ISSN-0866-854X
An Official Publication of The Vietnam National Oil and Gas Group Vol 10 - 2009
PETRO
PETRO
Petro
ietnam
VIETNAM
JOURNAL
ENMP TROVIET A
Percolation theory in research
of oil-reservoir rocks
Comprehensive CO2 EOR study - Study on Applicability of
CO
2 EOR to Rang Dong field
Comprehensive CO2 EOR study - Study on Applicability of
CO2 EOR to Rang Dong field
Publishing Licences No. 170/GP - BVHTT dated 24/04/2001; No. 20/GP - S§BS 01, dated 01/07/2008
Editor - in - chief
Dr.Sc. Phung Dinh Thuc
Deputy Editor-in-chief
Dr. Nguyen Van Minh
Dr. Vu Van Vien
Dr. Phan Tien Vien
Members of the
Editorial Board
Eng. Vu Thi Chon
Dr. Hoang Ngoc Dang
Dr. Nguyen Anh Duc
BSc. Vu Xuan Lung
Dr. Hoang Quy
Eng. Hoang Van Thach

Comprehensive CO2 EOR study - Study on
Applicability of CO
2 EOR to Rang Dong field
24
Novel surfactans for high temperature, high
salinity emhanced oil recovery applications
34
Quasi-dynamic and dynamic random analysis of
mooring system of FPSO installed at White-Tiger field
using hydrostar and ariane-3D softwares
Prediction of aquatic organism impact on rig
submerged structures of oil and gas field
At Cuu Long basin
66
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1
Introduction
In reality, the reservoir rock space is a very
complex metamerism; however when caculating
according to the common way, in many cases, we
consider the void structure in the rocks as similar
fractal, and use suitable statistical approximate for-
mula to demonstrate the space in form of effective
homogene. When researching the layers, we take
the rock samples from one layer with different col-
lector parameter. To get a parameter value (grain
density, porosity, permeability, saturation etc.) of a
researched object, we calculate the average value
of parameters measured from samples of the same
object. Therefore, the real space is inhomogeneous

plex structure.
Introduction to Percolation Theory
In this writing, the meaning of the term “perco-
lation” is only limited within the permeation or the
penertration of the fluid into the solid matters with
voids. When percolating into solid objects, the fluid
penetrates into sites which has capability of contain-
ing fluid or it flows in bonds, capillary segments con-
necting the sites in the space.
Sites, bonds and types of percolation
Starting from simple cells, for example net of
squares (Figures 2a). Cells with black round spot
are called reservoir sites, white cells are called
empty sites (no reservoir). If we call p the probabili-
Ass. Prof. Dr. Nguyen Van Phon
Hanoi University of Mining and Geology
Percolation theory in research
of oil-reservoir rocks
Abstract
Following the articles about fractal geometry in the research of oil-reservoir rocks [1, 2], in this article,
the author will introduce the application of percolation theory in researching the permeability process of fluid
in void space in general, and fractured rock in particular.
Percolation theory is a mathematical method which has been introduced since the early 1950s, and it
has been applied widely in social and human sciences, and technological sciences since 1970s. Through
this work, the author would like to suggest applying the percolation theory in researching the layers of oil-
reservoir rock, based on the similarity between geometrical forms of percolation process and physical
nature of permeability process of fluid in void space. In the final part of this work, the author proposes the
procedure of calculating the permeability in fractured rocks according to well-log datas, based on applica-
tion of percolation theory.
petroleum EXPLORATION &

percolation.
Percolation threshold and unlimited group
For low value p, there are only groups with dif-
ferent sizes. When p increases the number of
reservoir sites or the number of bonds also
increases, creating a chance for groups in the net
to increase their size. If p continues to increase,
the groups also grow gradually, and they can inte-
grate to each other through a common bond to
form a bigger group. Until reaching an ultimate
value p = p
c
, the big groups will become unlimited-
size group and the ultimate probability p
c
is called
percolation threshold. The percolation threshold p
c
is an ultimate probability enabling an unlimited
group to form in a large net. With p > p
c
unlimited
group are enlarged more and more, extend form
margin to margin (in 2D) or from face to face (in
3D) of a large net. With p < p
c
there is no unlimit-
ed group in the net.
Percolation threshold p
c

