| Symbols | Designation | Unit |
|---|---|---|
| Letters | ||
| A | Cross-sectional area | m2 |
| g | Gravitational acceleration | ms-2 |
| Pf | Oil phase pressure | kgm-1s-2 |
| Pk | Kinematic pressure | kgm-1s-2 |
| Ps | Sand phase pressure | kgm-1s-2 |
| Pw | Water phase pressure | kgm-1s-2 |
| qf | Volume flow rate of oil | m3s-1 |
| qs | Volume flow rate of sand | m3s-1 |
| qw | Volume flow rate of water | m3s-1 |
| t | Time | hrs or s |
| Vm | Volume of mixture | m3 |
| wo | Oil velocity | ms-1 |
| ws | Sand velocity | ms-1 |
| ww | Water velocity | ms-1 |
| z | Axial distance | m |
| β | Fluid-particle interaction coefficient | kgm3s-1 |
| Δz | Change in length | m |
| ε | Oil concentration (volume fraction) | - |
| ϕ | Suspended sand concentration (volume fraction) | - |
| σ | Deposited sand concentration (volume fraction) | - |
| ϕ’ | Total sand concentration (volume fraction) | - |
| θ | Water concentration (volume fraction) | - |
| ρf | Oil density | kg/m3 |
| ρs | Sand density | kg/m3 |
| ρw | Water density | kg/m3 |