# 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).

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