should be chosen to
put the exploiting well, and the well has to pener-
trate an unlimited group.
A new problem is raised here: With the proba-
bility p in the square net, how we calculate the aver-
age size (average number of sites and bonds) of the
group and the proportion of sites belong to unlimit-
ed group P?
The quantity of groups, average size and space
of group correlation
In net of squares, identify the probability so that
a random cell (site) is a group which has the mini-
mum size s = 1, which means that it is a reservoir
site and independently standing among nonreser-
voir sites. The reservoir site has its own probability,
and around it is 4 adjacent nonreservoir sites with a
probability of (1-p) for each site. These five sites
cells (sites) are independent so they are cooperat-
ed in terms of probability by the product of probabil-
ity: n
1
= p(1 - p)
4
.
For the case of 2 reservoir sites standing
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groups can be formed in the net of squares. We
write:
n
S
= 2p
S
(1 - p)
2S+2
(1)
For p < 1, if S  ∞, n
S
 0 is the probability
for a group which has sites S  ∞ aligning in net of
works is very low, nearly reaching 0.
In 3D, on a simple net of squares, each aligned
group including S will have (4S + 2) adjacent non-
reservoir blocks and sites which can be aligned in 3
perpendicular directions , the number of average of
groups (for a net of sites) is calculated as follows:
n
S
= 3p
S
(1 - p)
2S+2
(2)
For the case of hypercubic d-dimensions, each
site has 2d adjacent boxes; for internal sites of a S
group, sites creating lines will have (2d - 2) non-
reservoir sites. If two ends are considered, Group of

between two sites under a correlation group. If p 
p
c
, nearly equal to percolation, the scale (ratio level)
for typical average computation (volume in 3D, area
in 2D) is getting bigger to the scale “mini” around p
c
.
Then, the ratios are equivalent to one another. This
means that adjacent to level p
c
is a fractal which has
the similar structure with scale D~2.5 in 3D [9]. This
explains why at this level, the description of active
space becomes unsuitable for space which has
strong homogene.
Around percolation p
c
, correlation length ξ is
calculated as follows
ξ ~ |p - p
c
|
-x
,(4)
In which ultimate exponent does not depend on
the arrangement of net. In 3D, x ≈ 0.88, 2D, x ≈ 1.33,
[7, 11].
At the level p
c

for any point (crack) to contain (connect). If p is con-
sidered as common porosity inaccordance with sur-
veying terms, P is connecting porosity or opening
porosity (P ≤ p).
When logM(L) and logL are represented in loga
couple chart for net having large number of points,
Staufer (2003) found that chart was a line having
angle factor D = 1.9 (Fingure 4). D ≈ 1.9 is fractal
integral number of limitless group in 2D presenta-
tion space. Fractal dimensional numbers of limitless
group do not depend on arranging form of network
(triangle, square…) and only denpend on Euclid
position dimension. In 3D scale D ≈ 2.5.
In Figure 4, line chart shows that:
M (L) ~ L
1.9
,(6)
Meams that M(L) grows with L
1.9
, average den-
sity (5) is not a constant number but decrease L
-0.1
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4
times in rate grade. The larger scope is, the larger
the difference is. For example, average density P
(amount of workable oil) counted on an area of
reservoir with porosity of approximate p
c

than p
c
. Therefore, explorer shall use a sample with
L that is larger than ξ to calculate amount of oil
which may be exploited more exactly.
Of course, the amount of oil take from reservoir
layer depends on many other factors relating to fluid
flow in pore space and dynamtics characteristics in
osmotic packages such as diffission of fluid in mixed
space and force osmosis which shall be discussed
in another works.
Bethe net
In order to have exact solution for complex
structures, problem above is studied in form of
branch separated tree – Bethe net. Bethe net (or
Cayley tree) is tree shaped net with unlimited
dimensionals. Approximated calculation Bethe is
used to give anwser for tree problems. Therefore
complex structures with unlimited dimensional d are
Bethe net.
In order to understand structures with unlimited
dimensional d, we will start with d = 2: Area of circle
with radius r is πr
2
, its circle is equal to 2πr. Area S
of sphere (3D) radius r is 4πr
2
, and volume V is
propotional with r
3

