Thomas, Yoon–Nelson, and Adams–Bohart models were applied to the breakthrough curves, and the values of characteristic parameters are presented in Tables 4–6, respectively.

Table 4

Parameters of the Thomas model at different conditions

Parameters .	Pb .			Cd .			Zn .
	(mL/min mg) .	(mg/g) .	R2 .	(mL/min mg) .	(mg/g) .	R2 .	(mL/min mg) .	(mg/g) .	R2 .
Influent metal conc. (mg/L)
10	3.50	10.79	0.971	3.05	6.90	0.979	3.58	11.41	0.982
50	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
100	0.26	42.75	0.996	0.29	23.04	0.999	0.27	47.71	0.978
Flow rate (mL/min)
1	0.50	24.18	0.985	0.48	17.11	0.994	0.59	25.91	0.972
2	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
3	0.76	22.34	0.995	0.72	12.01	0.991	0.74	23.14	0.994
Bead height (cm)
2	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
4	0.49	24.96	0.992	0.55	19.85	0.998	0.46	25.12	0.992
6	0.43	25.88	0.977	0.52	20.64	0.993	0.42	25.83	0.966

Parameters .	Pb .			Cd .			Zn .
	(mL/min mg) .	(mg/g) .	R2 .	(mL/min mg) .	(mg/g) .	R2 .	(mL/min mg) .	(mg/g) .	R2 .
Influent metal conc. (mg/L)
10	3.50	10.79	0.971	3.05	6.90	0.979	3.58	11.41	0.982
50	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
100	0.26	42.75	0.996	0.29	23.04	0.999	0.27	47.71	0.978
Flow rate (mL/min)
1	0.50	24.18	0.985	0.48	17.11	0.994	0.59	25.91	0.972
2	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
3	0.76	22.34	0.995	0.72	12.01	0.991	0.74	23.14	0.994
Bead height (cm)
2	0.66	23.38	0.989	0.66	16.22	0.996	0.65	23.52	0.996
4	0.49	24.96	0.992	0.55	19.85	0.998	0.46	25.12	0.992
6	0.43	25.88	0.977	0.52	20.64	0.993	0.42	25.83	0.966

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Table 5

Parameters of the Yoon–Nelson model at different conditions

Parameters .	Pb .			Cd .			Zn .
	(min−1) .	(min) .	R2 .	(min−1) .	(min) .	R2 .	(min−1) .	(min) .	R2 .
Influent metal conc. (mg/L)
10	0.031	618.56	0.974	0.031	417.53	0.979	0.036	721.82	0.982
50	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
100	0.033	218.32	0.996	0.034	122.87	0.999	0.027	307.0	0.978
Flow rate (mL/min)
1	0.025	563.59	0.981	0.024	418.95	0.994	0.030	654.0	0.972
2	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
3	0.038	192.33	0.995	0.036	96.50	0.991	0.037	212.85	0.994
Bead height (cm)
2	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
4	0.024	534.57	0.992	0.028	450.56	0.998	0.025	571.58	0.992
6	0.022	848.88	0.977	0.026	654.28	0.993	0.023	792.94	0.966

Parameters .	Pb .			Cd .			Zn .
	(min−1) .	(min) .	R2 .	(min−1) .	(min) .	R2 .	(min−1) .	(min) .	R2 .
Influent metal conc. (mg/L)
10	0.031	618.56	0.974	0.031	417.53	0.979	0.036	721.82	0.982
50	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
100	0.033	218.32	0.996	0.034	122.87	0.999	0.027	307.0	0.978
Flow rate (mL/min)
1	0.025	563.59	0.981	0.024	418.95	0.994	0.030	654.0	0.972
2	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
3	0.038	192.33	0.995	0.036	96.50	0.991	0.037	212.85	0.994
Bead height (cm)
2	0.032	303.07	0.989	0.033	205.76	0.996	0.031	326.31	0.996
4	0.024	534.57	0.992	0.028	450.56	0.998	0.025	571.58	0.992
6	0.022	848.88	0.977	0.026	654.28	0.993	0.023	792.94	0.966

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Table 6

Parameters of the Adams–Bohart model at different conditions

Parameters .	Pb .			Cd .			Zn .
	× 10−3 (L/mg min) .	(mg/L) .	R2 .	× 10−3 (L/mg min) .	(mg/L) .	R2 .	× 10−3 (L/mg min) .	(mg/L) .	R2 .
Influent metal conc. (mg/L)
10	1.48	2,448.99	0.951	1.82	1,561.83	0.929	1.73	2,493.21	0.963
50	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
100	0.118	11,837.1	0.832	0.165	6,835.08	0.916	0.126	12,789.4	0.935
Flow rate (mL/min)
1	0.269	6,147.82	0.78	0.243	4,147.48	0.888	0.312	5,898.80	0.849
2	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
3	0.332	7,150.24	0.865	0.442	3,699.8	0.805	0.422	7,005.36	0.949
Bead height (cm)
2	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
4	0.247	6,146.78	0.836	0.276	4,308.68	0.897	0.225	5,318.43	0.926
6	0.214	5,419.16	0.781	0.277	3,970.51	0.894	0.321	4,668.57	0.925

Parameters .	Pb .			Cd .			Zn .
	× 10−3 (L/mg min) .	(mg/L) .	R2 .	× 10−3 (L/mg min) .	(mg/L) .	R2 .	× 10−3 (L/mg min) .	(mg/L) .	R2 .
Influent metal conc. (mg/L)
10	1.48	2,448.99	0.951	1.82	1,561.83	0.929	1.73	2,493.21	0.963
50	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
100	0.118	11,837.1	0.832	0.165	6,835.08	0.916	0.126	12,789.4	0.935
Flow rate (mL/min)
1	0.269	6,147.82	0.78	0.243	4,147.48	0.888	0.312	5,898.80	0.849
2	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
3	0.332	7,150.24	0.865	0.442	3,699.8	0.805	0.422	7,005.36	0.949
Bead height (cm)
2	0.299	6,872.58	0.901	0.403	4,455.01	0.878	0.336	6,369.43	0.895
4	0.247	6,146.78	0.836	0.276	4,308.68	0.897	0.225	5,318.43	0.926
6	0.214	5,419.16	0.781	0.277	3,970.51	0.894	0.321	4,668.57	0.925

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