Abstract
Because of a localized decrease in pressure, water may rise to a height above the oil-water interface and be produced through a horizontal well. The localized increase in the water-oil interface elevation creates a cone of water near the well. If a large enough drawdown is exerted on the reservoir, water will start replacing the oil in the production stream. The instant when water first enters the well is known as the critical drawdown or threshold drawdown. As the producing water-oil ratio increases, the operating cost of the well as well as the oil production cost will start increasing. At some point, the well may need to be shut-in to allow the water-oil interface to subside. In this situation, an optimum shut-in time exists, and it is dependent upon the subsidence time of the water cone.
Analytical solution for subsidence of water cone under a horizontal well is being presented in this paper. Usually, wells require a shut-in period if the drawdown exerted on the reservoir is above a critical value. But, depending on the amount of the drawdown exerted, the water cone can have a wide variety of shapes at the post-critical drawdown condition. To avoid this, the initial water cone shape in this solution, after the well is shut-in, is defined at the point of critical drawdown.
The water cone shape under a horizontal well at the point of critical drawdown is estimated here by developing an empirical formula. The cone shape is found to be a function of the critical oil production rate.
The water cone subsidence time is determined by solving the diffusivity equation using the separation of variables technique. The resulting solution shows that the subsiding instantaneous cone heights are exponentially related to time and are effected by hydraulic conductivity of reservoir, coefficient of specific storage of porous medium, the critical oil production rate and the reservoir geometry. Finally, the cone subsidence time is presented in a series of type curves that assumes various reservoir parameters.
