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PRODUCTION
TECHNOLOGY
Predicting production performanceusing a simplified modelNeither
hybebolic nor exponential models fully explain decline.So, why not
simply combine them?
Khaled Abdel Fattah, Kh. A., King Saud University, Saudi
Arabia
One of the most important tasks ofis predicting the oil and gas
that will berecovered from a reservoir. The choice offorecasting
method is critical for accurateforecasts that are, in turn, vital
for soundmanagerial planning. Decline curves are
widely used to convey information aboutpast production
performance and to fore-cast future performance and reserves. Anew
model to decline curve analysis hasbeen developed. The new model
uses anexponential decline to extrapolate a hy-perbolic decline to
prevent unrealisticallylong lifetime and reserve estimates.
INTRODUCTIONOne of the most important manage-
ment functions at all levels in an orga-nization is planning.
Forecasting plays a
key role in the planning process. Man-agement needs to reduce
the risks associ-ated with decision making, and one ofthe ways in
which this can be done isby anticipating future well
performancemore clearly. Extrapolation of produc-tion history has
long been considered themost accurate and defendable method
ofestimating remaining recoverable reservefrom a well and, in turn,
a reservoir. Thetechnique for relating production to timeis known
as decline curve analysis, and isa very useful tool for estimating
future
production. The decline curve is used of-ten to determine the
economic limit of a well, estimating the remaining reserves,and
forecasting the present worth of theoil and gas reserves in the
future.15
Three types of decline curves areconsidered, although only two
of threetechniques, namely, exponential and hy-perbolic, commonly
occur in reservoirs.The hyperbolic decline model predicts alonger
well life than is predicted by theexponential decline model. Also,
theexponential forecast provides the lowest
estimate of recoverable reserves. Experi-enced evaluators avoid
extrapolating hy-
perbolic declines over long time periods,because they frequently
result in unre-alistically high reserve and value esti-mates.68 The
characteristic of hyperbolicdecline, which is a continuously
decreas-ing decline rate, can result in extremely
long producing lives that are incompat-ible with experience and
expectations forequipment life. Many wells follow thetrend toward
an exponential decline intheir later life. Long and Davis9
devel-oped a log-rate-versus-time overlay tocope with this problem.
This type-curvematching has some disadvantages, main-ly due to the
non-uniqueness problemin determining the correct type-curve touse.
Robertson10 developed a productionrate equation that is hyperbolic
initiallybut asymptotically exponential with
time. He introduced a dimensionlessconstant; its value ranges
from 0 to 1 andis related to the abandonment pressure,and the rock
and fluid properties.
One of the main difficulties is to findthe transition point
between the hyper-bolic and exponential decline curves, thatis, the
endpoint of hyperbolic declineand the starting point of
exponentialdecline. Long and Davis,9 and Robert-son10 do not
determine an exponentialdecline rate that allows selection of
apoint at which the decline is expected to
follow an exponential decline. They as-sumed the exponential
decline rate wasknown based on experience with analo-gous wells or
experience with particularreservoirs. In this study, however, a
dis-tinct technique is formulated to find thisexponential decline
rate and determinethe transition point of transferring
fromhyperbolic to exponential decline.
DECLINE CURVE ANALYSIS
Exponential decline curve. The most
commonly used decline curve is exponen-tial because of its
simplicity. Equations of
exponential decline are given by:
q q - D to= ( )exp (1)
The above equation has two con-stants, the initial production
rate, qo, and
the exponential decline rate, D, which isconstant for all time.
Together, they yieldthe cumulative production:
Q = D( )q (2)
Hyperbolic decline curve. Hyperbolicdecline occurs when the
decline rate isno longer constant. Compared to expo-nential
decline, hyperbolic decline-curveequations estimate a longer
productionlife of the well.11
(3)The above equation has three con-
stants, the initial production rate, theinitial decline rate and
the hyperbolicexponent, n. The decline rate is not con-stant, but
changes with time:
Q q D n q qon
o on n
= ( )( ) ( ) 1 1 1 (4)In the above equations, the produc-
tion rate, q, is related to the initial pro-duction rate, qo,
time, t, and the decline
rate, D, at which production decline oc-curs. These equations
are used primarilyfor forecasting future production rates.Thus, one
normally wants to extract theparameters of the rate equation by
fit-ting it to actual production records fora well. The remaining
life of the well tothe abandonment can be calculated bythese
models. In addition, the integra-tion of these models with time
gives thecumulative production, from which onemay calculate the
amount of reserves inthe reservoir.1216
PROPOSED METHOD
an-e risks associ-r sks associ-
making, and one ofa ing, and one of which this can be done isis
can is
nticipating future well performancecipating fut ell per cemore
clearly. Extrapolation of produc-more clearly. Extrap ion of
produc-ion history has long been considered theion s long b
considered e
most accurate and defendable method ofmost and def ble
metestimating remaining recoverable reserveestimat remainin rable
refrom a well and, in turn, a reservoir. Thefrom a well and
servoir.
