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PAPER 2003-181
Using Decline Curves to Forecast WaterfloodedReservoirs: Fundamentals and Field Cases
R.O. Baker, T. Anderson, K. SandhuEpic Consulting Services Ltd.
This paper is to be presented at the Petroleum Society’s Canadian International Petroleum Conference 2003, Calgary, Alberta,Canada, June 10 – 12, 2003. Discussion of this paper is invited and may be presented at the meeting if filed in writing with thetechnical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered forpublication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.
ABSTRACT
Decline analysis is the most used technique for
forecasting reserves. Although decline analysis for gas
fields has been shown to have a strong theoretical
background, decline analysis for multiphase situations is
less clear. This paper suggests when it is appropriate to
use decline analysis for waterfloods and what is
happening physically when decline trends develop. It also
shows field situations which follow clear trends and
allow us to use decline techniques to diagnose field
behaviour. This paper presents field cases for
waterfloods and suggests a theoretical analysis that ties
in well with the observations from these field examples.
Field cases as well as analytical analysis/simulation(1)
generally support harmonic or hyperbolic decline for
late stage waterflood behavior. In other words, reservoir
factors generally lead to hyperbolic or harmonic decline
late in the waterflood life. However, that is not to say that
exponential (b=0) or “super” exponential decline (b<0)
never occur. When they do occur, usually non-reservoir
factors are involved.
This paper also shows how incremental oil recovery
can be calculated using decline methods accounting for
changes in fluid and injection rates.
The waterflood decline correlation period should have
the following criteria:
a. the watercut should be greater than 50%
b. the voidage replacement ratio should be close to
one
c. well count should be relatively constant
d. injection and fluid production rates should be
relatively constant
e. the reservoir pressure should be relatively
constant
PETROLEUM SOCIETYCANADIAN INSTITUTE OF MINING, METALLURGY & PETROLEUM
2
f. producing well pressures should be constant
g. the GOR should be relatively constant
h. the volume of water injected should be greater
than 25% of the hydrocarbon pore volume.
In order to properly access future waterflood
performance, we need to estimate what is controlling the
oil decline rate. After substantial water breakthrough has
occurred, the oil rate profile is usually controlled by:
a. relative permeability
b. changing volumetric sweep
c. water handling constraints
d. fluid rates handling constraints
e. permeability/injectivity in the near wellbore
regions
f. well positions.
Most successful waterfloods are hopefully in
reasonably good continuity reservoirs with moderate to
high permeabilities, therefore well interference is very
likely. However, because of well interference in such
moderate to high permeability reservoirs, individual well
decline analysis is to be used with caution. We would
therefore recommend using an aggregate analysis of a
group of wells as a more realistic scenario rather than a
sum of individual wells.
INTRODUCTION
Diagnosis of the character of producing wells is the
key skill that petroleum engineers in an operating
environment require. This characterization and
corresponding reservoir forecast/diagnosis task is most
often performed using the technique of decline analysis.
Because of its ease of use, decline analysis has a huge
appeal as a forecast method and is accordingly the most
widely used technique.
The pioneering work on production decline analysis
was performed by Arps(2) in 1944. Equations for pressure
decline were formulated empirically based on statistical
analysis of production data obtained from non-fractured
reservoirs. Production decline was considered to be
proportional to pressure decline through assumptions of
constant wellbore pressure and constant productivity
index.
Many others have made contributions to the techniques
of decline analysis(3-6). In particular, Fetkovich’s 1973
paper(7) showed that exponential decline is the long term
solution of the diffusivity equation with constant
wellbore pressure. Using Fetkovich’s techniques,
exponential, hyperbolic, and harmonic decline curves can
be identified based on Arps’ analysis. Fetkovich used
advanced decline analysis (ADA) to describe these new
techniques. Fetkovich’s work generally dealt with single-
phase flow, small constant compressibility systems with
radial outer boundaries, or linear systems with hydraulic
fractures. Fetkovich type curves are valid for circular
bounded reservoirs with a well in the center. As a result,
the work is very applicable to high pressure gas systems
or under-saturated liquids.
What made Fetkovich’s type curve approach work
very useful is that it allowed one to identify reservoir
properties from the analysis; furthermore, this work
showed that decline analysis has a solid basis in reservoir
engineering fundamentals. Fetkovich curves also allow a
consistency check on reservoir parameters versus
forecast. Thus, Fetkovich’s work allows a coupling of
physical parameters to decline analysis—at least for
single phase systems.
Fetkovich developed decline curve analysis that could
be applied using type curves, so that production decline
in hydraulically fractured reservoirs, stratified reservoirs,
and the effect of changing back pressure could be readily
analyzed. Thus, there is a very strong tie between decline
analysis and physical parameters, at least for single
phase, single well gas systems (i.e., where there are no
interference effects).
The purpose of this paper is to try and extend
advanced decline analysis techniques to multiphase
waterflooded/water drive and multiwell systems. This
topic was touched on by Laustsen, who presented a
practical overview of methods and use of decline curve
analysis(8). He identified common misinterpretations and
rules to avoid these misinterpretations. He stated two
important conclusions or “rules of thumb” for general
decline analysis, stressing that:
3
(1) “An understanding of the principles of decline
analysis, depletion mechanisms, and rock and fluid
characteristics is essential to establish reliable
decline interpretations; and
(2) Subtle changes to curve fits within the engineering
accuracy of the data can result in large differences
in estimated reserves.”
