Horizontal and Slanted Wells in Layered Reservoirs with Crossflow


Pengbo Lu







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The purpose of this report is to present new analytical pressure-transient solutions for horizontal and slanted wells in layered reservoirs with cross flow. We considered two different situations: (1) the pressure-transient behavior of a single slanted well crossing several layers; (2) interference between several horizontal wells located at di
erent positions. These layered systems can be bounded by two horizontal impermeable boundary planes at the top and the bottom, or either one of the boundary planes can be a constant-pressure boundary (the system either has a gas cap or an active aquifer).

We used the Laplace transform and double Fourier cosine transform to obtain the Green's functions for the layered and composite systems. For this type of problem, it is convenient to express the Green's function as the sum of two solutions: the point source solution and the solution of the homogeneous partial di
erential equation for each layer. The point source solution can be obtained in the Laplace space. However, due to the complication of the cross flow interfaces, we applied double Fourier cosine transform and obtained the solution of the homogeneous partial differential equation. The reflection and transmission method was introduced to solve the layered and composite systems, which can not be solved by the conventional methods.

The segmentation method was used to solve the pressure transient behavior. The wellbore was discretized into several segments and each segment was treated as uniform flux, then we set up a linear system and obtained the pressure drop solution in the Laplace space and transformed it back to the real space.

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