chnique for relating production to tichniqu ion to tinown as
decline curve analnownery useful tool forery use
uction. Thuction.d
n--s problemem
rect type-curve tove todeveloped a productionevelope ction
ation that is hyperbolic initiallyon that is hyperbo itiallyut
asymptotically exponential withymptot xponent with
time. He introduced a dimensionlessHe in dimen lessconstant; its
value ranges from 0 to 1 andc nt; its v rom 0 to dis related to the
abandonment pressure,is ted to t ent prand the rock and fluid
properties.a e rock a erties.
One of the main difficulties is to findof the m ulties isthe
transition point between thethe tion point etween tbolic and
exponential declibolic onential declis, the endpointis, theand the
sand thede
(
erbolic decline curve.er e curve Hyperbolicdecline occurs when
the decline rate isdecline occurs the de ne rate isno longer
constant. Compared to expo-n er consta ompared to enential decline,
hyperbolic decline-curvecline, hy olic declequations estimate a
longer productionstimate nger prlife of the well.ll.1111
))nDD ttoo+( )( n
The aboveThe abovstants
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in Eq.13, with n=1.7, to=28.7 monthsand Do=0.006873 /month.
7) Perform the production forecastfor an exponential decline
curve at anytime, t, greater than to by using Eq.17with qo= 850
bbl/month, n=1.7, to=28.7months and Do= 0.006873 /month.
8) Plot the oil production rate pre-dicted by both hyperbolic
and exponen-
tial decline curves versus time as shownin Fig. 4.
9) Determine the reserves to be pro-duced during the hyperbolic
segment byusing Eq. 4, which equals to 22,373 bbl,during the first
segment of 28.7 monthsbefore it changes to an exponential de-cline
curve, with qo= 850 bbl/month,n=1.7, to = 28.7 months, Do=
0.006873/month.
10) With the economic monthly rateinput, the model calculated
the num-ber of months until economic depletion
occurs and what the total economic re-serves are.
11) If the economic production rate,qe, is equal to 100
bbl/month, determinethe reserves to be produced during
theexponential segment by using Eq. 2,which is equal to 119,900 bbl
with qo=717 bbl/month, qe=100 bbl/month andD = 0.005145/month, from
the initialdecline of an exponential curve until theeconomic
production rate.
12) Determine the total reserves tobe produced during the
hyperbolic and
exponential segments, which is equal to142,273 bbl.
13) If we use the hyperbolic declinecurve only to fit the
production rate ver-sus time, the total reserves will be equalto
613,595 bbl for the time period, which equals to 3,168.5 months
(264years!), which corresponds from the ini-tial production until
the economic pro-duction limit, 100 bbl/month, as shownin Fig.
5.
The results have been compared withthe results of Long and Davis
and shown
in Table 1. It is clearly seen that the pro-posed model provides
similar results.9
CONCLUSIONSA new model for the production per-
formance of reservoirs was developed.The model uses an
exponential declineto extrapolate a hyperbolic decline toprevent
unrealistically long lifetime andreserve estimates.
The model includes a deterministicapproach to estimate the time
at whichone must use an exponential decline to
extrapolate a hyperbolic decline. Themodel introduces a simple
method to ob-
tain the point where the decline is expect-ed to hold and follow
an exponential de-cline. One can easily calculate reserves forthe
separate hyperbolic and exponential
decline segments and add them togetherto estimate the total
remaining reserves.
The proposed model is simple com-pared to the models available
in the liter-
Fig. 3. Decline rate predicted by hyperbolic decline model vs.
time.
Fig. 4. Oil production rate predicted by both hyperbolic and
exponential decline model
vs. time.
Fig. 5. Oil production rate predicted by hyperbolic decline
model vs. time.
o t andand
, rom the initialom the initialonential curve until theial curve
e
production rate.ro uc te.12) Determine the total reserves to)
Determine t otal res s to
be produced during the hyperbolic andbe produ during t yperbolic
and
exponential segments, which is equal toexpon ments, ch is
eq142,273 bbl.142,27
13) If we use the hyperbolic decline13) we use t olic decrve
only to fit the production rate ver-rve only to n rate v
time, the total reserves will be etime, t be13,595 bbl for the
ti13,59h equals to 3,h equal
, whic, whi
.
