There’s some maths in this post, but even for the mathematically challenged, it is really worth making the effort to understand what is going on here since skin can have such a huge impact on well productivity.

The ideal pressure profile is represented as total skin = 0 to describe a perforation that has no skin damage at all and where the pressure gradient in the reservoir increases towards the wellbore due to the fluids having to flow through an increasingly smaller cross-sectional area (flow convergence).

When the formation in the near wellbore region has been damaged (i.e. total skin > 0), the pressure drop in this damaged region (rd) increases as shown due to the effects of the near well bore damage. The greater the additional pressure drop the lower the productivity or injectivity.

The following equations are used to show mathematically how the concept of “Skin” (S’) can be included in the basic Darcy Equation for either Oil or Gas well inflow:

For oil:

For gas:

Where the terms used are expressed in oil field units:

S’ = Total Skin Factor [Dimensionless]

Pr = Reservoir Pressure [psi]

Pw = Flowing Bottom Hole Pressure [psi]

Q = Flow Rate [bbl/d or mmscf/d]

µ = Fluid Viscosity [Cp]

B = Formation Volume Factor [rb/stb]

k = Permeability [md]

h = Net Reservoir Thickness [ft]

r_{e} = Drainage Radius [ft]

r_{w} = Well Bore Radius [ft]

T = Temperature [^{o}R]

Z = Gas Deviation Factor

If you’ve got this far, it is possible to express the equation for the total Skin factor (S’) in the following way,

Where:

R_{d} = radius of the damaged zone (ft)

k_{d} = permeability of damaged zone (md)

This is important for perforating because it directly relates well productivity to the effectiveness of the well perforation.

### More from ‘The Perforator’s Guide to Formation Damage’

The Perforator’s Guide to Formation Damage. **Part 2**: How Skin Can Greatly Affect Flow Performance

The Perforator’s Guide to Formation Damage. **Part 3**: Perforation Skin and its influence on production