中文摘要：

基于 Huangs 精确 tri 部分的非线性的运动学的方程(1997 ) ，为在有低渗透的一个维的半无限的长多孔的媒介的非线性的流动的一个无尺寸的简化数学模型在内部边界上为经常的流动率的盒子被介绍。这个模型包含两倍动人的边界，包括一条内部移动边界和一条外部移动边界，它与在发情传导的古典 Stefan 问题不同：外部移动边界的速度与关于这条边界上的距离参数的未知压力函数的第二衍生物成正比。通过类似转变，非线性的部分微分方程(PDE ) 系统被转变成一个线性 PDE 系统。然后，一个分析答案为无尺寸的简化数学模型被获得。这个答案能被用于严格地在在石油工程应用的低可渗透的多孔的媒介为流动解决如此的非线性的数学模型检查数字方法的有效性。通过从准确分析解决方案的阴谋的比较曲线，最后，三个典型参数的敏感效果被讨论。这被结束与在无尺寸的批评压力坡度的减少，无尺寸的压力分发和无尺寸的压力坡度分发 becomemore 上的无尺寸的变量的敏感效果严肃；随无尺寸的假阀值压力坡度的增加，无尺寸的变量的敏感效果变得更严肃；无尺寸的阀值压力坡度(TPG ) 在外部移动边界上有大效果，但是在内部移动边界上有小效果。

英文摘要：

Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.