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PRODUCTION TECHNOLOGY
ature, and provides similar results whilesaving significant
amounts of time andeffort. In other words, this model is veryhandy
and easy to use, especially for rou-tine industry tasks.
LITERATURE CITED1 DeSorcy, G. J., Determination of oil and gas
reserves, Petroleum So-
ciety Monograph No.1, Second Edition, Canada, 2004.2 Lee, J. and
Wattenbarger, R. A, Gas Reservoir Engineering, 1st Ed.,
Society of Petroleum Engineers, Richardson, TX, 1996.3 Slider,
H. C., World-wide practical petroleum reservoir engineering
methods, Pennwell Publishing Co., Tulsa, Oklahoma, 1983.4 Arps,
J .J., Analysis of decline curves, Trans., AIME, Vol. 160,
1945, pp. 228-247.5 Koederitz, C. F., A. H. Harvery and M.
Hanarpour, Introduction to
petroleum reservoir analysis, Gulf Publishing Company,
Houston,Texas, 1989.
6 Kabir, M. I., Normalized Plot A Novel technique for
reservoircharacterization and reserves estimation, SPE 37031
presented atthe 1996 SPE Asia Pacific Oil and Gas Conference held
in Australia,28-31 Oct. 1996.
7 Purvis, R. A., Further analysis of production- performance
graphs,
J. Canadian Petroleum Technology,April 1987, pp. 74-79.8
Hayatdavoudi, A., Effect of Water-soluble gases on production
de-
cline, production stimulation, and production management,
SPE50781 presented at the 1999 SPE International Symposium
OilfieldChemistry held in Houston, Texas, 16-19 Feb., 1999.
9 Long, D. R., and M. J. Davis, , A new approach to the
hyperboliccurve.JPT, Vol. 40, 1988, pp. 909-912.
10 Roberston, S., Generalized hyperbolic equation, Unsolicited,
SPE18731, 1988.
11 Chen, Sh., A generalized hyperbolic decline equation with
rate-timedependent function, SPE 80909 presented at the SPE
Productionand Operations Symposium held in Oklahoma City,
Oklahoma,USA, 22-25 March 2003.
12 Chen, Sh., A generalized hyperbolic decline equation with
rate-time and rate-cumulative relationships, SPE 81427 presented at
theSPE 13th Middle East Show & Conference held in Bahrain 5-8
April2003.
13 Foster. G. A., and Wong, D. W., Reducing uncertainty in
reservoirmanagement using semi-analytical modeling and long term
dailydata acquisition, SPE 60309, presented at the 2000 SPE
RockyMountain Regional/Low Permeability Reservoirs Symposium
andExhibition held in Denver, Colorado, 12-15 March, 2000.
14 Fetkovich, M. J., Decline curve analysis using type curves,
paperSPE 4629 presented at the SPE 48th Annual Fall Meeting, Las
Vegas,Nev., Sept. 30-Oct. 3, 1973.
15 Spivey, J. P., A new algorithm for hyperbolic decline curve
fitting,
Paper SPE 15293 presented at petroleum industry Applications
ofMicrocomputers, Silver Greek, June 18-20, 1986.
16 Towler, B. F., and S., Bansal., Hyperbolic decline-curve
analysis,J.of Petroleum Science and Technology, 1993, pp.
257-268.
17 Nind, T.E.W., Principles of oil well production, 2nd Ed.,
Mc-Graw-Hill Inc., New York, 1981.
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constantsof hyperbolic decline, Oil and Gas J., Jan. 14, 1985, pp.
86-90.
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Pro-posed, Oi1 and Gas J., Jan. 21, 1985, pp. 77-80.
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Unsolic-ited, SPE 11329.
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analysis,J.Canadian Petroleum Technology, Vol. 38, No. 13, 1999,
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es-timating reserves using decline curves, Paper SPE 16925,
presentedat the SPE Hydrocarbon Economics and Evaluation
Symposium,Texas, March 2-3, 1987.
THE AUTHOR
Dr. Khaled Abdel Fattahobtained his BSc, MSc,and PhD degrees in
pe-troleum engineering fromCairo University in 1985,1988 and 1991
respec-tively. He joined CairoUniversity, Giza, Egypt, asan
instructor of petroleumengineering. He rose to
the rank of associate professor in 1997. In 1998he was awarded
the distinguished prize of post-graduate studies supervision from
the centerof the Advancement of Post-Graduate studiesand Research
in Engineering Sciences- CairoUniversity. Now, he is working with
King SaudUniversity at Riyadh, Saudi Arabia. PetroleumEngineering
Department, College of Engineer-ing, King Saud University, Saudi
Arabia, P.O.Box 800, 11421 Riyadh.
