底水油藏水平井产量公式研究

Study on Production Formula for Horizontal Wells in Reservoirs with Bottom Water

按照Joshi方法将水平井三维流动简化为垂直面和水平面的两个平面流动,分别应用镜像反映、叠加原理方法和保角变换方法推导出了底水边界油藏水平井垂直面和水平面内的产量公式;再利用电模拟方法得到底水油藏内水平井的产量公式;分析了水平段长度、偏心距、非均质性对水平井产量的影响。结果表明,偏心距对水平井产量影响较小,当水平段长度小于2000m时,偏心距对产量变化影响不超过6%;而储层非均质性对水平井产量影响较大,随着渗透率各向异性比kh/kv的增加,水平井的产量减小,垂向渗透率高的地层更有利于底水油藏水平井产量的提高。

By using Joshi’s method, a 3D flow in horizontal well was simplified as vertical and horizontal radial flows. Mirror reflection and superposition principle methods were used to obtain a production formula of vertical radial flow; production formula of horizontal radial flow was derived by using conformal transformation; an electric simulation method was used to obtain production formula in reservoirs with bottom water. In addition, the effect of horizontal section length, eccentricity and formation anisotropies on horizontal well productivity was analyzed. The results show that the eccentricity has minor influence on horizontal well productivity, when horizontal section length is less than 2000m, productivity change is no more than 6%. The influence of anisotropies on horizontal well productivity is large, with the increase of anisotropy ratio kh/kv, productivity of horizontal well decreases. The reservoir with higher vertical permeability is beneficial for increasing productivity.