Estimation of Permeability by Integrating Nuclear Magnetic Resonance (NMR) Logs with Mercury Injection Capillary Pressure (MICP) Data in Tight Gas Sands Zhi-qiang Mao • Liang Xiao • Zhao-nian Wang • Yan Jin • Xing-gang Liu • Bing Xie Received: 4 April 2012 / Revised: 3 July 2012 Ó Springer-Verlag 2012 Abstract It has been a great challenge to determine permeability in tight gas sands due to the generally poor correlation between porosity and permeability. The Schlumberger Doll Research (SDR) and Timur–Coates permeability models, which have been derived for use with nuclear magnetic resonance (NMR) data, also lose their roles. In this study, based on the analysis of the mercury injection experiment data for 20 core plugs, which were drilled from tight gas sands in the Xujiahe Formation of central Sichuan basin, Southwest China, two empirical correlations between the pore structure index ( ffiffiffiffiffiffiffiffiffi K =u p , defined by the square root of the ratio of rock permeability and porosity) and the R 35 (the pore throat radius corresponding to 35.0 % of mercury injection saturation), the pore structure index and the Swanson parameter have been developed. To consecutively estimate permeability in field applications, based on the study of experimental NMR measurements for 36 core Z. Mao State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, People’s Republic of China Z. Mao Key Laboratory of Earth Prospecting and Information Technology, Beijing, People’s Republic of China L. Xiao (&) Key Laboratory of Geo-detection, China University of Geosciences, Ministry of Education, Beijing, People’s Republic of China e-mail: [email protected]L. Xiao School of Geophysics and Information Technology, China University of Geosciences, Beijing, People’s Republic of China Z. Wang Y. Jin X. Liu B. Xie Southwest Oil and Gas Field Branch Company, PetroChina, Chengdu, Sichuan, People’s Republic of China 123 Appl Magn Reson DOI 10.1007/s00723-012-0384-z Applied Magnetic Resonance
Transcript
Estimation of Permeability by Integrating NuclearMagnetic Resonance (NMR) Logs with MercuryInjection Capillary Pressure (MICP) Datain Tight Gas Sands
Zhi-qiang Mao • Liang Xiao • Zhao-nian Wang •
Yan Jin • Xing-gang Liu • Bing Xie
Received: 4 April 2012 / Revised: 3 July 2012
� Springer-Verlag 2012
Abstract It has been a great challenge to determine permeability in tight gas sands
due to the generally poor correlation between porosity and permeability. The
Schlumberger Doll Research (SDR) and Timur–Coates permeability models, which
have been derived for use with nuclear magnetic resonance (NMR) data, also lose
their roles. In this study, based on the analysis of the mercury injection experiment
data for 20 core plugs, which were drilled from tight gas sands in the Xujiahe
Formation of central Sichuan basin, Southwest China, two empirical correlations
between the pore structure index (ffiffiffiffiffiffiffiffiffiffi
K=up
, defined by the square root of the ratio of
rock permeability and porosity) and the R35 (the pore throat radius corresponding to
35.0 % of mercury injection saturation), the pore structure index and the Swanson
parameter have been developed. To consecutively estimate permeability in field
applications, based on the study of experimental NMR measurements for 36 core
Z. Mao
State Key Laboratory of Petroleum Resource and Prospecting,
China University of Petroleum, Beijing, People’s Republic of China
Z. Mao
Key Laboratory of Earth Prospecting and Information Technology,
Beijing, People’s Republic of China
L. Xiao (&)
Key Laboratory of Geo-detection, China University of Geosciences,
Ministry of Education, Beijing, People’s Republic of China
China University of Geosciences, Beijing, People’s Republic of China
Z. Wang � Y. Jin � X. Liu � B. Xie
Southwest Oil and Gas Field Branch Company,
PetroChina, Chengdu, Sichuan, People’s Republic of China
123
Appl Magn Reson
DOI 10.1007/s00723-012-0384-z
Applied
Magnetic Resonance
samples, two effective statistical models, which can be used to derive the Swanson
parameter and R35 from the NMR T2 logarithmic mean value, have been established.
These procedures carried out on the experimental data set can be extended to
reservoir conditions to estimate consecutive formation permeability along the
intervals with which NMR logs were acquired. The processing results of several
field examples using the proposed technique show that the classification scale
models are effective only in tight gas reservoirs, whereas the SDR and Timur–
Coates models are inapplicable. The R35-based model is of significance in thin sands
with high porosity and high permeability, but the predicted permeability curves in
tight gas sands are slightly lower. In tight gas and thin sands, the Swanson parameter
model is all credible.
