一种有动外边界的一维径向不定常渗流解析解  

The Analytical Solution of One-dimensional Unsteady Radial Flow with Outside Moving Boundary

作　　者：邢国强[1] 王晓冬[1] 侯晓春[1] 刘少康 

机构地区：[1]中国地质大学(北京),北京100083 [2]中海石油(中国)有限公司天津分公司,天津300452

出　　处：《科学技术与工程》2014年第36期35-38,44,共5页Science Technology and Engineering

基　　金：国家科技重大专项(2011ZX05009)资助

摘　　要：在低渗透油藏中,采用启动压力梯度的方法能够简明扼要地表述低速非Darcy渗流现象。在油井恒定流压开采条件下,运用Green函数方法求解了含启动压力梯度、带有动边界的非线性不稳定渗流数学模型,揭示了动边界传播规律和油井产量递减特征。计算对比表明,随着生产时间延续,动边界向外扩展,压力扰动范围增大,弹性开采最大半径增加;启动压力梯度越大,动边界扩展越慢;给定启动压力梯度λD,对应的压力扰动最大值半径为rDmax=1.0+1.0/λD,此后停止传播,弹性开采动用面积达到最大值;动边界情形与半径为rDmax的封闭储层情形相比,产量递减较快,最大累计产量明显损失。In a reservoir with low permeability,the phenomena of Non-Darcy flow at low velocity can be described briefly to the point by threshold pressure gradients （TPG）.For an oil well at constant pressure production,a non-linear mathematical model of fluid transient flows with a moving outer boundary in the presence of TPGs is solved by Green＇ s functions method.Characteristics of both transmissions of the moving boundary and declines of the well production are proclaimed by the analytical solution of the model.As producing time elapses,it is shown that the moving boundary which indicates the increase of the maximum radius may develop as well as the pressure perturbation may spread.It is also demonstrated that the greater the TPG,the slower the boundary expansion.The maximum radius of pressure perturbation may be estimated by a formula rDmaax =1.0 ＋ 1.0/λ D at a given TPG.The drainage area may come to the maximum when the outer boundary stops expanding.Compared with the well in a reservoir closed by a circle of radius romax,the rate in the situation of TPGs will decline earlier but slower,which suggests that the production process of low permeability reservoirs would last longer.

关 键 词：低渗透油藏 启动压力梯度 动边界 产量递减 累计产量 

分 类 号：TE312[石油与天然气工程—油气田开发工程]