture deformation – a numerical study .
  • 2017. Hydraulic stimulation and friction laws for fracture deformation – a numerical study.
  • 2017. Hybrid FE-FV scheme for modeling pressure-induced fracture propagation in porous media using a phase-field approach.
  • 2017. High-accuracy phase-field models for brittle fracture based on a new family of degradation functions.
  • 2017. Handling of Fractures and Intersections in Finite Volume Methods.
  • 2017. Finite volume discretizations of poro-elasticity in high­ contrast media.
  • 2017. Discretization of mixed-dimensional problems using legacy codes.
  • 2017. An approach for simulation of hydraulic stimulation of a fractured geothermal reservoir.
  • 2017. A numerical approach for simulation of shear dilation of three-dimensional fracture networks.
  • 2016. Enhanced geothermal systems – modeling of fracture response to hydraulic stimulation.
  • 2016. A weakly symmetric finite volume method for elasticity with application to fractures in porous media.
  • 2015. Incorporating Geological Uncertainty in Error Control for Linear Solvers.
  • 2014. Modeling of Permeability Enhancement in Geothermal Reservoirs by Shear-Dilation Stimulation.
  • 2014. Mathematical modeling of permeability enhancement in geothermal reservoirs.
  • 2010. Near-well discretisations for anisotropic heterogeneous problems on flexible grids.
Academic anthology/Conference proceedings
  • 2020. Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. Springer.
  • 2019. Numerical Methods for Processes in Fractured Porous Media. Birkhäuser Verlag.
Masters thesis
  • 2018. Implementation of an MPFA/MPSA-FV Solver for the Unsaturated Flow in Deformable Porous Media.
  • 2014. Upscaling of heat-transport in complex heterogeneous media.
  • 2010. A multiscale approach to estimate large scale flow and leakage from geological storage.
Software
  • 2019. PorePy: A Simulation Tool for Fractured and Deformable Porous Media written in Python, v.1.0.
  • 2018. PorePy: A Simulation Tool for Fractured and Deformable Porous Media written in Python, versjon 0.4.3.
  • 2017. PorePy: A Simulation Tool for Fractured and Deformable Porous Media written in Python.
  • 2017. PorePy: A Python Simulation Tool for Fractured and Deformable Porous Media. Version 0.2.
  • 2016. Finite volume discretizations for Biot's equations.
Popular scientific article
  • 2015. Hvordan håndtere usikkerhet ved CO2-lagring. Bergens Tidende.
  • 2014. Sprekker er nøkkelen til dyp jordvarme. Bergens Tidende.
Doctoral dissertation
  • 2019. Phase-field Modeling and Simulation of Brittle Fracture.
  • 2018. Numerical modeling of shear stimulation in naturally fractured geothermal reservoirs.
  • 2010. Robust Control Volume Methods for Reservoir Simulation on Challenging Grids.
Academic chapter/article/Conference paper
  • 2019. Numerical investigation of wing crack initiation and propagation due to shear slip.
  • 2019. Enhanced fluid convection and heat transfer near the bottom of the IDDP-1 well in Krafla, NE Iceland.
  • 2019. Anisotropic Poroelastoplastic Constitutive Model of Fractured Rocks.
  • 2018. Three-dimensional numerical modelling of fracture reactivation due to fluid injection in geothermal reservoirs.
  • 2016. Modelling of the Shear Dilation Based Hydraulic Stimulation in Enhanced Geothermal Systems Considering Fractures in Different Scales.
  • 2015. Simulation of Slip-Induced Permeability Enhancement Accounting For Multiscale Fractures.
  • 2013. Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: inexact solvers and improved transport upscaling.
  • 2012. Mass conservative domain decomposition for porous media flow. 23 pages.
  • 2012. Mass Conservative Domain Decomposition for Fractured Porous Media.
  • 2012. MULTISCALE SIMULATION OF NON-DARCY FLOWS. 8 pages.
  • 2010. Monotone Multi-dimensional Upstream Weighting on General Grids.
  • 2010. A Multiscale Framework for Simulating Multi-phase Flow on Flexible Grids.
  • 2008. Monotonicity for control volume methods on unstructured grids. 13 pages.
  • 2008. Discretization schemes for anisotropic heterogeneous problems on near-well grids. 12 pages.
Poster
  • 2019. Simulation of temperature and pressure driven fracture deformation.
  • 2019. Phase-field Modeling of Brittle Crack Propagation in Saturated Porous Media.
  • 2019. Automatic picking for induced seismicity in Iceland using an EAT (Empirically Aggregated Template) methodology.
  • 2018. Outcrop fracture characterization for geothermal reservoirs: challenges in optimizing inputs for reservoir models.
  • 2018. Mixed-dimensional poroelasticity for deformable fractured porous media.
  • 2018. Induced seismicity in a geothermal reservoir: a case study in the Reykjanes peninsula in Iceland.
  • 2018. Efficient Linear Solvers for Mixed-dimensional Flow Problems in Fractured Porous Media.
  • 2017. High-accuracy phase-field models for brittle fracture.
  • 2017. Fracture Deformation Models in Geothermal Reservoirs.
  • 2017. Finite Volume Methods for Flow and Transport in 3-Dimensional Fractured Porous Media.
  • 2017. Coupling Conditions for Finite Volume Methods for Fractured Porous Media.
  • 2017. BDDC Preconditioner for Robust Discretization of Flow in Fractured Porous Media.
  • 2016. Cell centered finite volume discretization of fractured deformable porous media.
  • 2015. Modeling of Hydroshearing in Geothermal Reservoirs.
  • 2015. Coupling Issues Arising from Combining Fracture Phase-Field Models with Biot Poroelasticity.

