Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions
Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions
复制标题
未知边界条件下非均质含水层张量水力电导率估算
作者：
J. Jiao;Ye Zhang
本文提出了一种基于物理的反演方法，利用混合公式和坐标变换同时估计承压含水层在环境流或抽水条件下的水力传导系数张量、稳态流场和边界条件。与现有的间接反演技术不同，基于物理的方法不需要正演模拟来评估模型数据失配。它在模型域中施加了水头和达西通量的连续性，同时在测量位置结合了观测值（水头、达西通量或井速）。如果有足够的测量，它会产生一个适定的逆方程组，可以用粗网格和非线性优化有效地求解。当泵送和注入处于活动状态时，使用井速作为测量值，并且不需要通量采样。该方法成功地测试了合成含水层问题与规则和不规则的几何形状，不同的水文相和流动模式，并增加电导率各向异性比。在水头测量误差增大的情况下，所有问题都有稳定的逆解。对于一组给定的观测值，反演精度受到电导率各向异性比的强烈影响。电导率估计也受流型的影响：在一个水文相内，当达西通量分量非常小时，垂直于流线的相应方向电导率变得不那么可识别。最后，即使含水层边界的位置未知，反演也是成功的。在这种情况下，反演域由测量的位置定义。
A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.