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

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

After simplification

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

Figure 2-24: Linear Flow through Series Beds

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