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. 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 –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)SWICHA –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)TARGET –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

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 Problem Elder, J. W. (1967) J. Fluid Mech. 27 (3) Voss, C. I., W. R. Souza (1987) Wat. Resour. Res. 23, E/H=4 L/H=2 Temperature-induced buoyancy Solute-induced buoyancy Heater Salt Source

L E H C=1 C=0 Elder Problem Elder, J. W. (1967) J. Fluid Mech. 27 (3), // Controlling parameter

L E H C=1 C=0 Elder Problem Elder, J. W. (1967) J. Fluid Mech. 27 (3), // Controlling parameter

Results Notes No fully accepted results (computer or lab). Maybe no unique solution. Elder, J. W. (1967) J. Fluid Mech. 27 (1), Elder, J. W. (1967) J. Fluid Mech. 27 (3), Woods, J. A., et al. (2003) Wat. Resour. Res. 39, Thorne & Sukop (2004) Elder (1967) 20% 60% 20% 60% 20% 60% 20% 60% 20% Year 1Year 2 Year 10Year 4 Year 15Year 20

Results Frolkovič, P., H. De Schepper (2001) Adv. Wat. Res. 24, Thorne & Sukop Thorne & Sukop (2004) Frolkovič & De Schepper (2001) 20% 40% 60% 80% 20% 40% 60% 80% 20% 40% 60% 80% 20% 40% 60% 80% 20% 40% 60% 80% 20% 40% 60% 80% Year 15 Year 4 Year 1Year 2 Year 10 Year 20

Results (year 15) Thorne & Sukop Thorne & Sukop (2004) Elder (1967) Thorne & Sukop (2004) Frolkovič & De Schepper (2001) Year 15 20% 40% 60% 80% 20% 60%