Horizontal-Well Productivity Equations With Both Uniform-Flux and Uniform-Pressure Wellbore Modes

Abstract

Abstract This paper concerns the estimation of pseudosteady-state horizontal-well productivity with emphasis on handling two types of wellbore conditions: uniform-flux and uniform-pressure. We present rigorous (analytically) and simplified PI (productivity index) equations which can easily handle the above two wellbore conditions within a consistent framework. The presented simplified PI equations were verified successfully (i) through detailed mathematical/physical analyses, and (ii) against the more rigorous solutions and published examples, for wide ranges of drainage shape, permeability anisotropy, and well length. Introduction Numerous PI (productivity index) equations subjected to various well-reservoir conditions had been presented in the literature. Among them, the pseudostedy-state PI models presented by Babu-Odeh[1,2] and Goode-Kuchuck[3,4] appears to be more popular than the others. The former assumed uniform-flux along the wellbore whereas the latter assumed uniform-pressure (approximated by averaging pressure along the well length). The former is a set of simplified equations (and thus is more "accessible") while the latter involves more complicated infinite-series (but considered, by some, to be a more realistic wellbore condition than the uniform-flux). The main objective of this work is to "bridge" Babu-Odeh's[1,2] and Goode-Kuchuck's[3,4] PI equations by providing both rigorous and simplified PI equations for both uniform-flux and uniform-pressure wellbore conditions. This will provide freedom for users to choose their preferred wellbore condition (uniform-flux/-pressure) and to evaluate PI by either rigorous or simplified equation set. We successfully derived simplified PI equations for both uniform-flux and uniform-pressure (pressure-averaging) with excellent accuracy for practical applications. Well-Reservoir Configuration Fig. 1 presents the well configuration and the adopted coordinate system. A fully-open horizontal well of total-length Lh centered at (xw, yw, zw) produces from a box-shaped reservoir of dimensions 2xe (length; parallel to the horizontal-well axis), 2ye (width), and h (height). The well is parallel to x-axis. All reservoir boundaries are closed (no-flow). Boundary condition at the wellbore is either uniform-flux or uniform-pressure along the wellbore.