7/29/2023 0 Comments Drawdown definition hydrogeology![]() The quantity Δ V w is positive when water is added to the aquifer and negative when water is removed from the aquifer. Volume of representative elemental volume (L 3) Volume of water added to or removed from storage in an REV (L 3) A key quantity to define is the increment of fluid content, ζ (Equation 1), which has its origin in soil mechanics and the theory of poroelasticity (Biot, 1941 Wang, 2000). For precision, the verbal definition will be translated into an equation, although most hydrogeology textbooks follow Theis and omit doing so. In three-dimensions, the analog of specific heat is specific storage, in which the amount of water removed from a representative elementary volume REV per unit head decline is normalized by the volume of the REV. Theis’ definition of coefficient of storage is for two-dimensional radial flow. Today, “storativity” is used synonymously with “coefficient of storage,” and Theis’ verbal definition is the one commonly provided in textbooks and illustrated for a confined aquifer in Figure 1. Here, Theis backs away from using the term “specific yield” for a confined aquifer. Later consideration has shown it advisable to call this term the “coefficient of storage” of the aquifer and to define it as the quantity of water in cubic feet that is discharged from each vertical prism of the aquifer with basal area equal to 1 square foot and height equal to that of the aquifer when the water level falls 1 foot.” “The factor S in the equations given is called ‘specific yield’ in the text of the paper. However, Theis later elaborated on S in an Author’s Note added to a 1952 United States Geological Society (USGS) reprint of his 1935 paper. Theis in his 1935 paper provided no mechanistic insight to groundwater storage it was a property inferred from the heat flow analogy. Tellingly, the analogy to specific heat is the only attribute Theis provided for S, in contrast to a short description of the physical meaning of the coefficient of transmissibility T. ![]() ”įor groundwater storage, Theis used the variable S, which he originally called the “specific yield” in the quote above and not to be confused with “specific yield” of an unconfined aquifer. It appears probable, analogously, that in elastic artesian aquifers a specific amount of water is discharged instantaneously from storage as the pressure falls. “In heat-conduction a specific amount of heat is lost concomitantly and instantaneously with fall in temperature. This analogy has been recognized, at least since the work of Slichter, but apparently no attempt has been made to introduce the function of time into the mathematics of ground-water hydrology.” Therefore, the mathematical theory of heat-conduction developed by Fourier and subsequent writers is largely applicable to hydraulic theory. “Darcy’s law is analogous to the law of the flow of heat by conduction, hydraulic pressure being analogous to temperature, pressure-gradient to thermal gradient, permeability to thermal conductivity, and specific yield to specific heat. Theis prominently stated the heat flow analogy, as he did in his earlier letter to Lubin. Lubin provided Theis with the solution from Carslaw (1921) according to Banks (2015) which Theis duly noted in his paper. Is this problem in radial flow worked out?: Given a plate of given constant thickness and with constant thermal characteristics at a uniform initial temperature to compute the temperatures thruout the plate at any time after the introduction of a sink kept at 0 temperature? And a more valuable one from our standpoint: Given the same plate under the same conditions to compute the temperatures after the introduction of a sink into which heat flows at a uniform rate? I forgot to say that the plate may be considered to have infinite areal extent.” I think a close approach to the solution of some of our problems are probably already worked out in the theory of heat conduction. We have exact analogies in ground water theory for thermal gradient, thermal conductivity, and specific heat. ![]() “The flow of ground water has many analogies to the flow of heat by conduction. Theis conceptualized the well-drawdown problem in heat conduction terms, which he expressed in correspondence to his former college classmate, Clarence Lubin, who had become a mathematics professor at the University of Cincinnati (Freeze, 1985). The concept of storage is most frequently encountered in hydrogeology as the “ S” parameter in Theis’ (1935) solution.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |