PhD Studentship - Multiscale Methods for Hysteresis Effects in Geomechanics

University of Nottingham - Mathematical Sciences

Location: University Park

Supervised by Dr. Donald L. Brown and Dr. Savvas Triantafyllou (Faculty of Engineering).

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

During cyclic fluid injections into the subsurface for either Carbon Storage or GeoEnergy applications, the in-situ geomaterials experience complex fluid-rock interactions that may alter the flow and mechanical properties of the subsurface. A key rock mechanics processes in this setting are hysteresis effects on the geomaterial. Simulating and predicting this phenomenon is critical in mitigating environmental risks and is complicated by the multiscale nature of the subsurface. When considering only the flow aspects, multiscale finite elements have proven to be a very efficient way to include microscale information at the coarser flow scales, greatly expediting the computations.

Recently, when considering the case of a heterogeneous solid backbone, smooth hysteretic models in combination with robust multiscale finite element methodologies have proven efficient in providing high-fidelity and rapid simulation of the underlying mechanical processes. This approach has been successfully utilized in the case of mechanical structures. However, pore pressures evolving within the solid medium are expected to significantly affect its hysteretic response and thus need also to be accounted for. This is a direction not yet explored and has interesting applications in CCS, rock mechanics, and reservoir engineering. This project seeks to develop a coupled stress-pore pressure hysteretic operator to be fused in a multiscale finite element setting.

This PhD studentship aims to develop efficient techniques to better understand such complicated mechanics and flow models. For this project, persons with experience with numerical methods as well as ability to program in MATLAB or other programming languages would be at an advantage. This project will have considerable interaction with the GeoEnergy Research Centre (GERC) and British Geological Survey (BGS). For the interested students, to gain international experience in fluid-rock interactions in geomechanics, a secondment to GERCs partners at Virginia Tech, USA or China University of Mining Technology, Xuzhou, China, may be possible.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Engineering), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit the University of Nottingham application page:

For any enquiries please email:

This studentship is open until filled. Early application is strongly encouraged. 

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Midlands of England