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7/24/2019 Appraisal of Analytical Steamflood ModeIs
1/12
SPE
SPE 200;3
Appraisal of Analytical Steamflood ModeIs
H-L. Chen, Texas A&M U., and N,D. Sylvester, U. of Akron
SPE Members
CopW9htWSO,SOCletYf PetroleumErrgirreecanc.
TIIlspaperwee preparedforpreaantationat the @OthCaliforniaRegionalMeetingheldirrVentura,California,April4-S, 1S90.
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$teamflooding in heavy oil reservoirs is one of the
principal thermal oil recovery methods. This paper evaluates
the existing analytical steamflood models with respect to their
mechanisms and predk ive capabilities and compares them
with field data. The three steamflood models selected were: a
frontal advance model [Jones (1981)], a modified frontal
advance model [Farouq Ali (1982)], and a vertical gravity
override model [Miller and Leung (1985)]. Each model was
somewhat modified to improve its abil ity for the prediction of
production rate and/or history match of typical field
production data.
The Jones steamdrive model, with its empirically
determined scaling factors, was found to give a reasonable
history match of oil production for the Kern River field.
Fields with different characteristics will require an
adjustment of these scaling factors artdlor f ield property data
to achieve an acceptable history match. The modified Farouq
Ali steamdrive model gives a good history match without need
for empirical factors or adjustable parameters. It is thus
recommended for the prediction of steamdrive oil recovery
when fisld production data are unavailable. The Miller-Leung
gravity override steamflood model, which contains two
adjustable parameters, was found to posses the best W3rail
history matching capabili ties and is recommended for this
purpose.
ANDI ITFRATLW.BUUW
The injection of steam into heavy or pressure depleted oil
reservoirs has been a successful enhanced oii recovery
process for more than three dsoedes. A principat application
of the steam injection is steamflooding which is also termed
steam drive or steam displacement. In this process, steam is
continuously injected into
a
number of injection wells, and the
dispiaced fluids are produced from the production wells.
Ideally, the injected steam forms a steam saturation zone
around the vkinity of the injection welL The temperature in
the steam zone is nearly equal to that of the injected steam.
References and figures at end of paper.
Moving away from the injection well, the steam temperature
drops graduaily as the steam expands in response to the
pressure drop and heat losses to base formations. At a certain
distance, the steam condenses and forms a hot-oil bank. In the
steam zone, oil is displaced by the steam. In the hot oil zone
several changes take place which result in oil recovery. They
include heat losses the formation, thermat expansion of the oil,
and reduction of oil viscosity. In addition, residual saturation
may decrease and changm in relative permeability may occur
due to the variations of temperature and saturation.
There are three major options available in literature for
predicting the reservoir response to steamflocding. These
include: empirical correlations 2) , Simple analytical
models(l 13-7),and muit icomponent, multiphase numeri~al
simulators(8-11 ). Empirical correlations can be useful for
correlating data within
field and for predicting performance
of new wells in that or similar fields, However, use of such
correlations for situations much different from the ones that
led to their development can result in large discrepancies for
hist~. ~ matching.
Numerical simulators yield rigorous
solutions to the material and energy balances, However, their
results are sensitiva to the rock and fluid property input data
and other geological information, some of which may be
unattainable. In addition, large computation time is required
and numerical convergence, and stability problems suggest
that thermai simulators are not appropriate for short-cut
design and/or preliminary evaluation for steamflooding
projects. Thus, the incentive to develop simple analytical
models which account for the important mechanisms invotved
and for routine or approximate engineering prediction is
obvious. The existing analytical steamflood models can be
divided into two categories:
1. Frurrta/advance models: The steam-drive mechanism is
2.
modeled as a horizontal frontal displacement [Figure
1(a)]. The steam zone ISassumed to gmw horizontally
and the tendency of the steam to finger beyond the front
is suppressed by condensation.
Verlikal displacemet?t or gravity overz lemodels:
The
problem of gravity overr ide of the steam due to its low
la
. .
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2
APPRAISALOF ANALWICAL STEAMFLOODMODELS
SPE 20023
density assumes that the principal direction of steam
zone propagation is vertically downward [figure
2(b)].
