西南石油大学学报(自然科学版) ›› 1981, Vol. 3 ›› Issue (4): 49-57.DOI: 10.3863/j.issn.1000-2634.1981.04.004

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非定常渗流中的Hankel变换及其应用

吴玉树 葛家理   

  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:1981-11-20 发布日期:1981-11-20

THE HANKEL TRANSFORM AND ITS USE IN SOLVING THE PROBLEMS OF UNSTEADY-STATE FLOU THROUGH POROUS MEDIA

WU Yu-shu GE Jia-li   

  • Received:1900-01-01 Revised:1900-01-01 Online:1981-11-20 Published:1981-11-20

摘要:

本文定义了各种适合油藏工程常用边界条件的Hankel交换核函数,推到或给出了其反变换公式。作为Hankel变换应用实例,求解了双重空隙介质渗流微分方程组,在井底定压力生产条件下的解析解,从而阐明了Hankel变换是求解(平面)径向流问题十分有效的数学工具。

Abstract: The paper has defined Varous Hankel Transforms suitable for common boundary condition in reservoir engineering and deduced or presented their inverse transform formulae. As a practical example of using the Hankel Transform, the exact solution has been obtained for the defferential equation system of the double-porosity model at constant bottom-hole pressure. Hence, it has been proven that the Hankel transform is a most effective mathematical tool for solving the problems of radial flow of a slightly compressible fluid.