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.