边界元理论在复杂边界油藏部分射孔井渗流中的应用

APPLICATION OF BOUNDARY ELEMENT METHOD TO FLUID FLOW OF PARTLY PERFORATION WELL IN COMPLEX BOUNDARY RESERVOIR

受各种地质作用的影响,实际油藏的外边界往往是复杂多样的。在实际油藏开采过程中,为避免边底水突进或考虑其它工程因素,存在生产井部分射孔的情形。受求解方法局限性的限制,目前经典渗流力学理论还无法精确求解复杂外边界油藏中生产井层部分射孔问题。这里利用边界元理论在求解复杂边界域扩散问题的优点,从渗流理论出发,建立了复杂外边界油藏部分射孔井渗流数学模型;并采用Lord Kelvin点源解、贝塞尔函数积分和泊松叠加公式等方法,求解了复杂外边界油藏部分射孔井的边界元基本解;利用边界元的理论,建立了复杂外边界油藏部分射孔井井底压力响应数学模型;通过计算,得到了无因次压力和压力导数双对数理论图版,并在其基础上分析了复杂外边界油藏部分射孔井渗流特征及其影响因素。

According to the influence of internal agency,the boundary of actual reservoir is complex.In this article,by the fluid flow theory through porous media,we establish the mathematic model of partly perforation well in complex boundary reservoir.On the base of Lord Kelvin point-source solution,the integral of Bessel function,Poisson superimpose formula and boundary element method,we resolve it and obtain the boundary element basic solution.We establish the pressure response model of partly perforation well in complex boundary reservoir.The dimensionless pressure and pressure derivate double log type curve are obtain by calculating the pressure response function,and analysing the characters of fluid flow through porous media and its influence effects.