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Segregated production method for oil wells with active water coning
JOURNAL OF
ELSEVIER
Journal of Petroleum Science and Engineering 11 ( 1994) 21-35
PETROLEUM SCIENCE & ENGINEERING
Segregated production method for oil wells with active water coning A n d r e w K. W o j t a n o w i c z , H u i X u , Z a k i B a s s i o u n i Department of Petroleum Engineering, Agricultural Mechanical College, Louisiana State University, Baton Rouge, LA 70803-6417, USA (Received March 15, 1993; revised version accepted August 31, 1993)
Abstract This paper describes a simulation study of a novel method to control water coning in an oil producing well. The method uses a dual-completion configuration that is above and below OWC. In this configuration, the well section above OWC is completed in the oil zone and produces oil, while the well section completed below OWC in the water-saturated zone produces water both independently of and concurrently with oil production. Segregated water production creates a drain (rat hole water sink) to control the rise of the water cone. Coning control results from the effect of water sink on flow potential between the sink and oil-producing perforations. The study investigated simulated production performance of the well both with and without the rat hole water sink. At first, the water sink's position and flow rate were examined to determine the critical production rate of oil (i.e., maximum production rate without the water breakthrough). Next, the various amounts of water produced during oil production at rates greater than critical were compared. The comparison study used both lab data and field data from an actual well/reservoir system of known geometry and reservoir properties. The coning behavior of the production system with the rat hole water sink was mathematically modelled using the flow potential distribution generated by two constant-terminal-rate sinks located between the two linear boundaries and the constant-pressure outer radial boundary. The model was verified by using the existing and simulated data of water coning in conventional wells and by setting the water sink flow rate at zero, with oil being the only produced fluid. Also, verification tests were used to select the type of oil reservoir with the thick oil zone and the small dip angle for the comparison studies. The study demonstrates the existence of an active mechanism to control water coning with the rat hole water sink. It shows that a sink with low water flow rate may prevent the water cone from breaking through the oil zone and into the producing perforations so that the oil with no water cut can be produced above the critical flow rate. A simulation using the new method yielded less produced water and either the same or a higher oil rate than the conventional method. However, potential increase of oil production above its critical value is limited by the stability of the controlled water cone. Also, for high oil production rates, more precision is needed to control the water production rate.
1. Introduction
For years, water coning has been considered a
productivity problem that reduces daily oil production and leads to early a b a n d o n m e n t o f wells. Recently, environmental regulations added a new c o m p o n e n t to this problem, cost o f cleanup and
0920-4105/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0920-4105 (93 ) E0068-Z
22
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
disposal of produced water contaminated by oil during the production process. Parameters affecting water coning in vertical wells are: mobility ratio, oil zone thickness, ratio of gravity forces to viscous forces, well spacing, ratio of horizontal permeability to vertical permeability, well penetration and production rate. Although water coning is well known, its control is limited because only the latter four (out of seven) coning variables can be controlled. The mobility ratio effect on water coning was studied using scaled laboratory models (Soengkowo, 1969). Studies with a radial model (Soengkowo, 1969 ) showed that the mobility ratio inversely affects production performance. Studies with another three-dimensional model revealed that mobility ratio values greater than one engendered the worst coning effects (Khan, 1970): the higher the mobility ratio was, the faster the breakthrough occurred. The study showed that when the mobility ratio is greater than one, water coning develops quickly and the water cut increases rapidly. As production continued, the cone expanded in all directions and lowered oil production to within a few percent of its initial value. When the mobility ratio was less than one, the water cone first expanded outwards radially, and then it gradually rose towards the well. The changes in the water cut values were gradual and were spread over a long period of production. The pay-zone thickness affects water coning in relation to the water zone size. Studies show that as the ratio of water to oil zone thickness increases, coning severity also increases while other parameters remain unchanged (Khan, 1970.). Consequently, a serious coning problem might be expected at the end of production when most of the pay zone has been invaded by water. The third uncontrollable coning variable, the ratio of gravity force to viscous force, is a fundamental factor of the coning phenomenon because it determines when viscous force, which is induced by fluid flow, will overcome gravitational force, which is induced by the differences in fluid densities. In the laboratory experiments with the pie-shaped, radial model (Mungan,
1975), the ratio of gravity to viscous force was calculated as:
R~-
gApAkh
(1)
qoPo
where: Rgv = the ratio of gravity to viscous force; g = acceleration of gravity; Ap=density difference; A = model area; kh = horizontal permeability; qo = oil pumping rate; and/~o = oil viscosity. Figure 1 shows the increase in water cut caused by water coning during oil production. The results indicate that water coning is reduced at high values of Rgv. The first variable of water coning that can be controlled is well spacing. Its effect on water coning is also shown in Fig. 1. The figure clearly indicates that water coning can be dramatically reduced by drilling more wells at a closer spacing. However, the economics of such control is highly questionable. The other potentially controllable variable is the ratio of vertical to horizontal permeability. Figure 2 shows that a reduction of this ratio also reduces coning. Such an effect was observed in the Middle East at a large oil reservoir (Alikhan and Faroug, 1985) where a tar barrier ("tar mat" ) was present between oil and water zones. Technically, the permeability can be affected by fracturing the formation. However, the method is limited to shallow wells because in deep-well fracturing the improvement of vertical permeability is more likely to occur than that of horizontal permeability. o.5
i ~=
o
.~ 0.3
-4
<
g , ~
0.1 0
5
10 15 OIL RECOVERY, % of PV
20
~0
25
R~v- 19.1
Fig. 1. Effects of the gravity/viscous force ratio, R~v, and well spacing on water coning (Mungan, 1975).
23
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 PRODUCTION RATE, bbl 0.025 0.05
0.5 =2
1
02
0.4 t ..........
O
i ~ J 'l ~ / ~ o.3
.
.
.
.
01
002
10
+
: ...........
+ ...............
.....
Y
i
.
.
.
.
.
.
.
.
.
.
.
.
0.75 i
_ _
0.1
"1(5 O DE: I
.
F-
............
10 15 OIL RECOVERY,% of PV
20 0.25 0'.5 0.'75 WELL PENETRATION/ OIL ZONE THICKNESS
Fig. 2. Effect of the vertical/horizontal permeability ratio on water coning. 0
i
m c3 LU"
~...............
_J
i
/ day
Fig. 3. Effect of well penetration and oil production rate on water coning (Mungan, 1975).
800 700 600
o
500
0
o
300
"o 0 =.
200
-~
lOO
ID
'6:]
'65
'67
'69
'71
'73
'75
~
'79
'81
'83
°85
'87
Year Fig. 4. Production history o f o i l and water from the North Reservoir in the Lafitte field of Jefferson Parish, Louisiana (Cooke, 1989).
Well penetration can be controlled through completion practices. Early studies using an electrical model (Muskat, 1949) showed that coning would increase with increased well penetration. Also, in scale model studies (Mungan, 1975 ), a strong dependence of coning upon well penetration was shown as a relationship between the water breakthrough time and the fraction of the pay zone penetrated by a well. When the well penetration reached 75% of the oil zone thickness, the water breakthrough occurred almost instantly. To minimize coning, well penetration
should be minimum. Such a completion will certainly maximize oil recovery, but it will also minimize well productivity. Theoretically, the well completion design under conditions of water coning can be viewed as an optimization problem. Also, some recent studies show that horizontal completions in the top of an oil zone may prevent water coning, increase production rates, and improve oil recovery (Bourgeois, 1989; Abels, 1990). Oil production rate is easy to control. Its strong effect on coning has been proven in laboratory
24
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
studies (Fig. 3 ) and in oil field practices (Fig. 4) (Cooke, 1989). Figure 4 shows the annual production plots for oil and water from a shallow oil-bearing sand in the Lafitte field of Jefferson Parish, Louisiana. A steady increase of water production is evident and results from water encroachment and coning. More characteristic, however, are the drastic changes of water production caused by relatively small changes in oil production. It is clear from these plots that the two- to five-fold increase of water production resulted from the two-fold increase in oil production during 1971, 1979 and 1986. Control of water coning requires reduction of the oil production rate below the value of the critical rate. (Predictive models to calculate this rate have been recently reviewed in Abels (1990) and Hebert (1990). ) In many cases, however, it is not economical to keep the oil production rate below its critical value (Chatas, 1966). Moreover, once the breakthrough occurs, it may be difficult to return to the initial low value of water cut, even at the reduced oil rate, due to the irreversible change of the mobility ratio caused by the imbibition/drainage effects upon the relative permeabilities. The above analysis indicates that the theoretically available methods to control water coning have very limited practical applications. Hence, there is a need for innovations.
