Page 64 - Geology of Carbonate Reservoirs

DEPENDENT OR DERIVED ROCK PROPERTIES 45

Q = k(A/μ) • dP/dL

Figure 2.14 A modified Darcy apparatus to measure permeability, where fluid viscosity and

pressure can be varied to be more representative of subsurface reservoir conditions. The
original Darcy apparatus, a glass cylinder with mercury manometers and flow valves, was

designed to operate at atmospheric pressure with water only.

in pressures. Consider a laboratory apparatus (Figure 2.14 ) to measure permeability
of reservoir rock samples. In this system a rock sample of length dL and cross -

sectional area A is saturated with a fluid of dynamic viscosity μ , which fl ows through
dL at a rate Q . Under steady - state conditions, the upstream pressure is P , and the
downstream pressure is ( P – dP ). There is no flow through the sides of the sample

and there is no reaction between fluid and rock. Under these conditions, the modi-

fied Darcy ’ s law is
Q kdP
= ⋅
A μ dL

In this expression, k is the permeability coefficient and represents rock properties.

It is known as absolute or specifi c permeability and has the dimensions of an area.
The permeability expression is written

cm 3 A cm 2 dP atm
Q = k darcies ⋅ ⋅
)
(
s μ centipoise dL cm

Or, 1 darcy of permeability is defined as when a fluid with unit viscosity flows at a

2
3
rate of 1 cm /s from a rock sample with a cross - sectional area of 1 cm under a differ-

3
ential pressure of 1 atm/cm . It would be nice if reservoirs delivered 1 cm of fl uid for

2
each cm of surface area; however, most do not; consequently, the practical working
unit of permeability in the petroleum industry is the millidarcy (md), which is equal
2
− 15
2
2
− 15
to 0.0987 × 10 m . In ordinary applications, 1 md = 10 m and 1 darcy = 1 μ m .

Permeability varies greatly in carbonate reservoirs from values of less than 0.1 md

in tight, crystalline mosaics in mudstones to over 10 darcies in fracture, cavern, or
connected vug systems. Qualitatively, reservoir permeability values can be graded
in the following manner (North, 1985 ):