Transport of oil/water partitioning components during water injection
PETROVIETNAM
PETROVIETNAM JOURNAL
Volume 6/2021, pp. 37 - 42
ISSN 2615-9902
TRANSPORT OF OIL/WATER PARTITIONING COMPONENTS DURING
WATER INJECTION
Huynh Thi Thu Huong, Nguyen Huu Quang, Le Van Son, Tran Trong Hieu
Centre for Applications of Nuclear Technique in Indusry, Vietnam Atomic Energy Institute
Email: huonghtt@canti.vn
Summary
The oil/water partitioning components such as alkylphenols and aliphatic acids naturally exist in crude oil compositions at different
initial concentrations of hundreds or even thousands of ppm depending on the location of the reservoir compared to the site of original
rocks. During contact with sweeping injection brine, those compounds diffuse from oil phase to water phase due to oil/water partitioning
behaviours. As a result, their concentration in oil contacting with water will be attenuating during water injection. Their concentration
profile in water injection history contains the information related to diffusion in oil and water phase, interstitial velocity of water and oil
saturation.
This paper presents the research results of theoretical model and numerical model of the washed-out process of alkylphenols in the
late stage of water injection. The research results have proposed approximate analytical expression for concentration of alkylphenols
at the late stage of water flooding. In this regard, at the sufficient large injection volume the alkylphenol concentration attenuates
exponentially and the attenuation rate depends on parameters such as partitioning coefficient, oil saturation and interstitial velocity
of water and oil and diffusion coefficients. The simulation concentration results obtained from UTCHEM simulator for the 5-spot model
showed a good match with analytical calculation results.
The research results can be used as the basis for developing methods to assess water flooding systems as well as oil saturation. The
results can also be used for study of transport of non-aqueous phase liquid (NAPL) in environmental contamination.
Keywords: Residual oil saturation, waterflooding, tracer, partitioning organic compounds, enhanced oil recovery.
1. Introduction
Alkylphenols are aromatic compounds consisting of
In the process where oil comes into contact with the
injection water, because of oil/water partition properties
the alkylphenols diffuse from oil phase to water phase,
causing attenuation of their concentration in the two
phases over time. The attenuation rate of alkylphenol
concentration depends on several factors such as parti-
tion coefficient, diffusion coefficient, interstitial velocity of
phases, and the amount of remaining oil in pore volume.
Sinha, Asakawa, and Pope proposed a method using alkyl-
phenols as natural tracers to determine residual oil satu-
ration in the swept area based on their residence time in
water phase during water injection [6].
phenol nuclei and alkyl groups generated by alkylation
and isomerisation reactions in the source rock during
petroleum formation. For years, the existence and origin
of the organic phenolic compounds such as alkylphenols
and aliphatic acids in petroleum have been studied as in-
dicators to classify petroleum according to the origin of
hydrocarbons as well as to indicate petroleum migration
pathways [1 - 4]. The concentration distribution of alkyl-
phenols and their oil/water partition characteristics were
used by Taylor, Larter, and Dale to study petroleum migra-
tion in the North Sea fields [4]. Lucach, Bowler, and Lar-
ter studied the Dhahaban hydrocarbon system in Oman
based on the distribution variation of alkylphenols [5].
In Vietnam, the Tracer Laboratory of the Centre for
Applications of Nuclear Techniques in Industry (Vietnam
Atomic Energy Institute) has studied the transport of al-
kylphenols during waterflooding in oil recovery since
2014. The authors have proposed an analytical model de-
scribing the attenuation of alkylphenol concentration in
produced water over water injection time and conducted
Date of receipt: 17/8/2020. Date of review and editing: 17/8 - 10/12/2020.
Date of approval: 11/6/2021.
PETROVIETNAM - JOURNAL VOL 6/2021
37
PETROLEUM EXPLORATION & PRODUCTION
experiments to validate the analytical model
[7 - 9]. The study results also considered the
possibility of using alkylphenols as the natural
partitioning tracers to evaluate oil saturation
and determine the water contribution propor-
tion of injection wells to production wells.
