1 Introduction

The word ‘velocity’ is a familiar one in the public lexicon. It brings to mind a baseball flying past a swinging bat, or a car hurtling down the highway. For most people, velocity is synonymous with ‘speed’. However, for those in the sciences, the word velocity contains two important components: speed, as alluded to above, and the direction of movement. For those who study groundwater, both of these quantities are conveniently available through the application of Darcy’s Law (discussed in depth in the following section), which relates flow rate to measurable physical characteristics of aquifers and dates back to 1856. However, though Darcy’s Law is widely used to estimate groundwater velocity, it is only one of several methods currently available (Figure 1).

Contextual diagram showing selected alternative methods for determining groundwater velocity and their general classifications as direct or indirect methods
Figure 1 – Contextual diagram showing selected alternative methods for determining groundwater velocity and their general classifications as direct or indirect methods. All are discussed in detail in the following sections of this book. Clockwise from top: Darcy’s Law method, point dilution methods, heat pulse flowmeter method, IWPVP, ISPFS, PVP, and multi-well tracer tests.

As contaminants in groundwater have gained attention, and been found to depend — sometimes profoundly — on the details of aquifer structure for their fate and transport behaviors, opportunities to augment Darcy’s Law with alternative methods, such as those in Figure 1, have gained attention and value. The efforts to develop these technologies have varied both in approach and level of success. The technologies, discussed in later sections, that have shown promise are summarized in Table 1 and a graphical representation of the areas of strength, by classification from Figure 1, is given in Figure 2.

Conceptualization of the applicability of the groundwater velocity techniques discussed in the text
Figure 2 – Conceptualization of the applicability of the groundwater velocity techniques discussed in the text. The vertical axis indicates two aspects: increasing geologic complexity; and sediment texture. The horizontal axis reflects applicability as a function of scale, as defined by borehole spacing. The most reliable results at low scales come from instruments in dedicated holes (no wells) that are not limited by filter packs or well screen interferences. However, the dedicated borehole instruments require complete sediment collapse around the instruments. So, as aquifer sediments become more complex or cohesive, the in-well tools become preferred for small scale measurements. Intermediate scales may be characterized with either single-borehole techniques or Darcy-based methods that are insensitive at lower scales. At large scales (i.e., large distances between wells) Darcy methods suffer from uncertainties in the continuity of geological conditions between wells, so locations needing accurate velocity estimates might benefit from in-well measurements. The gray step pattern in the background of the Figure is a reminder that geologic REVs change with scale.

Table 1 – Summary of groundwater velocity measurement techniques discussed in the text. Within each of the method categories, the range of measurements can extend from a few centimeters per day to tens of meters per day, though this full range of performance is both tool specific and site specific, depending on conditions encountered. Cells colors are matched to Figure 2. [View a full-width version of  Table 1 on a separate web page.]

