The mixing model that PHREEQC uses for transport is not commonly used. Usually, the partial differential equations for advection and dispersion are solved with more standard numerical methods--implicit or explicit formulas for time and space.
You can use the mixing model, but you would have to study the manual for version 2 and probably get a copy of the book by Appelo and Postma, Groundwater, geochemistry and pollution.
PhreeqcRM is designed to run chemistry on a set of cells, but the user is expected to do all of the transport calculations.