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Non-Newtonian fluid, shear rate , complex fluid rheology, non-Darcy flow, non-linear dynamics, chaos in porous media.

It is well known that reservoir simulation studies are very subjective and vary from simulator to simulator. While SPE benchmarking has helped accept differences in predicting petroleum reservoir performance, there has been no scientific explanation behind the variability that has frustrated many policy makers and operations managers and puzzled scientists and engineers. In a recent book by the research group of R. Islam, a new approach is taken to add the Knowledge dimension to the problem. For the first time, reservoir simulation equations are shown to have embedded variability and multiple solutions that are in line with physics rather than spurious mathematical solutions. With this clear description, a fresh perspective in reservoir simulation is presented. Unlike the majority of reservoir simulation approaches available today, the 'knowledge-based' approach does not stop at questioning the fundamentals of reservoir simulation but offers solutions and demonstrates that proper reservoir simulation should be transparent and empower decision makers rather than creating a black box. Mathematical developments of new governing equations based on in-depth understanding of the factors that influence fluid flow in porous media under different flow conditions are introduced. Behavior of flow through matrix and fractured systems in the same reservoir, heterogeneity and fluid/rock properties interactions, Darcy and non-Darcy flow are among the issues that are thoroughly addressed. For the first time, the fluid memory factor is introduced with a functional form. The resulting governing equations are solved without linearization at any stage. A series of clearly superior mathematical and numerical techniques are also presented that allow one to achieve this objective. Mathematical solutions that provide a basis for systematic tracking of multiple solutions that are inherent to non-linear governing equations. This was possible because the new technique is capable of solving non-linear equations without linearization. To promote the new models, a presentation of the common criterion and procedure of reservoir simulators currently in use is provided. The models are applied to difficult scenarios, such as in the presence of viscous fingering, fractures, and others. It is demonstrated that the currently available simulators only address very limited range of solutions for a particular reservoir engineering problem. Examples are provided to show how the Knowledge-based approach extends the currently known solutions and provide one with an extremely useful predictive tool for risk assessment.