An early frontal advance model was that of Marx and
Langenheim(l 2) who applied an energy balance of a radially
growing steam zone In which one-dimensional conduction heat
losses, uniform steam zone and reservoir temperature were
assumed. Willman el al.(13) presented a model similar to
that of Marx and Langenheims but included the Buckley-
Leverett equation to estimate oil production from a hot water
zone ahead of the steam zone. Mandle and Volek(l $)extended
the concepts of Marx-Langenheim by including convective heat
transfer from the steam zone into the region ahead of the
condensation front at times greater than a cri tical time. The
model was modified by Myhill and Stegemeier(l 5) to calculate
the thermal efficiency after tha cri tical time to account for the
disparity observed in physical models versus theory.
Jones(l) noted that the Myhill and Stegemeier model often
overestimates the oil production, especially in the early phase
of a project because of the assumption that the oil displaced by
the steam zone is immediately produced. Thus, there was no
lag in oil production due to fi ll-up of any gas volume, or due to
the development of an oil bank. Jones(l) thus developed a
modified predictive model including the results of van
Lookeren(l 6) for taking into account the extent of steam
override, and introduced three empirical factors to account for
the dominant mechanisms during the three stages of
production.
Neuman (2S17, and Rhee and Doscher(3) proposed that
the principal direction of steam zone growth is vertically
downward In the horizontal reservoirs. Neumans(17) model
requires the data of relative permeabil ity to oil and water as
functions of temperature. Also, oil production from the
condensate zone was determined semi-empirically. Aydelotte
and Pope(4) used fractional flow theory and overal l energy
and material balances to account for changes in oil cut, gas
production, etc.. Also volumetric sweep eff iciency was taken
into account by using van Lookerens( 16) vertical sweep
efficiency and an empirical correlation given by Farouq
All( 18) for areal sweep efficiency {EA). This model is
restricted to horizontal, homogeneous, isotropic, and
incompressible reservoirs and only five spot sweep
corrections were included.
Doscher and Ghassemi(f 9)
proposed that he steamflood process consists of the heated oil
displaced by a gas drive mecharrism. Their model showed an
insensitivity of oil recovery to formation thickness, especially
during the early stage of production. Their experimental
results indicated that the oil/steam ratio increases with a
decrease of oil viscosity.
Unlike previous models, Vogel(20) proposed that oil
production was not driven by the growing steam zone, but vice
versa, He pointed out the general weakness of predictive
models based on simple energy balances of a growing steam
zone. With a predominantly overriding steam zone, the heat
balance calculations require that the steam produced In
production be accounted for as well as the steam that migrated
out of pattern, Vogel suggested that the total underground heat
requirement was equal to the heat in the steam chest plus the
heat flow upward and downward from the steam chest. He
concluded ;hat oil production must be determined from some
way other than steam zone growth,
Miller and Leung(6)
utilized the concepts of VogeI(20) and Neuman( 17, to
determine tka oil production rate by conductive heating of the
oil below the steam zone.
The purpose of this paper is to evaluate existing analytical
steamflood models with respect to their mechanisms and
predictive features. Three typical steam flooding models were
studied and modified by Chen(21): Jones(l) frontal advanced
model, Farouq Alis(5) modified frontal advance model, and
Miller and Leungs(6) vertical gravity ovarride model.
History-matching of field data were carried out for each model
to test its applicability.
Table 1 summarizes the characteristics and the
parameters for three steamflood models. Complete parameter
sensitivity analyses for each model are available in
Chens(21) dissertation.
The major modifications for each
model are presented in the Appendix section.
Jones(l) applied van Lookerens(l 6, method for the
optimal steam injection rate for a given set of steam and
reservoir parameters, and utilized the Myhill and
Stegemeier(l 5) method to predict oil production. In the
Myhill and Stegemeier model, the average thermal efficiency
of the steam zone was calculated by the Marx and
Langenheim(l 2) solution at early times while the Mandl and
Volek(l 4, method was used to account for heat transfer
through the condensation front after the critical t ime. Jones
model contains a number of empirical factors
(ACD, VODt VPD)
which were obtained through history matching for specific
sets of field production data. Thus, the adjustment of field data
may be necessary (TR, ht,hn ,t.toI) to achieve reasonable
history matching for some projects as shown in Jones Table 1.
In the original Jones model, the steam injection pressure was
calculated assuming a geometric relationship between
pressure and injection rate. The optimum steam injection rate
is taken to be the steam injection rate which gives the
maximum value for the vertical conformance factor (ARD)
Unfortunately, steam Injectivity test data is often not available
in the field.
