Calculating precise water saturation with hydraulic flow unit using leverett’s J-function. A case study of field a, Cuu Long basin, offshore Vietnam

PETROLEUM EXPLORATION & PRODUCTION

PETROVIETNAM JOURNAL

Volume 6/2020, pp. 30 - 36

ISSN 2615-9902

CALCULATING PRECISE WATER SATURATION WITH HYDRAULIC

FLOW UNIT USING LEVERETT’S J-FUNCTION. A CASE STUDY

OF FIELD A, CUU LONG BASIN, OFFSHORE VIETNAM

Phung Van Phong, Pham Thi Hong, Vu The Anh

Vietnam Petroleum Institute (VPI)

Email: phongpv@vpi.pvn.vn

Summary

Estimating water saturation is one of the main challenging aspects in reservoir characterisation. Good estimation of this parameter

enables us to calculate reserve accurately. Hence, it is of great importance to estimate precisely water saturation based on hydraulic

ﬂow units of reservoir rocks. In this paper, a modiﬁed J-function was used and developed to determine the water saturation in the

hydrocarbon reservoirs located in ﬁeld A, Cuu Long basin. The capillary pressure data (P_c) and water saturation (S_w) as well as routine

core sample analysis including porosity (φ) and permeability (K) were used to develop the J-function. First, the normalised porosity (Ф_z),

the rock quality index (RQI), and the ﬂow zone indicator (FZI) factors were used to classify all data into discrete hydraulic ﬂow units (HU)

containing unique pore geometry and bedding characteristics. Subsequently, the modiﬁed J-function was used to normalise all capillary

pressure curves corresponding to each of predetermined HUs. The results showed that the reservoir rock was classiﬁed into several

separate rock types with deﬁnite HUs and reservoir pore geometry. Eventually, the water saturation was determined using a developed

equation corresponding to each HU gained by normalised J-function. The equation is a function of rock characteristics including Ф_z,

FZI, lithology (J’), and pore size distribution index (∂). The proposed technique can be applied to any reservoir to determine the water

saturation in the reservoir, specially the ones with high range of heterogeneity in the reservoir rock properties.

Key words: Water saturation, rock quality index (RQI), hydraulic unit (HU), ﬂow zone index (FZI), Cuu Long basin.

1. Introduction

Flow regime of ﬂuid and accurate water saturation are

(1)

If oil and water are present in the reservoir, Equation

(1) can be written as Equation (2).

among the challenges in hydrocarbon reservoir studies

and extremely aﬀected by the geometry of pore size in the

reservoir. The results of diagenesis such as compaction,

cementation, oxidation and fracturing through geologi-

cal times will create irregular pore geometry. To precisely

determine water saturation of the reservoir rocks, a robust

model is proposed to simulate the ﬂow behaviour in the

reservoir. Up to now, there are numerous approaches to

determine water saturation. Among them, capillary pres-

sure curves are used more commonly because of their

direct relation to water level with each pore size throat

and distribution in reservoir rock. The capillary pressure is

expressed as the diﬀerence in pressure between the non-

wetting (P_nw) and wetting (P_w) phases as in Equation (1).

(2)

Moreover, the capillary pressure is also a function of

the interaction between rocks and ﬂuids. It is aﬀected by

several factors of rock such as pore geometry, r-pore ra-

dius (pore size), γ-interfacial tension and wettability with

θ being the contact angle as in Equation (3):

(3)

Normally, a reservoir consists of many intervals with

diﬀerent properties or heterogeneity. Each interval is re-

ﬂected by a speciﬁc shape of the capillary pressure curve

that reveals useful information about reservoir rock prop-

erty. And because of the heterogeneity existing common-

ly in the reservoir rocks, no single capillary pressure curve

can be considered as a representative of the reservoir.

Therefore, the capillary pressure curves need to be nor-

Date of receipt: 19/2/2019. Date of review and editing: 19/2/2019 - 9/3/2020.

Date of approval: 5/6/2020.

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malised into a single curve using a Leverett dimensionless

J-function [1] for a unique rock type with RQI known as

rock quality index and deﬁned by the square of perme-

ability and porosity of rock as follows:

As mentioned in Equations (4) and (5), the normalised

porosity as

FZI =

and ﬂow zone indicator (FZI) as

, Equation (11) can be re-organised as follows

(

)

z

[3]:

(12)

RQI = φ_z× FZI

(4)

(5)

Flow zone indicator is a unique and valuable factor to

quantify the ﬂuid ﬂow in a reservoir and is the one that

displays the relationship of petrophysical properties.

