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Attenuation of water coning using dual completion technology
Y. Ould-amer a , S. Chikh a,*, H. Naji b
a De partement de Ge nie Me canique, USTHB, B.P. 32 El Alia, Bab-Ezzouar, 16111 Algiers, Algeria b
Laboratoire de Me canique de Lille, UMR 8107, Polytech’Lille, USTL, France
Received 19 May 2003; accepted 14 April 2004
Abstract
Water coning causes a reduction of oil production and an increase of production costs. Dual completion (downhole
water sink) is one of the methods adopted to attenuate water coning. This work describes numerical results associated
with this completion technique. The water cone shape and water breakthrough time are investigated to define the
mechanism and performance of this technical procedure. The numerical results show that dual completion deforms the
shape of the cone. For instance, the top of the water– oil interface is shifted away from the well yielding (under high
water production rates) oil breakthrough into water perforations. The water breakthrough is proportional to dimensionless
density difference and horizontal permeability and inversely proportional to oil production rate, mobility, and anisotropy
ratios. High oil production rates yield elevation of water coning height that intercepts oil flow. Paradoxically, high
production rate at water sink is not recommended, the improvement of water breakthrough begins when dimensionless
density difference is greater than 0.05. The dual completion technique delays water breakthrough time (BT*). In general,the BT* is delayed by two times that of single completion and critical oil rate is augmented compared to single
completion.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Water coning; Dual completion; Downhole water sink; Breakthrough time
1. Introduction
Oil reservoirs with bottom water drive exhibit high oil recovery due to supplemental energy
imparted by the aquifer. A large oil production rate
may cause water to be produced by upward flow
mixed with oil. This phenomenon is known as water
coning and refers to the deformation of water– oil
interface which was initially horizontal.
Water coning has been a serious problem inmanaging reservoir recoveries; numerous authors
addressed this phenomenon (Muskat and Wyckoff,
1935; Muskat, 1949; Elkins, 1958; Karp et al., 1962;
Fortunati, 1962; Smith and Pirson, 1963; Chierici et
al., 1964; Outmans, 1964; Romero-Juarez, 1964;
Blake and Kueera, 1988; Ould-amer and Chikh,
2002). Their research investigated several issues
such as critical rate and/or breakthrough time calcu-
lations. It was found that the maximum water-free
oil production rate corresponds to the critical rate
0920-4105/$ - see front matter D 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.petrol.2004.04.004
* Corresponding author.
E-mail addresses: ould _ ameryacine _ [email protected]
(Y. Ould-amer), [email protected] (S. Chikh),
[email protected] (H. Naji).
www.elsevier.com/locate/petrol
Journal of Petroleum Science and Engineering 45 (2004) 109–122
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and the breakthrough time which represents the
period required by bottom water to reach the well’s
oil perforations. If oil production rate is above this
critical value, water breakthrough occurs. After breakthrough, the water phase may dominate the
total production rate to the extent that further oper-
ation of the well becomes economically not valuable
and the well must be shut down (Muskat and
Wyckoff, 1935; Meyer and Garder, 1954; Chaney
et al., 1956; Schols, 1972; Kuo and Debbrisay, 1983;
Hoyland et al., 1986; Chaperon, 1986; Abass and
Bass, 1988; Giger, 1989; Papatzacos et al., 1989;
Yang and Wattenbarger, 1991; Suprunowicz and
Butler, 1992; Yang, 1992; Guo and Lee, 1993;
Menouar and Hakim, 1995; Ould-amer and Chikh,
2003).
Several solutions have been developed to mini-
mise the impact of unwanted water in oil wells.
These methods are: (1) keeping production rate
below the critical value; (2) perforating far away
from the initial water– oil contact; and (3) creating
a water blocking zone around the well by injecting
cross-linking polymers or gels. Unfortunately, none
of these conventional methods are able to solve the
water breakthrough problem. Horizontal wells also
are used to minimise water coning. However, hor-
izontal wells are themselves not free of water influx problems. Like the vertical wells, typical critical oil
rates for avoiding water influx into horizontal wells
are too low for any economic recovery. A detailed
investigation of the cost and profits of horizontal
wells reveals several disadvantages for their use:
vulnerability to poor cementing, limited re-comple-
tion potential, and design constraints imposed by
drilling technology (Chugbo et al., 1989; Irrgang,
1994).
Downhole water sink technology (DWS) is one
of the solutions developed to reduce water coningin vertical oil completions. This technique requires
a dually completed well in the oil and water zones.
The oil and water perforations are separated by a
packer. As a result, the produced oil is water-free.
DWS technology has been investigated theoretically
(Wojtanowicz et al., 1991; Swisher and Wojtano-
wicz, 1995a,b) and experimentally (Shirman and
Wojtanowicz, 1997a,b).