Therefore, the computer program written to
evaluate the Jones model was modified to allow input of steam
injection rate and pressure, This modification was necessary
to permit comparison of model predictions with actual field
data.
Farouq Atis(5) model is a modif ied fontal advar ]d model
which considers the effect of steam gravity override using van
Lookerens( 16) method. At any instant of time during the
production, the model predicts both oil and water production-
displacement rates, the steam zone volume-thickness, the
heated zone average temperature and the water and oil
saturations. An advantage of the model is that It simulates the
dominant mechanistic features by material and energy
balances and does not employ empirical factors. However, this
produces the modets primary disadvantage in that several
parameters such as Sorst, Sor, Sst
and
Swir are required
which, unfortunately, are normally unknown and need to be
assumed or defaulted by using acceptable values. Also, it has
been shown by Chen(21 ) that the water saturation during
production affects the relative permeabilities and the
production rate, and the model predictions are very sensitive
to the accuracy of the Krw and Kro versus SW* which are
difficult to obtain through experiments. Even though the
experimental difficulties can be overcome, the data may not
represent the actual relative permeability versus saturation
I
----
7/24/2019 Appraisal of Analytical Steamflood ModeIs
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3
H. L. Chen and N. D. Sylvester
SPE 20023
relations due to the effect ot temperature and reservoir
heterogeneity. ,.I .}
relative permeabllities versus saturations
equations presented by Farouq Ali were based on the curves
presented by Gomma(22), These normalized curves were
obtained through history matching of the Kem River field data
reported by Chu and Trimble (23), The prediction of the
original Farouq Ati model for the Kern River A field production
data indicates it to be totally inadequate at long times (>1.5
years). Several important modifications were able to take into
account heat losses [Figure 2(a)] and displacement mechanism
[Figure 2(b)] to improve its deficiencies. These are discussed
in Appendix (b).
Miller and Leung(6) developed a simple gravity override
model which assumed a complete vertical overlaying steam
zone with a steam-condensate zone between the steam zone and
the oil zone below. They used one-dimensional, unsteady state
heat conduction to calculate the temperature distribution
inside the
COIIdWISate
and oil zones, and employed tha
Neuman(l 7) method to determine condensate zone thickness as
a function of fract;on of condensed steam that is produced from
the reservoir (fcp: 0.7-O.95).
They ciaimed that the modei
overrxedicts the oi l twoduction rate for fieid cases with iarge
patterns (> 10 acres)because the steam override may not be
fully developed in those cases. Therefore, another trmPirical
factor, the areal sweep efficiency (EA: 0.4-1,0) presented by
Aydelotte and Pope(4) was introduced for the field cases with
Iar9e
pattern area.
Chen(21) has shown that both values of
fcp and EA have substantial effects on the predicted oil
production rate.
in addition, the heat baiance which
determines the optimum steam injection rate was modified by
Chan(21) to take into account the fact that the steam injection
rate should be based orI cold water fed to a steam generator not
on saturated steam.
The five of fieid projects l isted in Table 2 were chosen for
history matching.
They represent smail [Kern-A(23), Kern-
Canfield(24), and Kern-San Joaquin(24)], medium [Kern-
Ten Pattern], and large pattern areas [Tia Juan].
The field production history data for each fieid case was
adapted from the Enhanced 011Recovery Fiei6 Report (27). A
time ir?crement of 1.2 month was used for the prediction of
Kern River A project, and 1.5 month for Kern-Canfield and
Kern-San Joaquin matches.
The time increment us d in
medals for Kern-Ten Pattern and Tia Juana was chosen ~~be
one month because the production history data was reported
monthly. it is noted that the Kern River A field data was the
oniy used to test the performance prediction for the modif ied
Farouq Alimodel because of the availability of reiati~e
permeability versus saturation relations which are required
by this model. The other four field production histories were
used to compare the predictive performance of the Jones and
Miiler-Leung models.
Figure 3(a) shows, the performance prediction for the
Kern River A field using the modiflad Farouq Ali model. Also
shown are the predictions obtained using the Myhill and
Wegemeier (15) model, the numerical simulation results of
Chu and Trimbie(2~), and the actual field data. Figure 3(b)
compares the calculated cumulative production versus time
results to
the field data. The agreement Is good with a
difference after 5 years of only 5.5% for cumulative oil
production. It is
apparent in
Figure 3(a) that the modified
Farouq All model gives superior predictions to those of
Myhill-Stegemeler and Chu-Trimble.