1 Introduction
Permeability is an important input parameter in reservoir evaluation and production
prediction procedures, it is also critical to accurately estimate this parameter in
reservoir simulation, especially in tight gas sandstones’ exploration and exploita-
tion. Numerous methods have been proposed to determine permeability from
porosity [1–3], but they are all limited to cases where there are simple and explicit
relationships between porosity and permeability. These methods are usually
unsuitable for tight gas sands which commonly show poor correlation between
porosity and permeability. Figure 1 shows the cross plot of porosity and
permeability acquired with core samples drilled from three intervals of X2, X4
and X6 in four boreholes. It clearly demonstrates that the relationship between
porosity and permeability appears to be varied in different intervals and boreholes.
The issue of the scatters of the data points can be addressed through the use of
variable transformations in the different zones or different hydraulic units [1, 4].
However, it is found that this procedure is very time-consuming and not practical
for routine use. In order to determine permeability as accurately as possible for
routine use, a new technique and two models are developed, which take advantage
of experimental capillary pressure and nuclear magnetic resonance (NMR) data sets.
The first model is based upon the relationship between the R35 value (the pore throat
radius corresponding to 35.0 % of mercury injection saturation) and the pore
structure index (ffiffiffiffiffiffiffiffiffiffi
K=up
), and the second is based upon the relationship between the
Swanson parameter and the pore structure index. Of these two models, the Swanson
parameter-based model yields more accurate results than the R35-based model, and
the former is the preferred one. Case studies show that the Swanson parameter
model is well suited for both tight gas reservoirs and conventional formations where
accurate permeability data set from core samples is available.
2 Method of Predicting Permeability Using Classification Scale Models
To obtain formation permeability from conventional logs, we try to use classifi-
cation scale models to construct the statistical relationships between core porosity
Z. Mao et al.
123
and permeability for different zones. Figure 2 shows the discrete points of the X4
and X6. It suggests that core sample data from the X4 and X6 sections indicate
similar ascendant tendency between porosity and permeability. However, the core
samples from the X2 section shown in Fig. 3 demonstrate a different trend between
porosity and permeability. In the following analysis, the problem of the permeability
estimation of the whole formation has been solved based on classification scale
models of the X2 section and of the X4 and X6 sections. Furthermore, in the
statistical model of the X4 and X6 sections, we have derived two relationships
which cover the porosity range of 0–8 % and of above 8 %. The porosity
classification criterion of 8 % is determined by the statistical presentation of the
core samples in Fig. 2.
In Figs. 2 and 3, it can be observed that there do exist correlations between
porosity and permeability if the data points of all the boreholes are separated into
two groups which represent section X2 and sections X4 and X6. By using the
established equations, reservoir permeability can be estimated consecutively. In
Fig. 3, we find that the fitting line can only be adopted to reservoir permeability
lower than 1.0 mD (1.0 mD = 0.987 9 10-3 lm2), for the thin sands hold
permeabilities higher than 1.0 mD, which is displayed in the right-hand upper part
triangle, the formation permeability will be underestimated. In Figs. 2 and 3, we
know that the correlation coefficients for these two models are not very high and
permeability cannot be predicted straightforwardly with a single parameter of
porosity. To include other factors that affect permeability and reduce the complexity
0.001
0.01
0.1
1
10
100
1000
0 5 10 15 20
Core porosity (%)
Cor
e pe
rmea
bilit
y (m
D)
X2_well A
X2_well B
X2_well C
X2_well D
X4_well B
X4_well C
X4_well D
X6_well B
X6_well D
Permeability abnormitycaused by microfracture
Thin sands withhigh porosity andhigh permeability
Fig. 1 Cross plot of core porosity and permeability with more than 2,400 core samples. These coresamples were drilled from X2 (the second section of the Xujiahe Formation), X4 (the fourth section of theXujiahe Formation) and X6 (the sixth section of the Xujiahe Formation) from four wells, in centralSichuan basin, Southwest China
Estimation of Permeability in Tight Gas Sands
123
of permeability estimation, new technique must be considered. In this study, we take
the NMR logs as a basic tool and establish two effective models of permeability
estimation.
