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Fracture Systems Permeability

Fracture Systems Permeability 2016-10-25T11:54:44+00:00

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:

Poiseuille's equation for fluid conductivity of capillary tubes

The total area available to flow is
Total area available to flow a=πr^2

So that the equation reduces to
Poiseuille's with total area available to flow

From Darcy’s law:
Darcy's law equation

After equating two last equations we have
equating Poiseuille's equation with total flow available with Darcy's equation

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

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

flow through slots of fine clearance and unit width, buckingham equation

By analogues to Darcy’s law:
fracture flow Buckingham analogue to Darcy Law

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

References

[1]

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