In recent years, horizontal wells have assumed an ever increasing role in the production of fluids from hydrocarbon reservoirs. While these wells significantly improve productivity in many cases, they also present difficult interpretation problems to engineers who must analyze and predict their behavior. In particular, analysis of pressure transient well test data and prediction of rate decline behavior are not straightforward. This is due to the complex system geometry; i.e., pressure and rate behavior are affected by reservoir boundaries, anisotropy, well length, well location in the reservoir, etc. Our major purpose is to present simple efficient algorithms for generating horizontal well pressure and rate responses, to facilitate analysis and prediction in these complex systems.

Analytical solutions for the pressure response for a uniform flux horizontal well in a finite anisotropic sealed rectangular box reservoir is well known and documented in several previous publications. The exact (constant rate) solution involves a product of three infinite series, which (if not treated carefully), can require a large computational effort to evaluate. The first objective of this paper is to show how the solution can be accurately evaluated over all time ranges with minimal computational effort. (In test runs on an IBM compatible 20 MHz 386DX, 12 log cycles of pressure data encompassing all flow regimes, were generated in under 9 seconds.)

Using the constant sandface rate pressure response, we show how to efficiently generate the variable sandface rate pressure response in the reservoir for both homogeneous and dual porosity systems. In this case, we work in both real and Laplace space to optimize the computational speed. As examples, we show how the method is applied to generate wellbore pressure response when wellbore storage effects are important, and to generate decline curves for constant wellbore pressure production.

Finally, using the Principle of Superposition in time, the pressure response for production at a sequence of constant rates (with or without wellbore storage effects) is generated. Buildup is included as a special case of multiple step rate production.

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