Analytical Well Models for Reservoir Simulation

Abstract

The computation of flowing-well bottomhole pressure from the pressure of the block containing the well or of well flow rate when the flowing bottomhole pressure is specified are important considerations in reservoir simulation. While this problem has been addressed by several authors, some important aspects of the problem are not treated adequately in the literature. We present an analytical method for computing the well-block factors (constants of the PI) for a well located anywhere in a square or rectangular block (aspect ratio between ½ and 2). Equations for well geometric factors and well fraction constants are given for gridblocks of various types, containing a single well, encountered in reservoir simulation studies. The equations given in this paper can be used for both block-centered and point-distributed grids in five- and nine-point two-dimensional (2D), finite-difference formulations. The radial flow assumption used in deriving the equations in this paper is not always strictly valid; however, for most practical situations it provides an adequate approximation for near-well flow.