Flow transiency on analytical modeling of subsurface solute transport
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RESEARCH ARTICLE
Flow transiency on analytical modeling of subsurface solute transport Xu Li 1,2 & Zhang Wen 2
&
Qi Zhu 2 & Hamza Jakada 3
Received: 29 March 2020 / Accepted: 5 June 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Groundwater flow velocity and dispersivity might be temporally or spatially variable rather than constant. In this paper, linearlyasymptotically or exponentially distance-dependent dispersivities and temporally exponential flow velocity were coupled to the conventional advection-dispersion equation. The mathematical models were established by considering the case of a coupled time-dependent velocity and scale-dependent dispersivities where one-dimensional (1D) semi-analytical solutions were obtained using the Laplace transform in a finite domain. The solution was verified by comparing it with a numerical solution, based on finite-element COMSOL Multiphysics. The impacts of different parameters of time-dependent flow velocity and scale-dependent dispersivities on breakthrough curves (BTCs) were thoroughly analyzed. The results show that a slight change of time-dependent flow velocity will lead to considerable change of BTCs, meaning that solute transport is sensitive to the temporally variable flow velocity. Secondly, a larger growth rate of the dispersivity in linear-asymptotically distance-dispersivity function can lead to a faster solute transport at early stage, but a lower concentration at late stage; as for the exponentially distance-dependent function, the growth rate of the dispersivity has the same effects on BTCs. Thirdly, it was observed that an increase in final steady velocity (or asymptotic velocity) will amplify the impacts on solute transport due to advection; as for the asymptotic dispersivity, it has similar impacts on the solute transport due to dispersion. Overall, our results show that the effects of time-dependent flow velocity and distance-dependent dispersivities are not negligible when describing solute transport process in subsurface hydrology. Keywords Time-dependent velocity . Distance-dependent dispersivity . Semi-analytical solutions . Finite domain
Introduction Both analytical and numerical techniques have been broadly used for contaminant transport in the subsurface for at least five decades to solve so-called advection-dispersion equation (ADE) (Ogata and Banks 1961; van Genuchten 1982; Wexler 1992). The solutions of ADE considering constant parameter coefficients were developed for one-, two- and three- dimensional domains in relatively homogeneous and isotropic Responsible Editor: Marcus Schulz * Zhang Wen [email protected] 1
School of Earth and Environment, Anhui University of Science and Technology, Huainan 232001, China
2
School of Environmental Studies, China University of Geosciences, Wuhan 430074, China
3
Department of Civil Engineering, Baze University, Abuja, Nigeria
medium (Park and Zhan 2001, Kocabas and Bulbul 2015). However, the validity of ADE with constant parameter coefficients has been frequently questio
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