In the last decade a growing interest was observed in low-cost adsorbents for heavy metal ions. Clinoptilolite is a mineral sorbent extracted in Poland that is used to remove heavy metal ions from diluted solutions. The experiments in this study were carried out in a laboratory column for multicomponent water solutions of heavy metal ions, i.e. Cu(II), Zn(II) and Ni(II). A mathematical model to calculate the metals' concentration of water solution at the column outlet and the concentration of adsorbed substances in the adsorbent was proposed. It enables determination of breakthrough curves for different process conditions and column dimensions. The model of process dynamics in the column took into account the specificity of sorption described by the Elovich equation (for chemical sorption and ion exchange). Identification of the column dynamics consisted in finding model coefficients β, KE and Deff and comparing the calculated values with experimental data. Searching for coefficients which identify the column operation can involve the use of optimisation methods to find the area of feasible solutions in order to obtain a global extremum. For that purpose our own procedure of genetic algorithm is applied in the study.