There are a number of sub-objectives for this paper;
these are to show:
1. How important an understanding of the waterflood
reservoir mechanism is to correctly forecasting
waterflood recovery;
2. How to identify, with production data, what are the
controlling factors in a waterflood;
3. The applicability of Lijek and Masoner’s work to real
field cases; and,
4. How supplemental techniques such as Recovery
Factor (RF) versus Hydrocarbon Pore Volume
Injected (HCPVI), log(WOR) versus cumulative oil
produced (Qo or Np), and log cumulative fluid
produced (Qo+Qw) versus Qo can be used to increase
one’s confidence level in decline analysis.
MISUSE OF DECLINE CURVES
Although decline analysis is, as indicated above,
overwhelmingly one of most used techniques, it is, in our
opinion, unfortunately one of the most misused
techniques as well. The main misuse of conventional
decline analysis stems from a lack of understanding of its
limitations; its ease of use means that one may overlook
the premise that it should only be applied in situations of
non-changing conditions. The behaviour of the reservoir
is therefore tacitly assumed to follow a trend that can be
depicted by simple analytical equations—even when in
fact the reservoir may be undergoing or subject to
changing conditions that make its description much more
complex. The parameters of decline analysis equations
are nevertheless easily matched with production data, and
the “calibrated” equation is then expected to accurately
forecast reserves. Unfortunately, with this empirical
technique, we can completely bypass the reservoir model
and the associated petrophysical, geological, and
reservoir parameters(9). According to Slider(10):
“Decline-curve analysis may be one of the most
misused and at the same time, one of the most neglected
reservoir engineering techniques. Decline–curve analysis
can only be used as long as the mechanical condition and
reservoir drainage stay constant in a well and the well is
produced at capacity. Their limitations lead to much
misuse.
On the other hand, the more theoretically inclined
petroleum engineer may not appreciate decline-curve
analysis and fail to use it to augment or backup his
theoretical prediction.”
Decline curves can be characterized by three factors:
(1) initial production rate or the rate at some particular
time (qoi), (2) curvature of the decline (b, which is the
Arps exponent), and (3) rate of decline (Di).
For single phase systems, oil rate is simply given by:
˜˜¯
ˆÁÁË
Ê+˜̃
¯
ˆÁÁË
Ê
D=
Sr
r
P
B
hkkq
w
eo
ro
ln
)(
m
....................................................... (1)
In single phase oil systems, since the terms
permeability (K), oil relative permeability (kro), pay
thickness (h), skin (S), and outer drainage radius (re) are
usually constant, the main variable controlling decline
rate is reservoir pressure drawdown (∆P) and more
specifically reservoir pressure. If pressure depletion is the
only varying factor, in a liquid expansion drive system,
before reaching the bubble point (which is assumed to be
a situation of constant compressibility), we would expect
to see an exponential type of decline (i.e., b = 0). This is
because, in such a situation, the change in oil rate Dqo is
proportional to reservoir pressure which is proportional to
cumulative oil withdrawals; therefore, qo µ (N-Np).
The oil formation volume factor and the oil viscosity
also change with depletion and therefore can control
decline rate. In solution gas drive systems, the
compressibility of the system changes and, as a result,
according to Fetkovich(7), typically solution gas drive
systems have hyperbolic type declines with b ª 0.3.
4
Generally, oil rate decline type is a function of two
main reservoir effects: (1) decreasing reservoir pressure
and (2) decreasing oil saturation due to water invasion or
increasing gas saturation. Oil rate production signatures
are a function of many parameters such as:
1. Transient effects;
2. Pressure depletion effects (resulting from a decrease
in average reservoir pressure);
3. Changes in fluid properties such as Bo, Bg, mo, and mg
with pressure depletion;
4. Operational effects (change in back pressure) and
skin buildup;
5. Relative permeability effects;
6. Changes in drainage area/well interference effects;
7. Interface movement (water-oil/gas-oil contact
movements);
8. Flood front movements in injection processes; and,
9. Pro-rationing of oil rates.
Because of the number of parameters, advanced
decline analysis (ADA) is not an easy problem to
deconvolve into individual parameters. Fetkovich’s work
extensively covers the first three points due to its focus
on single-phase assumptions. The literature generally
does not address related injection processes, however; in
these processes, relative permeability and flood front
movement can become controlling factors.
For the purpose of this paper, we will assume reservoir
pressure is maintained and that drainage area is constant.
Also, we will assume no changes in skin or operational
parameters. Most waterfloods are deployed in medium to
high permeability (Keff > 1 md)/low compressibility
reservoirs, so transient effects are relatively short lived (<
5 days); therefore, neglecting transient behaviour is
generally a valid assumption. Most wells are in a pumped
off condition, so assuming a constant bottom hole
pressure is also generally valid.
Waterflood Decline Analysis
In a waterflood or water drive system, the parameters
controlling decline rate result in a more complicated
analysis because parameters four to eight above generally
control oil production rate. This is true even though
reservoir pressure is constant. An idealized waterflood oil
response profile is shown in Figure 2 and Figure 3. After
primary depletion, waterflood begins; with water
injection, reservoir pressure generally increases rapidly
and gas collapse may occur. As a result, oil rate may rise
rapidly because oil relative permeability increases (due to
oil banking). The peak oil rate will be a strong function of
injection rates, pattern configuration, volumetric sweep
considerations, and permeability heterogeneity. During
these early waterflood stages, volumetric sweep changes
very rapidly. Oil rate production signature is controlled
by volumetric sweep efficiency and fill up considerations.
