FIG. 2 PORE-SIZE DISTRIBUTION
P
or
e
vol
u
me
,
cc/
g
70
60
50
40
30
20
10
0
Pore diameter, nm
10 100 1,000 10,000 100,000
Indiana 1
Indiana 2
Indiana 3
Wisconsin
FIG. 3 PERMEABILI TY
100
90
80
70
60
50
40
30
20
10
0
Pore diameter, nm
10 100 1,000 10,000 100,000
Indiana 1
Indiana 2
Indiana 3
Wisconsin
C
um
ul
ati
v
ep
or
e
v
olu
m
e,
%
FIG. 4 UNSTEADY-STATE PERMEABILITY, WISCONSIN SAMPLE
Pre
s
s
ure
,
MP
a
1. 2
1.0
0.8
0.6
0.4
0.2
0
Time, sec
1 10 100 1,000 10,000 100,000
Observed inlet pressure
Fitted inlet pressure
Observed outlet pressure
Fitted outlet pressure
Pconfning = 2Mpa, Kgas = 0.023 md
EQUATIONS
()
()
. ()
( ) ()
Kd
P
kT
L Dt
k
1
22
0 85 3
21 4
n
m
B
2
2
2
m
m rd
x
x {{
=
=
=
=-
Nomenclature
Kn = Knudsen number λ = Gas phase molecular mean free
path, m
d = pore diameter, m
kB = Boltzmann constant ( 1.3805× 10-23 J/K)
T = Temperature, K
δm = collision diameter of the gas molecule, m
P = Pressure, Pa
L = diffusion distance, m
D = diffusion coeffcient, m2/s
τ = tortuosity
t = diffusion time, s
φ = porosity
k = permeability, Darcy
ability to increase connectivity of macropores, boosting overall permeability. 4-5 Various criteria classify carbonate by pore size, rock fabric, and other
properties. Areas of porosity are divided
into macroporosity and microporosity
to help define complex pore characteristics. Microporosity values are in the
0. 3-62. 5 µm range, and macroporosity
values in the range of 4 µm to 4 mm.
Pore types also are defined by anticipated contribution to permeability.
Knudsen theory enabled analyzing oil-recovery mechanisms for different pore
types based on calculated gas flow in
porous media. Testers used decane in
the laboratory to stimulate oil-saturated
core samples during CO2 flooding.
Experimental procedure
Experiments used two sizes of outcrop
limestone: 50 mm in diameter × 100
mm long and 25 mm in diameter × 60
mm long. Gas permeability was 9 md,
15-20 md, and 200 md for the three Indiana limestone samples and 0.004 md
for the Wisconsin limestone sample.
Corresponding porosities were 19%,
14%, 18%, and 3%.
Unsteady-state permeability measurements quantified rock heterogenety.