Shirman and Wojtanowicz (1997a,b) conducted a
model DWS completion investigation using a trans-
parent Hele – Shaw model. Their results indicate that
oil production from wells with DWS completion
may have high economic merit and is technically
feasible. Coning in dually completed wells also has been investigated by Gunning et al. (1999). A
simple model for dual completion similar to that
of Wojtanowicz and Bassiouni (1994) was pro-
posed. A sharp interface is used between the fluids,
across which no fluid may flow. An analytical
solution is proposed for low flow rates where
gravity has a dominant effect. In order to overcome
this limitation (low flow rates), a numerical model
was used by Gunning et al. In both numerical
models, the ratio of the distances between the initial
water– oil interface and the water and oil comple-
tions was introduced. Their results indicate that in a
symmetric configuration corresponding to the ratio
of distances between the initial water– oil interface
and the lower water and upper oil completions,
water-free oil production is possible at rates up to
five times greater than those available with single
completions. Less improvement is obtained in
asymmetric situations where the ratio is different
from unity.
Several parameters affect water coning in vertical
oil producing wells: (1) oil production rate, (2)
mobility ratio, (3) density difference between fluids,(4) anisotropy, and (5) porosity. Our present para-
metric study simulated numerically the behaviour of
the water– oil interface and computed water break-
through time for a wide range of the cited param-
eters. This analysis allows us to obtain a detailed
and precise answer of dual completion performance
in a vertical well.
2. Formulation
A single well model (Azziz and Settari, 1986) is
used to evaluate the performance of the DWS
completion in the control of water coning in vertical
wells. The physical model and co-ordinate system
are shown in Fig. 1. The well is dually completed in
the oil and water zones (Fig. 2). The two comple-
tions are separated by a packer set inside the well at
the water–oil contact and the two fluids are consid-
ered incompressible and immiscible with constant
properties. The porous medium is homogeneous and
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anisotropic (the vertical permeability is less or great-
er than the horizontal permeability).Darcy’s law and the continuity equation describe the
flow of the two fluids.
Continuity:
j ð!V l Þ ¼
B
Bt ð/S l Þ þ Qla ð1Þ
Darcy’s law:
!V l ¼ ¯ K
kr l
ll
ðj P l þ ql g Þ ð2Þ
The subscript (l) indicates either the water (w) or
oil (o) phase and the subscript (a) can indicate either
oil completion (oc) or water completion (wc).
Substituting the Darcy velocity in Eq. (2) into Eq.
(1), the following equation is obtained:
j ¯ K kr l
ll
ðj P l þ ql g Þ
¼
B
Bt ð/S l Þ þ Qla ð3Þ
For each fluid phase, Eq. (3) is then written as
j ¯ K kr o
lo
ðj P o þ qo g Þ
¼
B
Bt ð/S oÞ þ Qoa ð4Þ
j ¯ K kr w
lw
ðj P w þ qw g Þ
¼
B
Bt ð/S wÞ þ Qwa ð5Þ
Adding Eqs. (4) and (5), and assuming that the
porous medium is completely saturated by the fluids,
then
j ¯ K kr o
lo
ðj P o þ qo g Þ
þ j ¯ K
kr w
lw ðj P w þ qw g Þ
¼ Qa ð6Þ
where
Qa ¼ Qoa þ Qwa ð7Þ
Additional equations closing the system are given
below
S w þ S o ¼ 1 ð8Þ
P c ¼ P o P w ð9Þ
The capillary pressure P c depends on water satu-
ration and is given by Eq. (25).
Fig. 2. Schematic of dual completion technique.
Fig. 1. Schematic of the physical domain and co-ordinate system.
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Substituting Eq. (9) into Eq. (6), yields the water
pressure equation
j ¯ K kr olo
ðj P w þ j P c þ qo g Þ
þ j ¯ K kr w
lw
ðj P w þ qw g Þ
¼ Qa ð10Þ
No flow boundary conditions are imposed on a
closed boundary. A constant pressure of the bottom
aquifer is used. These conditions are mathematically
written as
!V w
!n ¼ 0 at closed boundary or
jð P w þ qw g Þ !n ¼ 0 ð11Þ
P w ¼ P aq at z ¼ 0 and r w < r < r e ð12Þ
!n is the unit vector normal to the closed boundary.
Initially the oil zone is saturated with oil at irre-
ducible water saturation (S wi) and the water zone is
free of oil.
