Annulus pressure loss due to friction during hydraulic fracturing (laminar flow)

Input(s)

v: Average Velocity $(\mathrm{ft} / \mathrm{s})$

L: Pipe Length (ft)

$d_{0}$ : Inner Diameter of the Outer Pipe (in.)

$d_{1}$ : Outer Diameter of the Inner Pipe (in.)

$\mu_{p}$: Plastic Viscosity $(\mathrm{cP})$

$\tau_{y}$: Yield Point of the Liquid $\left(\mathrm{lb} / 100 \mathrm{ft}^{2}\right)$

Output(s)

$\Delta P_{f}$: Pressure Loss in the wellbore due to Frictions during Hydraulic Fracturing (psi)

Formula(s)

$$ \Delta P_{f}=\frac{\mu_{p} L v}{1000\left(d_{0}-d_{i}\right)^{2}}+\frac{\tau_{y} \cdot L}{200 \cdot\left(d_{0}-d_{i}\right)} $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publiching Co., Page: 31.