Long & DavisParameters method New Model
Initial production rate for the exponential decline, bbl/month
718 717
Exponential decline rate, 1/month 0.005157 0.005145
The time, to, at which the forecast should be changed from
ahyperbolic curve to an exponential curve, months 28.5 28.7
The reserves to be produced during the hyperbolic segment, bbls
21768 22373The reserves to be produced during the exponential
segment, bbls 120242 119900
The total reserves to be produced during the hyperbolic
andexponential segments, bbls 142010 142273
TABLE 1. Comparison of the results between Long & Davis
andthe New Model.
ves, Petroleum So-, etroleum So-, anada, 2004.ada, 2004.
, as Reservoir Engineering, 1st Ed.,Reservoir Engineering, 1st
Ed.,
g neers, Richardson, TX, 1996.ardson, TX, 19orld-wide practical
petroleum reservoir engineering- troleum r eser g
, Pennwell Publishing Co., Tulsa, Oklahoma, 1983., ennwell
Publishing lsa, Oklahom Arps, J .J., Analysis of decline curves,
Trans., AIME, Vol. 160,ps, J . J. , Analysis of decline c Trans. ,
AI . 160,1945, pp. 228-247.1945, pp. 228-247.
55 Koederitz, C. F., A. H. Harvery and M. Hanarpour,
Introduction toKoederitz, . Harvery and narpour, Introduction
topetroleum reservoir analysis, Gulf Publishing Company,
Houston,petroleu lysis, Gulf P ng Company, HTexas, 1989.Texas,
19Kabir, M. I., Normalized Plot A Novel technique for
reservoirKabir, M. alized Plot chnique forcharacterization and
reserves estimation, SPE 37031 presented atcharacter iza n and
reserves esti 37031 presethe 1996 SPE Asia Pacific Oil and Gas
Conference held in Australia,the 1996 SPE Asia Pacific Oil ce held
in Aus28-31 Oct. 1996.28-31 Oct. 1996.
urvis, R. A., Further analysis of production- performance graphs
urvis, R. A., ormance gra
n production de-de-ction management, SPE, SPE
nternational Symposium Oilfieldilfieldn, Texas, 16-19 Feb.,
1999.n, Texas, 16-19 F
. J. Davis, , A new approach to the hyperbolic. J. Davis, , A
new approac perbolic T Vol. 40, 1988, pp. 909-912.l. 40, 1988, pp.
909-912.
oberston, S., Generalized hyperbolic equation, Unsolicited,
SPE., Generalize ic equation, Un d, SPE18731, 1988.8.
11 Chen, Sh., A generalized hyperbolic decline equation with
rate-time., A generaliz e equation wit -timedependent function, SPE
80909 presented at the SPE Productiont function, at the SPE ionand
Operations Symposium held in Oklahoma City, Oklahoma,a rations Symp
oma City, O ,USA, 22-25 March 2003.U 25 March 20
1212 Chen, Sh., A generalized hyperbolic decline equation with
rate-Ch ., A general e equationtime and rate-cumulative
relationships, SPE 81427 presented at theti te-cumulative 1427
presenSPE 13th Middle East Show & Conference held in Bahrain
5-8 Apriliddle East Sho eld in Bahrai2003.
1313 Foster. G. A., and Wong, D. W., Reducing uncertainty
inFoste nd Wong, D. W., Reducing uncertaimanagement using
semi-analytical modeling andmanage semi-analytical modeling adata
acquisition, SPE 60309, presenteddata acq 60309, presentedMountain
Regional/Low PermeaMountainExhibition held in DenveExhibition h
144 Fetkovich, M. J., Fetkovich, M. SPE 4629SPE 4
. --
, he Error ie Error er SPE 16925, prese PE 16925, prese
ics and Evaluation Symposius and Evaluation Sympo.
HE AUTHORHE AUT
Dr. Khaled Abdel Fattahaled Abdel Fattaobtained his BSc, MSc,o d
his BSand PhD degrees in pe-an D degretroleum engineering fromtrol
engineerCairo University in 1985,Cair iversity i1988 and 1991
respec-198 1991 rtively. He joinetiv joiUniversity,Uan i
the rank ofankhe
