Chilingarian G.V. et al. Surface Operations in Petroleum Production, II
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235
As
noted previously, steam is an efficient heating medium in that much
of
its
energy is contained in the latent heat of vaporization, which is released with no
change in temperature as steam condenses upon contact with the oil-bearing
stratum.
As
a result, the heated stratum can be assumed to be at a constant
temperature
T,,
which is equal to the steam temperature. This assumption forms the
basis for a simplified treatment
of
heat losses
to
the surrounding formations during
a steam injection cycle (Marx and Langenheim,
1959).
On assuming a constant steam injection rate and a uniform thickness of oil-bearing
stratum, the bulk volume
of
the steamed zone,
V,,
at time
t
is
equal to:
The heat injection rate
qi
is given by the following formula:
qi=
(350/24)i,[h,+J;L,-c,(T,-
321)]
(7-4)
Dimensionless time
t,
is equal to:
and the
F,
factor is a function of dimensionless time as follows:
1
where:
cw
=
specific heat of water, Btu/lb- OF;
6
=
Marx-Langenheim function from Table 7-VI;
f,
=
mass friction;
ht
=
total formation thckness, ft;
hw
'S
khoh
Lv
Mob
M,
(2,
t
=
time, days;
t,
=
dimensionless time;
T,
=
temperature
of
the reservoir,
OF;
r,
=
temperature of the saturated steam,
O
F;
v,
=
bulk volume steamed, ft3; and
erfc
=
complementary error function.
=
enthalpy of saturated water, Btu/lb;
=
injection rate
of
wet steam measured as water, BFD;
=
thermal conductivity of overburden, Btu/hr-ft- OF;
=
latent heat of vaporization, Btu/lb;
=
heat capacity
of
overburden, Btu/ft3-
OF;
=
heat capacity of fluid-saturated rock, Btu/ft3-
OF;
=
heat injection rate, Btu/hr;
(7-6)
236
The above discussion shows that the heat losses from the oil-bearing stratum
through its top and bottom planes to the adjacent formations is dependent totally
on
t,;
in other words, the percentage heat losses increase directly with time and
inversely with the square of the oil-bearing formation thickness. The heat loss as a
function of these two variables is shown typically in
Fig.
7-7. The above correlation
shows that it is uneconomical to apply steam injection to relatively thin oil-bearing
formations because too
high
a percentage of the heat would be lost to the adjacent
strata.
For projects involving high-pressure steam injection, thin oil-bearing formations,
or low steam quality, the Mandl and Volek
(1969)
correlation provides a more
accurate determination of the steamed zone volume. This correlation
is
based
on
the
assumption that, after a certain critical time, the latent heat available in the
injection steam is barely sufficient to make up the heat losses to the adjacent
TABLE
7-VI
Marx-Langenheim functions
rD
F2
Fl
‘D
F2
4
‘D
0.0000
1.00000
0.00000
0.58 0.50271 0.36206
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.98882
0.98424
0.98075
0.97783
0.97526
0.97295
0.97083
0.96887
0.96703
0.96529
0.95147
0.94108
0.93245
0.92496
0.91826
0.91218
0.90657
0.90135
0.89646
0.85848
0.83160
0.80902
0.79033
0.77412
0.75964
0.74655
0.00010
0.00020
0.00030
0.00039
0.00049
0.00059
0.00069
0.00078
0.00088
0.00098
0.00193
0.00288
0.00382
0.00475
0.00567
0.00658
0.00749
0.00840
0.00930
0.01806
0.02650
0.03470
0.04269
0.05051
0.05818
0.06571
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1
.o
1.05
1.10
1.15
1.20
1.25
0.49802
0.49349
0.48910
0.48484
0.48071
0.47670
0.47281
0.46902
0.46
5
3 3
0.46174
0.45825
0.45484
0.45152
0.44827
0.44511
0.44202
0.43900
0.43605
0.43317
0.43034
0.42758
0.42093
0.41461
0.40859
0.40285
0.39736
0.37206
0.38198
0.39180
0.40154
0.41120
0.42077
0.43027
0.43969
0.44903
0.45803
0.46750
