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Knut-Andreas Lie

SINTEF, Mathematics and Cybernetics, Faculty Member

Norwegian University of Science and Technology, Department of Mathematical Sciences, Faculty Member

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I work as chief scientist at SINTEF, the largest independent research organization in Scandinavia, where I head the Computational Geosciences group at the Mathematics and Cybernetics department in Oslo. I hold a part-time Professor position at the Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU). My research interests include flow in porous media (multiscale methods, unstructured grids, grid coarsening, consistent discretizations, fast nonlinear solvers, flow diagnostics, CO2 storage, streamline methods, etc), numerical methods for nonlinear PDEs (high-resolution, front tracking, operator splitting, etc.), and heterogeneous high-performance computing (multicore, GPUs, etc).

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Papers by Knut-Andreas Lie

A multiscale streamline method for inversion of production data

Journal of Petroleum Science and Engineering, Nov 1, 2006

A Multiscale Mixed Finite Element Method For Vuggy and Naturally Fractured Reservoirs

Generalized travel-time inversion on unstructured grids

Journal of Petroleum Science and Engineering, Apr 1, 2009

An Unconditionally Stable Method for the Euler Equations

Journal of Computational Physics, Mar 1, 1999

Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements

Journal of Computational Physics, Dec 1, 2008

An Integrated Modeling Framework for Simulating Complex Transient Flow in Fractured Reservoirs with 3D High-Quality Grids

Modeling near-well transient flow with complex 3D fracture networks poses several challenges: the... more Modeling near-well transient flow with complex 3D fracture networks poses several challenges: the multiscale nature (millimeters to kilometers), long and deviating well trajectories, intricate fracture networks with fracture-fracture and fracture-well intersections, and high level of reservoir heterogeneities. We address these difficulties by proposing a comprehensive methodology for meshing, discretizing, and simulating transient flow in complex 3D fracture networks based on discrete fracture-matrix models. Our framework consists of three parts: (i) Given deviating wells and planar or nonplanar fractures and faults, we construct highquality 3D grids conforming to wells, hydraulic fractures, faults, and dominating natural fractures. We ensure sufficient mesh quality near important features using transfinite interpolation near wells and hydraulic fractures, combined with adaptive refinement in regions of interest. (ii) With the generated grid, we discretize the governing equations with a fully implicit finite- volume formulation with an inner-boundary well model and discrete fracture model. (iii) Finally, we analyze the results using suitable visualization tools, both for pressure-transient curves and 3D matrix/fracture data. The framework enables high-resolution numerical modeling of transient flow with complex fracture networks in 3D. We demonstrate the capacities through simple validation cases with comparisons against an industry-standard commercial well-testing software but also present highly complex cases with long and deviating well trajectories and highly detailed fracture networks. We present and analyze flow-transient behavior coupling the wellbore, the fracture network, and the matrix. We also present an approach to reliably diagnose complex multiple flow regimes on the pressure-transient curves combined with different-scale spatial pressure distribution. Comparison against the commercial software indicates that our framework does not introduce adverse grid-orientation effects for non-K-orthogonal grids which is able to robustly handle the details for fracture-network heterogeneities in 3D reservoirs. Overall, our framework is robust for simulating and analyzing realistic second-level transient effects and short-term well performance with complex fracture networks and heterogeneities. Detailed description of the 3D fracture networks, and accurate simulation of the near-well transient flow behavior can be achieved, which provides confidence to interpret the dynamic flow data at different scales and observe transport mechanisms in unconventional fractured reservoirs with multiple levels of heterogeneity.

GAWPS: A MRST-based module for wellbore proﬁling and graphical analysis of ﬂow units

Advances in geo-energy research, Dec 20, 2021

On obtaining optimal well rates and placement for CO2 storage

Computational Geosciences, Mar 22, 2017

A Front-Tracking Method for Efficient Simulation of Miscible Gas Injection Processes

All Days, Jan 31, 2005

A Method To Improve the Mass Balance in Streamline Methods

All Days, Feb 26, 2007

Multiscale Simulation of Polymer Flooding with Shear Effects

Transport in Porous Media, Apr 26, 2016

Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe

Computational Geosciences, Nov 26, 2015

An Open-Source Toolchain for Simulation and Optimization of Aquifer-Wide CO2 Storage

Energy Procedia, 2016

On the Artificial Compression Method for Second-Order Nonoscillatory Central Difference Schemes for Systems of Conservation Laws

