Pressure to grow fractures (Abe, Mura, et al.)
Input(s)
\(S_{c}\): Minimum Principle Stress (psi)
\(P_{p}\): Pore Pressure \((\mathrm{psi})\)
\(c_{f}\): Radius of Fracture (in.)
\(c_{i}\): Radius of Invaded Zone (in.)
Output(s)
\[
P_{\text {grow }}: \quad \text { Growth Pressure (psi) }
\]
Formula(s)
\[
\mathrm{P}_{\text {grow }}=\mathrm{S}_{\mathrm{c}} *\left(\frac{1-\left(\frac{\mathrm{P}_{\mathrm{p}}}{\mathrm{S}_{\mathrm{c}}}\right) *\left(1-\left(\frac{\mathrm{c}_{\mathrm{f}}}{\mathrm{c}_{\mathrm{i}}}\right)^{2}\right)^{0.5}}{1-\left(\left(1-\left(\frac{\mathrm{c}_{\mathrm{f}}}{\mathrm{c}_{\mathrm{i}}}\right)^{2}\right)^{0.5}\right)}\right)
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 326.