Many industrial fluids have non-Newtonian rheological behaviour. Amongst the wide variants in fluid behaviour are those that exhibit a yield stress. We describe these fluids and some of the limitations in their simplest mathematical descriptions. We then outline a range of different problems stemming from the petroleum industry in which these fluids play a key role, giving examples of where mathematical modelling can be effectively used to answer practical questions and where it appears to fall short of experimental reality.
Mathematical models have widely been used to predict, understand, and optimize complex physical processes in modeling and simulation of multiphase fluid flow in petroleum reservoirs. These models are important for understanding the fate and transport of chemical species and heat. With this understanding the models are then applied to the needs of the petroleum industry to design enhanced oil and gas recovery strategies.
While mathematical modeling and computer simulation have been successful in their applications to the recovery of conventional oil and gas, there exist a lot of challenges in their applications to unconventional oil and gas modeling. As conventional oil and gas reserves dwindle and oil prices rise, the recovery of unconventional oil and gas (such as heavy oil, oil sands, tight gas, and shale gas) is now the center stage. For example, enhanced heavy oil/oil sands recovery technologies are an intensive research area in the petroleum industry, and have recently generated a battery of recovery methods, such as cyclic steam stimulation (CSS), steam assisted gravity drainage (SAGD), vapor extraction (VAPEX), in situ combustion (ISC), hybrid steam-solvent processes, and other emerging recovery processes; horizontal well and hydraulic fracturing technologies have been very successful in the production of tight and shale gas reservoirs. This presentation will give an overview on challenges encountered in modeling and simulation of unconventional oil and gas reservoirs. It will also present some case studies for the applications of some recovery processes to heavy oilfields and shale gas reservoirs.
This study presents a development of the direction splitting algorithm for problems in complex geometries proposed in  to the case of flows containing rigid particles. The main novelty of this method is that the grid can be very easily fit to the boundaries of the particle and therefore the spatial discretization is very accurate. This is made possible by the direction splitting algorithm of . It factorizes the parabolic part of the operator direction wise and this allows to discretize in space each of the one-dimensional operators by adapting the grid to fit the boundary only in the given direction. Here we use a MAC discretization stencil but the same idea can be applied to other discretizations. Then the equations of motion of each particle are discretized explicitly and the so-computed particle velocity is imposed as a Dirichlet boundary condition for the momentum equations on the adapted grid. The pressure is extended within the particles in a fictitious domain fashion.
 Ph. Angot, J. Keating, and P. Minev. A direction splitting algorithm for incompressible flow in complex geometries. Comput. Methods Appl. Mech. Engrg, 117:111-120, 2012.
Honey bees have been in the news grabbing head-lines (e.g, ”EU Plan Bee for bee recovery”, BBC news; "Are honeybees losing their way ?" (National geographic)) in the last few years since the sudden collapse in honey bee colony sizes (also called as Colony Collapse Disorder(CCD)) observed over the winters of 2006-2008. In parallel with world wide efforts to find the source of this collapse and improve honeybee pest management to prevent its recurrence, we initiated a study aimed at understanding micro environment inside a beehive using modeling. Honeybees as a colony work hard to maintain temperature and humidity levels inside their beehive within narrow limits to ensure optimal growth conditions for their off-springs as well as to optimize their finite energy resources. Understanding and ensuring good comfortable environment inside a beehive has been long recognized by beekeepers as a way to help honeybees maintain a thriving colony.
Despite the long history of beekeeping and its extensive use in honey bee farming practice, little information is available about the conditions inside a honey beehive. In our study, using field data and observations, we constructed for the first time a realistic physical model of a beehive and its contents, and modeled the relevant heat and mass transfer processes describing the interaction of the honeybees with the air and simulated the 3-D flow inside the beehive. In my talk, I will discuss the challenges involved in modeling this problem, our findings regarding the changing conditions inside the beehive as we varied the ambient air temperatures and will showcase our recent efforts to use the developed model to suggest structural improvements to the basic beehive design.