Fast Algorithms for Cluster Dynamics in Multi-phase Flow Pore-networks

Recent 3D micro-CT visualisations of two-phase flow in porous media have revealed and confirmed pore-scale displacement mechanisms, such as trapped ganglion movement, as well as sudden interface advance (Haines jumps) and retraction (Berg et al., 2013; Reynolds et al., 2017.). Similarly, three-phase flow micromodel visualisations and core flood experiments have demonstrated the contribution of displacement of multiple isolated fluid clusters to overall fluid movement in porous media (Sohrabi et al., 2004). For decades, pore-network flow modelling has been a powerful tool to understand and predict the impact of micro-scale displacement mechanisms on macro-scale flow functions, such as relative permeability and capillary pressures, which are particularly difficult to measure for three phases. The hysteretic flow functions are essential for field-scale simulation of subsurface processes, such as CO2 storage, enhanced hydrocarbon recovery, as well as aquifer contamination and remediation. However, for the calculated functions to be representative in porous media of significant heterogeneity in structure and wettability, such as carbonates, shales and certain soils, ultra-efficient algorithms for identification, alteration and mobilisation of fluid clusters are essential. Previous modelling efforts have introduced a shortest path algorithm for multiple cluster displacements in three-phase flow (Al-Dhahli et al., 2013) and a highly efficient cluster alteration algorithm for two-phase flow with monotonically decreasing connectivity (Petrovskyy et al., 2018, in progress).
The focus of this project is to extend the implementation of efficient algorithms, developed in graph theory, to pore-network simulation of arbitrary two-phase and three-phase flow processes for full (increasing and decreasing) phase connectivity, capturing the above-described ganglion and interface dynamics. The developed pore-network model and the implemented displacement mechanisms will be validated through direct comparison with flow visualisation experiments of fluid cluster distributions for a range of heterogeneous porous media images and with small-scale direct simulation of multi-phase flow in porous media. The efficiency of the model will be evaluated by analysing the computational complexity of the various implemented algorithm for a range of flow processes, thus determining the scaling of computation times with model size. Moreover, calculated relative permeability and capillary pressures will be compared to measurements and, due to the expected efficiency, it will be possible to provide uncertainty analyses based on multiple simulations in representative porous media volumes.

This project will interact with ongoing research in IPE on multi-phase flow in complex porous media (EOR, carbonates). It requires a student with good computer science or applied maths skills.

Informal enquiries should be directed to the primary supervisor, Dr Rink van Dijke.

Applicants should have a first-class honours degree in a relevant subject or a 2.1 honours degree plus Masters (or equivalent). Scholarships will be awarded by competitive merit, taking into account the academic ability of the applicant.

Please complete our online application form and select PhD programme Petroleum Engineering, Petroleum Geoscience or Applied Geoscience within the application and include the project reference, title and supervisor names on your application. Applicants who do not include these details on their application may not be considered.

Please also provide a written proposal, at least one side of A4, outlining how you would approach the research project. You will also be required to upload a CV, a copy of your degree certificate and relevant transcripts and one academic reference. You must also provide proof of your ability in the English language (if English is not your mother tongue or if you have not already studied for a degree that was taught in English). We require an IELTS certificate showing an overall score of at least 6.5 with no component scoring less than 6.0 or a TOEFL certificate with a minimum score of 90 points.

Applicants MUST be available to start the course of study in October 2019.