Log(K )= 0.00153-0.0337
2+0.3702 -2.2295
R2 = 0.66
K = 0.0088e0.5097
R2 = 0.60
0.001
0.01
0.1
1
10
100
0 5 10 15 20
Core porosity (%)
Cor
e pe
rmea
bilit
y (m
D)
X4_well D
X4_well B
X4_well C
X6_well D
X6_well B
Fig. 2 Relationship between porosity and permeability in the X4 and X6 sections
Log(K )= 0.00133 - 0.0371
2 + 0.4078 - 2.5473
R2 = 0.62
0.001
0.01
0.1
1
10
100
1000
0 5 10 15 20
Core porosity (%)
Cor
e pe
rmea
bilit
y (m
D)
X2_well A
X2_well B
X2_well C
X2_well D
Thin sands withhigh porosity andhigh permeability
Fig. 3 Relationship between porosity and permeability in the X2 sections
Z. Mao et al.
123
3 Classical Models of Estimating Permeability from NMR Logs
Up to now, there are two models that take the advantages of the nuclear magnetic
resonance technology, known as Schlumberger Doll Research (SDR) and Timur–
Coates models [5–7]. They directly correlate the formation permeability with NMR
logs as follows:
KSDR ¼ C1 � um1 � Tn1
2lm; ð1Þ
KTIM ¼ uC2
� �m2
� FFI
BVI
� �n2
; ð2Þ
where KSDR is the permeability estimated from the SDR model and KTIM is the
permeability estimated from the Timur–Coates model, their units are millidarcy; uis the total porosity in percent; T2lm is the logarithmic mean value of the NMR T2
distribution in miliseconds; FFI is the free fluid index in percent; BVI is bulk
volume irreducible in percent, m1, n1, C1, m2 n2 and C2 are statistical model
parameters that can be derived from the experimental data sets of core samples.
When enough core samples are not available, m1, n1, C1, m2 n2 and C2 can be
assigned to empirical values of 4, 2, 10, 4, 2, and 10, respectively.
In practical applications, the determination of the FFI and BVI are solely
dependant upon the value of T2cutoff which separates the whole NMR T2 distribution
into two parts. The principle of determining FFI and BVI from the NMR spectrum is
shown in Fig. 4. The determination of an appropriate T2cutoff can be a cumbersome
problem and presently there is no universal applicable methodology of the T2cutoff
selection from the T2 distribution. Default T2cutoff values of 33.0 and 92.0 ms have
been proposed for clastic and carbonate reservoirs, respectively [7–10], and have been
used for many years. We found that in tight gas reservoirs and fractured carbonate
formations, the default values mentioned above usually result in erroneous results.
In this study, 35 plug samples in tight gas sands, and 1 in thin sands with high
porosity and high permeability, drilled from four wells in the Xujiahe Formation of
central Sichuan basin, Southwest China, are adopted for the NMR experimental test.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.1 1 10 100 1000 10000
T 2 (ms)
ampl
itud
e (v
/v)
BVI FFI
T 2cutoff
Fig. 4 Principle of determining FFI and BVI from NMR spectrum
Estimation of Permeability in Tight Gas Sands
123
The experimental data set is listed in Table 1. With the multivariate regression
analysis, the SDR and Timur–Coates models are calibrated as:
where R2 is the correlation coefficient. Equations (3) and (4) show that the statistical
parameters in SDR and Timur–Coates models deviate from their routine values
described in last subsection in our tight reservoirs, and the correlation coefficients in
our data set are too low to be used for direct permeability estimation.
Figure 5 shows the distribution of the T2cutoff values from Table 1. It suggests that the
default T2cutoff for the experimental NMR data set is different from 33.0 ms or another
fixed value, whereas the main distribution ranges from 17.0 to 24.0 ms, the weighted
average is 20.75 ms. In following applications of Eq. (4), the FFI and BVI estimations
are carried out by using 20.75 ms as T2cutoff in the whole target intervals.
Figure 6 shows an oilfield example of estimating permeability with Eqs. (3) and
(4) in the Xujiahe Formation, central Sichuan basin of Southwest China. In the first
track, the displayed curves are gamma ray (GR), spontaneous potential (SP) and
borehole diameter (CAL), their contribution is formation indication. The second
track is depth and its unit is meter. RT displayed in the third track is deep lateral
resistivity, and RXO is shallow lateral resistivity. In the fourth track, we show the
interval transit time log (DT), density log (RHOB) and compensated neutron log
(NPHI). They are used for porosity estimation. The fifth track of Fig. 6 indicates a
reasonable match between core-analyzed porosity (CPOR) and NMR-derived
porosity (PHIT). It suggests that the total NMR porosity is reliable and there will be
little error when it is applied in permeability estimation. In our applications, the BVI
was predicted by using 20.75 ms as T2cutoff. A comparison of defined T2cutoff (red
line in the sixth track) and core-derived results (Core_T2cutoff) illustrates that using
20.75 ms as T2cutoff is reasonable. From a detailed examination of estimated
permeability in the seventh track we find that the permeabilities estimated from
SDR (KSDR) and Timur–Coates models (KTIM) still deviate from the core-derived
permeability (CPERM), and they are all underestimated, especially the KTIM.
