Analytic Solution for Partially Completed Horizontal Wells with Simulation Validation

Abstract

Summary This paper presents an inflow model for partially completed (PC) horizontal wells that is validated against a simulation benchmark with performance evaluated in terms of a normalized dimensionless productivity index (PI). The model is based on a pressure-averaged uniform flux line-source solution that builds upon the model proposed in 1991 by Goode and Wilkinson (GW) and is validated against a numerical simulation-based benchmark. The model is then subjected to a series of tests where specific inputs are allowed to diverge from the assumptions used to derive it, effectively a form of “stress test.” The rationale was to determine model accuracy when applied to wells that do not conform to the idealized well used to develop the model. Inputs “stress tested” include well inclination, asymmetric completion placement, anisotropy, and a significantly larger number of (shorter) completions, up to around 100 (compared to just three in the original GW model). In all cases, the model performed reasonably well, with divergence from the numerical benchmark quantified. However, for all tests, it was found that model accuracy was dependent on the open fraction, with accuracy increasing as the open fraction increased while model reliability became suspect when the open fraction was ≲ 0.3. Practical usage guidelines and limitations are presented along with associated input ranges and estimated divergence from benchmark. The model is thought suitable for inclined and/or undulating wells with a large number of completions—both long and short—with or without asymmetric placement in presence of anisotropy.