Proppant settlement in fracture

Input(s)

$\rho_{p}$: Proppant Density $\left(\mathrm{lbm} / \mathrm{ft}^{3}\right)$

$\rho_{f}$: Fluid Density $\left(\mathrm{lbm} / \mathrm{ft}^{3}\right)$

$\mathrm{g}$: Gravity Acceleration $\left(\mathrm{ft} / \mathrm{s}^{2}\right)$

$d_{p}$: Particle Diameter $(\mathrm{ft})$

$v_{t}$: Terminal Particle Settling Velocity (ft/s)

Output(s)

$C_{D}$: Coefficient of Drag (unitless)

Formula(s)

$$ \mathrm{C}_{\mathrm{D}}=4 *\left(\rho_{\mathrm{p}}-\rho_{\mathrm{f}}\right) * \mathrm{~g} * \frac{\mathrm{d}_{\mathrm{p}}}{\rho_{\mathrm{f}} * \mathrm{v}_{\mathrm{t}}^{2}} $$

Reference(s)

Daneshy, A. 2013. Fundamentals of Hydraulic Fracturing, Daneshy Consultants International, Page: 74.