2. Segregated production method Figure 5 shows the principle of the segregated production method. The well is dual completed so that the lower perforations are placed in the water zone, and water can be produced both concurrently with and independently of oil production. These two producing streams are separated by a packer to prevent water from mixing with oil. Coning control is performed by adjusting the water production rate to the oil production rate so that the water cone does not break through the oil and enter the oil perforations. Physically, the water sink (water perforations) alters the flow potential field around the well so that the water cone is suppressed. Flow into the water sink gen-
WATER PRODUCTION OIL ~--~ PRODUCTION--
I . . , •
!
1 Qw 0 ~ ~ . I/--~ ..,...~ ~
.//
Ow > 0 TAIL PIPE ~ WATER SINK
!
!
OIL ZONE OIL ~--.~,~PERFORATIOt~ ~ ,,~ OWC
"-
WATER ZONE ~ WATER PERFORATIONS
Fig. 5. Principle of coning control using segregated production.
erates a downward viscous force which reduces the upward viscous force that is generated by the flow into the upper (oil) perforations. At equilibrium, a stable water cone is "held down" around and below the oil-producing perforations. The segregated production method has several potential advantages listed below. ( 1 ) The oil production rate increases without water breakthrough. (2) The well life extends beyond its value without coning control. (3) The oil recovery per well (and for the whole reservoir) increases due to the following mechanisms: (A) production can be continued with high levels of static OWC (caused by the bottom water-drive invasion), even when this level reaches the oil perforations, and (B) well productivity remains high because the near-well zone permeability to oil is not reduced by water encroachment. (4) Because produced water is not contaminated with crude oil, demulsifiers, or other agents used in oil production, the method is more likely to meet effluent discharge limitations set by the environmental regulations in the area. (5) The water cut of the produced oil is minimum. The purpose of this study is to evaluate the coning control potential of this method as well as to compare its performance to the conven-
A.K. Wojtanowiczet al. I Journal of Petroleum Science and Engineering 11 (1994)21-35
tional method of oil production under the conditions of bottom water drive. Mathematical simulation is used to predict the method's performance.
The mathematical model is used under the assumption that for any fixed production rate or bottom-hole pressure, with the water lying statically at the lower boundary of the oil zone, the pressure at the water-oil interface p(r,z) will satisfy the equation:
p(r,z)+po~g(h-z)=p(r,z)+po~gy=~
Well
Pb
II/I/I/II/III/
z
_
~
///I//
_
2 0q~ ~#c 0q~ q,r~ + r Or - k Ot
02~)
(3)
ro -
r
(4a)
rw
kt 4nkrw tD=ollcr2w, and q~D= Oo-~-(~i-q~)
(4b,c)
For steady-state conditions, the flow potential is:
(2)
where Pb is the formation pressure at the bottom of the oil zone at a point remote from the well, and po is the density of water. These assumptions, based on Muskat's theory (Muskat, 1949), stem from the reasons that water, being of greater density than oil, will, under static conditions, remain at the bottom of oil producing section. Therefore, its rise, as Fig. 6 shows, represents a dynamic effect in which the upward-directed pressure gradients associated with the oil flow are able to balance the hydrostatic head of the elevated water column. When the perforated sections of a well are short, their productions can be treated approximately as point sources. In this case, the spherical solution of the flow potential is a good ap-
I
proximation. The one-dimensional equation of the flow potential in spherical coordinates is:
To solve this differential equation, the following dimensionless parameters are defined:
3. Mathematical model of water sink
h
25
5
I
t Z
Fig. 6. Water coning model coordinates and nomenclature.
~D (rD,tD) -- rDe -- rD rDerD
(5)
The method of images can extend the above solutions to the finite-thickness reservoir. Figure 7A shows the method of images applied to a single zone. For this case, the steady-state flow potential is expressed as: ~)D(rD,tD)-- rDe-rDO 4- ~ rDerDo
~ rDe--rDji
i=l j=l
(6)
rDerDji
Calculation of the flow-potential distribution for a single zone using Eq. 6 is straight forward. For the double-zone system of oil underlain by water, and with two production sinks, the flow potential at a point of interest is superimposed from both sinks. Figure 7B shows the nomenclature for this case. The calculation procedure ineludes two basic steps: ( 1 ) Check whether the coning liquid is oil or water by separately calculating the flow potential at OWC induced by each sink; and (2) Calculate the coning profile using superposition of Eq. 6 and the iteration procedures until Eq. 2 is satisfied. The effect of vertical and horizontal permeabilities is implied in the definition of spherical permeability (Chatas, 1966) used in the model as:
3khkv
k - k h +2k~.
(7)
26
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 I
I I I I I
2ht lhlo h,
uO 9odnddar,/
h2o ~h]i~
lower boundary
dr~,~) qw
h2w
h2
Zh,
I I I I I
"B
A
Fig. 7. Flow potential model using method of images. (A) Single zone with one sink; (B) dual zone system (oil/water) with two sinks.
3.1. Model verification A literature search was conducted for a select number of established water coning models for comparison with the new model. A short deTable 1 Reservoir data for calculation examples Case 1
Case 2
Formation thickness (It) Oil zone thickness (ft) Oil perforation position
100 50 Top ofoil zone
Horizontalpermeability (mD) Vertical permeability (mD) Oil viscosity (cP) Oil density (g/cm 3) Water density (g/cm 3) Wellbore radius (It) Reservoir radius (ft)
1000 500 1 0.7 1 0.25 500
120 70 0-50 ft from the top 236 125 2.4 0.812 1.15 0.25 1300
scription of the selected models follows. A simple analytical model by Muskat (1949) describes water coning in a homogeneous system with a constant mobility ratio and an isopotential at initial OWC. Muskat used the model, together with his graphical method (Muskat and Wyckoff, 1935), to predict equilibrium conditions of water coning. Also, he correlated critical flow rates with well penetration for various oil zone thicknesses. Schols (1972) developed an empirical formula using a Hele-Show model to calculate the critical oil production rate. Meyer and Gardner (1954) presented a radial flow of oil under its own hydrostatic head. Both Schols' and MeyerGardner's methods provided the formulas for critical oil flow rate as a function of density differential, well penetration, oil-zone thickness, oil viscosity and permeability, and drainage area. Wheatley (1985) simulated oil/water coning using an approximate analytical technique. The
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
underlying assumptions were as follows: ( 1 ) oil partially flows into the well in the presence of underlying water; (2) the reservoir is homogeneous and bounded above by a horizontal impermeable barrier extending to a distance (drainage radius ) from the well; ( 3 ) the flow region is bounded below by the oil-water contact, which forms an upward cone near the well in response to the reduced pressure; (4) the flow of oil in the drainage area is assumed to be steady and radially symmetric; ( 5 ) the underlying water is stationary and entirely segregated from the oil; and (6) the fluids (oil and water) are considered to be incompressible. Based on these assumptions, Wheatly formulated a modified flow potential equation and an iterative procedure to calculate critical flow rate. Sobocinski and Cornelius (1965) developed correlations for predicting the time-dependent behavior of a water cone as it builds from the static water-oil contact to breakthrough. They noted that the previous analyses of the critical production rate disregarded the effect of time re-
quired for a cone to build up. They believed that, until the cone reached its critical height, a well could be produced, initially, at a rate higher than the critical rate. Using a laboratory, sand-packed model and a computer program for two-dimensional, two-phase, incompressible fluid flow, they examined the increase of cone height as a function of time. A correlation of dimensionless cone height versus dimensionless time was made based on the results from the physical model, computer program and dimensional analysis. Welge and Weber (1964) applied a numerical method, the alternating direction implicit procedure (ADIP), to simulate the water-coning behavior. The ADIP method was used to solve the diffusivity equation for two-phase flow in a two-dimensional grid system. Several improvements were made to increase precision of the saturation computations near the wellbore. The results were verified using the laboratory measurement data of Sobocinski and Cornelius ( 1965 ) as well as several case histories. The coning model developed in this research
1000
"0 v
=:==t ~.-.~-_.
Q) i-
0 v..