.
In example in Figure 5: Z = 4, original site is
covered by 4 sites A (the first system), second sys-
tem (or layer) will have 12 B site, the third will be 36
C sites therefore, the point network consisting of
the first system to the last system of 4 x 3
r
-1
site is
the outer site. Then, the network expand to r, the
last system consist of
4 x 3
r-1
/
2 x 3
r
-1
= 2/3 of the
total sites on Bethe net. This is equal to and correct
to
(Z-2)
/
(Z-1)
any Bethe net with Z at random.
From this point of view, we can expand to the
3D case, ratio of area of internal side and volume of
the ball whose radius is of r will reach the approxi-
mation ~1 when Z  ∞. This is fitted with the
expression (7) when 1/d  0. Now we can see that
Bethe net is an abnormal model; thus, when men-

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average number of sites connected with original site
to form each branch A. Each of these separate
branch is continuously divided into three smaller
infinite branches, T will still be average size of the
unit in each branch.
Next to site A, site B may be the containing with
probability p or non-containing with the probability
(1 - p). The non-containing sites will not be very
meaningful while the containing sites contribute (1 +
3T) point for this branch in which one is point B and
3T is three branches extended from this site.
Therefore:
(9)
The size of group originating from the site O is
0 if this site is non-reservoir site or (1+4T) if it is
reservoir site. Therefore:
(10)
Referring to (8), so S can be adjusted
according to (p
c
- p)
-1
for p < p
c
. For p > p
c

is an unlimited daisy chain, O must be of two unlim-
ited chains which consider them as the connection
part of a permeability group.
The probability to exist the arrow between O
and site A is (1 - Q). For case (c), we have probabil-
ity 6Q
2
(1 - Q)
2
(including 6 probabilities of arrange-
ment so that from O there are two arrows and 2
nonarrows which rotate indifferent directions). For
case (d) it will be 4Q(1 - Q)
3
; and for the case (e), it
will be (1 - Q)
4
. Total probability will be:
(12)
In fact, probability has function relation with
probability p. In fact, a chain line connecting from O
to site A is discontinuous if O and A are not connect-
ed (probability1 - p), or if O and A are connected but
fragmented on connecting to A (probability pQ
3
), it
can be computed as follows:
Q = (1-p) + pQ
3
(13)

site increases from p
c
to 1. In the space of p < p
c
the set status is below the permeation threshold P
=0. This means the reservoir rock space has the
critical void ratio (p
c
), the space will have the perme-
ation or the permeability will occurs at that time.
The finner the grain of the clastic rocks is, the
higher the critical void ratio value (p
c
) is; the void
rate of the fractured rock with the kinetic penetration
is usually lower than that of the crumb rock. This
relates to the specific surfaces and the channel
bend of the two mentioned above rocks.
In the basement of Bach Ho oil field and other
fields in Cuu Long basin, the hydrodynamic penetra-
tion occurs at fractures spaces (F
f
) and macrofrac-
tures while the capillary penetration occurs in
microfractures. The result of 270 granitoit fractured
samples analysis (2001) in basement of Bach Ho oil
field by Mr. P. A. Tuan showed that their average gen-
eral void ratio is 3.1% while the average open void
ratio is only 1.88%, it means that the close non-con-
nected void ratio makes up nearly 40% of the gener-

We consider space as rocks with different frac-
tures of random distribution. If there are not many
fractures in the space, it is unlikely that such frac-
tures cut each others, low connectivity, zero perme-
ability.The higher the density of fractures is, the
greater the probability for such fractures cut. each
others. If the critical density is to be outnumbered,
there will be a ratio f representing intersecting frac-
tures in the space, which forms the “unlimited
group” (Figure 8) and enables the fractured space
to let the fluid through – that means the non-zero
permeability.
Using the model Bethe net (Figure 5) with Z =
4 to demonstrate the fracture net , we have: f is den-
sity P, and p
c
= 1/3, and p is the probability so that
two random intersecting fractures cut At different
value of p, which is greater than the critical proba-
bility p
c
, then p would be directly proportional to P,
which is the ratio of intersecting fractures and
belong to unlimited group within the scope of stud-
ied volume. As P increases, the probability of leting
fluid through the space also increases. This princi-
ple is also applicable for the conductance of fracture
net if the carrying fluid follows the saturated fluid
(water) in the empty space of fractures. In this case
the Ohm Law and Darcy Law is compatible.

