The performance of the adsorption column is conveniently described through the concept of the breakthrough curve (Aksu et al. 2007). A plot of the ratio of concentrations (Ct/C0) versus time (t) or volume (v) of the effluent is known as the breakthrough curve (Ct/C0 versus time). The breakthrough curves illustrate the performance of fixed-bed columns, and the time to reach the breakthrough and shape of the breakthrough curve are the key characteristics for evaluating the adsorption capacity of a column because they directly affect the feasibility and economics of the adsorption process (Ahmad & Hameed 2010). An ideal breakthrough curve has a symmetric sigmoidal shape (S-shape) and the time required for the effluent concentration to reach 10% of the input concentration (Ct/C0 = 0.1) was defined as the breakthrough point time (tb). Table 2 represents various breakthrough parameters and their equations for determination (Luo et al. 2011; Nuić et al. 2013; Yagub et al. 2015).
Breakthrough parameters and their equations for determination
| Breakthrough parameters | Equations | |
|---|---|---|
| Breakthrough time, tb (min) | Time at  | |
| Exhaust time, te (min) | Time at  | |
| Column capacity, qc (mg) |  | Q and A are the flow rate (mL/min) and the area under the breakthrough curve, respectively. Cad = C0 − Ce, Ce is effluent metal ions concentration and C0 is influent metal ions concentration (mg/L). |
| Total amount of metal ions sent to the column, m (mg) |  | |
| Percentage removal of metals |  | |
| Adsorption capacity, q (mg/g) |  | X is the total mass of the adsorbent in the column (g) |
| Length of mass transfer zone (MTZ) (cm) |  | H is total depth of the adsorbent in the column (cm). |
| Breakthrough parameters | Equations | |
|---|---|---|
| Breakthrough time, tb (min) | Time at | |
| Exhaust time, te (min) | Time at | |
| Column capacity, qc (mg) | | Q and A are the flow rate (mL/min) and the area under the breakthrough curve, respectively. Cad = C0 − Ce, Ce is effluent metal ions concentration and C0 is influent metal ions concentration (mg/L). |
| Total amount of metal ions sent to the column, m (mg) | | |
| Percentage removal of metals | | |
| Adsorption capacity, q (mg/g) | | X is the total mass of the adsorbent in the column (g) |
| Length of mass transfer zone (MTZ) (cm) | | H is total depth of the adsorbent in the column (cm). |