Figure 4(a) shows that the Jones model predicts a lower
oi l production rate at the beginning and a highar production
rate for the longer times for Kern-Canfieid project. Figure
4(b) shows that aithough the Jones modei underpredicts the
cumulative oi l production, the prediction improves as time
increasp. As shown in Table 3, at the eyf of the 7.5 years, the
Jones modei overestimates the cumulative production by
2.1 EYO.
it
is seen in Figure 4 that the prediction of the
Miiier-Leung model is superior to the Jones model for this
fieN case.
The comparison between the Jones model and Kern-San
Joaqukt f ield is similar to the Kern-Canfield case. That 1s,the
oil production rate is underestimated at short times and
overestimated at long time as shown in Figure 5(a)t while the
prediction of the Miller-Leung model is just the reverse. The
Miller-Leung model with a iag time (z) of 61 days is capable
of predicting the production up to about 1.75 years. The
computer run was terminated after two years bacause the
thickness of the condensate and steam zones became iarger that
the net thickness of the reservoir. Table 3 shows that the
Jones model overestimates the cumulative production by
8.1770 at the end of the third y~ar, and the Miller-Leung
model overestimates the cumulative production by 3.39 % at
the end of the second year.
Figure 6(a) shows that both the Jones and Mii ler-Leung
modeis underestimate the oii production rate for Kern-Teil
Pattern field for the first two years. it also can be observed
from Figure 8(a) that the Milier-Leung prediction is
superior to Jones modei during this time.
Aithough the
predicted production rate of the Miller-Leung model decreases
sharpiy after 5.5 years, the MiIler-Leung model gives a more
accurate cumulative oil production up to about 5 years as
shown in Figure 6(a) and Tabie 3.
Figure 7(a) shows that neither model does weli in
predicting the measured oii production rates for the large
pattern case of the Tia Juana field aithough Figure 7(b) shows
that both models do reasonably well in predicting the
cumulative oil production. It should be noted that the Tia
Juana case is a poor candidate for triatory matching because the
less productive wells were steam stimulated, there were a
large number of unrepaired welis in the pattern, and the two
productive
zones
had oils of different viscosity. This may
explain the observed decline of oil production rate.
The following conclusions can be drawn form the
resuits of the steamflood model modification and evaluation:
1, The Jones modei with input of steam injectivity data
can be used to predict oil production for steamflooding projects
with properties similar to the Kern River field. For other
cases, the empirical factors or input data may require
adjustment to achieve better history-matching.
2. The modified Faro~q Ali model is the most realistic
steamflood modei because it simulates both 011and water phase
dominant mechanisms (such as the combination 6f frontal
advanoa and steam override) by matedal and energy baiances.
In addition, this model gives reasonably good prediction and
history-matching results without requiring any empirical
factors or adjustable parameters.
However, retatlve
permeablilty versus water saturation data is needed for fields
otker than Kern River A to obtain reasonable history-
matching.
101
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4
APWWSAL OF A?lALvrloAl STEAMFLOODMODELS
SPE 20023
3. For history-matchingof field data, the modified Miller
and Leung model is better than the Jones model. Careful
adjustment of the parameters fcp and EA yields accurate
history-matching.
4. Use of the modif ied Farouq All model is recommended
for predicting steamflood production when field production
history is not available. The Miller and Leung model is
recommended for trtstory matching of steamflood performance.
