Computing "anomalous" contaminant transport in porous media: the CTRW MATLAB toolbox

We describe the continuous time random walk (CTRW) MATLAB toolbox, a collection of MATLAB scripts and functions that compute breakthrough curves (BTCs) and one-dimensional/two-dimensional (1D/2D) resident concentration profiles for passive tracer dispersion. The transport model is based on the CTRW theory. CTRW includes as special cases the classical Fickian dispersion based advection-dispersion equation, multirate and mobile-immobile models, and the fractional-in-time derivative transport equation. Several models for treating the memory effects responsible for the anomalous character of dispersion have been implemented in the CTRW toolbox. In the current version of the toolbox, it is possible to solve explicitly for the forward problem (concentration prediction) in 1D and 2D and for the inverse problem (parameter identification from experimental BTC data) in 1D. Future extensions will include explicit treatment of sorbing tracers, simple subroutines for treating radial flow from wells, introduction of arbitrary initial conditions, treatment of heterogeneous domains by use of the Fokker-Planck with Memory equation, and treatment of transport in multidimensional systems.