The one-dimensional analytical solution describing the concen-
tration of APs in water phase Cw(x, t) is described as:
C *
x - × t
F
G
V
W
W
W
C
D
S
T
1
2
D
D
D
E
T
A
G
Cw
(
x, t
)
=
× C0 × 1+ Erf
(5)
T
G
B × t
T
2
×
G
H
W
X
A
U
2. Theory
in which, A, B and C* are parameters depending on APs partition
coefficient, oil saturation, dispersion coefficient in phases, and pore
velocity of water and oil:
Alkylphenols (APs) are trace compositions
in crude oil formed along with hydrocarbons
during geochemical processes, which have
the initial concentration in the oil phase in the
range from several ppm to thousands of ppm
depending on the field. During water injec-
tion, alkylphenols diffuse from oil phase to wa-
ter phase at the water-oil contact boundary in
pore spaces.
A = 1+
B = 1− So
C * =
1− So
At x = L when t → ∞, the approximate form of LnCw is shown in
(
K d −1
D*Lw + Kd SoD*Lo
v*wx + Kd Sov*ox
)
So
(
)
(
)
Equation (6):
C*
The advection-dispersion equation in oil-
water phase contact of alkylphenols with the
assumption that their concentration between
phases instantaneously reaches equilibrium is
expressed as Equation (1) [10]:
F
V
S
C
B
A
2 C *
D
T
W
GA
G
C0 −1+e
D
E
T
C*2
1
2
W
U
Ln
[Cw
(
L,t →∞
)
]
= −
t−
Ln
(
t
)
+Ln
(6)
G
W
π
G
W
W
X
G
H
r
r
∂
∂t
.
φ
(
SwCw +Kd SoCw
)
+.
(
Swφv*Cw +Kd Soφv*oCw
)
Equation (6) shows that the value of Ln(t) is very small compared
w
(1)
to t, so it can be considered that LnCw is approximately linear depen-
dent on the time of water injection. Figure 1 illustrates LnCw according
to Equation (5) and the approximate solution according to Equation
(6), representing the attenuation of APs concentration with different
partition coefficients in water phase over injection time. When injec-
tion time t is sufficiently long or the injected volume is large enough,
LnCw is almost linear over injection time, in which the slope of C*2/
− .
[
(
S
wφ Dw* +K Soφ Do*
).Cw
]
= 0
.
d
in which, ф is porosity of media, Cw is APs
concentration in water phase [M/L3]; Sw and
So are the saturation of water phase and oil
phase, respectively (Sw + So = 1); Kd is APs parti-
r
w
r*
tion coefficient; v* and are interstitial veloc-
vo
ity of water phase and oil phase, respectively
and Do* are dispersion tensors of APs
*
20
0
[L/T];
Dw
in water phase and oil phase, respectively
[L2/T], t is time [T].
Suppose that the porous media is infinite
homogeneous, the saturation of the phases is
constant, and the interstitial velocity of phases
is constant in the pore, the initial and bound-
ary conditions are as follows:
-20
-40
-60
+∞
−∞,0
)
C
x+
[
(
0,
I
J
K
0
Initial condition:
)(2)
(3)
Cw
(
x,0
)
=
0 x+
0
200
400
600
800
Boundary condition:
Cw
(
- ∞, t
)
= 0
Time since water injection
∂Cw
(
x, t
)
Figure 1. Illustrating LnCw according to Equation (5) - solid lines and approximate solutions according to
Equation (6) - dashed lines, for APs having Kd = 0.5, Kd = 1 and Kd = 2. When t is large, the value of LnCw
decreases linearly over time. The smaller the Kd , the faster the time to reach the linear asymptotic.
(4)
= 0
∂x
x→ +∞
PETROVIETNAM - JOURNAL VOL 6/2021
38
PETROVIETNAM
(4AB) represents the decline rate of APs concentration during wa-
ter sweeping. With the same injection conditions and oil satura-
tion, the smaller the Kd is, the greater the dispersibility into water
phase becomes and the faster the concentration decreases, and
vice versa.