I O0
Meyer 8, Garder Schols
0
Wheat/ey Muskat
0
Spherical Solution
0
10 0.0
0.2
0.4
Penetration
27
0.6
0.8
1,0
ratio
Fig. 8. Verificationusing other models with critical production rates.
28
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 1.0
l
0.9.
0.8'
l
7= a) r-
0.7
t~ t/l a) ¢-
0.6-
0.5.
°0~ C:
j
0.4
OAC
J
B.S.
E
Sphereical
0.3
l
I
0.2 i 0.1
0.0
0
1
2
3
4
Dimensionless
5
radial
6
7
distance
Fig. 9. Verification using other models with coning profiles.
was verified using a reservoir shown in Table 1 (Case 1) (Wheatly, 1985). Because the new model considers coning only before breakthrough occurs, verification involved comparisons of critical rates and coning profiles. Also, the comparison was made only for the oil-producing perforations with the water sink flow rate set to zero because the conventional coning models do not consider water-producing perforations. The critical oil flow rates were calculated for different penetration ratios. Figure 8 presents the results together with the critical oil flow rates calculated from other methods. The plots show that the critical oil flow rates calculated from this model match Wheatley's, are lower than Muskat's, and are higher than Meyer and Gardner's. Also, as might be expected intuitively, the model does not work well for well penetration values greater than 0.8 because it disregards the perforation length (the point sink is assumed to be located at the midpoint of perforations ). Figure 9 gives a comparison of the calculated water-coning profiles. In this figure, the OWC
profile is the water-coning profile calculated using the Oil-Water Contact equation, and the BS profile is the water-coning profile calculated from the Bounding Streamline equation (Wheatley, 1985). The spherical profile is the water-coning profile calculated by using the model from this research. The comparison shows a good match between the water-coning profile of this method and of other methods.
4. Mechanism of coning control with water sink
The objective of the first part of this study was to understand coning control using segregated production and define the limitations of this method. The first question was to identify a characteristic shape of the water cone induced by the water sink production at various values of water/oil ratio. Low and high levels of oil productions were studied using the reservoir data from Table l (Case 1 ). Figure l0 shows the development of water-
A.K. Wojtanowicz et al. /Journal of Petroleum Science and Engineering 11 (1994) 21-35 OtL SINK
,o
,,.,
29
UPPER BOUNDARY
lit
" ~11111
IIIII
o~.o t i
40 ~
.E-
I1tl
~°. . . . . . . . . . . . . . ---
tO 0
..11~
Illll =
I I II1 IIIIT
:
~iiE~
t.m
,,.,
- I~~
11111 [] °w~°°'° 1ll]
-10
-~ •1
OWC
r--,
.~
1] L / " WATER
Qw=70%
k
I IT
0
" ~°°'° •
Illll
I1
1
I
Ill 10
100
1000
SINK
Radial
distance ( f t )
Fig. 10. Water-cone shapes for varying water production rates; (qo= 100 bpd).
cone profiles for varying water production rates at a constant oil production rate of 300 bbl/day. The uppermost curve represents water coning without water sink. It is evident that breakthrough has occurred, after which the only fluid produced is water. In fact, the critical oil flow rate calculated from the new model for this case is 257 bbl/day. The curves Qw = 5% (20, and Qw = 10% Qo demonstrate the dramatic effect of low production at the water sink on the height of the water cone. The cone develops a circular, flat top surface (water table) that is 20 ft in diameter and located approximately 30 ft below the oil perforations. When water production increases so that Qw = 50% Qo, the water table is lowered, and the cone becomes a ring surrounding a relatively flat central water table with the well in its center. Both the ring height and the position of the water table are adversely affected by the water rate. When the water rate reaches 70% of the oil rate, the water table caves, and the oil breaks through the water and enters the lower perforations• The
above analysis indicates the importance of two geometrical variables associated with the watercone profile: the water ring height and the stability of the central water table. Figure 11 shows a higher oil rate ( 0 0 = 5 0 0 bbl/day) where the water breakthrough occurs even when water-sink production is 100 bbl/day, i.e., 20% Qo. As expected, a higher water/oil ratio is required to begin the coning control, with the most significant suppression of the water cone for Qw/Qo=25%. Thus, coning control with a high oil production rate is still feasible. Also, the diameter of the water ring remains the same, most likely because the position of the water sink is unchanged. However, the height and shape of the water ring is affected by the higher oil rate. The water ring becomes taller, thus indicating that some limiting value of oil production can be expected. This value would build the water ring so tall that the oil perforation would be surrounded by a water "levee" located 20 ft from and around the well. Therefore, it is postulated
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
30
01!
,o
"
'°
A
Upper boundary
sink
.E
TIIIIT llllil IIIIII •I IIII
TTTII'~ IIIII ~ IIIII i IIIII \
I l llIll o o.=,ooo,o ; --.~.=,~o,,o. ,.=~ooo,o . ~..~o,,o
UI r-
C
~0
tO 0
,o
IIIIII IIIIII - ,,,,,~ IIIII
IIY " ,~i ~II .~"'~ .~ IIIIV,t _~ ~I/i 7 ~k.
!
0
0. . . . . . . . . . . . . . . . . . .
-I0
r• i
]iiill
i;~,
IIII11
Water sink
~i}
......
! IIII '
~-
I0
I
Radial
distance
i
I00
I000
(ft)
Fig. 11. Limited range of the water-cone control for large oil production rate (qo= 500 bpd).
that when water sink control is used, the conventional concept of critical oil production, with water breaking into the oil perforations, may be inadequate. To substantiate the above predicament, the conventional critical oil flow rates were calculated and are shown in Fig. 12 as a function of the water/oil production ratio, Qw/Qo, and water-sink position, hw. The first observation is that, as intuitively expected, there is no critical oil production rate with this method because the water table is entirely controlled by the sink. However, the actual maximum oil rate exists and can be derived from stability conditions of the water cone, as illustrated in Figs. 13 and 14 and further discussed in the next section. Another interesting observation from Fig. 12 is that the water breakthrough can be avoided with relatively low values of water/oil production ratios, which tend to approach asympotically the values ranging from 0.27 to 0.85. This means, that for this method, values of the pro-
duction rate ratio that are smaller than one can be expected. The position of the water sink, hw, below the static OWC, strongly affects the amount of produced water. Figure 12 shows that lowering the water sink by 20 ft, i.e., increasing hw from 5 ft to 25 ft, results in a three-fold increase of water production while the oil production rate remains constant.
4.1. Maximum oil production rate The next step of this research was to define physical criteria which would limit the oil production rate. Stability of the controlled water cone appeared to be the criterion. Several simulated scenarios showed that as oil production increased, the position of the water table became more unstable• In other words, the controlled water cone became very sensitive to changes in the water/oil production rates as Fig. 13 shows in its correlation between the water table position and water sink production for various oil
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering I1 (1994) 21-35
/
2000
t~ "0 .0 ..0
1600 ....
t~ 1200 0 <,... 0 0 P,.
800
--
/ '
J
/
/
//
/// 7!
!
0
f"
,-
hw.s,, hw=-lO ft
400
hw=- 15 f!
0 •
hw=-20 f!
•
hw=-25 ft
0 0.0
0,2
0.4
Qw/Qo
0,6
0.8
(water-oil production ratio)
Fig. 12. Critical oil production rate versus water/oil ratio and water sink depth.
30 . . . . . . . . . .
0 t-,
•
Qo=lO0 b/d
•
Qo=200 b/d
•
Qo=300 b/d
•
Qo=400 b/d
•
Qo=500 b/d
•
Qo=600 b/el
•
Qo=800 b/d
A
Qo=IO00 b/d
O' o l w
-10, 0.0
0.5
Ow/Oo (water-oil
1.5
1.0
production
ratio)
Fig. 13. Response of water cone (water table height, hwo) to water production rate.
31
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
32
Upper boundary
011 s i n k
,0
':::: ....
A
/TTIIIIT
'11III/ \IIr_
J'llJJ
n
! "
Qw=300 b/d
•
Ow=400 b/d
•
Qw=500 b/d
•
Qw=600 b/d
•
Qw=700 b/d
30 OJ r.
I [ll|l II . .
,
I
et-
.
.
IIII1/ ..........
.
I Illl
20
l
lO j¢-, i'L
...............
-10
. .....
I[11
IIIili ¢
O 0
0 . . . .