to have a second fracture O’ ( with the same radius
c), which is arranged randomly in the volume. The
result is that the two fractures will cut each others.
In the fluid crystal physics (De Gennes, 1976), this
volume is defined as:
V
ex
= π
2
c
3
(17)
At a density of fracture N, the average number
of intersecting instances of each fracture is v = NV
ex
.
The Bethe net in Figure 5 shows that the probability
for an isolated fracture (does not have any fracture)
is p
o
= (1 - p)
4
. This probability can be presented
according to v as follows. Assume V
o
is wide volume,
in which there are disorder distribution of centre O of
fractures with the density N. Probability for a random
point in V
o

-n
will be the probability for a fracture
to be isolated (does not cut any fracture). But then
p
o
= (1 - p)
4
. So we have:
(20)
According to (20) we can see if the density N
 ∞, that means v  ∞ then the probability for p so
that two random intersecting fractures will be nearly
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7
equal to an unit If N is so small, n << 1 that p ~
v
/4. Because so (20) express
the connection between p, c, ℓ and N.
Take and , the conditions for
percolation threshold p
c
= 1/3 will divide (mặt) (ℓ, c)
into two domains (Figure 10), the percolation
domain in the right side of the dividend line, corre-
sponding to values and .
There will not be percolation if ℓ is too great,
density N is too small or c is too small (small frac-
tures).

presented as:
(21)
In which k is the permeability with the perme-
ability factor [m
2
].
Darcy speed is the volume flux (not the actual
speed of the fluid) and can present the connection
between it with the average speed of the fluid in the
porous hole F according to Dupuit-Forcheimer Law.
q = vΦ (22)
In the fractured space, the average speed
―
v of
the fluid between the two parallel sides will apply
Landau-Lifshitz Law (1971):
(23)
From (23) and (21) we can easily conclude that:
(24)
Take the approximate porosity F of the frac-
tured rocks as an replace (24) we can calcu-
late that:
(25)
Here, once again it is proved that in the frac-
tured rock space, permeability k depends on three
micro-structure factors: c, w and ℓ.
Expression (24) and (25) are true for the per-
meability which all fractures will connect with each
others completely, that’ means p ≡ P as the model
of Warren – Root (see instruction documents of

because of permeability effect:
(26)
In which, W is aperture of fracture, p is com-
mon porosity, p
c
is porosity limen for fuildl passing
permeability space, and Φ is leaky porosity or open
porosity, including carven and fracture porosity
which are called secondary one in some docu-
ments.
Define permeability basing on well log datas
According to the porosity result in bore well,
common porosity (p) in fractured rocks is calculate by
average of porosity Φ
D
and Φ
N
at the same depth;
secondary porosity Φ is calculated as following:
(27)
In which Φ
S
is calculated basing on sonic
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method at matrix rock without fracture.
Dimensions w, c and ℓ or fracture density in the

internuclear porosity (or block porosity); kinematical
permeability in large fractures and caves, capillary
in internuclear porosity and fractures. Large frac-
tures have small ratio in common porosity but play
an important and decisive role in effective perme-
ability. Minimum fractures and porosity of particles
play an important role in determining the ability of
product area. The penetration of fluid into an space
with 2 porosity is a complex process. In the porosi-
ty space of fractures, they are up to gradient pres-
sure of fluid, the minimum fractures and porosity
among particles are determined by wettability and
capillary force. The physical nature of permeability
in multi-fracture space are suitable with shape of
permeability. The analogy is the base to apply the
theory of permeability in an unsuitable space such
as fracture stones in Bach Ho oil field and other
fields in Cuu Long basin.
The evaluation and use of the permeability
density P(p) as the permeability effect factor is the
specific result of this construction to overcome the
disadvantage of Warren- Root model in order to
determine the k permeability in the fracture rock
space with two void and two permeabilities objects.
The author would like to thank fellows for help-
ing and exchanging experiences and ideas in the
work implementation…
This work is the result of the research project
KHCB 7.1.5206 sponsored by Ministry of Science
and Technology.

