# Mathematical modeling of a three-dimensional permeability tensor for reservoir simulation

Rogers, Felix John (2015) Mathematical modeling of a three-dimensional permeability tensor for reservoir simulation. Masters thesis, Memorial University of Newfoundland.

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## Abstract

Anisotropy is generally formed as a result of systematic orientation and shape of asymmetric grains making up the solid matrix of porous media. It is well known that porous media are often anisotropic. To calculate flow in such three dimensional media a permeability tensor must be used in Darcy's law. These anisotropic reservoirs cannot be properly studied with conventional simulators, which assume that the coordinate system used to describe the fluid flow aligns with the principal permeability axes. Thus, the coordinate axes are oriented in the same direction as these principal axes. Permeability actually varies in all directions and with increased use of directional wells, the ability to use correct permeability in the direction of fluid flow is important in predicting reservoir production characteristics. This will also help explain why and where oil accumulations occur. Many investigators have attempted to either develop a mathematical model to calculate anisotropic permeability of a system or to experimentally develop a procedure to measure directional permeabilities. This research involves creating this three-dimensional permeability tensor mathematically. Then, using the commercial reservoir simulator, the three-dimensional permeability tensor is included in the reservoir model. The tensor is rotated within each grid block to align the principal coordinate axes with the actual well path. The model with the three-dimensional permeability tensor is used to predict the oil production rate. The oil production rates are then compared to the conventional reservoir simulator results. Results from the reservoir simulations found that as the size reservoir grid refinement increased, so did the deviation in the oil production rates predicted comparing the conventional reservoir simulator wellpath. Also, from the simulations it was found that there is a difference in oil production rates when comparing the simulations with the tensor aligned with the wellpath to the conventional reservoir simulation and comparing the results to real field data will confirm which approach is more accurate.

Item Type: Thesis (Masters) http://research.library.mun.ca/id/eprint/12481 12481 Includes bibliographical references (pages 103-105). Reservoir, Simulation, Mathematical Modeling, Permeability Tensor Engineering and Applied Science, Faculty of May 2015 Submission Oil fields--Permeability--Mathematical models; Oil reservoir engineering--Mathematical models

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