The flow of miscible fluids through the beds of finite length to investigate the mechanism of displacement washing is presented through a diffusion-dispersion model. The model is based on phenomenon of diffusion-dispersion in porous cylindrical particles, e.g., fibers. The data of 4(th) stage industrial brown stock washer is used for simulation. Empirical relations have been found between key parameters such as cake thickness, fiber porosity, bed porosity and fiber consistency. Concentration of black liquor solids in discharge pulp and efficiency parameters have been correlated using least square principle.