Table 5.

Parameters of models evaluated for different experimental conditions (1st, 2nd, 3rd, 4th, 5th, 7th, 8^th cycle), and parameters of the model simulated from the curve fitting on Fig. 6 (6th and 9th cycle)

Cycles for testing models									Predicted cycles
	Cycle No	1st	2nd	3rd	4th	5th	7th	8th	6th	9th
Experimental conditions	H, mm		120			80	40		80	40
	co(Zn), mmol/L	1.067	1.067	1.067	1.787	0.770	1.083	1.051	1.083	1.054
	Q, mL/min			1.0				2.0	1.0	3.0
	qE, mmol/g	0.547	0.650	0.692	0.631	0.726	0.703	0.714	0.786	0.759
Dose–response model	kDR, -	11.312	13.599	20.167	18.523	18.338	14.747	7.111	18.324	4.079
	qDR, mmol/g	0.585	0.668	0.731	0.634	0.531	0.709	0.669	0.706	0.637
	r2	0.967	0.996	0.994	0.980	0.984	0.985	0.982	0.978	0.983
	RMSE	0.074	0.028	0.031	0.058	0.060	0.042	0.058	0.063	0.055
Thomas model	kT, L/(mmol h)	0.133	0.139	0.184	0.193	0.347	0.428	0.320	0.297	0.229
	qT, mmol/g	0586	0.669	0.732	0.635	0.532	0.711	0.680	0.704	0.653
	r2	0.962	0.994	0.993	0.981	0.983	0.987	0.964	0.975	0.966
	RMSE	0.081	0.034	0.033	0.056	0.060	0.044	0.076	0.065	0.132
Bohart-Adams model	kBA, L/(mmol h)	0.133	0.139	0.184	0.193	0.347	0.428	0.320	0.297	0.229
	qBA*, mmol/L	388.63	444.09	485.81	421.32	346.95	456.13	436.79	457.881	421.643
	qBA, mmol/g	0.586	0.669	0.732	0.635	0.532	0.711	0.681	0.702	0.657
	r2	0.962	0.994	0.993	0.981	0.983	0.986	0.964	0.974	0.950
	RMSE	0.081	0.034	0.033	0.056	0.060	0.044	0.076	0.066	0.135
Yoon-Nelson model	kYN, h−1	0.142	0.148	0.196	0.345	0.267	0.464	0.341	0.321	0.240
	τYN, h	82.345	94.097	102.937	53.303	67.913	31.740	15.246	63.000	10.605
	qYN, mmol/g	0.586	0.669	0.732	0.635	0.532	0.711	0.663	0.694	0.694
	r2	0.962	0.994	0.993	0.981	0.983	0.986	0.972	0.972	0.950
	RMSE	0.081	0.034	0.033	0.056	0.060	0.044	0.071	0.071	0.135
Wolborska model	βA, h−1	13.107	18.841	27.316	19.936	23.886	53.754	53.677	39.294	52.409
	qW*, mmol/L	537.42	569.40	562.09	444.66	434.65	479.94	737.37	547.415	800.676
	qW, mmol/g	0.810	0.858	0.847	0.670	0.666	0.748	1.150	0.839	1.248
	r2	0.813	0.894	0.924	0.948	0.873	0.958	0.782	0.882	0.892
	RMSE	0.170	0.131	0.112	0.309	0.161	0.326	0.372	0.140	0.237

c – the effluent zinc concentration (mmol/L), c₀ – the influent zinc concentration (mmol/L), t – the time (h), Q – the flowrate (L/h), v – the linear flow velocity (m/h), H – the fixed bed dept (m), m – the mass of the zeolite bed in column (g), V – the effluent volume (L), k_DR – the kinetic constant of Dose–response model (-), q_DR – the saturation capacity calculated from the Dose–response model (mmol/g), k_T – the rate constant of the Thomas model (L/(mmol h)), q_T – the saturation capacity calculated from the Thomas model (mmol/g), k_BA—the rate constant of the Bohart-Adams model (L /(mmol h)), q_BA^*– the adsorption capacity of the Bohart-Adams model (mmol/L), τ_YN – the time required for 50% of zinc breakthrough calculated from the Yoon-Nelson model (h), k_YN – the rate constant of the Yoon-Nelson model (h⁻¹), q_YN – the saturation capacity calculated from the Yoon-Nelson model (mmol/g), β_A – the kinetic coefficient of the external mass transfer (h⁻¹), q_w ^* – the sorption capacity of the Wolborska model (mmol/L)