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Types of Boundary Conditions

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  1. Types of Boundary Conditions • Specified head (including constant head) • h = f (x,y,z,t) • Specified flux (including no flow) • h/l = -ql/Kl • Head-dependent conditions • q = -Kb (hb – h)/b Implementation in MODFLOW

  2. Versions of MODFLOW MODFLOW 88/96 MODFLOW2000 MODFLOW2005

  3. MODFLOW88/96 Packages required required head dependent BCs 1 is required & PCG2

  4. RIVER Package Field setting Representation in the model

  5. hb= hR = head in the river q = -Kb (hb – h)/b Head Dependent Boundaries MODFLOW’s River Package

  6. m w Q = conductance x change in head

  7. m w Q = C (hR – hijk) hijk RBOT Gaining River Cell

  8. Q = C (hR – hijk) RBOT Losing River Cell

  9. Q = C (hR – hijk) RBOT Losing River Cell

  10. Q = C (hR – RBOT) RBOT Percolating River Cell

  11. Definitions Riverbed Conductance = (Kv/m) wL Leakance = Kv/m Resistance = m/Kv Kv = vertical hydraulic conductivity of riverbed sediments m = thickness of riverbed sediments w = width of the river L = length of the river within the cell

  12. Resistance River with sandy bottom = 1 day Small stream with silty bottom = 1- 10 days Stream/lake in till = 100 days

  13. Head Dependent Boundaries in MODFLOW88/96 Q = C h • River Package • Drain Package • General Head Boundary (GHB) Package • ET Package

  14. River Package Q = C (hR – hijk) where C =KvLw/m

  15. Drain Package

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

  17. General Head Boundary Package Boundary cell hB L h Q= C (hB-h) C = K A /L

  18. Evapotranspiration (EVT) Package …to be discussed later, when we do the Final Project

  19. GHB L Lake Model hB Q = C (hB - h) C = Conductance = K A/L K is the hydraulic conductivity of the aquifer between the model and the lake; A is the area of the boundary cell, perpendicular to flow.

  20. Streamflow Package (Prudic 1989)- see p. 127 A&W Q Allows for dynamic interchange of groundwater and streamflow; solves for stream stage. Manning’s Equation: d = (Q n / C w S1/2)3/5 n is Manning’s Roughness coefficient New MODFLOW Package available in MODFLOW2000. • Streamflow Routing Package (Prudic 2004)

  21. Estimating Manning’s n http://www.engineering.usu.edu/classes/cee/5470/wsp2339.pdf

  22. Other packages: • Wetland Module (Restrepo et al., GW,1998) • MODBRANCH (Swain, 1993) • Lake Package – Available in MODFLOW2000 (Cheng and Anderson, GW,1993) (Council, 1998) (Merritt and Konikow, 2000) Solves for lake levels

  23. Lake (LAK) Package Change in Storage = Outflow - Inflow Change in lake level = Change in Storage/Area

  24. Head Dependent Boundaries in original MODFLOW88/96 Q = C h • River Package • Drain Package • General Head Boundary (GHB) Package • ET Package Prudic’s 1989 Streamflow Package and a few other packages have since been added to MODFLOW88/96 and are available when running MODFLOW88/96 in Groundwater Vistas.