S o ¼ 1 S wi and S w ¼ S wi at hw < z < h;
r w < r < r e ð13Þ
S o ¼ 0 and S w ¼ 1 at 0 < z < hw; r w < r < r e ð14Þ
The introduction of dimensionless parameters re-
lated to rock characteristics, fluid properties, and
production (defined in the nomenclature) allows us
to rewrite Eqs. (5) and (10) as
B
B z * Ra kr w
B P w*
B z
þ
1
r *
B
Br * r * kr w
B P w*
Br *
ð NDqÞð NqwÞ ¼ 1
DaH
B
B
t *
ð/S wÞ þ Qwa* ð15Þ
and
Ra B
B z * kr o
Rkr
M þ kr w
B P w*
B z * þ kr o
Rkr
M
B P c*
B z *
þ
1
r *
B
Br * r * kr o
Rkr
M þ Kr w
B P w*
Br *
þ r * kr o Rkr
M
B P c*
B z *
ð NDqÞð NqwÞ ¼
Qa
DaH
ð16Þ
The set of equations to be solved consists of the
dimensionless pressure Eq. (16), the water saturation
Eq. (15), and the total saturation Eq. (8).
In the oil completion (until water breakthrough)only oil is produced and Q
w oc* is zero; however,
after breakthrough, Q o oc* decreases while Q
w oc*
increases. In the water completion, oil breakthrough
may or may not take place. When oil breakthrough
into the water perforations occurs, Q o wc* does not
increase continuously.
The boundary and initial conditions written in
dimensionless form, are
jð P w*Þ !
n ¼ 0 at a closed boundary ð17Þ
P w* ¼ P aq* at z * ¼ 0 and r w* < r * < r e* ð18Þ
S o ¼ 1 S wi and
S w ¼ S wi at hw* < z < h*; r w* < r * < r e* ð19Þ
S o ¼ 0 and
S w ¼ 1 at 0 < z * < hw*; r w* < r * < r e* ð20Þ
3. Numerical simulation
The governing equations are transformed into
algebraic equations by using the control volume
method (Patankar, 1980, 1981). The fully implicit
scheme is used and the relative permeabilities at
the block interfaces are evaluated using an asym-
metric second-order approximation that considers
two upstream points (Azziz and Settari, 1986).
The set of algebraic equations is solved by a block-iterative method. The iterative procedure is
stopped at each time step when a convergence
criterion is met between two consecutive iterations,
and it is set on the maximum relative error of
pressure less than 1%. A non-uniform grid of
40 24 nodes in r and z direction, respectively,
with a dimensionless time step of Dt * = 7 2 1011
are used to conduct the computations, with a finer
mesh grid near the well. The grid choice is based
on grid sensitivity analysis (Table 1).
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The code was validated by reconsidering the
work of Yang (1992), who studied, analytically,
water coning in vertical and horizontal wells. Fig.
3 illustrates the excellent agreement between our
results and those of Yang for water breakthrough
time prediction versus production rate.
4. Results and discussion
Three groups of dimensionless parameters were
distinguished and considered: (1) total dimension-
less production rates at oil and water completions;(2) fluid properties (mobility ratio and dimension-
less density difference); and (3) rock character-
istics (anisotropy ratio, horizontal Darcy number
and porosity). These parameters vary in the
f ol lo wi ng r an ge s: 1 0 10VQo c* V 25 10 10 ,
0VQwc* V 1.5 Qoc* , 0.1V M V 20, 0V NDqV 0.4,
0 < Ra V 1.4, 0 < DaH V 8 10 16, 0.1 V/V 0.4,
which illustrate practical situations.
The total dimensionless production rates are given
by
Qoc* ¼ 2pr w*
Z h*
h*h p*Qoc* dz * ð21Þ
Qwc* ¼ 2pr w*
Z hw*
hw*hwp*Qwc* dz * ð22Þ
No general forms exist for the capillary pressure
and relative permeability functions, there are several
commonly used empirical functions or data (Russel et
al., 2002). The Abass and Bass (1988) data which
provide capillary pressure are considered in the pres-
ent work. Their data was correlated using the follow-
ing expressions:
kr o ¼ 0:97=½1 þ expððS w 0:33Þ=0:11Þ 0:02
ð23Þ
kr w ¼ 1:90=½1 þ expððS w 0:91Þ=0:26Þ þ 1:80
ð24Þ
P c ¼ 2:09 106=½1 þ expððS w 0:09Þ=0:02Þ
þ 3190:60 ð25Þ
The shape of water–oil interface for single com-
pletion is considered as a reference for comparison.
In the plots (Figs. 5– 9), the dual completion is
referenced with Qwc* =1 . 5 Qoc* and the single com-
pletion with Qwc* = 0. High values of oil production
rates are considered with water production rates
within the water perforations being less or equal to
1.5 Qoc*. This choice is justified by the fact that
higher values could be harmful to the hydraulic
performance of well completion.
To clarify the position of well perforations in the
plots, two dashed rectangles are added and theyrepresent the limits of the oil and water comple-
tions. The use of DWS technology deforms the
cone profile shape, as illustrated in Fig. 4, at
different times of production. The top of water–
Table 1
Grid sensitivity for M =2, NDq = 0.1, DaH = 4 10 16, Ra = 0.2,
/= 0.2, Qoc* =25 10 10, Qwc* = 0
Dt * Number of nodes in BT* Relative
Radial
direction
Vertical
direction
difference
(%)
72 1011 30 18 0.245 1018 –
72 1011 40 24 0.274 1018 5.38
72 1011 50 30 0.272 1018 0.73
29 1014 40 24 0.270 1018 –
72 1011 40 24 0.274 1018 1.48
144 1010 40 24 0.277 1018 1.09
Fig. 3. Comparison of numerical simulations with published results
from Yang (1992).
