This study presents the application of a triple-porosity nonequilibrium model (TPNE) trifurcating the liquid phase within representative elementary volume (REV) in a saturated porous medium. The model accounts for both physical and chemical nonequilibrium conditions to capture the fate of solute through a porous medium. The governing equation is numerically solved using the finite volume method and validated with semi-analytical solution of dual advection dispersion equation (DADE). Temporal moment analysis is carried out to demonstrate the model's response for a range of Peclet and Damkohler numbers. The sensitivity of number of input parameters is highlighted using global sensitivity analysis. A sensitivity-based model calibration using parameter estimation package (PEST) is employed to describe observed BTC through a heterogeneous soil column. The TPNE model captured the skewed BTC with enhanced accuracy compared with mobile immobile (MIM) model. It is concluded that TPNE model is capable of capturing the detailed signature of the various processes of a skewed breakthrough curve (BTC) having multiple inflection points.