Geometry of Nature. San Francisco Freeman.
[10]. Snarskii A.A. (2007). Did Maxwell know
about the percolation threshold? Uspekhi
Fizicheskikh Nauk. 177(12). 1341 – 1344.
[11]. Stauffer D., and Akarony A., (2003).
Introduction to Percolation Theory. Taylor and
Francis (2003).
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9
Fig. 1. Inhomogeneous real space and effective homogeneous space
Fig. 2. Site percolation and bond percolation
Fig. 3. Different configuration of the group
of 4 sites in net of squares
Fig. 4. M(L) is L’s funtion, for network
having area L
2
=10
10
arrange in
rectangle net p
c
= 1/2
(according to Staufer 2003)
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Method
The study was based on collecting and classi-
fying the analyses of BI.1 and BI.2 sandstones:
petrology and sedimentology (grain size, cement
and matrix compositions), reservoir properties
(porosity, water saturation, NTG ratio); and deposi-
tional environments and constructing cross sections
and maps:
- Constructed 6 geophysic-geological cross
sections (3 strike sections through the basin and 3
sections across the basin):
Section 1: NW-SE, at the Northern part of the
basin, through blocks 15-1 and 01-02 (Figure 1).
Section 2 : NW-SE, at the central part of the
basin, through blocks 16-1, 09-1 and 09-3 (Figure 2).
Section 3: E-W, at the Southern part of the
basin, through blocks 16-2, 09-1 and 09-3 (Figure 3).
Section 4: NE-SW, at the Western margin of
the basin, through blocks 15-1, 15-2, 16-1, 16-2 and
17 (Figure 4).
Section 5: NE-SW, at the central part of the
basin, through blocks 01, 15-1, 15-2, 16-1, 09-1 and
09-3 (Figure 5).
Section 6: NE-SW, at the Eastern part of the
basin, through blocks 01, 15-2, 09-2, 09-1 và 09-3
(Figure 6).
- Constructed 12 distribution maps of thick-
ness, grain size, matrix and cement content, poros-
ity, water saturation and net to gross ratio of BI.1
and BI.2 subsequences.

a part of block 09-1 and 09-3. Generally, BI.1 is thin-
ner than BI.2, except in block 16 and 09-3.
Grain size
Maps showing grain size distribution of BI.2
and BI.1 are presented in Figures 9 and 10. Figure
9 show that the grain size of BI.2 sands varies from
very fine-fine (<0.25mm) in block 16, the Southern
of block 09-1, the Eastern of block 09-2 and the
Northwestern of block 15-1, to medium (0.25-
0.5mm) in the remaining area, except in the centre
of block 01-02 where grain size becomes very
coarse (0.5-1mm).
Figure 10 shows that the grain size of BI.1
sands varies from very fine-fine (<0.25mm) in the
Nothern of block 16, 09-1, the Southern of block 09-
2, to medium (0.25-0.5mm) in the Southern of block
16, the Northern of block 15-1 and 01, the Eastern of
block 15-2, to coarse (0.5-1mm) in the Southern of
block 01, 15-1 and the Northeastern of block 15-2.
Commonly, the grain size tends to larger in
the Northern part of the basin than in the Southern.
Especially in BI.1, the boundary between the two
area can be seen clearly (black bold line in Figure
10).
Matrix and Cement
The average contents of matrix and cement
were collected and mapped over the whole basin for
BI.2 and BI.1 subsequences individually (Figures 11
and 12). Figure 11 shows that the matrix and
cement content of BI.2 varies from 4 to over 30%.

