A transient mathematical model has been followed to study the displacement washing of pulp bed composed of porous, compressible and cylindrical shaped fibres. The flow pattern of wash liquid through the bed can be described by a dispersion flow model involving Peclet number and Blot number. The effect of porosity along with Peclet number and Biot number on the solution profile of exit solute concentration via breakthrough curves has been studied. Concentration of solute adsorbed on fibre surface and intrapore solute concentration are related by Langmuir adsorption isotherm. Displacement washing has been simulated using a laboratory washing cell. Five runs of experiments have been performed on pulp beds formed from unbeaten, unbleached kraft fibres to check the authenticity of theoretical results. Axial dispersion coefficient is found to be influenced by interstitial velocity as well as the bed consistency. Washing process is affected collectively by Peclet number, Biot number and bed porosity.