Finally, using a unique J-function can normalise capil-

lary pressure curves into a single curve for a deﬁnite hy-

draulic ﬂow unit as in Equation (13) [4, 5]:

According to Equation (5), the normalised J-function

can be applied to a single rock type with uniform rock

properties (RQI).

(13)

2. Theory overview

Re-writing Equation (3) gives:

(14)

To determine hydraulic units and allows(?) a suitable

relationship among porosity, permeability, capillary pres-

sure and geological variation in the reservoir rock, the

mean hydraulic unit radius (r_mh) need to be determined

and can be deﬁned by the ratio of cross-sectional area to

wetted perimeter as in Equation (6) [2]:

By substituting Equation (14) into Equation (13), one

can derive:

(15)

(6)

For a single hydraulic ﬂow unit with unique FZI value,

the J-function can be written as follows with J’ and ∂ rep-

resenting lithology and pore size distribution index, re-

spectively [5]:

According to Darcy's and Poiseuille's Laws, a relation-

ship between porosity and permeability can be derived as

shown in Equation (7) with φ and τ representing porosity

and tortuosity, respectively [2].

(16)

(7)

Where:

8

The relationship between rock porosity and permea-

bility depends on both geometrical characteristics of pore

size (radius) and pore shape. Combining Equations (6) and

(7), the permeability can be re-written as Equation (8):

(17)

According to Equations (16) and (17), water satura-

tion in the reservoir can be calculated by a function of

normalised water saturation, irreducible water saturation

and J-function for each hydraulic ﬂow unit.

(8)

The mean hydraulic radius in terms of surface area per

unit grain volume (S_gv) and porosity can be expressed by:

3. Regional setting and reservoir property

The study area is located in the Cuu Long basin. The

basin is an Early Tertiary rift basin situated oﬀ the south-

east coast of Vietnam. Geo-dynamic processes and envi-

ronments dominate the oﬀshore basin evolution related

to plate tectonic events, such as: northern collision of In-

dia with Asia ~53Ma ago and related extrusion tectonics

until the present day; escape tectonics of the Indochina

Block; the Philippine trench roll back; the opening of the

East Sea/Bien Dong (Late Oligocene - Early Miocene); the

northern collision of the Australian plate with Southern

Sunda land Indochina and its oﬀshore basins; NW-SE

(9)

According to Equations (8) and (9), substituting r_mh

into the Kozeny and Carmen relationship from Equation

(8), the rock permeability can be presented as follows:

(10)

Dividing both sides of Equation (10) by the porosity

and then taking square root, the equation can be re-writ-

ten as follows:

(11)

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PETROLEUM EXPLORATION & PRODUCTION

opening of the basin began in Late Eocene(?)

Oligocene time; the opening of the basin is re-

lated to crustal stretching associated with the

clockwise rotation of Indochina; the basin is

located at the trailing edge of the Wang Chao/

Hau River fault system, which currently con-

trols the position of the Mekong delta; the ba-

sin and the neighbouring Nam Con Son basin

are separated by the Con Son swell, a trans-

gressional feature potentially linked to the NS

trending ‘Vietnam Transform’; the ‘Vietnam

Transform’ deﬁnes the present shelf break oﬀ-

shore Vietnam. It ‘accommodates’ the defor-

mation along the eastern boundary of the In-

dochina block. Thus, coeval NW-SE extension

and NS shearing are reckoned to occur during

the Cuu Long basin opening.

mainly of illite and chlorite with minor kaolinite. These clays occur

mainly as uniform mats coating detrital grains and to a lesser extent

as feldspar and mica grains replacement. Locally, authigenic illite oc-

curs as thin ribbons, or short ﬁbres/webs occluding and bridging pore

spaces. It is likely that this kind of illite morphology causes perme-

ability barriers that inhibit pore-ﬂuid ﬂow, i.e. it severely reduces the

permeability of these sandstones. Additionally, the laumontite ce-

ment is present in minor to common amounts and occurs mostly as

large, euhedral, tabular crystals more than 50 mm long. These mainly

ﬁll intergranular pores and/or partly replace detrital feldspar grains.