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oil interface is shifted to the right (away from thewell) yielding, in certain situations, oil break-
through into the water sink.
Fig. 5 shows the development of water cone
profiles for two values of oil production rate with
and without dual completion at t *=0.95 1018. In
the single completion case, the water – oil interface
develops as a classical cone which is very sensitive to
production rate. At Qoc* = 2 0 10 10 which corre-
sponds to a very high value of the production rate,
the water invades rapidly in a wide region of the oil
zone affecting the oil production performance. Thewater intercepts the oil flow into well perforations.
The well perforations in the water zone constitute a
water sink affecting considerably the shape of the
cone. Not only is water retained, but the top of the
cone is shifted to the right and is located at approx-
imately r *=1.5. At Qoc* = 10 10 10, the dual com-
pletion technique retains the rapidly upcoming water
coning. Indeed, for a same period of production,
water has broken through into oil perforations for
the single completion; whereas, in dual completion
Fig. 4. (a) Shape of the water cone in 3D view in dual completion at t *= 1.261 1018; (b) shape of the water–oil interface at different time of
production when DWS, completion is used, (a) and (b) M = 2 , NDq= 0.1, DaH = 4 10 16, Ra = 0.2, /= 0.2, Qoc* = 10 10 10,
Qwc* = 1 5 10 10.
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case, the top of water–oil interface is located at adimensionless distance of 0.5 below the oil well. At a
Qoc* = 2 0 10 10, which corresponds to a very high
value of oil production rate (Fig. 5), even if water has
not broken through oil perforations at this stage of
production, the development of the cone is important.
Indeed, its tendency to be higher and to move away
from the well could intercept the oil flow. It is
evident from these plots that multiplying oil produc-
tion rate by a factor 2, in dual completion, causes
development of a cone and the position of its top is
raised by twice as much. Physically, the water sink alters the flow potential field around the well so that
the water–oil interface is retained. At each point, the
upward vertical component of viscous force generat-
ed by the flow into the oil perforations is reduced by
the downward vertical component of the second
viscous force generated by the flow into the water
sink.
The effect of mobility ratio on water–oil interface
development is illustrated in Fig. 6. With a single
completion, the water cone expands vertically towards
Fig. 5. (a) 3D view of the water cone shape in single completion for Qoc* = 20 10 10; (b) shape of the water–oil interface in single and dual
completions for two values of dimensionless oil production rate, (a) and (b) M = 2, NDq = 0.1, DaH = 4 10 16, Ra = 0.2, / = 0.2, Qoc* =10
10 10, t *= 0.95 1018.
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the well rather than outward radially. The use of a dual
completion deforms the classical cone shape. The top
of the cone is shifted to the right. At this stage of
production, the oil breakthrough into water sink is still
taking place for M = 2, whereas for M = 6, oil stops
flowing into the water perforations. During the first
stage of production, the viscous force, generated bythe flow into the water sink, overcomes the viscous
force generated by the flow into oil perforations. The
inverse behaviour occurred at this stage of production
(t *=0.70 1018). When viscous forces arise due to
the resistance of the flow they are important and
prevail, the oil mobility is reduced, this situation
accelerates the upward motion of water into oil
perforations.
The gravity force (dimensionless density differ-
ence) represents an important parameter that can
affect the cone profile considerably. When the vis-cous force resulting from natural drive due to oil
perforations overcomes the gravitational force in-
duced by difference in fluid densities, water coning
occurs. As shown in Fig. 7, the cone is very devel-
oped in both directions (horizontal and vertical) and
reaches the oil perforations for a single completion
and at low values of dimensionless density difference
(NDq= 0.05 for example). At a dimensionless densi-
ty difference (NDq= 0.2) four times greater than the
previous value, the water cone profile is less devel-
oped and is located at about a dimensionless distance
of 0.5 below the bottom of the oil perforations. With
dual completion, the water– oil interface behaves
differently and the top of the cone is kept away fromthe well. High values of NDq means that water
arrival at oil perforations is more delayed, yet the
duration of oil flow into the water sink is longer.
From these plots, the gravity force, aided by viscous
force generated by the flow into the water sink,
allows retention of rapid upward flow of water into
oil perforations.
Another parameter affecting the water coning
behaviour is the ratio of vertical to horizontal
permeability, also termed as anisotropy ratio ( Ra).
