The Critical Production Rate in Water-Coning System

Abstract

Abstract Water coning is the mechanism in which the oil/gas - water contact locally rises toward the perforated interval in a partially penetrated oil/gas well. Numerical and physical models have been built to study the performance of water coning under different boundary conditions. A fully implicit, strongly coupled mathematical model was formulated to handle rapid pressure-saturation changes. On the other hand, a plexiglass model was constructed to obtain a qualitative and quantitative description of water-coning phenomenon. An analytical description of water coning under different flow conditions was developed. Introduction In water coning, the oil/gas - water interface locally rises toward the well completion interval resulting in water production, hence reducing the oil/gas productivity and ultimate recovery for the well. Two forces control the mechanism of water coning:dynamic flow force (applied force), andgravity force. Water breakthrough occurs when the pressure drop caused by the applied force is slightly less than or equal to the gravitational force. The phenomenon of water coning has been investigated by many authors. Most of the work has been devoted to calculating the maximum possible oil/gas production rate without water production, the critical rate. Muskat and Wychoff assumed oil was produced from a well which partially penetrates the oil zone, while the water remains in static pressure equilibrium. Formulas and charts were presented to calculate the maximum production rate without producing water. Arthur followed the same type of analysis employed by Muskat and Wychoff to develop a graphical solution to the problem. Meyer and Garder came up with an approximate equation assuming radial flow and the water cone interface just touching the perforations. Chaney, et al., studied water and gas coning by means of potentiometric analyzer and mathematical analysis. A set of curves was introduced to calculate the maximum water-free oil production rates for various geometric reservoirs. Chierici, et al., used the potentiometric model technique and Muskat's theory to calculate the maximum permissible water-free oil production. They assumed that the volume of the water aquifer was very small. Numerous authors applied reservoir simulation to study water-coning behavior for various reservoir parameters. Experimental work has been conducted by many investigators to study water-coning phenomenon and/or to calculate the critical production rate. Giger presented an empirical formula based on experimental and mathematical models. Wheatley developed an analytical solution to calculate the critical oil rate assuming a constant potential at the wellbore and the drainage radius. Also, the oil-water contact was assumed to be in static pressure equilibrium with the oil. Hoyland presented correlations to predict the critical oil rate based on a calculation made with a simulation model. The water zone was represented by a bottom layer with infinite "porosity" and a column of infinite "porosity" and permeability at the drainage radius. Piper, et al., extended Wheatley's method to account for the effect of the cone height on the pressure gradient within the oil zone. P. 351^