Because of changing fluid rates, changing injection rates,
as well as rapidly changing volumetric sweep in the early
time period (i.e., until watercuts exceed 50%), the
application of decline analysis may lead to erroneous
results. In other words, decline analysis on waterfloods
requires that volumetric sweep efficiency has stabilized,
or at least is changing very slowly (in effect, attained
pseudo steady state conditions). Obviously, the point
when water breaks through to producers is a function of
mobility ratio (the ratio of displacing fluid—water—to
displaced fluid—oil), phase mobility (the ratio of relative
permeability to viscosity for that phase), and permeability
heterogeneity. Often in waterfloods that are not facility
limited, fluid rates and injection rates will change as
water breakthrough occurs as shown in Figure 3.
After oil production peaks, water breakthrough occurs.
Some time after that, volumetric sweep changes much
more slowly. In this period, oil rate profile is strongly
controlled by mobility effects—most prominently, by
relative permeability.
To repeat, after breakthrough, (late stage) the
waterflood oil rate signature is mainly controlled by
relative permeability effects. In the early time period until
watercuts are greater than 50%: because of changing fluid
rate, injection rate, and rapidly changing volumetric
sweep, using decline analysis is futile. In other words,
decline rate analysis on waterfloods requires that the
volumetric sweep efficiency has stabilized. Thus, there
are a number of criteria for the selection of waterflood
decline correlation periods; these are: (1) watercuts
5
greater than 50%, (2) the voidage replacement ratio
(VRR) should be close to one, (3) constant well counts
and pattern configuration, (4) relatively constant injection
rates and fluid production rates, (5) relatively constant
reservoir pressure, (6) constant producing well pressures,
(7) GORs should be relatively constant, and (8) the
volume of water injected needs to be high, >25% HCPVI.
These conditions basically ensure that we have a
relatively constant pressure situation in which the decline
signature is dominated by relative permeability rather
than by volumetric sweep considerations, consistent with
a relatively mature waterflood.
REVIEW OF WATERFLOOD DECLINEANALYSIS; THEORETICAL LITERATURE
In the literature, there has been some excellent work
done on understanding waterflood decline characteristics.
This literature implicitly assumes, during late stage
waterflood decline, that drainage area and swept area are
quasi-constant. Ershaghi and Omoregie(11) derived a
straight line relationship between the factor x = -
ln(WOR) -1/WOR -1 and cumulative production Qo.
Startzman and Wu(12), Timmerman(13), and others have
shown that a plot of log(WOR) versus Qo can yield a
straight line relationship and has the advantage of being
simpler to understand than the Ershaghi x-plot technique.
Lo et al.(14) showed that the slope of the log (WOR)
versus cumulative oil plot is equivalent to Ershaghi’s x-
plot technique at high water-oil ratios. A rough “rule of
thumb” for using the above techniques is that watercut
must be greater than 50%. These methods have been
shown by both analytical and numerical modeling to
hold. In addition, there are numerous field examples that
confirm this straight line behaviour of log(WOR) versus
cumulative oil, and this is especially true for waterfloods
in medium grade oil reservoirs.
The Ershaghi x-plot technique and the log (WOR)
versus cumulative oil technique were shown to have a
strong physical connection to 1D relative permeability
characteristics by Ershaghi(15), Lijek(16), Lo et al(14), and
Baker(17). Lo et al.(14) showed that the slope of log(WOR)
versus Qo could be used to determine swept volume if
relative permeability characteristics of the reservoir were
known(1).
Lijek(16) and Baker(17)showed that oil rate decline was
hyperbolic (i.e., 0 < b < 1) or harmonic (i.e., b = 1)
depending upon whether fluid rates were constant or
changing. All of the above techniques are only applicable
when volumetric sweep is quasi–constant; if so, then
relative permeability controls decline rates.
Lo(14) et al. showed that, for some layered systems or
for gravity override systems where the volumetric sweep
continues to change, the plot of log(WOR) versus
cumulative oil was not a straight line. We have also noted
for floods that were neither strongly gravity nor viscous
dominated that the log(WOR) versus cumulative oil (Np)
plot was not a straight line, and have indicated that the
lack of straight line behaviour was due to the fact that
quasi-steady-state volumetric sweep was not reached
until very late times(17).
The above references are based on the observation that
a large part of a plot of log(krw/kro) versus Sw is linear.
The above techniques rely on a water-oil relative
permeability relationship that is given by:
wS
rw
ro Aeproductionoil
productionwater
k
k -µ= ....................................... (2)
Timmerman states that generally large portions of the
relative permeability curves can be approximated by the
above equation for some reservoirs(13).
In recent years, Masoner, using a different relative
permeability relationship, has shown that hyperbolic
decline is likely to occur(19). Masoner shows that
waterflood decline is likely to be hyperbolic with an Arps
exponent (b) ranging from 0.25 to 0.8. Masoner used a
Corey equation type approximation to oil relative
permeability to yield a hyperbolic decline as described in
Equation (3)
( )ba oDro Sk = ................................................................... (3)
Both Lijek16 and Masoner19 address the nature of
decline characteristics in situations where relative
permeability controls waterflood/EOR behaviour and
where there is a constant drainage area. Both authors
show that the nature of decline—i.e., Arps exponent
6
“b”—when oil rate profile is controlled by relative
permeability, is strongly a function of injection
(throughput) rates and fluid production. These authors’
results are slightly different, because they assume
different relative permeability functions.
The methods of both Lijek(16) and Masoner(19) assume:
1. Buckley-Leverett theory applies;
2. Quasi-steady-state volumetric sweep (i.e., unchanging
with time), which implies a constant drainage area;
3. Little pressure variation within the swept zone; and,
4. Reservoir pressure does not change significantly with
time.
The most restricting limitation is that the volumetric
sweep remains constant. Nonetheless, practical
experience shows that there are a large number of field
cases where harmonic or hyperbolic decline occurs and
plots of log(WOR) versus cumulative oil yield straight
line behaviour. This is especially true for waterfloods in
heavy oil and for waterfloods in heterogeneous fields.
