一维非稳态渗流方程的动边界解法  

MOVING BOUNDARY SOLUTION OF ONE-DIMENSIONAL UNSTEADYSEEPAGEMODEL

作　　者：刘洪 Liu Hong(School of Science,East China University of Technology,Nanchang 330013,China)

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《数值计算与计算机应用》2023年第4期368-377,共10页Journal on Numerical Methods and Computer Applications

摘　　要：一维非稳态渗流模型求解是试井研究的基础,这类模型目前解法分解析解法和数值解法两大类,解析解法主要通过拉普拉斯变换及数值反演完成,数值解法则主要依赖网格划分和方程离散.以动边界思想为基础,本文提出了一维非稳态渗流模型第三类解法——非线性方程迭代解法,基于稳态依次替换法和质量守恒定律,视压力探测半径内区域渗流为稳态流动,将非稳态渗流方程转化为稳态方程,分析不同流动时间下探测半径变化规律,推导建立了不同外边界条件下探测半径的非线性控制方程,最后通过牛顿法求解非线性方程得到不同时刻井底压力,对比非线性方程迭代解与解析解显示计算误差较小,且主要是计算初期误差稍大,与传统的解析解法和数值解法相比,非线性方程迭代解法精度较高、算法简单,每个时间步仅需解一个非线性方程,显著减少了计算时间,可以在其他一维非稳态渗流问题中推广应用。One-dimensional unsteady seepage model is the basic model in well-test research,existing solution includes two categories such as analytic solution and numerical solution.Analytic solution is depend on Laplace transform and numerical Inversion,and Numerical solution is depend on mesh generation and equation discretization.Iterative solution of non-linear equation is present which is direct solution for One-dimensional unsteady seepage equation.Based on steady state sequential replacement method and mass conservation equation,the unsteady seepage equation is solved by transformed as steady seepage equation,the non-linear equation of investigation radius under different outer boundary were build,well-bore pressure and Investigation radius at each moment were obtained by Newton method.The error between iterative solution and analytic solution is small,and bigger error appeared in early stage.Compared with analytic solution and numerical solution,the iterative solution can be spread used in other One-dimensional unsteady seepage problems because of its simple algorithm,acceptable accuracy and fewer time-consuming.

关 键 词：非稳态 非线性方程 迭代解法 试井 探测半径 

分 类 号：TE312[石油与天然气工程—油气田开发工程]