Numerical analysis of stable brine displacements for evaluation of density-dependent flow theory

doi:10.1016/S1464-1909(01)00014-4

Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere

Volume 26, Issue 4, 2001, Pages 325-331

https://doi.org/10.1016/S1464-1909(01)00014-4 Get rights and content

Abstract

A numerical modelling approach, used for the analysis of stable brine displacement results, is described. The purpose of the analysis is to evaluate recent theoretical advances in modelling of density-dependent flow and transport. The data analysis involved two stages. A model based on the classical density-dependent transport theory was developed for the first stage of the analysis. Transport parameters were obtained using a sequential fitting method. The numerical model was then modified to incorporate a non-linear dispersion theory that had been recently proposed for high concentration displacements. This modified model was used to reanalyse the results obtained from the brine displacement experiments. Overall, the results of the analysis indicated that a modified transport model was required to adequately describe stable brine displacements.

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This issue has been investigated in detail in several studies that assess the numerical dispersion arising from different discretization methods (e.g., Radu et al., 2011) or that propose techniques to alleviate this error (e.g., Suciu et al., 2013; Wu et al., 2019; Pathania et al., 2020). Despite its recognized importance, however, numerical dispersion in groundwater solute transport modeling has received little attention in the water resources literature, and it is seldom discussed as a potential source of error in modeling applications (Watson and Barry, 2001; Woods et al., 2003). Recently developed integrated surface–subsurface hydrological models (ISSHMs), such as CATchment HYdrology (CATHY; Camporese et al., 2010), HydroGeoSphere (HGS; Brunner and Simmons 2012), and MIKE SHE (Long et al., 2015), are being increasingly used not only for catchment-scale flow applications but also for coupled simulations of solute transport in the surface–subsurface continuum (e.g., Liggett et al., 2015; Scudeler et al., 2016b; Daneshmand et al., 2019; Gatel et al., 2019).
Integrated surface–subsurface hydrological models (ISSHMs) are increasingly being used for the assessment of contaminant transport in the environment, in addition to their more common use in water flow applications. However, the subsurface solute transport solvers in these models are prone to numerical dispersion errors. Numerical dispersion is a well-known issue in groundwater modeling, but its impacts on the results of ISSHM simulations are still poorly understood. In this study, the CATchment HYdrology (CATHY) model is used to assess the potential impacts of numerical dispersion on the simulation of coupled surface–subsurface solute transport. We first simulate the subsurface transport of a nonreactive tracer in two soil column test cases (1D and 3D) with known analytical solutions. The subsurface solute transport solver in CATHY adopts a computationally efficient time-splitting technique whereby the advection component of the governing equation is solved on elements and the hydrodynamic dispersion component is solved on nodes. Comparison between simulation results and analytical solutions with different mesh discretizations and different values for the hydrodynamic dispersion coefficients allows for accurate quantification of the numerical dispersion error and yields insights into the parameters and other factors that control it. It is shown that, taken alone, the advection and dispersion solvers are very robust, but their combination can result in significant numerical dispersion, stemming from the exchange of concentration information from elements to nodes and vice versa in the time-splitting procedure. The tests also show that these errors can be kept under control by ensuring that the grid Péclet number is in the range 0.5-1.0 or smaller. We then apply CATHY in a third test case involving two synthetic hillslopes (concave and convex) in fully coupled surface–subsurface mode, in order to examine the impact of this subsurface numerical dispersion on simulated streamflow hydrographs, in particular with reference to pre-event water contributions to runoff. Here as well the results show that the effect of numerical dispersion can be controlled by keeping the grid Péclet number sufficiently small. This work provides a new set of benchmark test cases for integrated surface–subsurface hydrological models, extending to solute transport the flow-only suite of benchmarks recently published in two intercomparison studies.
