Vol.2, No.2, 120-123 (2010) Natural Science
http://dx.doi.org/10.4236/ns.2010.22020
A new method of building permeability model in
low-permeability reservoir numerical simulation
Yong-Chao Xue1, Lin-Song Cheng1, Lei Su2
1CMOE Key Laboratory of Petroleum Engineering in China University of Petroleum, Beijing, China;
2The institute of Exploration and Development of LiaoHe oil Field, Panjin, China
Received 22 October 2009; revised 24 November 2009; accepted 15 December 2009.
ABSTRACT
Aiming at solving the problem that big differ-
ence exists between logging permeability and
true permeability of micro-fractured low-
permeability sand reservoir, this paper puts
forward a new method to revise logging per-
meability by using primiparity data of oil field.
This method has been successfully applied to
revise logging permeability of micro-fractured
low-permeability sand reservoir in Baiyushan
area of Jing’An oil field, which shows that the
method is reliable because the geological model
building through the permeability which has
been handled by this method accords with the
real reservoir significantly.
Keywords: Logging Permeability; Micro-Fractured;
Low-Permeability Reservoir; Revise
1. INTRODUCTION
In recent years, about 60 to 70 percent of discovered
reserves are low-permeability ones, it’s anticipated that
most of discovered reserves in the future will be
low-permeability reservoir, how to develop it efficiently
is getting counted [1-3]. Development plan and effect are
determined by the performance characteristic research of
low permeability reservoir, permeability is a key factor
characterizing fluid flow. There are lots of problems in
the evaluation of permeability in micro-fractured low-
permeability reservoir. The relationship between logging
and core analysis permeability, which is caused by de-
veloped fracture, is too complicated to be used in reser-
voir engineering and numerical simulation [4-5]. Due to
non-linear fluid flow, the actual flow characteristics of
reservoir couldn’t be reflected by logging permeability
and core permeability correctly. For solving reservoir
performance evaluation of oil field development produc-
tion, the performance permeability used in research, the
actual flow characteristics of reservoir could be reflected
by which of test and primiparity data, is very important
for logging permeability corrected method.
2. AIBRATION CLCULATION POCEDURE
OF LGGING PRMEABILITY
2.1. Calculating Reservoir Permeability
Using Primiparity Data Files
Since particularity of micro-fracture in low-permeability
reservoir, if logging permeability is used for reservoir
engineering evaluation and numerical simulation calcu-
lation directly, severe deviation will occur, causing the
inaccuracy of result. However, reservoir development
performance is the objective behavior of reservoir actual
flow characteristic. Performance permeability, calculated
by reservoir development performance files, is the true
permeability in reservoir. During oil field production,
well yield [4] is usually calculated by the equation of
radius fluid flow deliverability. On the contrary, reser-
voir performance permeability is solved by that equation,
concrete Equation is written below [6-10]:
e
w
T
ln
2
r
Qr
KhP
 
π (1)
where KT is reservoir dynamic permeability, μm2; Q is
well yield, cm3/s (sub); μ is oil viscosity in formation,
mPa s; re is supply radius, cm; rw is oil well radius, cm;
h is reservoir thickness, cm.
For the convenience of calculation, standard units of
Darcy law are used in the variables above. When practi-
cally applied, well yield needs to be conversed to sub-
surface volume with volume factor. Half of well spacing
could be substituted for re, because re is in the range of
logarithm, with small effect on the results.
2.2. The Calculation of Reservoir Logging
Permeability
The result of sequent point by point treatment in log
interpretation model is usually used for logging perme-

Y. C. Xue et al. / Natural Science 2 (2010) 120-123
121
ability, since the interval of log sample density is 0.125m,
and performance permeability calculated by actual pro-
duction files is located in some production interval, there
is asymmetry between them. Logging permeability in
target stratum must be averaged by actual production
intervals, in order to build corresponding relationship
with the permeability of actual production intervals. The
permeability expression of actual production intervals
calculated by average method of logging permeability is
described below:

