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Department of Mathematics

Simplified models for numerical simulation of geological CO2 storage, 2016

Odd Andersen

Advisors: Inga Berre, Sarah E. Gasda and Halvor M. Nilsen

Short description of project:

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.

 

Link to thesis at BORA-UiB: http://bora.uib.no/handle/1956/15477