Energy and Power En gi neering, 2011, 3, 194-197
doi:10.4236/epe.2011.32025 Published Online May 2011 (http://www.SciRP.org/journal/epe)
Study on Advanced Water Injection Time in Low
Permeability Reservoir
Lijun Wang, Linli Wei
Department of Pet rol eu m En g ineeri n g , Northeast Petroleum University, Daqing, China
Received January 6, 2011; revised March 17, 2011; accepted April 22, 2011
Abstract
A certain formation pressure level must be kept due to the threshold pressure of the low-permeability reser-
voir during the seepage. Advanced water injection can keep the formation pressure at a higher level and keep
a higher pressure gradient, which is an effective way to develop low-permeability reservoir. Based on the
mechanism of advanced water injection and characteristic of porous flow in low permeability reservoir, a
seepage model considering threshold pressure gradient is established to determine the formation pressure
distribution at anytime as the water is injected at a constant speed. The optimum water injection time for the
advanced water injection technology can be determined by using this model. The calculated result coincides
basically with the numerical simulation result, which indicates that the model put forward in this paper is
feasible.
Keywords: Advanced Water Injection, Injection Time, Reservoir Pressure, Threshold Pressure Gradient
1. Introduction
Advanced water injection technology is an effective way
to develop low-permeability and extra-low-permeability
reservoir, which can timely supplement formation energy,
improve the formation pressure, maintain a high oil pro-
duction and decrease the declining rate law marked [1-7].
Besides, it can prevent the deterioration of crude oil
properties, effectively keep the oil percolating channel
expedite, and enhance the water injection swept volume
[8-10]. The determination of reasonable injection time
and ultimate injection time of advanced water flooding is
a common problem considered in developing low-per-
meability and extra low permeability oilfield. Presently,
the parameters of advanced water flooding, such as for-
mation pressure, injection pressure, cumulative water
injection quantity, water injection intensity, injection
time, etc. are mainly studied by numerical simulation
technology [11-13]. Unfortunately, numerical simulation
needs massive data and workload. Meanwhile, because
the geologic reservoir description is not clear at the early
development stage, the simulation calculation can have a
great error. By applying the mathematic model of
non-steady flow in low permeability reservoir and con-
sidering the pressure gradient, the mathematic model of
the pressure distribution is established. With this model,
the relation between the formation pressure and injection
quantity is determined, and then the optimum injection
quantity and injection time is figured out, so as to the
pressure distribution between the water injection well
and the oil production well. The pressure distribution
determined by using the suggested model is basically
coincided with the numerical simulation result.
2. Principle of Advanced Water Flooding
Advanced water flooding is an effective method for de-
veloping low permeability oilfield, which has great sig-
nificance for improving the development effect of oil-
field by water flooding. Advanced water flooding has
several advantages [14-16]:
1) The low-permeability and fractured reservoir has
fluid-solid coupling effect. Fractured system and the pore
throat have extreme pressure sensitivity, and the reser-
voir has threshold pressure (non-Darcy flow). With ad-
vanced water flooding, formation pressure can be main-
tained at a high level, keeping a pressure gradient higher
than the threshold pressure gradient [2]. In other words,
effective driving pressure system can be established, and
the low-permeability, fractured reservoir can be devel-
*Project supported by the National Natural Science Foundation of China
(Grant Nos: 50634020).