The moderate to strong development of laumontite in some samples

The study interval was formed in ﬂuvial to

lacustrine environments with some interbed-

ded sandstone and claystone based on the

detailed facies, grain size and petrographic

analysis of the cores. In terms of reservoir

properties, log and core data show that res-

ervoir cementation is in advanced stages, es-

pecially in the deeper parts of the reservoir.

Some core thin sections indicate good visible

primary porosity while most others have com-

plete primary porosity occlusion. And most

of the thin sections contain some amount of

secondary porosity, bringing to light the im-

portance of distinguishing measured porosity

from connected porosity.

Figure 1. The relationship of permeability and porosity in the reservoir according to core sample analysis

200

Most of the sandstones contain a large

amount of cement and authigenic minerals.

The main authigenic minerals observed in

SEM analysis include quartz, diagenetic clays,

zeolite (laumontite), albite and calcite. Quartz

cement is present in common to very abun-

dant amounts in all examined sandstones. It

occurs mostly as euhedral crystals (from 5 mm

– 10 mm to more than 100 mm in length) that

are surrounded by detrital quartz grains and/

or occluding intergranular pores and pore

throats. The strong development of quartz ce-

ment is one of the main factors that strongly

reduces both primary intergranular porosity

and permeability of all sandstones at the in-

terval. Moreover, the authigenic clays consist

150

100

50

0

0.00

0.20

0.40

0.60

0.80

1.00

Water saturation (frc)

Figure 2. Distribution of capillary pressure curves of 60 reservoir rock samples.

PETROVIETNAM - JOURNAL VOL 6/2020

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considerably reduces intergranular porosity.

Calcite cement is generally minor and occurs

mainly as sparry crystals ﬁlling intergranular

pores. Secondary albite is present in minor

amounts and often occurs as ﬁne, subhedral

to euhedral crystals of 5 mm to more than

20 mm. They are often surrounded partly by

detrital feldspar grains.

of all reservoir core data. As shown in this ﬁgure, there is a high hetero-

geneity in the reservoir rock properties. For example, given the same

value of porosity, the permeability could be changing up to 100 times.

The statistical data of 60 core samples with a complete data set are dis-

4. Database and methodology

Database is used to complete the study

including porosity (φ), permeability (k), irre-

ducible water saturation (S_wir) and capillary

pressure (P_c) vs. water saturation (S_w) ob-

tained from core analyses in the Cuu Long

basin. The huge PVT result from 485 rou-

tine core data and 60 complete data sets

of capillary pressure measured by porous

disk method are analysed. Figure 1 shows

a large permeability and porosity variation

Figure 3. Relationship of reservoir quality index (RQI) and normalised porosity in ﬁeld A.

Table 1. Rock properties of 60 samples taken from the capillary pressure curves

Permeability

(K), md

1.75

2.66

2.49

2.24

0.22

0.34

0.50

5.50

0.15

0.71

0.68

0.47

0.36

0.20

3.38

1.06

0.11

0.29

2.32

0.14

0.30

0.15

0.90

6.72

0.67

0.66

0.04

0.09

0.30

0.17

Sample No.

Porosity (φ)

S_wir

Sample No.

Porosity (φ)

S_wir

(K), md

0.04

192.80

8.19

50.37

0.32

708.77

3.49

0.47

40.04

37.29

0.05

340.42

670.00

418.00

259.00

0.03

1

2

3

4

5

6

7

8

0.08

0.16

0.13

0.15

0.11

0.18

0.08

0.13

0.10

0.05

0.14

0.17

0.16

0.07

0.10

0.13

0.12

0.06

0.07

0.08

0.10

0.09

0.07

0.62

0.18

0.28

0.17

0.46

0.11

0.30

0.41

0.16

0.62

0.14

0.16

0.17

0.80

0.66

0.31

0.25

0.27

0.31

0.25

0.23

0.21

0.20

0.22

0.23

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

0.08

0.11

0.10

0.08

0.09

0.10

0.09

0.11

0.08

0.10

0.09

0.10

0.09

0.08

0.12

0.10

0.11

0.10

0.06

0.07

0.08

0.26

0.31

0.35

0.56

0.52

0.48

0.32

0.59

0.38

0.39

0.43

0.36

0.38

0.44

0.50

0.41

0.46

0.44

0.46

0.40

0.35

0.44

0.41

0.64

0.45

0.40

0.43

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

0.63

29.40

64.00

79.60

11.80

4.45

0.16

1.07

0.98

0.70

4.30

3.71

4.46

1.66

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played in Table 1. Figure 2 demonstrates the measured

capillary pressure curves and water saturation. This ﬁgure

reveals that more than one hydraulic ﬂow unit in the res-

ervoir can be observed clearly. Therefore, the J-function

cannot be used to normalise all the capillary data into

a single curve and it is required to classify the data into

separate hydraulic ﬂow units having the same type of cap-

illary pressure curves.

