MULTIAQUIFER WELL SIMULATION
Outlined below is a summary of the
modifications made by Schreuder & Davis,
Inc. (SDI) to the numerical groundwater code
MODFLOW (McDonald & Harbaugh, 1984) to
allow simulations of multiaquifer pumping
and monitor wells using published formula
(Bennett et al. 1982). Bennett et al made the
following assumptions to develop numerical
equations for simulating multiaquifer wells.
1. The sum of pumping rates in each
screened aquifer equals the total
pumping rate from the well.
2. The head in the well is a constant in
all screened aquifers.
3. The head at the well can be calculated
using the Theim equation
hw= h* Qklog.(r./rw)/
(2 r Tijk), [1]
where h, is the head at the well, h* is
the head at the node in the cell
containing the well; Qkis the pumping
rate for a well screened in layer k, r,
is the effective radius of the
simulated pumped well; r, is the well
radius; and Tijk is the harmonic mean
of the transmissivity at the node.
4. Tje numerical nodal head estimates,
h, is assumed to be the effective
radius, r,, from the well. The distance
approximation used in MODMAQWE
is
r= 0.28 [(T /T, )1/2 D2 + (TI
/Ty,)'/2 D,2 ] //[(T/Txx)1/4 +
(Txx/Tyy)1/4],
where T, and T are the
transmissivity in the xdirection and
ydirection of the node containing the
well, and Dx and Dy are the cell length
in the xdirection and ydirection
(Peaceman, 1983).
Using the above, the pumping rate in a layer
is
Qk = [2 Tijk hijk/log(rar,)] [2 Tijk
log(r/rw)] [Ek Tijk hijk/Ek Tij +
[Tijk QwT/Ek Tijk, [2]
where hijk is the head at the node containing
the well, and QwT is the total pumping rate
of the multiaquifer well.
Qk was incorporated into MODFLOW's
well package subroutine WEL FM and is used
to calculate the water budget in subroutine
WELIBD. The head at the well, hw, is
calculated after calculating Qk and written
to a hydrograph file.
Bennett et al modified the USGS main
frame threedimensional finitedifference
flow model for multiaquifer wells and tested
the model against an analytical solution
provided by Papadopulos (1966). SDI's
revised code MODMAQWE was similarly
tested. The validation test simulates a single
multiaquifer well in a 2layer artesian
infinite aquifer system with zero leakance.
The initial head was 10 feet in the upper
layer and 30 feet in the lower layer.
Transmissivities were 1000 and 4000 ft2/day
in the upper and lower layers, respectively.
The storativity was 0.0001 in both layers, and
the well radius was 0.5 foot. Simulations
were conducted for two total pumping rates:
0 and 62,832 ft3/day. The results, shown in
Figures Bl through B4, were obtained using
1000foot grid spacing with 47 rows and 47
columns. These results agree well with the
analytical solution and the results obtained
by Bennett et al. (1982, Figures 5 and 6).
B1
5.l
SM
