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Harmonic-Average Permeability

Harmonic-Average Permeability 2016-10-25T11:54:44+00:00

Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Permeability:

Harmonic-Average Permeability

Permeability variations can occur laterally in a reservoir as well as in the vicinity of a well bore. Consider Figure 2‑24 which shows an illustration of fluid flow through a combination of series beds with different permeabilities. For a steady-state flow, the flow rate is constant and the total pressure drop  is equal to the sum of the pressure drops across each bed, or
Total pressure drop is equal to sum of the pressure drops

Substituting for the pressure drop by applying Darcy’s equation, i.e., Equation (2-28), gives:
Substituting for pressure drop by applying Darcy's equation

After simplification
Substituting for pressure drop by applying Darcy's equation simplified

General expression for average permeability of a series layered formation with n layer is:
General expression for average permeability of a series layered formation with n layer

Linear Flow through Series Beds
Figure 2-24: Linear Flow through Series Beds

For radial systems with series layers the following general equation can be produced for average permeability:
General equation average permeability-layered-series

References

[1]

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