in which, fo and fw are the oil cut and the water
cut, respectively. Replace Equation (11) to Equa-
tion (10):
C
S2
am
ai
fo
f w
fo
K d + 2 K d
D
D
T
=
(12)
T
f w
E
U
The slope is described as
From the above equations, recall the decline
rate of LnCw (L, t → ∞) be the leaching rate at the
late stage of water flooding:
2
*
[
(
1− So
)
]
×
vwx + Kd Sovo*x
]
C *2
(7)
a =
=
*
*
×
×
4×
[
1+
(
Kd −1
)
S
(
1− So
)
DLw +Kd S DLo
×
×
×
×
×
o
o
C
S2
fo
f w
DL*o+D*
2
*2
D
D
T
T
1+
K d
(
1−So
)
v
Let a = ai + am, in which:
wx
(13)
E
U
2
*2
a=
2
4D* S2Kd2+4
(
)
(
1−S
)
S Kd +4DL*w
(
1−S
)
(
1− So
)
v
×
wx
(8)
ai =
Lo
o
Lw
o
o
o
2
*
2
4DLo So2 Kd + 4
(
D *Lo + D *Lw
)
(
1− So
)
So K d + 4D*Lw
(
1− So
)
×
At the late stage of water flooding, oil is al-
*2
2
(
1− So
(
)
So v*wx v*ox K d + So2 v K d2
most immobile as also known as residual oil, fo
= 0 and So = Sor, the attenuation of APs concen-
tration in the production water is in accordance
with the exponential law of the injection time or
respectively the injection volume. Obviously, the
decline rate depends on the partition coefficient
of APs (Kd), the oil saturation (So), the dispersion
coefficients of APs in phases (D*Lo, D*Lw) and the
pore velocity of water v*wx.
ox
2 (9)
am =
4DL*o So2
We have
d2 + 4
DL*o + D *Lw
)
(
1− So
)
So K d + 4D*Lw
(
1− So
)
S2
T
U
C
S2
*
am
ai
So
1− So
vox
So
1− So
v*ox
C
D
D
E
2
(10)
(11)
D
D
T
T
=
×
K d + 2 ×
K
×
×
d
*
T
v wx
v*wx
E
U
and
v*xo 1− So fo
=
×
v*xw
So
f w
3. Simulation results
The advection-dispersion transport of APs
from the oil phase into water phase during the
water injection has been simulated on ¼ 5-spot
models using UTCHEM (The University of Texas's
Chemical Simulator software), developed by the
University of Texas [11].
UTCHEM was used to run 3D homogeneous
single-layered reservoir models with ¼ 5-spot
pattern, including 2 specific cases:
• Immobile oil model having initial oil satura-
tion and residual oil saturation of 0.35;
• Mobile oil model having initial oil saturation
of 0.65 and residual oil saturation of 0.35.
The models have the size of 165 m × 165 m
× 12 m divided into 55 × 55 × 4. The flow rate of
injection water is 65.34 m3/d.
The general parameters of the models are:
- Porosity ф = 0.2, water viscosity μw = 0.7 cp,
oil viscosity μo = 4 cp;
- Longitudinal and transverse dispersivity
are αDL = 0.03 m, αDT = 0.003 m;
Figure 2. Illustration of APs concentration distribution in space at water injection of 0.6 PV in mobile
oil model (Soi = 0.65, Sor = 0.35).
PETROVIETNAM - JOURNAL VOL 6/2021
39
PETROLEUM EXPLORATION & PRODUCTION
Table 1. The partition coefficient Kd of APs and initial concentration of APs used in the models
Partitioning coeꢀcient
Initial concentration in oil
Initial concentration in
water phase (mg/L)
Alkylphenols
phase (mg/L)
Kd = Co Cw
Phenol
0.16
0.58
0.75
1.34
1.61
3.09
7.37
1.6
5.8
10
10
10
10
10
10
10
4-Methylphenol (4MP)
2-Methylphenol (2MP)
4-Propylphenol (4PP)
3,4-Dimethylphenol (34DMP)
2,4-Dimethylphenol (24DMP)
4-Ethylphenol (4EP)
7.5
13.4
16.1
30.9
73.7
- Relative permeability curve is
described by Corey model: critical water
saturation Scwr = 0.3, residual oil saturation
Sor = 0.35, water endpoint: 0.15, oil endpoint
0.85, water exponent: 1.5, oil exponent: 2,
endpoint mobility ratio: 1.
1.0E+02
1.0E-01
1.0E-04
1.0E-07
1.0E-10
1.0E-13
Phenol
4MP
2MP
The APs initial concentration in oil phase
and water phase and partition coefficient be-
tween phases determined in the experimen-
tal data of the Tracer Laboratory of CANTI are
listed in Table 1. All compounds are supposed
to have the same density, alkane number and
chemical properties but different in partition
coefficient.