SIAM Journal on Scientific Computing, 2003

An Adaptive Newton–ASPEN Solver for Complex Reservoir Models

Building an open-source community for subsurface flow simulation

The MATLAB Reservoir Simulation Toolbox (MRST) is a unique research tool for rapid prototyping an... more The MATLAB Reservoir Simulation Toolbox (MRST) is a unique research tool for rapid prototyping and demonstration of new computational methods for flow in porous media. The software has a large user base all over the world in both academia and industry. My group is also one of the key contributors to OPM Flow, the world's first open-source reservoir simulator aimed at full industry use. In addition, we are currently developing Jutul, an upcoming Julia code for high-performance demonstrators of subsurface flow. In the talk, I will briefly describe the MRST and OPM Flow platforms, how they came to be, compare and contrast their development and ownership models, and outline some of the factors that have contributed to their current success. MRST was originally an internal research tool that has, over the last ten years, morphed into the de-facto standard tool for researchers who want to learn about subsurface flow, and obtain a head start for their own research prototypes. MRST is organized as a minimal core module offering basic data structures and functionality for representing grids and physical parameters relevant to porous media flow, and a large set of add-on modules offering discretizations, solvers, physical models, and a wide variety of simulators and workflow tools. In the modules, you will find many tutorial examples that explain and showcase how MRST can be used to make general or fit-for-purpose simulators and workflow tools. The modular structure makes it easy to add new or modify existing functionality, and many of the 60 currently released modules are authored entirely or in part at other institutions. The software is licensed under the viral GPL license, with copyright of the core parts vested at SINTEF, where we heavily rely on the code for both our contract work and academic research. The software exists as an add-on to the commercial MATLAB product, which greatly simplifies the process of getting started, but also poses certain restrictions on usage and performance potential. (Except for graphical interfaces, large parts of MRST also work well with GNU Octave.) OPM Flow aims to simulate many of the same physical processes as MRST, but its disruptive power comes from being a drop-in replacement for commercial reservoir simulators that have been developed and validated over decades. Such simulators, which are used for development planning and day to day operations of oil and gas fields and CO2 storage operations, are highly complex, expensive and difficult to modify as the source codes are not available. OPM Flow is a collaborative effort, developed in collaboration with Equinor, NORCE, and others, to provide an open-source alternative that enables more open innovation. The simulator is written in high-performance C++ and is released under the GPL license. A key requirement for the development has been that the new simulator should reproduce virtually identical simulation results as contemporary commercial tools both in hindcasting decades of production histories and in forecasting future production. Achieving this has been a vast undertaking filled with stumbling blocks and a lot of reverse engineering. The two platforms are approaching the same goal of open-source simulation of subsurface flow from opposing ends: MRST educates users in subsurface simulation and embeds them directly at the research front by giving access to the codes behind scientific papers, while OPM’s greatest achievement is that users may not notice that they have switched from an expensive closed code to a modern open-source simulator with high potential for computational speedup.

Incompressible Solvers for Single-Phase Flow

Cambridge University Press eBooks, Aug 8, 2019

Unstructured PEBI Grids Conforming to Lower-Dimensional Objects

Cambridge University Press eBooks, Nov 25, 2021

Categorization of Norwegian Continental Shelf Formations in Terms of Geological CO2 Storage Potentials

Energy Procedia, Jul 1, 2017

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

All Days, Feb 21, 2011

A robust and efficient simulation technique is developed based on the extension of the mimetic fi... more A robust and efficient simulation technique is developed based on the extension of the mimetic finite volume method to multiscale hierarchical hexahedral (corner-point) grids via use of the multiscale mixed finite element method. The implementation of the mimetic subgrid discretization method is compact and generic for a large class of grids, and thereby, suitable for discretizations of reservoir models with complex geologic architecture. Flow equations are solved on a coarse grid where basis functions with subgrid resolution accurately account for subscale variations from an underlying fine-scale geomodel. The method relies on the construction of approximate velocity spaces that are adaptive to the local properties of the differential operator. A variant of the method for computing velocity basis functions is developed that utilizes an adaptive local-global algorithm to compute multiscale velocity basis functions by capturing the principal characteristics of global flow. Both local and local-global methods generate subgrid-scale velocity fields that reproduce the impact of fine-scale stratigraphic architecture. By using multiscale basis functions to discretize the flow equations on a coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields on the underlying fine grid.The accuracy and efficacy of the multiscale method is compared to that of fine-scale models and of coarse-scale models with no subgrid treatment for several two-phase flow scenarios. Numerical experiments involving two-phase incompressible flow and transport phenomena are carried out on high-resolution corner-point grids that explicitly represent example stratigraphic architectures found in real-life shallow marine and turbidite reservoirs. The multiscale method is several times faster than the direct solution of the fine-scale problem and yields more accurate solutions than coarse-scale modeling techniques that resort to explicit effective properties. The accuracy of the multiscale simulation method with adaptive local-global velocity basis functions are compared to that of the local velocity basis functions. The multiscale simulation results are consistently more accurate when the local-global method is employed for computing the velocity basis functions.

