One-dimensional solute dispersion along unsteady flow through a heterogeneous medium,dispersion being proportional to the square of velocity

Abstract

One-dimensional solute transport, originating from a continuous uniform point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Velocity is considered as directly proportional to the linear spatially-dependent function that defines the heterogeneity. It is also assumed temporally dependent. It is expressed in both the independent variables in degenerate form. The dispersion parameter is considered to be proportional to square of the velocity. Certain new independent variables are introduced through separate transformations to reduce the variable coefficients of the advection–diffusion equation to constant coefficients. The Laplace Transformation Technique (LTT) is used to obtain the desired solution. The effects of heterogeneity and unsteadiness on the solute transport are investigated.

Editor D. Koutsoyiannis; Associate editor F.F. Hattermann

Citation Kumar, A., Jaiswal, D.K., and Kumar, N., 2012. One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrological Sciences Journal, 57 (6), 1223–1230.     

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含混合裂隙、孔隙介质的纵波衰减规律研究

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Multi-physics modeling of flow and transport in porous media using a downscaling approach

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A new approach for phase transitions in miscible multi-phase flow in porous media

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly.In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton-Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.     

Cyclic hysteretic flow in porous medium column: model, experiment, and simulations

A periodic vertical movement of the groundwater table results in a subsequent cyclic response of the water content and pressure profiles in the vadose zone. The sequence of periodic wetting and drying processes can be affected by hysteresis effects in this zone. A one-dimensional saturated/unsaturated flow model based on Richards’ equation and the Mualem (Soil Sci. 137 (1984) 283) hysteresis model is formulated which can take into account multi-cycle hysteresis effects in the relation between capillary pressure and water content. The numerical integration of the unsaturated flow equation is based on a Galerkin-type finite element method. The flow domain is discretised by finite elements with linear shape functions. Simulations start with static water content and pressure profiles, which correspond to either a boundary drying or wetting retention curve. To facilitate the numerical solution of the hysteretic case an implicit non-iterative procedure was chosen for the solution of the nonlinear differential equation. Laboratory experiments were performed with a vertical sand column by imposing a high frequency periodic pressure head at the lower end of the column. The total water volume in the column, and the periodic water content profile averaged over time were measured. The boundary drying and wetting curves of the relation between water content and capillary pressure were determined by independent experiments. The simulations of the experimental conditions show a clear effect of the hysteresis phenomenon on the water content profile. The simulations with hysteresis agree well with the measurements. Computed dimensionless water content profiles are presented for different oscillation frequencies with and without consideration of hysteresis.     

A new benchmark semi-analytical solution for density-driven flow in porous media

A new benchmark semi-analytical solution is proposed for the verification of density-driven flow codes. The problem deals with a synthetic square porous cavity subject to different salt concentrations at its vertical walls. A steady state semi-analytical solution is investigated using the Fourier–Galerkin method. Contrarily to the standard Henry problem, the cavity benchmark allows high truncation orders in the Fourier series and provides semi-analytical solutions for very small diffusion cases. The problem is also investigated numerically to validate the semi-analytical solution. The obtained results represent a set of new test case high quality data that can be effectively used for benchmarking density-driven flow codes.     

An extended stability criterion for density-driven flows in homogeneous porous media

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非均匀介质热蠕变流动的数值求解

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Nonequilibrium effects in models of three-phase flow in porous media

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黏弹介质中勒夫波频散问题的统一解及其动态特征分析

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