Mathematical model for darcy forchheimer flow with applications to well performance analysis



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Well performance and productivity evaluation is a fundamental role of petroleum engineers and this is done at different phases of petroleum production; from the reservoir to the well bore through the tubulars and ultimately to the stock tank. This task requires physical and mathematical models that adequately characterizes oil and gas flow at these different phases of petroleum production.

This thesis reviews different scenarios where the effects of non-linearity in flow is apparent in petroleum and gas reservoirs and can not be neglected any more. Laboratory experiments were carried out on core samples to show non-linearity in flow, which confirms deviation from the traditional Darcy law, used in reservoir flow modeling.

Historically non-Darcy flow has only been reckoned with in high flow rate gas wells, in which it has been treated as a 'rate dependent' skin factor and has been assumed to act only in the vicinity of the well-bore, while neglecting the reservoir. This work seeks to show the inherent errors due to the negligence of this phenomenon, which is fundamental to the calculation of the productivity index of the well. Using the modified non-linear Darcy law as the equation of motion to model filtration in porous media, this new model is compared to the conventional Darcy law. Proposed method delivers robust framework to model non-linear flow in the reservoir.

The result of this project will contribute to knowledge by equipping reservoir engineers with a robust technique to analyze well performance; this approach will provide better evaluation tool for selecting wells for remedial operations such as work-over or stimulation.