Obviously, the initial volumetric sweep controls to a very
large extent the water-oil ratio versus cumulative oil (Np)
profile. However, in unfavorable mobility ratio and
heterogeneous reservoir waterflood situations, water
breakthrough occurs relatively early and then volumetric
sweep may increase very gradually with time.
Summarizing the literature, the waterflood
performance of fields and wells can be governed, in some
cases, by not only relative permeability but as well by
heterogeneity and by gravity and viscous forces.
Therefore, theory may provide guidelines, but a
pragmatic approach should be taken.
Review of Empirical Waterflood Literature onDecline Behaviour
Empirically, Wong and Ambastha have shown for
Canadian waterfloods that decline is on average
hyperbolic(20). In our experience, a very high percentage
of waterfloods worldwide have indeed been observed to
have hyperbolic decline, but we have definitely observed
field cases of exponential and harmonic decline as well.
Most waterflood simulation studies show
hyperbolic/harmonic decline characteristics. Generally,
heavy oil waterfloods are most likely to have harmonic or
high Arps exponent values of b > 0.7 indicating
hyperbolic decline. In the case of very light oil in a
relatively homogeneous reservoir with “piston like”
displacement, volumetric sweep efficiency will dominate
the oil rate profile; decline will be very rapid and decline
analysis techniques will not be useful. Laustsen also
confirms this conclusion(8).
Unfortunately, many statistical empirical studies of
decline rates and decline types in the literature do not
include information about drive mechanism, well counts,
reservoir pressure, or watercut and GORs. Arps showed
that, for his study areas, 90% of the fields exhibited
hyperbolic decline character; he observed no harmonic
declines. Bush and Helander’s Oklahoma study showed
mainly harmonic/hyperbolic decline types(21). Ramsay
and Guerrero showed that hyperbolic and harmonic
declines were typical(22). Schuldt et al. indicated that
Alaskan waterflooded oil reservoirs are generally
expected to follow hyperbolic decline behaviour(23).
Campbell (1959) states that “most decline seems to
follow hyperbolic decline most closely, the value b =
0.25 being a good average of many curves examined. It is
seldom that b exceeds 0.6(24).”
Selection of Waterflood Decline CorrelationPeriod
Before substantial water breakthrough (watercut ≥
50%) occurs, decline analysis is unlikely to be a good
technique because pressurization and volumetric sweep
effects are likely to dominate the oil production signature.
Oil rates at this stage may be inclining. However, after
volumetric sweep efficiency is in a relatively constant
state, oil rate will decline because relative permeability is
then the main variable. In order to select a correlation
period for waterflood, we would propose the following
criteria:
1. Watercuts should be greater that 50%;
2. Voidage replacement ratios (VRR) should be close to
unity;
3. Injection and production well count should be
relatively constant;
7
4. Fluid production and injection rates should be
relatively constant;
5. Reservoir pressure should be relatively constant;
6. Producing well pressures should be constant;
7. gas-oil ratios should be constant; and,
8. The volume of water injected should be greater than
25% of the hydrocarbon pore volume.
This paper will focus on waterflood response;
therefore, transient effects and pressure depletion effects
will be ignored. Obviously, if well count is changing or
infill drilling is occurring, the oil rate will be strongly
affected. If reservoir pressure is declining and VRR<1.0,
then some of the reservoir energy is being supplied by
expansion energy rather than the waterflood. Thus, it is
unlikely in such a situation that the decline rate or Arps
exponent will be constant. Similarly, if gas-oil ratios are
increasing, it is probable that pressure is declining and
therefore, expansion energy rather than waterflood drive
is dominating. The rule of thumb of watercuts being
greater that 50% insures that sufficient water
breakthrough has occurred and that relative permeability
rather than volumetric sweep now controls oil rate
decline as shown in Figure 4.
A simulation model was constructed to test the validity
of decline methods and timing of applicability for decline
methods for field cases. We also examined how relative
permeability, pattern imbalance, changing fluid rates, and
viscosity ratio changed decline rate behaviour.
Field Cases
Over 20 reservoirs have been studied in detail using
the correlation period selection criteria. Table 3 shows
the selected pools and corresponding decline analyses
including the Arps exponent “b.” To supplement the
analysis, log (WOR) versus Np (cumulative oil
produced), log cumulative fluid (Qo+Qw) versus Np, and
RF versus HCPVI have been used to assist in determining
the decline type.
A complete analysis is demonstrated on two pools, the
Provost Lloydminster ‘O’ pool and Taber South
Mannville ‘A’ pool.
Provost Lloydminster ‘O’ Pool
The Provost Lloydminster ‘O’ pool has been on
production since September 1973 and has produced a
total of 5.0 106m3 of oil. This pool is considered a heavy
to medium oil with 23.8˚API gravity, and a density of
911.0 kg/m3. With an areal extent of approximately 1315
ha, and a pay thickness of 3.1 m, the original oil in place
(OOIP) for the Lloydminster ‘O’ pool is 10.1 106m3
(waterflood area plus primary). Primary production
occurred until January 1977, when water injection began,
with minimal volumes of water being injected. Injection
rates were increased dramatically in 1995, where the field
averaged 15,000 m3/d of injected water. The recovery
factor to date for the Lloydminster ‘O’ pool is
approximately 50% OOIP. The composite plot for
Lloydminster ‘O’ pool is shown in Figure 5. All data for
Provost Lloydminster ‘O’ pool was obtained from the
public data source (AEUB)(25).
