This is a model of two superpositioned parallelipiped
initial source volumes
with nonequilibrium sorption. The source
areas retain significant
nonequilibrium mass, and are visible at
the left side of the plume.
This is a plot of concentration on
the plane z=0, which
cuts through the initial source
solutions in SOLUTRANS all assume a uniform one-dimensional flow
field in the positive x direction. There is three-dimensional
dispersion with different coefficients allowed in all three
directions. One set of solutions assumes equilibrium in the solute
and adsorbed phases (Leij et. al., 1991), while another set of
solutions allows nonequilibrium (kinetic) conditions (Leij et. al.,
With the nonequilibrium solutions, the solute may be out of
equilibrium with some of the adsorption sites. Van Genuchten and
Wagenet (1989) and Leij et. al. (1993) describe two common ways of
conceptualizing nonequilibrium transport; a ``two-site'' concept and
a ``two-region'' concept. Both concepts lead to similar partial
differential equations that are, in fact, written as a common
dimensionless partial differential equation. In the two-site
concept, some fraction of adsorption sites are at equilibrium while
other sites are not. At the nonequilibrium (kinetic) sites, a
first-order rate law governs adsorption. In the two-region concept,
there is mobile pore water and immobile pore water and both are in
equilibrium with the sorption sites that they are in contact with.
Solute migrates by advection and dispersion in the mobile region,
and first-order diffusion transfers solute mass from the mobile
region to the immobile region (Coats and Smith, 1964; van Genuchten
and Wierenga, 1976).
Separate first-order decay coefficients may be specified for the
equilibrium and the nonequilibrium phases. The nonequilibrium models
allow you to examine the distribution of equilibrium (mobile water)
concentrations, nonequilibrium (immobile water) concentrations, and
the total (aqueous + adsorbed) concentration.
Unlike the solutions of Domenico and Robbins (1985, Groundwater,
v. 23, p. 476.) and Domenico (1987, Jour. Hydrol. v. 91, p. 49),
these solutions do not make approximations that cause errors near
the source. These are exact solutions which involve some numerical
Both the equilibrium and nonequilibrium solutions allow four
different source geometries:
- rectangular inlet area
- circular inlet area
- parallelipiped (rectangular box) initial volume
- cylindrical initial volume
The ten solutions implemented in SOLUTRANS are listed below:
- Rectangular inleat, equilibrium, steady-state
- Rectangular inlet, equilibrium
- Rectangular inlet, nonequilibrium
- Circular inlet, equilibrium, steady-state
- Circular inlet, equilibrium
- Circular inlet, nonequilibrium
- Parallelepiped initial volume, equilibrium
- Parallelepiped initial volume, nonequilibrium
- Cylinder initial volume, equilibrium
- Cylinder initial volume, nonequilibrium
Using the superposition features
built into SOLUTRANS, it is possible to model contaminant sources
that have irregular distributions in time and space as shown
here . See the figure
above for an example of source superposition.
All these solutions may be used to create simpler
two-dimensional, one-dimensional, and diffusion-only solutions, if
SOLUTRANS User Interface
has a seamless, Windows-standard user interface. It has been
designed to be very simple and fast. Most common modeling operations
are executed at the push of a button on the
main screen. Mathematical model input data are accessed directly in a
spreadsheet-like grid. Data can be imported and exported using the Windows
SOLUTRANS can produce three types of plots: 1) concentrations vs.
distance along a line, 2) concentrations vs. time at a point, and 3)
surface plots of concentrations vs. location on a plane. Press here
to see examples of plot types (1) and (2), and see the above plot
for an example of type (3).
Plots are made on the screen, and may be exported to the Windows
Clipboard or to disk files in either bitmap (.BMP) or metafile
(.WMF) format. Concentration data may also be exported directly in
comma-delimited ASCII files for use with other visualization
software programs. Data may also be exported in .GRD format files
for surface plotting using SURFER software.
The following forms of on-line help are available: tips that
automatically display when you pause over a control,
context-sensitive help (F1 key), and a Windows-standard help file.
The help file is indexed, searchable, printable, and it contains
embedded jumps to related topics.
the information about how to use the software is in the on-line help
system. The SOLUTRANS Manual is a 7 x 9 inch spiral bound booklet
containing the following sections.
- Introduction - describes the software and how to install
- Tutorial - step-by-step development and modification of a
SOLUTRANS model, showing screens as they appear in the process.
- Method Employed - a detailed section describing the
governing equations and the general nature of the analytic
- Modeling Tips - includes advice about parameter units,
computational speeds, superposition, 1-D, 2-D, and
diffusion-dominated transport models, etc.
- Program Checks - 42 separate checks of the solutions
implemented in SOLUTRANS. The model input files for the check
models are included on the software diskettes.
SOLUTRANS System Requirements
- 32-bit Windows operating system (Windows 95/98/NT as of this
- 4 MB of hard disk space
- 8 MB of memory
- The commercial SOLUTRANS license is a typical software
license; one license allows installation on one computer at a
- The academic license is a site license available for qualified
educational institutions and is restricted to academic,
- Purchase of either license includes unlimited support to make
sure that SOLUTRANS operates properly on your system.
H. and B. D. Smith. 1964. Dead-end pore volume and dispersion in
porous media. Soc. Petrol. Engr. Jour., v. 4, p. 73-84.
Leij, F. J., T. H. Skaggs, and M. Th. van Genuchten. 1991.
Analytical solutions for solute transport in three-dimensional
semi-infinite porous media. Water Resources Research, v. 27(10), p.
Leij, F. J., N. Toride, and M. Th. van Genuchten. 1993.
Analytical solutions for nonequilibrium solute transport in
three-dimensional porous media. Journal of Hydrology, v. 151, p.
Leij, F. J. and S. A. Bradford. 1994. 3DADE: A computer program
for evaluating three-dimensional equilibrium solute transport in
porous media. U. S. Salinity Laboratory Research Report No. 134,
Leij, F. J. and N. Toride. 1997. N3DADE: A computer program for
evaluating nonequilibrium three-dimensional solute transport in
porous media. U. S. Salinity Laboratory Research Report No. 143,
van Genuchten, M. Th. and J. C. Parker. 1984. Boundary conditions
for displacement experiments through short laboratory soil columns.
Soil Science Soc. of Am. Jour., v. 48, p. 703-708.
van Genuchten, M. Th. and R. J. Wagenet. 1989. Two site/two
region models for pesticide transport and degradation: theoretical
development and analytical solutions. Soil Science Soc. of Am.
Jour., v. 53, p. 1303-1310.
van Genuchten, M. Th. and P. J. Wierenga. 1976. Mass transfer
studies in sorbing porous media: 1. analytical solutions. Soil
Science Soc. of Am. Jour., v. 40, p.