Pumping Test in Leaky and Unconfined Aquifers I. Leaky aquifers Theis solution assumes that all the water pumped is from storage within the aquifer. When this assumption is not met, the observed response to pumping deviates from the Theis solution, as illustrated below: 1 3 s 5 1 10 100 1000 10000 Observation data t Tests Affected by Leaky Confining Beds (Heath, 1983) Theis: no leakage Leakage from storage in confining bed Leakage from other aquifers Theis solution K’, S’ b’ K, S b Q rS2 s = wu( ) where u = 4πT 4Tt Semi-confined (Hantush & Jacob) (leakage from elastic storage in confining bed) Q s = Hu( ,β) 4πT 1/ 2 r 1/ 2 Tb' where β = ()S' S B = 4B K' Leaky (some water from other aquifer) Q s = wu, r 4πT ( B) r K' where = r B Tb' II. Water Table Aquifer Approach #1 (Approximation) The change in transmissivity due to dewatering is assumed to be negligible, that is, T ≈ Kb , where b is the initial aquifer saturated thickness. Then the Theis equation can be applied to an unconfined aquifer with storage coefficient for confined aquifer replaced by specific yield, Sy, Q rS2 s ==wu(), u y 44πT Tt This approach is reasonable only when the drawdown is significantly smaller than the saturated thickness,s ≤ bthat is, Approach #2: (Concept of delayed yield) Stage 1: Similar to response in confined aquifer. No physical dewatering yet. Water pumped is from storage. The value of S estimated from aquifer test represents confined storage coefficient. Stage 2: Intermediate, similar to response in leaky aquifer. Water pumped is partly from storage and partly from gravity drainage. Stage 3: Water pumped is drawn mostly from gravity drainage. Drawdown response conforms to some Theis-type curve again. The value of S estimated from aquifer test represents Sy (specific yield) for unconfined aquifer. 12 3 Neuman solution Q s = wu(,,) u Γ 4πT AB rS2 where u = for early time-drawdown data A 4Tt 2 rSy u = for later time-drawdown data B 4Tt 2 r Kz b is initial aquifer thickness Γ = 2 b Kh Effect of partial penetrating wells The effect of partial penetrating wells is negligible if (1) The length of pumping well screen is close to aquifer saturated thickness (2) The observation well is fully penetrating (3) The observation well is located sufficiently Partially Partially Fully far away, i.e., penetrating penetrating penetrating pumping observation observation well well well r > 1.5b Kh Kv r b Well Loss There is usually a difference between the aquifer head and the water level inside the well bore. This difference is referred to as ‘well loss’. The magnitude of well loss is controlled by pumping rate, well diameter, degree of partial penetration, and aquifer properties. Slug Test (also known as piezometer test, falling/rising head test, or response test) A known volume of water is quickly taken from (or added to) a well. The rate at which the water level falls or rises is measured. • Inexpensive alternative to pumping test • Estimated parameters represents much smaller area than pumping test Three major methods to analyze slug test data: • Papadopulos, Bredehoeft & Cooper (confined aquifer, fully penetrated well) • Hvorslev (confined aquifer, partially penetrated well) • Bouwer & Rice (unconfined aquifer, fully or partially penetrated well) r2 ln(L R) K = e 2Let37 t37: time when the water level h(t)/h0 reaches 37% of initial change Kansas Geological Survey Guidelines for Slug Tests ¾Three or more slug tests should be performed at a given well. If the well has not been properly developed prior to slug testing, the slug test itself might cause additional development. This can be detected by a shift in the calculated transmissivity during the repeated slug tests. Also the slug test can mobilize fine material, which can result in a decrease in formation transsmissivity. ¾Two or more different initial displacements should be used during testing of a given well. A series of tests with initial head displacement, Ho, which varies by a factor of at least 2, should be employed; however, the first and last tests should have the same Ho so that a dynamic skin effect can be detected. ¾The slug should be introduced in a near-instantaneous fashion and a good estimate of the initial displacement should be obtained. This is a basic assumption of the slug-test methodology. While it is easy to accomplish in a low permeability system, it can be difficult to do in a system that has a very rapid response. ¾Appropriate data-acquisition equipment should be used. Manual methods of measurement might be satisfactory for a well in a low permeability sediment that responds over a period of many minutes to hours. For more permeable formations where the total period of response can be less than one minute, a data logger with a pressure transducer is mandatory. The pressure transducer should have the proper sensitivity for the planned head displacement. ¾An observation well should be employed for estimation of the storage parameter. A single well is fairly insensitive to the value of the storage parameter for several reasons. If possible, a nearby monitoring well screened across the same interval should be used to determine the storage coefficient. ¾Method chosen for data analysis should be appropriate for site conditions. Ensure that the chosen method is correct: confined or unconfined aquifer, fully penetrating or partially penetrating well. ¾Use of pre- and post analysis plots should be an integral component of the analysis. Even though care was taken to select the proper method of analysis based on the field conditions (point 6), it is still possible that either the method which was selected, or some assumption that went into the analysis, is wrong. Careful examination of the data plot versus the theoretical model of the test data should be made. While this seems to be an obvious point, in many cases the field data are analyzed with an automated curve- fitting program. A human should still review the final plot. ¾Appropriate well construction parameters should be employed. The effective screen length and screen diameter are critical parameters. If the well is gravel packed, the length and diameter of the gravel pack should be used if the gravel pack is significantly more permeable than the formation. However, if well development is incomplete, the screen length may be more appropriate than the length of the gravel pack. Key Reference: Butler, J.J., 1997, The Design, Performance,. and Analysis of Slug Tests, Lewis Publishers, FL..