Table 3 Mathematical models applied to MR curves.

1

Aghbashlo

\(\:MR=\text{exp}\left(-\frac{{k}_{1}t}{1+{k}_{2}t}\right)\)

Semi-Theoretical

^48,49

2

Henderson - Pabis

\(\:MR=a\:\text{e}\text{x}\text{p}\left(-kt\right)\)

^50,51,52

3

Lewis (Newton)

\(\:\text{M}\text{R}=\text{e}\text{x}\text{p}\left(-\text{k}\text{t}\right)\)

4

Midilli

\(\:\text{M}\text{R}=\text{a}\text{*}\text{e}\text{x}\text{p}\left(-\text{k}{\text{t}}^{n}\right)+bt\)

5

Modified Midilli (I)

\(\:\text{M}\text{R}=\text{e}\text{x}\text{p}\left(-\text{k}{\text{t}}^{n}\right)+bt\)

^53,54

6

Modified Midilli (II)

\(\:\text{M}\text{R}=\text{a}\text{*}\text{e}\text{x}\text{p}\left(-\text{k}{\text{t}}^{n}\right)+b\)

7

Logarithmic (Asymptotic)

\(\:\text{M}\text{R}=\text{a}\text{*}\text{e}\text{x}\text{p}\left(-\text{k}\text{t}\right)+c\)

Empirical

^50,51,52

8

Modified Page

\(\:\text{M}\text{R}=\text{e}\text{x}\text{p}\left(-{\left(\text{k}\text{t}\right)}^{\text{n}}\right)\)

9

Page

\(\:\text{M}\text{R}=\text{e}\text{x}\text{p}\left(-\text{k}{\text{t}}^{\text{n}}\right)\)

10

Wang-Sigh

\(\:MR=1+bt+a{t}^{2}\)

11

Weibullian (I)

\(\:\text{M}\text{R}=\text{e}\text{x}\text{p}\left(-{\left(\frac{t}{\alpha\:}\right)}^{\beta\:}\right)\)

^53,54

12

Weibullian (II)

\(\:\text{M}\text{R}={10}^{-{\left(\frac{t}{\delta\:}\right)}^{n}}\)