Density-Dependent Flows

1
Density-Dependent Flows

• Primary source
• Users Guide to SEAWAT A Computer Program for
  Simulation of Three-Dimensional Variable-Density
  Ground-Water Flow
• By Weixing Guo and Christian D. Langevin
• U.S. Geological Survey
• Techniques of Water-Resources Investigations
  6-A7, Tallahassee, Florida2002

2
Sources of density variation

• Solute concentration
• Pressure
• Temperature

3
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

4
Others

• 3DFATMIC 
• 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.
• 3DFEMFAT
• 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
  finite-difference method.
• FEFLOW
• 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
• 3D finite element, saturated / unsaturated,
  density driven flow and transport model
• SWICHA (old)
• 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).

5
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

6
Converting between
7
Mass Balance

• (with sink term)

8

• Product Rule

9
Density
(and soon T!)

• Chain rule

10
Water Compressibility
11
Medium Compressibility
12
Specific storage

• Volume of water per unit change in pressure

13
Densities

• Freshwater 1000 kg m-3
• Seawater 1025 kg m-3
• Freshwater 0 mg L-1
• Seawater 35,000 mg L-1

14
Flow Equation
15
Darcys law
16
CDE
17
Program Flow
18
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)

19
Henry Problem
20
Henry
21
Hydrocoin
22
Elder Problem
C0
E/H4 L/H2
Temperature-induced buoyancy
Solute-induced buoyancy
H
C1
Elder, J. W. (1967) J. Fluid Mech. 27 (3)
609-623 Voss, C. I., W. R. Souza (1987) Wat.
Resour. Res. 23, 1851-1866
23
Elder Problem
// Controlling parameter
Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623
24
Elder Problem
// Controlling parameter
Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623
25
Results
Year 1
Year 2
60
20
Year 10
Year 4
60
60
20
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
26
Results
Thorne Sukop
80
60
80
Year 1
Year 2
40
60
40
20
20
80
Year 4
Year 10
80
60
60
40
20
40
20
Year 15
Year 20
80
80
80
80
60
60
40
40
20
20
Frolkovic, P., H. De Schepper (2001) Adv. Wat.
Res. 24, 63-72
27
Results (year 15)
Thorne Sukop
Year 15
20
60
Year 15
80
80
80
60
40
20
28
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