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### & GROUNDWATER VISTAS

Effective Diffusion Coefficient

In last month's newsletter we discussed diffusion.  This month we continue on this theme with a discussion on the effective diffusion coefficient. A couple of calculators are also given which provide you with different methods of calculating this coefficient.

What is the effective diffusion coefficient?

The effective diffusion coefficient takes into account the fact that diffusion can only take place through pore openings because mineral grains block many of the possible pathways.

How is the effective diffusion coefficient calculated?

There is no method of measuring an effective diffusion coefficient in the field, and so they must be calculated from other properties. Most equations for calculating the effective diffusion coefficient are empirical in nature, with portions that are either determined through laboratory experiments, or with the use of fitting parameters. Most of the equations follow a general structure given by:

Dd'=wDd

Where Dd' represents the effective diffusion coefficient, Dd is the bulk diffusion coefficient, and w is some scaling value that accounts for the structure of the porous medium.

How does the physical properties of the porous medium effect the effective diffusion coefficient?

There are many different physical properties of the porous medium that can effect the effective diffusion coefficient, the most obvious being porosity. The effective diffusion coefficient will increase with increasing porosity, as there will be less media to prevent the movement of the ions. In addition, depending on the nature of the porous media, the species may adsorb onto the mineral surfaces, decreasing the diffusion as well.

What are some example values of the effective diffusion coefficient?

The effective diffusion coefficient varies significantly depending on the nature of the porous medium, and the species diffusing itself. Bulk diffusion coefficients for some ions in water are given below; these would then have to be scaled to account for the presence of the porous medium (taken from Domenico and Schwartz, 1998).

 Cation Dd (10-6 cm2/s) Anion Dd (10-6 cm2/s) H+ 93.1 OH- 52.7 Na+ 13.3 F- 14.6 K+ 19.6 Cl- 20.3 Rb+ 20.6 Br- 20.1 Cs+ 20.7 HS- 17.3 Mg2+ 7.05 HCO3- 11.8 Ca2+ 7.93 CO32- 9.55 Sr2+ 7.94 SO42- 10.7 Ba2+ 8.48 Ra2+ 8.89 Mn2+ 6.88 Fe2+ 7.19 Cr3+ 5.94 Fe3+ 6.07

Using these values, the effective diffusion coefficient can then be calculated using one of the following equations/calculators:

Greenkorn(1983)

Dd'=µnDd

Where µ is an empirical value less than one, and n is porosity.

Dd   cm2/s

n

µ

Dd':   cm2/s

Greenkorn & Kissler(1972)

Dd'=(n/æ)Dd

Where æ is tortuosity, which will be discussed in the next newsletter.

Dd   cm2/s

n

æ

Dd':   cm2/s

Hellferich(1966)

The Hellferich equations give a range of values for the effective diffusion coefficient from:

Dd'=(n/2)Dd

to:

Dd'=(n/(2-n))2Dd

Dd   cm2/s

n

Dd': from to   cm2/s

Groundwater Vistas is a groundwater flow and transport model that can be used to simulate the movement of contaminants, via advection, dispersion and diffusion, in the subsurface.

In next month's newsletter we will discuss tortuosity, which is a value describing the path of the water through the porous media.

References

Domenico P.A. and Schwartz, F.W. (1998). Physical and Chemical Hydrogeology. Published by John Wiley & Sons, Inc. New York, NY.

Fetter, C.W. (1994). Applied Hydrogeology; Third Edition.  Published by Prentice-Hall, Inc., Englewood Cliffs, NJ.

Freeze, R.A. and Cherry, J.A. (1979). Groundwater. Published by Prentice-Hall, Inc., Englewood Cliffs, NJ.

Groundwater Vistas (GV) is a sophisticated Windows graphical user interface for 3-D groundwater flow & transport modeling . GV couples a powerful model design system with comprehensive graphical analysis tools. Developed by the author of ModelCadTM, GV is a model-independent graphical design system for MODFLOW MODPATH (both steady-state and transient versions), MT3DMS, MODFLOWT, MODFLOW-SURFACT, MODFLOW2000, GFLOW, RT3D, PATH3D, SEAWAT and PEST.

New Features in Groundwater Vistas Version 5 include:

• New Model Versions: GV5 will support PEST Version 11, MT3DMS Version 5, MODFLOW-SURFACT Version 3, MODFLOW2000V1.17, and MODFLOW2005.
• Pest Version 11 comes with GV5
• GV5 now supports two types of regularization
• GV5 now checks for all of the common errors encountered in SVD calibration runs
• GV5 supports an analytic element model called SPLIT
• GV5 has newly rewritten charting cabailities
• ESI's new Remote Launch technology allows many simulations to be run when running Automated Sensitivity Analysis and Monte Carlo simulations (with Remote Launch purchase)
• GV5 supports the new MODFLOW2005 runoff/recharge package that includes the effects for flow through the unsaturated zone

Other New Features in Groundwater Vistas version 5.0 include:

• Better model reports
• Automatic run time logs
• Custom contour levels
• Easier boundary condition editing
• Custom output control
• Changing boundary types
• and Much, Much More!!!