Dimensionless pressure drop across a skin at the well face

Input(s)

$k$: Effective Permeability of Flowing Phase (D)

$h$: Net Formation Thickness (m)

$P_{i}$: Initial Reservoir Pressure (psi)

$P_{1 h r}$: Pressure at 1 hour on semi-log straight line or its extension (psi)

$P_{w s}$: Shut in Pressure (psi)

$P_{w f}$: Bottomhole Pressure at a flowing well (psi)

$v_{s c}$: Specific Volume at Standard Conditions $(\mathrm{cc} / \mathrm{g})$

$q$: Production Rate $\left(\mathrm{m}^{3} / \mathrm{h}\right)$

B: Formation Volume Factor (Reservoir Volume/Standard Volume)

$\mu$: Viscosity of Flowing Fluid (cP)

$c_{t}$: Total System Effective Isothermal Compressibility $\left(\mathrm{kg} / \mathrm{cm}^{2}\right)^{-1}$

$r_{w}$: Well Radius $(\mathrm{m})$

$m$: Slope of Semi-Log Graph $\left(\mathrm{kg} / \mathrm{cm}^{2}\right) / \log$ cycle for Liquid

$\varnothing$: Porosity (Per cent)

Output(s)

$P_{D w}$: Dimensionless Pressure at the well face (dimensionless)

$s$: Skin Effect (dimensionless)

Formula(s)

$$ \begin{gathered} P_{D w}+s=\frac{k h\left(P_{i}-P_{w s}\right)}{0.4568 v_{s c} q B \mu} \\ s=1.151\left[\frac{\left(P_{1 h r}{ }^{2}-P_{w f}{ }^{2}\right)}{m}-\log _{10} \frac{k}{\varnothing \mu c_{t} r_{w}^{2}}+0.0919\right] \end{gathered} $$

Reference(s)

Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University, Page: (5.13).