10000

1000

100

HU#5, K = 337175 φ^3.8549

HU#4, K = 42101 φ^3.3619

HU#3, K = 36714 φ^3.7966

HU#2, K = 3275.1 φ^3.3917

10

HU#1, K = 603.48 φ^3.5903

1

0.1

0.01

0.001

0.0001

0.00001

According to the data shown, irreducible water satu-

ration broadly varies from 0.15 up to 0.65 depending on

the sample properties.

0

0.05

0.1

0.15

0.2

0.25

Porosity (frc)

Figure 4. Permeability and porosity distribution with FZI classiﬁed in ﬁeld A.

5. Results and discussions

After rock quality index (RQI) and normalised poros-

ity (φ_z) are estimated by the equations mentioned above,

the results are plotted together in Figure 3. Commonly,

all data are in correlation with unit slope having the same

mean value of FZI factor. Based on the data and Figure 3,

several hydraulic ﬂow units such as HU#1, HU#2, HU#3,

HU#4 and HU#5 can be deﬁned as separate rock types

with the mean values of FZI being 10.7, 33.1, 71.1, 123.1

and 220.8, respectively. It is clear that hydraulic ﬂow units

with higher FZI values will have a faster ﬂow of the ﬂuids

in the reservoir.

Figure 5. Frequency of FZI to deﬁne HU in ﬁeld A.

Figure 4 illustrates the relationships of the permeabil-

ity and porosity grouping by FZI category (Figure 5). With

200

HU#1, Pc = 5.7077Sw^-6.382

HU#2, Pc = 4.3315Sw^{- 4.382}

HU#3, Pc = 2.1706Sw ^-3.6

10

HU#4, Pc = 1.9219Sw ^{- 2.659}

150

HU#5, Pc = 0.3715Sw ^{- 2.833}

8

HU#5, J = 0.2516Swn ^-1.26

HU#4, J = 0.1587Swn ^-1.305

6

100

HU#3, J = 0.227Swn^-1.348

HU#2, J = 0.085Swn^-1.325

HU#1, J = 0.0627Swn ^-1.514

4

50

0

2

0

0.00

0.20

0.40

0.60

0.80

1.00

0.00

0.20

0.40

0.60

0.80

1.00

Normalized water saturation (frc)

Water saturation (frc)

Figure 6. Five capillary pressure data sets for obtained hydraulic ﬂow units in Field A.

Figure 7. J-function and normalised water saturation for each hydraulic ﬂow unit.

Table 2. Rock characteristics and equations obtained for each hydraulic ﬂow unit

ꢅermeaꢆilitꢇ

ꢈꢉuation

ꢊormaliꢋed ꢃꢂfunction

ꢈꢉuation

J = 0.0627 × S_wn

ꢅore ꢋiꢌe radiuꢋ

ꢀꢁIꢂmean

ꢃꢄ

ꢀ

ꢈꢉuation

R = 27.17 × S_wn

R = 77.88 × S_wn

R = 108.00 × S_wn

R = 151.84 × S_wn

-1.514

1.514

1.325

1.305

HU#1

HU#2

HU#3

HU#4

HU#5

10.7

33.1

71.1

123.1

220.8

0.063

0.085

0.158

0.227

0.2516

0.660502

0.754717

0.766284

0.74184

K = 603.48ϕ3.5903

K = 42101ϕ3.3619

K = 36714ϕ3.7966

K = 3275.1ϕ3.3917

K = 603.48ϕ3.5903

-1.325

J = 0.085 × S_wn

-1.305

J = 0.1587 × S_wn

-1.348

1.348

1.26

J = 0.227 × S_wn

-1.26

0.793651

J = 0.2516 × S_wn

R = 280.83 × S_wn

PETROVIETNAM - JOURNAL VOL 6/2020

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detailed relationships of porosity and permeability and combining

with the obtained hydraulic ﬂow units, the available capillary pres-

sure curves can be divided into ﬁve categories. Figure 6 shows the

ﬁve capillary pressure data sets for ﬁve hydraulic ﬂow units. Fol-

lowing that, each of these capillary pressure curves is normalised

into a single curve that represents hydraulic ﬂow unit.

