非均质表皮层径向双层承压井流数学模型的半解析解

考虑表皮层和未扰动承压层的非均质性、各向异性以及竖向越流补给作用,建立了径向双层承压三维井流的数学模型,采用Laplace变换和矩阵理论求得表皮层和未扰动承压层的水头降以及井壁流量的半解析解.应用所求解编制计算程序,分析了表皮层沿竖向随机变化的渗透性对承压层井流的影响,结果表明:表皮层非均质变化形态决定了表皮层内和其附近处的水头降以及井壁流量的竖向分布规律,表皮层对承压层渗流产生的影响范围与承压层的竖向渗透系数大小有关;改善井周岩土介质渗透性或增大"负表皮层"厚度可提高抽水井产量;表皮层径向渗透系数较小时,承压层的水头降幅度主要取决于承压层径向渗透系数的大小,而当表皮层径向渗透系数较大时,承压层径向渗透系数和竖向渗透系数均对承压层水头降有较大影响.

A Mathematical Model and its Semi-analytical Solution for the Flow of Anisotropic Confined Aquifer with Two Radial Layers Considering Heterogeneity of Well Skin

Considering the properties of heterogeneity and anisotropy of wellbore skin, a math-ematical model for the unsteady 3D flow in an anisotropic confined aquifer with two radial layers is developed. Using the Laplace transform technique and matrix theory, the solutions of draw-down for skin zone and formation zone, as well as the distribution of flux along well screen, are derived. Basing on the derived solutions, a numerical program is developed, and the flow sub-jected to stochastic change of permeability of layered skin zone is analyzed. The results indicate that: the vertical distribution of drawdown within skin zone and its vicinity, as well as the flux along well screen depend on the vertical heterogeneity of skin zone. While the influence range of skin zone is closely related with the vertical permeability of confined aquifer. Improvement of permeability or increasing thickness of negative skin can effectively raise well production. The magnitude of drawdown is mainly decided by the vertical permeability of formation zone and less influenced by the radial permeability of formation zone when radial permeability in skin zone is low, while the drawdown is obviously affected by not only the vertical permeability but also the radial permeability of formation zone when radial permeability in skin zone is comparatively large.