Table 3.
List of mathematical models, references, coefficients and statistical parameters
| Sr. no. | Models name, mathematical expression and refence | Coefficients | R2 | χ2 | RMSE |
|---|---|---|---|---|---|
| 1 |
Lewis model (Bruce 1985) MR = exp(− kt) |
k = 0.0016 | 0.9900 | 6.50×10−4 | 0.0254 |
| 2 |
Page model (Page 1949) MR = exp(− ktn) |
k = 0.0013, n = 1.0296 | 0.9903 | 6.31×10−4 | 0.0249 |
| 3 |
Henderson and Pabis model (Henderson and Pabis 1961) MR = a exp(− kt) |
k = 0.0016, a = 0.9997 | 0.9899 | 6.54×10−4 | 0.0254 |
| 4 |
Logarithmic Model (Togrul and Pehlivan 2002) MR = a exp(− kt) + c |
k = 0.0012, a = 1.1214, c = −0.1584 | 0.9949 | 3.34×10−4 | 0.0181 |
| 5 |
Two term model (Henderson 1974) MR = a exp(− k0t) + b exp(− k1t) |
k0 = 0.0464, k1 = 0.0016, a = 0.0058, b = 0.9987 | 0.9898 | 6.64×10−4 | 0.0254 |
| 6 |
Wang and Singh Model (Wang and Singh 1978) MR = 1 + at + bt2 |
a = −0.0013, b = 4.3485×10−7 | 0.9841 | 1.03×10−3 | 0.0319 |
| 7 |
Approximation of diffusion Model (Yaldiz et al. 2001) MR = a exp(− kt) + (1 − a) exp (−kat) |
k = 0.0018, a = 1.4276 | 0.9908 | 5.98×10−4 | 0.0243 |
| 8 |
Verma Model (Verma et al. 1985) MR = a exp(− kt) + (1 − a) exp(− gt) |
a = 1, g = 1.1217, k = 0.0016 | 0.9899 | 6.54×10−4 | 0.0254 |
| 9 |
Hii, Law & Cloke Model (Hii et al. 2009) MR = a exp(− ktn) + c exp(− gtn) |
n = 1.0773, k = 9.1985×10−4, a = 0.4298, g = 9.2010×10−4, c = 0.5409 | 0.9908 | 5.97×10−4 | 0.0240 |