Density-Dependent Flows

Primary source:

User’s Guide to SEAWAT: A Computer Program for Simulation of Three-Dimensional Variable-Density Ground-Water Flow

By Weixing Guo and Christian D. LangevinU.S. Geological SurveyTechniques 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 

– 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).

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

• Chain rule

(and soon T!)

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

714.0m kg 35

m kg 100010253

3

dC

d

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

L

E

H

C=1

C=0

Elder ProblemElder Problem

Elder, J. W. (1967) J. Fluid Mech. 27 (3) 609-623Voss, C. I., W. R. Souza (1987) Wat. Resour. Res. 23, 1851-1866

E/H=4

L/H=2Temperature-induced buoyancySolute-induced buoyancy

Heater

Salt Source

L

E

H

C=1

C=0

Elder ProblemElder Problem

Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623

// Controlling parameter

L

E

H

C=1

C=0

Elder ProblemElder Problem

Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623

// Controlling parameter

ResultsResults

Notes• No fully accepted results (computer or lab).• Maybe no unique solution.

Elder, J. W. (1967) J. Fluid Mech. 27 (1), 29-48Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623

Woods, J. A., et al. (2003) Wat. Resour. Res. 39, 1158-1169

Thorne & Sukop (2004)

Elder (1967)

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ResultsResults

Frolkovič, P., H. De Schepper (2001) Adv. Wat. Res. 24, 63-72

Thorne & Sukop

Thorne & Sukop (2004)

Frolkovič & De Schepper (2001)

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Elder (1967)

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