摘要
在前人工作的基础上,建立了非牛顿幂律流体有界双重介质试井模型.根据模型的特点,提出了相应的特征值问题,求出了特征值和特征函数.定义了油层压力关于空间变量的正交积分变换.根据特征函数系的完备正交性和矩阵微分方程理论,获得了油层压力分布以及井底压力,压力导数的实空间解析解(无穷级数形式).首次直接根据实空间解析解绘制了样版曲线,并在同一张双对数坐标纸上描出拉普拉斯方法制作的样版曲线,同时给出二者间的误差走势图.通过对比分析发现,随着级数项数的增大,根据解析解制作的样版曲线逐渐逼近拉普拉斯方法制作的样版曲线.新疆油田实例证实了该方法的有效性.研究结果进一步补充,完善了试井分析理论.
A non-Newtonian power-law fluid testing model through dual porosity reservoirs is presented, based on the studies of forerunners. According to the model＇s property, the paper presents related eigenvalue problems. The eigenvalue and eigenvalue function are obtained. The orthogonal transformation of the pressure in reservoir is defined. Analytical solutions of the reservoir pressure , bottomhole pressure and its derivative are obtained （in the form of infinite series） using the theory of matrix differential equations and the completeness of eigenvalue functions. Typical curves are directly made by analytical solutions first time, and another typical curves through Laplace transformation are given on the same log-log curve plot. Meanwhile, a trend chart for errors is given. It is found by contrast that the typical curves here approach the Laplace typical curves gradually as the number of terms in infinite series increases. The example of producing wells in Xinjiang Oilfield has shown the usefulness of this method. Results in this paper have supplemented and improved the well test analysis theories.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2007年第4期397-404,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
2006年度高等学校博士学科点专项科研基金(20060615003)
关键词
非牛顿幂律流体
双重介质
样版曲线
特征值问题
实空间解析解
正交变换
non-Newtonian power-law fluid
dual porosity
type curve
eigenvalue problem
analytical solution in real space
orthogonal transformation
