单层开采的圆形定压边界两层油藏压力动态分析

Pressure transient analysis of two layers cross-flow reservoir perforated partially with constant pressure outer boundary

为更好地分析具有越流的多层油藏的压力动态,采用有效井径的概念,在半透壁模型的基础上建立了圆形定压边界、两层越流油藏单层开采时的渗流数学模型。通过拉氏变换得到了拉氏空间中以Bessel函数表示的精确解。数值反演计算结果表明,单层开采的两层油藏与全部打开的两层油藏的压力动态基本相同,都表现为3个阶段:早期是介于两个渗透层之间的均质流动;中间为过渡段,导数曲线出现下凹特征;晚期表现为整个油藏的均质特征,随着边界距离的增加,压力导数值趋近于0.5。半透率越大过渡段出现得越早,导数曲线下凹程度越小;储容比越大导数曲线峰值越小,导数曲线下凹程度越小;随着两层渗透率比值变小,过渡段变短,导数曲线下凹程度变小。

Based on the semi-permeable model, the effective hole-diameter mathematical model of a two-layer cross-flow reservoir perforated partially is solved rigorously. The exact solutions obtained are expressed in terms of ordinary Bessel functions by using the Laplace transform. The numerical computation of these solutions is made by Crump numerical inversion method. Pressure behavior of a two-layer cross-flow reservoir perforated partially is the same as that of a two-layer cross-flow reservoir. There are three stages. At the early time, pressure behavior is homogenenous. At the intermediate time, curve of pressure derivative is sunken. At the late time, the system reaches a homogenous behavior characterizing the total producing system. The value pressure derivative is close to 0.5 with the increasing of outer boundary. The larger the semi-permeability is, the earlier the transition occurs and the flatter the curve of pressure derivative is. The larger the storability is, the smaller the peak value of pressure derivative is. As the heterogeneity in permeability becomes smaller, the transition becomes shorter.