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Heavy metal pollution is a growing environmental and health concern. Heavy metal ions, like Cu(II), undergo the Fenton reaction, producing hydroxide radicals and superoxides that cause DNA mutation (crosslinking and depurination) and carcinogenic damage to the living organisms. This study evaluates the performance of olive stones for Cu(II) removal from effluents in a continuous simulated process under different operating conditions using Aspen Adsorption® V8.0. Flow rate, bed height, and initial metal ion concentration were varied to analyze the effect of these parameters on the bed performance. The fastest breakthrough time was 5 h when the system was run at a flow rate of 2 L/s, 1 m bed height, and 5 ppm initial metal ion concentration. The optimal conditions for the process were found to be 1 m bed height, 2 ppm initial metal ion concentration, and 0.5 L/s flow rate at which 0.543 mg/g metal adsorption capacity of the bed was observed. Under these conditions, bed life was observed to be 163.8 h. The aim of this work is to provide motivation towards usage of low-cost biosorbents for industrial scale adsorption processes.