Evaluation of Zero-Net-Rate Pumping Tests
Accurately estimating the distribution of aquifer properties is key to understanding contaminant movement in the subsurface. The distribution of aquifer properties is typically addressed using slug or constant-rate well tests, and the pros and cons of these tests are well known. Slug tests are appealing because they avoid removing contaminated water, but their results are affected by well skin and the small volume of displaced water limits the volume of aquifer that can be evaluated. Constant-rate well tests have the disadvantage of requiring disposal of potentially contaminated water, but they can generate properties that are more representative than slug tests, and they can be used to estimate well efficiency and storativity, which are difficult to characterize using slug tests. Periodic pumping tests are appealing because they have many of the advantages and few of the disadvantages of slug and constant-rate well tests. Periodic pumping tests involve cycling the pumping rate with a regular period and measuring the resulting response in monitoring wells. Some of these tests involve imposing a periodic rate on a constant mean rate. However, other tests involve moving water out and back into the well at rates that are balanced so the net rate after each period is zero. Some zero-net-rate (ZNR) well tests use rates that follow a sinusoidal pattern, whereas others use a square wave pattern that switches between a constant rate of pumping and a constant rate of injection to achieve a zero-net rate. ZNR well tests appear to be a useful compromise between slug and constant rate tests, but methods for conducting and analyzing the results from these tests have received limited evaluation. Periodic pumping tests are typically evaluated through recorded pressure responses to a disturbance source. Recent work has demonstrated that the strain field in the vadose zone shows a response to disturbances in the underlying aquifer. Various instrument designs are available that can record vertical and horizontal strain to very precise resolutions (10-9 ε). Measuring the strain in the vadose zone can present lower costs than measuring pressure in a monitoring well, so using strain could improve the resolution of ZNR tests, as well as make these tests potentially cheaper. A ZNR periodic pumping system was constructed and used to perform tests in the Clemson, South Carolina area. The system was designed to pump and inject with a periodic square-wave, so pumping occurs at a constant rate for half the period and is followed by injection at the same rate for half the period resulting in no net gain or loss of water from the aquifer. The system is designed to generate flow rates from 1 to 3.5 gallons per minute (gpm) with a capacity of 875-gallon per half period. Pressure and strain monitoring points are located in the vicinity of the pumping well. A series of 10 ZNR periodic pumping tests were conducted at the field site, with periods ranging from 2 to 540 minutes. Pressure data were collected and recorded in four monitoring wells in various locations around the pumping well. In addition, vertical and horizontal strain and tilt data were recorded in various locations around the pumping well. Traditional aquifer tests, including slug tests and constant-rate pumping tests were conducted at the field site to provide a baseline of aquifer parameter estimates that are compared the results of ZNR tests. Pressure data measured at monitoring wells during ZNR tests were analyzed utilizing an analytical solution (Streltsova, 1988) that assumes a confined aquifer and estimates hydraulic diffusivity and transmissivity using the time lag and amplitude of the pressure signal. The storativity can be separated out from the hydraulic diffusivity using the transmissivity estimate. The time-lag and amplitude of the pressure signals were estimated using a Fourier transform. The time-lag of the primary period of the pressure increases as a linear function of distance from the pumping well, and it increases as the square root of the period of the ZNR test over a range of periods spanning two orders of magnitudes. The first few harmonics follow similar trends, but the higher frequency harmonics diverge from this trend. Strain and tilt data from various instruments in the vadose and saturated zones are periodic during ZNR tests. The time lags of the strain components increase roughly linearly with distance from the well. Many of the time lags of the strain data from the vadose zone are similar to the time lags observed in the pressure data from a similar distance and pumping period. Theoretical experiments were performed to understand how pressure and strain responds to ZNR periodic pumping. The time-lags of the simulated pressure responses match the field data trends. The results were used to validate the Streltsova (1988) solution for periodic pumping to estimate hydraulic diffusivity. Hydraulic diffusivity was estimated to be 1.8 x 10-2 m2s-1 < Dh < 9.0 x 10-2 m2s-1 using pressure data from all the wells during ZNR tests. Transmissivity was estimated to be 0.8 x 10-4 m2s-1 < T < 4.3 x 10-4 m2s-1. Assuming Storativity = T/Dh gives 1.1 x 10-3 < S < 19 x10-3. Transmissivity is used to estimate the hydraulic conductivity, K, by dividing by the assumed aquifer thickness. Two constant-rate pumping tests were conducted and analyzed using two conceptual models: The Hantush (1961) solution was used to analyze data assuming confined conditions and the Neuman (1974) solution was used to analyze data assuming unconfined conditions. The Hantush (1961) solution estimated transmissivity to be 1.6 x 10-4 m2s-1 < T < 1.8 x 10-4 m2s-1 when using data from all the wells. Storativity was estimated to be 4.4 x 10-3 < S < 8.2 x 10-3. Assuming Dh = T/S gives 0.22 x 10-2 m2s-1 < Dh < 3.6 x 10-2 m2s-1. The Neuman (1974) solution estimated transmissivity to be 0.80 x 10-4 m2s-1 < T < 0.84 x 10-4 m2s-1. Total storativity (S + Sy) was estimated to be 22 x 10-3 < S < 110 x 10-3. Storativity excluding the Sy term was estimated to be 2.2 x 10-3 < S < 2.5 x 10-3. Assuming Dh = T/S gives 0.073 x 10-2 m2s-1 < S < 0.36 x 10-2 m2s-1. Two slug tests were performed on the pumping well, PW-2. The Bouwer and Rice (1976) solution for slug tests was used to analyze the data. This solution works for both confined and unconfined conditions, so both conceptual models were covered through the analysis. Hydraulic conductivity was estimated to be 1.95 x 10-6 ms-1 < K < 2.49 x 10-6 ms-1. Statistical comparison show generally no significant difference in the estimates of Dh, K, or S made using ZNR and conventional pumping tests.. However, the total storage estimated by the Neuman (1974) solution for unconfined settings is larger than that estimate using the Streltsove analysis applied to the ZNR tests. This is likely because the Neuman solution considers delayed yield from storage that the water table, whereas the Streltsova (1988) solution assumes confined conditions. The analysis also indicates that there is a statistically significant difference between parameters estimated with conventional slug tests and those measured with either constant-rate pumping tests or ZNR tests. Hydraulic diffusivity is estimated from the time-lag and the distance from the well. The time-lags of the strain data from the vadose zone are similar to the lags of the pressure data from a similar distance. This indicates that hydraulic diffusivities estimated from the strain data measured in the vadose zone would be similar to the estimates from the pressure data measured in the aquifer. There appear to be sign reversals in some of the strain data that were corrected to estimate the time lag. The dissolved oxygen (CO) concentration was measured during several ZNR tests to evaluate the feasibility of using the procedure to increase contaminant degradation kinetics that are related to DO. The results indicate that DO can be increased during the cycling of ZNR tests in some cases.