Using the composite plot, it can be seen that the most
appropriate correlation period for decline analysis is late
1998 to December 2002 (end of data set). In this time
period, the injection rate, injection well count, production
well count, and GOR are all constant. The watercut is
above 50% and the VRR (Figure 6) has stabilized and is
close to unity. Pre-1995, the VRR was quite erratic.
Using an earlier correlation period would only represent
the effects of decreasing well count and changing total
fluid rates on the reservoir.
Interpretation of the log (WOR) versus Np (Figure 7)
and log(Qo+Qw) (cumulative fluid) versus Np (Figure 8)
plots assists analysis as supplemental techniques for
determination of decline behavior. The log (WOR) and
log (cumulative fluid) plots for Lloydminster ‘O’ pool are
linear in mid to late time, indicating a hyperbolic - or
harmonic decline. The recovery factor (RF) versus
hydrocarbon pore volume injected (HCPVI) plot for the
Lloydminster ‘O’ pool is shown in Figure 9. The
performance of this pool due to water injection is quite
good. At 2 pore volumes (PV) of injection, secondary
recovery due to waterflood is almost 40%. Break over
point occurs at 15% recovery factor and 25% HCPVI,
indicating good waterflood performance. As subsequent
pore volumes of water are injected, the curve has a
slowly decreasing slope.
8
Setting Arps exponent equal to 0 and 1 to observe the
exponential (Figure 10) and harmonic declines (Figure
11), respectively, the resultant decline curves do not fit
the data very well. Note that the log (WOR) versus
cumulative oil (Np) plot, log cumulative fluid (Qo+Qw)
versus Np, and RF versus HCPVI plots all show clear
trends that can be easily extrapolated. Also note that,
despite the large amount of water pore volumes injected,
there is still good waterflood response. Using a harmonic
or exponential decline on this pool (b value too high or
too low) could result in an over- or under-estimation of
recoverable reserves, respectively.
Using commercial software to determine the Arps
exponent for this pool for the correlation period of 1998
to December of 2002, it was found that a “b” value equal
to 0.36 gave the best fit to the data. In comparison to the
exponential and harmonic decline curves, the hyperbolic
curve with an Arps exponent b=0.36 matches the data
quite well and is representative of the reservoir’s decline
behavior.
TABER SOUTH MANNVILLE ‘A’
The Taber South Mannville ‘A’ pool has been on
production since December 1963 and has produced a total
of 1,800 103m3 of oil. This pool is considered a heavy oil
with 18.1˚API gravity, and a density of 945.9 kg/m3.
With an areal extent of approximately 1394 ha, and a pay
thickness of almost 8 m, the original oil in place for the
Taber South Mannville ‘A’ pool is 14.1 106m3
(waterflood area plus primary). Primary production was
minimal, reaching less than 1% RF. This pool has been
under waterflood since January 1966, and has a
secondary recovery factor of 13% with 85% HCPVI.
Field water injection rate was relatively constant at 4,000
m3/d until 1994, when it was increased to approximately
13,000 m3/d. The composite plot for Taber South
Mannville ‘A’ is shown in Figure 13. All data used in
analysis of the Taber South Mannville ‘A’ pool has been
obtained from the public data source (AEUB)(25).
From the composite plot, there are two possible
correlation periods that would be acceptable for
evaluating decline. These time periods are 1989 to 1992
and 1997 to December 2002. Both periods have constant
fluid rates, GOR, water injection rates, and well counts
(both injectors and producers). Watercut is above 50%
and VRR is relatively stable for both time periods (Figure
14). As the later correlation period has a slightly more
stabilized VRR (has been stable for a longer time period)
and is more representative of what is currently occurring
in the pool, it is used for analysis.
The log (WOR) versus Np plot is shown in Figure 15.
This plot clearly exhibits two linear regions. The first is
between 800 103m3 and 1,000 103m3, and the second
correlation period occurs between 1,200 103m3 and 1,800
103m3. The first linear correlation period (800 to 1,000
103m3) has a very similar slope to the second correlation
period on the log (WOR) plot. Both linear periods
demonstrate a hyperbolic - to harmonic decline behavior
for this pool. As in the previous example, the log(WOR)
versus Np, log(Qo+Qw) versus Np, and the RF versus
HCPVI plots show clear trends, at least before infill
drilling programs are implemented.
The log cumulative fluid versus Np plot for the Taber
South Mannville ‘A’ pool is shown in Figure 16. The two
linear periods can clearly be seen on this plot, and are
separated by a disjoint in the slope between the two
regions. This disjoint can be partly attributed to changing
total fluid rate (caused by an increase in injection and
production wells). The late time region of the plot
demonstrates a linear slope, indicating a hyperbolic to
harmonic decline, depending on how fluid rates are
changing. Extrapolating the WOR curve for each linear
region to WOR = 25, and translating the slopes of each
linear region to the end of the data set, two recovery
factors are predicted based on the OOIP. The
extrapolation of the first linear portion leads to a recovery
of 14.2% OOIP, whereas extrapolation of the second
linear region leads to a recovery of 17% OOIP. This
gives an incremental recovery of 2.8% OOIP, which
corresponds to about 400 103m3.
To date, secondary recovery due to waterflood is
approximately 13%. Extrapolation of the RF versus
HCPVI plot to 1 pore volume gives approximately 16%
total RF (waterflood + primary). The RF versus HCPVI
plot for Taber South Mannville ‘A’ pool is shown in
Figure 17. In this plot, the curve does not have a constant
9
slope (change in slope is denoted by the arrow), and the
varying slope could be due to changes in interpattern
flows.
Using commercial software to confirm the harmonic
decline exponent (b) for the Mannville ‘A’ pool, both
b=0 and 1 were used on the selected correlation period.
