Catalog of Derivative Plots

Derivative analysis is a powerful diagnostic technique for the interpretation of data from pumping tests. Use of the derivative in pumping test analysis can highlight many flow regime features that otherwise may be hard to discover when inspecting drawdown data alone.

A catalog of derivative plots, showing the theoretical drawdown and derivative signatures on log-log axes for different flow regimes, is a useful reference to the practicing hydrogeologist when performing derivative analysis. For example, Figure 1 shows the drawdown and derivative response for a finite-diameter pumping well with wellbore storage in an infinite nonleaky confined aquifer.

Figure 1. Wellbore storage flow regime, infinite nonleaky confined aquifer.

One observes the wellbore storage flow regime at early time when the drawdown and derivative curves both exhibit unit (1:1) slopes (Figure 1). Radial flow in an infinite-acting aquifer shows up as a plateau on the derivative response.

An extensive catalog of derivative plots is available at the Aquifer Testing 101 section of the AQTESOLV web site to help you with derivative analysis. Use the catalog to become familiar with the derivative plot signatures for various well/aquifer geometries corresponding to different flow regimes.

Importance of Smoothing Derivative Data

Derivative analysis is a powerful diagnostic tool that enhances the interpretation of pumping test data. Hydrogeologists use the technique to identify flow regimes, discern boundary conditions and refine the selection of aquifer models.

Derivatives are not measured directly in the field; rather, they are computed by numerical differentiation from drawdowns collected during a pumping test. Straightforward calculation of the derivative from neighboring drawdown measurements typically leads to noisy derivative data. Therefore, smoothing routines are employed to obtain a cleaner derivative signal (Bourdet et al. 1989; Spane and Wurstner 1993).

To appreciate the importance of derivative smoothing, consider field data measured in a deep piezometer during a constant-rate pumping test performed in an unconfined aquifer (Kruseman and de Ridder 1994). Figure 1 is a derivative plot for the piezometer showing drawdown (squares) and derivatives (crosses) computed without smoothing (nearest neighbor method). Without smoothing, the derivative data provide little useful information for the interpretation of this test.

Figure 1. Derivative plot showing derivatives computed without smoothing.

Application of the Bourdet method to smooth the derivatives leads to a derivative plot with useful information (Figure 2). The trough in the derivative curve shown in Figure 2 is typical for an unconfined aquifer with delayed yield. The derivative signature suggests the possibility of using a mathematical model by Neuman (1974) to interpret the data.

Figure 2. Derivative plot showing derivatives computed with Bourdet smoothing.

AQTESOLV features three smoothing methods for computing derivatives including the Bourdet and Spane methods.

More information on derivative analysis is available at Aquifer Testing 101.

Hydraulics of Wells

Hydraulics of Wells by M. S. Hantush (1964) is available for download. This classic work is a recommended reference for the bookshelf of every practicing hydrogeologist.

To find more aquifer testing materials including other links to downloadable resources, check out my reference list at the Aquifer Testing 101 web site.

Three-Day Aquifer Testing Course in Baltimore

I'm very excited about the upcoming aquifer testing course entitled Advanced Aquifer Testing Techniques Featuring AQTESOLV: New Concepts, Field Methods and Data Analysis Procedures to be held in Baltimore, Maryland, USA on April 24-26, 2012. It's the first time that we've offered the three-day course in the USA since 2009.

The instructors at this year's course will include Dr. Jim Butler of the Kansas Geological Survey, Dr. Shlomo Neuman of the University of Arizona and myself. Dr. Butler is well known for his essential book The Design, Performance and Analysis of Slug Tests as well as numerous papers on pumping tests and slug tests. Dr. Neuman, who will be a special guest instructor at the course, is acclaimed for his important contributions to the published literature on the interpretation of pumping tests in unconfined and leaky confined aquifers. I'll be on hand to give personalized instruction on the use of AQTESOLV.

We'll be holding the course at the Camden Yards Conference Event Center in Baltimore's very attractive Inner Harbor area. Camden Yards is the highly regarded ballpark of the Baltimore Orioles; as a bonus, course participants will have a special opportunity to attend an evening baseball game on Day 2 of the course.

For more information and to register for the course, please visit the Midwest Geosciences web site. I hope that you can join us!

Fort Collins 2011

I'm back from another well-attended aquifer testing short course held at the headquarters of In-Situ, Inc.on October 5 and 6, 2011 and the sixth consecutive year that we've traveled to Ft. Collins, CO to present Aquifer Testing for Improved Hydrogeologic Site Characterization Featuring AQTESOLV and the In-Situ LevelTROLL.

Analysis of recovery data combining Agarwal method and derivative analysis.

The course covered topics relating to designing, performing and analyzing both slug tests and pumping tests and included hands-on use of AQTESOLV as a teaching tool. As part of my lectures, I spent a good deal of time going over the finer points of diagnostic methods for pumping tests including derivative analysis, a technique widely practiced in the petroleum industry for well test analysis. I further introduced the class to the Agarwal method for analyzing recovery tests which also drew a lot of attention.

Thanks to all who attended the course and to In-Situ for hosting us! I look forward to doing it again next year.

Enhancing Reliability of Slug Test Data Analysis

Data from an overdamped slug test in a well with a fully submerged screen (screen below water table) may exhibit a concave upward appearance on a plot of log normalized head vs. time. The curvature can make analysis by straight-line methods such as Bouwer and Rice (1976) somewhat ambiguous.

Analysis of slug test data using recommended normalized head range.

Butler (1998) suggests matching straight-line slug test solutions to data within recommended normalized head ranges to overcome ambiguity associated with slug test data curvature and thereby enhance the reliability of data analysis. AQTESOLV, advanced software for slug test analysis, includes the recommended normalized head ranges to assist you with visual curve matching.

Learn more about recommended normalized head ranges and slug testing in Aquifer Testing 101 at the AQTESOLV web site.

Summit in Lawrence, Kansas

On today's date in 1969, Neil Armstrong made history by becoming the first man to walk on the moon. Forty-two years later, July 20th marks another red-letter day with the conclusion of the 1^st Lawrence Summit hosted by Jim Butler and attended by Dan Kelleher and myself. The summit met its primary goal of laying the groundwork for future aquifer testing short courses around the world.

GEMS Research Site (Butler et al. 2000)

Unforgettable moments during the visit included a tour of the venerable Kansas Geological Survey and its GEMS research site, a view of the Allen Field House from Jim's bleacher seats ("Rock, Chalk, Jayhawk!") and a reverential pilgrimage to the James Naismith ("Inventor of Basketball") Memorial. Without question, though, the unsurpassed highlight of the summit was the delightful sushi dinner served to perfection by Jim's daughter, Mai. Many thanks to Jim and wife Yun for their warm hospitality throughout the Lawrence Summit!