A mathematical model is developed which predicates the performance of cylindrical ion exchange bed involving comparing of axial dispersion model for cation exchange column with different assumption, this model permits the performance to predicate the residence time within the bed with the variance, axial dispersion and Pecklet No. to indicated deviation from plug flow model.
Two type of systems are chosen for positive ions first with divalent ions (Ca+2) to exchange with resin of Na+1form used as application in water softener units and second with monovalent ions (Na+1) to exchange with resin of H+1 form used as application in deionize water units with two parameters effected in the operation of the two systems different flow rate and different feed concentration by their effect on axial dispersion in each one where the system are compare from the performance which describe in term of breakthrough time other parameters (the time equivalent to usable capacity "tu" , time equivalent to equilibrium capacity "tt" and length of unused bed "HUNB") are calculated in the operation condition that with axial dispersion are very important in predicated the best condition to operation the cation exchange column as a softener and deionize units.