0.47663
0.48569
0.49469
0.50362
0.51250
0.52131
0.53006
0.53875
0.54738
0.55596
0.57717
0.59806
0.61864
0.63892
0.65893
~
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.2
5.4
4
0.30411
0.29963
0.29535
0.29126
0.28734
0.28358
0.27996
0.27649
0.27314
0.26992
0.26681
0.26380
0.26090
0.25810
0.25538
0.25275
0.25021
0.24774
0.24534
0.24381
0.24075
0.23856
0.23642
0.23434
0.2 3 2 3 2
0.22843
0.22474
1.12356
1.15375
1.18349
1.21282
1.24175
1.27029
1.29847
1.32629
1.35377
1.38092
1.40775
1.43428
1.46052
1.48647
1.51214
1.53755
1.56270
1.58759
1.61225
1.63667
1.66086
1.68482
1.70857
1.73212
1.75545
1.80153
1.84686
237
TABLE
7-VI
(continued)
tD
F21
4'
tD
F2
Fl
tD
F2
F,
0.09
0.1
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.73460
0.72358
0.73079
0.68637
0.67079
0.65668
0.64379
0.63191
0.62091
0.61065
0.60105
0.59202
0.58305
0.57545
0.56781
0.56054
0.55361
0.54699
0.54066
0.53459
0.5
2 8 7 6
0.52316
0.51776
0.51257
0.50755
0.07311
0.08040
0.09467
0.10857
0.12214
0.13541
0.14841
0.16117
0.17370
0.18601
0.19813
0.21006
0.22181
0.23340
0.24483
0.25612
0.26726
0.27826
0.28914
0.29989
0.31052
0.32104
0.33145
0.34175
0.35195
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
0.39211
0.38709
0.38226
0.37762
0.37317
0.3 6 8 8 7
0.36473
0.36074
0.3 5 6 8 8
0.35315
0.34955
0.34606
0.34267
0.33939
0.33621
0.33311
0.33011
0.32719
0.32435
0.32159
0.31890
0.31627
0.31372
0.31123
0.30880
0.67866
0.69814
0.71738
0.73637
0.75514
0.77369
0.79203
0.81017
0.82811
0.84586
0.86343
0.88032
0.89803
0.91509
0.93198
0.94871
0.96529
0.98172
0.99801
1.01416
1.03017
1.04605
1.06180
1.07742
1.09292
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
0.22123
0.21788
0.21470
0.21165
0.20875
0.02597
0.20330
0.20076
0.19832
0.19598
0.19374
0.19159
0.18952
0.18755
0.18565
0.18383
0.18208
0.18041
0.17881
0.17727
0.17580
0.17440
0.17306
1.89146
1.93538
1.98765
2.02129
2.06334
2.10482
2.14576
2.18617
2.22608
2.26550
2.30496
2.34298
2.38106
2.41873
2.45600
2.49289
2.52940
2.56555
2.60135
2.63682
2.67196
2.70679
2.741 3
1
'
Fl
=
e'D erfc
t,
+
2
tD/r
-
1;
F2
=
e'D erfc
tD
.
This
table is used in conjunction with eqs.
7-3, 7-4,
J-r
J-
7-5,
and
7-6.
I .I
OIL-BEARING FORMATION THICKNESS.
5
FT
10
TIME,
TOTAL
DAYS
Fig.
7-7.
Cumulative heat
losses
from the oil-bearing formation to the adjacent strata as a function
of
time and formation thckness. (After Leutwyler,
1965;
courtesy
of
the Society
of
Petroleum Engineers of
AIME.)
238
formations plus raising the temperature level of the newly penetrated formations to
the steam temperature.
Up
to the critical time, heat transfer from the steam front is
conductive, whereas subsequently it becomes both conductive and convective.
Myhill and Stegemeier (1978) provided convenient charts for determination
of
the
volume of the steamed zone for any given set
of
conditions.
Steam displacement is not necessarily frontal in many viscous oil reservoirs
subjected to steam injection. Gravity override by the steam may result in only the
upper part of an oil-bearing formation being contacted for a period
of
time, which
will affect the determination of the steamed zone in the early stages of the project.
With time, the steamed zone thckness will gradually grow downward in the
formation to eventually achieve the predicted steamed zone volume.
STEAM INJECTION TECHNIQUES
Steam injection at the present time is applied through two different techniques:
cyclic or continuous flooding. Each technique has economic and operating ad-
vantages over the other in specific applications, and selection of the steam injection
technique to be used should only be made after a thorough economic evaluation of
the project characteristics.
