Estimation of effective hydrogeological parameters by considering varying heterogeneity and pumping rates

Darcy’s law and pumping tests, Tabu searches (TS) integrated with the Adjoint State Method (ASM), are two upscaling approaches used to transform local hydrogeological parameters at the scale of measurement into effective parameters on larger scales. This study proposed the above methods in order to estimate the effective parameters of heterogeneous and anisotropic aquifers at different degrees of heterogeneity (variances and correlation lengths). The results revealed three important principles: (1) the means of the effective transmissivities by Darcy’s law under different Dirichlet boundary conditions are used as the real ones in this study, because the optimal values under different Dirichlet boundary conditions are very close to each other at the same level of heterogeneity; (2) the estimations by TS integrated with ASM at low degrees of heterogeneity are much closer to the means of optimums by Darcy’s law than the estimations at high degrees of heterogeneity. Regardless of the pumping rate, the optimum at high degrees of heterogeneity is not good enough to represent the total study field. In considering the estimations at low degrees of heterogeneity, the drawdown caused by a low pumping rate is not sufficient to identify the effective parameters, while the drawdown caused by a higher pumping rate is useful for estimating the effective parameters. This suggests that the range of pumping rates influences the results estimated by TS and ASM, and the effective parameters identified using the effective range of pumping drawdown are more than enough to represent the whole study aquifer. With a larger variance of heterogeneity, the range of the pumping rate becomes smaller, leading to results closest to those estimated by Darcy’s law; (3) the estimations are influenced by the variances of heterogeneity more than the correlation lengths of heterogeneity.