Table 3 Relationship between pressure gradient and velocity under different sand concentration
From: Influence of particle size on non-Darcy seepage of water and sediment in fractured rock
Number | Concentration (kg/m3) | Pressure gradient (MPa/m) | Velocity (m/s) | Polynomial function | Power function |
|---|---|---|---|---|---|
1 | 20 | 0.38 | 0.10 | \(G_{p} = 155.61V^{2} - \, 41.24V + \, 3.72\) R2 = 0.9882 | \(G_{p} = 0.29e^{9.04V}\) R2 = 0.9259 |
2.10 | 0.17 | ||||
5.08 | 0.27 | ||||
6.98 | 0.35 | ||||
15.27 | 0.44 | ||||
24.92 | 0.52 | ||||
4.54 | 0.17 | ||||
2 | 40 | 7.62 | 0.30 | \(G_{p} = 118.08V^{2} - \, 36.42V \, + \, 7.43\) R2 = 0.9970 | \(G_{p} = 2.14e^{4.28V}\) R2 = 0.9954 |
11.11 | 0.40 | ||||
19.21 | 0.50 | ||||
27.98 | 0.60 | ||||
5.71 | 0.11 | ||||
3 | 60 | 9.30 | 0.26 | \(G_{p} = 108.12V^{2} - \, 7.42V \, + 5.38\) R2 = 0.9956 | \(G_{p} = 3.74e^{4.07V}\) R2 = 0.9953 |
15.24 | 0.35 | ||||
24.16 | 0.40 | ||||
33.81 | 0.51 | ||||
7.94 | 0.16 | ||||
12.70 | 0.27 | ||||
4 | 80 | 22.22 | 0.35 | \(G_{p} = 55.04V^{2} + 119.60V - 11.08\) R2 = 0.9602 | \(G_{p} = 4.50e^{4.35V}\) R2 = 0.8968 |
28.57 | 0.44 | ||||
35.24 | 0.51 |