Density-Dependent Flows
Primary source:
User’s Guide to SEAWAT: A Computer Program for
Simulation of Three-Dimensional Variable-Density GroundWater Flow
By Weixing Guo and Christian D. Langevin
U.S. Geological Survey
Techniques of Water-Resources Investigations 6-A7,
Tallahassee, Florida2002
Sources of density variation
• Solute concentration
• Pressure
• Temperature
USGS
•
HST3D
– Three-dimensional flow, heat, and solute transport model
•
HYDROTHERM
– Three-dimensional finite-difference model to simulate multiphase ground-water
flow and heat transport in the temperature range of 0 to 1,200 degrees Celsius
•
MOCDENSE
– Temperature is assumed to be constant, but fluid density and viscosity are
assumed to be a linear function of the first specified solute.
•
SEAWAT and SEAWAT-2000
– A computer program for simulation of three-dimensional variable-density ground
water flow
•
SHARP
– A quasi-three-dimensional, numerical finite-difference model to simulate
freshwater and saltwater flow separated by a sharp interface in layered coastal
aquifer systems
•
SUTRA and related programs
– 2D, 3D, variable-density, variably-saturated flow, solute or energy transport
Others
•
3DFATMIC
–
•
3DFEMFAT
–
•
3D finite element, saturated / unsaturated, density driven flow and transport model
SWICHA (old)
–
•
FEFLOW (Finite Element subsurface FLOW system) saturated and unsaturated conditions. FEFLOW is a
finite element simulation system which includes interactive graphics, a GIS interface, data regionalization
and visualization tools. FEFLOW provides tools for building the finite element mesh, assigning model
properties and boundary conditions, running the simulation, and visualizing the results.
FEMWATER
–
•
3-D finite-element flow and transport through saturated-unsaturated media. Combined sequential flow and
transport, or coupled density-dependent flow and transport. Completely eliminates numerical oscillation due
to advection terms, can be applied to mesh Peclet numbers ranging from 0 to infinity, can use a very large
time step size to greatly reduce numerical diffusion, and hybrid Lagrangian-Eulerian finite-element approach
is always superior to and will never be worse than its corresponding upstream finite-element or finitedifference method.
FEFLOW
–
•
3-D transient and/or steady-state density-dependent flow field and transient and/or steady-state distribution
of a substrate, a nutrient, an aerobic electron acceptor (e.g., the oxygen), an anaerobic electron acceptor
(e.g., the nitrate), and three types of microbes in a three-dimensional domain of subsurface media.
three-dimensional finite element code for analyzing seawater intrusion in coastal aquifers. The model
simulates variable density fluid flow and solute transport processes in fully-saturated porous media. It can
solve the flow and transport equations independently or concurrently in the same computer run. Transport
mechanisms considered include: advection, hydrodynamic dispersion, absorption, and first-order decay.
TARGET (old)
–
–
3D vertically oriented (cross section), variably saturated, density coupled, transient ground-water flow, and
solute transport (TARGET-2DU);
3D saturated, density coupled, transient ground-water flow, and solute transport (TARGET-3DS).
Freshwater Head
• SEAWAT is based on the
concept of equivalent
freshwater head in a saline
ground-water environment
• Piezometer A contains
freshwater
• Piezometer B contains water
identical to that present in
the saline aquifer
• The height of the water level
in piezometer A is the
freshwater head
Converting between:
Mass Balance
• (with sink term)
• Product Rule
Density
(and soon T!)
• Chain rule
Water Compressibility
Medium Compressibility
Specific storage
• Volume of water per unit change in
pressure:
Densities
•
•
•
•
Freshwater: 1000 kg m-3
Seawater: 1025 kg m-3
Freshwater: 0 mg L-1
Seawater: 35,000 mg L-1
d 1025 1000kg m

3
dC
35 kg m
3
 0.714
Flow Equation
Darcy’s law
CDE
Program Flow
Benchmark Problems
•
•
•
•
Box problems (Voss and Souza, 1987)
Henry problem (Voss and Souza, 1987)
Elder problem (Voss and Souza, 1987)
HYDROCOIN problem (Konikow and
others, 1997)
Henry Problem
Henry
Hydrocoin
Elder Problem
Salt Source
E
C=0
E/H=4
H
L/H=2
Temperature-induced
buoyancy
Solute-induced buoyancy
C=1
L
Heater
Elder, J. W. (1967) J. Fluid Mech. 27 (3) 609-623
Voss, C. I., W. R. Souza (1987) Wat. Resour. Res. 23, 1851-1866
Elder Problem
L
C=1
H
C=0
E
// Controlling parameter
Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623
Elder Problem
L
C=1
H
C=0
E
// Controlling parameter
Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623
Results
Year 1
Year 2
60%
20%
Thorne & Sukop (2004)
Elder (1967)
Year 4
Year 10
60%
20%
60%
20%
Year 15
Year 20
20%
60%
20%
60%
Notes
• No fully accepted results (computer or lab).
• Maybe no unique solution.
Elder, J. W. (1967) J. Fluid Mech. 27 (1), 29-48
Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623
Woods, J. A., et al. (2003) Wat. Resour. Res. 39, 1158-1169
Results
Thorne & Sukop
Year 1
80%
60%
40%
20%
Year 2
80%
60%
40%
20%
Thorne & Sukop (2004)
Frolkovič & De Schepper (2001)
Year 4
80%
Year 10
80%
60%
60%
40%
20%
40%
20%
Year 15
Year 20
80%
80%
80%
80%
60%
40%
20%
Frolkovič, P., H. De Schepper (2001) Adv. Wat. Res. 24, 63-72
60%
40%
20%
Thorne & Sukop
Results (year 15)
Year 15
Thorne & Sukop (2004)
Elder (1967)
20%
60%
Year 15
Thorne & Sukop (2004)
Frolkovič & De Schepper (2001)
80%
80%
80%
60%
40%
20%