4PP
34DMP
24DMP
4EP
0
2
4
6
8
10
Injected pore volume (PV)
The water injection takes place up to 10
PV of the model to investigate the APs con-
centration decrease at the end of the injection
stage. It is assumed that the concentration of
APs between phases instantaneously reaches
equilibrium while oil and water are in contact.
Figure 2 illustrates the spatial concentration
distribution of APs at water injection of 0.6 PV
for the mobile oil model.
(a)
1.OE+02
1.OE-01
1.OE-04
Phenol
4MP
2MP
1.OE-07
1.OE-10
1.OE-13
4PP
34DMP
24DMP
4EP
Figure 3 shows the concentration of APs
in produced water in both models, in which
the smaller the Kd is, the faster the leaching
rate becomes, and vice versa.
0
2
4
6
8
10
Injected pore volume (PV)
The concentration obtained from calcula-
tion of the analytical solution in accordance
with Equation (5) matches well with the simu-
lation data in both models of mobile and im-
mobile oil at the late stage of water injection
(> 2 PV). The root mean square error (RMSE)
between the simulation data and the calcula-
(b)
Figure 3. Concentration curves of APs in produced water of the ¼ 5-spot having immobile oil (Soi = Sor = 0.35,
a) and the ¼ 5-spot having mobile oil (Soi = 0.65 Sor = 0.35, b). Solid lines present the simulation data from
UTCHEM software, while dashed lines present the calculation results of Equation (5).
tion data during the injection stage is shown in Table 2. The results
show that the value of RMSE from 0 - 2 PV is greater than that at the
PETROVIETNAM - JOURNAL VOL 6/2021
40
PETROVIETNAM
Table 2. The root mean square error (RMSE) between the simulation data and the analytical solution during the injection stage
Phenol
(Kd = 0.16) (Kd = 0.58)
4MP
2MP
(Kd = 0.75)
4PP
(Kd = 1.34)
34DMP
(Kd = 1.61)
24DMP
(Kd = 3.09)
4EP
(Kd = 7.37)
Water injection (PV)
Immobile oil model
1.813
0 - 1
1 - 2
2 - 3
3 - 4
4 - 5
5 - 10
1.445
0.080
1.585
0.130
1.638
0.150
1.883
0.220
0.064
0.009
0.001
< 0.001
1.174
1.930
0.183
0.062
0.015
0.002
0.123
1.950
2.382
0.177
0.197
0.059
0.170
0.003
0.010
0.015
0.044
< 0.001
< 0.001
< 0.001
< 0.001
< 0.001
< 0.001
< 0.001
< 0.001
< 0.001
0.005
< 0.001
< 0.001
Mobile oil model
1.744
0 - 1
1 - 2
2 - 3
3 - 4
4 - 5
5 - 10
1.115
0.118
1.377
0.161
1.469
0.169
1.849
0.169
0.029
0.007
0.003
< 0.001
1.285
1.939
0.109
0.025
0.004
0.002
0.215
2.103
2.469
0.118
0.144
0.046
0.147
0.001
0.004
0.006
0.018
< 0.001
< 0.001
< 0.001
0.002
0.003
0.007
< 0.001
< 0.001
< 0.001
< 0.001
0.002
< 0.001
end of the injection stage, in which the APs with higher Kd
represents the higher RMSE value.
tem as well as oil saturation. The results can also be used
for study of transport of non-aqueous phase liquid (NAPL)
in environmental contamination.
5. Conclusions
Acknowledgements
The analytical solution of the advection-dispersion
equation describing the attenuation of concentration of
APs compounds in produced water was approximated as
an exponential function at the late stage of water flood-
ing when the injection time or injected volume is large
(>1 PV). The analytical solution was validated by applying
the ¼ 5-spot model to calculate the concentration of 7 AP
compounds to compare with the results of numerical sim-
ulation using UTCHEM simulator. The results show that,
when the injection time is large enough to reach injec-
tion of 2 PV or more, the approximate analytical solution
matches quite well with the simulation results. The RMSE
value is less than 0.2 for the APs having Kd less than 3. The
analytical solution also shows that the APs concentration
in produced water decreases exponentially over injection
time and the factors affect the concentration attenuation
rate include partition coefficient, diffusion coefficients,
interstitial velocity and oil saturation. The approximate
solution obtained in this study provides a better under-
standing of the factors influencing the attenuation of the
APs concentration than the semi-experimental formula
proposed by Huseby et al [10].
