My research work centres around three main themes, notably:

  1. Fundamentals of Granular Material Mechanical Behaviour
  2. Petroleum Geomechanics
  3. Ice growth, Structure and Osmotic Environment in Biological Tissues

My work is funded by NSERC, CIHR, Alberta Energy Research Institute, and Whitaker Foundation.

Granular materials are endowed with a porous structure, and hence are multi-phasic in nature. Their mechanical behaviour is dependent on pressure (stress) level, and they exhibit dilation (increase in volume) when sheared. In petroleum geomechanics, we encounter granular materials such as oil-sands, and one of the problems of interest to me is their propensity to dilate and fluidize (lose strength) under variable oil reservoir pumping and thermal loads. On the other hand, biological tissues are no more than a bio-fluid penetrated capillary porous medium also endowed with microstructure (e.g. orientation of collagen fibres) upon which basic principles of mechanics and thermodynamics can be applied. It is because the basic principles of continuum mechanics are the underpinnings of all above three listed research themes that I have been successful in addressing each topic with great depth and breadth.

Fundamentals of granular material mechanical behaviour: My research on the subject dates as far back during my PhD days when I examined the issue of localization of deformation into thin shear bands in geostructures, and thereby, proposed a numerical algorithm for its computation based on a newly developed finite element method. The originality of the computational work was duly recognized with the award of the first R.J Melosh medal for best paper in finite element analysis held at Duke University , USA . in 1989 (see pict). Today, my work continues to be recognized and cited in numerous papers in computational geomechanics. Current work involves the study of ratcheting behaviour of granular materials and the investigation of stress-dilatancy through micromechanical analysis (both theoretically and experimentally). (click here for papers)

(a) Slow cyclic deformation of sand behind retaining wall

(b) Force chains formation & buckling along dilatant deformation paths

Petroleum geomechanics: My research work in oilsand and sand production are well known in the petroleum geomechanics community. Some aspects of my research in granular materials, such as those related to dilatancy, have been used into petroleum engineering applications where stresses and deformations are at issue. As such, I have developed and written a finite element based geomechanics module for the Computer Modelling Group. This module is an integral part of CMG’s well known reservoir simulator that is used internationally.

 During the last few years, I have embarked myself into studying the problem of sand production in unconsolidated granular materials, having secured two research grants from the Alberta Energy Research Institute (AERI). The challenge is to understand the physics of fluidization in sand bodies so as to construct a numerical model that can be used by the oil industry to manage sand production issues in oilwells. Our work was even retained into the finals of the 15th R.J Melosh competition in finite element analysis held at Duke University in March 2003. Currently, a reservoir simulation company in Calgary expressed interest in our sand production work, and we are in the process of applying it to real field problems pertaining to oil reservoirs. In this particular case, technology transfer is evident. (click here for papers)

(a) The Problem: REV for modelling

(b) Damaged zone with wormholes around perforated well

Ice growth, structure and osmotic environment in biological tissues: This has been a new area of study that I have recently expanded into where mathematical as well as numerical models describing freezing processes in capillary porous media such as tissues have been established. Funding for this research endeavour has been provided by a grant from the Whitaker Foundation, with Dr. Muldrew from Medicine. In fact the research borrows somewhat from my previous works on ice lensing in soils including the modelling of the growth of an ice bulb around a buried pipeline carrying chilled gas and traversing frozen soils. Hence, a major effort has been undertaken in the past few years to transfer the knowledge of soil freezing to tissue freezing in biological systems, given that some aspects of the problems are astoundingly similar.

The freezing of tissues has been approached within a classical Stefan problem framework, except that solute diffusion, together with freezing point depression due to solute concentration and pore size, have to be coupled with the phase change problem. A finite element algorithm, which tracks the freezing front without requiring re-meshing, has been developed for the simple case of a water body. Tissue microstructure, solute and freezing point depression are being currently investigated. The finite element model is still being developed and constitutes a major advance in Biomedical Engineering and Computational analysis. Aspects of the model are being currently tested as a predictive tool for the treatment planning of prostate cancer in cryosurgery. Numerous papers have been published in very good scientific and engineering journals. It is noted that the numerical component of the work was also retained into the finals of the 15th R.J Melosh competition in finite element analysis, Duke University , in March 2003. (click here for papers)

New Research Endeavour: Computational Cryosurgery

(a) Prostate MRI

(b) FE Mesh

(c)  Solid Rendering

(d) IceBall

(e) Damaged Tissue Zone