Introduction to Basic Ground-Water Flow

By the earthDr!

Constructing Ground-Water Equipotentials

The value of using contour maps and equipotential maps to define ground-water flow has been illustrated. How is a contour map or equipotential map constructed? First it is necessary to install a minimum of three wells. Perforated pipe is used so that water can drain into the well from the surrounding saturated soils. Three wells are needed for triangulation. Let's see just what is triangulation. In this figure, three wells are depicted in a triangular orientation. The perforated pipe or well screen for our example penetrates approximatelty one foot into the water table. A survey is done to locate the position of each well, both horizontally and vertically. The elevation of the top of well, commonly known as the top of casing, is measured in the survey. All future ground-water levels are measured from the top of the well casing. Subtracting the measured depth to ground-water from the surveyed elevation for the top of the well casing results in the establishment of the water table elevation at that, and only that, well. The elevation of the water table can be established in similar fashion for the position of the water table at the remaining two wells. Now an imaginary line can be constructed on the survey paper between the well with the highest water level elevation and the well with the lowest water elevation. In our example figure to the left, monitoring well No. 1 has the highest ground-water level and monitoring well No. 3 has the lowest ground-water level. The ground-water level at monitoring well No. 1 is at an elevation of 90 feet and the ground-water level at monitoring well No. 3 is at an elevation of 70 feet. The ground-water level at monitoring well No. 2 is at an elevation of 80 feet. The 80 foot elevation must be somewhere on this imaginary line joining monitoring well numbers one and three. Obviously if the surface of the water table is a plane, an 80-foot elevation must be halfway between the 90 foot elevation at monitoring well No. 1 and the 70 foot elevation at monitoring well No. 3. We can now construct a line from the location of monitoring well No. 2 to that point on the imaginary line that has an elevation equal to 80 feet.The line produced by this construction, in this case, would be called the 80-foot contour. Water elevations determined along this 80-foot contour from any additional wells installed along this contour would also have water table elevations of 80 feet. Please note that the 80-foot contour would be at a right angle to an arrow arrow that could be drawn depicting ground-water flow. Ground-water flow is at a right angle to the constructed contour level. Contour levels are used to construct surface maps. Surface maps utilizing contour levels are typically called topographic maps. The contours from these maps indicate points of equal elevation. If contour levels are closely placed, it indicates that surface elevation is changing more over short distances than in other areas where they are not closely spaced. If the ground-water level at monitoring well No. 2 had been 83 feet; then, the 83-foot elevation would have been 13/20 along the imaginary line joining monitoring well No. 1 and No. 3. Often times this is, at best, an approximation. The change in the water level along this imaginary line, joining the monitoring well with the highest water table elevation and the monitoring well with the lowest water table elevation, normally is not changing at a constant rate nor is the surface of the water table normally a plane.

In a 3-dimensional view such as this, it is possible to display the equipotential lines in a plan view (downward view) and in a cross-sectional view (side view). Notice that all of the plan view equipotential lines are paired in like manner with cross-sectional equipotential lines of the same magnitude. These paired equipotential lines describe a plane or a surface. Equipotential surfaces assist in visualization of water-table flow, but from a 3-dimensional perspective. Wells screened at a common equipotential surface have the same static water level (total head - potential) even if the wells are constructed to different depths (elevations).

Practically, it is not possible to complete a well so that the screened interval only intersects one, and only one, equipotential surface. Therefore, let's assume that all the wells have such infinitesimally small-screen lengths so as to preclude them from intersecting any more than one equipotential surface. In other words, all (short-screened) wells constructed with the well screened across the same equipotential surface have the same measured ground-water elevation in the well regardless of the final completion depth of the wells. This figure depicts flat, but slightly, downwardly oriented equipotential surfaces - like the pages in a book which is leaning to the side in your bookcase. The 70 foot equipotential surface can be described locating two other wells somewhere else on this surface, provided that at least one of these wells intersect this surface at a different depth.

But how likely is it to locate the 70 foot equipotential surface that is of itself an infinitesimally small cross-sectional area with an infinitesimally small well screen? The answer to this is that the 70 foot equipotential surface does not have to be intersected by even one well with an infinitesimally small well screen. To simplify the solution to this problem: assume that there are numerous wells situated to either side of the 70 foot equipotential at various spatial locations
. Just as interpolation was used to define the equipotential lines for the water table, interpolating between two wells with static water levels just above and below the 70 equipotential surface can be used to approximately define the 70 equipotential surface. Equipotential surfaces do not have to be plane or flat, regardless of whether they are in the water table or in a confined aquifer (we will discuss a confined aquifer later). Equipotential surfaces can be bent into varied shapes. Bent equipotential surfaces are more commonly the rule even under naturally occurring hydrogeologic conditions that are unaffected by pumping of the ground water. We will see this in future examples. Arrows to define ground-water flow can't be located at a right angle to the equipotential surface. Arrows to denote ground-water flow direction are located normal to the constructed equipotential surface. Remember, that ground-water flow is typically in 3 dimensions and that equipotential lines are just the surface expression of a equipotential surface.