%4)
= dimensionless steam zone size
API
c1
q,
&
fc p
fsdh
hfs
= specific gravity of oi l at 60 F, dimensionless
= specif ic heat of phase i, Btu/lbm-F
= areal sweep efficiency
x vertical sweep efficiency
= tondensed steam produced, fraction
= cownhole steam quality, fraction
= enthalpy of saturated steam at steam temperature,
Btu/lbm
hn
= net zone tl~ickness,ff
hs = steam zone thickness, ft
ht
-
grosszonethickness, ft
ist
= steam injection rate, cold water equivalent BWp O
Kh = thermal oonductfvity of cap rock and base rock,
Kro
Krw
Lvdh
b
%
N
N
P
%
qoi
qw
Btu/ft-hr-F
x relative permeabil ity to oi l, fraction
= relative permeability to water, fraction
= latent heat of steam, Btu/lb
= heat capacity of cap rock and base rock, Btu/ft3-F
9
heat capacity of steam zone, Btu/ft3-F
= oil originally in place, bbl
= cumulated oil displacement, bbl
= cumulative oil production, bbl
= oil productionrate, BOpD
= pre-steamoil productionrate, BOPD
= water production rate, BWPD
6
= heat Injection rate, Btu/hr
QI
- heat bsses to cap rock andsteam zone, Btu
G>
= oil displacement rate,BOpD
Qw
= waterdisplacementrate, BWPD
so
= oil saturation, fraction
%c
= condensate zone oil saturation, fraction
Soi =
initial oil saturation, fraction
Sor
= residual oil saturation, fraction
Scrst = steamflood residual oil saturation, fraction
%s
= steam zone oil saturation, fraction
Sq =
steam saturation in the steam zone, fraction
SW
=water saturation, fraction
s~
- (~-swir) (-Swir-Sorw). dimensionless
Sw/r
= irreducible water saturation, fraction
t
= time, hr
tc
= critical time, hr
c D
= dimensionless critical time
At
- t ime increment, hr
tB T
= steam breakthrough time, hr
T1,2 =
temperature at condit ions 1 and 2, F
Ts
= steam temperature, F
TR
= initial formation temperature, F
v~
= bulk volume of the pattern, ft3
B
= VB -s(rr+l), fti
oD
= dimensionless displaced oil prtiucad
vpD
=
Initial pore void fil led with steam as water,
dimensionless
Vs(t) = steam zone volume at time t, f@
VsBT = steam zone volume at breakthrough, ft3
a
= reservoir thermal diffusivity, ft2/day
@
= porosity, dimensionless
z = constant (=3.14159)
P
= density of phase i, lbm/ft3
s = lag time, days
v
= viscosity , cp
Voi
= oil viscosity at ini tkd reservoir condition, cp
(n)
= at time step n, dimensionless
avg = average temperature condition
sdh
= steam at downhole condition
o = oil phase
s
= steam phase
R
= rock phase
w
= water phase
1. Jones, J.:
Steam Drive Model for Hand-Held
~~~~~;able Calculators, J. Pet. Tech. (Sept. 1981)
.,
2.
Neurnan, C.H, A Mathematical Mo ,el of Steam Drive
Process-Application; paper SPE 47.,7, presented at the
California Regional Meeting of the SPE, Ventura,April 2-
4, 1975.
3. Rhee, S.W., Doscher, T.M.: A Method for Predicting 011
Recovery hy Steamflooding Including the Effects of
Dlstillatkm and Gravity Overrlde~ Sot.
Pet. Eng. J Aug.
1980) 249-66.
mm
7/24/2019 Appraisal of Analytical Steamflood ModeIs
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H. L. Chen and N. D. Syfvester SPE 20023
4,
5.
6.
7.
8.
9.
10.
lf.
12.
13,
Aydelotte, S.R, and Pope, G.A.: A Simplified Predictive
Model for Steamdrive Performance: J. Pet. Tech. (May
1983) 991-1002.
Farouq All , S.M.: Steam Injection Theories - A Unified
Approacht paper SF2 10746, presented at California
Regional Meeting of the SPE, San Francisco, March 24-
26, 1982.
Miller, M.A. and Leung, W.K.: A Simple Gravity Override
Model of Steamdrive paper SPE 14241, presented at the
60th Annual Technkal Conference and Exhibition of the
Society of Petroleum Engineers held in Las Vagas, Sept.
22-25, 1985.
Wingard, J.S. and Orr, F.M. Jr.: An Analytical Solution
for Steam/Oil/Water Displacement; paper SPE 19667,
presented at the 64th Annual Technical Conference in San
Antonio, TX, Oct. 8-11, 1989.
Coats, K.H., George W.D., Chu, C. and Marcum, B.E.:
Three-Dimensional Simulation of Steamflooding: Sot.
Pet. Eng. J. (Dec. 1974), 573-92.
Crookston, R.B., Culham, W.E., anfi Chen, W.H.: A
Numerical Simulation Model For Thermal Recovery
processes,- Sot. Pet. Eng. J. (1979) 19, 37s58.
Vinsome, P.K.W., and Westeweld, J.: *A Simple Method
for Predicting Cap and Base Rock Heat Losses in Thermal
Reservoir Simulators,
J. Can, ~e?. Tech.,
19,
No. 3
(1980) 87-90.
Barry, R.: A General Thermal Model: paper SPE 11713,
presented at the California Regional Meeting in Ventura,
March 23-25, 1983.
