Presented in this paper is a theoretical and experimental study of water cone development and reversal. The theoretical study employed a new analytical method, called moving spherical sink model (MSSM), for accurate modeling of flow in the vicinity of a limited-entry well in a heterogeneous (kv,kh) reservoir. In contrast to other analytical models, MSSM does not lose validity in the near-well zone. It calculates pressure precisely at and outward from the borehole surface. This high resolution of MSSM in well's vicinity enables studying flow mechanisms that have been beyond competence of conventional models such as pressure distribution outside well's completion and development and reversal of water coning.
The results of this water coning study show that for oil production rates below critical (breakthrough) rate there are two equilibrium shapes of the water cone: lower (stable), and upper (unstable). Also shown is a hysteresis of the water cone height development and reversal caused by the increase – decrease scheme of production rate. The paper explains why reversing the cone is difficult because it requires reduction of production rate much below its critical value. It also describes how to determine the water cone reversal rate.
The experimental part of this study provides verification of the theoretical findings using a physical model. The results, summarized in this paper, showes all four stages of the water cone histeresis: from equilibrium cone buildup with increased production rates, to stability loss followed with water breakthrough at critical production rate, to continuing water breakthrough in spite of decreasing production rates, to water cone reversal at very low value of the reversal production rate.
This study provides basic understanding of stability mechanisms that control three-dimensional water coning. It also provides an analytical method for finding the cone reversal production rates.