L. J. WANG ET AL.
195
oped effectively.
2) Water is injected through Injection wells before oil
wells are put into production, so the balance of reservoir
pressure system will not be broken. Thus, the water in-
jected can uniformly displace the oil from the injection
well to the surrounding production oil wells, which ef-
fectively improves the swept volume and displacement
efficiency of the reservoir. As a result, when the wells
are put into production, the formation pressure is higher
than the original formation pressure, the phenomenon of
formation oil degassing can be avoided or reduced, and
the physical properties variation of crude oil viscosity,
density and so on are avoided, which is beneficial to oil
flow.
3) Generally, low-permeability oil fields are pres-
sure-sensitive. During the development process of si-
multaneous or delay water injection, the formation en-
ergy can not be supplied timely and the formation pres-
sure will decline greatly, causing the formation porosity
decline, natural fracture close and permeability reduce. It
is very difficult for this kind of permeability reduction to
recover through raising the formation pressure, perma-
nent formation damage will occur inevitably. With an
early supplement of formation energy, a certain degree of
formation pressure can be maintained by advanced water
flooding, which can prevent such kind of permeability
damage and improve the development effectiveness of
water flooding.
3. Instable Percolation Mathematical Model
in Low Permeability Reservoir
Percolation mathematical model considering threshold
pressure gradient can be written as follows:
2
2
1pp
G
rr t r 




 
1p
e
(1)
For initial condition,

,0
w
pr p (2)
For boundary condition,
2π
w
rr
p
rG
rk
Q
h







  (3)

0
rRt
pG
r






 
pprRt
e
where, w is bottom hole pressure, Pa; is formation
thickness, m; is radius, m; is water injection
rate m3/s; w is wellbore radius, m; e is initial for-
mation pressure, Pa; Gis threshold pressure gradient,
Pa/m;
p
r
h
r

Qt p

is fluid viscosity, Pa·s; is permeability, m2. k
According to the mathematical model above, the for-
mula of pressure distribution can be deduced:

 
0
ln 1
2π
e
Qt rr
pp GRtr
khRtRt









(4)
where, the movement law of actuate external boundary


Rt needs to be obtained. In order to obtain


Rt ,
let’s consider the case of a water injection well with con-
stant injection volume.
When the water well is injected with constant volume,
the intake volume


Qt is a constant. And here only
threshold pressure gradient is considered. According to
material balance equation [16]:



22
dπ
d
tw
QCRtr hp
t





(5)
e
pp p

 (6)
Through calculation, the equation of motion can be
obtained:
 
20
24π
12 1
w
khRtG
tRt rQ







(7)
Substitute the inner boundary condition, w, rrw pp

,
into formula (4), the bottom pressure can be gotten:

 
0
ln 1
2π
ww
we w
Qt rr
pp GRtr
khRtRt


 




(8)
By means of trial method, actuate external boundary
can be obtained, and then the reservoir pressure distribu-
tion at any time can be obtained.
4. Application of Percolation Model in
Advanced Water Flooding in Low
Permeability Oilfield
In a low-permeability oilfield, fundamental parameters
are given in Table 1.
Table 1. Fundamental parameter s.
Parameter Value Unit
Permeability 5.2 mD
Water viscosity 1 mPa.s
Porosity 0.137 ——
Initial pressure 7.3 MPa
Effective thickness 10 m
Wellbore radius 0.1 m
Threshold pressure gradient 0.032 MPa/m
Water injection 15 m3/d
Overall compressibility factor 12.4 10–3 MPa/m

L. J. WANG ET AL.
196
and advanced water injection for 9 different injection
strategy with the time of 1 to 8 months. As shown in
Figure 2, formation pressure gradually ascends as the
advanced injection time increases, but the increasing
trend is more and more slightly.
The most important feature of instable percolation in
low permeability reservoir is that the formation pressure
or energy propagation is connected with the propagation
time, namely it enlarges as time elapses [16]. As the in-
crease of water injecting time, the area swept by injected
water expands gradually and the formation pressure also
increases. According to the instable infiltrating fluid
mathematical model in low permeability reservoir, the
external boundary affected by pressure wave in a certain
injection time can be calculated. The formation pressure
will decrease as the distance to water well increases (as
Figure 1).
0
2
4
6
8
10
12
14
16
18
050100 15020025
0
Advanced 1 month
Advanced 2 month
Advanced 3 month
Advanced 4 month
Advanced 5 month
Advanced 6 month
Advanced 7 month
Advanced 8 month
The distance to the water well/m
Reservoir pressure/MPa
According to the boundary condition of the model,
when the distance to water well is greater than or equal
to the actuate boundary, the present formation pressure
will maintain at the original formation pressure, 7.3 MPa.
The average reservoir pressure at various advanced in-
jection time is obtained by weighting the formation
pressure within the actuate area, as shown in Table 2.
The following empirical equation [17] can be used to
calculate the pressure maintenance level of advanced
injection in low permeability oilfield. Figure 1. Reservoir pressure versus advanced injection time.
0.12580
130.4
sK