Marx, J.W. and Langenheim, R.H.: Resewoir Heating by
Hot Fluid Injections Trans., AlME (1959) 216, 312-
15.
Willman, B.T., Vallerory, V.V, Runberg, G.W. Cornelius.
A.J., and Powers, L~W.:
Laboratory Studies of Oil
Recovery by Steam Injection; J. Pet. Tech. (July 1961j
681-90.
14. Mandl, G. and Volek. C.W.: Heat and Mass Transport In
Steam-Drive Processes, Sot. Pet. Eng. J. (March 1969)
46, 59-79; Trans., AIME.
15. Myhlll, N.A. and Stegemeier, G. A.: Steam-Drive
Correlation and Prediction, J, Pet. Tech. (Feb.
1978)173-182.
16. van Lookeren, J.: Calculation Methods for Linear and
Radial Steam Flow in Oil Resewolr; paper SPE 6788
presented at the 52th Technical Conference and
Exhibit ion, Denver, Colo. Oct. 9-12, 1977.
17. Neurmn, C.H,: A Gravity Override Model of Steamdrive,
J,. F . Tech.
(Jan. 1985) 163-6%
18. Farouq All, S.M.: Graphical determination of 011Recovery
in a Five-Spot Steamflood paper SPE 2900, presented at
the Rocky Mountain Regional Meeting of SPE, Casper, WY.,
June 8-9, 1970.
19. Doscher, T.M, and Gh&ssemi, F.: The Influence of Oil
Viscosity and Thickness on the Steam Drive; J. Pet. Tech.
(Feb. 19S3) 291-98.
20, Vogel, J.V.:
Simplified Heat Calculations for
Steamflood, J. Pet, Tech (July 1984) 1127-35.
21. Chen, H.-L.: Analytical Modeling of Thermal Oil Recovety
by Steam Simulation and Steamflooding,- Ph.D.
Dissertation, The University of Tulsa, Tulsa, Oklahoma
(1987),
22. Gomma, E.E,: Correlation for Predicting Oil RecoveV by
Steamflood; J.
Pet. Tech.
(Feb. 1980) 325-32.
23. Chu, C. and Trimble, A.E.: Numerical Simulation of Steam
Displacement-Field Performance Applications, J. Pet.
Tech. (June 1975) 765-76.
24. Greaser- G.R. and Shore. R.A.: Steamffocd Performance in
25.
26.
27.
28.
----., ... .
the Kern River Field, paper SPE 8834, presented at the
1s Joint SPE/DOE Symposium on Enhanced Oil Recovery,
Tulsa, OK, April 20-23, 1980.
Oglesby, K.D., Belvins, T.R., Rogers.E.% and Johnson*
W.M.: Status of the Ten-Pattern Steamflood Kern River
Field, California J. Pet. Tech. Oct.1982 2251-57.
de Harm, H.J. and van Lookeren: Early Results of the
First Large-Scale Steam Soak Project in the Tia Juana
Field, West Venezuela J. Pet Tech. (Jan. 1969) 101-
10.
Enhanced 011 Recovery Field Report, 11, 2, Society of
Petroleum Engineers (1986).
Somerton, W.H., Keese, J.A., and Chu, S.L.: Thermal
Behavior of Unconsolidated Oil Sandst Sm. Pet. Eng. J.
(oct. 1974) 513-21.
29. Leung, W.K.: A Simple Gravity Override Predictive
Model, M.S. Thesis, The University of Texas, Austin
(1986)
APpFNW
The changes made to the Jones model permit direct input
of steam injection rate and pressure, and dimensionless
volume of displaced oil produced as:
NPSoi
VO 3= [-~(~oi.sor)l
1
where Np is used insiead of Nd in the original Jones paper(l)
[Eq(A-25)] since VODIs a function of the amount of displaced
oil which equals the total amount of mobile oil less the
cumulative oil production.
Several modif ications have been made to the Farouq Ali
model to improve its predictive capability.
I Tim
The critical time calculation recommended by Mand19and
Volek(14) was used :
t.= [ -xqtcD
4 Kh MA
(2)
I
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7 H. L. Chen and N. D. Syfvester
SPE 20023
In Figure 2(b), the solid line indicates the extent of
displacement by steam, The displaced volume Is the volume
~
between the dashed and sol id lines. The material baiance for
the displacement element is given below.
