Effective dispersion in conditioned transmissivity fields |
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| Institution: | 1. Department of Civil and Building Engineering, and Architecture (ICEA), Università Politecnica delle Marche, Italy;2. Department of Civil, Environmental and Architectural Engineering (ICEA), University of Padova, Italy;1. LUSAC (EA 4253), Université de Caen Basse-Normandie, Site Universitaire, BP 78, 50130 Cherbourg-Octeville, France;2. Hydraulics Laboratory, Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, box 2448, B-3001 Leuven, Belgium;1. Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN, USA;2. Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA;3. Department of Biosystems Engineering and Soil Science, University of Tennessee, Knoxville, TN, USA;4. Department of Geosciences, Texas Tech University, Lubbock, TX, USA;5. Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA;1. Department of Statistics, Athens University of Economics and Business, 76 Patission Str., GR-10434 Athens, Greece;2. IIHR – Hydroscience & Engineering, 100 C. Maxwell Stanley Hydraulics Laboratory, The University of Iowa, Iowa City, IA 52242-1585, USA;1. LEN Technologies, Oak Hill, VA, USA;2. Department of Civil Engineering, The University of Texas at Arlington, Arlington, TX 76019-0308, USA |
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| Abstract: | We analyze the impact of conditioning to measurements of hydraulic transmissivity on the transport of a conservative solute. The effects of conditioning on solute transport are widely discussed in the literature, but most of the published works focuses on the reduction of the uncertainty in the prediction of the plume dispersion. In this study both ensemble and effective plume moments are considered for an instantaneous release of a solute through a linear source normal to the mean flow direction, by taking into account different sizes of the source. The analysis, involving a steady and spatially inhomogeneous velocity field, is developed by using the stochastic finite element method. Results show that conditioning reduces the ensemble moment in comparison with the unconditioned case, whereas the effective dispersion may increase because of the contribution of the spatial moments related to the lack of stationarity in the flow field. As the number of conditioning points increases, this effect increases and it is significant in both the longitudinal and transverse directions. Furthermore, we conclude that the moment derived from data collected in the field can be assessed by the conditioned second-order spatial moment only with a dense grid of measured data, and it is manifest for larger initial lengths of the plume. Nevertheless, it seems very likely that the actual dispersion of the plume may be underestimated in practical applications. |
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| Keywords: | Solute transport Conditioning Inhomogeneous flow Stochastic finite element method |
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