Transmissivity from long-term pumping test at a hard-rock aquifer
Simple solutions for the constant-head pumping test result are discussed, based on the Birsoy-Summer’s and the Jacob-Lohman’s equations. Transmissivity from pumping data is compared to recovery’s for validation purpose.
Introduction
During Fall 2005, constant head test was conducted at a well (Well No.1), located on the foothill of the western Sierra Nevada. The completion report for this well indicates that water was produced from fractures at 295 ft, 333 to 334 ft, 390 to 405 ft, 509 to 510 ft, and 775 ft in depth. Most of the water production was from 775 ft in depth. The pump was set to a depth of 525 ft.
The duration of pumping was about 18 days and the average pumping rate was 185 gpm. Initially, the pumping rate of the well was about 300 gpm. After the first day of the pumping, the pumping level was stabilized at about 210 to 220 ft, to allow the constant head test to be performed. The pumping rate then fell to about 140 gpm after 4 days of pumping.
To obtain more discharge, the pumping rate was then purposely increased. The pumping level was then stabilized at about 310 ft in depth for the rest of the test, maintained above the majority of fracture’s depths. After 18 days of pumping, the rate gradually had fallen to about 160 gpm at the end of the pumping period. Figure 1 shows the decline in pumping rates with time for Well No.1.
Figure 1. Pumping rate during constant drawdown test.
Two analytical methods for constant head test are evaluated:
- Birsoy-Summers method (1980).
- Jacob-Lohman method (1952, in Lohman, 1979).
Birsoy-Summers method
Birsoy-Summers method presents an analytical solution for pumping at different discharge rates. It applies the principle of superposition to Jacob’s approximation of the Theis equation. Kruseman and deRidder (2000) provide the step by step procedures, and example on how to calculate the transmissivity and storage coefficient using Birsoy-Summers (on p.181-185).
Figure 2 is the plot of specific discharge versus the “adjusted time” for pumping test at Well No.1. The graph shows interesting relation between pumping duration and tranmissivity values. Pumping on the first day indicates a transmissivity of 2,640 gpd/ft. Tranmissivity from the next three days of pumping is 480 gpd/ft. Evaluation of the last fourteen days of test data gives a transmissivity of 290 gpd/ft. This occurrence of decreasing transmissivity is generally known as “scale effect”, where longer pumping duration causes larger radius of influence. How the “scale effect” is happened?
Figure 2. Birsoy-Summer's method.
In general, large yielding well is commonly placed in a highly fractured area. As a cone of depression or radius of influence spreads, it eventually encounters less fractured rocks at some distance from the test well. Lesser fractures mean lesser connectivity to transmit water. This explanation for “scale effects” is applicable when there is no significant recharge boundary (flowing river, etc.) that would make the transmissivity appear higher.
Jacob-Lohman method
Figure 3 shows graph for the second method, Jacob-Lohman’s. This method is commonly used for free-flowing wells, where the drawdown in the well is constant and that the discharge decreases with time (Kruseman and deRidder, 2000). Procedure to calculate transmissivity can be learned at Lohman’s (1979) page 23-27. The late and long time measurements provide a transmissivity value of 290 gpd/ft.
Figure 3. Jacob-Lohman's method.
Recovery
Water-level recovery was measured frequently for one week after pumping stopped (Figure 4). Kurseman and deRidder (2000, p.196), and Lohman (1979, p. 27) suggested Theis or Cooper-Jacob method to calculate transmissivity from recovery data. The pumping rate average is 185 gpm. Cooper Jacob recovery method gives transmissivity of 280 gpd/ft, indicates the best value for the deep fracture zone tapped by Well No. 1.
Figure 4. Recovery graph.
In summary, transmissivity from recovery gives value in close agreement with the pumping data (on both calculation methods). Thus, it confirmed the validity of both methods as recovery data is commonly assumed to give better transmissivity value. For analyzing pumping data, the Jacob-Lohman method is easier to execute but inferior to the Birsoy-Summer’s in showing tranmissivity progression through time.
How about the Storage Coefficient? I would like to hear your thought. Please leave your comment here. Thank you.
References
- Kruseman, G.P., and de Ridder, N.A., 1994, Analysis and evaluation of pumping test data (2nd ed): ILRI publication 47, Wageningen, The Netherlands, 377 p.
- Lohman, S.W. 1979. Ground-water hydraulics: U.S. Geological Survey Professional Paper 708, 70 p.
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Thank you, Kevesha. I really appreciate that you have taken time to come here. I will definitely refer to http:watersisweb.org also. Just need to setup a good place for friend’s list.
Be careful, transmissivity and storativity have no meaning or utility in crystalline rock wells because the terms cannot be used to predict the performance of any other well in the same “aquifer” or of the “aquifer” itself. In other words, matching an exponential integral curve or some variant to data does not prove the utility/meaning of the terms generated and use of the method beyond the governing assumptions is absolutely incorrect. Matching a curve to itself is interesting but says little of the aquifer.
Regards
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Please
I Want to calculat The KZ (Horizontal Hydrolic)
Please provide me the equation
Thank you
Mustafa Hadi