TL;DR: The mathematical theory of ground-water hydraulics has been based entirely on a postulate that equilibrium has been attained and therefore that water-levels are no longer falling.
Abstract: When a well is pumped or otherwise discharged, water-levels in its neighborhood are lowered. Unless this lowering occurs instantaneously it represents a loss of storage, either by the un-watering of a portion of the previously saturated sediments if the aquifer is nonartesian or by release of stored water by the compaction of the aquifer due to the lowered pressure if the aquifer is artesian. The mathematical theory of ground-water hydraulics has been based, apparently entirely, on a postulate that equilibrium has been attained and therefore that water-levels are no longer falling. In a great number of hydrologic problems, involving a well or pumping district near or in which water-levels are falling, the current theory is therefore not strictly applicable. This paper investigates in part the nature and consequences of a mathematical theory that considers the motion of ground-water before equilibrium is reached and, as a consequence, involves time as a variable.
TL;DR: The slug test as discussed by the authors is used to determine the hydraulic conductivity or transmissibility of an aquifer by measuring the rate of rise of the water level in a well after a certain volume or slug of water is suddenly removed from the well.
Abstract: ~. help ed. steady Proc. With the slug test the hydraulic conductivity or transmissibility of an aquifer is determined from the rate of rise of the water level in a well after a certain volume or 'slug' of water is suddenly removed from the welL. The slug test is simpler and quicker than the Theis pumping test because observation wells and pumping the well are not needed. With the slug test the portion of the aquifer 'sampled' for hydraulic conductivity is smaller than that for the pumping test even though with the latter, most of the head loss also occurs within a relatively small distance of the pumped well and the resulting transmissibility primarily reflects the aquifer conditions near the pumped welL. Essentially instantaneous lowering of the water level in a well can be achieved by quickly removing water with a bailer or by partially or completely submerging an object in the water, letting the water level reach equilibrium, and then quickly removing the object. If the aquifer is very permeable, the water level in the well may rise very rapidly. Such rapid rises can be measured with sensitive pressure transducers and fast-response strip chart recorders or x-y plotters. Also it may be possible to isolate portions of the perforated or screened section of the well with special packers for the slug test. This not only reduces the inflow and hence the rate of rise of the water level in the well, but it also makes it possible to determine the vertical distribution of the hydraulic conductivity. Special packer techniques may have to be developed to obtain a good seal, especially for rough casings or perforations. Effective sealing may be achieved with relatively long sections of inflatable stoppers or tubing. The use of long sections of these materials would also reduce leakage flow from the rest of the well to the isolated section between packers. This flow can occur through gravel envelopes or other permeable zones surrounding the casing. Sections of inflatable tubing may have to be long enough to block off the entire part of the well not used for the slug test. High inflation pressures should be used to minimize volume changes in the tubing due to changing water pressures in the isolated section when the head is lowered. So far, solutions for the slug test have been developed only for completely penetrating wells in confined aquifers. Cooper et at. (1967) derived an equation for the rise or fall of the water level in a well after sudden lowering or raising, respectively. Their equation was based on nonsteady flow to a pumped,
TL;DR: In this article, a solution for the change in water level in a well of finite diameter after a known volume of water is suddenly injected or withdrawn is presented, and a set of type curves computed from this solution permits a determination of the transmissibility of the aquifer.
Abstract: A solution is presented for the change in water level in a well of finite diameter after a known volume of water is suddenly injected or withdrawn. A set of type curves computed from this solution permits a determination of the transmissibility of the aquifer.
TL;DR: In this article, a sequential inverse approach is developed to interpret results of hydraulic tomography, which uses an iterative geostatistical inverse method to yield the effective hydraulic conductivity of an aquifer, conditioned on each set of head/discharge data.
Abstract: Hydraulic tomography (i.e., a sequential aquifer test) has recently been proposed as a method for characterizing aquifer heterogeneity. During a hydraulic tomography experiment, water is sequentially pumped from or injected into an aquifer at different vertical portions or intervals of the aquifer. During each pumping or injection, hydraulic head responses of the aquifer at other intervals are monitored, yielding a set of head/discharge (or recharge) data. By sequentially pumping (or injecting) water at one interval and monitoring the steady state head responses at others, many head/discharge (recharge) data sets are obtained. In this study a sequential inverse approach is developed to interpret results of hydraulic tomography. The approach uses an iterative geostatistical inverse method to yield the effective hydraulic conductivity of an aquifer, conditioned on each set of head/discharge data. To efficiently include all the head/discharge data sets, a sequential conditioning method is employed. It uses the estimated hydraulic conductivity field and covariances, conditioned on the previous head/discharge data set, as prior information for next estimations using a new set of pumping data. This inverse approach was first applied to hypothetical, two-dimensional, heterogeneous aquifers to investigate the optimal sampling scheme for the hydraulic tomography, i.e., the design of well spacing, pumping, and monitoring locations. The effects of measurement errors and uncertainties in statistical parameters required by the inverse model were also investigated. Finally, the robustness of this inverse approach was demonstrated through its application to a hypothetical, three-dimensional, heterogeneous aquifer.
TL;DR: In this article, a generalized radial flow model for hydraulic test data is presented, which considers the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically.
Abstract: Models commonly used for the analysis of hydraulic test data are generalized by regarding the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically. Mathematical solutions for this generalized radial flow model are derived for the standard test conditions: constant rate, constant head, and slug tests. Solutions for the less common, sinusoidal test are contained within the general solutions given. Well bore storage and skin are included and the extension to dual-porosity media outlined. The model is presented as a model of fractured media, for which it is most likely to find application because of the problem of choosing the appropriate flow dimension.