arXiv subjects

Tor Harald Sandve

Publications and source records attributed to Tor Harald Sandve.

12 recordsLinked to original sources

arXiv2026

Efficient design of continuation methods for hyperbolic transport problems in porous media

Full-physics modeling of multiphase flow in porous media, e.g., for carbon storage and groundwater management, requires the nonlinear coupling of various physical processes. Industry standard nonlinear solvers, typically of Newton-type, are not unconditionally convergent and computationally expensive. Homotopy continuation solvers have recently been studied as a robust and versatile alternative. They tackle challenging nonlinear problems by first solving a simple auxiliary problem and then tracing a solution curve towards the more complex target problem. Robustness and efficiency of the method depends on the iterative numerical curve tracing algorithm as well as on careful design of the auxiliary problem. We assess the traceability of the solution curve for different choices of the auxiliary problem. For the Buckley-Leverett equation, modeling two-phase flow in one dimension, we exemplarily compare the previously introduced vanishing-diffusion and linear constitutive laws homotopy continuation, and a new approach based on the entropy solution of the problem. This provides insight toward systematically and robustly designing homotopy continuation methods for solving complex multiphase flow in porous media.

math.NA↗

arXiv2026

A Machine-Learned Near-Well Model in OPM Flow

Recent advances in reservoir simulation increasingly utilize hybrid approaches that couple physics-based simulators with machine-learning (ML) components. ML components offer high fidelity to training data and fast inference, enabling efficient and accurate modeling of complex multi-scale or multi-physics phenomena. Modern reservoir simulators rely on automatic differentiation (AD) to support efficient and flexible strategies for nonlinear solvers, inverse problems, and optimization problems. Efficient hybrid modeling therefore requires tight integration of the ML components with the simulator's AD framework. We present the first integration of neural networks into the high-performance reservoir simulator OPM Flow. Networks are trained in TensorFlow and imported into OPM, where they are accessed as native AD functions. This presents an efficient framework for hybrid modeling and enables seamless integration in existing simulator workflows. As an application, we introduce a novel, data-driven near-well model. Near-well models are essential in reservoir simulation for accurately representing singular pressure gradients around wells. Commonly used are the Peaceman near-well model and its extensions, or local grid refinement around the wells. Peaceman-type models are limited to simplified flow regimes, whereas local grid refinement is computationally expensive. We address these limitations by training a neural network to infer a Peaceman-like well index from fine-scale ensemble simulations of the near-well region. It is then integrated into OPM Flow with the new framework. Tested on relevant examples for CO$_2$ storage, the method offers high fidelity to fine-scale results at low computational cost, demonstrating the potential of the OPM Flow-Neural Network framework for hybrid modeling.

math.NA↗

arXiv2025

Performance of an open-source image-based history matching framework for CO$_2$ storage

We present a history matching (HM) workflow applied to the International FluidFlower benchmark study dataset, which features high-resolution images of CO$_2$ storage in a meter-scale, geologically complex reservoir. The dataset provides dense spatial and temporal observations of fluid displacement, offering a rare opportunity to validate and enhance HM techniques for geological carbon storage (GCS). The combination of detailed experimental data and direct visual observation of flow behavior at this scale is novel and valuable. This study explores the potential and limitations of using experimental data to calibrate standard models for GCS simulation. By leveraging high-resolution images and resulting interpretations of fluid phase distributions, we adjust uncertain parameters and reduce the mismatch between simulation results and observed data. Simulations are performed using the open-source OPM Flow simulator, while the open-source Everest decision-making tool is employed to conduct the HM. After the HM process, the final simulation results show good agreement with the experimental CO$_2$ storage data. This suggests that the system can be effectively described using standard flow equations, conventional saturation functions, and typical PVT properties for CO$_2$-brine mixtures. Our results demonstrate that the Wasserstein distance is a particularly effective metric for matching multi-phase, multi-component flow data. The entire workflow is implemented in a Python package named pofff (Python OPM Flow FluidFlower), which organizes all functionality through a single input file. This design ensures reproducibility and facilitates future extensions of the study.

physics.flu-dyn↗

arXiv2025

Solving Biot poroelasticity by coupling OPM Flow with the two-point stress approximation finite volume method

Finite volume methods are prevalent in reservoir simulation due to their mass conservation properties and their ability to handle complex grids. However, a simple and consistent finite volume method for elasticity was unavailable until the recently developed two-point stress approximation finite volume method (TPSA). In this work, we show how to couple TPSA to an established flow simulator, using OPM Flow as our primary example. Due to this choice of numerical methods, the coupling is naturally handled at the cell centers, without requiring interpolation operators. We propose a fixed stress coupling scheme and reuse algebraic multi-grid preconditioners, which are known to be effective for two-point flux finite volume methods. Numerical examples illustrate the flexibility of the approach and we showcase how the introduction of solid mechanics impacts the behavior of compartmentalized flow systems.

