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Macroscopic capillary pressure in multi-phase porous media flows

School of Engineering

About the Project

Although multi-phase flow in porous media is an established research field for decades, its theoretical background is still being developed. Recent advances include a new macroscopic theory of capillarity based on the volume averaging method. The theory includes the new derivation of the macroscopic momentum balance equation for the wetting/non-wetting fluid interfaces, and the associated new definition of the macroscopic capillary pressure. The main benefit of the new theory is that it incorporates the effect of the average direction of pores on the resulting capillary force, which is neglected in conventional models. In order to apply the new theory a new set of constitutive relationships needs to be developed.

This aim of this PhD project is to establish the relationship between the macroscopic capillary pressure and relevant geometrical properties of fluids within the pores, for a series of porous media typical for reservoir rocks. This will be done through an extensive experimental or computational programme in two stages: 2D experiments, 3D imbibition/drainage experiments. Both sets of experiments will start with idealised regular pore geometry, followed by the pore configuration typical for natural reservoir rocks. The outcome of the project will be novel relationships that need to be built into numerical simulation models of macroscopic multi-phase flows in porous media.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in Civil, Petroleum or Chemical Engineering; Physics.

Essential background: Fluid mechanics and porous media flows.

Experience in programming, data processing, and image analysis will be an advantage. Good written and spoken communication skills are essential.


• Apply for Degree of Doctor of Philosophy in Engineering (Distance Learning)
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV

Informal inquiries can be made to Professor D Pokrajac (), with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

It is possible to study this project entirely by distance learning. Interested parties should discuss this with Professor Pokrajac.

Funding Notes

This project is advertised in relation to the research areas of the discipline of multiphase flows in porous media. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Additional research costs up to £3,000 may be required to support experimental work. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THIS PROJECT


Starnoni, M., Pokrajac, D. (2020) On the macroscopic momentum balance equation for the fluid-fluid interfaces in two-phase porous media flows, Advances in Water Resources 135, Article number 103487.

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