Abstract
In this work, theoretical models have been formulated, validated, and applied to evaluate the production decline performance of a fractured vertical well with reorientated fractures in an anisotropic formation with an arbitrary shape by using the boundary element method. More specifically, the coordinate transformation method was applied to convert the anisotropic system to an equivalent isotropic system, while a coupled matrix-fracture flow model is proposed in the Laplace domain. Then, the boundary element method is applied to solve the fluid flow problem in the matrix, while the Laplace-transform finite difference method is used to numerically obtain the pressure solutions for each fracture segment. Furthermore, the effect of orientated fractures can be examined by generating the Agarwal-Gardner type decline curves, during which two flow regimes including transient flow regime and boundary dominant flow regime can be found. The orientated fractures only affect the transient flow regimes and the boundary dominant flow can be affected by the area and shape of the reservoir. The fracture conductivity is found to be the most important parameter dominating the early production rate. The larger the anisotropic factor, the larger production rate during the early times. Also, the primary fracture angle is more sensitive than the orientated fracture angle. Subsequently, this newly proposed method has been validated and then extended to a field application, demonstrating that the production decline curves for a fractured well with reorientated fractures can be analyzed in a reasonable and accurate manner.
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