I [ 1 1
i
t
II111 /
k
IIIIl& / i
II +T/,r
OWC F
[.
"" • !
Water
slnk
1
tO0
10
Radial
distance
Fig. 14. w a t e r c o n e instability m e c h a n i s m - -
production rates. For a low oil production rate (100 bbl/day), the water table is stable and insensitive to small changes in the water rate. For a high oil production rate (1000 bbl/day), the water sink has to produce 360 bbl/day to control the water table at 20 ft below the oil perforations. However, there is no stability in this control because a small decrease in water production (360 bbl/day to 330 bbl/day) would cause an instantaneous water breakthrough. Moreover, an increase in water production (360 bbl/day to 430 bbl/day) would create a "flip-flop" condition, i.e., the oil would break through into the water perforations. The second criterion for maximum oil production rate is the position (height) of the watercone ring. As Fig. 14 shows, when oil is produced at 1000 bbl/day, no coning control is possible at all. For low production of the water sink (below 500 bbl/day), the water-cone ring reaches the upper boundary, thus preventing any inflow of oil to the well. On the other hand, the increase of water production from 500 bbl/day to 600 bbl/
I000
(ft)
e x c e s s i v e oil rate ( 1000 b b l / d a y ) .
day brings the water ring down but simultaneously causes the oil to break through into the water sink. Therefore, proper design of segregated production systems should consider two effects: ( 1 ) sensitivity of the water table to fluctuations in water production, and (2) restricted inflow performance caused by the water ring.
5. Simulated performance of an actual well
The water coning control model was applied to a field case. Table 1 (Case 2) (Welge and Weber, 1964 ) lists the field reservoir data. The production history shows that the initial oil production rate was 50 bbl/day. After 315 days of production, the oil production rate was increased to 80 bbl/day, and water breakthrough occurred at the same time. The oil production rate was then reduced to 65 bbl/day and 45 bbl/ day, but the coning was neither eliminated nor reduced. After 3000 days of production, the total oil produced was 136 Mbbl and the total water
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
33
Table 2 Comparison of well performance with and without water sink Water sink depth below static OWC (It)
Oil production rate
Water production rate
Water ring height
(bbl/day)
(bbl/day)
(ft)
Water table distance from oil perforations (ft)
No watersink 10 15 20
68 80 80 80
68 34 48 50
19 6.5 5
25 50 45
353025v
20-
Z15¢t~ ¢-
!0-
¢-
5-
0 eo
OWC
0-5-
-IO -15
-
-20
I
WATER SINK
1
10
Radial
distance
100
I000
(ft)
Fig. 15. Optimum control of water cone - - field example.
produced was also 136 Mbbl. Therefore, the average oil and water production rates during the production period were 68 bbl/day. First, let us explain why water breakthrough happened and could not be eliminated. Based on the reservoir data, the critical oil flow rate calculated using the new model is 21.6 bbl/day. This means that, from the start of production, the oil production rate was above its critical value. However, because the water breakthrough coincided with the production increase to 80 bbl/day,
it may seem that this production increase caused the water breakthrough, when, in fact, it did not. For this case, the water breakthrough time, calculated using Sobocinski's model (Sobocinski and Cornelius, 1965 ), was 387 days for an oil production rate of 50 bbl/day and 191 days for an oil production rate of 80 bbl/day. This means that after 315 days of oil production at a rate of 50 bbl/day the slowly developing water cone almost reached the oil perforations. At this point, the oil production rate was increased to 80
34
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
bbl/day, and the water breakthrough occurred immediately, The water sink model was used to simulate segregated production in this reservoir with the maximum oil production rate set at 80 bbl/day, This rate was determined through several simulation runs using various rates of oil and water, At this rate, the water cones were stable with minimum restriction of the inflow performance. Table 2 shows a comparison of the simulated coning control for various positions of water sink. The optimal production rates of water sink are 34 bbl/day, 48 bbl/day and 50 bbl/day for the water sink positions at 10 ft, 15 ft and 20 ft below the original OWC, respectively. The water cone's geometries are documented in Table 2 and Fig. 15. Also included in Fig. 15 is the water-coning profile at the critical oil flow rate (21.6 bbl/day ) without water sink. At this rate, the water breakthrough would not have occurred, but production would have been very limited compared to the oil production rate of 80 bbl/day. The advantage of using water sink is evident. With the water sink, higher oil production and lower water production can be obtained. Another important advantage of this method is that the shape of the water cone can be flattened in the vicinity of producing perforations at the late stage of a well's production with OWC approaching the perforations. Such a control would result in the recovery of additional oil residing above OWC.
Nomenclature
c
g h hw ho
k,k~,kh P Pb
Q~ Qo
compressibility ( 1/atm ) gravity acceleration (cm3/s 2) thickness (cm) water sink distance from OWC (ft) height of water cone's "table" (ft) permeability, spherical, vertical, horizontal (D) pressure (atm) formation pressure at OWC (arm) water production rate (bbl/day) oil production rate (bbl/day)
qo r rD rDo
rDSz rDe rw Rw t tD z y Pw /~ /to
Ap
laboratory oil pumping rate (cm3/s) radius (cm) dimensionless radius dimensionless distance to real sink dimensionless distance to image sink dimensionless reservoir radius wellbore radius (cm) dimensionless ratio of gravity force to viscous force time (s) dimensionless time vertical distance between any point in the reservoir and oil sink (cm) water-cone height at any point of water coning profile (cm) water density (g/cm 3) viscosity (cP) oil viscosity (cP) difference of water/oil densities (g/cm 3)
~ ~t~
porosity (fraction) flow potential (atm) initial formation flow potential (atm) dimensionless flow potential
6. Conclusions
As evidenced in this study, the method of segregated production has the advantages of increasing the oil production rate, decreasing the water production rate and improving oil recovery. However, these good results must be treated with caution due to the limitations of the mathematical simulation method used. The most important limitations are: ( 1 ) the inability of this model to simulate the oil and water production after the water breakthrough; and (2) a lack of analytical representation of the oil/water transition zone and related effects of water saturation changes. References Abels, H.P., 1990. A laboratory study of water coning in horizontal wells. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Alikhan, A.A. and Faroug, S.M., 1985. State-of-the-art water
A.K. Wojtanowicz et aL / Journal of Petroleum Science and Engineering 11 (1994) 21-35 coning modelling. SPE 13744, 4th Middle East Oil Show of SPE, Bahrain, March 11-14. Bourgeois, E.A., 1989. The evaluation of horizontal well completion for recovery of bypassed oil in a South Louisiana bottom water drive reservoir. M.S. thesis, Louisiana State Univ., Baton Rouge, La. Chatas A.T., 1966. Unsteady spherical flow in petroleum reservoirs. Soc. Pet. Eng. J., (June): 102-114. Cooke, M.S., 1989. A reservoir engineering and coning study of shallow oil sand in the Lafitte Field of Jefferson Parish, Louisiana. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Hebert, L.E., 1990. An experimental study of the effects of water coning in a horizontal well in bottom water drive reservoir. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Khan, A.R., 1970. A scaled-model study of water coning. J. Pet. Technol., (June): 771-776. Meyer, H.I. and Gardner, A.O., 1954. Mechanism of two immiscible fluids in porous media. J. Appl. Phys., 25 (11 ): 1400-1406.
35
Mungan, N., 1975. A theoretical and experimental coning study. Soc. Pet. Eng. J., (June): 247-254. Muskat, M., 1949. Physical Principles of Oil Production. McGraw-Hill, New York, N.Y., pp. 345-355. Muskat, M. and Wyckoff, R.D., 1935. An approximate theory of water coning in oil production. Trans. AIME, pp. 144-163. Schols, R.S.: 1972. An empirical formula for the critical oil production rate. Erdoel Erdgas Z., 88( 1 ): 6-11. Sobocinski, D. and Cornelius, A., 1965. A correlation for predicting water coning time. J. Pet. Technol., (May): 594-600. Soengkowo, I., 1969. Model studies of water coning in petroleum reservoirs with natural water drives. Ph.D. diss., Univ. Texas at Austin, Austin, Tex. Welge, H.J. and Weber, A.G., 1964. Use of two-dimensional methods for calculating well coning behavior. Soc. Pet. Eng. J., (Dec.): 345-355. Wheatley, M.J., 1985. An approximate theory of oil/water coning. SPE 14210.
