The pulp washing is a process in which soluble and insoluble materials which are adsorbed on the fiber surface are removed with the introduction of external fluid. The state of diffusion, adsorption, dispersion, desorption occurs throughout the process of solute removal and is described by the mathematical models. In the present study, a non-linear model of pulp washing is solved using a hybrid collocation scheme with the experimental data of a paper mill. The study highlights the effect of peclet number (the ratio of advection to diffusion) for the case of perfect mixing and displacement. Besides, the effect of dispersion coefficient and interstitial velocity on exit solute concentration are also discussed. The results reveal that medium range of peclet number increases the washing efficiency.