More information in national current research information system (CRIStin)

Submitted manuscripts:

  1. B. Gou, K.W. Bandilla, F. Doster, E. Keilegavlen, M.A. Celia: A Vertically-integrated Model with Vertical Dynamics for CO2 Storage, Water Resources Research, submitted.
  2. T.H. Sande, I. Berre, E. Keilegavlen, J.M. Nordbotten: An automated MINC method for simulation of heat transport in fractured geothermal reservoirs, Mathematical Geosciences, submitted.

Peer reviewed publications:

  1. E. Keilegavlen, J.M. Nordbotten: Inexact linear solvers for control volume discretizations in porous media, Computational Geosciences, in press.
  2. T.H. Sandve, E. Keilegavlen, J.M.  Nordbotten (2014): Physics-based preconditioners for flow in fractured porous media, Water Resources Research,, 50(2), 1357-1373.
  3. S. Alyaev, E. Keilegavlen, J. M. Nordbotten (2014): Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media, SIAM Multiscale Modeling and Simulation, 12(1) 335-363. Preprint.
  4. A. Rotevatn, T.H. Sandve, E. Keilegavlen, D. Kolyukhin, H. Fossen (2013): Deformation bands and their impact on fluid flow in sandstone aquifers: the role of natural thickness variations, GeoFluids, 13 (3), 359-373.
  5. A. Sandvin, E. Keilegavlen, J. M. Nordbotten (2013): Auxiliary variables in multiscale simualtions, Journal of Computational Physics, 238, 141-153. Preprint.
  6. J.O. Skogestad, E. Keilegavlen, J. M. Nordbotten (2013): Domain Decomposition Strategies for Non-linear Flow Problems in Porous Media, Journal of Computational Physics, 234, 439-451. Preprint.
  7. E. Keilegavlen, J. Kozdon and B. Mallison (2012): Multi-dimensional upstream weighting for multi-phase flow on general grids, Computational Geosciences 16(4) 1021-1042. Preprint.
  8. E. Keilegavlen, J.M. Nordbotten, A. Stephansen (2012): Tensorial Relative Permeabilities: Origin, Modelling and Discretization, International Journal of Numerical Analysis and Modeling 9 (3), 701-724. Preprint.
  9. E. Keilegavlen and I. Aavatsmark (2011): Monotonicity for MPFA methods on triangular grids, Computational Geosciences 15 (1), 3-16.
  10. S. Mundal, E. Keilegavlen and I. Aavatsmark (2010): Simulation of Anisotropic Heterogeneous Near-well Flow using MPFA Methods on Flexible Grids, Computational Geosciences 14 (4), 509-525.
  11. E. Keilegavlen, J. M. Nordbotten and I. Aavatsmark. (2009): Sufficient monotonicity criteria are necessary for control volume methods, Applied Mathematical Letters 22 (8), 1178-1180. Preprint.
  12. E. Keilegavlen and J. Berntsen (2009): Non-hydrostatic pressure in sigma-coordinate ocean models, Ocean Modelling 28(4), 240-249. Preprint.