BI.1 is lower than those of BI.2 probably due to
strong extrusive activities in this period. Meanwhile,
in the centre of block 15-2, the Eastern of block 16
and block 09-1, porosity of BI.1 is higher than those
of BI.2. The reason probably is BI.2 sediments were
deposited far from sedimentary source in deltaic
environment to shallow marine with more abun-
dance of clays.
Water saturation
Water saturation distributions of BI.1 and BI.2
are presented in Figures 15 and 16. Figure 15
shows that in BI.2 low water saturation areas are in
the Northern to the Eastern and the centre of block
15-2. In blocks in the Southern, water saturation is
high (over 80%), except block 09-3, a part of block
09-1 and 16. The boundary between the two areas
is presented by the black bold line in the map.
In reverse to BI.2, water saturation in BI.1
varies in range of 40% in a trend from block 09-1 to
the Eastern of block 16 and the centre of block 15-
2, to more than 80% in block 15-1, the Eastern of
block 09-2, and a part of block 16. In Northern area,
sands are mostly water filled (Figure 16).
Similar to the distribution of porosity, low water
saturations gather in block 01-02, 15-1, the centre
and Eastern of block 15-2, the Eastern of block 16,
09-1 and the Western of block 09-3. However,
water saturation increases from BI.2 to BI.1 in block
01-02, 15-1 and the Eastern of block 15-2.
Reversely, in the centre of block 15-2, the Eastern

it can be concluded that good reservoirs can be
found in the Northern part at BI.2, while they can be
found in the Southern part at BI.1. The possible rea-
sons are:
- Different sedimentary sources of the two
areas. Sediments of the Northern area might be
supplied by the paleo Dong Nai river or other paleo-
rivers in the central Vietnam with short transporta-
tion pathway. Sediments of the Southern area might
be supplied by paleo-rivers in the Southern Vietnam
with rather far transportation pathway.
- Either structures of BI.1 in the Northern area
were destroyed by extrusive activities or there is no
top seal due to lack of claystone.
- In BI.2, although structures exist, reservoir
capacity is still low due to abundant claystone.
Reference
1. La Thi Chich (2001), Petrology, Publishing
house of Ho Chi Minh City National University, p.
265-322.
2. Nguyen Ngoc Cu et al. (1998), “Oil-bearing
reservoir formations in Vietnam”, Vietnam
Petroleum Institute science conference, Hà Nội.
3. Pham Tuan Dung and Pham Van Hung
(2001), “Geological structure of Lower Miocene No
23 reservoir, Bach Ho field”, Petroleum conference,
Hà Nội.
4. Nguyen Van Dung (2004), Petrological char-
acteristics, postdepositional deformations and their
impacts on porosity and permeability of Oligocene-

The Study Of Rocks In Thin Sections, W. H.
Freeman and Company, San francisco, USA.
12. J.H.Barwis, J.G.McPherson & J.R.J
Studlick (1990). Sandstone Petroleum Reservoirs,
Springer-Verlag.
13. Maurice Tucker (1989), Techniques In
Sedimentology, Blackwell Scientific Pub
14. O. Serra (1989), Sedimentary
Environments From Wireline Logs, Schlumberger.
15. Reineck-Singh (1980), Depositional
Sedimentary Environments, Springer-Verlag Berlin-
Heidelberg-Newyork.
16. Ngo Thuong San và nnc (1993),
“Stratigraphy and Lithology of The Mekong Basin”,
Proceedings of the international seminar on the
stratigraphy of Southern shelf of Vietnam. Ha Noi.
17. Supakorn Krisadasima, Nguyen Tien Long,
Hoang Thanh Bang, Ngo Quang Hien, Chanwichai
Suksawat and Nguyen Thanh Long (2006),
“Overview of Clastic Reservoir Potential in Block 9-
2 Cuu Long Basin, Vietnam”, Technical Forum
Clastic_Carbonate Reservoir, Ho Chi Minh City.
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Fig. 1. Geophysic-geological cross section along NW-SE direction in the Northern area
Fig. 2. Geophysic-geological cross section along NW-SE direction in the central area
Fig. 3. Geophysic-geological cross section along NW-SE direction in the Southern area