Based on the principle of NMR logs, the transverse relaxation time T2 consists of
three parts. They are the bulk relaxation time, the surface relaxation time and the
diffusion relaxation time. Their relationship can be expressed as follows [7, 11, 12]:
1
T2
¼ 1
T2B
þ 1
T2S
þ 1
T2D
; ð5Þ
where
1
T2S
¼ q2
S
V
� �
; ð6Þ
1
T2D
¼ DðcGTEÞ2
12; ð7Þ
Z. Mao et al.
123
Ta
ble
1D
ata
set
of
NM
Rm
easu
rem
ents
from
36
plu
gsa
mp
les
inti
gh
tg
assa
nd
sin
the
Xu
jiah
eF
orm
atio
no
fce
ntr
alS
ich
uan
bas
in,
So
uth
wes
tC
hin
a
Wel
ln
ame
Ho
rizo
nS
amp
len
um
ber
Dia
met
er(c
m)
Len
gth
(cm
)P
oro
sity
(%)
Air
per
mea
bil
ity
(mD
)T
2lo
gar
ith
mic
mea
n(m
s)
Irre
du
cib
lew
ater
satu
rati
on
(%)
T2cuto
ff
(ms)
Wel
lA
T3
X4
X3
2.5
54
.04
15
.20
5.8
72
9.0
94
0.4
22
2.8
5
Wel
lA
T3
X4
X5
2.5
43
.34
16
.00
5.2
43
9.7
43
7.9
41
9.5
9
Wel
lA
T3
X4
X6
2.5
53
.22
14
.00
1.0
82
8.5
63
7.0
61
3.3
4
Wel
lA
T3
X4
X7
2.5
53
.15
13
.10
0.5
81
7.5
64
1.5
71
0.8
6
Wel
lB
T3
X6
J16
2.5
53
.56
3.9
00
.08
13
.13
48
.90
7.1
9
Wel
lB
T3
X6
J17
2.5
53
.70
5.1
00
.16
17
.90
61
.85
22
.77
Wel
lB
T3
X6
J18
2.5
54
.18
5.9
00
.20
18
.89
49
.94
12
.46
Wel
lB
T3
X6
J19
2.5
53
.08
6.4
00
.28
17
.92
45
.24
11
.62
Wel
lB
T3
X6
J21
2.5
53
.49
5.0
00
.15
8.2
64
2.2
94
.74
Wel
lC
T3
X4
B1
12
.54
3.2
31
3.3
03
.06
39
.50
32
.50
14
.41
Wel
lC
T3
X4
B1
32
.54
3.5
61
2.1
01
2.2
96
3.7
32
3.8
31
3.7
3
Wel
lD
T3
X2
R2
2.5
54
.29
4.8
00
.13
8.6
46
3.1
99
.58
Wel
lD
T3
X2
R3
2.5
43
.49
11
.40
0.2
32
6.9
36
0.6
84
1.8
1
Wel
lD
T3
X2
R4
2.5
43
.38
15
.30
0.2
32
6.7
35
5.9
92
8.8
3
Wel
lD
T3
X2
R5
2.5
43
.40
11
.60
0.2
04
4.7
03
4.9
12
2.5
4
Wel
lD
T3
X2
R6
2.5
53
.71
19
.90
90
.65
12
3.9
63
1.2
25
5.7
6
Wel
lD
T3
X2
R7
2.5
53
.40
14
.80
1.0
57
5.1
83
3.6
63
4.5
8
Wel
lD
T3
X2
R8
2.5
43
.24
16
.30
0.5
84
9.9
33
5.8
42
5.5
2
Wel
lD
T3
X2
R9
2.5
44
.01
14
.50
0.1
72
5.0
15
6.0
72
7.1
4
Wel
lD
T3
X2
R1
02
.54
3.0
71
5.3
00
.27
43
.67
44
.67
30
.60
Wel
lD
T3
X2
R1
12
.55
3.2
71
1.7
00
.21
35
.60
43
.77
21
.81
Wel
lD
T3
X2
R1
22
.54
3.2
79
.50
0.2
13
5.3
34
2.2
02
1.1
9
Wel
lD
T3
X2
R1
32
.54
3.1
19
.20
0.1
63
3.3
64
1.1
92
1.3
9
Wel
lD
T3
X4
R1
42
.54
4.0
08
.80
0.6
22
0.4
15
8.5
71
9.1
3
Estimation of Permeability in Tight Gas Sands
123
Ta
ble
1co
nti
nu
ed
Wel
ln
ame
Ho
rizo
nS
amp
len
um
ber
Dia
met
er(c
m)
Len
gth
(cm
)P
oro
sity
(%)
Air
per
mea
bil
ity
(mD
)T
2lo
gar
ith
mic
mea
n(m
s)
Irre
du
cib
lew
ater
satu
rati
on
(%)
T2cuto
ff
(ms)
Wel
lD
T3
X4
R1
52
.55
3.5
76
.30
0.3
31
0.1
26
7.8
41
9.0
3
Wel
lD
T3
X4
R1
62
.54
3.9
81
1.6
00
.89
29
.11
47
.12
20
.49
Wel
lD
T3
X4
R1
72
.54
3.9
08
.80
0.9
13
0.5
35
0.3
82
3.4
8
Wel
lD
T3
X4
R1
82
.54
3.8
91
1.0
00
.57
19
.98
45
.89
13
.36
Wel
lD
T3
X4
R1
92
.54
3.5
37
.40
0.6
22
9.0
94
2.3
51
8.5
9
Wel
lD
T3
X4
R2
02
.55
4.0
46
.70
0.2
