A Note on the Skin Effect

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Abstract
Horner and van Everdingen have shown that the pressure drop within the wellbore, as a result of having produced the well at a constant rate q for time t, where t is sufficiently large, is: (Equation 1) van Everdingen observed that better agreement between theory and well performance can be obtained if, instead of assuming the permeability is ke everywhere about the well, it is assumed the permeability near the wellbore is substantially reduced as a result of drilling, completion and/or production practices. In order to account for the additional pressure drop he introduced the dimensionless quantity S, the skin effect factor, so that Eq. 1 becomes: (Equation 2) Eq. 2 might have also been obtained as follows. Assume a zone of altered permeability ka exists about the well out to a radius ra, and beyond that the unaltered, external permeability ke. The additional pressure drop required to overcome this skin of reduced permeability may be calculated with sufficient accuracy using the incompressible flow equation; for Brownscombe and Collins have shown almost no difference between compressible and incompressible steady-state flow, in the vicinity of the wellbore, and the small volume of fluid in the vicinity of the wellbore makes unsteady-state mechanics unnecessary. Then, (Equation 3) The sign of this skin pressure drop will be positive or negative depending upon whether the altered permeability ka is smaller or larger, respectively, than the external permeability ke.
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