Method Scale Examples Instrumentation/Description Comments Application for best advantage
Darcy-based methods
  • generally, ~10 m to ~100m separation between wells
  • local to regional investigations common
  • conventional site investigation based on water level survey and estimation of hydraulic conductivity (K)
  • wells and water level tapes or sondes
  • measure head in wells for gradient across domain and obtain domain K value. Data collection requires minutes per well
  • scale dependent on the number and spacing of K measurements
  • scale dependent on the method of K measurement
  • limited by measurable differences in water levels, heterogeneity between wells, and hydraulic connectedness between wells
  • generalized flow characterization
  • forecasting of overall plume migration
  • application of Darcy’s Law in digital models
  • computer
  • match field distribution of hydraulic head in a computer model through calibration informed by field data on geology, hydraulic conductivity – generally, requires days to weeks to complete
In-well velocity techniques
  • centimeter to meter scale measurements from single wells
  • larger scale flow patterns possible with multiple wells and complimentary information (e.g., geophysical, Darcy, modeling)
  • point dilution and finite dilution point dilution (FVPD) methods
  • Drost et al., 1968; Brouyere et al., 2008
  • pump, packers, tracer injection system
  • inject solute tracer into test interval in well and, with mixing, measure concentration decline – requires minutes to hours to complete
  • measured flow depends on possible interferences from filter packs (if present), disturbed zone in the borehole outside well casing, and the well screen
  • best results expected in wells that have been developed extensively
  • PFM measured time averaged fluxes over days to weeks, other methods return minutes to hours for measurements
  • Some techniques can be coupled with other sensors or sampling ports
  • local flow patterns
  • verification of Darcy’s law calculations
  • identification of preferred flow zone in vertical profiles
  • direct velocity measurements in cohesive sediments (silt and clay content), or high gravel fraction
  • passive flux meter (PFM)
  • Hatfield et al., 2004
  • PFM instrument supplied by vendor
  • deploy instrument into well or borehole and leave for days to weeks – recover instrument and send to laboratory for analysis
  • in-well point velocity probe (IWPVP)
  • Osorno et al., 2018
  • in-well probe, tracer injection pump, datalogger
  • deploy in well or borehole, release tracer (saline, deionized water, or heat) – reposition and repeat for profiling – requires minutes to hours to complete each test
  • colloidal borescope
  • Kearl and Roemer, 1998
  • in-well instrument with camera, up-hole monitor and computer
  • deploy in well or borehole, allow flow to re-equilibrate, track colloids in water as they pass through the instrument in the well – requires minutes to hours to complete
  • heat pulse flowmeter (HPF)
  • Kerfott and Massard, 1985
  • probe supplied by vendor must be packed in glass beads and a ‘fuzzy packer’, up-hole control panel
  • deploy in well or borehole, activate heater, record temperature changes at thermistors. Interpretation may require expert assistance – requires minutes to complete
  • direct velocity technique (DVT)
  • Essouayed et al., 2019)
  • in-well device, up-hole tracer injection and detection system
  • deploy in well or borehole, release tracer into window drain tube at known rate while monitoring outflow concentrations – requires minutes to hours to complete
Dedicated borehole techniques
  • centimeter to meter scale measurements from single boreholes
  • larger scale flow patterns possible with multiple boreholes and complimentary information (e.g., geophysical, Darcy, modeling)
  • point velocity probe (PVP)
  • Labaky et al., 2007
  • probe(s) attached between lengths of casing, tracer injection system and datalogger
  • deploy instrument as multilevel stack or single in dedicated borehole that is allowed to collapse around the casing – release tracer (e.g., saline, deionized water, heat) and track as it moves on the perimeter of the instrument – requires minutes to hours to complete
  • require borehole dedicated to the instrument
  • subject to interferences related to disturbed zone surrounding borehole
  • scale depends on number of instruments deployed
  • PVP can be coupled with other sensors or sampling ports
  • vertical flow measurable in principle but ISPFS vertical flow data should be interpreted with particular caution
  • local flow patterns
  • non-cohesive sediments (usually high component of sand)
  • permanent installations suitable for time series measurements
  • multilevel deployment useful for mass discharge monitoring
  • in-situ passive flow sensor (ISPFS)
  • Ballard, 1996
  • instrument supplied by vendor, up-hole control panel
  • deploy the instrument in dedicated borehole that is allowed to collapse around the casing – warm the outside surface to steady state and measure final temperature distribution on surface – requires minutes to hours to complete

Figure 2 is provided only as a general indication of the methods’ areas of strength. For example, the greatest strengths of the single borehole methods arise from their ability to identify relatively small-scale geologic features (centimeters to meters in size) that affect contaminant transport in important ways, such as preferred flow channels. Such features can be continuous over large scales, making single borehole methods relevant over any scale of practical value to hydrogeological studies. However, the larger the scale the more measurement points are required to ensure an accurate characterization. This could become cost prohibitive in many cases, so single borehole methods are likely to be most used in investigations at relatively small spatial scales.

Of the single borehole methods, the dedicated instrument methods (probes not expected to be reclaimed from the borehole and reused elsewhere) are expected to be the most reliable because they are subject to fewer sources of bias, such as filter packs and well screens. Offsetting this advantage, is their dependence on good contact between the instrument and the aquifer sediments and this restricts their use to non-cohesive aquifers (with generally high components of sand or fine gravel) and carefully executed methods of emplacement. As geologic complexity increases, an aquifer may be more reliably accessed with a well and the in-well methods may be preferred.

At scales of tens or hundreds of meters, Darcy’s Law based approaches are expected to gain utility and cost-effectiveness. As with the single borehole methods, larger scale problems require a larger number of monitoring points, i.e., wells or piezometers, to ensure the variability of the aquifer is represented in the ultimate data set. Nevertheless, in regional scale studies, wells may be placed kilometers apart. Large inter-well spacings tend to reduce the apparent variability in flow, which can be appropriate if a large-scale picture of flow patterns is the goal of the work. If such averaging is of concern — at any scale — then the single borehole methods could provide data that are complimentary to the Darcy-based methods, especially for cases where small and intermediate scales of investigation are of interest.


Groundwater Velocity Copyright © 2020 by J.F. Devlin. All Rights Reserved.