井周堵塞对承压含水层定流量回灌渗流场影响的半解析研究

Semi-analytical solutions for groundwater flow dynamics in confined aquifers under constant-rate injection considering clogging of aquifers around well

为分析定流量条件下回灌堵塞对井周含水层渗流响应的影响,采用指数形式的渗透系数衰减方程反映堵塞作用下井周含水层渗透特性的时变效应,建立了考虑堵塞效应的定流量非完整回灌井流力学模型,采用变量代换、Laplace变换和有限余弦Fourier变换得到了井周含水层中水位抬升在Laplace空间的解,应用Stehfest数值逆变换方法获得了实时空间内的水头抬升和回灌压力。参数分析结果表明,较小的渐近渗透系数K_(r,∞)会增加回灌过程中水头抬升和回灌压力,并加剧含水层达到拟稳态时的渗流响应;较大的渗透系数衰减指数λ仅增加回灌过程中水头抬升和回灌压力,但不影响含水层达到拟稳态时的渗流响应;因Kr,∞和λ不同而引起的水头差在井筒处达到最大值并沿径向距离逐渐减小。研究结果可以为定流量回灌中井周含水层堵塞的识别与预测提供理论依据。

To investigate the effect of clogging of aquifers around well on the flow dynamics in the well vicinity during the constant-rate recharge using a partially penetrating injection well,an analytical model for well hydraulics was proposed with special consideration of the clogging-related permeability reduction,which was assumed to reduce exponentially with time.By means of the variable substitution and the Laplace and finite Fourier cosine transforms,the solutions for the hydraulic head increment in the Laplace domain were derived and then the solutions in the real-time domain were obtained using the Stehfest numerical inversion method.A parametric study indicates that:a smaller asymptotic hydraulic conductivity K_(r,∞)can not only increase the hydraulic head increment and the injection pressure during the recharge process but also accelerate the flow dynamics of the recharged aquifer at the quasi-steady state,whereas a larger permeability reduction exponentlonly result in larger hydraulic head increment and the injection pressure during the recharge process but doesn’t affect the flow dynamics at the quasi-steady state.The hydraulic head difference distribution due to various Kr,∞andlvalues reaches its maximum value in the wellbore and then decreases gradually with the radial distance.The findings of this study can offer theoretical reference for the estimation and prediction of the clogging in the aquifer around well during the constant-rate injection test.