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This research report documents the Fortran program N3DADE (Nonequilibrium 3-Dimensional Advection-Dispersion Equation) which may be used to evaluate analytical solutions described by Leij et al. [1993]. The analytical solutions pertain to selected cases of three-dimensional solute transport during steady unidirectional water flow in porous media of semi-infinite length in the longitudinal direction, and of infinite length in the transverse directions. The solutions may also be applied to one- and two-dimensional problems. Transport and flow properties of the medium are assumed to be macroscopically uniform. Nonequilibrium solute transfer can occur between two domains in either the liquid or the adsorbed phase. The transport equation contains terms for solute movement by advection and dispersion, and for solute retardation, first-order decay, and zero-order production. Solute concentrations are calculated as a function of time and space in a three-dimensional Cartesian coordinate system.

This report serves as both a user manual for the program and as documentation of the general analytical solutions of the boundary, initial and production value problems involved. A comprehensive set of specific solutions is presented using Dirac, Heaviside and exponential functions to describe the initial, boundary and production profiles. A rectangular or circular inflow area is specified for the boundary value problem, while for the initial and production value problems the respective initial and production profiles are defined for parallelepipedal, cylindrical, or spherical regions of the soil. Solutions are given for volume-averaged or resident concentrations, as well as for flux-averaged or flowing concentrations.

The user manual gives a detailed description of the computer program, including the subroutines used to evaluate the analytical solutions for optimizing model parameters. Input and output files for all major problems are also included.

The manual provides:

  • A list of main program variables
  • The format of the input file
  • Listings of sample input and output files
  • The source code N3DADE.FOR
Release Date
United States Department of Agriculture
Contact Name
Skaggs, Todd
Contact Email
Public Access Level
Program Code
005:040 - Department of Agriculture - National Research
Bureau Code
005:18 - Agricultural Research Service