Reservoir Simulation Using Bottomhole Pressure Boundary Conditions

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Abstract
This paper presents results derived from potential flow theory for single-phase flow in the region near an injection or production well. The relations obtained are directly applicable to reservoir studies where coarse grid systems, which cannot account for near-wellbore flow, are used to describe flow within the reservoir. Near-wellbore effects have received only minor attention in the literature.1–7 This work concentrates on a general solution to this flow problem. Relations are derived for a system with one or two wells located in a rectangular area and for n wells located in an infinite area. The paper also gives a method that accounts for areal flow behavior near a wellbore in cross-sectional simulations. Comparisons of the analytical results with computer results using Peaceman's5 relationship for the effective wellbore radius of a simulator well show good agreement for cases where the wells are located at the block center regardless of the grid size or the position of the well block within the grid system. The paper also illustrates how pressure boundary conditions can be applied in cases where the wells are not located at the center of a grid block. The derived relationships are applicable for a simulator based on either five- or nine-point formulations.

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