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.