Research paper Hydrodynamics of porous formations: Simple indices for calibration and identification of spatio-temporal scales M. El-Rawy a, b , F. De Smedt b , O. Batelaan c , U. Schneidewind d , M. Huysmans b , W. Zijl b, * a Department of Civil Engineering, Faculty of Engineering, Minia University, Minia 61111, Egypt b Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium c National Centre for Groundwater Research and Training, School of the Environment, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia d Department of Engineering Geology and Hydrogeology, RWTH Aachen University, Lochnerstr. 4-20, 52064 Aachen, Germany article info Article history: Received 14 January 2016 Received in revised form 2 August 2016 Accepted 22 August 2016 Available online 25 August 2016 Keywords: Absolute permeability Basins Characteristic indices Double constraint methodology Groundwater hydrodynamics Hydraulic conductivity Spatial and temporal scales abstract 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 conduc- tivity 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 conductiv- ities, on the scales of such flow systems, simple Flux/Potential (F/P) ratios are obtained from two hy- drodynamic 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 sys- tem 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. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction to basin hydrodynamics At the basin scale, groundwater hydrodynamics shows extremely complex flow patters. Time-dependent and spatially variable multi-scale undulations of the water table induce a hier- archy of continually growing and disappearing nested flow sys- tems. The water moves rapidly through the local shallow flow systems, while it moves slowly through the regional deep ones (Foster and Hirata, 1988; T oth, 2009). The different residence times of the water in the different flow systems strongly influence its chemical composition (T oth, 2009). Fourier decomposition of the spatial multi-scale undulations of the moving water table leads to a superposition of time-dependent Fourier flow systems, in which each flow system is characterized by its orientation, phase and wavelength. The spatial extent of each flow system can then be characterized by its penetration depth, while its temporal behavior can be characterized by its decay time (Stolwijk et al.,1996; Meekes, 1997; Zijl, 1999; T oth, 2009). Two parameters, absolute permeability and hydraulic conduc- tivity, play a major role in the fluid dynamic models that are used by the “oil and gas community” and the “groundwater community.” This common interest has a great potential for constructive overlap between the two communities. The growing interest in basin hy- drodynamic systems in relation to their contained resources may be considered as an important step, not only in the field of research and development related to modeling, but also for applied studies as, for instance, carbon capture and storage, and exploration and production of natural gas to replace coal, lignite, peat and wood as producers of energy (Verweij, 1993; T oth, 2009). This paper deals with (i) the characterization of spatial and temporal scales of groundwater hydrodynamics in basins and (ii) the identification of parameters - especially hydraulic conductivity and/or absolute permeability - in relation to these space-time scales. Characterization of the hydrodynamic scales is based on * Corresponding author. E-mail address: VUB@zijl.be (W. Zijl). Contents lists available at ScienceDirect Marine and Petroleum Geology journal homepage: www.elsevier.com/locate/marpetgeo http://dx.doi.org/10.1016/j.marpetgeo.2016.08.018 0264-8172/© 2016 Elsevier Ltd. All rights reserved. Marine and Petroleum Geology 78 (2016) 690e700