math.NA↗

arXiv2025

A Coarsening Approach to the Troll Aquifer Model

Effective management of pressure communication and interference between concurrent CO$_2$ storage operations is essential for the development of gigaton-scale storage hubs. Coarse models in reservoir simulation offer a simplified representation of the subsurface to efficiently predict pressure distribution. By averaging properties over larger grid blocks, coarsened models significantly reduce computational demands, enabling faster and more manageable simulations. The approach focuses on preserving key physical properties, namely cell connectivity (transmissibilities) and storage capacity (pore volumes). The effectiveness of the coarsened model is demonstrated by applying the improved well location derived from the coarsened model to the full-resolution Troll aquifer model, resulting in improved pressure distribution. The coarsened model enabled the execution of approximately 100,000 simulations over five days using a local server with 144 CPUs, an effort that would have required around seven months using the original model. The coarsening methodology is implemented using pycopm, an open-source tool design to tailor geological models based on industry-standard grid formats, facilitating its application to other models and applications in reservoir engineering.

physics.geo-ph↗

arXiv2025

Benchmarking CO$_2$ Storage Simulations: Results from the 11th Society of Petroleum Engineers Comparative Solution Project

The 11th Society of Petroleum Engineers Comparative Solution Project (shortened SPE11 herein) benchmarked simulation tools for geological carbon dioxide (CO$_2$) storage. A total of 45 groups from leading research institutions and industry across the globe signed up to participate, with 18 ultimately contributing valid results that were included in the comparative study reported here. This paper summarizes the SPE11. A comprehensive introduction and qualitative discussion of the submitted data are provided, together with an overview of online resources for accessing the full depth of data. A global metric for analyzing the relative distance between submissions is proposed and used to conduct a quantitative analysis of the submissions. This analysis attempts to statistically resolve the key aspects influencing the variability between submissions. The study shows that the major qualitative variation between the submitted results is related to thermal effects, dissolution-driven convective mixing, and resolution of facies discontinuities. Moreover, a strong dependence on grid resolution is observed across all three versions of the SPE11. However, our quantitative analysis suggests that the observed variations are predominantly influenced by factors not documented in the technical responses provided by the participants. We therefore identify that unreported variations due to human choices within the process of setting up, conducting, and reporting on the simulations underlying each SPE11 submission are at least as impactful as the computational choices reported.

physics.geo-ph↗

arXiv2023

Copula modeling and uncertainty propagation in field-scale simulation of CO$_2$ fault leakage

Subsurface storage of CO$_2$ is an important means to mitigate climate change, and to investigate the fate of CO$_2$ over several decades in vast reservoirs, numerical simulation based on realistic models is essential. Faults and other complex geological structures introduce modeling challenges as their effects on storage operations are uncertain due to limited data. In this work, we present a computational framework for forward propagation of uncertainty, including stochastic upscaling and copula representation of flow functions for a CO$_2$ storage site using the Vette fault zone in the Smeaheia formation in the North Sea as a test case. The upscaling method leads to a reduction of the number of stochastic dimensions and the cost of evaluating the reservoir model. A viable model that represents the upscaled data needs to capture dependencies between variables, and allow sampling. Copulas provide representation of dependent multidimensional random variables and a good fit to data, allow fast sampling, and coupling to the forward propagation method via independent uniform random variables. The non-stationary correlation within some of the upscaled flow function are accurately captured by a data-driven transformation model. The uncertainty in upscaled flow functions and other parameters are propagated to uncertain leakage estimates using numerical reservoir simulation of a two-phase system. The expectations of leakage are estimated by an adaptive stratified sampling technique, where samples are sequentially concentrated to regions of the parameter space to greedily maximize variance reduction. We demonstrate cost reduction compared to standard Monte Carlo of one or two orders of magnitude for simpler test cases with only fault and reservoir layer permeabilities assumed uncertain, and factors 2--8 cost reduction for stochastic multi-phase flow properties and more complex stochastic models.

math.NA↗

arXiv2022

Impact of deformation bands on fault-related fluid flow in field-scale simulations

