Downhole operating pressure (hydraulic fracturing)
Input(s)
\(\Delta P_{f}\): Pressure Loss Sourced by Friction (psi)
\(\Delta P_{p}\): Pressure Loss sourced by Perforations(psi)
\(\Delta P_{h}\): Hydrostatic Pressure Change (psi)
\(P_{i n j}\): Injection Pressure \((\mathrm{psi})\)
D: Fracture Elevation Depth (ft)
\(G_{f}\): Fracture Gradient \((\mathrm{psi} / \mathrm{ft})\)
Output(s)
\(P_{F}\): Downhole Operating Pressure \((\mathrm{psi})\)
Formula(s)
\[
\begin{gathered}
P_{F}=G_{f} \cdot D \\
G_{f}=\frac{P_{i n j}+\Delta P_{h}-\Delta P_{f}-\Delta P_{p}}{D}
\end{gathered}
\]
Reference(s)
Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 25.