- In the present study, a phenomenological model of deep-bed filtration is suggested. It combines an advection-dispersion equation with an equation of nonlinear multistage accumulation kinetics. The model includes dispersion and accounts for temporal and spatial changes in media porosity. It is suggested that at any location inside the column the filter deposit is formed first as an irreversible ripening layer, followed by formation of reversible deposit during the operable stage. The latter continues until the deposit reaches locally its maximum value. Then, filter breakthrough takes place. The equations are solved numerically, using an explicit finite-difference scheme. The results compare favorably with laboratory experiments at an EPA facility, and with field experiments performed by Mekorot– Israeli Water Company.