In this paper, a semi-analytical solution of multiprocess non-equilibrium (MPNE) transport equations with linear and exponential distance-dependent dispersivity is developed. The model has been used to simulate the laboratory experimental data of chloride and fluoride solutes through a 15 m long heterogeneous soil column. It is observed that a better fit to the observed breakthrough curves is obtained, when the mass transfer between advective and non-advection region is considered. It is also observed that both linear and exponential distance-dependent dispersion models give a good fit to the observed breakthrough curves, however, the exponential distance-dependent dispersion model gives a much better fit. The estimated transport parameters can be used for simulation of observed data of reactive plume through the porous media at field scale and also for the remediation of contaminated subsurface soil.