Flow through fracture in response to pressure gradient

Input(s)

μ\mu : Fluid Viscosity (cP)

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

PfP_{f}: Fracture Pressure (psi)

ScS_{c}: Least Principle Stress (psi)

EE: Young Modulus (psi)

ΔP\Delta P: Pressure Gradient (psi)

Output(s)

Q: Flow Rate (ft3/s)\left(\mathrm{ft}^{3} / \mathrm{s}\right)

Formula(s)

Q=(πΔP8μ)((L(1v2)(PfSc)E)3)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.


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