Dimensionless fracture width for linear vertical fracture (Geertsma & Klerk)

Input(s)

$C$: Over-all Fluid-Loss Coefficient $\left(\mathrm{m} /\left(\mathrm{s}^{0.5}\right)\right)$

$h$ : Fracture Height (m)

E: Young's Modulus of the Formation Rock $\left(\mathrm{kg} / \mathrm{m}-\mathrm{s}^{2}\right.$ )

$i$ : Fluid Injection Rate $\left(\mathrm{m}^{3} / \mathrm{s}\right)$

$t$ : Total time for Fluid Injection (s)

$w_{w}$ : Fracture width at the Wellbore (m)

$V_{s p t}$ : The Spurt Volume $\left(\mathrm{m}^{3} / \mathrm{m}^{2}\right)$

Output(s)

$K_{L}$: Dimensionless Fracture Length (dimensionless)

$K_{u}$: Reciprocal Dimensionless Fracture Width (dimensionless)

$K_{s}$: Dimensionless Fluid-Loss Coefficient (dimensionless)

$K_{\eta L}$: Dimensionless Variable (dimensionless)

Formula(s)

$$ \begin{gathered} K_{L}=C L h / i \sqrt{t} \\ K_{u}=C \sqrt{t} / w_{w} \\ K_{s}=C \sqrt{t} / V_{s p t} \\ K_{\eta L}=21.8\left(\frac{i}{h C^{2}}\right)^{3}\left(\frac{\mu}{E t}\right) \end{gathered} $$

Reference(s)

Williams, B. B., Gidley, J. L., \& Schechter, R. S. (1979). Acidizing fundamentals. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME, Page: 40.