ELSEVIER
Journal of Petroleum Science and Engineering 11 ( 1994) 21-35
PETROLEUM SCIENCE & ENGINEERING
Segregated production method for oil wells with active water coning A n d r e w K. W o j t a n o w i c z , H u i X u , Z a k i B a s s i o u n i Department of Petroleum Engineering, Agricultural Mechanical College, Louisiana State University, Baton Rouge, LA 70803-6417, USA (Received March 15, 1993; revised version accepted August 31, 1993)
Abstract This paper describes a simulation study of a novel method to control water coning in an oil producing well. The method uses a dual-completion configuration that is above and below OWC. In this configuration, the well section above OWC is completed in the oil zone and produces oil, while the well section completed below OWC in the water-saturated zone produces water both independently of and concurrently with oil production. Segregated water production creates a drain (rat hole water sink) to control the rise of the water cone. Coning control results from the effect of water sink on flow potential between the sink and oil-producing perforations. The study investigated simulated production performance of the well both with and without the rat hole water sink. At first, the water sink's position and flow rate were examined to determine the critical production rate of oil (i.e., maximum production rate without the water breakthrough). Next, the various amounts of water produced during oil production at rates greater than critical were compared. The comparison study used both lab data and field data from an actual well/reservoir system of known geometry and reservoir properties. The coning behavior of the production system with the rat hole water sink was mathematically modelled using the flow potential distribution generated by two constant-terminal-rate sinks located between the two linear boundaries and the constant-pressure outer radial boundary. The model was verified by using the existing and simulated data of water coning in conventional wells and by setting the water sink flow rate at zero, with oil being the only produced fluid. Also, verification tests were used to select the type of oil reservoir with the thick oil zone and the small dip angle for the comparison studies. The study demonstrates the existence of an active mechanism to control water coning with the rat hole water sink. It shows that a sink with low water flow rate may prevent the water cone from breaking through the oil zone and into the producing perforations so that the oil with no water cut can be produced above the critical flow rate. A simulation using the new method yielded less produced water and either the same or a higher oil rate than the conventional method. However, potential increase of oil production above its critical value is limited by the stability of the controlled water cone. Also, for high oil production rates, more precision is needed to control the water production rate.
1. Introduction
For years, water coning has been considered a
productivity problem that reduces daily oil production and leads to early a b a n d o n m e n t o f wells. Recently, environmental regulations added a new c o m p o n e n t to this problem, cost o f cleanup and
0920-4105/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0920-4105 (93 ) E0068-Z
22
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
disposal of produced water contaminated by oil during the production process. Parameters affecting water coning in vertical wells are: mobility ratio, oil zone thickness, ratio of gravity forces to viscous forces, well spacing, ratio of horizontal permeability to vertical permeability, well penetration and production rate. Although water coning is well known, its control is limited because only the latter four (out of seven) coning variables can be controlled. The mobility ratio effect on water coning was studied using scaled laboratory models (Soengkowo, 1969). Studies with a radial model (Soengkowo, 1969 ) showed that the mobility ratio inversely affects production performance. Studies with another three-dimensional model revealed that mobility ratio values greater than one engendered the worst coning effects (Khan, 1970): the higher the mobility ratio was, the faster the breakthrough occurred. The study showed that when the mobility ratio is greater than one, water coning develops quickly and the water cut increases rapidly. As production continued, the cone expanded in all directions and lowered oil production to within a few percent of its initial value. When the mobility ratio was less than one, the water cone first expanded outwards radially, and then it gradually rose towards the well. The changes in the water cut values were gradual and were spread over a long period of production. The pay-zone thickness affects water coning in relation to the water zone size. Studies show that as the ratio of water to oil zone thickness increases, coning severity also increases while other parameters remain unchanged (Khan, 1970.). Consequently, a serious coning problem might be expected at the end of production when most of the pay zone has been invaded by water. The third uncontrollable coning variable, the ratio of gravity force to viscous force, is a fundamental factor of the coning phenomenon because it determines when viscous force, which is induced by fluid flow, will overcome gravitational force, which is induced by the differences in fluid densities. In the laboratory experiments with the pie-shaped, radial model (Mungan,
1975), the ratio of gravity to viscous force was calculated as:
R~-
gApAkh
(1)
qoPo
where: Rgv = the ratio of gravity to viscous force; g = acceleration of gravity; Ap=density difference; A = model area; kh = horizontal permeability; qo = oil pumping rate; and/~o = oil viscosity. Figure 1 shows the increase in water cut caused by water coning during oil production. The results indicate that water coning is reduced at high values of Rgv. The first variable of water coning that can be controlled is well spacing. Its effect on water coning is also shown in Fig. 1. The figure clearly indicates that water coning can be dramatically reduced by drilling more wells at a closer spacing. However, the economics of such control is highly questionable. The other potentially controllable variable is the ratio of vertical to horizontal permeability. Figure 2 shows that a reduction of this ratio also reduces coning. Such an effect was observed in the Middle East at a large oil reservoir (Alikhan and Faroug, 1985) where a tar barrier ("tar mat" ) was present between oil and water zones. Technically, the permeability can be affected by fracturing the formation. However, the method is limited to shallow wells because in deep-well fracturing the improvement of vertical permeability is more likely to occur than that of horizontal permeability. o.5
i ~=
o
.~ 0.3
-4
<
g , ~
0.1 0
5
10 15 OIL RECOVERY, % of PV
20
~0
25
R~v- 19.1
Fig. 1. Effects of the gravity/viscous force ratio, R~v, and well spacing on water coning (Mungan, 1975).
23
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 PRODUCTION RATE, bbl 0.025 0.05
0.5 =2
1
02
0.4 t ..........
O
i ~ J 'l ~ / ~ o.3
.
.
.
.
01
002
10
+
: ...........
+ ...............
.....
Y
i
.
.
.
.
.
.
.
.
.
.
.
.
0.75 i
_ _
0.1
"1(5 O DE: I
.
F-
............
10 15 OIL RECOVERY,% of PV
20 0.25 0'.5 0.'75 WELL PENETRATION/ OIL ZONE THICKNESS
Fig. 2. Effect of the vertical/horizontal permeability ratio on water coning. 0
i
m c3 LU"
~...............
_J
i
/ day
Fig. 3. Effect of well penetration and oil production rate on water coning (Mungan, 1975).
800 700 600
o
500
0
o
300
"o 0 =.
200
-~
lOO
ID
'6:]
'65
'67
'69
'71
'73
'75
~
'79
'81
'83
°85
'87
Year Fig. 4. Production history o f o i l and water from the North Reservoir in the Lafitte field of Jefferson Parish, Louisiana (Cooke, 1989).
Well penetration can be controlled through completion practices. Early studies using an electrical model (Muskat, 1949) showed that coning would increase with increased well penetration. Also, in scale model studies (Mungan, 1975 ), a strong dependence of coning upon well penetration was shown as a relationship between the water breakthrough time and the fraction of the pay zone penetrated by a well. When the well penetration reached 75% of the oil zone thickness, the water breakthrough occurred almost instantly. To minimize coning, well penetration
should be minimum. Such a completion will certainly maximize oil recovery, but it will also minimize well productivity. Theoretically, the well completion design under conditions of water coning can be viewed as an optimization problem. Also, some recent studies show that horizontal completions in the top of an oil zone may prevent water coning, increase production rates, and improve oil recovery (Bourgeois, 1989; Abels, 1990). Oil production rate is easy to control. Its strong effect on coning has been proven in laboratory
24
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
studies (Fig. 3 ) and in oil field practices (Fig. 4) (Cooke, 1989). Figure 4 shows the annual production plots for oil and water from a shallow oil-bearing sand in the Lafitte field of Jefferson Parish, Louisiana. A steady increase of water production is evident and results from water encroachment and coning. More characteristic, however, are the drastic changes of water production caused by relatively small changes in oil production. It is clear from these plots that the two- to five-fold increase of water production resulted from the two-fold increase in oil production during 1971, 1979 and 1986. Control of water coning requires reduction of the oil production rate below the value of the critical rate. (Predictive models to calculate this rate have been recently reviewed in Abels (1990) and Hebert (1990). ) In many cases, however, it is not economical to keep the oil production rate below its critical value (Chatas, 1966). Moreover, once the breakthrough occurs, it may be difficult to return to the initial low value of water cut, even at the reduced oil rate, due to the irreversible change of the mobility ratio caused by the imbibition/drainage effects upon the relative permeabilities. The above analysis indicates that the theoretically available methods to control water coning have very limited practical applications. Hence, there is a need for innovations.