Subsurface storage of CO2 is predicted to rise exponentially in response to the increasing levels of CO2 in the atmosphere. Large-scale CO2 injections into the subsurface require understanding of the potential for fluid flow through faults to mitigate risk of leakage. Here, we study how to obtain effective permeability of deformation bands in the damage zone of faults. Deformation bands are relatively small, low permeability features that can have a significant effect on flow dynamics, however, the discrepancy of scales is a challenge for field-scale simulation. A new analytical upscaling model is proposed in order to overcome some of the shortcomings of conventional upscaling approaches for heterogeneous porous media. The new model captures the fine-scale impact of deformation bands on fluid flow in the near-fault region, and can be derived from knowledge of large-scale fault properties. To test the accuracy of the model it is compared to fine-scale numerical simulations that explicitly include individual deformation bands. For a wide range of different stochastically generated deformation bands networks, the upscaling model shows improved estimate of effective permeability compared to conventional upscaling approaches. By applying the upscaling model to a full-field simulation of the Smeaheia storage site in the North Sea, we show that deformation bands with a permeability contrast higher than three orders of magnitude may act as an extra layer of protection from fluid flow through faults.

physics.geo-ph↗

arXiv2022

Field-scale impacts of long-term wettability alteration in geological CO$_2$ storage

Constitutive functions that govern macroscale capillary pressure and relative permeability are central in constraining both storage efficiency and sealing properties of CO$_2$ storage systems. Constitutive functions for porous systems are in part determined by wettability, which is a pore-scale phenomenon that influences macroscale displacement. While wettability of saline aquifers and caprocks are assumed to remain water-wet when CO$_2$ is injected, there is recent evidence of contact angle change due to long-term CO$_2$ exposure. Weakening of capillary forces alters the saturation functions dynamically over time. Recently, new dynamic models were developed for saturation functions that capture the impact of wettability alteration (WA) due to long-term CO$_2$ exposure. In this paper, these functions are implemented into a two-phase two-component simulator to study long-term WA dynamics for field-scale CO$_2$ storage. We simulate WA effects on horizontal migration patterns under injection and buoyancy-driven migration in the caprock. We characterize the behavior of each scenario for different flow regimes. Our results show the impact on storage efficiency can be described by the capillary number, while vertical leakage can be scaled by caprock sealing parameters. Scaling models for CO$_2$ migration into the caprock show that long-term WA poses little risk to CO$_2$ containment over relevant timescales.

physics.geo-ph↗

arXiv2021

Numerical studies of long-term wettability alteration effects in CO$_2$ storage applications

The wettability of the rock surface in porous media has an effect on the constitutive saturation functions that govern capillary pressure and relative permeability. The term wettability alteration refers to the change of this property over time by processes such as CO$_2$ interactions with the rock. In this work, we perform numerical simulations considering a two-phase two-component flow model including time-dependent wettability alteration in a two-dimensional aquifer-caprock system using the open porous media framework. Particularly, we study the spatial distribution over time of injected CO$_2$ into the aquifer neglecting and including wettability alteration effects. The numerical simulations show that wettability alteration on the caprock results in a loss of containment; however, the CO$_2$ front into the caprock advances very slow since the unexposed caprock along the vertical migration path also needs to be changed by the slow wettability alteration process. The simulations also show that wettability alteration on the aquifer results in an enhancement of storage efficiency; this since the CO$_2$ front migrates more slowly and the capillary entry pressure decreases after wettability alteration.

physics.geo-ph↗

arXiv2019

The Open Porous Media Flow Reservoir Simulator

The Open Porous Media (OPM) initiative is a community effort that encourages open innovation and reproducible research for simulation of porous media processes. OPM coordinates collaborative software development, maintains and distributes open-source software and open data sets, and seeks to ensure that these are available under a free license in a long-term perspective. In this paper, we present OPM Flow, which is a reservoir simulator developed for industrial use, as well as some of the individual components used to make OPM Flow. The descriptions apply to the 2019.10 release of OPM.

cs.OH↗

arXiv2017

Heterogeneity Preserving Upscaling for Heat Transport in Fractured Geothermal Reservoirs

In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there is a need to develop discretization strategies that also limit computational effort. In this paper we present an upscaling methodology for geothermal heat transport with fractures represented explicitly in the computational grid. The heat transport is modeled by an advection-conduction equation for the temperature, and solved on a highly irregular coarse grid that preserves the fracture heterogeneity. The upscaling is based on different strategies for the advective term and the conductive term, respectively. The coarse scale advective term is constructed from sums of fine scale fluxes, whereas the coarse scale conductive term is constructed based on numerically computed basis functions. The method naturally incorporates a coupling between the matrix and the fractures via the discretization, so that explicit transfer terms that couple solution variables in the fractures and the matrix are avoided. Numerical results show that the upscaling methodology performs well, in particular for large upscaling ratios, and that it is applicable also to highly complex fracture networks.

cs.CE↗