Peer reviewed book chapters:

  1. F. Doster, E. Keilegavlen, J.M. Nordbotten: A robust implicit pressure explicit mass method for multi-phase multi-component flow including capillary pressure and buoyancy. In Computational Methods for CO2 Geo-sequestration & Compressed Air Storage, Edited by Rafid Al-Khoury, Jochen BundSchuh, ISBN: 9781138015203, CRC Press.
  2. E. Keilegavlen, J.M. Nordbotten: Conservative inexact solvers for porous media flow, Proceedings of the 21st International Conference on Domain Decomposition Methods, to be published in Springer Lecture Notes in Computational Science and Engineering.
  3. J.M. Nordbotten, E. Keilegavlen, A. Sandvin (2011): Mass conservative domain decomposition for porous media flow, In: Finite Volume Method - Powerful Means of Engineering Design, Edited by PhD. Radostina Petrova, ISBN: 978-953-51-0445-2, InTech.

Conference proceedings:

  1. E. Keilegavlen, J.O. Skogestad, J.M. Nordbotten (2014): Domain decomposition preconditioning for non-linear elasticity problems, Proceedings of 11th Word Congress of Computational Mechanics, Barcelona.
  2. T.H. Sandve, I. Berre, E. Keilegavlen, J.M. Nordbotten (2013): Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: Inexact solvers and improved transport upscaling, Proceedings of the thirty-eight workshop on geothermal reservoir engineering, Stanford University.
  3. T.H. Sandve, E. Keilegavlen, J.M. Nordbotten (2012): Mass conservative domain decomposition for fractured porous media, Proceedings of the XIX International Conference on Water Resources (CMWR).
  4. S. Alyaev, E. Keilegavlen, J.M. Nordbotten (2012): Multiscale simulations of non-Darcy flows, Proceedings of CMWR XIX.
  5. E. Keilegavlen, J.M. Nordbotten, A. Stephansen (2011): Simulating two-phase flow in porous media with anisotropic relative permeabilities, Proceedings of SPE Reservoir Simulation Symposium, SPE 141552.
  6. E. Keilegavlen, J. Kozdon and B.T. Mallison (2010): Monotone Multi-dimensional Upstream Weighting on General Grids,  Proceeding of the 12th European Conference on the Mathematics of Oil Recovery (ECMOR XII).
  7. A. Sandvin , J.O. Skogestad, E. Keilegavlen  and J.M. Nordbotten (2010): A Multiscale Framework for Simulating Multi-phase Flow on Flexible Grids, Proceedings of ECMOR XII.
  8. H.M. Nilsen, P.A. Herrera, M. Ashraf, I. Ligaarden, M. Iding, C. Hermanrud, K.-A. Lie, J.M. Nordbotten, H.K. Dahle and E. Keilegavlen (2010): Field-case simulation of CO2-plume migration using vertical-equilibrium models, Proceedings of GHGT 10.
  9. P.A. Herrera , J.M. Nordbotten B.F. El-Faour, E. Keilegavlen and H.K. Dahle (2010): The impact of natural heterogeneity on CO2 migration in deep saline aquifers, Proceedings of British Hydrological Society International Symposium 2010.
  10. E. Keilegavlen and I. Aavatsmark (2008): Monotonicity for control volume methods on triangular grids, Proceedings of ECMOR XI.
  11. S. Mundal, E. Keilegavlen and I. Aavatsmark (2008): Discretisation schemes for anisotropic heterogeneous problems on near-well grids, Proceedings of ECMOR XI.

 

 


PdD thesis: Robust Control Volume Methods for Reservoir Simulations on Challenging Grids

Master thesis: Modeling the non-Hydrostatic Pressure in sigma-Coordinate Ocean Models 

PhD in Applied Mathematics - Reservoir Simulation, thesis

Master degree in Applied Mathematics - Hydrodynamics and Ocean Modeling, thesis 

 

Current activities:

Stimulation of fracture networks via shear dilation: The project considers the coupling of porous media flow with geo-mechanics to investigate the opening of fractures during fluid injection. See the GeoStim project for more information.

Dynamic reconstruction models for the simulation of CO2 injection: The goal of this work is to extend the applicability of a popular class of methods that is tailored for simulating CO2 injection. This is joint work with researchers at Princeton University.

Inexact linear solvers and physics-based preconditioners for porous media flow: This has been a long ongoing effort which aims to design a holistic framework for solvers, upscaling and discretization based on control volume disrcetizations of porous media flow. Recent work considers the adaption of the framework to account for stochastic parameter fields.

Preconditioners for non-linear elasticity problems: The project considers the construction of non-linear preconditioning of Newton's method for the solution of problems in elasticity. Special attention is paid to the treatment of spatial scales.

Software:

Contributed together with Tor Harald Sandve a module for Discrete Fracture Matrix modeling to the Matlab Reservoir Simulation Toolbox, released by Sintef.