一种计算底水油藏水锥形态与见水时间的新方法

目前多数针对底水锥进的研究其基本假设为油水界面至井底的压力梯度是一定值，即垂向单位距离的地层压降相同，不符合主要压降存在于井底周围的实际认知。为了准确计算底水油藏生产中实际压力分布规律及油井见水时间等问题，针对底水油藏部分射开井生产特征建立了数学模型，采用拉普拉斯变换和分离变量法等方法进行求解，得到了部分射开井的真实压力分布，准确计算了水锥形态和见水时间，并分析了油井产量以及垂向渗透率对底水油藏见水时间和水锥形态的影响。通过实例验证该方法计算所得油井见水时间误差更小，并分析发现油水界面至井底的压力梯度变化整体呈“L”型；随着油井产量的减小，油井见水时间延长，水锥变“窄”；垂向渗透率越小，相同产量下水锥锥进速度越慢，水锥锥体变小，该方法对底水油藏高效开发具有一定意义。

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.