2. Segregated production method Figure 5 shows the principle of the segregated production method. The well is dual completed so that the lower perforations are placed in the water zone, and water can be produced both concurrently with and independently of oil production. These two producing streams are separated by a packer to prevent water from mixing with oil. Coning control is performed by adjusting the water production rate to the oil production rate so that the water cone does not break through the oil and enter the oil perforations. Physically, the water sink (water perforations) alters the flow potential field around the well so that the water cone is suppressed. Flow into the water sink gen-
WATER PRODUCTION OIL ~--~ PRODUCTION--
I . . , •
!
1 Qw 0 ~ ~ . I/--~ ..,...~ ~
.//
Ow > 0 TAIL PIPE ~ WATER SINK
!
!
OIL ZONE OIL ~--.~,~PERFORATIOt~ ~ ,,~ OWC
"-
WATER ZONE ~ WATER PERFORATIONS
Fig. 5. Principle of coning control using segregated production.
erates a downward viscous force which reduces the upward viscous force that is generated by the flow into the upper (oil) perforations. At equilibrium, a stable water cone is "held down" around and below the oil-producing perforations. The segregated production method has several potential advantages listed below. ( 1 ) The oil production rate increases without water breakthrough. (2) The well life extends beyond its value without coning control. (3) The oil recovery per well (and for the whole reservoir) increases due to the following mechanisms: (A) production can be continued with high levels of static OWC (caused by the bottom water-drive invasion), even when this level reaches the oil perforations, and (B) well productivity remains high because the near-well zone permeability to oil is not reduced by water encroachment. (4) Because produced water is not contaminated with crude oil, demulsifiers, or other agents used in oil production, the method is more likely to meet effluent discharge limitations set by the environmental regulations in the area. (5) The water cut of the produced oil is minimum. The purpose of this study is to evaluate the coning control potential of this method as well as to compare its performance to the conven-
A.K. Wojtanowiczet al. I Journal of Petroleum Science and Engineering 11 (1994)21-35
tional method of oil production under the conditions of bottom water drive. Mathematical simulation is used to predict the method's performance.
The mathematical model is used under the assumption that for any fixed production rate or bottom-hole pressure, with the water lying statically at the lower boundary of the oil zone, the pressure at the water-oil interface p(r,z) will satisfy the equation:
p(r,z)+po~g(h-z)=p(r,z)+po~gy=~
Well
Pb
II/I/I/II/III/
z
_
~
///I//
_
2 0q~ ~#c 0q~ q,r~ + r Or - k Ot
02~)
(3)
ro -
r
(4a)
rw
kt 4nkrw tD=ollcr2w, and q~D= Oo-~-(~i-q~)
(4b,c)
For steady-state conditions, the flow potential is:
(2)
where Pb is the formation pressure at the bottom of the oil zone at a point remote from the well, and po is the density of water. These assumptions, based on Muskat's theory (Muskat, 1949), stem from the reasons that water, being of greater density than oil, will, under static conditions, remain at the bottom of oil producing section. Therefore, its rise, as Fig. 6 shows, represents a dynamic effect in which the upward-directed pressure gradients associated with the oil flow are able to balance the hydrostatic head of the elevated water column. When the perforated sections of a well are short, their productions can be treated approximately as point sources. In this case, the spherical solution of the flow potential is a good ap-
I
proximation. The one-dimensional equation of the flow potential in spherical coordinates is:
To solve this differential equation, the following dimensionless parameters are defined:
3. Mathematical model of water sink
h
25
5
I
t Z
Fig. 6. Water coning model coordinates and nomenclature.
~D (rD,tD) -- rDe -- rD rDerD
(5)
The method of images can extend the above solutions to the finite-thickness reservoir. Figure 7A shows the method of images applied to a single zone. For this case, the steady-state flow potential is expressed as: ~)D(rD,tD)-- rDe-rDO 4- ~ rDerDo
~ rDe--rDji
i=l j=l
(6)
rDerDji
Calculation of the flow-potential distribution for a single zone using Eq. 6 is straight forward. For the double-zone system of oil underlain by water, and with two production sinks, the flow potential at a point of interest is superimposed from both sinks. Figure 7B shows the nomenclature for this case. The calculation procedure ineludes two basic steps: ( 1 ) Check whether the coning liquid is oil or water by separately calculating the flow potential at OWC induced by each sink; and (2) Calculate the coning profile using superposition of Eq. 6 and the iteration procedures until Eq. 2 is satisfied. The effect of vertical and horizontal permeabilities is implied in the definition of spherical permeability (Chatas, 1966) used in the model as:
3khkv
k - k h +2k~.
(7)
26
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 I
I I I I I
2ht lhlo h,
uO 9odnddar,/
h2o ~h]i~
lower boundary
dr~,~) qw
h2w
h2
Zh,
I I I I I
"B
A
Fig. 7. Flow potential model using method of images. (A) Single zone with one sink; (B) dual zone system (oil/water) with two sinks.
3.1. Model verification A literature search was conducted for a select number of established water coning models for comparison with the new model. A short deTable 1 Reservoir data for calculation examples Case 1
Case 2
Formation thickness (It) Oil zone thickness (ft) Oil perforation position
100 50 Top ofoil zone
Horizontalpermeability (mD) Vertical permeability (mD) Oil viscosity (cP) Oil density (g/cm 3) Water density (g/cm 3) Wellbore radius (It) Reservoir radius (ft)
1000 500 1 0.7 1 0.25 500
120 70 0-50 ft from the top 236 125 2.4 0.812 1.15 0.25 1300
scription of the selected models follows. A simple analytical model by Muskat (1949) describes water coning in a homogeneous system with a constant mobility ratio and an isopotential at initial OWC. Muskat used the model, together with his graphical method (Muskat and Wyckoff, 1935), to predict equilibrium conditions of water coning. Also, he correlated critical flow rates with well penetration for various oil zone thicknesses. Schols (1972) developed an empirical formula using a Hele-Show model to calculate the critical oil production rate. Meyer and Gardner (1954) presented a radial flow of oil under its own hydrostatic head. Both Schols' and MeyerGardner's methods provided the formulas for critical oil flow rate as a function of density differential, well penetration, oil-zone thickness, oil viscosity and permeability, and drainage area. Wheatley (1985) simulated oil/water coning using an approximate analytical technique. The
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
underlying assumptions were as follows: ( 1 ) oil partially flows into the well in the presence of underlying water; (2) the reservoir is homogeneous and bounded above by a horizontal impermeable barrier extending to a distance (drainage radius ) from the well; ( 3 ) the flow region is bounded below by the oil-water contact, which forms an upward cone near the well in response to the reduced pressure; (4) the flow of oil in the drainage area is assumed to be steady and radially symmetric; ( 5 ) the underlying water is stationary and entirely segregated from the oil; and (6) the fluids (oil and water) are considered to be incompressible. Based on these assumptions, Wheatly formulated a modified flow potential equation and an iterative procedure to calculate critical flow rate. Sobocinski and Cornelius (1965) developed correlations for predicting the time-dependent behavior of a water cone as it builds from the static water-oil contact to breakthrough. They noted that the previous analyses of the critical production rate disregarded the effect of time re-
quired for a cone to build up. They believed that, until the cone reached its critical height, a well could be produced, initially, at a rate higher than the critical rate. Using a laboratory, sand-packed model and a computer program for two-dimensional, two-phase, incompressible fluid flow, they examined the increase of cone height as a function of time. A correlation of dimensionless cone height versus dimensionless time was made based on the results from the physical model, computer program and dimensional analysis. Welge and Weber (1964) applied a numerical method, the alternating direction implicit procedure (ADIP), to simulate the water-coning behavior. The ADIP method was used to solve the diffusivity equation for two-phase flow in a two-dimensional grid system. Several improvements were made to increase precision of the saturation computations near the wellbore. The results were verified using the laboratory measurement data of Sobocinski and Cornelius ( 1965 ) as well as several case histories. The coning model developed in this research
1000
"0 v
=:==t ~.-.~-_.
Q) i-
0 v..
I O0
Meyer 8, Garder Schols
0
Wheat/ey Muskat
0
Spherical Solution
0
10 0.0
0.2
0.4
Penetration
27
0.6
0.8
1,0
ratio
Fig. 8. Verificationusing other models with critical production rates.
