The surface complexation approach has been applied to describe the adsorption of lead and proton onto a heterogeneous natural porous medium (red pozzolan) at constant ionic strength (0.1 mol L-1). Acid−base titration experiments were used to determine the minimum number of sites needed to describe the surface heterogeneity. Lead adsorption tests at several pH and total lead concentration were used to complete the model structure, whose adjustable parameters (site concentrations and apparent formation constants) were determined by nonlinear multivariate regression of titration and adsorption data. The final model represents the acid−base properties of the surface by the presence of two amphoteric sites, SOH and TOH, and a monoprotic one, MOH; whereas lead adsorption is considered only onto SOH and MOH sites. The model allows a good representation of the experimental behavior in the whole experimental range (pH = 4−10 for titration, pH = 3.5−6.0 and total lead concentration from 8.8 × 10-5 to 7.3 × 10-4 mol L-1 for adsorption experiments). Theoretical surface speciation shows that lead adsorption occurs mostly onto site MOH at low pH level and on both SOH and MOH sites at higher values. The model was independently validated by simulating Pb and pH breakthrough experiments performed in small chromatrographic columns. Experimental breakthroughs are well predicted by an advection−dispersion transport model coupled with the chemical equilibrium routine (IMPACT), without any parameter adjustment. A large spreading of Pb and pH breakthroughs was calculated and experimentally observed, even in the absence of any kinetic effect. That spreading is explained in terms of the concomitant presence of competitive adsorption and surface heterogeneity.