This study proposed an asymptotic relation to estimate the first-order mass transfer in multiprocess non-equilibrium model (MPNE) for solute transport through stratified porous media. The applicability of the proposed relation was tested with concentration data of reactive and non-reactive solutes through stratified porous media under the different hydraulic gradients. Semi-analytical solution of MPNE transport equation incorporating scale-dependent dispersivity was employed for simulating experimental breakthrough curves. MPNE transport model with scale-dependent dispersivity and constant mass transfer coefficient underestimated the solute mass at observation points. MPNE with constant and asymptotic mass transfer coefficient was then compared, and it was found that experimental breakthrough curves with the proposed relation were better simulated. The study concluded that averaging the mass transfer coefficient over higher scale and applied to a lower scale of observation, or vice-versa, will attribute to the scale dependent behavior. The skewed shape of breakthrough curve was also discussed in details, and it was found that immobile liquid phase was contributing to the prolonged tail concentration. This study further enhances the simulation and prediction capabilities of MPNE for large stratified aquifers.