28
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35 1.0
l
0.9.
0.8'
l
7= a) r-
0.7
t~ t/l a) ¢-
0.6-
0.5.
°0~ C:
j
0.4
OAC
J
B.S.
E
Sphereical
0.3
l
I
0.2 i 0.1
0.0
0
1
2
3
4
Dimensionless
5
radial
6
7
distance
Fig. 9. Verification using other models with coning profiles.
was verified using a reservoir shown in Table 1 (Case 1) (Wheatly, 1985). Because the new model considers coning only before breakthrough occurs, verification involved comparisons of critical rates and coning profiles. Also, the comparison was made only for the oil-producing perforations with the water sink flow rate set to zero because the conventional coning models do not consider water-producing perforations. The critical oil flow rates were calculated for different penetration ratios. Figure 8 presents the results together with the critical oil flow rates calculated from other methods. The plots show that the critical oil flow rates calculated from this model match Wheatley's, are lower than Muskat's, and are higher than Meyer and Gardner's. Also, as might be expected intuitively, the model does not work well for well penetration values greater than 0.8 because it disregards the perforation length (the point sink is assumed to be located at the midpoint of perforations ). Figure 9 gives a comparison of the calculated water-coning profiles. In this figure, the OWC
profile is the water-coning profile calculated using the Oil-Water Contact equation, and the BS profile is the water-coning profile calculated from the Bounding Streamline equation (Wheatley, 1985). The spherical profile is the water-coning profile calculated by using the model from this research. The comparison shows a good match between the water-coning profile of this method and of other methods.
4. Mechanism of coning control with water sink
The objective of the first part of this study was to understand coning control using segregated production and define the limitations of this method. The first question was to identify a characteristic shape of the water cone induced by the water sink production at various values of water/oil ratio. Low and high levels of oil productions were studied using the reservoir data from Table l (Case 1 ). Figure l0 shows the development of water-
A.K. Wojtanowicz et al. /Journal of Petroleum Science and Engineering 11 (1994) 21-35 OtL SINK
,o
,,.,
29
UPPER BOUNDARY
lit
" ~11111
IIIII
o~.o t i
40 ~
.E-
I1tl
~°. . . . . . . . . . . . . . ---
tO 0
..11~
Illll =
I I II1 IIIIT
:
~iiE~
t.m
,,.,
- I~~
11111 [] °w~°°'° 1ll]
-10
-~ •1
OWC
r--,
.~
1] L / " WATER
Qw=70%
k
I IT
0
" ~°°'° •
Illll
I1
1
I
Ill 10
100
1000
SINK
Radial
distance ( f t )
Fig. 10. Water-cone shapes for varying water production rates; (qo= 100 bpd).
cone profiles for varying water production rates at a constant oil production rate of 300 bbl/day. The uppermost curve represents water coning without water sink. It is evident that breakthrough has occurred, after which the only fluid produced is water. In fact, the critical oil flow rate calculated from the new model for this case is 257 bbl/day. The curves Qw = 5% (20, and Qw = 10% Qo demonstrate the dramatic effect of low production at the water sink on the height of the water cone. The cone develops a circular, flat top surface (water table) that is 20 ft in diameter and located approximately 30 ft below the oil perforations. When water production increases so that Qw = 50% Qo, the water table is lowered, and the cone becomes a ring surrounding a relatively flat central water table with the well in its center. Both the ring height and the position of the water table are adversely affected by the water rate. When the water rate reaches 70% of the oil rate, the water table caves, and the oil breaks through the water and enters the lower perforations• The
above analysis indicates the importance of two geometrical variables associated with the watercone profile: the water ring height and the stability of the central water table. Figure 11 shows a higher oil rate ( 0 0 = 5 0 0 bbl/day) where the water breakthrough occurs even when water-sink production is 100 bbl/day, i.e., 20% Qo. As expected, a higher water/oil ratio is required to begin the coning control, with the most significant suppression of the water cone for Qw/Qo=25%. Thus, coning control with a high oil production rate is still feasible. Also, the diameter of the water ring remains the same, most likely because the position of the water sink is unchanged. However, the height and shape of the water ring is affected by the higher oil rate. The water ring becomes taller, thus indicating that some limiting value of oil production can be expected. This value would build the water ring so tall that the oil perforation would be surrounded by a water "levee" located 20 ft from and around the well. Therefore, it is postulated
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
30
01!
,o
"
'°
A
Upper boundary
sink
.E
TIIIIT llllil IIIIII •I IIII
TTTII'~ IIIII ~ IIIII i IIIII \
I l llIll o o.=,ooo,o ; --.~.=,~o,,o. ,.=~ooo,o . ~..~o,,o
UI r-
C
~0
tO 0
,o
IIIIII IIIIII - ,,,,,~ IIIII
IIY " ,~i ~II .~"'~ .~ IIIIV,t _~ ~I/i 7 ~k.
!
0
0. . . . . . . . . . . . . . . . . . .
-I0
r• i
]iiill
i;~,
IIII11
Water sink
~i}
......
! IIII '
~-
I0
I
Radial
distance
i
I00
I000
(ft)
Fig. 11. Limited range of the water-cone control for large oil production rate (qo= 500 bpd).
that when water sink control is used, the conventional concept of critical oil production, with water breaking into the oil perforations, may be inadequate. To substantiate the above predicament, the conventional critical oil flow rates were calculated and are shown in Fig. 12 as a function of the water/oil production ratio, Qw/Qo, and water-sink position, hw. The first observation is that, as intuitively expected, there is no critical oil production rate with this method because the water table is entirely controlled by the sink. However, the actual maximum oil rate exists and can be derived from stability conditions of the water cone, as illustrated in Figs. 13 and 14 and further discussed in the next section. Another interesting observation from Fig. 12 is that the water breakthrough can be avoided with relatively low values of water/oil production ratios, which tend to approach asympotically the values ranging from 0.27 to 0.85. This means, that for this method, values of the pro-
duction rate ratio that are smaller than one can be expected. The position of the water sink, hw, below the static OWC, strongly affects the amount of produced water. Figure 12 shows that lowering the water sink by 20 ft, i.e., increasing hw from 5 ft to 25 ft, results in a three-fold increase of water production while the oil production rate remains constant.
4.1. Maximum oil production rate The next step of this research was to define physical criteria which would limit the oil production rate. Stability of the controlled water cone appeared to be the criterion. Several simulated scenarios showed that as oil production increased, the position of the water table became more unstable• In other words, the controlled water cone became very sensitive to changes in the water/oil production rates as Fig. 13 shows in its correlation between the water table position and water sink production for various oil
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering I1 (1994) 21-35
/
2000
t~ "0 .0 ..0
1600 ....
t~ 1200 0 <,... 0 0 P,.
800
--
/ '
J
/
/
//
/// 7!
!
0
f"
,-
hw.s,, hw=-lO ft
400
hw=- 15 f!
0 •
hw=-20 f!
•
hw=-25 ft
0 0.0
0,2
0.4
Qw/Qo
0,6
0.8
(water-oil production ratio)
Fig. 12. Critical oil production rate versus water/oil ratio and water sink depth.
30 . . . . . . . . . .
0 t-,
•
Qo=lO0 b/d
•
Qo=200 b/d
•
Qo=300 b/d
•
Qo=400 b/d
•
Qo=500 b/d
•
Qo=600 b/el
•
Qo=800 b/d
A
Qo=IO00 b/d
O' o l w
-10, 0.0
0.5
Ow/Oo (water-oil
1.5
1.0
production
ratio)
Fig. 13. Response of water cone (water table height, hwo) to water production rate.
31
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
32
Upper boundary
011 s i n k
,0
':::: ....
A
/TTIIIIT
'11III/ \IIr_
J'llJJ
n
! "
Qw=300 b/d
•
Ow=400 b/d
•
Qw=500 b/d
•
Qw=600 b/d
•
Qw=700 b/d
30 OJ r.
I [ll|l II . .
,
I
et-
.
.
IIII1/ ..........
.
I Illl
20
l
lO j¢-, i'L
...............
-10
. .....
I[11
IIIili ¢
O 0
0 . . . .
I [ 1 1
i
t
II111 /
k
IIIIl& / i
II +T/,r
OWC F
[.
"" • !
