Theory of aquifer tests

Abstract

The development of water supplies from wells was placed on a rational basis with Darcy's development of the law governing the movement of fluids through sands and with Dupuit's application of that law to the problem of radial flow toward a pumped well. As field experience increased, confidence in the appli cability of quantitative methods was gained and interest in developing solutions for more complex hydrologic problems was stimulated. An important mile stone was Theis' development in 1935 of a solution for the nonsteady flow of ground water, which enabled hydrologists for the first time to predict future changes in groundwater levels resulting from pumping or recharging of wells. In the quarter century since, quantitative groundwater hydrology has been enlarging so rapidly as to discourage the preparation of comprehensive textbooks. This report surveys developments in fluid mechanics that apply to ground water hydrology. It emphasizes concepts and principles, and the delineation of limits of applicability of mathematical models for analysis of flow systems in the field. It stresses the importance of the geologic variable and its role in governing the flow regimen. The report discusses the origin, occurrence, and motion of underground water in relation to the development of terminology and analytic expressions for selected flow systems. It describes the underlying assumptions necessary for mathema tical treatment of these flow systems, with particular reference to the way in which the assumptions limit the validity of the treatment. � � � 77 THEORY OF AQUIFER TESTS Unit cross-sectional area A. ARTESIAN AQUIFER Unit cross-sectional area Water table B. WATER-TABLE AQUIFER FIGURE 18 .-Diagrams for coefficient of storage. of the angle of inclination of the water table. The product of the last two factors is the component of head change acting normal to the aquifer surface. The importance of interpreting correctly the phrase "component of head change" which appears in the definition of the storage coefficient cannot be overemphasized. Examine figure 18B, which depicts, in schematic fashion, a horizontal

A parallel implementation of the confined-unconfined aquifer system model for subglacial hydrology: design, verification, and performance analysis (CUAS-MPI v0.1.0)

“…The confined case has an analytical solution on an unbounded domain (Theis, 1935), which can be tested on a bounded numerical domain as long as the flow is far from the boundaries. Moreover, analytical solutions for a bounded domain can be constructed based on the unbounded solution using the method of images, since equation (A1) with constant transmissivity is linear (Ferris et al, 1962). We choose to verify the two types of boundary conditions implemented in CUAS-MPI by considering the case where a pump is at equal distance from two Dirichlet boundaries having zero hydraulic head (h(x, t) = h(y, t) = 0, ∀ x, y → −∞), and two Neumann boundaries across which the flow is zero ( ∂h ∂x = ∂h ∂y = 0, ∀ x, y → ∞).…”

“…We choose to verify the two types of boundary conditions implemented in CUAS-MPI by considering the case where a pump is at equal distance from two Dirichlet boundaries having zero hydraulic head (h(x, t) = h(y, t) = 0, ∀ x, y → −∞), and two Neumann boundaries across which the flow is zero ( ∂h ∂x = ∂h ∂y = 0, ∀ x, y → ∞). The analytical solution for such a configuration consists of a superposition of image wells placed across the domain boundaries (Ferris et al, 1962), where the solution accuracy grows with the number of image wells. Specifically, the analytical solution can be described in terms of the drawdown s = h(x, y, 0) − h(x, y, t) of an initially uniform hydraulic head, as the series…”

Revision of archive recovery tests using analytical and numerical methods on thermal water wells in sandstone and fractured carbonate aquifers in the vicinity of Budapest, Hungary

“…There are several methods to obtain K, η and S from step drawdown tests (Birsoy and Summers 1980;Clark 1977;Eden and Hazel 1973). Important contributions have been published on how to cope with the limitations of the Theis (1935) method: a well of finite diameter in which the stored water present in the well is incorporated in the test (Papadopulos and Cooper 1967); well losses, as initially included by Clarke (1977); a case in which a well might be subject to variable discharge yield, as solved by Birsoy and Summers (1980); the solution to low hydraulic and constant head boundary found by Ferris et al (1962); the question of the presence of vertical and horizontal variation of the hydraulic conductivity and storage coefficient, as solved by Neuman (1975); leakage input to the drawdown cone and the partial penetration case successfully examined by Hantush (1956Hantush ( , 1961; the delay yield response solved by Boulton (1954), Boulton and Streltsova (1978), which presented a solution for an aquifer test carried out in a fractured medium. Certainly, neither the identification of the various flow components, nor the data related to the physical media affecting the flow response in an abstraction well can be involved in an aquifer test data analysis carried out using analytical solutions, and especially in the case of a double porosity medium.…”

A Type‐Curve Approach for Evaluating Aquifer Properties by Interpreting Shallow Strain Measured During Well Tests

“…Transient pressure signals from hydraulic well tests have been analyzed using analytical solutions since long before computing capabilities made numerical inversion feasible. Theis (1935) and Cooper and Jacob (1946) present some of the first solutions used for well test analysis, and many others have been derived since then (Ferris et al, 1962;Kruseman & deRitter, 1970;Streltsova, 1988). Time series plots of dimensionless pressure are commonly referred to as "type curves" (Ferris et al, 1962;Gringarten, 1987;Reed, 1980).…”

“…Theis (1935) and Cooper and Jacob (1946) present some of the first solutions used for well test analysis, and many others have been derived since then (Ferris et al, 1962;Kruseman & deRitter, 1970;Streltsova, 1988). Time series plots of dimensionless pressure are commonly referred to as "type curves" (Ferris et al, 1962;Gringarten, 1987;Reed, 1980). Aquifer properties (e.g., transmissivity and storage), processes (e.g., leakage, delayed yield), or geometries (e.g., boundaries, reservoir shape) affect the shapes of type curves.…”