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    考虑孔隙堵塞的Forchheimer型地下水回灌模型

    A Forchheimer’s Law-Based Well Hydraulics Model Considering Pore Void Clogging for Groundwater Injection

    • 摘要: 为分析回灌堵塞对井周高速非达西流动的影响,采用Forchheimer方程描述非达西流动,并引入随时间变化的固有渗透系数KD(t)和惯性渗透系数KN(t)以表征堵塞效应,建立了考虑孔隙堵塞的广义非达西径向井流模型.通过拟线性处理和Laplace变换推导了模型的拟稳态近似半解析解,并发展了基于分段非线性Galerkin方法的数值解.分析结果表明:在定流量试验中,KD(t)与KN(t)的减小和堵塞范围rc的增大会提高堵塞区的水头抬升s,但对非堵塞区几乎没有影响,且rc大于非达西流动区时,KN(t)的减小将导致非达西流动范围的增大;在定水头试验中,KD(t)、KN(t)的减小与rc的增大均会降低整个含水层的s,且KD(t)的下降会限制非达西流动对水头抬升的影响.此外,堵塞引起的渗透衰减使s-logr曲线在r=rc处出现拐点,造成定水头试验的s-logt曲线在上升阶段呈现“先升后降”特征.上述现象在非达西流动主导时更为显著,该研究成果可为回灌堵塞的动态评估与预测提供理论依据.

       

      Abstract: This study developed a generalized non-Darcian radial flow model incorporating pore clogging effects to analyze its impact on high-velocity flow around a recharge well.The non-Darcian flow was described using the Forchheimer equation,with time-dependent intrinsic hydraulic conductivity (KD(t)) and inertial hydraulic conductivity (KN(t)) introduced to characterize clogging evolution.A quasi-steady-state approximate semi-analytical solution was derived using linearization and Laplace transform,and a numerical solution was developed using the segmented nonlinear Galerkin method.Results show that:in constant-rate injection tests (CRTs),decreased KD(t) and KN(t) or increased clogging zone radius (rc) elevates the hydraulic head (s) in the clogged zone but has negligible impact on the unclogged region.When rc exceeds the non-Darcian flow zone,reduced KN(t) expands the non-Darcian flow region.In constant-head injection tests (CHTs),decreased KD(t) and KN(t) or increased rc reduce s throughout the aquifer,with KD(t) reduction limiting the influence of non-Darcian flow on s.The permeability reduction due to clogging causes an inflection point at r=rc on the s-logr curve in both CRTs and CHTs and a “rise-then-fall” pattern on the s-logt curve in CHTs.These characteristics are more pronounced under dominant non-Darcian flow.The findings provide a theoretical basis for dynamic assessment and prediction of aquifer clogging.

       

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