 (9) Table 2. Average reservoir pressure at various advanced
injection time.
where,
s

is pressure level, %.
Water flood timing Average reservoir pressure (MPa)
Advanced 1 month 7.38
Advanced 2 month 7.45
Advanced 3 month 7.53
Advanced 4 month 7.6
Advanced 5 month 7.68
Advanced 6 month 7.75
Advanced 7 month 7.82
Advanced 8 month 7.9
The average permeability of the experimental area is
5.2 × 10–3 μm2, the calculated reasonable pressure main-
tenance level of this area is 106%. The initial reservoir
pressure is 7.3 MPa, so the appropriate pressure should
be 7.74 MPa. As shown in Tabl e 2, only when advanced
injection time reaches 6 month, can the reservoir pres-
sure be around the reasonable value of 7.74 MPa. There-
fore, 6 month is the optimal advanced injection time.
5. Comparison to Numerical Simulation
Result
Numerical simulation was implemented on synchronic
7
7.2
7.4
7.6
7.8
8
051015 202530 3540 4550
Production time/month
Reservoir pressure/MPa
Synchronic water
Advanced 1 month
Advanced 2 month
Advanced 3 month
Advanced 4 month
Advanced 5 month
Advanced 6 month
Advanced 7 month
Advanced 8 month
Figure 2. Pressure variation of different injection strategy in simulated area.

