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Density-Dependent Flows

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

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Density-Dependent Flows

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  1. 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

  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 • Chain rule (and soon T!)

  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. Darcy’s 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. L Salt Source E Heater Elder Problem C=0 E/H=4 L/H=2 Temperature-induced buoyancy Solute-induced buoyancy H C=1 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 L C=1 H C=0 E // Controlling parameter Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623

  24. Elder Problem L C=1 H C=0 E // Controlling parameter Elder, J. W. (1967) J. Fluid Mech. 27 (3), 609-623

  25. Results Thorne & Sukop (2004) Elder (1967) Year 1 Year 2 60% 20% Year 4 Year 10 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 (2004) Frolkovič & De Schepper (2001) Thorne & Sukop 80% Year 1 60% Year 2 80% 40% 60% 40% 20% 20% Year 4 Year 10 80% 80% 60% 60% 40% 20% 40% 20% Year 15 Year 20 80% 80% 80% 80% 60% 60% 40% 40% 20% 20% Frolkovič, P., H. De Schepper (2001) Adv. Wat. Res. 24, 63-72

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

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