A new method for calculating water cone shape and water breakthrough time of bottom-water reservoir

In the most of the current studies on bottom water coning, it is basically assumed that the pressure gradient from the oil-water contact to the bottom hole is constant. Based on this assumption, however, the formation pressure drop of vertical unit distance is equal, which is not accordant with the actual cognition that the pressure drop is mostly distributed around the bottom hole. In order to accurately calculate the distribution laws of actual pressure in bottom-water reservoirs and the water breakthrough time of oil wells during the production, this paper established a mathematical model based on the production characteristics of some perforated wells in bottom-water reservoirs, and solved the model by means of Laplace transform method and variable separation approach. Accordingly, the true pressure distribution in some perforated wells was figured out, and water cone shape and water breakthrough time were calculated accurately. Then, the effects of well yield and vertical permeability on the water breakthrough time and water cone shape of bottom-water reservoir were analyzed. Finally, it was experimentally verified that by virtue of this method, the calculation error of the water breakthrough time is much smaller. It is indicated that the change of the pressure gradient from the oil-water contact to the bottom hole is overall in the shape of L. With the decline of well yield, the water breakthrough time of oil well is prolonged and the water cone gets narrow. The lower the vertical permeability is, the slower the water coning at the same yield is and the smaller the water cone is. In conclusion, this method is of certain significance to the efficient development of bottom-water reservoirs.