Hydrodynamics of porous formations: Simple indices for calibration and identification of spatio-temporal scales

This paper proposes simple indices to characterize the hydrodynamic conditions of groundwater flow systems and parameters of a basin on different space-time scales, i.e., quantities characterizing a complex phenomenon in a relatively simple way. It focuses especially on the identification of hydraulic conductivity in relation to the space-time scales. Two indices, decay time and penetration depth, are derived on the basis of Fourier flow systems. For the determination of parameters, especially hydraulic conductivities, on the scales of such flow systems, simple Flux/Potential (F/P) ratios are obtained from two hydrodynamic models: a flux model (F), in which measured fluxes (flow rates) are specified, and a potential model (P), in which measured potentials or pressures are specified. The F/P ratios are the basis for the double constraint method (DCM), which is shown to be applicable as a simple and efficient calibration methodology for hydraulic conductivity in single phase flow and absolute permeability in multi-phase flow. The index approach is exemplified using a hydrogeological case study of an aquifer-aquitard system in Belgium, which shows sufficient similarity to larger-scale basin hydrodynamics. It is shown that the indices allow to identify the scale of the relevant parameters, mainly hydraulic conductivity, while the F/P ratios indicate where and how measurement of potentials or pressures and flow rates can be used to determine the hydraulic conductivity on that scale.