Low values of this ratio result in a very dumped
upward motion of the water–oil interface in single
completion as shown in Fig. 8. In dual completion
situations, the cone shape is greatly affected at low
values of Ra. The water– oil interface motion is
reversed and oil breakthrough takes place. The top
of the cone in this case is shifted to the right and is
located at a dimensionless radial distance of ap-
proximately 3. At high values of Ra, the cone
shape is not affected; however, its motion toward
oil perforations is decreased compared to the single
completion. With a dual completion, and at high
anisotropy ratio, the upward flow of water into oil perforations is delayed by viscous force due to the
Fig. 6. Shape of the water– oil interface in single and dual
completions for two mobility ratios for NDq = 0.1, DaH = 4 10 16,
Ra = 0.2, / = 0.2, Qoc*=10 10 10, t *= 0.70 1018.
Fig. 7. Shape of the water– oil interface in single and dual
completions for two values of dimensionless density difference for
M = 2, DaH = 4 10 16, Ra = 0.2, /= 0.2, Qoc* = 1 0 10 10,
t *= 0.92 1018.
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flow into the water sink. At a low anisotropy ratio,
the downward vertical component of viscous force
generated by the flow to water perforations over-
comes the upward vertical component of viscous
force due to the flow into oil perforations. This
situation causes oil to break into water perforations.
Nevertheless, this case may easily be avoided byreducing the water production rate.
Oil recovery from the well is principally radial,
indicating the important role played by the horizontal
permeability. The placement of perforations in the
water zone in order to drain the water phase,
deforms the cone shape and causes the motion of
its top away from the well (Fig. 9). The radial
location of this top is proportional to the permeabil-
ity. The water–oil interface motion is faster for less
permeable reservoirs. Physically, this situation results
from slower flow in the radial direction for the less permeable rocks.
From this analysis of the cone shape, it is apparent
that oil breaks into water perforations in certain
situations. The simulation results indicate that there
exists a critical flow rate in the water sink which
should not be exceeded in order to avoid oil break-
through. In fact, there is competition between two
forces (upward and downward) owing to the dual
sink. For instance, one should optimise both oil and
water production so that the interface is always main-
tained in between oil and water perforations. Fig. 10 is
a graph that provides the oil breakthrough time BToil*
versus water production rate. When water production
rate (Qwc* ) in the water sink is less or equal to
approximately 2 10 10 the oil breakthrough does
not occur.The previous analysis of the water– oil interface
behaviour provides an answer to the cone shape when
dual completion is used. It is shown by our data that
the interface is not stable for all ranges of parameters
Fig. 9. Shape of the water– oil interface in single and dual
completions for two values of horizontal permeability M = 2,
ND q = 0. 1, /= 0. 2, Q o c* = 10 10 1 0 , Da V = 8 10 1 7 ,
t *= 0.40 1018.
Fig. 8. Shape of the water– oil interface in single and dual
completions for two values of anisotropy ratio for M = 2, NDq = 0.1,
DaH = 4 10 16, / = 0.2, Qoc* = 1 0 10 10, t *= 0.69 1018.
Fig. 10. Influence of water production rate (in water sink) on oil
breakthrough time in dual completion for M = 2 , NDq = 0.1,
DaH = 4 10 16, Ra = 0.2, / = 0.2, Qoc* =10 10 10.
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investigated and water can break into oil perforations.
Thus, other results on water breakthrough time are
documented and discussed.
For all of the parameters, three cases of water produc tion rate (Qwc* ) i n th e wat er s in k w ere
examined: Qwc* = 0 that corresponds to single com-
pletion, Qwc* =0.8 Qoc* and Qwc* =1.5 Qoc* in du-
ally completed wells.
Fig. 11 shows a decrease of water breakthrough
time (BT*) when the production rate increases in both
single or dual completions. The use of DWS comple-
tion allows a delay of the water breakthrough for a
period of time that is not different for two values of
water production rate. In a dually completed well, the
BT* is improved by approximately a factor of two
compared to single completion. Also the analysis of
BT* in single completion shows that for an oil
production rate less than about 2.5 10 10, water
does not break into oil perforations, i.e., this value
corresponds to the critical oil rate. Dual completion
yields an increase in the critical oil production rate,
which goes from 2.5 10 10 in single completion to
5 10 10 in dual completion. As explained previ-
ously in the cone analysis, the upward vertical com-
ponent of the viscous force due to oil perforations is
reduced by the downward vertical component of the
second viscous force due to the water sink.The mobility ratio affects oil recovery. The higher
the mobility ratio ( M ), the faster the water break-
through occurs, as shown in Fig. 12. For values of M
greater than 10, water coning is delayed only for a
short period of time by the use of DWS technology.
As explained in the cone profile analysis, when
viscous forces are important and predominate, the
oil mobility is reduced yielding faster upward motion
of the water–oil interface. The BT* is slightly greater
at Qwc* / Qoc* = 1.5 compared to BT* at Qwc* / Qoc* = 0.8,
only for the range of M between 2.5 and 10. An
asymptotic behaviour of BT* is observed in single or
dual completions for values of M less than a certain
critical value. It is an indication of critical oil rate. It
starts from values of M less than 0.25 in singlecompletion and less than 1 for a dually completed
well.