This research work has been implemented through
the Project entitled “Study on the application of oil satu-
ration determination method using partitioning organic
compounds in oilfields” under the grant of Vietnam’s Min-
istry of Science and Technology.
References
[1] Marisa Ioppolo - Armanios, The occurrence and
orrigins of some alkylphenols in crude oils. Curtin University
of Technology, 1996.
[2] Steve Later and Barry Bennet,“Now you see them,
now you don’t, now you might see them again! A review of
the systematics of alkylphenol occurrence in conventional
and heavy oil petroleum systems”, 2011 CSPG/CSEG/CWLS
Conference, Calgary, Alberta, Canada, 9 - 11 May, 2011.
[3] B.Bennett and S.R.Larter, “Partition behaviour of
alkylphenols in crude oil/brine systems under subsurface
conditions”, Geochimica et Cosmochimica Acta, Vol. 61,
No. 20, pp. 4393 - 4402, 1997. DOI: 10.1016/S0016-
7037(97)88537-7.
The research results can be used as the basis for devel-
oping the methods of assessment of water flooding sys-
[4] Paul Taylor, Steve Larter, Martin Jones, Jason Dale,
and Idar Horstad,“The effect of oil-water-rock partitioning
PETROVIETNAM - JOURNAL VOL 6/2021
41
PETROLEUM EXPLORATION & PRODUCTION
on the occurrence of alkylphenols in petroleum systems”,
Geochimica et Cosmochimica Acta, Vol. 61, No. 9, pp. 1899
- 1910, 1997.
from crude oil”, Petrovietnam Journal, Vol. 6, pp. 24 - 29,
2019.
[9] To Ba Cuong, Nguyen Hong Phan, and
Nguyen Huu Quang, Interwell tracer method using
partitioning compounds naturally existing in crude oil
for determination of residual oil saturation, Petrovietnam
Journal, Vol. 10, pp. 38 - 43, 2016.
[5] Sandra O.Lucach, Bernard F.J.Bowler, Neil Frewin,
and Steve R.Larter, “Variation in alkylphenol distributions
in a homogeneous oil suite form the Dhahaban petroleum
system of Oman”, Organic Geochemistry, Vol. 33, No. 5, pp.
581 - 594, 2002.
[10] Olaf Huseby, A.Haugan, J.Sagen, Jiri Muller, Barry
Bennett, S.R.Larter, Eustathios S.Kikkinides, A.K.Stubos,
Faraz Yousefian, Jean-Francois Thovert, and P.M.Adler,
“Transport of organic components from immobile
and bypassed oil in porous media”, Applied Chemical
Engineering, Vol. 49, No. 5, pp. 1085 - 1094, 2003. DOI:
10.1002/aic.690490504.
[6] R.Sinha, K.Asakawa, G.A.Pope, and K.Sepehmoori,
“Simulation of natural and partitioning interwell tracers to
calculate saturation and swept volumes in oil reservoirs”,
SPE/DOE Symposium on Improved Oil Recovery, Tulsa,
Oklahoma, 17 - 21 April 2004.
[7] Nguyễn Hồng Phan, Nguyễn Hữu Quang, Tô Bá
Cường, Huỳnh Thị Thu Hương, và nnk, “Phát triển mô hình
mô phỏng quá trình vận động của các chất chỉ thị tự nhiên
(NPIT) để đánh giá trữ lượng dầu trong khai thác”, Viện Năng
lượng Nguyên tử Việt Nam.
[11] Center for Petroleum and Geosystems
Engineering, University of Texas, “Reservoir engineering
research program. Volume II: Technical documentation
for UTCHEM - 9.0 - A three-dimensional chemcical flood
oy2b17l2qo85afq62g.kr/download/gms/UTCHEM_Tech_
Doc.pdf.
[8] Huynh Thi Thu Huong, Le Thanh Tai, Nguyen Huu
Quang, and Le Van Son, “Determination of contribution
proportion of injection wells in oil production by interwell
tracer method using partitioning organic compounds
PETROVIETNAM - JOURNAL VOL 6/2021
42
6 trang
20/04/2022
1600
Bạn đang xem tài liệu "Transport of oil/water partitioning components during water injection", để tải tài liệu gốc về máy hãy click vào nút Download ở trên
File đính kèm:
- transport_of_oilwater_partitioning_components_during_water_i.pdf