72
8.1
83
8.8
81
4.7
0
Wel
lD
T3
X4
R2
12
.54
3.9
07
.20
0.5
03
4.0
54
3.4
12
1.1
0
Wel
lD
T3
X6
R2
22
.54
3.3
09
.30
1.0
34
7.1
43
7.6
92
5.8
4
Wel
lD
T3
X6
R2
32
.54
3.1
98
.80
0.2
42
5.2
14
2.1
61
4.6
7
Wel
lD
T3
X6
R2
42
.55
3.2
01
3.1
00
.49
30
.62
39
.43
17
.90
Wel
lD
T3
X6
R2
62
.54
3.3
08
.80
0.8
54
3.1
93
7.1
82
2.5
5
Wel
lD
T3
X6
R2
7-1
2.5
44
.85
7.8
00
.50
35
.02
40
.10
22
.01
Z. Mao et al.
123
where T2 is the transverse relaxation time, T2B is the bulk relaxation time, T2S is the
NMR surface relaxation time, T2D is the diffusion relaxation time. Their units are
milliseconds. q2 is the T2 surface relaxivity (T2 relaxation strength of the grain
surfaces) in micrometers per millisecond, and SV is the ratio of pore surface to fluid
0%
10%
20%
30%
40%
50%
3~10 10~17 17~24 24~31 31~38 38~45 45~52 >52
T 2cutoff (ms)
Freq
uenc
e (%
)
Fig. 5 Distribution of T2cutoff values for 36 core samples
Fig. 6 Comparison of permeabilities estimated from the SDR and Timur–Coates models using NMRlogs with core-derived results (black points)
Estimation of Permeability in Tight Gas Sands
123
volume. For simple shapes, SV is a measure of the pore size. For example, for a
sphere, the surface-to-volume ratio is 3r, where r is the radius of the sphere. D is the
molecular diffusion coefficient in square micrometers per millisecond. c is
gyromagnetic ratio of a proton. G is the field-strength gradient in tesla per meter.
TE is in millisecond.
Generally, T2B is the intrinsic relaxation property of pore fluid. It is controlled by
the physical properties of the fluid, such as viscosity and chemical composition, its
value is fixed for a given pore fluid. Therefore, the transverse relaxation time is
mainly determined by surface relaxation and diffusion relaxation. In gas-bearing
formations, rock is the wetting phase and the micro-pore space occupied by
irreducible water is small, so SV is small, and the signal of the irreducible water
decays fast. Hence, irreducible water has a relatively short T2 relaxation time.
Natural gas is considered to be a non-wetting phase. It occupies the macro-pore
space, and the diffusion coefficient of natural gas is much higher than that of water
and light oil. The T2 relaxation time of natural gas is mainly contributed by diffusion
relaxation time [7].
Figure 7 shows a comparison of the NMR T2 distributions which are obtained
from experimental NMR measurement under fully brine saturation and from field
NMR logs under the same gas-bearing interval, respectively. The dotted line in
Fig. 7 is the T2cutoff of this core sample. From Fig. 7, it can be observed that in
gas-bearing formations, the spectrum of the field NMR logs moves to the left and
overlaps with the bound water’s due to the effect of diffusion relaxation.
