Comprehensive Simulation of Horizontal-Well Performance

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Abstract
Summary: The simulation of the performance of a horizontal well has generated certain new and important challenges. These include the partial penetration of the well in the horizontal direction within the allocated drainage area, the positioning of the well between the vertical boundaries, the distance from the parallel horizontal boundaries, and the permeability anisotropy. In addition, there are special problems in the simulation of the response of fractures (natural and induced) in regard to their contact with the well (longitudinal or transverse), their conductivity, and the conductivity distribution along the fracture. We developed new numerical techniques to facilitate the simulation of these diverse problems. We use a locally refined perpendicular bisection grid to describe the horizontal (or deviated) wellbore. The grid is strictly orthogonal for the anisotropic case, and wellbore blocks are almost regular octagonal prisms. The transition to the coarse Cartesian grid is also orthogonal. The fully implicit formulation ensures the stability of the numerical solution. Our results are found to be in excellent agreement with published analytical or semianalytical approximations. In addition, the results offer flexibility that is not possible with analytical solutions. The grid system used is particularly amenable to handling practical problems with real reservoir geometries and configurations. This paper presents a comprehensive numerical simulation of problems associated with horizontal wells, including the arbitrary positioning of the well within a fully anisotropic medium. Hydraulic or natural fracmres that intersect the well in the longitudinal or transverse direction are simulated for both infinite and finite conductivities.