1
2sh
1
11
L
,,
n
nj
j
i
i
KMzV
h
n
Kh












(2)
where L
K

is the average logging permeability of res-
ervoir production intervals, μm2;

sh
,,
j
KMzV  is the
permeability of j sample site in i sublayer, μm2; φ, Mz,
Vsh is the porosity, the median grain diameter, the shale
content of j sample site in i sublayer; hi is the thickness
of reservoir production intervals, m; n1 is the number of
logging permeability point in i sublayer; n2 is the num-
ber of sublayer in piezometric intervals.
2.3. The Correction of Logging Permeability
Reservoir performance permeability, calculated by
primiparity data files, could reflect the actual flow char-
acteristics in reservoir, which is closer to the true one.
Because there is great distinction between logging per-
meability and performance permeability in fractural
low-permeability reservoir, when logging permeability is
corrected by performance permeability, the correction
coefficient

has to be introduced, the

can be cal-
culated by Formula 3:

1
2
e
w
T
L
sh
1
11
ln
2
,,
n
nj
j
i
i
r
Qr
KhP
KKMzV
h
n
h
















π (3)
where

is correction coefficient which is revise log-
ging permeability to performance permeability, the val-
ues varies by wells. The greater of

, the more differ-
ence between logging permeability and performance
permeability, the logging permeability can’t reflect res-
ervoir effluent seepage characteristic. The less of

, the
less difference between logging permeability and per-
formance permeability, the logging permeability can
approximately reflect reservoir effluent seepage charac-
teristic.
As to every production well, only one

value can
be calculated by Formula 3, but, when building 3D per-
meability model, the every point logging permeability
need to be revised. Only using every point revised per-
meability, the 3D permeability model can better reflect
reservoir actually effluent seepage characteristic. So the
Formula 4, dynamic correction model of logging per-
meability, can be used to correction every point logging
permeability.
sh
(,, )PermKMz V


 (4)
where Perm is logging permeability after performance
correction, for reservoir permeability model, μm2;
With the value of

, logging permeability of each
well could be corrected to performance permeability
point by point, then performance permeability model,
which is closer to the true reservoir, would be estab-
lished for the research of reservoir engineering and nu-
merical simulation.
When using this method, the problems below should
be noticed. 1) In order to ensure that only single phase
flow occurs, initial production should be taken as possi-
ble; 2) Well flow rate must be conversed to sand face
one by volume factor; 3) Don’t use multiple zones
commingled test data; 4) If the area of reservoir is large,
fluid viscosity varies , it needs to be treated zone by
zone.
3. APPLICATION
In this paper, Chang 4+5 reservoir in Baiyushan area of
Jing’An oil field is chosen as an example. Baiyushan
area of Jing’An oil field is situated at NE-SW nose like
structure on the Shanbei slope of Ordos basin, Chang
4+5 reservoir is generally delta front subfacies deposite,
major reservoir is subsea distributary channel sand, most
of reservoir lithology are fine sandstone, siltstone and
argillaceous siltstone; Major reservoir sand type is lithic
arkose; The average porosity of reservoir is 12.4%, the
average permeability of reservoir is 1.05×10-3μm2, it’s a
typical sand reservoir with low porosity and permeability.
Structural microfracture developed in reservoir has been
discovered during production. When production history
is matched with the model established by logging per-
meability, no matter how to regulate relative permeabil-
ity, it’s shown that match water injection is smaller than
true one, match oil production is smaller than true one.
According to logging permeability correction method
above, logging permeability performance correction co-
efficient

of wells in region of interest were calcu-
lated (Table 1, partial wells shown). From Table 1: it’s
seen that great difference exists between performance