A multiscale streamline method for inversion of production data

Journal of Petroleum Science and Engineering, Nov 1, 2006

A Multiscale Mixed Finite Element Method For Vuggy and Naturally Fractured Reservoirs

Generalized travel-time inversion on unstructured grids

Journal of Petroleum Science and Engineering, Apr 1, 2009

An Unconditionally Stable Method for the Euler Equations

Journal of Computational Physics, Mar 1, 1999

Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements

Journal of Computational Physics, Dec 1, 2008

An Integrated Modeling Framework for Simulating Complex Transient Flow in Fractured Reservoirs with 3D High-Quality Grids

Modeling near-well transient flow with complex 3D fracture networks poses several challenges: the... more Modeling near-well transient flow with complex 3D fracture networks poses several challenges: the multiscale nature (millimeters to kilometers), long and deviating well trajectories, intricate fracture networks with fracture-fracture and fracture-well intersections, and high level of reservoir heterogeneities. We address these difficulties by proposing a comprehensive methodology for meshing, discretizing, and simulating transient flow in complex 3D fracture networks based on discrete fracture-matrix models. Our framework consists of three parts: (i) Given deviating wells and planar or nonplanar fractures and faults, we construct highquality 3D grids conforming to wells, hydraulic fractures, faults, and dominating natural fractures. We ensure sufficient mesh quality near important features using transfinite interpolation near wells and hydraulic fractures, combined with adaptive refinement in regions of interest. (ii) With the generated grid, we discretize the governing equations with a fully implicit finite- volume formulation with an inner-boundary well model and discrete fracture model. (iii) Finally, we analyze the results using suitable visualization tools, both for pressure-transient curves and 3D matrix/fracture data. The framework enables high-resolution numerical modeling of transient flow with complex fracture networks in 3D. We demonstrate the capacities through simple validation cases with comparisons against an industry-standard commercial well-testing software but also present highly complex cases with long and deviating well trajectories and highly detailed fracture networks. We present and analyze flow-transient behavior coupling the wellbore, the fracture network, and the matrix. We also present an approach to reliably diagnose complex multiple flow regimes on the pressure-transient curves combined with different-scale spatial pressure distribution. Comparison against the commercial software indicates that our framework does not introduce adverse grid-orientation effects for non-K-orthogonal grids which is able to robustly handle the details for fracture-network heterogeneities in 3D reservoirs. Overall, our framework is robust for simulating and analyzing realistic second-level transient effects and short-term well performance with complex fracture networks and heterogeneities. Detailed description of the 3D fracture networks, and accurate simulation of the near-well transient flow behavior can be achieved, which provides confidence to interpret the dynamic flow data at different scales and observe transport mechanisms in unconventional fractured reservoirs with multiple levels of heterogeneity.

GAWPS: A MRST-based module for wellbore proﬁling and graphical analysis of ﬂow units

Advances in geo-energy research, Dec 20, 2021

On obtaining optimal well rates and placement for CO2 storage

Computational Geosciences, Mar 22, 2017

A Front-Tracking Method for Efficient Simulation of Miscible Gas Injection Processes

All Days, Jan 31, 2005

A Method To Improve the Mass Balance in Streamline Methods

All Days, Feb 26, 2007

Multiscale Simulation of Polymer Flooding with Shear Effects

Transport in Porous Media, Apr 26, 2016

Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe

Computational Geosciences, Nov 26, 2015

An Open-Source Toolchain for Simulation and Optimization of Aquifer-Wide CO2 Storage

Energy Procedia, 2016

On the Artificial Compression Method for Second-Order Nonoscillatory Central Difference Schemes for Systems of Conservation Laws