all parameters associated with the Equations 16

and 17 are computed, the water saturation for

each hydraulic ﬂow unit is calculated. Figure 8 il-

lustrates examples of the matching result of water

saturation between J-function and well log inter-

pretation of reservoir rocks by dissimilar hydraulic

ﬂow units. This is a case study in which the meth-

od is applied for calculating water saturation in

the reservoir, Cuu Long basin. Table 2 summarises

all information including rock characteristics, li-

thology index, pore size distribution index, pore

geometry constant, J-function and pore size ra-

dius equations observed for each hydraulic ﬂow

unit. Meanwhile, Table 3 demonstrates the com-

parison results of water saturation between the

proposal approach and well log interpretation for

all 18 wells in the ﬁeld.

Figure 7 demonstrates J-function and normalised water satu-

ration (S_wn) plotted along and presents the speciﬁc shape of one

single capillary pressure curve for each hydraulic ﬂow unit. When

As the results in the Table 3, the tiny dis-

crepancy from around 1% to 9%, the most-likely

around 3% of water saturation between well log

interpretation and the method - J-function appli-

cation - illustrates the usefulness and applicability

of this approach in future works.

6. Conclusions

The water saturation is determined by a new

proposed technique. The ﬂow zone indicator (FZI)

approach is applied to separate the reservoir rock

into ﬁve zones having similar rock characteristics,

Figure 8. Comparison results of water saturation between well log interpretation and J-function

approach by dissimilar hydraulic ﬂow units. The result is an example taken from Zone A at well 3.

Table 3. Average water saturations by well log interpretation and J-function approach

Toꢃ

ꢄꢅ

ꢆottom

ꢄꢅ

ꢇꢈeraꢉe ꢊ_w

ꢋꢌ ꢍ function aꢃꢃroach

ꢇꢈeraꢉe ꢊ_wfrom well

ꢅiꢂcreꢃancꢌ

ꢎꢏꢐ

ꢀell

ꢁoneꢂ

loꢉ interꢃretation

0.406

0.311

0.238

0.207

0.38

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

A

B

A

B

A

B

A

B

A

B

A

B

A

B

A

B

XXXX

YYYY

0.38

0.308

0.25

0.21

0.374

0.31

6%

1%

-5%

-1%

2%

0.321

0.441

0.4

3%

0.45

-2%

-5%

2%

-2%

-4%

1%

-3%

-2%

9%

-9%

6%

0.422

0.418

0.55

0.33

0.56

0.35

0.588

0.22

0.359

0.62

0.26

0.426

0.538

0.317

0.565

0.339

0.579

0.242

0.33

0.661

0.245

-6%

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PETROLEUM EXPLORATION & PRODUCTION

which are considered as hydraulic ﬂow units (HU). The

measured capillary pressure curves are divided into ﬁve

categories based on the determined hydraulic ﬂow units.

Then J-function is used to normalise all capillary curves

that represent these ﬂow units. The discrepancy of water

saturation between well log interpretations and the pro-

posal approach is inconsiderable.

[2] Ali Abedini and Farshid Torabi, “Pore size

determination using normalized J-function for diﬀerent

hydraulic ﬂow units”, Petroleum, Vol. 1, No. 2, pp. 106 - 111,

2015.

[3] P.C.Carman, “Fluid ﬂow through granular beds”,

Chemical Engineering Research and Design, Vol. 75, pp. 32 -

48, 1997. DOI: 10.1016/S0263-8762(97)80003-2.

Finally, the results indicated that the mentioned

method is dependent on several rock properties and is

not controlled to the speciﬁc reservoirs; it can be applied

to any reservoir rocks having high heterogeneity in the

future.

[4] Ekwere J.Peters, Advanced petrophysics: Dispersion,

interfacial phenomena/wettability, capillarity/capillary

pressure, relative permeability. Live Oak Book Company,

2012.

[5] S.M.Desouky, “A new method for normalization of

capillary pressure curves”, Oil & Gas Science and Technology,

Vol. 58, No. 5, pp. 551 - 556, 2003.

References

[1] M.C.Leverett, “Capillary behaviour in porous

solids”, Transactions of the AIME, Vol. 142, No. 1, pp. 152 -

169, 1941. DOI: 10.2118/941152-G.

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