精确的拉普拉斯数值反演方法及其应用

AN APPLICATION OF AN ACCURATE AND EFFICIENT NUMERICAL INVERSION OF THE LAPLACE TRANSFORM IN MODERN WELL-TESTING ANALYSIS

介绍了一种拉普拉斯变换数值反演的新方法（Ｃｒｕｍｐ方法）以及它在油气井现代试井分析中的应用。在数值解例中，将Ｃｒｕｍｐ方法和精确解及Ｓｔｅｈｆｅｓｔ方法分别作了比较。Ｇｒｕｍｐ方法无论在计算精度、数值弥散还是在数值振荡上都有很大改进。用此方法绘制的典型曲线更精确。

A new numerical inversion of the Laplace transform(Crump' s method ) is present-ed.This method is applied in modern well testing analysis. Crump' s method , Stehfest'smethod and exact solution are compared in examples cited. The results show that Crump'smethod is more accurate and stable. The type-curves derived by this method are more exactthan those derived by Gringarten et al.