Capture Zone Analysis using MODFLOW
--Introduction-We will simulate the flow system described below using a computer program called
MODFLOW with a pre- and post-processor known as Groundwater Vistas. MODFLOW
was developed by the USGS; it is the most popular groundwater flow model in the U.S. It
solves the general form of the groundwater flow equation and therefore, can simulate
three-dimensional, heterogeneous, transient or steady-state conditions.
Please also consult the companion document that gives directions for using
MODFLOW with Groundwater Vistas. A description of the problem is given below. You
should read this material and familiarize yourself with the details of the problem before
attempting to use Groundwater Vistas.
Conceptual Model
The unconfined aquifer shown in Fig. 1 consists of outwash filling a buried glacial
valley. The outwash has a maximum thickness of 100 ft. The hydraulic conductivity of
the aquifer is estimated to be 30 ft/day. Recharge from precipitation is estimated to be
0.006 ft/day (around 24 in/yr). Runoff from upland areas provides an additional
recharge of 0.003 ft/day along the sides of the valley, for a total of 0.009 ft/day. A
shallow perennial river flows through the center of the valley. There is a two foot thick
(b) layer of sediment at the bottom of the river. The vertical hydraulic conductivity (Kz) of
the riverbed sediments is estimated to be 2 ft/day, so that the leakance (Kz/b) beneath the
river is is 1 day-1. A shallow well located close to the river pumps at a rate of 50,000
ft3/day (around 0.4 MGD).
Modeling Objectives
The objectives are to delineate the capture zone of the well and to quantify the effects
of pumping on groundwater flow to the river.
Methodology
Use MODFLOW to:
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calculate the steady-state distribution of heads without pumping;
calculate the steady-state distribution of heads with pumping;
calculate the drawdown caused by pumping;
calculate the fluxes in and out of the river under pumping conditions.
This will require two MODFLOW runs: run 1 is a steady-state simulation without the
pumping well and run 2 is a steady-state simulation with the pumping well. Run 2 uses
the head distribution computed in run 1 as the starting heads so that drawdown may be
calculated.
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MODFLOW Design
Grid
We will use a three layer model with 11 columns and 23 rows. The grid is shown in Fig. 2.
Note that x = y = 200 ft. Layer 3 is 60 ft thick; layer 2 is 20 ft thick and layer 1 has
variable thickness as defined by the water table. Note the location of the river and the
well. Also note that the simulated aquifer narrows with depth to approximate the
geometry of the buried valley. That is, layer 1 has 11 columns of active nodes, layer 2 has
7 columns and layer 3 has only 5 columns of active nodes.
Boundary Conditions
(1) The aquifer is underlain by impermeable bedrock that forms a no flow boundary. (2)
At the top of the problem domain, water is recharged to the aquifer forming a specified
flow boundary condition. (3) The head in the river is equal to 100 ft and forms a specified
head boundary in layer 1, column 6. (For our purposes we will assume that the gradient
of the river is zero within the problem domain.) (4) The boundaries at the east and west
edges of the aquifer represents no flow conditions since the surrounding bedrock is
relatively impermeable (Fig. 1). (5) The aquifer extends farther to the north and south
beyond the problem domain shown in Fig. 2. Therefore, the boundaries at the north and
south ends of the model are not physical boundaries. We will use hydraulic boundary
conditions here; we assume no flow hydraulic boundaries at the north and south ends of
the model so that flow lines will be directed toward the river.
Parameters
Hydraulic Conductivity. We will assume that the aquifer is homogeneous and isotropic
and the hydraulic conductivity is therefore a constant and equal to 30 ft/day.
Leakance. Leakance is equal to vertical hydraulic conductivity divided by thickness.
Confirm that leakance for layer 1 is 1.5 day-1, except for the river node where leakance is
equal to 1.0 day-1. Leakance for layer 2 is 0.75 day-1. By convention in MODFLOW, the
bottom layer (our layer 3) has no leakance.
Recharge rate. Recharge is equal to 0.006 ft/day everywhere in layer 1, except for the river
nodes in column 6 where recharge is equal to zero and for all the nodes in columns 1 and
11, where recharge is equal to 0.009 ft/day.
Well discharge rate. The well is located in layer 1, column 7, row 12. It has a discharge rate
of -50,000 ft3/day.
Layer type. Layer 1 is a type 1 (unconfined) layer. We will simulate layers 2 and 3 as type
3 (variable) layers.
Convergence criterion. We will use a convergence criterion of 0.001 ft.
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