Equivalent Freshwater Head Research Articles

Stream functions and equivalent freshwater heads for modeling regional flow of variable‐density groundwater: 1. Review of theory and verification

Steady state flow of variable‐density groundwater is simulated using equivalent freshwater heads and stream functions. On the basis of the work by De Josselin de Jong (1960,1969), fluids with different fluid densities are replaced by one hypothetical fluid, and singularities are introduced along interfaces where the actual fluids change densities. The basic flow equation describing variable‐density flow, written in terms of equivalent freshwater head, is used to derive the corresponding stream function equation and associated boundary conditions. Neumann boundary conditions for the stream function equation can be determined from gradients of equivalent freshwater heads along the boundary. Stream functions provide a direct representation of the groundwater flow pattern and flow rates where fluid densities vary in space. In comparison, equivalent freshwater heads and fluid densities describe the two driving forces, hydraulic gradient and buoyancy force, but head gradients do not necessarily describe the flow direction of variable‐density groundwater in isotropic media. Comparison of the finite element formulations indicates that potential errors in the centroid‐consistent velocity calculation based on the stream function solution can be expected to be smaller than those in the velocity calculation based on the head solution for cross‐sectional flow models, because discretization in the vertical direction is typically finer than in the horizontal direction.

Stream functions and equivalent freshwater heads for modeling regional flow of variable‐density groundwater: 2. Application and implications for modeling strategy

Stream functions and equivalent freshwater heads are used to simulate steady state flow of variable‐density groundwater in a regional, cross‐sectional flow model through the Palo Duro Basin, Texas, where fluid densities vary between 1.0 and 1.15 g/cm3. Centroid‐consistent velocities computed from the stream function solution allow a more precise interpretation of local flow patterns in cross‐sectional models than those from the head solution. Effects of significant fluid density variation on the regional groundwater flow pattern are studied by comparing simulation results that incorporate spatially varying, time‐invariant densities with those that assume uniform density. Modeling shows that the regional groundwater flow pattern in the Palo Duro Basin is not significantly affected by variations in fluid densities, indicating that the topographically driven flow component dominates buoyancy forces associated with dense brines. An exception is near the eastern boundary where high fluid densities cause stronger downward flow. However, simulated equivalent freshwater heads in the variable‐density model differ significantly from simulated heads in the freshwater density model, which is important for model calibration. In addition to the well‐known problems of hydraulic parameter and boundary condition uncertainties, modeling strategies for regional flow systems require consideration of uncertainties associated with fluid density and evaluation of equivalent freshwater head data.

Stream functions and equivalent fresh-water heads for modeling regional flow of variable-density groundwater (2) application and implications for modeling strategy

Stream functions and equivalent fresh-water heads for modeling regional flow of variable-density groundwater (2) application and implications for modeling strategy

Stream functions and equivalent fresh-water heads for modeling regional flow of variable-density groundwater (1) review of theory and verification

Stream functions and equivalent fresh-water heads for modeling regional flow of variable-density groundwater (1) review of theory and verification

The saltwater-freshwater interface in the Tertiary limestone aquifer, southeast Atlantic outer-continental shelf of the U.S.A.

Abstract Hydrologic testing in an offshore oil well abandoned by Tenneco, Inc., determined the position of the saltwater-freshwater interface in Tertiary limestones underlying the Florida-Georgia continental shelf of the U.S.A. Previous drilling (JOIDES and U.S.G.S. AMCOR projects) established the existence of freshwater far offshore in this area. At the Tenneco well 55 mi. (∼88 km) east of Fernandina Beach, Florida, drill-stem tests made in the interval 1050–1070 ft. (320–326 m) below sea level in the Ocala Limestone recovered a sample with a chloride concentration of 7000 mg l −1 . Formation water probably is slightly fresher. Pressure-head measurements indicated equivalent freshwater heads of 24–29 ft. (7.3–8.8 m) above sea level. At the coast (Fernandina Beach), a relatively thin transition zone separating freshwater and saltwater occurs at a depth of 2100 ft. (640 m) below sea level. Fifty-five miles (∼88 km) offshore, at the Tenneco well, the base of freshwater is ∼1100 ft. (∼335 m) below sea level. The difference in approximate depth to the freshwater-saltwater transition at these two locations suggests an interface with a very slight landward slope. Assuming the Hubbert interface equation applies here (because the interface and therefore freshwater flow lines are nearly horizontal) the equilibrium depth to the interface should be 40 times the freshwater head above sea level. Using present-day freshwater heads along the coast in the Hubbert equation results in depths to the interface of less than the observed 2100 ft. (640 m). Substituting predevelopment heads in the equation yields depths greater than 2100 ft. (640 m). Thus the interface appears to be in a transient position between the position that would be compatible with present-day heads and the position that would be compatible with predevelopment heads. This implies that some movement of the interface from the predevelopment position has occurred during the past hundred years. The implied movement is incompatible with the hypothesis that the freshwater occurring far offshore in this area is trapped water remaining since the Pleistocene Epoch.