Fig. 13 shows the effect of the dimensionless density
difference (NDq) on BT*. For the most part, use of a
Fig. 11. Influence of dimensionless total production rate on water
breakthrough time in single and dual completions for M = 2,
NDq = 0.1, DaH = 4 10 16, Ra = 0.2, / = 0.2.
Fig. 12. Influence of mobility ratio on water breakthrough time in
single and dual completions for NDq = 0.1, DaH = 4 10 16,
Ra = 0.2, / = 0.2, Qoc* =10 10 10.
Fig. 13. Influence of dimensionless density difference on water
breakthrough time in single and dual completions for M = 2,
DaH = 4 10 16, Ra = 0.2, / = 0.2, Qoc* = 1 0 10 10.
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dual completion considerably delays the water coning
at high values of NDq. The improvement due to DWS
yields a BT* at least two times greater when NDq is
increased from 0.1 to 0.2. Increasing water production
allows delay of water arrival at the oil perforations for
values of Qwc* / Qoc* = 1.5 and 0.8, owing to the stabilis-
ing effect of gravity at high values of NDq (Fig. 13).
The gravitational force, induced by the difference in
fluid densities, add to the downward vertical compo-
nent of viscous force due to the water sink, hinderingwater breakthrough. For NDq< 0.05, the effect of
DWS on BT* is still sensitive. Nevertheless, the effect
of water production rate on BT* seems to be negligible.
The effects of the rock characteristics on BT*
are shown in Figs. 14– 16 through the anisotropy
ratio ( Ra), the horizontal permeability ( DaH) and
the porosity (/) . An improvement of BT* is
recorded when the well is dually completed. The
augmentation of water production rate from Qwc* /
Qoc* = 0.8 to Qwc* / Qoc* = 1.5 does not significantly
improve the delay of water into oil perforations.
It is noticed that for good rock characteristics (low
values of Ra, high Da and /) a better enhancement is reached. An asymptotic behaviour of BT* versus
Ra is shown in Fig. 14, it corresponds to a critical
oil production rate.
5. Conclusions and remarks
Results of numerical simulations related to wa-
ter– oil interface behaviour and BT* were analysed
and documented for single and dual completions.
With a parametric study of dual completion tech-nology, the cone profile shape and the performance
of this technique were discussed arriving at the
following conclusions:
(a) The use of dual completion deforms the cone
profile shape in most cases. The top of water – oil
interface moves away from the well.
(b) The use of high oil production rates yields an
elevation of water coning height that would
intercept oil flow.
Fig. 14. Influence of anisotropy ratio on water breakthrough time in
single and dual completions for M = 2, NDq= 0.1, DaH = 4 10 16,
/= 0.2, Qoc* =10 10 10.
Fig. 16. Influence of porosity on water breakthrough time in single
a nd d u al c om pl e ti o ns f or M = 2 , N Dq= 0.1, Ra = 0.2,
DaH = 4 10 16, Qoc* =10 10 10.
Fig. 15. Effect of horizontal permeability on water breakthrough
time in single and dual completions for M = 2 , NDq= 0.1,
DaV = 8 10 17, / = 0.2, Qoc* =10 10 10.
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(c) For dimensionless water production rates greater
t ha n 2 10 10, t he o il b re ak s i nt o w at er
perforations. The water breakthrough time is
proportional to dimensionless density differenceand horizontal permeability and inversely propor-
tional to oil production rate, mobility, and
anisotropy ratios.
(d) For rock reservoir with high anisotropy ratio,
the cone shape, induced by DWS technology,
takes the classical behaviour occurring in
single completion after a short period of
production.
(e) At low NDq numbers, the values of BT* for Qwc* /
Qoc* = 0.8 and Qwc* / Qoc* = 1.5 are not too different,
thus the use of high production rate at water sink
is not recommended. The improvement begins
when dimensionless density difference is greater
than 0.05.
(f) Using the dual completion, water breakthrough is
delayed. In general, the BT* is doubly delayed
compared to single completion situation.
(g) The critical oil production rate is improved
compared to a single completion.