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Determination of fractured basement per-
meability in White Tiger oil field from well log
data by artificial neural network system
using zone permeability as desired output
MSc. Tran Duc Lan
R&E Institute - Vietsovpetro
Abstract
Recently, some authors have suggested using the Artificial Neural Network (ANN) method
to determine permeability from log data. An ANN is built from the permeability of cores. This
method is highly applicable in sedimentary rocks[1], [4]. However, due to the limitation in coring
methods and laboratory measurements, core permeability is not truly representative for the per-
meability in the fractured basement rock in well bores.
In our study about fractured basement in White Tiger Field, offshore Vietnam, instead of
using core permeability, we have used zone permeability as desired outputs of an ANN to cal-
culate permeability profile in wells. Zone permeability, which was estimated from built-up pres-
sures and production log test data has high reliability and directly represents for the permeabil-
ity of the well bore rock.
We have determined the permeability for 16 wells in the field where both zone permeabili-
ty and well log data are available. For quality control, the calculated permeability is compared
reversely to zone permeability. The correlation coefficients are very high, commonly greater than
0.98.
Having calculated permeability and input well log data i.e. samples (more than 55,000 sam-
ples) in these 16 wells, we have been building a system of dozens of ANNs (called ANN sys-
tem) to determine permeability for wells which have only well log data.
p
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ty sections – permeability profile).
Artificial neural network introduction
The first artificial neuron was produced in
1943 by the neurophysiologist Warren McCulloch
and the logician Walter Pits. But the technology
available at that time did not allow them to do too
much. The ANN theory then was developed further
by Minsky and Papert. In 1969, they published a
book to summarize criticized issues in ANN theory
and presented valuable study for later develop-
ment of ANN. Since then, ANN was restored and
applied widely [3].
In fact, ANN is a computer program. It is pro-
grammed based on mathematical models using
ANN theory. An ANN has abilities to learn and to
run. In another word, an ANN has two main
processes. These are training and running
processes [2].
A model of an ANN is shown in Figure 1. It is
used to determine permeability from well log data.
There are three layers in the ANN, which are input
layer, hidden layer and output layer. The input layer
contains 6 nodes corresponding to logging curves
of GR, DT, NPHI, RHOB, LLD and LLS (or MSFL).
The hidden layer contains 7 nodes and the output
layer contains 1 node representing permeability.
Between layers, there are connections and weights.
In the model, an ANN divides complex prob-
lems into simpler tasks. Each task is solved at a rel-
evant node by a so-called processing element (PE).

ability from well log data
Determination of permeability profile for the wells
having well log data and zone permeability
One of the most important characteristics in
training process of an ANN is the statistical analysis
based on the majority of samples. It ensures that
the output values are closest to the desired output
values of predominant samples.
An example is in the Table 1. The table con-
tains 2 groups of samples. Group A contains sam-
ples from 1 to 5. Group B contains samples from the
6 to 10. Sample 11 has the input value similar to that
(1)
(2)
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20
in group A but the desired output is similar to the
desired output in group B. After training and running
processes, the output value of sample 11 will be
similar to the out put values in group A.
By using zone permeability values as desired
outputs for the statistical analysis in an ANN, we
suggest a procedure to determine permeability from
well log data as in Figure 3.
We calculated permeability for 16 wells, which
have enough both zone permeability and well log
data, belong White Tiger oil field. Figure 4 and

zones for training and 16 zones for cross-validation
testing. Figure 7 is the cross plot of zone permeabil-
ity which predicted by ANN system (kz-ANN) on
cross-validation testing data set against actual zone
permeability (kz-PLT). The correlation coefficient is
greater than 0.89.
We used this ANN system to calculate the per-
meability profile for 85 wells in the fractured base-
ment reservoir of White Tiger oil field. Figure 8
shows the permeability profiles, which were predict-
ed by the ANN system, of some wells having only
well log data.
Conclusions
The success in using zone permeability as
desired output for statistical analysis in an artificial
neural network to determine permeability from well
log data has opened a new trend in application of
ANN. Desired output data is not set separately for a
single sample, instead we use averaged number to
for a group of samples. This averaging method is
highly practical, especially when we can not choose
the desired outputs for each particular input data.
By dividing input data i.e. samples into smaller
groups, we can manage a huge amount of input
data for training processes. An ANN is designed for
one specific group of input samples. Depends on
the number of groups, we will have an ANN system.
This ANN system is flexible. It is easy to add new
input data to save running time in re-training
processes.

Fig. B is a zoom in of fig. A at zone 3600-3660m
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Fig. 6. Zone permeability from BUP-PLT (K-TV)
vs. zone permeability from ANN (K-AN1z)
Fig. 7. Comparison between actual zone permeability
kz-PLT and prediction zone permeability kz-ANN
with 16 zones of testing data set
Fig. 8. Permeability profile prediction by ANN system from the wells having only well log data
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