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7/31/2019 2.4 Rock Permeability
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2.4 Permeabili t y of reservoir rock
2 The unit of permeability
3 The conditions of measuring absolutepermeability
4 Applicable condition of Darcy's law
as ermea y an ec o as ppage
on Permeabilityra ua on o orma on n permea y
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2.4 Permeability of reservoir rock
7 Factors af fect in the ma nitude of
permeabil ity
9 Flow Syst ems of Sim ple Geomet ry
10 Average perm eabilit y of combinat ion
layers11 The relat ionship of permeabilit y and
ot her ro ert of rock
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rock
In 1856, Darcy investigated the flow ofwa er roug san ers .
s exper men a appara us s s ownin Fig
Darcy interpreted his observations soas to y e resu ts essent a y as g ven n
equation.
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hhK
upstream pressure
21
L
of rockexperimental apparatus
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Definition of ermeabilit
Permeability is the ability of fluids to
pass roug a porous ma er a .
3
1 Darcy =
( ) ( )cmatmcm 112
1 Darcy = 0.987 x 10-8 cm2
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ere,
cylindrical sand pack of cross-sectional area A
P is pressures drop across the cylindrical
sand pack .
s v scos y o e u
, ,
characteristic of the sand pack.
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2 The unit of permeability
Darc CGS PERM SI
L cm cm ft cm
A cm2 cm2 ft2 cm2
P atm dyn/cm2 psia MPa cp p cp mpa.s
Q cm3/s cm3/s bbl/day cm3/s
Kdarcy cm
2
perm m
2
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Physical significance of one Darcy
One Darcy is defined as the permeability that
to flowat a rate of 1 cm3/s through a cross
sectional area of 1 cm2 when the pressure
gradient is 1 atm/cm.
1 Darcy (d)=1000 millidarcy (md)
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permeability
The orous medium must be 100 er centsaturated with the flowing fluid.
No interaction between the fluid and theporous media
Laminar flow .
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EXAMPLE 4
If the length of a core sample is 3cm ,and the
cross-sec on area s cm . n er a pressure
difference of 2atm, the core sample will bepermit a fluid of 1 cp (centipoise ) viscosity to
flow at a rate of 0.5cm3/s throu h.
Calculate permeability of core sample .
:
.0.375K D= = = ( )
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,be permit a fluid of 3 cp (centipoise ) viscosity
to flow at a rate of 0.167cm3/s through,
n er t e same pressure erence.
0.167 3 3L
.
2 2
K D
A P
= = =
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Characteristic of absolute permeability:
The permeability is a property of rockalone,dependent on the porous media size and
s r u on o roa on y, no on e uused.
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'
1) Mid-high permeability
3 23.5u=
c
K
2) Low permeabilityFig.1 relations between velocity and
pressure gradient
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2). Klinkenberg Effect
Klinkenberg Effect Effect of Gas Slippage
expressed that the flow rate of gas at solid
surface of pore is not zero.
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is greater than liquid Permeability
It has been found that gas permeabilitiessometimes vary with the pressure of gas,
and that gas permeability is greater than
.
ca illar tubes.
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3). Effect of gas slippage on Permeability
Measurements
800
001um2
1
200
400
0.
2
3
0
0 2 4 6 8 10 co2
p,
the reciprocal of the mean pressure
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or eac gas a s ra g ne s o a ne or eobserved permeability as a function of the reciprocal
o e mean pressure o e es .
- -gas yield the straight line with the greatest slope
, .
All the lines when extra olated to infinite meanpressure ( ) intercept the permeability axis
at a common oint.
1 0p
=
This point is designated kL or the equivalent liquidpermea ty.
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The linear relationship between the observed
permea y an e rec proca o mean pressuremay be expressed as follows:
K = K 1+ b /
=
permeability,
b=constant for a given gas in a given medium
g=measure permea y us ng e arcy equa on
for gas flow.
= mean flowing pressure of the gasp
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)b
1(K KgKp
K
P
1r
b 22 d n=
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permeability
grade permeability evaluation
2u m
3 210 um
> 1 >1000 Very good
10.1 1000100 good
. .
0.010.001 101 fair
- .
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ac ors a ec ng e magn u e opermeability
(a) Shape and size of sand grains(b) Grain packing and Cementation
(c) Fracturing and solution
ore ze an onnec v y
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1) The experimental laboratory determinations
A . determinations on small samples of
Apparatus for measuring of permeability with liquid
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0 02Q P u L2 2
1 2
( )P P
Apparatus for measuring of permeability with gas
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310K =
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a
C b
w iS
=
. . ,
of the fluid and the porous medium
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9 Flow S stems of Sim le Geometr
Horizontal Flow.
Horizontal rectilinear( steady-state flow is
.
1 2( )kA P P
L
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.
A radial-flow system, analogous
, .
e wQ
=
e w
e eis measured
rw the radius at which Pwis measured.
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10 Average permeability of combination
1 . Consider the case where the flow s stem islayers
comprised of layers of porous rock separated
from each other b infinitel thin im ermeablebarriers as shown in Fig. Parallel combination
n
k h
1j
nk
=
=jh
=
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Radial flow
Qt = Q1+ Q2 + Q3
t = 1 2 3
j jk hn
k=
=
1
j
j =
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2 Another ossible combination for flow
systems is to have the beds of different
shown in Fig. series combination
Linear flowP1- P2 = P1+P2+P3
Qt = Q1= Q2 = Q3
n
k =
/j j
L k
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Radial flow
- = + +Qt = Q1= Q2 = Q3
ln
e wQu R R
=e w
ln e
wRRadial flow- series combination
1ln i
R
1i i
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11 The relationship of permeability and
other property of rock
Fig. parallel bundle of capillary tubes pack
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Consider a system comprised of a bundle of
cap ary u es o e same ra us an eng ;The e uation for flow of fluids in circular conduits:
4
0 1 2( )r P P
8uLq e vo ume ra e o ow, cm s
fluid viscosit mPa.s(P1-P2)pressure loss over length L,
ro ra us o cap ary u e , cm,
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2)The relationship of permeability and pore radius
If the fluid-conducting channels in a porous medium
tubes of same diameters, then the flow rate through
4
nA r P
8uL=nnumber of capillary tubes per unit cross-
rradius of capillary tube
A total cross-sectional area
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From Darcys law it is also known that :
' K A P
u L
=
Equating Darcys and Poiseuilles equation:
'Q Q=4 4
KA P nA r P n r = = (1)8 8uL uL
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,
2PV n A r L
n r
= = =(2)
b
r
K r= =(3)
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3)The relationship of permeability and specific
sur acesurface area S is the total area exposed within
the pore space per unit of bulk volume .
22a n r
S n r n r
= = = = =
b
2 322 4
S S
= = = 28 KK
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Let Sp be the internal surface area per unit of pore
volume ,Ss be the total area exposed within thepore space per unit of grain volume
a=
PV
(1 )P SS S S = =
1 1S
S = =
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Gaocaini-Equation
3 3
3 2 2 22 2 2 (1 )P SK
S S S = = =
LLL
2 2 2 2K = = =
S P
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EXAMPLE 1
A core sample from a uniform sandstone formation-3 2
of 0.17
(b) Specific surface areas Sp and Ss.
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.conditions that should be met when measuring
.
to measure permeability of reservoir rock? How
.