Nomenclature
DaH radial Darcy number ( DaH = k H/ ho2) DaV vertical Darcy number ( DaV = k V/ ho
2)
Dq density difference (Dq= qw qo)
DWS downhole water sink
g gravity acceleration (m/s2)
h total height of the physical domain (h = ho +
hw, m)
h* dimensionless total height of the physical
domain
ho oil zone height (m)
ho* dimensionless oil zone height
h p oil perforation height (m)h p* dimensionless oil perforation height
hw water zone height (m)
hw* dimensionless water zone height
hwp water perforation height (m)
hwp* dimensionless water perforations height
K ¯ permeability tensor
k H horizontal permeability (m2)
kr l relative permeability to phase l
kr oiw relative permeability to oil at irreducible
water saturation
kr wor relative permeability to water at residual oil
saturation
k V vertical permeability (m2)
M mobility ratio ( M = RKr lo/ lw)!n normal vector to boundary
NDq dimensionless density difference (NDq=
(qw qo)/ qw)
Nqw dimensionless expression (Nqw = qw gho/
P woc)
P aq pressure at bottom aquifer (Pa)
P c capillary pressure (Pa)
P c* dimensionless capillary pressure ( P c* =( P c Dq gz )/(Dq gho))
P l phase pressure (Pa)
P l * dimensionless pressure phase ( P l *=( P l +
qw gz P woc)/(Dq gho))
P woc initial pressure at water– oil contact (Pa)
Qa total production rate (m3/s)
Qa* total dimensionless production rate (Eq. (21))
Qa total production rate by unit reservoir volume
(s 1)
Qla phase production rate by unit reservoir
volume (s 1)
Qla* dimensionless phase production rate
Qwc* dimensionless water production rate in water
sink
r radial co-ordinate (m)r * dimensionless radial co-ordinate (r *= r / ho)
Ra anisotropy ratio, Ra = DaV/ DaH
r e total radius of the physical domain (m)
r e* total dimensionless radius
Rkr relative permeability ratio ð Rkr ¼ kr wor =kr oiwÞ
r w* dimensionless well radius
r w well radius (m)
S l phase saturation
S or residual oil saturation
S wi irreducible water saturationt time (s)
t * dimensionless time (t *= P woc t / lw)!V l phase filtration vector (m/s)
z vertical co-ordinate (m)
z * dimensionless vertical co-ordinate ( z *= z /
ho)
Greek symbols
ql fluid phase density (kg/m3)
/ porosity
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ll dynamic viscosity (Pa.s)
j gradient operator
Subscriptsa zone completion (a = oc, wc)
l phase (l =o, w)
* dimensionless
References
Abass, H.H., Bass, D.M., 1988. The critical production rate in water
coning system. SPE 17311, Permian Basin Oil and Gas Recov-
ery Conference, Midland, TX. March 10–11.
Azziz, K., Settari, A., 1986. Petroleum Reservoir Simulations.
Elsevier, London.
Blake, J.R., Kueera, A., 1988. Coning in oils reservoirs. Math. Sci.
13, 36 –47.
Chaney, P.E., Noble, M.D., Henson, W.L., Rice, T.D., 1956. How to
perforate your well to prevent water and gas coning. Oil Gas J.
55, 108–114.
Chaperon, I., 1986. Theoretical study of coning toward horizontal
and vertical wells in anisotropic formations: subcritical and crit-
ical rates. SPE 15377, 61st Annual Technical Conference and
Exhibition, New Orleans, LA. Oct. 5–8.
Chierici, G.L., Ciucci, G.M., Pizzi, G., 1964. Asymmetric study of
gas and water coning by potentiometric models. JPT, 923–929
(Aug.).
Chugbo, A.I., Roux, G.D., Bosio, J.C., 1989. Thin oil columns,
most people think horizontal wells, Obagi field case suggestscontrary. SPE 19599, 64th Annual Technical Conference, San
Antonio, TX, Oct. 8–11.
Elkins, L.F., 1958. An Unusual Problem of Bottom Water Coning
and Volumetric Water Invasion Efficiency. 33rd Annual Fall
Meeting of SPE, Houston, TX, Oct. 5–8. Paper SPE 1121-G.
Fortunati, F., 1962. Water coning at the bottom of the well. SPE
544, Technical Note, 1–9.
Giger, F.M., 1989. Analytic two dimensional models of water crest-
ing before breakthrough for horizontal wells. SPE 15378, SPE
Reservoir Engineering Journal, 409– 416 (Nov.).
Gunning, J., Paterson, L., Poliak, B., 1999. Coning in dual com-
pleted systems. JPSE, (23), 27 – 39 (Aug.).
Guo, B., Lee, R.L.H., 1993. A simple approach to optimisation
of completion interval in oil/water coning systems. SPE23994, SPE Reservoir Engineering Journal, 249 – 255 (Nov.).
Hoyland, L.A., Papatzacos, P., Skaeveland, S.M., 1986. Critical rate
for water coning, correlation and analytical solution. SPE Euro-
pean Conference, London, Oct. 20 – 22, pp. 59 – 70.
Irrgang, H.R., 1994. Evaluation and management of thin oil column
reservoirs in Australia. APEA J., 64.
Karp, J.C, Lowe, D.K., Marusov, N., 1962. Horizontal barriers for
controlling water coning. JPT, 783 – 790 (July).
Kuo, M.C.T., Debbrisay, C.L., 1983. A simplified method for water
coning predictions. SPE 12067, 5th Annual Technical Confer-
ence and Exhibition, San Francisco, CA, Oct. 5–8.
