Abstract

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, shows 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.

Introduction

The term "water coning" refers to the deformation of the oil-water interface caused by pressure drawdown at the oil-producing completion. Since the pressure gradient is the largest in the vicinity of the wellbore, the deformation of the interface assumes a conical shape. The phenomenon is also referred to as three-dimensional water coning. If vertical component of the pressure gradient in the oil zone is greater than the density difference between water and oil, water will breakthrough into the oil completions and will be produced. The maximum water free oil production rate is termed "critical rate". After the breakthrough occurs, not only will the production of water reduce the productivity of the well, but additional equipment for produced water separation and disposal will be required. All oil reservoirs with bottom water drive are subject to water coning at some stage of their depletion.

Water coning has long been a problem in oil fields and has been studied by many researchers. Typically, these studies were aimed at determining critical rates or/and breakthrough times. Coning reversal has not been considered in these studies because of a very long time required for the reversal. Recent results published by Butler and Jiang showed that time required for water cone to return to the initial conditions after the well is shutdown is greater than 3.5 years. Unfortunately, the authors did not address another practical issue: coning reversal without shutting the well down. It seems feasible that after water breakthrough occurs some reduction of production rate might reverse the cone and eliminate water cut. Our literature survey on this subject showed no published data available in the technical literature which could answer the question: "What is the necessary reduction in production rate that would eliminate water breakthrough and bring the water cone back down to the stable position below the oil completion?"

The objective of this paper was to determine conditions for coning reversal using theoretical analysis and an experimental study.

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