Page 206 - Geology of Carbonate Reservoirs

FRACTURE PERMEABILITY, POROSITY, AND S W 187

most applicable to siliciclastic sandstones and less so to carbonates). As noted in
2

the next paragraph, values for Hubbert ’ s Nd could not be reliably defined and other

methods had to be developed to model flow in fractures.
7.2.1 Fracture Permeability

2
Nelson (2001) notes that the value of Nd could not be reliably defi ned when

attempts were made to model fl uid flow in fractures. In order to model fl uid fl ow in

fractures, the parallel plate theory for fl uid flow was developed. The essence of this

theory is the assumption that flow occurs between two smooth parallel plates a dis-

tance e apart. The following equation represents flow that should pass through the
two plates:
Q e 3 dh ρ g
= ⋅ ⋅
A 12 D dl μ

where Q is discharge in volume per time, A is area of the slot between the plates,
D is plate spacing, or the average distance between regularly spaced parallel plates,
and e is slot width. This is the expression for laminar fl ow in parallel fractures with
only nominal variation in fracture width.
The Darcy equation deals with matrix permeability or, as Nelson (2001) calls it,
the “ intact portion of the rock, ” whereas the equation for fl ow in parallel fractures

deals only with the theory of flow between parallel plates. An expression to deal

with flow through both matrix and parallel fractures was developed by Parsons
(1966) . The combined flow expression is

e cos α
2
3
k fr = k r +
12 D
and flow through fractures only is given by

k f = e 2 ⋅ ρ g
12 μ

where k fr = Permeability of matrix (intact rock) plus fracture
k f = Fracture permeability
k r = Matrix permeability

α = Angle between the fracture planes and the axis of the subsurface pres-

sure gradient
Of course, the underlying assumptions for all of these equations are that fl ow is
laminar, the plates are smooth and do not move, and fracture width and spacing are
constant. The equations provide a method for estimating fracture permeability
knowing some of the fracture properties. If the assumed conditions are not met,
these equations will not provide realistic results.
It is also important to understand that fracture permeability ( k f ) and fracture
width ( e ) decrease exponentially with depth and confining pressure. According to