Menouar, H.K., Hakim, A.A., 1995. Water Coning and Critical
Rates in Vertical and Horizontal Wells. SPE Middle East Oil
Conf. Bahrein, March 11–14. Paper SPE 29877.
Meyer, H.I., Garder, A.O., 1954. Mechanics of two immiscible
fluids in porous media. J. Appl. Phys. 25, 1400.Muskat, M., 1949. Physical Principles of Oil Production. Mc Graw-
Hill, New York.
Muskat, M., Wyckoff, R.D., 1935. An approximate theory of water
coning in oil production. Trans. AIME 114, 144–159.
Ould-amer, Y., Chikh, S., 2002. Dynamique d’un ecoulement huile-
eau dans les milieux poreux naturels. Sixieme Seminaire inter-
national sur la physique energetique, Bechar, Algeria, 21–23
Oct. 2002.
Ould-amer, Y., Chikh, S., 2003. Transient behavior of water–oil
interface in an upward flow in porous media. J. Porous Media 6
(2), 1 –12.
Outmans, H.D., 1964. Effect of Coning on Clean Production Rate
of Well in Heterogeneous Reservoir. 39th Annual Fall Meeting
SPE, Houston, TX, October 11–14. Paper SPE 893.
Papatzacos, P., Herring, T.M., Martinsen, R., Skaeveland, S.M.,
1989. Cone breakthrough time for horizontal wells. SPE
19822, Annual Technical Conference and Exhibition, San Anto-
nio, TX, Oct. 8–11.
Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow Mc
Graw-Hill, New York.
Patankar, S.V., 1981. A calculation procedure for two-dimensional
elliptic situations. Numer. Heat Transf. 4, 409–425.
Romero-Juarez, A., 1964. Characteristic of Oil Production Related
to Water Coning. Reservoir Eng. J., 1–34. SPE.
Russel, T.J., Larry, W.L., Arnaud, M.D., 2002. Prediction of capil-
lary fluid interfaces during gas or water coning in vertical wells.
SPE 77772, Annual Technical Conference and Exhibition, SanAntonio, TX, Sept. 29–Oct. 2.
Schols, R.S., 1972. An empirical formula for the critical oil pro-
duction rate. Erdoel-Erdgas-Z. 88 (1), 6–11.
Shirman, E.I., Wojtanowicz, A.K., 1997a. Water coning hysterisis
and reversal for well completion using the moving spherical
sink method. SPE 37467, Production Operations Symposium,
Oklahoma, March 9–11.
Shirman, E.I., Wojtanowicz, A.K., 1997b. Water coning reversal
using downhole water sink theory and experimental study.
SPE 38792, Annual Technical Conference and Exhibition, San
Antonio, TX, Oct. 5 – 8.
Smith, C.R., Pirson, S.J., 1963. Water coning control in oil well
by fluid injection. SPE 613, Reservoir Engineering Journal,
314– 326 (Dec.).Suprunowicz, R., Butler, R.M., 1992. Vertical confined water drive
to horizontal well, Part:1. Water and oil of equal densities. J.
Can. Pet. Technol. 31 (1).
Swisher, M.D., Wojtanowicz, A.K., 1995a. In situ-segregated pro-
duction of oil and water—a production method with environ-
mental merit field application. SPE 29693, Exploration and
Production Environmental Conference, Houston, TX, March
27–29.
Swisher, M.D., Wojtanowicz, A.K., 1995b. New dual completion
method eliminates bottom water coning. SPE 30697, Annual
Technical Conference and Exhibition, Dallas, TX, Oct. 22 – 25.
Y. Ould-amer et al. / Journal of Petroleum Science and Engineering 45 (2004) 109–122 121
7/25/2019 Attenuation of Water Coning Using Dual Completion Technology, 2004
http://slidepdf.com/reader/full/attenuation-of-water-coning-using-dual-completion-technology-2004 14/14
Wojtanowicz, A.K., Bassiouni, Z.A., 1994. Segregated produc-
tion method for oil wells with active water coning. JPSE,
(11), 21–35 (April).
Wojtanowicz, A.K., Xu, H., Bassiouni, Z.A., 1991. Oil well coning
control using dual completion with tailpipe water sink. SPE21654,Production Operation Symposium,Oklahoma,April 7 – 9.
Yang, W., 1992. An Analytical Solution to Two-Phase Flow in
Porous Media and its Application to Water Coning. Reservoir
Eng. J., 1–38. SPE.
Yang, W., Wattenbarger, R.A., 1991. Water coning calculations for
vertical and horizontal wells. SPE 22931, 66th Annual Techni-cal Conference and Exhibition, Dallas, TX, Oct. 6–9.
Y. Ould-amer et al. / Journal of Petroleum Science and Engineering 45 (2004) 109–122122