Cyclic
steam
injection
Cyclic steam injection, as the name implies, involves alternating cycles of
injecting steam and producing oil from the same well (Fig. 7-8). It is primarily a
stimulation technique that, through a viscosity reduction of viscous crude oil and
wellbore cleanup effects, assists natural reservoir energy in creating crude oil flow to
the wellbore. In certain instances, cyclic steam injection may be used as a prelude to
a continuous steamflood to clean out the oil-bearing strata in what will become the
I
I
I
I
I
I
I
I
1
TIME,
MONTHS
Fig.
7-8.
Typical performance (oil production) of a well using cyclic steam injection. (After Adams and
Khan,
1969; courtesy
of
the Society
of
Petroleum Engineers
of
AIME.)
239
injection well for the steamflood. Generally, cyclic steam injection is used until the
oil production becomes marginal, and then the project is converted to a continuous
s
teamflood.
The first step in a cyclic steam project is to inject steam into a well for a period
which may last from one to several weeks, depending on the formation thickness,
the oil saturation, and the number of previous injection cycles which have been
performed. Following completion of the injection of the predetermined amount of
steam, the well is closed-in and a
soak
period of possibly one week is allowed. This
enables the transfer of heat by conduction through a greater portion
of
the
oil-bearing formation. After a sufficient soaking period, a pump is lowered into the
well and production of oil is started. Oil production continues until the rate of
recovery reaches an uneconomic level, at which point the whole process is repeated.
The response to cyclic steam injection can vary considerably with different types
of reservoirs. In California,
U.S.A.,
where generally there are thick, steeply dipping
oil-bearing sand structures, gravity drainage is prevalent and many steam injection
cycles are effective as heated, reduced-viscosity
oil
continues to flow down by
gravity to the producer. Multiple steam injection cycles are common, with as many
as
42 steam injection cycles on a single well having been reported.
For relatively flat oil-bearing strata, the gravity drainage effect is much less
pronounced, and the driving force for movement
of
the crude oil to the production
well is the energy supplied by the injection steam. The number of economic steam
injection cycles which can be applied to a flat oil-bearing structure is generally much
lower than that in a steeply-dipping reservoir.
Regardless of the type of reservoir involved, cyclic steam injection generally
becomes less efficient with each successive cycle because heat penetration further
from the point of injection is required after extraction of the oil closest to the
producer. Figure 7-8 depicts the declining recovery curve over a three-cycle injec-
tion. Both peak and average oil production rates tend to decrease with each
succeeding injection cycle, and increasing amounts of injection steam are required.
During the initial steam injection cycle, up to
30
barrels
of
oil are recovered per
barrel of water injected as steam, which is equivalent to an oil-to-water ratio
of
30
to 1. Generally a cyclic steam injection project is considered to have become
marginal when this ratio starts to approach
0.22
which is equivalent to one barrel of
oil recovered for every 4.55 barrels of water injected as steam. At this point, the cost
of the fuel burned in the steam generator plus the other site operating costs tend to
approach the value of the net oil recovery.
The parameters
of
the cyclic steam injection process are quite complex, and no
reliable mathematical treatments for predicting crude oil recovery have been devel-
oped. A number of simplified approaches have been proposed in the literature for
determining the time-dependent oil recovery rate from a cyclic steam stimulation.
The reader is referred to the following references for a more detailed treatment of
the subject: Towson and Boberg (1967), Boberg and Lantz (1966), De Haan and
Schenk (1969).
The most difficult value to determine in
a
cyclic steam stimulation project
is
the
240
Qoh
temperature of the heated zone as a function of time. The stimulation ratio,
-
may be determined by the following formula:
Q,
where:
poc
=
oil viscosity in the cold formation, cP;
poh
=
oil viscosity in the heated formation, cP;
Q,,
=
oil production rate prior to steam stimulation, bbl/D;
QOh
=
oil production rate following steam stimulation, bbl/D;
re
=
drainage radius, ft;
rh
r,
=
well radius, ft.
to the following form:
=
heated zone average radius, ft; and
For very high cold oil viscosities, the stimulation ratio equation may be reduced
In other words, the stimulation ratio or percentage
of
increase in oil production with
cyclic steam stimulation in formations having highly viscous oil depends primarily
on the radius of the heated zone. It is for this reason that highly viscous oil-bearing
deposits require more steam per stimulation cycle than do more normal heavy oil
deposits. In the former, the drainage radius is essentially equal to the heated zone
radius and basically independent of the well spacing.
