Types of Boundary Conditions 1.Specified head (including constant head) h = f (x,y,z,t) 2.Specified flux (including no flow) h/ l = -q l /K l 3.Head-dependent.

Types of Boundary Conditions

1. Specified head (including constant head) h = f (x,y,z,t)

2. Specified flux (including no flow)

h/l = -ql/Kl

3. Head-dependent conditions

q = -Kb (hb – h)/b

Implementation in MODFLOW

Versions of MODFLOW

MODFLOW 88/96MODFLOW2000MODFLOW2005

& PCG2

required

required

1 is required

headdependentBCs

MODFLOW88/96Packages

Field setting

Representationin the model

RIVER Package

Head Dependent BoundariesMODFLOW’s River Package

hb= hR = head in the river

q = -Kb (hb – h)/b

Q = conductance x change in head

w

m

RBOT

Gaining River Cell

Q = C (hR – hijk)

hijk

w

m

RBOT

Losing River Cell

Q = C (hR – hijk)

RBOT

Losing River Cell

Q = C (hR – hijk)

RBOT

Percolating River Cell

Q = C (hR – RBOT)

Definitions

Riverbed Conductance = (Kv/m) wL

Leakance = Kv/m

Resistance = m/Kv

Kv = vertical hydraulic conductivity of riverbed sediments

m = thickness of riverbed sedimentsw = width of the riverL = length of the river within the cell

River with sandy bottom = 1 day

Small stream with silty bottom = 1- 10 days

Stream/lake in till = 100 days

Resistance

Head Dependent Boundariesin MODFLOW88/96

• River Package• Drain Package• General Head Boundary (GHB) Package• ET Package

Q = C h

River Package

Q = C (hR – hijk)where C =KvLw/m

Drain Package

Drain Package

Q = C (hijk-d)where d = head in the drain.Q = 0 if hijk<d

General Head Boundary Package

hB

Boundary cell

h

Q= C (hB-h)C = K A /L

L

Evapotranspiration (EVT) Package

…to be discussed later,when we do the Final Project

hB

L

C = Conductance = K A/LK is the hydraulic conductivity of the aquifer between the model and the lake;A is the area of the boundary cell, perpendicular to flow.

GHB

Q = C (hB - h)

• Streamflow Routing Package (Prudic 2004)

New MODFLOW Package available in MODFLOW2000.

• Streamflow Package (Prudic 1989)- see p. 127 A&W Q

Allows for dynamic interchange ofgroundwater and streamflow; solvesfor stream stage.

Manning’s Equation:

d = (Q n / C w S1/2)3/5

n is Manning’s Roughness coefficient

http://www.engineering.usu.edu/classes/cee/5470/wsp2339.pdf

Estimating Manning’s n

• Lake Package – Available in MODFLOW2000

(Cheng and Anderson, GW,1993) (Council, 1998) (Merritt and Konikow, 2000)

• MODBRANCH (Swain, 1993)

• Wetland Module (Restrepo et al., GW,1998)

Other packages:

Solves for lake levels

Lake (LAK) Package

Change in lake level = Change in Storage/Area

Change in Storage = Outflow - Inflow

Head Dependent Boundariesin original MODFLOW88/96

• River Package• Drain Package• General Head Boundary (GHB) Package• ET Package

Q = C h

Prudic’s 1989 Streamflow Package and a few otherpackages have since been added to MODFLOW88/96and are available when running MODFLOW88/96in Groundwater Vistas.