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Efficient numerical methods for deformable porous media. Application to carbon dioxide storage.

Periodic Reporting for period 1 - poro sos (Efficient numerical methods for deformable porous media. Application to carbon dioxide storage.)

Reporting period: 2016-09-01 to 2018-08-31

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.
We have followed a systematic mathematical approach to perform fundamental research towards the application of our interest, that is, the efficient solution of complex models associated with CO2 storage. In particular, we have worked in several representative model problems of increasing difficulty that had to be fully understand prior to dealing with our target application. We have developed efficient numerical methods to deal with flow problems in rigid and deformable porous media, in fractured porous media and important multiphysics problems coupling flow and porous media applications. Highly efficient solvers, based on multigrid and multilevel methods have been proposed for these challenging problems, and they have also been combined with techniques based on multilevel Monte-Carlo approaches to deal with the uncertainty appearing in relevant porous media applications, as those considered in the objectives of the project.

A wide range of disseminations have been carried out to make public the results of the project. In particular, the obtained results have been published/submitted via fourteen scientific publications in international highly respected journals. In addition, they have been presented in eleven international conferences, two of which have been plenary talks, eight invited talks and one contributed presentation. The applicant also has given an invited talk for a general audience about the experience of this MSCA grant.
The results obtained from this project have significantly contribute to removing barriers in the numerical simulation of geomechanical problems, regarding the efficient solution of the mathematical models. We have designed fully coupled iterative solvers for this type of problems in porous media, which were missing in the literature. Moreover, we have combined these techniques with uncertainty in parameters, offering novel approaches which are suitable for real applications.
Thus, the developed algorithms have contributed to move the state-of-the-art of simulation forward in many fields in which porous media problems play an essential role, and in this way the industry can benefit from these algorithms for computational simulation. Therefore, we believe that the advances achieved in this project are of interest to the scientific community, and due to the fact that the main application in this project, the storage of CO2, is an essential task for the sustainability of the earth, the achievements in this line can have a notable impact on the society.
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