Uncertainty Assessment of Solute Mixing in Heterogenous Porous Media

Flow state variables and attributes of porous media vary across a wide range of spatial (and temporal) scales. Typical observations of these properties arise from a variety of experimental techniques, each of which has its own spatial resolution, associated uncertainty and cost. As an example, permeability can be evaluated through microfluidics experiments, core-flooding laboratory experiments, or field-scale well tests. These provide compelling evidence that the key statistics of parameters driving the physical processes occurring in porous media vary across scales. A firm scientific foundation for the characterization of basic mechanisms associated with flow fields in porous media therefore requires a robust understanding of all relevant processes and properties across the spectrum of relevant length and time scales, based on a multiscale approach that allows the fusion of real-world data.
While statistical techniques are available to assist advancement in this direction, these typically involve a single variable of interest at a unique observation scale. As a key objective, an original theoretical and computational framework will be developed to seamlessly assimilate data associated with diverse variables collected at a range of scales and combine these to provide predictions of flow dynamics along with a quantification of the associated uncertainties. The main goals of the project include: (a) scale-bridging (transfer information from one scale to another) using analytical and computational tools; (b) incorporating data collected into a model representing dynamics of the porous system at any other scale of observation; (c) inferring corresponding scaling parameters from measured data.
The project aligns with EPSRC themes of Energy, Engineering and Global Uncertainties. It focuses on developing analytical methods and computational tools to tackle fundamental research challenges related to underground engineering. Through developing tools for quantification of uncertainty in flow in porous media, new knowledge will be provided for the design of strategies for the use of geo-energy or remediation of groundwater resources. Therefore, the project will support the UK Energy security plans and has the potential to support the UK to cope with Environmental Changes.

International and industrial partners
The project will be supported by international academic partners from Politechnico di Milano, Department of Civil and Environmental Engineering (Italy) and University of Southern California (USA), who provide supervision on stochastic modelling aspect of the project and host the PhD student. Also, industrial partner BIOAZUL, SL. (Spain) will provide data for verification of computational tools that will be developed in this project.

Impact on Students. The primary impact will be on the 50+ PhD students trained by the Centre. They will be high-quality computational scientists who can develop and implement new methods for modelling complex systems in collaboration with scientists and end-users, who are comfortable working in interdisciplinary environments, have excellent communication skills and be well prepared for a wide range of future careers. The students will tackle and disseminate results from exciting PhD projects with strong potential for direct impact. Exemplar research themes we have identified together with our industrial and international partners: (i) design of electronic devices, (ii) catalysis across scales, (iii) high-performance alloys, (iv) direct drive laser fusion, (v) future medicine exploration, (vi) smart nanofluidic interfaces, (vii) composite materials with enhanced functionality, (viii) heterogeneity of underground systems.

Impact on Industry. Students trained by HetSys will make a significant impact on UK industry as they will be ideally prepared for R&D careers to help to address the skills shortage in science and engineering. They will be in high demand for their ability to (i) work across disciplines, (ii) perform calculations that come along with error estimates, and (iii) develop well-designed software that other researchers can readily use and modify which implements novel solutions to scientific problems. More generally, incorporating error bars into models to take account of incomplete data and insufficient models could lead to significantly enhanced adoption of materials modelling in industry, reducing trial and error, and costly/time-consuming R&D procedures. The global market for simulation software is expected to more than double from now to 2022 indicating a very strong absorptive capacity for graduates. Moreover, a recent European Materials Modelling Consortium report identified a typical eight-fold return on investment for materials modelling research, leading to cost savings of 12M Euros per industrial project.

Impact on Society. Scarcity of resources and high energy requirements of traditional materials processing techniques raise ever-increasing sustainability concerns. Limitations on jet engine fuel efficiency and the difficulties of designing materials for fusion power stations reflect the social and economic cost of our incomplete knowledge of how complex heterogeneous systems behave. High costs of laboratory investigations mean that theory must aid experiment to produce new knowledge and guidance. By training students who can develop the new methodology needed to model such issues, HetSys will support society's long term need for improved materials and processes.

There will also be a direct impact locally and regionally through engagement by HetSys in outreach projects. For example we will encourage CDT students to be involved with annual 'Inspire' residential courses at Warwick for Year 11 girls, which will show what STEM subjects are like at degree level. CDT students will present highlights from projects to secondary-school pupils during these courses and also visit local schools, particularly in areas currently under-represented in the student body, in coordination with relevant professional bodies.

Impact on collaboration. Our international partners have identified the same urgent challenges for computational modelling. We will build flourishing links with research institutes abroad with long term benefit on UK research via our links to computational science networks. Shared research projects will strengthen links between academic staff and industry R&D personnel and across disciplines. The work will also lead to accessible, robust and reusable software. The Centre will achieve cross-disciplinary academic impact on the physical and materials sciences, engineering, manufacturing and mathematics communities at Warwick and beyond, and on the generation of new ideas, insights and techniques.