两种新的不稳定渗流点源函数

对两类有直线型补给边界的一维不稳定渗流问题进行了研究 ,给出了直线型补给边界的定义和表达式。应用积分变换方法解析求解两类一维有源和补给边界的不稳定渗流问题 ,得到两种新的不稳定渗流点源函数 ,该函数可直接用于构造试井分析的数学模型。以改进的矩形油藏试井分析数学模型为例 ,说明了新点源函数的应用方法和表现特征。分析和计算结果表明 ,渗透系数θ反映了补给边界相对渗透能力 ,而传统的定压、封闭边界是直线型补给边界的极限形式 ,渗透系数取给定值时的压力诊断曲线位于定压和封闭边界两种情形之间。

TWO TYPES OF NEW NOVEL POINT SOURCE FUNCTIONS FOR TRANSIENT FLOW IN POROUS MEDIA

Two kinds of problems for unsteady fluid flow with leaky linear boundaries in one dimensional media are investigated. The linear boundary with leaky conditions is formulated first. On the basis of the boundary condition, two kinds of problems about transient flow with points source in one dimensional porous media are evaluated analytically by using integral transformation. Two types of novel point source functions, which can be direct employed in construct of solutions for well test analysis, are presented. Both expressive characteristics and concrete applications of the functions are illustrated with improved solutions for well test analysis in two dimensional rectangle reservoirs. It is expressed that the penetration coefficient can denote the penetrating ability of leaky boundaries while traditional boundaries either no flow or constant pressure are limited patterns of the leaky linear condition. It is shown that a pressure diagnosis curve for a fixed penetration coefficient is situated between a no flow boundary and a constant pressure boundary.