Therefore, this part is considered as the contribution of bound water. Hence, large
BVI is calculated by using experimental T2cutoff values and permeability is
underestimated.
0
0.3
0.6
0.9
0.1 1 10 100 1000 10000
Relaxation Time T 2 (ms)
Rel
ativ
e Po
pula
tion
T 2cut off
Fig. 7 Comparison of the NMRT2 distribution in gas-bearingformations [13]. � Irreduciblewater saturation; ` fully brinesaturated; ´ field NMR T2
distribution in gas-bearingintervals corresponding to thesame depth of the core sample[13]
Z. Mao et al.
123
4 Novel Models of Estimating Permeability by Integrating Laboratory NMRwith Mercury Injection Capillary Pressure (MICP) Data
4.1 Morphologic Characteristics of MICP Curves
Generally, the MICP curve is shown in semi-log coordinates. However, if it is
expressed in log–log coordinates, a hyperbolic curve will be obtained [14–18] as
shown in Fig. 8.
The expression of the capillary pressure curve can be written as [18–20]:
log10
Pc
Pd
� �
� log10
SHg
SHg1
� �
¼ C; ð8Þ
where Pd is the threshold pressure, Pc is the mercury injection pressure, in units of
megapascal; SHg is the mercury injection saturation, SHg? is the non-wetting phase
saturation under infinite mercury injection pressure in percent and C is the
geometric prefactor.
Based on the experimental data sets, Guo et al. [18], Swanson [19], and Xiao
et al. [21] found that the inflexion point of the capillary pressure curve corresponds
to the mercury injection saturation threshold in the main pore system which
primarily controls the fluid flow (point A in Fig. 8). If SHg is plotted on the X-axis
and SHg/Pc is on the Y-axis, the inflexion point is located right at the apex, and is
called the Swanson parameter. Before the apex appears, the non-wetting fluid
occupies all of the effective pore spaces, whereas after the apex, the non-wetting
fluid will take the micro-pore space, correspondingly the flow transmissibility is
greatly reduced. The sound relationship between the Swanson parameter and the
pore structure index (ffiffiffiffiffiffiffiffiffiffi
K=up
) suggests that permeability can be derived from the
MICP curve.
4.2 Models of Estimating Permeability Based on Mercury Injection Data
Based on the analysis above, 20 plug samples were adopted for carrying out
mercury injection experiment, these 20 core samples were drilled from the same full
0
10
20
30
40
50
0 30 60 90
S Hg (%)
SH
g/P
c
0.1
1
10
100
110100
S Hg (%)
Pc (
Mpa
)
A
The Swanson parameter
Fig. 8 Diagram of obtaining Swanson parameter from the mercury injection capillary pressure curve
Estimation of Permeability in Tight Gas Sands
123
diameter cores with some of 36 core samples mentioned above, they are considered
as the same core samples. During the experimental process, the maximum mercury
injection pressure is designed as 20.48 MPa to ensure the experimental results can
completely reflect the pore structure of tight gas sands. The experimental data set is
listed in Table 2. The correlation of the core data set between the Swanson
parameter and the pore structure index is shown in Fig. 9, and a statistical model
was established for later permeability estimation from MICP curves.
In Fig. 9, we understand that the correlation between the Swanson parameter and
the pore structure index is very pronounced, and the correlation coefficient reaches
0.9624. The relationship can be applied to permeability estimation once the
Swanson parameter and total NMR porosity are obtained. Therefore, we can
proceed to predict formation permeability: (1) to interpolate MICP curves using a
cubic spline function; (2) to cross plot the mercury injection saturation (SHg) versus
(SHg/Pc) in linear coordinates (see Fig. 8); (3) to derive the Swanson parameter from
the apex by using the maximum principle; (4) to construct the relationship between
the Swanson parameter and the pore structure index.
