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Data-driven Upscaling for Flow in Fractured Porous Media

Project Description

Simulation of multiphase flow in fractured porous media is a challenging task given the inherent uncertainties in the porous media properties, fractures geometry and fractures properties. The high permeability contrast between the fractures and the background porous material (Matrix) results in a multi-scale flow features that are difficult to capture without extensive computing resources. The goal of this project is to develop data-driven upscaling methods for fractured reservoirs using modern deep learning techniques to address multi-query tasks including uncertainty propagation, risk assessment, flow control and optimization. The upscaled models will act as an accurate proxy for the full-scale flow simulations in fractured media.

Numerical and analytical upscaling techniques of flow in fractured media is a subject of active research [c.f., 1 and the references within]. Generally, numerical upscaling techniques are cable of producing high quality results but relies on solving local/semi-local problems with a total computational cost in the same order of magnitude of the full-scale numerical simulation without upscaling. Combining numerical upscaling techniques with efficient methods for representing fractures on regular/semi-regular grid, namely the embedded discrete fracture model (EDFM), provides a powerful framework for extracting upscaled models for flow in fractured media [2]. The most basic method of upscaling is the single porosity hybrid model, where small scale fractures are lumped with the porous media properties (aka. matrix) to form a pseudo-matrix, while the large fractures are explicitly represented using EDFM. A further refinement of the model is based on adopting a dual porosity (DP) formulation, where small to medium scale fractures and the matrix are represented with a dual porosity model, and the large fractures are explicitly represented using EDFM.

In this project, we propose a data-driven upscaling technique for fractured media using training data generated using full scale numerical simulations and numerical upscaling methods. We plan to supplement the data driven models with different analytical methods [c.f. 3] as an additional input feature (i.e. residual learning). In this context, an off-line learning phase would be utilized to collect training data and then this data will be utilized to build a powerful automatic upscaling machine learning model that is able to generalize beyond the training data. Further, we aim to build machine learning models that are able to know when it makes mistakes and avoids silent failure modes. Building on the recently developed techniques [4, 5] and modern machine learning architectures (i.e. feature pyramid networks [6]), we will develop a generic upscaling framework where small and medium scale fractures are upscaled into an effective matrix rock permeability while large-scale fractures are explicitly represented by EDFM.

We will focus on modelling fractured geothermal reservoirs where the location and precise direction of fractures are uncertain. The developed techniques will be utilized to quantify the uncertainties in the thermal breakthrough and optimize flow rates.

Essential skills:
— Master’s degree in computational mathematics, physics or in a relevant engineering discipline with strong computational skills.
— Ability to write reports, collate information and present it in a clear and engaging manner.
— Excellent communication skills.

Desirable skills:
— Bayesian statistics and machine learning
— Computational methods for PDEs.
— Experience with machine learning libraries (sklearn, pytorch, keras, etc.)
— Experience with open source modelling packages (DuMux, deal.II, MRST, FEniCS or similar projects

To make an application, please visit the website.

Funding Notes

Scholarships will cover tuition fees and provide an annual stipend of approximately £15,009 for the 36 month duration of the project and is available to applicants from the UK, EU and overseas.

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