L. J. WANG ET AL.
197
Numerical simulation analysis shows that the optimum
time of water injection is 6 months. With 6 months of
advanced water injection, the reservoir pressure is 7.81
MPa, and 0.51 MPa higher than the initial reservoir pres-
sure. When advanced injection time is more than 6
months, the variation of reservoir pressure is negligible.
6. Conclusions
1) Through advanced water injection, the formation
pressure can be maintained at a high level, high pressure
gradient can be established; the oil flow channel can be
kept open to the maximum extent; the formation damage
can be prevented to some extent and the development
effectiveness of water flooding can be improved.
2) Based on the low-permeability unstable seepage
model, the best advanced water injection time is obtained,
which is consistent with the numerical simulation results,
verifying the correctness of the theoretical model.
3) Advanced water injection can improve the conduc-
tivity capacity of low permeability reservoirs, so as to
increase the production and enhance oil recovery. The
results obtained in this paper should have an important
and guiding significance to the development of low per-
meability reservoirs, and provide a basis to develop other
similar oilfields.
7. References
[1] R. F. Wang, X. L. Li, B. Li, Y. H. Wang, Li. M. Kang
and Z. Q. Bai, “Timing of Rational Advanced Water In-
jection and Limit Water Injection,” Henan Petroleum,
Vol. 17, No. 6, 2003, pp. 21-23.
[2] R. F. Wang, Z. Q. Song, H. Yong, L. Zhao and B. Hu,
“Utilizing Advanced Water Injection to develop Low
Permeability Pool,” Fault-Block Oil and Gas Field, Vol.
10, No. 3, 2003, pp. 43-45.
[3] Y. T. Li, Z. Y. Liu, Q. H. Lv, X. G. Wu and Z. Y. Zhang,
“Research and Application on Technology of Advance
Water Flooding in Guyunji Oilfield,” Special Oil and Gas
Reservoirs, Vol. 14, No. 5, 2007, pp. 58-60.
[4] D. P. Li, “The Development of the Low Permeability
Sandstone Oilfield,” Petroleum Industry Press, Beijing,
1995, pp. 174-177.
[5] P. C. Liu, F. H. Li, K. Li and Y. D. Wang, “Advance
Water Injection in Reverse Nine-Spot Well Pattern in
Block 119 of Xinli Oilfield,” Journal of Oil and Gas
Technology, Vol. 29, No. 6, 2007, pp. 120-123.
[6] F. J. Ma, J. C. Hu, J. Zhuang, Q. L. Shi and Q. Wu, “The
Application and Practice of Advanced Water Injection in
Low Permeability Reservoir of XinLi,” Special Oil and
Gas Reservoirs, Vol. 12, No. 3, 2005, pp. 47-49.
[7] Z. Y. Zhan, X. M. Wu, X. J. Liu and H. Y. Qi, “Devel-
opment Technique and Results Interpretation of Advance
Water Flooding in Wuqi Oilfield,” Inner Mongulia Pet-
rochemical Industry, No. 8, 2007, pp. 191-193.
[8] J. H. Wang, “Low Permeable Oilfield to Run before to
Note the Research of Water,” Fault-Block Oil and Gas
Field, Vol. 12, No. 3, 2005, pp. 53-54.
[9] J. X. Chen, Q. H. Huang and L. Sun, “Application of
Advanced Water Flooding in Low Porosity and Perme-
ability Oilfield,” Inner Mongulia Petrochemical Industry,
No. 10, 2005, pp. 102-104.
[10] Q. J. Che, J. A. Lei, Y. X. Ran and Z. Y. He, “Effects of
Advanced Water Flooding in Extra-Permeability Oilfield
Development,” Pertroleum Geology and Oilfield Devel-
opment in Daqing, Vol. 22, No. 1, 2003, pp. 20-22.
[11] C. S. Zhu, L. S. Cheng and S. J. Zhang, “Approximate
Solution for Non-Steady Flow in Low-Permeability Res-
ervoir,” Journal of Southeast Petroleum University, Vol.
30, No. 4, 2008, pp. 69-72.
[12] S. Q. Li, L. S. Cheng, X. S. Li and F. Hao, “Non-Linear
Seepage Flow Models of Ultra-Low Permeability Reser-
voirs,” Petroleum Exploration and Development, Vol. 35,
No. 5, 2008, pp. 606-612.
doi:10.1016/S1876-3804(09)60092-6
[13] M. G. Zhao, H. F. Zhou and D. F. Chen, “Investigation
and Application on Gas-Drive Development in Ultra-Low
Permeability Reservoir,” Journal of Hydrodynamics, Vol.
20, No. 2, 2008, pp. 254-260.
doi:10.1016/S1001-6058(08)60054-2
[14] Z. D. Lei, S. Q. Cheng, X. F. Li and H. P. Xiao, “A New
Method for Prediction of Productivity of Fractured Hori-
zontal Wells Based on Non-Steady Flow,” Journal of
Hydrodynamics, Vol. 19, No. 4, 2007, pp. 494-500.
doi:10.1016/S1001-6058(07)60145-0
[15] M. L. Zhang and Y. M. Shen, “Study and Application of
Steady Flow and Unsteady Flow Mathematical Model for
Channel Networks,” Journal of Hydrodynamics, Vol. 19,
No. 5, 2007, pp. 572-578.
doi:10.1016/S1001-6058(07)60155-3
[16] Y. F. Zhai, “Fluid Mechanics in Porous Medium,” Petro-
leum Industry Press, Beijing, 2003, pp. 61-62.
[17] D. F. Wang, Z. X. Li, J. Y. Zhao, Y. H. He and F. Hao,
“Advance Water-Flooding Theory for Low-Permeability
Reservoirs and Its Application,” ACTA Petrolei Sinica,
Vol. 28, No. 6, 2007, pp. 78-81.