Derivation of an equation for radionuclide transport in porous media

To analytically predict the transport of radionuclides in porous media, it is necessary to develop a complete mathematical model. This means that the mechanisms must be described and the governing equations derived, along with their general solutions for the transport processes. The four major mechanisms---advection, dispersion, adsorption-desorption and ion exchange, and degradation---are physically described and mathematically modeled. Based on the classic principle of mass conservation in a control volume, the governing equation for the transport of radionuclides in porous media is derived, which may be called the advection-dispersion equation. Some general solutions of the governing equation are obtained by using constant dispersion coefficients. In addition, some ambiguities of the advective-dispersion equation are solved, and this equation is extended to fractured media