PUBLICATIONS - Report, "Consideration of total energy loss in theory of flow to wells,"

                        GEOLOGICAL SURVEY
                        RESTON, VA. 22092

In Reply Refer To:                            August 20, 1980
EGS-Mail Stop 411


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


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