Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Permeability:

Fracture Systems Permeability

In many sand and carbonate reservoirs the formation frequently contains solution channels and natural or artificial fractures. These channels and fractures do not change the permeability of the matrix but do change the effective permeability of the system.  In order to determine the contribution made by a fracture or channel to the total conductivity of the medium, it is necessary to express their conductivity in terms of Darcy’s law.

Channels:
Recalling Poiseuille’s equation for fluid conductivity of capillary tubes:

The total area available to flow is

So that the equation reduces to

From Darcy’s law:

After equating two last equations we have

If r is in centimeter, then K in darcy is given by:

Fracture:
For flow through slots of fine clearance and unit width, Buckingham reported that

By analogues to Darcy’s law:

Where h is in cm, the permeability of a fracture in darcy is given by