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考虑启动压力梯度的致密气藏渗流数学模型解析解研究

断块油气田

2004年 11卷第06期

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Title

Study on the Analytical Solution of Mathematical Model for the Tight Gas Reservoir about Start-up Gradient

作者

梁　彬　李　闽　曾凡华　欧成华　杜　凯

Authors

Liang Bin ,Li Min, Zeng Fanhua,et al

单位

西南石油学院油气藏地质及开发工程国家重点实验室

摘要

对存在启动压力梯度的致密气藏不稳定渗流数学模型进行分析时,常用的方法是在拉式空间运用格林函数法进行求解,但这个解无法反演到实空间而获得解析解。根据拉式变换及其逆变换的性质引入了附加函数,得到了形式简明的实空间上的解析解。通过对比多组解析解和数值反演的结果表明该解析解的计算精度在5 %以内,因而此解析解可以在工程中应用。

Abstract

When analyzing the mathematical model of the unsteady

flow in the tight gas reservoir which has start-up pressure

gradient ,its usual method is using Green Function to obtain

the solution in the Laplace Space , yet which cannot be

inverted to real space to acquire the analytical solution.Based

on the nature of Laplace transformation and inverse Laplace

transformation , this paper introduces the additional function

and obtains the concise analytical solution in the real space.

The comparison of the results of analytic solution and

numerical inversion shows that , the calculation accuracy is

within 5 percent , and thus it can be applied to the

engineering.

关键词：

致密气藏　启动压力梯度　拉式空间解　解析解;

Keywords:

Tight gas reservoir ,Start-up gradient , The solution in the Laplace space ,Analytical solution

;

基金项目

DOI