Y. C. Xue et al. / Natural Science 2 (2010) 120-123
122
Table 1. Log interpretation permeability dynamic correction coefficient.
Well name Daily rate
（m3/d）
Drawdown
（MPa）
Thickness
（m）
Logging perme-
ability
(×10-3μm2)
Performance
permeability
(×10-3μm2)
Permeability
correction coeffi-
cient
Yu35-23
Yu36-22
Yu36-23
Yu37-21
Yu37-23
Yu37-27
Yu38-21
Yu38-22
Yu38-23
Yu38-24
Yu38-30
Yu38-31
Yu38-35
Yu39-25
Yu39-27
Yu39-29
Yu39-33
Yu39-37
Yu40-20
Yu40-21
Yu44-22
5.78
6.82
7.71
9.93
14.48
10.13
7.28
7.21
12.83
12.94
10.90
9.06
8.69
13.35
23.00
8.76
10.59
8.96
11.71
10.13
14.13
6.93
6.83
6.83
5.33
7.53
7.53
5.53
5.93
6.73
6.73
6.73
7.23
6.33
7.53
7.53
6.93
6.83
6.33
5.83
5.93
3.73
7.90
8.60
9.05
8.65
10.50
14.00
8.40
15.60
27.00
3.90
17.70
17.80
14.75
18.45
9.70
9.05
15.30
8.50
11.90
20.10
9.95
1.03
1.65
1.22
0.76
0.72
0.90
0.84
0.78
0.85
1.25
1.35
1.33
0.51
1.15
0.73
1.00
1.16
1.12
0.62
0.88
0.65
5.67
6.23
6.69
11.56
9.83
5.16
8.41
4.18
3.79
26.45
4.91
3.78
4.99
5.16
16.90
7.49
5.44
8.94
9.06
4.56
20.43
5.52
3.79
5.50
15.12
13.65
5.72
10.02
5.34
4.45
21.11
3.65
2.83
9.71
4.47
23.24
7.49
4.68
7.97
14.58
5.19
31.56
permeability and logging permeability. The biggest was
31.56 times, the smallest was 2.83 times, 5 to 10 times is
in general. It was clarified that logging permeability was
much smaller than performance one, true flow charac
teristics of reservoir couldn’t be reflected. On the other
FLPTH：field liquid production total history, FLPT：field liquid
production total (model)
(a) Cumulative liquid production
FOPTH：field oil production total history, FOPT：field oil production
total (model)
(b) Cumulative oil production
FWPTH：field water production total history, FWPTH：field water
production total (model)
(c) Cumulative water production
FWCTH：field water cut total history, FWCTH：field water cut total
(model)
(d) Composite water cut
Figure 1. Development history marching curve of Baiyushan
Chang4+5 reservoir in Jing’an oil field.
hand, it was the reason why the actual development of
reservoir couldn’t be matched using permeability model
established by logging permeability directly.

Y. C. Xue et al. / Natural Science 2 (2010) 120-123
123
According to the logging permeability correction co-
efficient of each well, the logging permeability of each
well were corrected point by point (0.125p/m), then the
dynamic corrected logging permeability of each well
were yielded. On basis of it, permeability model of res-
ervoir numerical simulation was established, and pro-
ducing history was matched. Chart 1 is the result of his-
tory match. From the chart 1, we can conclude that, the
field liquid production total history is 86.00×104m3, his-
tory match is 84.98×104m3, error is 1.19% (Figure 1(a));
field oil production total history is 49.00×104m3, history
match is 47.65×104m3, error is 2.76% (Figure 1(b));
field water production total history is 29.44×104m3, his-
tory match is 29.98×104m3, error is 1.84% (Figure 1(c));
field water cut total history is 34.2%, history match is
35.3%, error is 3.22% (Figure 1(d)); moreover, all the
producing history procedure match better (Figure 1), the
reservoir numerical simulation accuracy requirement is
met. It was shown that the method was more coincide
with oil field production, better effect of matching.
4. CONCLUSIONS
1) Aiming at the evaluation problem of log interpretation
permeability in micro-fractured low permeability reser-
voir, the correction method of logging permeability us-
ing oil field development performance files was pro-
posed, then numerical simulation model, which is closer
to the actual permeability in reservoir, was established.
The method had a good effect on Baiyushan area of
Jing’An oil field.
2) Reservoir numerical simulation model, established
by development performance files, is favour of the im-
provement of reservoir numerical simulation reliability.
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