摘要
结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.
With finite difference method and Laplace transform,a Laplace transform difference method for well-test problem with one-dimensional seepage flow is proposed.Firstly,time variable is eliminated by Laplace transform.Then the mathematics model is solved with finite difference method.Finally the wellbore pressure or production is obtained with numerical inversion algorithm.A comparison with finite difference method solution and analytic solution shows that the calculating error of Laplace transform difference method is smaller than that of finite difference method,though it consumes more time in each step.Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment result and space grid.
出处
《计算物理》
CSCD
北大核心
2012年第2期245-249,共5页
Chinese Journal of Computational Physics
基金
国家油气重大专项(2011zx00513
2011zx05015)资助项目
关键词
拉普拉斯变换
有限差分法
试井
误差
Laplace transform
finite difference method
well-test
error
