Half of the total length $\begin{array}{l}X_f = 0.5 \cdot L_f\end{array}$ of the hydraulically induced vertical plane fracture (see Fig. 1).

Fig. 1 – Hydraulic fracture schematic showing fracture half-length (X_f), fracture height (h_f) and fracture width (w_f).

For the fractured vertical well the geometrical skin-factor $\begin{array}{l}S_G\end{array}$ is related to Fracture half-length $\begin{array}{l}X_f\end{array}$ as:

(1)	$\begin{array}{l}\displaystyle S_G= -\ln \left(\frac{X_f}{r_w} \right) + \frac{1.65 -0.328 \, u + 0.116 \, u^2}{1+0.18 \, u + 0.064 \, u^2 +0.05 \, u^3}\end{array}$

where

$\begin{array}{l}u = \ln F_{CD}\end{array}$
$\begin{array}{l}F_{CD}\end{array}$	dimensionless hydraulic fracture conductivity

In case of high dimensionless hydraulic fracture conductivity (corresponding to infinite conductivity fracture case) the skin-factor model can be simplified:

(2)	$\begin{array}{l}\displaystyle S_G = -\ln \left(\frac{X_f}{2\, r_w} \right)\end{array}$

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