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.