Groundwater Velocity

2.5.3 Groundwater Velocity

One common, basic relationship connects the flow rate (Q), the velocity (v), and the cross- sectional area of flow (A) in virtually all equations describing flow of fluids, regardless of the scientific (engineering) field of study:

(2.32) One form of Darcy’s law states that the velocity of groundwater flow is the product

Q=v×A

of the hydraulic conductivity of the porous medium (K ) and the hydraulic gradient (i):

(2.33) However, this velocity, called Darcy’s velocity, is not the real velocity at which water

v=K×i

particles move through the porous medium. Darcy’s law, first derived experimentally, assumes that the groundwater flow occurs through the entire cross-sectional area of a sample (porous medium) including both voids and grains (adequately, Darcy’s velocity is called “smeared velocity” in Russian literature). Since the actual cross-sectional area of flow is smaller than the total area (water moves only through voids), another term is introduced to account for this reduction—linear groundwater velocity (v L ). From Eq. (2.32) it follows that that the linear velocity must be greater than Darcy’s velocity: v L ≥ v. One handy parameter that can be used to describe the reduced cross-sectional area of

flow is effective porosity (n ef ), defined as that portion of the overall rock porosity which allows free flow of groundwater (see Section 2.3.1). Accordingly, linear groundwater velocity is expressed by the following equation:

The linear groundwater velocity is appropriate when used to estimate the average travel time of groundwater, and Darcy’s velocity is appropriate for calculating flow rates. Neither, however, is the real groundwater velocity, which is the time of travel of a water particle along its actual convoluted path through the voids. It is obvious that, for practical purposes, the real velocity cannot be measured or calculated.

Two main forces act upon individual water particles that move through the porous medium: friction between the moving water particles and friction between the water particles and the solids surrounding the voids. This results in uneven velocities of in- dividual water particles: some travel faster and some slower than the overall average velocity of a group of particles (Fig. 2.45). This phenomenon is called mechanical dispersion and it is very important when quantifying the transport of contaminants dissolved in groundwater (more on fate and transport of contaminants is given in Chap. 5). Because of mechanical dispersion, the spreading of individual water (or dissolved contaminant) particles is in all three main directions with respect to the overall groundwater flow direction: longitudinal, transverse and vertical. Accurate calculation of travel times and arrival times of water and contaminant particles therefore has to include the phenomenon

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F IGURE 2.45 Schematic presentation of mechanical dispersion caused by varying velocity of water particles and tortuous flow paths between porous medium grains. (Franke et al., 1990.)

of dispersivity. At the same time, quantifying dispersivity accurately, without extensive field testing, including tracing, is virtually impossible.

As explained earlier, the nature of groundwater flow in fractured rock and karst aquifers differs from that in intergranular porous media. Large fractures and conduits, filled with water, do not behave as “Darcian continuum” and the concept of hydraulic conductivity and effective porosity does not apply. Groundwater velocity in such cases cannot be calculated in a meaningful way without extensive field investigations specif- ically targeting particular fractures or conduits—a very expensive proposition for any project type. Dye tracing and tracing with environmental isotopes remain investigative techniques of choice when assessing groundwater flow velocities in fractured rock and karst aquifers (see Benischke et al., 2007; Geyh, 2000).

Because of the unique nature of porous media in karst, groundwater velocity can vary over many orders of magnitude even within the same aquifer system. One should there- fore be very careful when making a (surprisingly common) statement such as “ground- water velocity in karst is generally very high.” Although this may be true for flow taking place in karst conduits and large fractures, a disproportionately greater volume of any karst aquifer has relatively low groundwater velocities (laminar flow) through small fis- sures and rock matrix. However, most dye tracing tests in karst are designed to analyze possible connections between known (or suspect) locations of surface water sinking and locations of groundwater discharge (springs). Because such connections involve some kind of preferential flow paths (sink-spring type), the apparent velocities calculated from the dye tracing data are usually biased toward the high end.