应用正交积分变换求解有界双重介质模型

Solutions for Dual Porosity Testing Models of Finite Boundary Reservoirs Using Orthogonal Transformation

根据有界双重介质试井模型的特点,建立了外边界定压和外边界封闭2种情形下的特征值问题,求出了相应的特征值和特征函数,定义了油层压力关于空间变量的正交积分变换.对试井模型施行正交积分变换并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).与Stehfest数值反演法结果进行比较,验证了本文方法的有效性,进一步补充、完善了试井分析理论.

A dual porosity testing model of finite boundary reservoirs is presented, based on the studies of the forerunners. According to the model＇s character, the paper has presented related eigenvalue problem,including closed external boundary and constant pressure condition at external boundary. The eigenvalue and eigenvalue function were obtained. The orthogonal transformation of the pressure in reservoir is defined. An analytical solution of the reservoir pressure distribution and wellbore bottom pressure distribution were obtained, form of infinite series, using theory of matrix differential equation and the completeness of eigenvalue functions. The effectiveness of this paper＇s method is verified,comparing with the Stehfest algorithm＇s result . The paper＇s results have supplemented and improved the well test analysis theories.