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A non-linear advection dispersion model involving Peclet number (Pe) and intraparticle diffusion coefficient is proposed for displacement washing process of porous particles. Non-linear model equations are solved using cubic Hermite collocation method (HCM) to compute exit and average solute concentrations. Effect of different parameters such as Peclet number, intraparticle diffusion coefficient and bed porosity (ε) has been discussed theoretically as well as graphically. Industrial parameter such as displacement ratio (DR) is calculated by using model predicted values. Effect of different parameters on displacement ratio, exit and average solute concentrations is discussed through surface plots.