• A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media 

      Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Sorin Iuliu (Research report, 2017)
      In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic ...
    • Dimensional reduction of a fractured medium for a polymer EOR model 

      Dugstad, Martin Sandanger; Kumar, Kundan; Pettersen, Øystein (Journal article; Peer reviewed, 2021)
      Dimensional reduction strategy is an effective approach to derive reliable conceptual models to describe flow in fractured porous media. The fracture aperture is several orders of magnitude smaller than the characteristic ...
    • Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem 

      Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey (Journal article; Peer reviewed, 2021)
      The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing ...
    • Impact of time-dependent wettability alteration on the dynamics of capillary pressure 

      Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian (Journal article; Peer reviewed, 2020)
      Wettability is a pore-scale property that has an important impact on capillarity, residual trapping, and hysteresis in porous media systems. In many applications, the wettability of the rock surface is assumed to be constant ...
    • Implicit linearization scheme for nonstandard two-phase flow in porous media 

      Kassa, Abay; Kumar, Kundan; Gasda, Sarah; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      In this article, we consider a nonlocal (in time) two‐phase flow model. The nonlocality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed‐point iterative ...
    • Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations 

      Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Radu, Florin Adrian (Conference object; Peer reviewed; Journal article, 2019)
      Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical ...
    • Iterative solvers for Biot model under small and large deformation 

      Borregales Reveron, Manuel Antonio; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      We consider L-scheme and Newton-based solvers for Biot model under large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthermore, the fluid compressibility is assumed to be ...
    • Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments 

      Hanson, Erik Andreas; Hodneland, Erlend; Lorentzen, Rolf Johan; Nævdal, Geir; Nordbotten, Jan Martin; Sævareid, Ove; Zanna, Antonella (Lecture Notes in Computational Science and Engineering, Chapter; Peer reviewed; Journal article, 2019)
      Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the ...
    • A Mixed Approach to the Poisson Problem with Line Sources 

      Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2021)
      In this work we consider the dual-mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is nonstandard, as the line source causes the solutions to be ...
    • Modeling of relative permeabilities including dynamic wettability transition zones 

      Kassa, Abay; Gasda, Sarah E.; Kumar, Kundan; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      Wettability is a pore-scale property that impacts the relative movement and distribution of fluids in a porous medium. There are reservoir fluids that provoke the surface within pores to undergo a wettability change. This ...
    • On the optimization of the fixed‐stress splitting for Biot's equations 

      Storvik, Erlend; Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian (Peer reviewed; Journal article, 2019)
      In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. ...
    • A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments 

      Landa-Marban, David; Liu, Na; Pop, Iuliu Sorin; Kumar, Kundan; Pettersson, Per; Bødtker, Gunhild; Skauge, Tormod; Radu, Florin Adrian (Peer reviewed; Journal article, 2019)
      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, ...
    • Practical approaches to study microbially induced calcite precipitation at the field scale 

      Marban, David Landa; Tveit, Svenn; Kumar, Kundan; Gasda, Sarah (Journal article; Peer reviewed, 2021)
      Microbially induced calcite precipitation (MICP) is a new and sustainable technology which utilizes biochemical processes to create barriers by calcium carbonate cementation; therefore, this technology has a potential to ...
    • Robust iterative schemes for non-linear poromechanics 

      Borregales Reveron, Manuel Antonio; Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2018)
      We consider a non-linear extension of Biot’s model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the ...
    • A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media 

      Radu, Adrian Florin; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Kumar, Kundan (Peer reviewed; Journal article, 2015-12)
      In this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is ...
    • A singularity removal method for coupled 1D–3D flow models 

      Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2019)
      In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this ...
    • Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery 

      Endo Kokubun, Max Akira; Radu, Florin Adrian; Keilegavlen, Eirik; Kumar, Kundan; Spildo, Kristine (Peer reviewed; Journal article, 2019)
      We study a heuristic, core-scale model for the transport of polymer particles in a two-phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when ...
    • An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube 

      Marban, David Landa; Bødtker, Gunhild; Kumar, Kundan; Pop, Iuliu Sorin; Radu, Adrian Florin (Peer reviewed; Journal article, 2020-01-21)
      In this paper, we derive upscaled equations for modeling biofilm growth in porous media. The resulting macroscale mathematical models consider permeable multi-species biofilm including water flow, transport, detachment and ...