Mathematical Model and Application of Areal Sweep Efficiency for Irregular Well Patterns

Areal sweep efficiency is a critical indicator in reservoir development. Accurate calculation of the waterflood areal sweep efficiency of a well pattern provides a theoretical basis for optimizing injection-production strategies and enhancing effective field development. However, in calculating the areal sweep efficiency of irregular well patterns, the inclusion of streamlines with excessively low corresponding flow rates can lead to an overestimation of the swept area. To address this issue, the concepts of critical flow velocity and critical streamlines were introduced, leading to the derivation of the parametric equation for critical streamlines. By considering the boundary-curve equations of the swept region for each well pair, an analytical solution for the areal sweep efficiency was obtained, thereby proposing a calculation method for the areal sweep efficiency of irregular well patterns. Compared with theoretical results for regular well patterns, the relative error of the calculated areal sweep efficiency is less than 5%, with the critical flow velocity corresponding to a pressure gradient magnitude of 0.05 times the average pressure gradient along the main streamline of the well pair. When applied to an actual irregular well pattern, the method yields an areal sweep efficiency of 0.119 km2, corresponding to a sweep coefficient of 27.2%.