Using b=0, it is evident that the exponential decline curve
does not match the data set (see Figure 18), reinforcing
the previous assessment that the reservoir is not
exhibiting exponential decline behavior. Use of an
exponential decline for this pool could significantly
underestimate the total recoverable reserves.
As shown in Figure 19, a much better fit to the data
can be achieved using a harmonic decline exponent, b=1.
The best fit for this correlation period is a “super”
harmonic decline, with b=1.3 (Figure 20). Figure 15 to
Figure 17 allow us to clearly identify the incremental oil
due to infill drilling. As indicated before, the
extrapolation to an economic water – oil ratio (30) in
Figure 15 and Figure 16 before and after infill drilling,
respectively, yields an incremental recovery of 2.8%
OOIP, corresponding to about 400 103m3.
Masoner Technique—Matching Fluid Rates forPredicting Decline Type
The Masoner(26) (Chevron) method can also be used to
determine the decline behavior of a reservoir. This
method makes corrections for changing fluid rates, and
makes the assumption that the drainage volume, recovery
process, and relative permeability remain constant. The
technique is valid for multi-phase flow where the decline
is dominated by relative permeability effects. Briefly, in
using the Masoner method, the engineer regresses on
decline parameters to match a correlation period.
The Masoner technique of matching fluid production
levels was used to confirm the decline behavior for the
Taber South Mannville ‘A’ reservoir. Using fluid rates
and selecting a decline period, it can be seen that the
Masoner technique also confirms the hyperbolic to
harmonic decline behavior (Table 1) for the correlation
period of 1997 to 2002. Using this same correlation
period, an oil rate plot was generated, which outlines the
historical oil rate and the Masoner predicted oil rate (see
Figure 21).
From Figure 21, it can be seen that the Masoner
predicted oil rate has an excellent fit to the historical data.
The excellent match of historical data for the Taber South
Mannville ‘A’ pool demonstrates that the changes in fluid
rates are mainly due to accelerated production. Usually,
the application of the Masoner technique does not
provide this level of accuracy when history matching.
The accuracy of the fit obtained during the selected
match period of 1997 to 2002 is shown in Figure 21, as
demonstrated by the minimal deviation between the
Masoner predicted oil rate curve and the historical oil rate
curve. This excellent fit to historical data using the
decline period of 1997 to 2002 demonstrates that the pool
is exhibiting a hyperbolic decline and confirms earlier
analysis.
SUMMARY OF FIELD CASES
Over 50 Alberta waterflooded pools were reviewed for
this study, with the selection of the pools being made at
random. A total of 21 pools were studied in detail, pools
selected for this study and their corresponding decline
analysis summaries are listed in Table 2. Alberta pools
were chosen because of ease of access to public data. The
decline correlation periods for the selected pools were
chosen using the criteria of:
ß watercut greater than 50%;
ß VRR close to 1;
ß constant well counts;
ß constant fluid and injection rates;
ß constant reservoir pressure;
ß constant producing well pressures;
ß constant GOR; and,
ß greater than 25% HCPVI.
For the majority of the pools studied, it has been found
that achieving a correlation period for greater than a five-
year interval has been difficult. This has been in part due
to changing well counts, varying injection rates, and
fluctuations in total fluid rates. All the pools were
analyzed using the above correlation period on the
traditional oil rate versus time plots and supplemental
10
analysis using the log(WOR) versus Np, log(Qo+Qw)
versus Np, and RF versus HCPVI plots was used to
determine decline type. Based on the supplemental
analysis, it has been found that, for the selected
correlation periods, the waterfloods are generally
exhibiting hyperbolic to harmonic decline behavior. The
hyperbolic to harmonic decline behavior is represented
by a linear trend in the slope of the logarithmic curve of
the supplemental plots.
Using commercial software to confirm the value of the
Arps exponent “b,” it has been found that for the selected
pools, the mean value of b=0.68. The frequency of
number of pools and Arps exponent are shown in Figure
22.
In Figure 22, it can be seen that 14 out of the 21
(approximately 67%) pools selected have an Arps
exponent greater than 0 and less than 1 (0<b<1), whereas
the remaining pools have a “super” harmonic decline
(b>=1), representing 33% of the selected pools. No pools
were found to have b=0, with the exception of Peejay
Halfway pool exhibiting a “super” exponential decline in
late stages (not shown in the tabulations).
The performance of all pools was strongly affected by
changing well counts, changing fluid rates, and changing
injection rates, making it difficult to achieve longer than a
five-year correlation period. Generally, operators of the
waterflooded pools we examined showed aggressive and
successful optimization. For our selected waterfloods, the
“average” field exhibited a high hyperbolic - to harmonic
decline character. One field exhibited a precipitous drop
off in the late time region followed by a hyperbolic
decline. Although not demonstrated here, often individual
well decline was much harder to analyze because the data
was “noisy.” Simulation studies on pools show that
changes in fluids rates indicate that capture efficiency
changes between wells.
The log (WOR) versus Np, log(Qo+Qw) versus Np, and
RF versus HCPVI plots are recommended as
supplementary diagnostic tools. These functions are less
“noisy” (i.e., exhibit smoother curves), making them
easier to use in analysis. Trends exhibited by these
functions assist in the determination of decline behavior.
CONCLUSIONS
1. Decline analysis and reserves estimation using decline
analysis should be fundamentally grounded in a good
understanding of what factors control decline. The
same decline techniques should not be applied blindly
to all fields and all drive mechanisms. Specifically,
arbitrarily using an exponential decline approach
(log(qo) versus time assumed to be linear) for water
drive, solution gas drive, and gravity drainage systems
is neither technically nor empirically correct. Late
stage waterflood behavior is generally hyperbolic or
harmonic in nature, if reservoir factors dominate.