Simulation of long-term transient density-dependent transport in groundwater

A numerical model for the economical simulation of long-term transient response in density-dependent transport problems is introduced. Although a classical Galerkin finite element approach is used, emphasis on optimum efficiency throughout the development results in a scheme that is found to be significantly less costly than comparable existing schemes. This advantage in efficiency increases the scope of simulation problems that can be handled within the constraints of a limited research budget. Some distinctive aspects are the elimination of static quantities in the fluid continuity equation, achieved by the introduction of equivalent freshwater head, and the elimination of numerical integration, achieved by the deliberate choice of linear elements. As a result of this choice, fluid velocities are discontinuous across the element boundaries. It is shown, however, that the solution obtained with discontinuous velocities approaches that obtained with continuous velocities as the grid is refined, and that the two types of solutions give essentially the same results when the elements are in the same size range. The model is applied to simulate the complete transient response for a well-known problem of seawater intrusion in a confined aquifer. The simulation is performed with both the constant dispersion coefficient used by previous researchers, and a more physically realistic velocity-dependent dispersion coefficient. Responses are found to be substantially different for the two types of coefficients, with the velocity-dependent dispersion coefficient producing much slower convergence to a state of dynamic equilibrium, and a much more pointed saltwater toe, which at the bottom of the aquifer tends to a sharp interface at equilibrium. Finally, it is shown by means of large-scale applications that the model is capable of efficiently simulating the long-term transient response in systems of practical significance.

Seawater intrusion in continuous coastal aquifer-aquitard systems

The problem of seawater intrusion in a confined coastal aquifer is investigated. The aquifer is overlain by a leaky aquitard and both units extend continuously out under the sea. The problem is formulated in terms of the two governing differential equations, the fluid continuity equation written conveniently in terms of equivalent freshwater head, and the mass continuity equation. Use of linear rectangular finite elements, with direct integration and an iterative solution technique lead to an efficient numerical scheme that is capable of handling long simulation periods. The results, for a 300 m thick aquifer overlain by a 100 m thick aquitard, show that the aquitard has a controlling influence on the salt distribution. A zone of mixing in the aquifer is found to extend for several kilometres in the seaward as well as the landward direction. The time period required by the system to attain a state of dynamic equilibrium after a perturbation is applied may be of the order of centuries. The aquitard is found to cause a downward and seaward displacement of the average salt front.

Cyclic flow of salt water in the Biscayne aquifer of southeastern Florida

Observations over a period of nearly 20 years confirm the fact that the salt-water front in the Biscayne aquifer along the coast of the Miami area, Florida, is dynamically stable at a position seaward of that computed according to the Ghyben-Herzberg principle. During periods of heavy recharge the fresh-water head is high enough to cause the fresh water, the salt water, and the zone of diffusion between them to move seaward. In addition to this bodily movement of the system, there is a seaward flow of diluted salt water in the zone of diffusion. When the fresh-water head is low, salt water in the lower part of the aquifer intrudes inland, but some of the diluted sea water in the zone of diffusion continues to flow seaward. Cross sections showing equipotential lines in terms of equivalent fresh-water head show that the sea water flows inland, becoming progressively diluted with fresh water, to a line along which there is no horizontal component of flow, after which it moves upward and returns to the sea. The cyclic flow acts as a deterrent to the encroachment of sea water because of return to the sea of a part of the inland flow.