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Unformatted text preview: , then the model will
assume that it is located above the uppermost node associated
with the well (that is, above the node located closest to the
land surface or wellhead). Specifying the location of the pump
intake will not affect the net discharge from the well, nor the
inflows and outflows at any particular node. Instead, it will
only affect the routing of flow and solute within the borehole. Head Loss Terms
MODFLOW computes the head at a blockcentered
node of a finitedifference grid on the basis of a fluid mass
balance for fluxes into and out of the volume of the cell of
interest, including flow in or out of a well located within the
surface area (and volume) of that cell. However, because of differences between the volume of a cell and the volume of a
wellbore, as well as differences between the average hydraulic
properties of a cell and those immediately adjacent to a well, it
is not expected that the computed head for the node of a finitedifference cell will accurately reproduce or predict the actual
head or water level in a well at that location. Furthermore,
if the length of the open interval or screen of a vertical well
is greater than the thickness of the cell, then the head in the
well would be related to the head in the groundwater system
at multiple levels (and at multiple locations for a nonvertical
well). Thus, if the user needs to estimate the head or water
level in a well, rather than just the head at the nearest node,
then additional calculations are needed to correct for the several factors contributing to the difference between the two.
Following the development and discussion of Jacob
(1947), Rorabaugh (1953), Prickett (1967), and Bennett and
others (1982), the difference between the head in the cell and
the head in the well (the celltowell drawdown) can be calculated with a general wellloss equation as:
, (2) where hWELL is the composite head (or water level) in the
well (L), n is the index of nodes in a multinode well, hn is the
head in the nth cell associated with the well (L), Qn is the flow
between the nth cell and the well (L3/T) (negative for flow out
of the aquifer and into the well), A is a linear aquiferloss coefficient (T/L2), B is a linear wellloss coefficient (T/L2), C is a
nonlinear wellloss coefficient (TP/L(3P1)), and P is the power
(exponent) of the nonlinear discharge component of well loss.
Equation 2 can alternatively be expressed in terms of the water
level in the well as:
. (3) Equation 3 states that the head in the well is equal to the
head in the node in which the well is located (hn) plus several
headloss terms (noting again that for a pumping well, all of
the Q terms would be negative in sign). The head at the node,
hn, is calculated by the finitedifference solution to the partial
differential equation of groundwater flow. The first headloss
term (AQn) accounts for head losses in the aquifer resulting
from the well having a radius less than the horizontal dimensions of the cell in which the well is located (that is, celltowell head losses); the second term (BQn) accounts for head
losses that occur adjacent to and within the borehole and well
screen (that is, skin effects); and the third term (
) accounts
for nonlinear head losses due to turbulent flow near the well.
Most previous approaches for simulating head losses
have included only the aquiferloss term (AQn) (see, for
example, Prickett, 1967; Trescott and others, 1976; Bennett
and others, 1982; Anderson and Woessner, 1992; Planert,
1997; Neville and Tonkin, 2004). This common approach
assumes that aquifer losses can be calculated on the basis of
the Thiem (1906) steadystate flow equation and that head loss Conceptual Model and Numerical Implementation
due to skin and local turbulence effects are negligible, such
that equation 3 becomes: , 5 (8) (4)
where T is transmissivity of the aquifer (L2/T), ro is the effective (or equivalent) radius of a finitedifference cell (L), and rw
is the actual radius of the well (L).
The effective radius of the cell is equivalent to the radius
of a vertical pumping well that would have the same head as
that calculated for the node of the cell. Because ro is typically
much greater than rw, the head in a pumping (withdrawal)
well will typically be lower than the modelcomputed head
for the cell. Several assumptions underlie the use of the Thiem
(1906) equation for estimating the aquifer loss, including that
the aquifer is confined; the well is vertical and the screen fully
penetrates a cell; the well causes radially symmetric drawdown; the well causes no vertical flow in the aquifer containing the well or from units above and below the aquifer; the
transmissivity is homogeneous and isotropic in the cell containing the well and in the neighboring cells; and flow between
the cell and well is at steady state for the time period used to
solve the general groundwater flow equations in MODFLOW.
Peaceman (1983) indicates that the effective external
radius of a rectangular finitedifference cell for isotropic
porous media is given by
(5) where ro is calculated by MNW2 using equation 8 on the basis
of a userspecified value of rw and values of Δx, Δy, Kx, and Ky
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This document was uploaded on 01/20/2014.
 Winter '14

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