Numerical Groundwater Flow Modeling, Part 1

This is the first in a series of blogs on the topic of numerical groundwater flow modeling. The concept of groundwater flow, introduced here, is fundamental to groundwater modeling. Groundwater flow is fairly easy to understand because it is analogous to heat flow, which we experience nearly daily. For example, the heat from your hot coffee (or tea if you prefer), flows from the liquid, through the mug, into the room (or your hands) when the coffee is hotter than the room temperature (Figure 1). If the mug is insulated, the flow of heat slows down. Conversely, a cup of iced tea will warm up to room temperature if left to sit. Thus, heat moves toward areas of cold until the temperature of the coffee/tea and room are the same; then the two are in equilibrium. At equilibrium, there is no flow of heat in any direction (assuming the room is perfectly enclosed and insulated). Aha! Our first assumption! Assumptions are very important in numerical modeling, as you will see.

Figure 1

Figure 2

Let’s transition this concept to groundwater. You may have heard the phrase “water seeks its own level” which is a succinct way to say, water will seek an equilibrium level (thanks to gravity). With heat flow, we saw the movement of heat based on the difference in temperature (high toward low), whereas with groundwater, we see the movement based on the difference in level, specifically groundwater flows “downhill.” Of course it does; except when it doesn’t! So, the concept of “downhill” must be more inclusive than just from high elevation to low elevation. Just like the heat from the coffee can move vertically up to the air above, down to the table below, and in basically all directions seeking equilibrium; groundwater flows from the location where potential energy is high (like the top of a hill) to a location where potential energy is lower (like the bottom of a hill).

Potential is not a complex concept and you have likely experienced it yourself if you have ever filled a balloon with water on a hot summer day. Imagine your water balloon has a pinhole leak and you place the water balloon on the ground with the pinhole pointed to the sky (Figure 2). The water exits the balloon and shoots upward into the air (not downhill at all). This is because the stretched balloon pushes on the water. Outside of the balloon, the pressure is lower, i.e., atmospheric pressure. The potential energy in the stretched balloon is being transferred to the water, causing it to shoot out of the balloon. This stops when the balloon is no longer stretched out and the pressure of the water, air, and balloon are in equilibrium.

There you have it. Now we can say groundwater flows from high potential to low potential and we are free to define potential as elevations and/or pressures (as long as the datum is defined). This is the essence of groundwater modeling.

So, what is the pressure or potential that drives groundwater flow? It is gravity and the weight of the earth though which the water flows. A classic example of groundwater flow is illustrated in the cross-section of a stream valley (Figure 3). In this example, groundwater levels beneath the hill (right) are higher than levels beneath the stream (left). We can describe the levels in terms of elevation or potential and we can draw lines (dashed orange) of equal potential (equipotential lines).

Figure 3

Equipotential lines are not the same as the topographic elevation! The force of gravity drives the groundwater through the hill toward the stream and groundwater flows along the flowline (blue arrow). The velocity of the groundwater can be fast or slow, depending on the resistance to flow imparted by aquifer properties (e.g., hydraulic conductivity). Close to the stream, the groundwater begins to flow upward toward the stream because the stream is the lowest potential even though it is higher in elevation than the groundwater beneath it. Groundwater discharges to streams when the elevation of the stream channel intersects the groundwater equipotential lines. To maintain the conditions shown in this cross-section, there must be a steady recharge of water coming into the hill (assume percolation from rainfall) and a steady discharge of water to the stream; otherwise, there will be no equipotential difference between the hill and the stream, thereby ceasing the flow (like in our coffee mug and balloon).

In the classic example above, we have introduced some physical features of groundwater flow that go into groundwater modeling, including topography, equipotential lines, hydraulic conductivity, recharge from precipitation, and discharge to streams. However, groundwater models don’t have hills, streams, or rain, they are composed of mathematical equations. Numerical groundwater models can be described as simplified simulations of physical phenomena.

Stay tuned for the next LWS blog of this series, we will discuss how these physical phenomena are turned into equations that we use to make calculations, but without boring anyone with the math!

If you have any water resources issues, LWS can help; please contact us for help at 303-350-4090 or by email.

Maura Metheny, Ph.D., P.G.: maura@lytlewater.com

Bruce Lytle, P.E.: bruce@lytlewater.com

Anna Elgqvist, EI: anna@lytlewater.com

Subscribe to LWS blogs HERE!

References

Figure 1: Flickr.com, 2021. Steam rising from hot coffee. Available online at https://www.pinterest.com/pin/490259109407758215/, (accessed 10/29/21).

Figure 2: Inner Child Fun, 2021. Water balloon yo-yos. Available online at https://innerchildfun.com/2011/07/water-balloon-yo-yos.html, (accessed 10/29/21).

Figure 3: BCcampus Open Publishing, 2021. Chapter 14 Groundwater. Available online at https://opentextbc.ca/geology/chapter/14-2-groundwater-flow/, (accessed 10/29/21).