Numerical Groundwater Flow Modeling, Part 4
Hydraulic properties and model grids
Figure 1: Grand Canyon
In Part 3 (February 2, 2022) of the LWS series on numerical groundwater modeling, we described the basic elements of the groundwater flow equation. This week’s LWS blog describes the use of model grids to describe hydraulic properties.
Hydraulic properties can be very heterogeneous because geologic materials (e.g., clay, silt, sand, gravel) are deposited in a variety of ways and often in layers that make the hydrologic properties differ spatially on small and large scales. Grand Canyon is a great example of the layering principles that, although not ubiquitous, are very common in aquifer systems (Figure 1).
Different materials typically have different properties. Imagine pouring water into a bucket of sand. The water quickly flows into the sand and occupies the pore space between the grains. If a hole develops in the bottom of the bucket, the water will easily drain out of the sand. In contrast, after pouring water into a bucket of clay, it will take a while for the water to enter pores between the clay particles, then slowly make its way to the bottom and exit the bucket. Can you believe that even though the clay resists the flow of water, a bucket of clay can hold much more water than a bucket of sand? This is one reason why the clumping type of cat litter is made of clay and why gardeners like a little clay in their flower beds. The way clay and sand retain or allow water to pass is related to the hydraulic or aquifer properties of the clay and sand.
Porosity is the hydraulic property that describes the amount of open space (pores) in a material. We will stick with unconsolidated material here, such as sand, silt, clay and gravel, but there is open space in solid rock, just not very much. Examples of the way grains of sand and grains of clay can be arranged (Figure 2) demonstrate that the sand rests on its neighbors and that leaves some pores but makes a fairly solid surface, whereas clays can settle in a very unstable way that leaves large amounts of open space. Have you ever stepped off a riverbank onto a sandy river bottom or into a muddy river bottom? Very different experiences!
Figure 2: Porosity in sand and clay. Modified from Woessner and Poeter (2020)
Permeability and hydraulic conductivity (“K”) are related to the connectedness of the pores. If many water-filled pores are connected, the water can move from one pore to the next. If there are few connections, less water can flow. Sands and gravels, which have fewer pores, have a higher number of connected pores, whereas clays tend to have more pores but fewer connections. Clay also has a stronger chemical attraction to water than sand, which increases its water-holding capacity. Therefore, porosity and hydraulic conductivity are related to the size, shape, and arrangement of the grains.
Now imagine our bucket with a layer of sand at the bottom, a layer of clay in the middle, and a layer of sand on top. Water entering from above will percolate through the upper sand but will be slowed down by the clay. This stratification or layering is very common in geologic materials (Figure 1), which is why model grids are so necessary and handy to characterize these naturally-occurring geologic strata. The properties of the sand and the clay can be represented in different grid cells so the impact of each material on groundwater flow can be represented.
Figure 3: Block-Centered finite-difference grid. Modified from McDonald and Harbaugh (1988)
Each and every grid cell can be assigned a unique set of hydrologic properties, or commonly, layers of grid cells are used to represent stratified materials. For example, the five-layer block diagram (Figure 3) depicts a grid with medium sand (layer 1), silt (layer 2), clay (layer 3), gravel and sand (layer 4) and coarse sand (layer 5). There are 255 grid cells in the 5 rows, 9 columns, and 5 layers. In a block-centered grid of the MODFLOW code, the calculations are represented in the center of the cell. Other model codes offer different grid configurations.
If you have any groundwater resources issues that may require the development and/or interpretation of a numerical model, LWS can help; please contact us!
Maura Metheny, Ph.D., P.G.: maura@lytlewater.com
Bruce Lytle, P.E.: bruce@lytlewater.com
Anna Elgqvist, EI: anna@lytlewater.com
Marlena McConville: marlena@lytlewater.com
REFERENCES
McDonald, M. and Harbaugh, A.W. (1988) A Modular Three-Dimensional Finite Difference Ground-Water Flow Model. In: Techniques of Water-Resources Investigations, Book 6, U.S. Geological Survey, 588.
Woessner, W. and Poeter, E., 2020. Hydrogeologic Properties of Earth Materials and Principles of Groundwater Flow. The GROUNDWATER PROJECT. Available from GW-project.org.