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Understanding the discharge behaviour of saline groundwater into fresh surface water can be critical for the effective management of water resources. While variable density flow has been studied intensely in a number of settings, the role it plays on the discharge behaviour of saline groundwater into freshwater streams is often neglected when calculating salt loads into a stream. The aim of this study was to determine what role variable-density flow behaviour plays in surface water/groundwater interaction in a stably-stratified fresh surface water/saline groundwater interface. The mixed convection ratio M, a measure of the ratio of density driven flow to advective driven flow, was defined for a matrix of one-dimensional numerical simulations that employed both varying hydraulic and density gradients. Vertical salt breakthrough into the surface water only occurred in the advection dominated cases (M < 1) and the salt flux into the surface water increased with increasing groundwater concentration until M reached a value of 1. Beyond this, when the flow was driven by the density difference between the two fluids (M > 1) vertical discharge of salt into surface water did not occur and the saltwater/freshwater interface migrated downwards with increasing density differences between the two fluids. This study therefore shows that there is a critical concentration difference that maximises salt loads to a surface water body and that a density-invariant approach to estimate the salt flux into the surface water (as the product of flow velocity determined through a potentiometric analysis and groundwater concentration) may be inadequate, especially where large density differences exist between the fresher surface water body and the underlying saline groundwater. The study is a purely theoretical approach and conclusions were drawn from simplified 1D simulations. Hence, further laboratory and modelling work is needed to confirm and test the plausibility of these findings for more realistic 2D and 3D cases.
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Computer models must be tested to ensure that the mathematical statements and solution schemes accurately represent the physical processes of interest. Because the availability of benchmark problems for testing density-dependent groundwater models is limited, one should be careful in using these problems appropriately. Details of a Galerkin finite-element model for the simulation of density-dependent, variably saturated flow processes are presented here. The model is tested using the Henry salt-water intrusion problem and Elder salt convection problem. The quality of these benchmark problems is then evaluated by solving the problems in the standard density-coupled mode and in a new density-uncoupled mode. The differences between the solutions indicate that the Henry salt-water intrusion problem has limited usefulness in benchmarking density-dependent flow models because the internal flow dynamics are largely determined by the boundary forcing. Alternatively, the Elder salt-convection problem is more suited to the model testing process because the flow patterns are completely determined by the internal balance of pressure and gravity forces.
Validation of classical density-dependent solute transport theory for stable, high-concentration-gradient brine displacements in coarse and medium sands
2002, Advances in Water Resources
Citation Excerpt :
When analysing the results from each displacement experiment, initial guesses for the soil parameters in the four soil regions (regions I–IV) were selected. Values for the soil porosity and spreading parameter (either the longitudinal dispersivity or hydrodynamic dispersion coefficient) in the lowest soil region (region I) were then determined using the optimisation programme to fit a numerical solute breakthrough curve to the experimental breakthrough curve at level L2 [27]. The best-fit values for the porosity and spreading parameter were completely determined by the shape of the solute breakthrough curve at level L2, the distance between the probes at levels L1 and L2, and the separation of the breakthrough curves between level L1 (entered as a boundary condition) and L2.
A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcy's and Fick's laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcy's law was not necessary. On the other hand, an extension to Fick's Law was needed to model the experimental data accurately.
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2023, ANZIAM Journal

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Numerical analysis of stable brine displacements for evaluation of density-dependent flow theory

Abstract

Adv. Water Resour.

An Experimental Investigation of High Concentration Displacements in Saturated Porous Media

Experimental investigation of brine transport through sand

Experimental evaluation of a brine transport model

A review of the influence of clay-brine interactions on the geotechnical properties of Ca-montmorillonitic clayey soils from western Canada

Canad. Geotech. J.

Numerical analysis of the snow-plow effect

Soil Sci. Soc. Am. J.

Numerical analysis of the precursor effect

Soil Sci.

Effect of salinity on the drying behaviour of mine tailings

Long-term stability of spent nuclear fuel waste packages in Gorleben salt repository environments

Nucl. Tech.