To understand the process of dynamic fixed bed adsorption behavior of BF affected by bed depth and flow rate better, two mathematical models were used to describe the breakthrough curves. The breakthrough curves fitted by the Adams–Bohart and Thomas models are also presented in Fig. 9a and b. The Adams–Bohart model  equation ABT378 expressed as follows:equation(17)lnCtC0=KABC0t-KABN0ZFwhere KAB (L mg−1 min−1) represents the kinetic constant, N0 (mg L−1) is the saturation concentration, Z (cm) is the bed depth of the fixed bed column and F (cm min−1) is complete flower the superficial velocity defined as the ratio of flow rate to the cross section area of the bed. The Thomas model  is expressed by Eq. (18):equation(18)lnC0Ct-1=KTq0mQ-KTC0twhere KT (mL min−1 mg−1) represents the Thomas model constant, q0 (mg g−1) is the equilibrium adsorption capacity of the sorbents. The other parameters have their usual meanings as described for the two models. The calculated values of parameters along with the correlation coefficient (R2) of the two models are displayed in Table 6.