Spatial correlation analysis between hydraulic conductivity and specific storage in a heterogeneous sandbox by hydraulic tomography

Hydraulic conductivity (K) and specific storage (S_s) are closely related to porosity, the compressibility of aquifer skeleton, connectivity of pores, sorting of the grains, and many others. These well-known relationships promote the investigation of the correlation between spatially varying K and S_s values and their sensitivity to the overlying materials stresses in heterogeneous aquifers. However, the costs of the field experiments for this investigation limit us to a laboratory heterogeneous sandbox aquifer. Before the laboratory experiments, we conducted numerical experiments to verify our tools and approaches. Specifically, we tested the ability of the recently developed hydraulic tomography (HT) for mapping K and S_s fields in two cases. One case in which S_s field was correlated with the K field, and the other was uncorrelated. With the assurance of the ability of our approaches, the laboratory experiments mimicking the numerical ones followed. Accurate drawdown predictions of different flow events in the laboratory experiments further guarantee the reliability of the estimated detailed K and S_s fields. The estimated K and S_s fields reveal that the S_s field's variability is much less significant than K and has much longer correlation scales. Further, the K distribution is closely related to the distribution of sand grain sizes in the sandbox, while S_s is not. Moreover, S_s estimates show a decreasing trend with depth. This trend does not exist in K estimates, indicating that S_s is highly sensitive to overburden stresses and K is not. Lastly, there is no clear spatial correlation between K and S_s, and the variability of S_s is critical in predicting the transient behavior of groundwater flow.