S/N

Model Name

Model Equation

Reference

1.

Newton/Lewis

$MR=\exp \left(-kt\right)$

[59]

2.

Page

$MR=\exp \left(-k{t}^n\right)$

[55]

3.

Modified Page

$MR=\exp \left[{\left(-kt\right)}^n\right]$

[60]

4.

Modified Page II

$MR=\exp \left(-k{\left(\frac{t}{L^2}\right)}^n\right)$

[61] [62]

5

Modified Page III

$MR=k\exp {\left(-\frac{t}{d^2}\right)}^n$

[63]

6.

Henderson and Pabis

$MR=a\exp \left(-kt\right)$

[64]

7.

Logarithmic

$MR=a\exp \left(-kt\right)+c$

[65]

8.

Two Term

$MR=a\exp \left(-k_{0}t\right)+b\exp \left(-k_{1}t\right)$

[66]

9.

Two Term Exponential

$MR=a\exp \left(-kt\right)+\left(1-a\right)\exp \left(kat\right)$

[60]

10.

Wang and Singh

$MR=M_O+at+b{t}^2$

$MR=1+at+b{t}^2$

[67] [68]

11.

Singh et al.

$MR=\exp \left(-kt\right)-akt$

[4]

12.

Approximation of Diffusion (or Diffusion Approach)

$MR=a\exp \left(-kt\right)+\left(1-a\right)\exp \left(-kbt\right)$

[65]

13.

Verma et al.

$MR=a\exp \left(-kt\right)+\left(1-a\right)\exp \left(-gbt\right)$

[69]

14.

Modified Henderson and Pabis

$MR=a\exp \left(-kt\right)+b\exp \left(-gt\right)+c\exp \left(-ht\right)$

[50]

15.

Aghabashlo Model

$MR=\exp -\left(\frac{k_{1}t}{1+k_{0}t}\right)$

[70]

16.

Ademiluyi Modified

$MR=a\exp -{\left(kt\right)}^n$

[71]

17.

Weibull

$MR=\exp \left(-{\left(\frac{t}{a}\right)}^b\right)$

[72]

18.

Midilli et al.

$MR=a\exp \left(-k{t}^n\right)+bt$

[61]

19.

Peleg Model

$M-M_O=-\frac{1}{k_1+t{k}_2},\frac{\text{d}m}{\text{d}t}=R=-\frac{k_1}{k_1+t{k}_2}$

[32]

20.

Silva et al.

$MR=\exp \left(-at-b{t}^{\frac{1}{2}}\right)$

[73]

21

Thompson

$t=aIn\left(MR\right)+b{\left[In\left(MR\right)\right]}^2$

[74]

22.

Geometric

$MR=a{t}^{-n}$

[75]

23.

Combined Two Term and Page

$MR=a\exp \left(-k{t}^n\right)+b\exp \left(-h{t}^n\right)$

[76]