UNITED STATES DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY RESTON, VA. 22092 In Reply Refer To: August 20, 1980 EGS-Mail Stop 411 GROUND WATER BRANCH TECHNICAL MEMORANDUM NO. 80.10 Subject: PUBLICATIONS - Report, "Consideration of total energy loss in theory of flow to wells," by R. L. Colley and A.B. Cunningham. The analytical solutions developed for drawdown induced by pumping wells assume that the flux entering the well is uniformly distributed along the screened zones and that the head along the well screen is constant. The Theis nonleaky solution, and the Hantush leaky aquifer solution for fully penetrating wells, for example, make those assumptions. The assumptions imply that all of the head (or energy) loss takes place within the aquifer. Actually the drawdown in a pumped well represents the "resistance" of the aquifer and energy loss in flowing through the screen and up the well bore to the intake. Jacob (1947) and Rorabaugh (1953) attempted to represent these components of energy loss by using an equation for drawdown in the pumped well of the form: s(subscript w) = BQ + CQ (superscript n) Jacob assume n to be 2 and Rorabaugh considered the more general case of n as any constant. Their approach tends to couple an aquifer head loss component associated with radial flow in the aquifer to a lumped term that represents all the other head losses associated with getting the flow to the pump intake. In the attached paper, Cooley and Cunningham analyze the total energy losses in an aquifer-well system in a general manner. They develop a coupled numerical scheme for unsteady flow in single or multiple confined or semi-confined aquifers and in the well penetrating the system. The results of their numerical experiments suggest that for value of aquifer hydraulic conductivity greater than about 0.015 meter/min (about 530 gpd/square ft) and for pumping rates greater than about 1.2 meter/min (about 315 gpm) that a significant region of non-radial flow can develop because of the head losses in the well. They note that these numerical studies suggest that the non-radial flow related to energy losses in the well can lead to significant errors in estimates of aquifer transmissivity computed from drawdown data from the pumped well if the aquifer hydraulic conductivity is greater than about 0.03 m/min (about 1050 gpd/square ft). Cooley and Cunningham offer a qualitative explanation for development of a non-radial flow region. Water movement in the aquifer tends to follow a path such that the total energy loss (the sum of all energy losses in the well and in the aquifer) is minimized. For relatively low hydraulic conductivity the flow paths in the aquifer tend to be more nearly radial than for cases involving relatively high hydraulic conductivity. This is because for a fixed pumping rate the lower the value of hydraulic conductivity, the greater the proportion of total head losses that occur in the aquifer. Thus, total energy loss is dominated by aquifer head losses, which are minimized by all water taking the shortest possible flow path--the radial one. Conversely, the larger the hydraulic conductivity, the less the relative significance of the head losses in the aquifer and the flow paths will tend to be those that minimize energy losses in the well. Energy losses in the well are minimized if most of the slow into the well is near the pump intake. Therefore, in this case, flow paths in the aquifer are directed more toward the top of the well. We are not aware of field confirmation of the phenomenon of non- radial flow to fully penetrating wells in aquifers having uniform hydraulic conductivity. We would appreciate being advised of field data pertinent to this question. Limited additional copies of the attached paper and of the following references are available upon request to the Ground Water Branch. Jacob, C. E., 1947, Drawdown test to determine effective radius of artesian well: Trans. Am. Soc. Civ. Eng., vol. 112, p. 1047-1070. Rorabaugh, M. I., 1953, Graphical and theoretical analysis of step drawdown test of artesian well: Proceedings, Am. Soc. Civ. Eng., vol. 79, separate no. 362, 23 p. (s) Charles A. Appel for E. P. Patten Acting Chief, Ground Water Branch Enclosure WRD Distribution: A (Memo only), B (limited), S (Memo only), FOLPUBLICATIONS - Report, "Consideration of total energy loss in theory of flow to wells,"