Over the last 150 years, the global temperature has risen at an accelerating pace. Human activity through emissions of greenhouse gases are considered the main cause of this relentless warming. Carbon dioxide (CO2) is one of the major greenhouse gases, which is most challenging to deal with, due to its prevalence as a by-product from industrial processes and electricity generation. To reduce greenhouse gas emissions into the atmosphere, CO2 capture and storage is considered as a highly relevant technology, and its study is therefore under active consideration. Due to their ubiquitous presence, deep saline aquifers provide the most substantial carbon dioxide storage capacity. The injection of CO2 into deep saline aquifers typically results in elevated pressure in the vicinity of the injection well. Due to the high injection pressure, the stress distribution in the reservoir region can change significantly, and therefore deformation of the porous medium must be considered to guarantee safety assessments of the injection process. This can result into uplift, fracture formation, and activation of existing faults. Therefore, there are potential risks to humans and ecosystems that arise from the leakage of CO2, or the displacement of saltwater from the saline to the fresh-water aquifers. The aim here is to advance in the applied mathematics techniques needed in this context. We will study modern numerical techniques and novel concepts, to be able to make a significant step forward in the numerical simulation of CO2 storage research. This involves detailed analysis to ensure accuracy of the numerical solutions, development of highly efficient multilevel solution methods for complicated governing nonlinear systems of partial differential equations (PDEs), but also uncertainty quantification (UQ) and the corresponding solution techniques.