The only modification made for the Miller-Leung model
is m the calculation of optimum steam injection rate whkh
The oil displacement rate, ~o, is given by:
was originally presented by Leung (29) as:
Qi
Q.= Av~ S~)-SOr t)
(19)
ist=
(27)
5.6146 PWLvdhAt
The water displacement rate, Qw, is given by: To account for the fact that the sleam injection rate should be
based on cold water fed to a steam generator,
Eq (27) becomes
C)w = AVS@[St)- l -Sst -S.rst)]
is t-
Qi
(28)
= AVS$(S$)- 1+Sst -+Sor$t)
20)
5.6146 p~[hfs+fsdhLvdh-& (TR-32)]
Then, the overail material balance on oil-water zone between
where the amount of heat injected, Q i is calculated by
t(n) and t(n+f ) is as follows:
Vogel(20) as:
For oil :
Qj=4K~A(Ts-TR)@+ AhsMs(Ts-TR) (29 )
Qo - qoAt =
[VB-VY)]I$[S$+)- S$)] (21 )
Assume that VB - @+)= v;, then
for wate~
Qw -
qwAt =
V:@[s$+ )- s ?] .
= V:o[(l -s +)- Sg)-(1-swsg)]
= v@@lw+)]
(22)
From Eqs (21) and (22) we have
*=
W&[sy+wq
(23)
w
Qw-v@o
(n)- - s +l ) l
From the fractional f iow eqution, we can write
fw=~=~
(24)
qo+q~
1+Kro~w
Krwpo
Let,
qo Kro~w c
= . .
(25)
qw K~oVo
(n+ )
Substituting Eq (25) into (23) and solving for So
gives
Sy (1+C)+
Qo-CQw
Sy+l) =
t$v;
(26)
1+C
-..
111
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Wb ~qp~g~
Me
1
Summary of Steamflooding Models
Jones (1981)
Farouq Ali (1982)
Miller and Leung (1985)
rype
of the Modal
FrontalAdvanoe
Modified Frontal Advance
Vertbal Advanoe Gravity Override
Cftaracteristios
1. Predkts ~,~, Ehs,and
Fos.
1,
Prediits
~,~,qw,So,~, and
1. Pradiote~ and ist.
andTaW
2. Adjustment of fW SW,%s. ~,ad
2. Empirkal coefficientssuchas
2. Requires defaulted values for
and EAv lu s
maybe
nacaasaryor
AcDtVOD, Vpo areused.Data
Sorst,Sor,%irl ad %t.
for reasonablehistory-rnafohiftg.
suchas TR,hn,~i mayneed
3. Km, Kmvs.&data needed
3. Tuningof f ield data for history=
to be adjustedto obtaingood
when a ffefd0sss other than
matching is notnecessary.
history matching for some
Kern Riier-A field is evaluated.
field cases.
Tuningof hn may needed for
reasonable history-matching.
Comparison d
Underpradots ~ at short t imes
Was notevaluated for field cases Setter pradktbn than Jones model
Predictive Ability
and
over-shoots
he measured
other than Kern River-A project.
especially for large ~atterrt area fieftf
values at bnger time for large
cases (see Tabte 3).
., pattern area oases.
[see Figures 6(a) and 7(a)]
Sensitive
isto Soit sdh
ist~sdh$orst
fcP EA, ~i, hi, S~, ~c
Parameters
lBbles Z
Data Used
for History Matching
Field T~ TR
kaI(TI ) WOI(T2) ~01
qoi
f~dh API Soi ht hn
(:F) (~) [cp(F)j [GP(F)] (CP) (BOPD)
(ft) (ft)
Kern River A
380 95 1380(100) 47(200)
1380 25 0.7 15 0.5 75 9rJ
iChu.Trlmble(23)]
Kern-Canfield
300
100 1700(100) 10[230)
f700 15 0.7
13.5 0.51 125 80
iQreaaar-Shoro(24)]
Kern.SanJoaquin
300 90 1000(100) 10(250) 1000 10
0.75 14.5 0.52 33 29
iGraaaar-Shoro(24)]
Kern-1O Pattern
400 SO 2710(85) 4(350)
2710 230 0.7 14
0.50 97 97
iO@aabyet 4J2S)]
(acres)
(BWPD) {tt2/D) (BTU/tt3
2.5
2.7
2.7
60.7
137
0.345
225
0.31
300
0.2s 300
0.33
6000
0.33
5s000
0.96
1.097
1.097
0.870
0.9s
35.0
3s.4
38.4
35.7
35,0
laJuana
400 113 27S0(1 13) S{350)
2780 1S40 0.6 15 0.71 250 200
[da Haan6
m Lookardq
-112
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Fmb$aNp
m
Kem.Canfield
132677
(7.5)
Kern.San
28928(2.0)
Joaquln
37507(3.0)
Kern-Ten 334346a
Pauorn
(6.0)
TiaJuana
10414373
(5.5)
Comparisonof \hs History Match Roaultafor
Ulllmato Cumulative 011 Production
%%
NP %
udU@@Qcs
Lkl?lsl~
124053 -6.50
136531
2.t5
(7.5)
(7. s)
42912
1s.21
40571
8.17
(3.0)
(3.0)
3131158
-9.35
3572606
6.84
(6.0)
(6.0)
110800s4
6.39
---- ----
(5.5)
Np
136198
(7.5)
30943
(2.0)
3313459
(6.0)
10073073
(5.5)