Water
slnk
1
tO0
10
Radial
distance
Fig. 14. w a t e r c o n e instability m e c h a n i s m - -
production rates. For a low oil production rate (100 bbl/day), the water table is stable and insensitive to small changes in the water rate. For a high oil production rate (1000 bbl/day), the water sink has to produce 360 bbl/day to control the water table at 20 ft below the oil perforations. However, there is no stability in this control because a small decrease in water production (360 bbl/day to 330 bbl/day) would cause an instantaneous water breakthrough. Moreover, an increase in water production (360 bbl/day to 430 bbl/day) would create a "flip-flop" condition, i.e., the oil would break through into the water perforations. The second criterion for maximum oil production rate is the position (height) of the watercone ring. As Fig. 14 shows, when oil is produced at 1000 bbl/day, no coning control is possible at all. For low production of the water sink (below 500 bbl/day), the water-cone ring reaches the upper boundary, thus preventing any inflow of oil to the well. On the other hand, the increase of water production from 500 bbl/day to 600 bbl/
I000
(ft)
e x c e s s i v e oil rate ( 1000 b b l / d a y ) .
day brings the water ring down but simultaneously causes the oil to break through into the water sink. Therefore, proper design of segregated production systems should consider two effects: ( 1 ) sensitivity of the water table to fluctuations in water production, and (2) restricted inflow performance caused by the water ring.
5. Simulated performance of an actual well
The water coning control model was applied to a field case. Table 1 (Case 2) (Welge and Weber, 1964 ) lists the field reservoir data. The production history shows that the initial oil production rate was 50 bbl/day. After 315 days of production, the oil production rate was increased to 80 bbl/day, and water breakthrough occurred at the same time. The oil production rate was then reduced to 65 bbl/day and 45 bbl/ day, but the coning was neither eliminated nor reduced. After 3000 days of production, the total oil produced was 136 Mbbl and the total water
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
33
Table 2 Comparison of well performance with and without water sink Water sink depth below static OWC (It)
Oil production rate
Water production rate
Water ring height
(bbl/day)
(bbl/day)
(ft)
Water table distance from oil perforations (ft)
No watersink 10 15 20
68 80 80 80
68 34 48 50
19 6.5 5
25 50 45
353025v
20-
Z15¢t~ ¢-
!0-
¢-
5-
0 eo
OWC
0-5-
-IO -15
-
-20
I
WATER SINK
1
10
Radial
distance
100
I000
(ft)
Fig. 15. Optimum control of water cone - - field example.
produced was also 136 Mbbl. Therefore, the average oil and water production rates during the production period were 68 bbl/day. First, let us explain why water breakthrough happened and could not be eliminated. Based on the reservoir data, the critical oil flow rate calculated using the new model is 21.6 bbl/day. This means that, from the start of production, the oil production rate was above its critical value. However, because the water breakthrough coincided with the production increase to 80 bbl/day,
it may seem that this production increase caused the water breakthrough, when, in fact, it did not. For this case, the water breakthrough time, calculated using Sobocinski's model (Sobocinski and Cornelius, 1965 ), was 387 days for an oil production rate of 50 bbl/day and 191 days for an oil production rate of 80 bbl/day. This means that after 315 days of oil production at a rate of 50 bbl/day the slowly developing water cone almost reached the oil perforations. At this point, the oil production rate was increased to 80
34
A.K. Wojtanowicz et al. / Journal of Petroleum Science and Engineering 11 (1994) 21-35
bbl/day, and the water breakthrough occurred immediately, The water sink model was used to simulate segregated production in this reservoir with the maximum oil production rate set at 80 bbl/day, This rate was determined through several simulation runs using various rates of oil and water, At this rate, the water cones were stable with minimum restriction of the inflow performance. Table 2 shows a comparison of the simulated coning control for various positions of water sink. The optimal production rates of water sink are 34 bbl/day, 48 bbl/day and 50 bbl/day for the water sink positions at 10 ft, 15 ft and 20 ft below the original OWC, respectively. The water cone's geometries are documented in Table 2 and Fig. 15. Also included in Fig. 15 is the water-coning profile at the critical oil flow rate (21.6 bbl/day ) without water sink. At this rate, the water breakthrough would not have occurred, but production would have been very limited compared to the oil production rate of 80 bbl/day. The advantage of using water sink is evident. With the water sink, higher oil production and lower water production can be obtained. Another important advantage of this method is that the shape of the water cone can be flattened in the vicinity of producing perforations at the late stage of a well's production with OWC approaching the perforations. Such a control would result in the recovery of additional oil residing above OWC.
Nomenclature
c
g h hw ho
k,k~,kh P Pb
Q~ Qo
compressibility ( 1/atm ) gravity acceleration (cm3/s 2) thickness (cm) water sink distance from OWC (ft) height of water cone's "table" (ft) permeability, spherical, vertical, horizontal (D) pressure (atm) formation pressure at OWC (arm) water production rate (bbl/day) oil production rate (bbl/day)
qo r rD rDo
rDSz rDe rw Rw t tD z y Pw /~ /to
Ap
laboratory oil pumping rate (cm3/s) radius (cm) dimensionless radius dimensionless distance to real sink dimensionless distance to image sink dimensionless reservoir radius wellbore radius (cm) dimensionless ratio of gravity force to viscous force time (s) dimensionless time vertical distance between any point in the reservoir and oil sink (cm) water-cone height at any point of water coning profile (cm) water density (g/cm 3) viscosity (cP) oil viscosity (cP) difference of water/oil densities (g/cm 3)
~ ~t~
porosity (fraction) flow potential (atm) initial formation flow potential (atm) dimensionless flow potential
6. Conclusions
As evidenced in this study, the method of segregated production has the advantages of increasing the oil production rate, decreasing the water production rate and improving oil recovery. However, these good results must be treated with caution due to the limitations of the mathematical simulation method used. The most important limitations are: ( 1 ) the inability of this model to simulate the oil and water production after the water breakthrough; and (2) a lack of analytical representation of the oil/water transition zone and related effects of water saturation changes. References Abels, H.P., 1990. A laboratory study of water coning in horizontal wells. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Alikhan, A.A. and Faroug, S.M., 1985. State-of-the-art water
A.K. Wojtanowicz et aL / Journal of Petroleum Science and Engineering 11 (1994) 21-35 coning modelling. SPE 13744, 4th Middle East Oil Show of SPE, Bahrain, March 11-14. Bourgeois, E.A., 1989. The evaluation of horizontal well completion for recovery of bypassed oil in a South Louisiana bottom water drive reservoir. M.S. thesis, Louisiana State Univ., Baton Rouge, La. Chatas A.T., 1966. Unsteady spherical flow in petroleum reservoirs. Soc. Pet. Eng. J., (June): 102-114. Cooke, M.S., 1989. A reservoir engineering and coning study of shallow oil sand in the Lafitte Field of Jefferson Parish, Louisiana. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Hebert, L.E., 1990. An experimental study of the effects of water coning in a horizontal well in bottom water drive reservoir. M.Sc. thesis, Louisiana State Univ., Baton Rouge, La. Khan, A.R., 1970. A scaled-model study of water coning. J. Pet. Technol., (June): 771-776. Meyer, H.I. and Gardner, A.O., 1954. Mechanism of two immiscible fluids in porous media. J. Appl. Phys., 25 (11 ): 1400-1406.
35
Mungan, N., 1975. A theoretical and experimental coning study. Soc. Pet. Eng. J., (June): 247-254. Muskat, M., 1949. Physical Principles of Oil Production. McGraw-Hill, New York, N.Y., pp. 345-355. Muskat, M. and Wyckoff, R.D., 1935. An approximate theory of water coning in oil production. Trans. AIME, pp. 144-163. Schols, R.S.: 1972. An empirical formula for the critical oil production rate. Erdoel Erdgas Z., 88( 1 ): 6-11. Sobocinski, D. and Cornelius, A., 1965. A correlation for predicting water coning time. J. Pet. Technol., (May): 594-600. Soengkowo, I., 1969. Model studies of water coning in petroleum reservoirs with natural water drives. Ph.D. diss., Univ. Texas at Austin, Austin, Tex. Welge, H.J. and Weber, A.G., 1964. Use of two-dimensional methods for calculating well coning behavior. Soc. Pet. Eng. J., (Dec.): 345-355. Wheatley, M.J., 1985. An approximate theory of oil/water coning. SPE 14210.