2. The waterflood decline correlation period should have
the following criteria:
a) the watercut should be greater than 50%
b) the voidage replacement ratio should be close to
one
c) well count should be relatively constant
d) injection and fluid production rates should be
relatively constant
e) the reservoir pressure should be relatively
constant
f) producing well pressures should be constant
g) the GOR should be relatively constant
h) the waterflood is mature; i.e., the volume of
water injected should be greater than 25% of the
hydrocarbon pore volume.
3. In light of the above, the criterion of watercut >50%
for waterflood suggested by SPE and Petroleum
Society of CIM is not sufficient to properly forecast
future production.
4. In our experience, full waterflood decline occurs only
after ª50% watercut (WOR >1.0) due to a relatively
slowly increasing volumetric sweep at that point.
Numerous simulation/analytical studies confirm this
characteristic decline start. This conclusion does
depend upon mobility ratio effects and permeability
heterogeneity: the higher the permeability
heterogeneity, the faster decline behaviour occurs.
11
5. Another factor which significantly impacts volumetric
sweep is infill drilling. Infill well programs often
increase volumetric sweep more dramatically by
increasing the number of pressure sink/withdrawal
points.
6. RF versus HCPVI, log(WOR) versus Np, log(Qo+Qw)
versus Np, and Masoner plots are very useful in
identifying infill well incremental oil recovery.
7. Exponential decline (b=0), super exponential (“ultra-
fast”) decline (b<0) and super hyperbolic (“ultra-
slow”) decline (b>1) do occur. Exponential or super
exponential decline can occur if there is skin buildup
at the injectors. Super exponential decline generally
occurs because of rapid watering out of a “hot streak”
such as a natural fracture, induced fracture, or small
“hot streak” layer. Super hyperbolic decline generally
occurs because of multiplying or rising fluid/injection
rates. Super hyperbolic decline can also occur in a
multilayer reservoir.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the fine
contributions of many individuals in the reservoir
engineering literature regarding the techniques of decline
analysis as well as the Alberta Energy and Utilities Board
for providing an excellent database for production data.
The authors would also like to acknowledge Eric
Denbina, Kent Edney, Bette Harding, Frank Kuppe, and
Shelin Chugh for their assistance and many helpful
suggestions in making this paper a reality.
REFERENCES
1. Baker, R.O, Sandhu, K., and Anderson, T., ”Using Decline
Curves to Forecast Waterflooded Reservoirs: Modeling
Results,” paper 2003-163 prepared for presentation at the
54th Annual Technical Meeting of the Petroleum Society of
CIM, CIPC 2003, Calgary, AB, June 10 – 12, 2003.
2. Arps, J.J., “Analysis of Decline Curves,” Trans. AIME,
1945.
3. Muskat, M.: Physical Principles of Oil Production,
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4. Sandrea, R. and Nielsen, R.F., Dynamics of Petroleum
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5. Ershaghi, I., Handy, L.L., and Hamdi, M., “Application of
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6. Currier, J.H. and Sindelar, S.T., “Performance Analysis in
an Immature Waterflood: The Kuparuk River Field,” paper
20775 presented at the SPE ATCE, New Orleans, LA,
September 23-26,1990.
7. Fetkovich, M.J., “Decline Curve Analysis Using Type
Curves,” JPT, June 1980.
8. Laustsen, D., “Practical Decline Analysis Part 1 – Uses
and Misuses,” JCPT Distinguished Authors Series article,
November 1996.
9. Gringarten, : “Evolution of Reservoir Management
Techniques from Independent Methods to an Integrated
Methodology, Impact on Petroleum Engineering
Curriculum, Graduate Teaching and Competitive
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10. Slider H.C.: Worldwide Practical Petroleum Reservoir
Engineering Methods, PennWell Books, PennWell
Publishing Company, Tulsa, OK, 1983.
11. Ershaghi, I. and Abdassah, D.: “A Prediction Technique
for Immiscible Processes Using Field Performance Data,”
JPT, April 1984.
12. Startzman, R.A. and Wu, C.H.: “Discussion of Empirical
Prediction Technique for Immiscible Processes,” JPT,
1984.
13. Timmerman, E.H.: Practical Reservoir Engineering, Part
ll, Methods for analyzing output from equations and
computers , PennWell Books, PennWell Publishing
Company, Tulsa, OK, 1982.
14. Lo, K.K., Warner, H.R., and Johnson, J.B., “A Study of the
Post-Breakthrough Characteristics of Waterfloods,” JPT,
April 1990.
15. Ershaghi, I., “A Method for Extrapolation of Cut vs
Recovery Curves,” JPT Forum, February 1978.
16. Lijek, S.J.: “Simple Performance Plots Used in Rate-time
Determination and Waterflood Analysis,” JPT, October
1989.
17. Baker, R.O.: “Reservoir Management for Waterfloods –
Part 2,” J C P T Distinguished Authors Series article,
January 1998.
12
18. Baker, R.O. and McClernon, L.L., “Estimation of
Volumetric Sweep Efficiency of a Miscible Flood,” JCPT,
February 1998.
19. Masoner, L.O., “Decline Analysis’ Relationship to
Relative Permeability in Secondary and Tertiary
Recovery,” paper 39928 presented at the SPE Rocky
Mountain Regional/Low Permeability Reservoirs
Symposium and Exhibition, Denver, CO, April 5-8, 1998.
