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Bioremediation for Sustainable Environmental Cleanup

(Xexp) by means of goodness-of-fit analysis, which is evaluated by the regression coefficient R² and

the average relative error (ARE) (Dhanasekaran et al. 2017) defined by the following expression:

(Xi,calc −Xi,exp )

ARE = ¹⁰⁰ ∑ⁿ

—

Eq. 3.5

i=1

n

Xi,exp

The proximity of the value of R² to one (Tan and Hameed 2017) and ARE values lower than

35% (Tsai et al. 2016) indicate a good fit of the model to the experimental data.

To exemplify the application of these models, the work system was compounded by Azolla

biomass with a contaminant solution of copper, for which a continuous reactor was assembled,

whose dimensions were 15 cm in height, 15.9 cm³ in volume and an internal diameter of 1.161 cm,

which was completed with 4.3 g of biomass with a particle size between 1.18–0.5 mm and then a

Cu(II) solution of 50 mM concentration was passed upstream at a fixed flow rate of 0.5 mL min^–1

and the Cu(II) concentration at the reactor outlet was measured at different volumes by ultraviolet-

visible spectrophotometry. From the breakthrough curves obtained (C/C0 versus V graph) the

nonlinear fitting models mentioned above were applied and the corresponding parameters listed in

Table 3.4 were obtained.

Table 3.4. Obtained parameters with the Thomas–Bohart-Adams and Yoon-Nelson models for the adsorption of copper onto

Azolla biomass in fixed bed reactor.

Azolla-Cu

Thomas

Model

KTH

2.39

q 0 calc

0.6222

q 0 exp

0.679

R²

0.996

ARE

8.39

Bohart-Adams Model

KAB

1.637

No calc

0.1951

No exp

8.68E-2

R²

0.9770

ARE

125

Yoon-Nelson Model

Kyn

0.1005

τcalc

136.3

τexp

135.0

R²

0.996

ARE

0.96

From the data obtained for the modeling of the experimental breakthrough curve it can be

observed that both the Thomas and Yoon-Nelson models are the most appropriate to describe the

behavior of the experimental data, since both have R² greater than 0.99 and an ARE less than 35%,

which would indicate that the value of the parameters calculated by the model and the experimental

one are very similar. These models adequately fit adsorption processes where external and

internal diffusions are not the limiting step (Aksu and Gönen 2004). Both models have analogous

mathematical equations, so they were expected to predict similar fits (Chu 2020), however, from

each of them, different information about the system under study can be obtained. The Thomas

model allows estimating the maximum amount of adsorbate retained in the solid phase, from the

calculated q0 which resulted to be 0.622 mmol g^–1. On the other hand, the Yoon-Nelson model

allows knowing the value of the time required for the concentration in the effluent to be equal to

50% of the input, the latter, determined by the parameter τ, was 136 min.