WEL6 1

WELL PACKAGE• Simulates the discharge or recharge of water from

wells.• Simulates a prescribed flow boundary (Neuman)

condition.• Given that Q is the rate of flow to or from the well or

boundary, negative Q represent discharge and a positive Q represent discharge.

• The user specifies the discharge associated with each individual well, and these are summed within the program to obtain a total discharge from a cell.

WEL6 2

WELL PACKAGE

• The well package does not accommodate wells which are open to more than one layer of the model.

• Well perforated in multiple layers are represent as a group of single-layer wells, – each opened to one of the layers tapped by the multi-

layered, – each having an individual Q term specified for each

stress period ,

WEL6 3

WELL PACKAGE• The discharge of the multi-layer well must be apportioned in in some

way among the individual layers, externally to the model program• A common method of external apportionment is to divide the well

discharge in proportion to layer transmissivity,

where Qijb is the discharge from layer b to a particular i,j well in a given stress period, Qwij

is the well discharge in that stress period, Tijb is the transmissivity of layer b, ΣT represents the sum of the transmissivites of all layers penetrated by the well, and m to n includes all of the subscripts for layers open to the well.

n

mpijp

ijbijijb

T

TQwQ

WEL6 4

WELL PACKAGE

Head at a Well in a Single Layer• The head value at the node in

a cell is representative of the average value of head throughout the cell.

• If a well is present in a cell, this average head value can be considered to be the head at some distance re from the well.

• The distance re is calculated as follows,

The area of the cell is equal to DELRj×DELCi

DELCi

DELRj

Nodeij

Well

WEL6 5

WELL PACKAGE• The area is converted to that of a circle,

therefore,

giving,

Thus the head at re is hij, the head at

the node

• We use Theim’s Equation to calculate head at the well. If,hw is the head at the well,

hij is the head at radius re

Qw is the pumping (-) or injection (+) rate,

T is the transmissivity of the cell, andrw is the well radius, then for a

Confined aquifer,

Unconfined aquifer,

re

Well

DELRj

DELCi

2eij rDELCDELR

ij

e

DELCDELRr

w

ewijw r

r

T

Qhh ln

2

w

ewijw r

r

K

Qhh ln22

WEL6 6

WELL PACKAGEHead in a Well Perforated Through a Multi-Aquifer

System• MODFLOW calculates the head in each layer of a

well perforation, however, the measured water level in a well, hw, is an integrated head over all the perforated layers and is given by,

where Qw is the total pumping , Tijb is the transmissivity of cell i,j,b, hijb is the head in cell i,j,b, reb is the converted radial distance in cell b, and rw is the radius of the well. The indices m to n includes all of the subscripts for zones open to the well.

n

mb

w

e

ijb

Wn

mb

w

e

ijb

n

mb

w

e

ijbijb

w

rr

TQ

rr

Tr

r

hT

h

ln2

ln

ln

WEL6 7

WELL PACKAGEPumpage for Multi-Aquifer System• For most multiple-aquifer systems the

equation,

is sufficient to estimate the distribution of pumping over the perforated layers.

• A more accurate method involves external iterations,1. Estimate Qijb from the above equation

2. Calculate hijb with MODFLOW using the calculated Qijb

3. Calculate hw from

4. Calculate a new Qijb using the equation,

5. Return to step 2.

n

mpijp

ijbijijb

T

TQwQ

n

mb

w

e

ijb

Wn

mb

w

e

ijb

n

mb

w

e

ijbijb

w

rr

TQ

rr

Tr

r

hT

h

ln2

ln

ln

w

e

bwijbijb

rr

hhTQ

bln

)(2

WEL6 8

WELL PACKAGE

• The primary source of groundwater recharge into low-land basins is mountain front recharge.

• Mountain front recharge is the water that infiltrates into the zones of coarse material that extend from the base of the mountain into the basin (alluvial fans)

• The quantity of water potentially available for recharge is assumed to be equal to the precipitation minus evapotranspiration.

WEL6 9

WELL PACKAGE• As an example, a mountain front

recharge estimate developed for the Upper San Pedro Basin by Anderson et al (USGS) is,

where

qrech is the recharge rate per unit area (inches/year), andP is the precipitation for a catchment in excess of 8 inches per year.

• The figure on the right shows the average precipitation within each mountain catchment that contributes to the Upper San Pedro basin.

Note: this equation is applicable only to the Upper San Pedro Basin

Pqrech ln98.040.1ln

WEL6 10

WELL PACKAGE• For each catchment, the

product of qrech with the area gives the amount of recharge water.

• The recharge from these catchments is then distributed to active cells along the outside edge of the model boundary.

• The recharge into these boundary cell is modeled using recharge wells.

• A well is present at each of the boundary cells unless it is a no-flow boundary

WEL6 11

WELL PACKAGE

NPWEL—is the number of well parameters.

MXL—is the maximum number of wells using parameters.

MXACTW—is the maximum of wells in use during any stress period, including those defined using parameters.

WEL6 12

WELL PACKAGE

IWELCB—is a flag and unit numberIWELCB>0, unit number to which cell-by-cell terms will be written when SAVE BUDGET or a non-zero value of ICBCFL is specified in output control.IWELCB=0, cell-by-cell terms not written.IWELCB<0, well pumping for each well will be written when SAVE BUDGET or a non-zero value of ICBCFL is specified in output control

WEL6 13

WELL PACKAGE

[Option]—is an optional list of character values.AUXILIARY abc or AUX abc—defines an auxiliary variable named abc, which is read for each well as part of Items 4 and 6.Up to 5 variable can be specified, each preceded by AUXLIARY or AUX.CBCALLOCATE or CBC—indicates that memory should be allocated to store cell-by-cell flows for each well in order to make these flows available for use in other packages.

WEL6 14

WELL PACKAGE

PARNAM—is the name of a parameter. This name can consist of 1 to 10 characters, and is not case specific.

PARTYP—is parameter type. There is only one parameter type for the WEL Package—the volumetric discharge rate, Q.

Parval—is the parameter value.NLST—is the number of wells that are

included in the parameter.

WEL6 15

WELL PACKAGEITMP—is a flag and a counter.

ITMP<0, non-parameter well data from last stress period will be reused.ITMP≥0, ITMP will be the number of non-parameter wells read for current stress period.

NP—is the number of parameters in use in current stress period.

Layer—is the layer number of the cell that contains the well

Row—is the row number of the cell that contains the well.

Column—is the column number of the cell that the contains the well.

WEL6 16

WELL PACKAGEQfact—is the factor used to calculate the

well discharge rate from the parameter value. The discharge rate is the product of Qfact and the parameter value.

Q—is the volumetric discharge rate. A positive value is recharge and a negative value is discharge.

[xyz]—represent the value of any auxiliary variable for a well that has been defined in Item 2. The auxiliary variable must be present in each repetition of of Item 4 and 6 if they are defined in Item 2.

Pname—is the name of the parameter being used in the current stress period. NP parameter names are read.

WEL6 17

WELL PACKAGE

No Parameters

WEL6 18

WELL PACKAGE Parameters