20. Wong, K.H. and Ambastha, A.K., “Decline Curve
Analysis for Canadian Oil Reservoirs Under Waterflood
Conditions,” paper 95-08 presented at the 46th Annual
Technical Meeting of the Petroleum Society, Banff, AB,
May 14-17, 1995.
21. Bush, J.L. and Helander, D.P., “Empirical Prediction of
Recovery Rate in Waterflooding Depleted Sands, JPT,
September 1968.
22. Ramsay Jr., H.J. and Guerrero, E.T., “The Ability of Rate-
Time Decline Curves to Predict Production Rates,” JPT,
February 1969.
23. Schuldt, D.M., Suttles, D.J., Martins, J.P., and Breit, V.S.,
“Post-Fracture Production Performance and Waterflood
Management at Prudhoe Bay,” paper 26033 presented at
the SPE Western Regional Meeting, Anchorage, AK, May
26-28, 1993.
24. Campbell, J.M.: Oil Property Evaluation, Prentice-Hall
Inc, September 1959.
25. Alberta Energy and Utilities Board, ”Alberta’s Reserves of
Crude Oil, Oil Sands, Gas, Natural Gas Liquids and
Sulphur,” AEUB, December 2002.
26. Masoner, L.O., “A Decline Analysis Technique
Incorporating Corrections for Total Fluid Rate Changes,”
paper 36695 prepared for presentation at the 1996 Annual
Technical Conference in Denver, Co.
13
PVT
Bo 1.042Bno 1
Decline Period
Start Date: 01/01/1997End Date: 12/01/2002
Decline Parameters
D 0.0406b 0.8168
qoi 675.39
qfi 8964.33r2 0.9946
Table 1 Parameters for Decline Behavior: Decline Period 1997-2002
Field PoolCorrelation Period
b log(WOR)log(Qw +
Qo)Secondary
RF%(OOIP)HCPVI
%(OOIP)
Pembina Nisku ‘T’ 1999-2001 1 linear linear 15 36
Provost Lloydmijnster ‘O’ 1998-2003 0.36 linear linear 50 550
Provost Upper Mnvl ‘OOO’ & Elrs ‘S’ 1999-2001 0.47 linear linear 11 43
Taber South Mannville ‘A’ 1997-2003 1 linear linear 13 85
Viking Kinsella Sparky ‘I’ 1997-2003 0.8 linear linear 13.5 110
Taber South Mannville ‘B’ 1975-1986 1 linear linear 35 270
Caroline Rundle ‘A’ 1994-2003 1 linear linear 36 80
Jenner Upper Mannville ‘O’ 1997-2003 0.5 linear linear 24 400
Bigoray Cardium ‘B’ 2000-2003 0.44 linear linear 48 190
Gift Slave Point ‘A’ 1999-2003 0.5-1 linear linear 19 30
Medicine River Basal Quartz ‘B’ 1997-2000 0-0.5 linear linear 9.5 23
Parflesh Upper Mannville ‘G’ 1998-2000 0.5 linear linear 40 110
Joffre D-2 1977-1983 0.9 linear linear 19 38
Rycroft Charlie Lake ‘A’ 1993-1997 1 linear linear 33 80
Peejay Halfway 1975-1979 0.5-1 linear linear 37 80
Sunset Triassic ‘A’ 1973-1978 0.446 linear linear 17 35
Little Bow Upper Mannville ‘U’ 1990-1995 1 linear linear 23 180
Pembina Ostracod ‘E’ 1998-2000 0.5-1 linear linear 35 65
Grand Forks Sawtooth ‘MM’ 1995-2003 1 linear linear 51 835
Rainbow Keg River ‘EE’ 1999-2003 0.1 linear linear 66 430
Chauvin Mannville ‘A’ 1974-1983 0.41 linear linear 17 80
Table 2 Selected Pools, Correlation Periods, and Decline Analysis Summaries
14
Figure 1 Decline Behavior
Figure 2: Typical Waterflood Oil Rate Response
15
Figure 3: Selection of Decline Correlation Period
16
Figure 4: Schematic Areal View of Water Swept Zones in Waterfloods
Figure 5 Composite Plot for the Provost Lloydminster ‘O’ Pool
17
Figure 6 VRR Plot for Lloydminster ‘O’ Pool
Figure 7 log (WOR) vs. Np for the Lloydminster ‘O’ Pool
18
Figure 8 log(Qo+Qw) vs. Np for the Lloydminster ‘O’ Pool
Figure 9 RF vs. HCPVI for the Lloydminster ‘O’ Pool
19
Figure 10 Exponential Decline Curve for the Lloydminster ‘O’ Pool
Figure 11 Harmonic Decline Curve for the Lloydminster ‘O’ Pool
20
Figure 12 Best-Fit Decline for Lloydminster ‘O’ Pool (b=0.36)
Figure 13 Composite Plot for Taber South Mannville ‘A’
21
Figure 14 VRR Plot for Taber South Mannville ‘A’
Figure 15 log (WOR) vs. Np for the Taber South Mannville ‘A’ Pool
22
Figure 16 log Cumulative Fluid vs. Np for the Taber South Mannville ‘A’ Pool
Figure 17 RF vs. HCPVI for Taber South Mannville ‘A’ Pool
23
Figure 18 Exponential Decline for the Taber South Mannville ‘A’ Pool
Figure 19 Harmonic Decline for the Taber South Mannville ‘A’ Pool
24
Figure 20 Super Harmonic Decline of Taber South Mannville ‘A’ Pool
Figure 21 Masoner Predicted Oil Rate for Taber South Mannville ‘A’: Decline Correlation Period 1997-2002
25
Figure 22 Distribution of Arps Exponent (b)
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