Based on the experimental data sets of cores from conventional reservoirs,
Lafage [22] had pointed out that the R35 parameter (the pore throat radius
corresponding to 35.0 % of mercury injection saturation) is closely related to
Table 2 Parameters associated to mercury injection capillary pressure data for 20 core samples
Well
name
Horizon Sample
number
Diameter
(cm)
Length
(cm)
Porosity
(%)
Air
permeability
(mD)
The Swanson
parameter
R35
(lm)
Well A T3X4 X5 2.54 3.34 16.00 5.24 71.67 1.03
Well A T3X4 X6 2.55 3.22 14.00 1.08 32.90 0.68
Well B T3X6 J18 2.55 4.18 5.90 0.20 26.19 0.53
Well B T3X6 J21 2.55 3.49 5.00 0.15 4.81 0.10
Well C T3X4 B11 2.54 3.23 13.30 3.06 67.50 1.41
Well D T3X2 R2 2.55 4.29 4.80 0.13 11.27 0.19
Well D T3X2 R3 2.54 3.49 11.40 0.23 17.03 0.36
Well D T3X2 R6 2.55 3.71 19.90 90.65 878.02 13.21
Well D T3X2 R8 2.54 3.24 16.30 0.58 45.99 0.72
Well D T3X2 R10 2.54 3.07 15.30 0.27 32.71 0.68
Well D T3X2 R11 2.55 3.27 11.70 0.21 15.94 0.33
Well D T3X2 R12 2.54 3.27 9.50 0.21 12.85 0.26
Well D T3X4 R14 2.54 4.00 8.80 0.62 17.10 0.20
Well D T3X6 R17 2.54 3.90 7.80 0.50 43.88 0.71
Well D T3X4 R18 2.54 3.89 11.00 0.57 50.63 1.04
Well D T3X4 R19 2.54 3.53 7.40 0.62 23.86 0.44
Well D T3X4 R20 2.55 4.04 6.70 0.27 17.86 0.31
Well D T3X6 R22 2.54 3.30 9.30 1.03 43.21 0.85
Well D T3X6 R23 2.54 3.19 8.80 0.24 18.96 0.52
Well D T3X6 R24 2.55 3.20 13.10 0.49 24.86 0.34
Z. Mao et al.
123
permeability. In order to check the effects of pore structure on the permeability in
tight gas sands, we also considered the model which correlates the R35 with the pore
structure index. Therefore, we reused the experimental data set listed in Table 2,
and constructed the relationship between the R35 and the pore structure index, which
is expressed by Eq. (9). From Eq. (9), we know that sound correlation exists
between R35 and the pore structure index. From the established equation we can
directly estimate permeability by using the MICP data,ffiffiffiffi
K
u
s
¼ 0:1511� R35 þ 0:1523; R2 ¼ 0:961; ð9Þ
where R35 is referred to the pore throat radius corresponding to 35.0 % of mercury
injection saturation in micrometers, K is the rock permeability in millidarcy.
4.3 Determination of the Swanson Parameter and R35 from NMR Logs
In order to use the equations shown in Fig. 9 and Eq. (9), we have to first calculate
the Swanson parameter and R35. In practical applications, there are limited numbers
of capillary pressure data sets due to the economic and efficiency reasons. To solve
this problem, Xiao et al. [23] has pointed out that the Swanson parameter can be
estimated from NMR logs by using quadratic regression analysis. The data sets
listed in Tables 1 and 2 illustrates that the quadratic regression analysis is not
always practicable. Especially in tight gas sands, the negative Swanson parameter
may be estimated. This is not reasonable. In this paper, based upon the analysis of
36 experimental data sets from tight gas reservoirs, we developed two new
techniques which can be used to derive the Swanson parameter and R35 from the
NMR T2 distribution.
y = 0.0023x + 0.1682
R2 = 0.9624
0
1
2
3
1 10 100 1000
The Swanson parameter( S Hg/P c)A
The
por
e st
ruct
ure
inde
x
Fig. 9 Relationship between the Swanson parameter and the pore structure index
Estimation of Permeability in Tight Gas Sands
123
Detailed examinations of the NMR responses and MICP measurement acquired
with the 20 core samples described in the above subsection show that there is a close
correlation between the Swanson parameter and the logarithmic mean T2 value. The
relationship is expressed in Eq. (10). Therefore, we can derive the Swanson
parameter from the NMR T2 distribution. The correlation between the logarithmic
mean T2 value and R35 is shown in Fig. 10,
SHg�
Pc
� �
A¼ 8:3794� e0:038�T2lm ; R2 ¼ 0:803: ð10Þ
By using relationships expressed in Eqs. (9) and (10) (Figs. 9 and 10), we can
predict formation permeability from NMR logs. Furthermore, when this approach is
extended to reservoir conditions, consecutive permeability curves can be derived.
Fortunately in this study, one core sample (No. R6 in Tables 1, 2) was drilled from
the thin sands with high porosity and high permeability, and the experimental
measurements of NMR and MICP were obtained. These data are used in establishing
the permeability estimation model. The established models in this paper may be
available not only in tight gas sands, but also in conventional reservoirs.
