R. E. Volker

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face

Experimental investigation of contaminant transport in coastal groundwater

Contaminant transport in coastal aquifers is of increasing interest since, with the development of coastal areas, contaminants from surface sources may enter coastal aquifers and pollute the groundwater flow. Coastal groundwater flow is complicated because of the presence of a freshwater-saltwater diffusion zone and the tidal variation of sea level at the seaward end. This paper investigates experimentally the behaviour of contaminant plumes with different densities in an unconfined coastal aquifer. Experiments were performed in a flow tank filled with glass beads as the porous medium. Results show that the dense contaminant has a more diffusive front than the less dense one in the seaward direction towards the coastline. The plume becomes more diffusive when it travels closer to the saltwater interface. On the contrary, the less dense contaminant presents a relatively sharp outline. It tends to migrate in the upper portion of the aquifer and exits in a concentrated manner over a small discharge area at the coastline, not further seaward under the sea. Non-dimensional parameters show that instabilities occur in our experiments for a density difference of 1.2% or larger between the contaminant and the ambient water. The experimental results provide guidance for field monitoring and numerical modelling

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution

Experimental examination of solute transport by surface runoff from low-angle slopes

The removal of chemicals in solution, by overland flow from agricultural land has the potential to be a significant source of chemical loss from zero-till and surface mulched farming systems. The objective of this study was to determine the magnitude of solute loss by surface runoff from agricultural systems. Previous experiments have enhanced the understanding of the exchange process, but the initial soil conditions together with the tracer application method in these experiments have meant that in some cases the results have limited applicability to field situations. In this study, two different sets of experiments were carried out to determine the magnitude of solute loss by surface runoff. These experiments entailed the surface application of bromide to (1) field scale plots 18 m long by 2 m wide and (2) repacked soil cores 236 mm in diameter; followed by the application of simulated rainfall in both cases. The most substantial finding of the field experiments was that the quantities of solute in surface runoff varied greatly with soil type and structure (0.07-14.9% of the applied bromide). Also, on some soils, large quantities of tracer were measured in the surface runoff even after several hours of infiltration. The experiments on soil cores showed that soil structure plays an important role in the quantity of chemical that may be transported in the surface runoff. These field results showed that, in certain systems, solute movement by overland flow is an important transport mechanism, which should be considered when budgeting for chemical loss.

Numerical correction for finite-difference solution of the advection—dispersion equation with reaction

Abstract A correction for truncation errors associated with a finite-difference solution of the advection-dispersion equation with reaction is developed from a Taylor analysis. An explicit finite-difference scheme is used to show the effect of these truncation errors on the solution of an advection-dispersion equation with a first-order reaction term. The criteria for the stability of the finite-difference solutions are derived using a matrix method proposed by Smith (1978). Comparison with an analytical solution shows that the uncorrected errors are not negligible and that by correcting the finite-difference scheme for them the results will be more accurate. The approach can also be used for correcting other finite-difference schemes whenever they do not have second-order accuracy.

Numerical modelling of contaminant transport in coastal aquifers

This paper employs a two-dimensional variable density flow and transport model to investigate the transport of a dense contaminant plume in an unconfined coastal aquifer. Experimental results are also presented to show the contaminant plume in a freshwater-seawater flow system. Both the numerical and experimental results suggest that the neglect of the seawater interface does not noticeably affect the horizontal migration rate of the plume before it reaches the interface. However, the contaminant will travel further seaward and part of the solute mass will exit under the sea if the higher seawater density is not included. If the seawater density is included, the contaminant will travel upwards towards the beach along the freshwater-saltwater interface as shown experimentally. Neglect of seawater density, therefore, will result in an underestimate of solute mass rate exiting around the coastline.

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland flow from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff.