MCMFIT: A Program to fit a generalized non-linear advection- dispersion model to experimental data

The problem of estimating model parameters is encountered frequently in practice. There are several packages available for estimating the parameters for linear advection-dispersion equations (ADE) for which there are exact solutions (e.g., CXTFIT, TFMFIT, etc.). For non- linear transport equations, the use of standard numerical solutions (e.g., Crank-Nicolson) to estimate parameters is very time consuming and hence inefficient. On the other hand, mixing-cell solutions are very efficient by comparison. In particular, the solution obtained from the improved mixing cell model has been found to agree very well with the results of a numerical Crank-Nicolson solution while being much more efficient. Thus, an improved mixing cell model has been used hereto estimate model parameters for a variety of transport models. The code, MCMFIT, makes use of nonlinear least-squares fitting to find optimal parameter values by matching improved mixing cell model predictions with measured experimental data. The experimental data can be either in the form of a breakthrough curve or concentrations within a soil profile. The program can handle linear, Freundlich, Langmuir, and S- curve adsorption isotherms in conjunction with the transport equation. Both equilibrium and non- equilibrium (fully kinetic and two site adsorption) cases can be dealt with along with first- and third-type surface boundary conditions. Use of the program is demonstrated with a number of examples. Both synthetic data as well as data from yield and laboratory experiments have been used in the illustrative examples.