5 Case Studies
A field example in tight gas sands from the central Sichuan basin, Southwest China,
is shown in Figs. 11 and 12. In this example, the target intervals have been acquired
with conventional logs, NMR logs and limited MICP data. In Fig. 11, it is clearly
indicated that the Swanson parameters calculated from NMR logs match fairly well
with those from the capillary pressure data, whereas the estimated R35 is slightly
underestimated when R35 is wider than 0.50 lm. From these two cross plots, we
conclude that the Swanson parameter model may be preferred over that of the R35
model.
y = 0.1547e0.0364x
R2 = 0.7511
0
4
8
12
16
0 20 40 60 80 100 120 140
T 2lm (ms)
R35
(µm
)
Fig. 10 Correlation between the T2 logarithmic mean from NMR and R35 value
Z. Mao et al.
123
Figure 12 demonstrates results of estimated permeability curves by using of
different models which integrate NMR T2 distributions with MICP data. The
physical significance of these curves, shown in the first four tracks, is the same as
that of the curves in Fig. 6. It can be observed that the target formation presents
strong heterogeneity. The porosity in the upper part of section X4 reads from 5.0 to
7.0 %, whereas in the lower part of section X2, the porosity increases to 16.0 %.
The measured core permeabilities also show a wide distribution. In section X4, it is
lower than 1.0 mD, but in section X2, it is well above 1.0 mD, some are even higher
than 10.0 mD. The T2cutoff of 20.75 ms (T2cutoff) is very close to that of the core-
derived results (Core_T2cutoff). In section X4, predicted permeability curves based
on the Swanson parameter model (Perm_Swanson) and curves based on the
classification scale models which have been shown in Fig. 2 (Perm) match fairly
well with the core permeability points, whereas the results based on the R35 model
(Perm_R35), the Timur–Coates model, and the SDR model all deviate from those of
the core data. Especially the Timur–Coates model produces a large deviation. The
permeability results shown in Fig. 12 suggest that in tight gas sands, the irreducible
water saturation derived from the T2 spectrum using a fixed T2cutoff will be of no
practical use because of overlapping T2 distributions from gas and irreducible water.
In section X2, both models based on the Swanson parameter and the R35 are suitable
for formations both of low and high permeabilities, whereas the classification scale
models, the Timur–Coates model and the SDR model cannot accurately predict
permeabilities above 5.0 mD, and the classification scale models cannot be even
applied to reservoirs with permeability higher than 1.0 mD.
6 Uncertainty of the Permeability Estimation Models
To analyze the uncertainty of these models that used for permeability estimation, the
absolute errors between the permeabilities predicted by using the Swanson
parameter model, the classification scale models, the R35-based model and the
core-analyzed permeabilities are statistical and they are displayed in Figs. 13, 14,
1
100
10000
The Swanson parameter from mercury injectioncapillary pressure curves
The
Sw
anso
n pa
ram
eter
cal
cula
ted
from
res
ervo
ir N
MR
log (a)
0.1
1
10
100
1 10 100 1000 10000 0.1 1 10 100
R 35 from mercury injection capillary pressurecurves ( µm)
R35
cal
cula
ted
from
res
ervo
ir N
MR
log
(µm
)
(b)
Fig. 11 Comparison of the Swanson parameter and R35 calculated from core studied and NMR logs.a Comparison of the Swanson parameter. b Comparison of the R35
Estimation of Permeability in Tight Gas Sands
123
15, separately. To make the statistical absolute errors much more reasonable, all
permeabilities are expressed in logarithm. From Figs. 13, 14, 15, it can be observed
that the permeability estimated by using the Swanson parameter model for all
formations is close to the core permeability, the absolute error between them
approximate to zero, the permeability estimated by using the classification scale
models and the R35-based model are underestimated. These results can be
interpreted from Fig. 12. The Swanson parameter model is usable in tight gas and
conventional reservoirs. But the classification scale models are only available in
tight gas formations and underestimate the formation permeability in thin sands with
Fig. 12 Comparison of permeabilities calculated from five different models and air permeabilitiesobtained from core samples in sections X2 and X4
Z. Mao et al.
123
high porosity and high permeability. For the R35-based model, it can be used to
estimate accurate reservoir permeability in thin sands, but underestimate reservoir
permeability in tight gas sandstones.
7 Comparative Analysis and Discussion
By comparing the results shown in Figs. 6 and 12, it is concluded that the
permeability predicted from the classification scale models can be accurate up to the
limit of 1.0 mD, while they cannot be suitable for thin sands with high porosity and
high permeability, which are of great significance in tight gas reservoirs. Even