The calculation of the stimulation ratio is difficult because of reservoir rock
parameters and other factors which can affect the uniform distribution
of
steam
through the oil-bearing stratum. Among these factors are:
(1)
bypassing of steam
through crevices and fractures in the formation,
(2)
relative permeability hysteresis,
(3)
gravity segregation of the steam, and
(4)
formation fracturing during the steam
injection cycle. The effect of temperature on relative permeabilities
of
oil
and water
is presented in Fig.
7-9.
Steamflooding
Steamflooding, or steam drive as it is frequently termed, is a process very similar
to waterflooding. A basic difference between the two processes is that steam
provides both thermal and mechanical energy to enhance the recovery
of
viscous
crude oils, whereas cold water as typically used in a waterflood can only provide
mechanical energy.
In a steamflood, a suitable pattern
of
injection wells surrounded by production
wells is selected, with the pattern largely dependent on the geology of the formation
241
WATER
SATURATION,
%
Fig.
7-9.
Effect
of
temperature on relative permeabilities of oil and water. (After Weinbrandt et al.,
1975;
courtesy
of
the Society
of
Petroleum Engineers
of
AIME.)
Fig.
7-10.
Schematic diagram of a typical continuous steam injection project arrangement.
242
to be flooded. Typically
5,
7-, and 9-spot patterns are being used with injection
wells driving the crude oil to producing wells. Figure 7-10 shows a typical steamflood
layout.
Steam is continuously injected into the selected injection wells and drives the
crude oil to the producing wells surrounding the injection wells in a sweeping
pattern through the oil-bearing stratum. Ideally, the injected steam forms a steam
saturated zone around the injection wells as schematically shown in Fig. 7-11. The
temperature of the steam-saturated zone approaches the temperature
of
the injec-
tion steam. As the steam penetrates the oil-bearing stratum away from the point of
injection, there is a reduction in temperature as steam continues to expand as a
result of the decrease in pressure. At some distance from the injection well, the
steam condenses and forms a hot water bank. This distance is a direct function
of
the initial steam temperature and the rate
of
pressure changes with distance from
the point
of
injection. The hot-water bank continues to flow toward the producing
wells, giving up heat to the stratum in its forward movement and pushing the oil
ahead
of
it.
Steamflood oil recovery is dependent on several factors. Probably most influen-
tial in the recovery process is the hot-water flood zone where the water at elevated
temperatures provides (1) heat to reduce the oil viscosity, and
(2)
displacement
volume to force the oil ahead
of
it toward the producing wells. The largest oil
saturation reduction is generally achieved in the hot waterflood zone as a result of
crude oil swelling, reduced crude oil viscosity, improved formation permeability on
expansion with temperature increase, and the displacement effect
of
the hot water.
In the steam-invaded zone, the oil saturation is reduced by the combined effects
INJECT
WET
Sa
PRODUCE
OIL AND WATER
STEAM ZONE COLD RESERVOIR
-
Fig. 7-11. Schematic diagram
of
reservoir heating
by
steam injection. (Modified after Marx and
Langenheim, 1959.)
243
of gas drive, viscosity reduction, steam distillation, and solvent extraction. The gas
(steam) drive effect is usually important, and steam distillation can contribute
significantly to the improved delivery of certain crudes.
The actual operation of a steamflood seldom follows the ideal pattern. When
steam is initially injected, it seeks the flow path of least resistance and forms
a
finger-like channel through this flow path to the producing wells. With time and
continued steam injection, the steam finger, being less dense than the oil, moves
upward in the oil-bearing stratum and blankets the oil. The gravity override by the
steam results in sweeping of the upper portion of the oil-bearing stratum by steam
and the lower portion by hot water, thus giving rise to nonuniform vertical oil
extraction efficiencies.
