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A new Sleipner benchmark model has recently been released. Basic petrophysical parameters are included in the dataset but it is intended that further modelling work should be carried out in order to refine parameter estimates. In this study we have developed a rapid calibration workflow, in the open source Matlab Reservoir Simulation Toolbox (MRST). We use this workflow to calibrate model parameters such that results match plume outlines interpreted from seismic data, also provided in the benchmark dataset. This is made feasible by the use of hybrid vertical equilibrium (VE) modelling and adjoint-based, continuous optimisation, using automatic differentiation. Parameters have been found which lead to simulation results that provide a reasonable match to the plume outline in the top layer, when using a slightly modified model top surface. This workflow provides a useful tool which allows us to use monitoring data to improve simulation models during and after CO2 injection.

Poster presented at the Trondheim CCS Conference 2019 The Gassum Formation on the Norwegian Continental Shelf serves as the principal case study for the CO2-Upslope project. The top surface of this formation is gently sloping, and characterized by a number of macro-scale structural traps, a few large faults, a large number of small faults, and small-scale depth variations that can be inferred and extrapolated from the seismic data. In the study presented in this paper, we estimate the amount of macro- and sub-scale trapping potential of the formation based on interpreted 2D seismic lines and identified faults. The seismic lines provide the depth of the caprock at each point along straight lateral paths. In the available data, a few dozen such lines cross the study area at various angles. A number of medium and large faults could be explicitly identified and mapped, as they correlate between several of these lines. In addition, hundreds of small-scale faults are only visible as discontinuities along individual lines. The extent and shape of these small faults between the seismic sections cannot be explicitly known from the data. In order to investigate trapping potential, we start out by constructing multiple realizations of the top surface, constructed to be faithful to both large-scale topography and small-scale statistical properties. We use a tensor spline surface approximation to represent the surface trend, with added stochastic small-scale variations consistent with the statistical properties of the line data. Moreover, we include a distribution small-scale faults that are only visible as discontinuities in the seismic lines by adding assumptions on their general orientations and lengths. At the timescales associated with long-term CO2 plume migration, it can generally be assumed that vertical equilibrium has been reached and that the CO2 slowly flows as a thin wedge right under the top surface, driven by gravity forces. Based on this assumption, we apply spill-point analysis and upscaling techniques on our sets of top surface realizations to explore the possible range of values for total structural trapping and plume retardation potential, and how they depend on the assumptions made. We also study the impact of the placement of the injection site, and how much of the total structural storage potential can be actually realized based on the position of the site and the injection strategy.

Carbon capture and storage (CCS) is a proposed strategy to reduce global emissions of greenhouse-gases. The basic principle is to capture CO2 from power generation or other industrial activities and inject it into deep geological formations for permanent storage. CCS is considered practically indispensable by the Intergovernmental Panel on Climate Change (IPCC) in order to reach internationally agreed climate targets. It can be understood as a bridge technology intended to limit emissions from fossil-fuel based economic activities while working toward the longer-term goal of a sustainable energy system. Since the purpose of CCS is to permanently prevent large quantities of CO2 from entering the carbon cycle, the practical storage capacity and long-term safety of candidate storage sites are important questions to address. As for other industrial subsurface operations, numerical simulations based on mathematical models of the involved physics play a key role in helping us understand the processes taking place underground. However, existing industrial simulators for 3D subsurface multi-phase flow are typically developed for the support of hydrocarbon production. Such simulators are by nature limited in their ability to handle problems at the very large spatial and temporal scales that must be taken into account when investigating CO2 storage issues. To properly address the full range of questions related to CO2 injection and migration, a variety of mathematical models of different complexity is needed, ranging from detailed multi-physics models describing local conditions around the injection sites, to simplified or mathematically upscaled descriptions capable of modeling developments at much larger spatial scales and timeframes. This thesis addresses the development, analysis and efficient implementation of simplified mathematical models specially designed to address questions related to longterm CO2 storage. One class of such models enables computationally efficient longterm simulations based on the assumption of vertical equilibrium (VE). Under this assumption, vertical flow in the storage formation is neglected, which allows for reducing the dimensions of the governing equations and corresponding simulation domain from three to two, while still preserving important 3D effects. A different numerical approach is based on analysis of storage site geometry, and provides a near-instant way of predicting long-term migration pattern and assessing trapping capacity. Together, these methods can be applied as parts of larger workflows set up to address more complex questions related to CO2 storage. The work presented in this thesis contributes to the field of mathematical modeling of CO2 storage with several new developments, including: mathematical derivation and inclusion of additional physical effects into the VE modeling framework (compressibility, geomechanics, hysteresis models), and assessment of the impacts; efficient algorithms for spill-point analysis of the storage site caprock, and evaluating their applicability for CO2 migration prediction, trapping capacity estimation and well placement support, based on testing on real/realistic datasets; robust implementation of vertical-equilibrium models in a fully-implicit, blackoil framework, combining most of the modeling capabilities that have been published for these types of models (dissolution, residual trapping, capillary pressure, caprock rugosity, and dynamic fluid properties derived from equations of state), followed by testing and validation based on real aquifer models from the North Sea; use of the aforementioned approaches in combination with gradient-based nonlinear optimization methods to identify practical injection scenarios that maximize stored CO2 while minimizing migration out of the target formation. In the spirit of promoting reproducible computational research [94], most of the computer code underlying the results presented has been made freely available as open software in the form of a separate module, MRST-co2lab, to the MATLAB Reservoir Simulation Toolbox (MRST), developed, maintained and published by the Computational Geosciences group of SINTEF ICT, Department of Applied Mathematics. The exception is the work on geomechanics, which has not yet been made part of the public code, but is in the pipeline for a future release. The introduction to this thesis is written as a tutorial that introduces some of the basic theory underlying the papers, and also demonstrates the practical use of the software by gradually outlining a full code example based on a publicly available dataset of the Johansen formation.

Berggrunnen under Nordsjøen har et stort potensial som felles lagringssted for CO₂ fra industri i hele Nord-Europa.

Carbon capture and storage has been proposed as a viable option to reduce CO 2 emissions. Geological storage of CO 2 where the gas is injected into geological formations for practically indefinite storage, is an integral part of this strategy. Mathematical models and numerical simulations are important tools to better understand the processes taking place underground during and after injection. Due to the very large spatial and temporal scales involved, commercial 3D-based simulators for the petroleum industry quickly become impractical for answering questions related to the long-term fate of injected CO 2 . There is an interest in developing simplified modeling tools that are effective for this type of problem. One approach investigated in recent years is the use of upscaled models based on the assumption of vertical equilibrium (VE). Under this assumption, the simulation problem is essentially reduced from 3D to 2D, allowing much larger models to be considered at the same computational cost. So far, most work on VE models for CO 2 storage has either assumed incompressible CO 2 or only permitted lateral variations in CO 2 density (semi-compressible). In the present work, we propose a way to fully include variable CO 2 density within the VE framework, making it possible to also model vertical density changes. We derive the fine-scale and upscaled equations involved and investigate the resulting effects. In addition, we compare incompressible, semi-compressible, and fully compressible CO 2 flow for some model scenarios, using an in-house, fully-implicit numerical code based on automatic differentiation, implemented using the MATLAB reservoir simulation toolkit. publishedVersion