Modeling Groundwater Flow and Transport

The main purpose for numerically modeling flow and transport in groundwater systems is to solve a variety of problems. For example, a city may use groundwater to supply its public water system; city officials use a model to plan where wells should be located. In another case, wastes may leak into the ground from an industrial facility. A model is used to determine where the contamination is moving and guide scientists in how best to clean it up. Models draw from mathematics, geology, chemistry, and biology.

Overview of the Modeling Process

Modeling flow and transport begins by gathering information about the problem and conceptualizing how the natural system functions based on available data. When the data are gathered and interpreted in a conceptual model, the computer model may then be run. The modeling process begins by setting up the computer model to match the conceptual model, then inputting all the data. Inputs represent the best estimate of how the system functions, but in reality, the result is uncertain. Normally the input values change as the model is calibrated (i.e., adjusted to fit the actual groundwater system).

Once calibration of the model is achieved, results are generated for the specific problem to be solved. In models of water-supply wells, results may be generated to show how the groundwater elevation changes at the well over time when the well is pumped at different rates. Alternately, results may be generated to show how pumping the well affects groundwater discharge into a critical wetland area or stream. In contamination studies, results normally are generated to show the groundwater area that has been contaminated, or the time period that will be required before a chemical moves to the area of a water-supply well. The modeler will decide which results should be generated in order to best present the solution to the problem.

Input Data: Flow and Transport

As noted above, groundwater flow models first require input data, which describe the geometry or shape of the system to be modeled. Questions to ask could be: How thick, wide, and long is the area to be modeled? What types of soils and underlying geological materials are present? How easily can groundwater move through the geologic material in the project area? The person operating the computer model assigns the characteristics of the geologic materials (e.g., permeability and thickness) in the computer program to match the real situation.

The modeler needs information about where the groundwater originates and where it is going. Recharge areas correspond to locations where water enters the groundwater system, either by precipitation that percolates downward through the soil, or where rivers, streams, and lakes leak water into the subsurface. Wastewater disposal and stormwater runoff from city streets also can enter a groundwater system as part of the recharge. Aquifer storage and recovery systems are yet another means by which a groundwater system is recharged.

Discharge areas correspond to locations where water leaves the groundwater system, either naturally via seeps, springs, and streams, or artificially via pumping at wells. In modeling groundwater flow, recharge and discharge areas become the boundary conditions that constrain the model.

Groundwater flows in the direction of the hydraulic gradient. The hydraulic gradient of a river is the slope of the water surface; similarly, the hydraulic gradient of a groundwater system is the slope of the water level in the aquifer . The general direction of groundwater flow can be estimated by determining the direction of the hydraulic gradient. Measurements of groundwater hydraulic head at three or more locations provide this information (see box on this page).

Transport.

When preparing to model the transport of a chemical, the modeler must determine the supply, or source, of the chemical to the groundwater, and where it occurs. The source term for modeling describes the mass (amount) per unit of time (mass loading) entering the groundwater system. For example, it could be determined that nitrate enters the groundwater at a wastewater pond, and it enters at a rate of 9 kilograms per day.

When a chemical moves in groundwater, it disperses within the pore spaces in the aquifer. It also may stick, or adsorb, onto soil particles. A parameter called the dispersivity is used to characterize the dispersion behavior of the chemical. The net effect of dispersion is a dilution of the concentration of the chemical. Another parameter, called the retardation factor, is used to describe the tendency for a chemical to adsorb onto the soil or aquifer particles. The retardation factor has the effect of slowing down the rate of transport.

Many chemical compounds change their identity in groundwater when they undergo a chemical reaction. One chemical compound can turn into another. This process is addressed in transport models by a decay parameter, or decay rate. The model predicts a decrease in the original chemical with time. Some models may track the new chemical(s) formed by decay.

Model Calibration

Calibration is an important procedure in modeling. The computer uses all input data (e.g., recharge, discharge, geologic characteristics) to calculate how the groundwater occurs and how it moves as a function of the input data. During calibration, the model is fit to the actual groundwater system.

In order to judge how well the model fits the actual groundwater system, calibration targets are needed. For example, groundwater flow models calculate the elevation of the groundwater at many locations. When the groundwater elevation is measured in a well at some or all of these locations, then a comparison can be made. The model calculations can be compared to the field measurements; thus, the field measurements become the calibration targets. Calibration targets are then developed that show flow rates (e.g., the discharge of groundwater at a spring or into a river). Calibration targets also can be developed for chemical concentrations in groundwater (e.g., the concentration of a chemical in water pumped from one or more wells).

Calibration traditionally was performed by the trial-and-error method. The modeler simply changed an input value to the model (e.g., hydraulic conductivity or a boundary condition). The model was then executed and the new results were again compared to the calibration targets. This procedure was repeated, perhaps dozens (or even hundreds) of times, until it was no longer possible to obtain a better match to the calibration targets. Today, new computer tools have become available that use sophisticated algorithms to make the calibration changes automatically.

see also Aquifer Characteristics; Artificial Recharge; Fresh Water, Natural Composition of; Fresh Water, Physics and Chemistry of; Groundwater; Hydrogeologic Mapping; Pollution of Groundwater; Supplies, Public and Domestic Water.

Mark Cunnane

Bibliography

Freeze, R. Allan, and John A. Cherry. Groundwater. Upper Saddle River, NJ: Prentice Hall, 1979.

Spitz, Karlheinz, and Joanna Moreno. A Practical Guide to Groundwater and Solute Transport Modeling. New York: John Wiley & Sons, 1996.

DETERMINING GROUNDWATER FLOW DIRECTION

Groundwater hydraulic head is the elevation of the groundwater in a well. By determining the hydraulic head at three or more locations in a groundwater flow system (e.g., by measuring the static water level in wells), hydrologists can draw a map showing lines (contours) of equal hydraulic head. These lines are much like topographic contours showing the land surface elevation, but instead of land, they show the elevation of groundwater hydraulic head. The general direction of groundwater flow under typical conditions occurs at 90degree angles to the contour lines, and from higher to lower hydraulic head.