考虑弱透水层的单井注抽试验解析模型研究

New Analytical Solution of Single-Well Push-Pull Test in an Aquifer-Aquitard System

单井注抽(Single-Well Push-Pull,SWPP)试验被广泛用于获取含水层的溶质运移参数,但现有的SWPP试验数学模型中往往忽略了弱透水层的影响。针对含水层-弱透水层系统的径向弥散过程,将弱透水层效应考虑到SWPP试验中,建立了含水层-弱透水层系统中考虑混合效应的SWPP试验数学模型,采用拉普拉斯变换和格林函数法获得模型的半解析解,并通过与前人的解析解模型进行对比,验证了本模型的可靠性。敏感性分析结果表明:在SWPP试验中,弱透水层的分子扩散系数对含水层中溶质运移产生的影响不可忽略,当考虑弱透水层的分子扩散作用时,含水层注入阶段和抽取阶段早期井筒内溶质穿透曲线越低,抽取阶段晚期井筒内溶质穿透曲线越高。数值模拟研究结果也表明:当弱透水层渗透系数与含水层渗透系数的比值接近0.01时,半解析解模型的误差可以忽略,精度可以满足工程需求。

The Single-Well Push-Pull(SWPP)test has been widely used to estimate solute transport parameters of aquifers.However,the influence of aquitard is often ignored in the previous SWPP analytical solutions.Considering the aquitard effect on the SWPP test,this paper estalishes a mathematical model for the radial dispersion process in an aquifer-aquitard system,and derives the semi-analytical solution by using Laplace transform and Green’s function method.To test the reliability of the model,the paper compares with the previous analytical solution.Sensitivity analysis indicates that in the SWPP test the diffusion coefficient of aquitard has a non-negligible effect on the solute radial transport of the aquifer-aquitard system.When considering the molecular diffusion of aquitard,the lower the peak value of Breakthrough Curves(BTC)at well screen in injection phase and early extraction phase,the higher the peak value of BTC in late extraction phase.In addition,the numerical simulation study also shows that the error of the analytical solution in the study can be ignored and the accuracy can meet the engineering requirements when the ratio of permeability coefficient in the aquitard to that in the aquifer is close to 0.01.