Apply today for an industry PhD at the University of Adelaide, with Shell Global Solutions.

Exact solutions for conservation law systems: applications to CO2 storage

Currently, upscaling of CO2 injection into a reservoir saturated by water from core scale up to the numerical cell or a reservoir is a challenge. For immiscible two-phase flow in layer-cake reservoirs, the models for pseudo relative permeability are developed for viscous-, gravity-, and capillary-dominant cases, and for combined cases. Dissolution of CO2 in water along with capillary, chemical and stratigraphic entrapments are not accounted for. Moreover, the areas of applicability and validity of those models are not available. The attempt to define the applicability domains in the 3D Euclidian space of dimensionless capillary-viscous and gravity-viscous numbers and aspect ratio have been made, but the result is far away from the practical reservoir simulations.

Fortunately, two approaches allow to solve the above-mentioned problems:

(i) The current semi-analytical upscaling techniques allow handling diffusive-dispersive fluxes but are not applicable to kinetics non-equilibrium models. The asymptotic technique developed for relaxation systems allows transforming the kinetics non-equilibrium systems into those with non-equilibrium kinetics, in the first-order approximation.

(ii) The technique for averaging 2- or 3-D two-phase three-component transport using analytical 1-D solutions to close the system has been proposed but has never been used for the system CO2-brine-rock. This approach allows extension from one mass balance equation like Buckley-Leverett or Koval to two-phase multicomponent flows. This performance would provide the segregated flow model for the system CO2-brine. The approach will lead to upscaled model for two-phase multicomponent flows, like displacement of water by CO2 in aquifers accounting for chemical reactions, dissolution of CO2 in water, and evaporation of water into CO2.

This innovative PhD project will explore these novel approaches to modelling CO2 injectivity. The successful candidate will work with researchers at the University of Adelaide and Shell Global Solutions to develop an analytical tool that predicts the nature of CO2 propagation in heterogeneous media while accounting for diverse factors that influence flow dynamics. As part of this project the student will undertake a remote internship with Shell to produce the project deliverables.

Scholarship

The successful candidate will receive a University of Adelaide Research Scholarship at the value of $34,210 p.a. (indexed annually), for 3.75 years. It is likely to be tax exempt, subject to Taxation Office approval. Details of terms and benefits will be provided to the candidate in their Conditions of Award.

Eligibility criteria

Despite the project is in the area of reservoir engineering, the main research is focused on mathematical physics, exact and asymptotic solutions of non-linear partial differential equations, and analytical methods in  fluid mechanics. MSc or high quality Honours in applied or pure mathematics, theoretical physics are the best fit. However, holders of MSc in engineering who can demonstrate high skills in Calculus II, III and fluid mechanics are also encouraged to apply. Scientific publications is a bonus.

The successful candidate must be able to enrol as a full-time PhD student at the University in the year of the offer. They must remain based in Adelaide, South Australia for the duration of the award.

Application process:

To apply, please email the following documents to principal supervisor Prof Pavel Bedrikovetski (pavel.bedrikovetski@adelaide.edu.au) with the name of the scholarship in the subject line:

• CV
• Cover Letter (of not more than 2 pages) outlining your interest in the PhD project and describing how your background and research area align with the project
• Degree certificates and relevant academic transcripts, with translations of non-English documentation

General enquiries

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