Novel mathematical approaches for multiscale modelling of three-phase porous media flow

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This is a joint bid from the Department of Mathematics (MACS) and Institute of Petroleum Engineering (IPE) at Heriot-Watt University in Edinburgh and will involve researchers across both departments. Both departments have established a virbant cross-disciplinary environment thanks to the current Bridging the Gaps grant held by the PI, Prof. Dugald Duncan. All named investigators are members of two major joint research institutes of the Edinburgh Research Partnership in Engineering and Mathematics (www.erp.ac.uk), the Maxwell Institute of Mathematical Sciences and the Edinburgh Collaboration of Subsurface Science and Engineering (ECOSSE). Both are part of the 22M funding initiative of the Scottish Funding Council to foster interdisciplinary research in mathematics and engineering across Edinburgh. Furthermore the Maxwell Institute is a partner in the 4.7M Science and Innovation Grant to found the interdisciplinary Numerical Algorithms and Intelligent Software Centre (NAIS).Our proposal aims to consolidate existing and create new cross-disciplinary collaborations that will complement and enhance the world-leading research profiles of MACS and IPE. We propose to explore the feasibility of novel mathematical approaches for multiscale modelling of three-phase (e.g. oil, gas, water) porous media flow. For this we will cross traditional boundaries between engineering disciplines (i.e. petroleum, hydrology, and industrial porous media applications), physics, and applied mathematics and have assmebled a team of experts from the different disciplines. Our studies will be highly speculative and adventurous because we simply do not know if a suitable alternative to three-phase Darcy's law can be developed in such a way that it can be solved in the mathematically robust and efficient manner that is required for successful use in daily engineering applications. However, an alternative is required because Darcy's law is intrinsically not valid in certain flow regimes, that is when one or more phases move as discontinuous blobs and ganglia. Yet it is exactly this situation that is of most interest to engineering, for example when predicting the migration of small volumes of toxic groundwater contaminants or residual oil in a depleted hydrocarbon reservoir. The high risk and speculative research nature of our work would not necessarily attract funding despite being of fundamental importance in many applications: It is too speculative and blue sky for industrial support where lead time to product is months, not years and would struggle to be funded from other sources due to its novely, interdisciplinarity, and range of approaches. Yet, if our initial studies show that an alternative to Darcy's law for three phase-flow is feasible, the outcomes will have a major impact on engineering and mathematical disciplines: A possible alternative or improvement of Darcy's law for three-phase flow will have a fundamental influence in improving enhanced oil recovery techniques. Such techniques aim to extract hydrocarbons from declining oil fields such as they are frequent in the U.K. sector of the North Sea and world-wide. They will also be the key to improving the remediation of groundwater contaminants, predicting subsurface CO2 storage, and a variety of other industrial porous media applications (e.g., wood processing). Our research will also tackle important and challenging mathematical and computational issues, such as development of efficient and reliable algorithms, upscaling methods, numerical stability and convergence proofs, or error estimation, all of which must be able to cope with the highly non-linear physics inherent to three-phase flow and the orders-of-magnitude variation in parameter and associated uncertainties arising in industrial applications.