SIAM Journal on Scientific Computing, 2003

An Adaptive Newton–ASPEN Solver for Complex Reservoir Models

Building an open-source community for subsurface flow simulation

The MATLAB Reservoir Simulation Toolbox (MRST) is a unique research tool for rapid prototyping an... more The MATLAB Reservoir Simulation Toolbox (MRST) is a unique research tool for rapid prototyping and demonstration of new computational methods for flow in porous media. The software has a large user base all over the world in both academia and industry. My group is also one of the key contributors to OPM Flow, the world's first open-source reservoir simulator aimed at full industry use. In addition, we are currently developing Jutul, an upcoming Julia code for high-performance demonstrators of subsurface flow. In the talk, I will briefly describe the MRST and OPM Flow platforms, how they came to be, compare and contrast their development and ownership models, and outline some of the factors that have contributed to their current success. MRST was originally an internal research tool that has, over the last ten years, morphed into the de-facto standard tool for researchers who want to learn about subsurface flow, and obtain a head start for their own research prototypes. MRST is organized as a minimal core module offering basic data structures and functionality for representing grids and physical parameters relevant to porous media flow, and a large set of add-on modules offering discretizations, solvers, physical models, and a wide variety of simulators and workflow tools. In the modules, you will find many tutorial examples that explain and showcase how MRST can be used to make general or fit-for-purpose simulators and workflow tools. The modular structure makes it easy to add new or modify existing functionality, and many of the 60 currently released modules are authored entirely or in part at other institutions. The software is licensed under the viral GPL license, with copyright of the core parts vested at SINTEF, where we heavily rely on the code for both our contract work and academic research. The software exists as an add-on to the commercial MATLAB product, which greatly simplifies the process of getting started, but also poses certain restrictions on usage and performance potential. (Except for graphical interfaces, large parts of MRST also work well with GNU Octave.) OPM Flow aims to simulate many of the same physical processes as MRST, but its disruptive power comes from being a drop-in replacement for commercial reservoir simulators that have been developed and validated over decades. Such simulators, which are used for development planning and day to day operations of oil and gas fields and CO2 storage operations, are highly complex, expensive and difficult to modify as the source codes are not available. OPM Flow is a collaborative effort, developed in collaboration with Equinor, NORCE, and others, to provide an open-source alternative that enables more open innovation. The simulator is written in high-performance C++ and is released under the GPL license. A key requirement for the development has been that the new simulator should reproduce virtually identical simulation results as contemporary commercial tools both in hindcasting decades of production histories and in forecasting future production. Achieving this has been a vast undertaking filled with stumbling blocks and a lot of reverse engineering. The two platforms are approaching the same goal of open-source simulation of subsurface flow from opposing ends: MRST educates users in subsurface simulation and embeds them directly at the research front by giving access to the codes behind scientific papers, while OPM’s greatest achievement is that users may not notice that they have switched from an expensive closed code to a modern open-source simulator with high potential for computational speedup.

Incompressible Solvers for Single-Phase Flow

Cambridge University Press eBooks, Aug 8, 2019

Unstructured PEBI Grids Conforming to Lower-Dimensional Objects

Cambridge University Press eBooks, Nov 25, 2021

Categorization of Norwegian Continental Shelf Formations in Terms of Geological CO2 Storage Potentials

Energy Procedia, Jul 1, 2017

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

All Days, Feb 21, 2011

A robust and efficient simulation technique is developed based on the extension of the mimetic fi... more A robust and efficient simulation technique is developed based on the extension of the mimetic finite volume method to multiscale hierarchical hexahedral (corner-point) grids via use of the multiscale mixed finite element method. The implementation of the mimetic subgrid discretization method is compact and generic for a large class of grids, and thereby, suitable for discretizations of reservoir models with complex geologic architecture. Flow equations are solved on a coarse grid where basis functions with subgrid resolution accurately account for subscale variations from an underlying fine-scale geomodel. The method relies on the construction of approximate velocity spaces that are adaptive to the local properties of the differential operator. A variant of the method for computing velocity basis functions is developed that utilizes an adaptive local-global algorithm to compute multiscale velocity basis functions by capturing the principal characteristics of global flow. Both local and local-global methods generate subgrid-scale velocity fields that reproduce the impact of fine-scale stratigraphic architecture. By using multiscale basis functions to discretize the flow equations on a coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields on the underlying fine grid.The accuracy and efficacy of the multiscale method is compared to that of fine-scale models and of coarse-scale models with no subgrid treatment for several two-phase flow scenarios. Numerical experiments involving two-phase incompressible flow and transport phenomena are carried out on high-resolution corner-point grids that explicitly represent example stratigraphic architectures found in real-life shallow marine and turbidite reservoirs. The multiscale method is several times faster than the direct solution of the fine-scale problem and yields more accurate solutions than coarse-scale modeling techniques that resort to explicit effective properties. The accuracy of the multiscale simulation method with adaptive local-global velocity basis functions are compared to that of the local velocity basis functions. The multiscale simulation results are consistently more accurate when the local-global method is employed for computing the velocity basis functions.