Flow through fracture in response to pressure gradient

Input(s)

$\mu$ : Fluid Viscosity (cP)

$L$: Length $(\mathrm{ft})$ v: Poisson (dimensionless)

$P_{f}$: Fracture Pressure (psi)

$S_{c}$: Least Principle Stress (psi)

$E$: Young Modulus (psi)

$\Delta P$: Pressure Gradient (psi)

Output(s)

Q: Flow Rate $\left(\mathrm{ft}^{3} / \mathrm{s}\right)$

Formula(s)

$$ Q=\left(\frac{\pi * \Delta P}{8 * \mu}\right) *\left(\left(\frac{L *\left(1-v^{2}\right) *\left(P_{f}-S_{c}\right)}{E}\right)^{3}\right) $$

Reference(s)

Mark D. Zoback., Reservoir Geomechanics, Cambridge University Express, UK, Page: 142.