边界元理论在缝洞型非均质油藏渗流研究中的应用

Application of boundary element theory to the study of percolation in heterogeneous fractured-vuggy reservoirs

张烈辉 李成勇 刘启国 李允

Zhang Liehui Li Chengyong Liu qiguo Li Yun

从渗流力学基本理论出发,建立了缝洞型非均质油藏直井渗流数学模型。采用Lord Kelvin点源解、贝塞尔函数积分和泊松叠加公式等方法求解出了缝洞型非均质油藏直井渗流的边界元基本解,建立起了缝洞型非均质油藏直井井底压力响应边界元解模型。通过理论计算得到了无因次压力和压力导数与无因次时间双对数理论图版,并详细分析了井在内区高渗带不同位置和高渗带位于油藏不同方位等情形对井底压力动态的影响。

A mathematic model for describing percolation in vertical well in heterogeneous fractured-vuggy reservoirs was built based on fluid flow mechanics in porous medium.By using Lord Kelvin point source solution,Bassel integration and superimpose formula,boundary element fundamental solutions(BEFS) are derived for percolation in vertical wells in heterogeous fractured-vuggy reservoirs and a BEFS model of bottom hole pressure in vertical wells in heterogeneous fractured-vuggy reservoirs is also established.Log-log type curves of dimensionless pressures and pressure derivatives vs.dimensionless time are plotted through theoretical calculation;and the effects of wells located in different areas of high-permeability zones and high-permeability zones located in different parts of the reservoirs upon the bottom hole pressure behaviors are analyzed in detail.

10.11743/ogg20070415