Kinetic Models

Non-Linear Forms

Equation Number

References

Pseudo-First Order:

$\frac{\text{d}{Q}_t}{\text{d}t}=K_1\left(Q_e-Q_t\right)$

(3)

[20]

$Q_t=Q_e\left(1-{\text{e}}^{-K_{1}t}\right)$

(4)

Pseudo-Second Order:

$\frac{\text{d}{Q}_t}{\text{d}t}=K_2{\left(Q_e-Q_t\right)}^2$

(5)

[21]

$Q_t=\frac{K_2{Q}_e^{2}t}{1+K_2{Q}_{e}t}$ and $h=K_2{Q}_e^2$

(6)

Intraparticle Diffusion:

$Q_t=K_{int}{t}^{\frac{1}{2}}+C$

(7)

[22]

Elovich Model:

$\frac{\text{d}{Q}_t}{\text{d}t}=\alpha {\text{e}}^{-\beta Q_t}$

(8)

[23]

$Q_t=\frac{1}{\beta }\ln \left(1+\alpha \beta t\right)$

(9)

Fractional Power:

$Q_t=K{t}^v$

(10)

[24]

Avrami:

$Q_t=Q_e\left\{1-\exp {\left[-\left(K_{AV}t\right)\right]}^{n_{AV}}\right\}$

(11)

[25]

Tobin:

$Q_t=\frac{Q_e{K}_T{t}^{n_T}}{1+K_T{t}^{n_T}}$

(12)

[26]