Gravity overrides are aggravated by the presence of a gas zone in the formation
(Farouq Ali and Meldau, 1979). Injection of the steam at the bottom of the
oil-bearing strata may be effective in reducing override severity, but this is only
recommended for highly homogeneous reservoirs and those devoid of a bottom-water
zone. In multilayered formations, steam injection should be applied at multiple
vertical intervals to ensure uniform distribution throughout the oil-bearing stratum.
It is frequently desirable to conduct one cyclic steam injection run on the
producing wells in a steamflood pattern prior to initiation
of
the steamflood. This is
done in order to reduce the resistance to flow which would be imposed by the cold
oil near the producing wells when oil movement is initiated in the oil-bearing
stratum by the steamflood.
Using the steam injection process, the major portion of crude oil is currently
being produced by the steamflood technique. Use of the technique, however, does
not automatically ensure an economically justifiable project. The application of
steamflooding of a given reservoir should only be considered after a thorough
evaluation of the geology of the formation, and the various factors required for a
successful steamflood project. Table
7-1
lists several steam injection projects and the
formation characteristics. Of importance are reservoir depth, reservoir pressure,
thickness of the oil-bearing stratum, permeability, oil saturation, and the crude oil
gravity. The presence of a primary or secondary gas cap tends to aggravate gravity
override, but may enhance a real coverage and rapid heating of the crude oil. This
can be particularly effective in thin sands. The effect
of
a bottom-water zone on
steamflooding depends in large measure on the properties
of
the reservoir rock and
the fluids, and the type
of
flooding scheme employed. The bottom-water zone can
serve as a bypass for the injection steam, or it can be used to achieve steam
penetration and the improved conductance of heat into the reservoir.
Oil recovery from a steamflood project may be predicted from computer models,
scaled physical models as shown in Fig. 7-10, numerical simulation, and published
correlations. For more detailed coverage of oil recovery prediction methods on a
steamflood project, the reader is referred to Gottfried (1965), Farouq Ali (1966,
1970, 1981), Flock et al. (1967), Davies et al. (1968), Fairfield (1968), Adams and
Khan (1969), Shutler (1970), Moss (1974), Bursell and Pittman (1975), Neuman
(1975), Cook (1977), Crookston et al. (1977), Ferrer and Farouq Ali (1977), Myhill
244
and Stegemeier (1978), O’Dell and Rogers (1978), Gomaa (1980), Jones (1980).
Extensive studies have shown that ultimate oil recovery from a steamflood
project in many cases depends on the volume of the reservoir which is steamed
(Myhill and Stegemeier, 1978). Thus production near the end of the steamflood can
be estimated from the following equation:
where:
Np
F
h,
h,
Soi
Sorsi
V,
+
=
fractional porosity.
It is necessary to estimate the value of
F,
which varies from 70 to 100% for most
applications (Myhill and Stegemeier, 1978). Jones (198Q) used field test data
to
develop approximate values of
F
as a function of the mass of steam injected.
In general, steamflooding has been found to be a very effective enhanced oil
recovery technique when applied to the suitable reservoirs and conducted properly.
There are examples where as much as 75% of the oil in-place has been recovered
from
a
reservoir, and the average recovery of the oil in-place has been in the 45-55%
range. Considering that only 10-15% of the oil in-place can typically be recovered
in heavy oil reservoirs by primary production methods, it is obvious that
steamflooding can be a valuable tool in the production of viscous crude oils.
=
cumulative oil recovered, bbl;
=
ratio of actual to theoretical oil production, fraction;
=
net oil-bearing sand thckness, ft;
=
total formation thckness,
ft;
=
initial oil saturation, fraction;
=
saturation following steamflooding, fraction;
=
bulk volume steamed, ft3; and
RECENT DEVELOPMENT IN STEAM INJECTION TECHNIQUES
As the application of steam injection to the enhanced recovery of heavy crude
oils has expanded in recent years, there have been a number of developments
designed to increase the recovery ratio and economics of the process.
Steam
additives
Even though steamflooding is the most successful of all enhanced oil recovery
processes, its efficiency could be further improved
if
certain problem areas could be
overcome. Gravity override, or the tendency of steam to heat the upper portion of
an oil-bearing formation in preference to the lower portion, results in poor areal and
vertical sweep efficiencies which limit the recovery of crude oil. An additional
problem is the premature breakthrough of the injected steam to the producing wells
creating steam bypass channels, with consequent loss of effective use of the bypass