A novel 3-D model for the water cresting in horizontal wells

In the presence of bottom water, a drop in the reservoir pressure due to fluid production causes the aquifer water to expand and to flow into the reservoir. Therefore, hydrocarbon production from a well is limited by the critical flow rate. The main purpose of this study is to investigate the breakthrough time and the critical rate by using a novel 3-D horizontal well model. Based on the hypothesis that the horizontal well is located in any position of a circular reservoir with no-flow boundary on the top of the reservoir and constant pressure boundary at the bottom, the horizontal well has been regarded as an infinite conductivity line sink and then a 3-D steady-state flow model of the horizontal well is set up. A point sink pressure solution can be obtained with the Fourier transform. The result of the pressure distribution of the uniform flux horizontal well can be presented by means of the principle of superposition. According to the stable water cresting theory, this study confirms the stable height of water cresting and the critical rate. Meanwhile, it can re-confirm the breakthrough time at a specific rate. The output of a comparison between this 3-D model and the reservoir numerical simulator (Eclipse) shows the method presented here can be applied to investigate the behavior of a water cresting and to predict the breakthrough time at the bottom water driver reservoir.