%
2.65
3.39
-0.90
.3.28
1. Thenumbernaldaheparentfwalsrdkatestheuitimateoilpmdwtbnyearby thefielddataorpredkfivemdal.
2. % difference [(Np,model.
NpMd)1fJP.f~~x1~
Heat condid lon to cap
rock
4
Stec.rn ZO= 011zone
+
+
Heatcanductlon ta base rack
(a) Frontal AdVCWICedDisplacement
Heat ccmductkrn to caD rack
Steam zone
4
Haofnowto
undeftyfngzone
Condenwte
011zone
= 20023
----- -- --
1-T*
ASEOCK
(a) Heai Losses
x
,a
n
--
,/
R,H
0 0:
*71W
,+
INITIAL (1)
%.$:
SW*8W
fkal
(1+1
so swat
$WI-seidor.t
(b) Dlsplaoement Meohanism
Figure 2. Control Volumo for
Energy
end Material Eralencee
(b) Vertical or Gravity Overrtde Dtsptacement
(Modified Farouq Ali Model]
Note: ~ k the dkectlon of heat transfer
~ k thedkecflonofsteam@owth
Ffguro1. lhe Mechonf$rnof St-m Displocemonf
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1- 1
I
I
I
I
I
t
Otn
I
S V
Tk[YCARM
(a) oil Production Ratevs. Time(At= 0.1 year)
(b) Cumulat ive Oil Productionve. Time (At.= 0.1 year)
Figure 3, History Match of Kern River - A
Data
I
.a
TIK
IWRIr
(a) Oil Production Rate vs. Time (At -0.125 year)
d
m
I .m
m.m
. . .
S.n
.
Tna
w
(b) Cumulat ive Oil Production vs. Time (At = 0.125 year)
B
FigUre
4. HietorY Matoh ot Kern - Cenfed at a
m
7/24/2019 Appraisal of Analytical Steamflood ModeIs
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*E 20023
d
1
i
1
:euklo mr-w~
rmlmalws -
d,
,4aKerlaa
I
I.*
1.40
mm
.40
a
aw
1.40
TM -
(a) 011
Production Rate vs. Time (At -0.125 year)
(b) Cumulative 011 Production vs. Time (At -0.125 year)
Figure 5. History
Matoh of Karn - San Joaquin
Data
am
.
b
-s
4rn .
/
,$
r :
*
Ira
:Mr4 .
9
~om .
I
/
iia.
s
F:a.m W O PA-
ml lm nM s
,maammm.
l.a
9.41
4.*
s.o
4.U
Tin? m
(a) Oil Product ion Rate vs. Time (At -1 Month)
+
i d .
a
Ii :
Xsl,m Wm4-lo Mm
i
. ~*-
i
4QEa -
*4
n.m
S.U
4.n
s.n
- .m
.a
1.48
11= -
b) Cumulat ive 011Production vs. Time (At -1 Month)
Figure 6. History Match of Kern . Ten Pattern Data
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sPE
20029
3
h=88
S417
-t
=~
8-
-L
8
8
8
8
F - TIA _
m87
/
,
Mw.utuwss
.
SOW
, J@ES
@
TIME (YSAM)
(a) Oil Production Rate vs. Time (At = 1 Month)
L
_ FIEIG 71A JWJU
.
WSF1-mMs -
8 , J- MOOSL
TX= -
(b) Cumulative Oil Production vs. Time (At = 1 Month)
Figure 7. History
Match of Tia Juana
Data
116