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

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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:

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(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.

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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

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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

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“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;

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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.

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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,

McGraw-Hill Book Company Inc., 1949.

4. Sandrea, R. and Nielsen, R.F., Dynamics of Petroleum

Reservoirs under Gas Injection, Gulf Publishing Co.,

1974.

5. Ershaghi, I., Handy, L.L., and Hamdi, M., “Application of

the x-Plot Technique to the Study of Water Influx in the

Sidi El-Itayem Reservoir, Tunisia,” JPT, 1987.

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

advantages of Oil Companies”, SPE 39713.

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)