5.4 Data Analysis
Following test completion, time‑drawdown and time‑discharge rate data must be generated (Figure 10) in a form usable for test analysis. Data may need to be corrected for instrument accuracy errors and operator errors. It may also be necessary to correct the data for water‑level changes not directly related to the pumping test such as precipitation events and additional drawdown (or drawup) due to changes in the pumping rate of nearby wells. The first step is to correct the collected water level data, then compute drawdown.
Correcting Water Level Data
Most hydrogeologists convert transducer data to equivalent water levels and then correct the data for barometric effects, and for natural pre‑pumping water level trends and well interference responses. However, they rarely report instrument and operator errors that affect raw water level measurements. These conditions should also be accounted for when water level data are corrected, and drawdown computed. A discussion of water level corrections that addresses a number of factors including accounting for instrument and operator error follows.
Correction for instrument and operator errors are presented using the following example. Assume a water level measured during a constant rate pumping test at 100 minutes is 25.870 m below the top of the casing monitoring point. This measurement is recorded using electronic water‑level measuring tape #2 of the three tapes used to record water level changes at the site. This tape was calibrated to a standard steel tape and found that the readings should be uniformly reduced by 0.006 m (instrument error): WL = 25.870 m ‑ 0.006 m = 25.864 m. The operator attempted to quantify how precisely she could measure the water level and took three measurements of the background water level in this well before pumping was initiated: 20.545 m, 20.549 m, and 20.543 m. This results in an average water level of 20.547 with a range of 0.002 to ‑0.004 m. Thus, the operator error was expressed as a standard deviation is 0.003 m. So, the water level measured by an operator using electric tape #2 is 25.864 with a standard deviation of 0.003 m. The background water level is reported as follows.
20.547 m +/‑0.003 m (average) – 0.006 m (instrument error) =
20.541 m +/‑0.003 m (background)
The drawdown is calculated as follows.
25.864 m +/‑0.003 m (operator error) – 20.541 m +/‑0.003 m (operator error) =
5.323 m +/‑error
The error computed when adding or subtracting is determined as follows.
(error12+error22)0.5 = ((0.003)2 + 0.003)2 )0.5 = 0.004 m
The reported drawdown at 100 minutes is then 5.323 m+/‑0.004 m. Though rarely done the computed drawdown value should be plotted with error bars. At scales typically used to compute time‑drawdown data, small error bars will be difficult to depict and are usually omitted.
The example above illustrates how to correct water level measurements assuming only measurement and operator errors are present. This is rarely the case. A number of other conditions can also affect observed water levels and require adjustment (correction) of the water level data before drawdown attributed to only the formational properties can be computed.
- A naturally occurring trend in water levels occurring before and during the time test period. For example, if the pre‑pumping water level was declining at a rate of 0.25 m per day then starting with the background water level at the beginning of the test, water level data would need a correction of (0.25 m/d)(1 d/1440 min) = 0.00017 m/minute as the test proceeds. For example, at 100 minutes since the beginning of the test, the background water level would have declined (100 min) (0.00017 m/min) = 0.017 m, so the measured water level at 100 minutes would have to be corrected by adding 0.017 m to the measured water level (the measured water level reflects the natural declining rate).
- Starting or stopping of pumping from nearby wells. When the cone of depression of a pumping well that is not used for the test overlaps an observation or pumping well used for the test, additional drawdown occurs as explained in Section 11. This will be recorded as an anomalous increase or decrease of drawdown. If these events are short lived, the field water level trend prior to the disturbance can be extended and the observed water level data corrected by substituting water levels for the trend before interference occurred.
- Recharge or impermeable boundary effects. Recharge or impermeable boundaries can slow or increase drawdown rates (respectively) in the pumping well or observation wells. When the goal is to generate time‑drawdown data for analyses, these records can be truncated as trends change and the early data used in analyses. Another option is to analyze the data using image well theory as described in Section 11.
- Well construction effects. The rate of drawdown measured in the pumping well can be influenced by well construction design (fully or partially penetrating screens) and turbulence as water enters the well bore and flows to the pump (well loss). Both conditions result in greater drawdown than if the wells were 100 percent efficient (i.e., neither condition was present). Corrections are needed before drawdown can be computed. Corrections for partial penetration and well loss are presented in Section 12. Delay of drawdown in the pumping well may be caused by storage in the well bore. This is a problem because many analysis techniques assume the well bore to have infinitesimal diameter such that pumped water is immediately removed from the aquifer. In the field, water initially comes from water stored in the well bore before impacting the aquifer causing drawdown to proceed more slowly than the theoretical model represents. This is particularly problematic when there is a relatively low discharge rate from a large diameter well.
- Barometric pressure, tidal, and direct loading effects on confined systems. Observation well drawdown in confined aquifers can also be affected by these influences. Correction methods are described in references such as Todd and Mays (2005). Transducer data need to be calibrated to water level measurements and instrument errors using manufacturer’s specifications. In addition, if the transducers are unvented, corrections for changes in barometric pressure during the test period are required (Todd & Mays, 2005). An example of manufacturer’s information is provided by Solinst™ at this link↗.
- Effects of local recharge events (rainstorms), changing river stage, tidal changes, and diurnal evapotranspiration from phreatophytes on unconfined aquifers. These effects can influence observed water levels in unconfined systems (e.g., Todd & Mays, 2005). Water level data exhibiting these effects during a pumping test require correction prior to calculating drawdown.
Corrected water level data are then used to compute drawdown data. The resulting time‑drawdown data are used to compute aquifer properties.
Determining the Test Pumping Rate for Analysis
Discharges measured during the pumping test are used to calculate the effective discharge rate for analysis of time‑drawdown data. The pumping rate, time, and, if required, the new adjusted rate, are recorded on the data sheets during a test. When a constant‑rate test is conducted, the effective rate is computed from time‑weighting the measured pumping rates and then computing an average pumping rate. If gauge accuracy is known, error can be assigned.
An example of computing a time‑weighted average pumping rate is provided in this paragraph. A 2‑hour pumping test is designed at a rate of 3,740 L/minute (L/ min). However, a constant rate was not obtained during tests, which is not unusual. Assume that the discharge measurement record is 3,710 L/min at 10 minutes, 3,751 L/min at 20 min, 3,741 L/min at 30 min, 3,750 L/min at 60 min, and 3,731 L/min at 120 min. The time‑weighted average rate is computed as ((3,710 L/min x 10 min) + (3,751 L/min x 10 min) + (3,741 L/min x 10 min) + (3,750 L/min x 30 min) + (3,731 L/min x 60 min)) / (120) min = 3,737 L/min.