prediction of reservoir behavior from laboratory data
TRANSCRIPT
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Prediction of Reservoir Behavior from Laboratory Data
By
E.
C. BABSON ·
MEMBER
A.I.M.E.
(Los Angeles Meeting. October 1942
ABSTRACT
IN order to explore the possibility of predict
ing reservoir performance from laboratory
data,
behavior
of
a hypotheticallow-permeabil
ity
reservoir has been estimated by applying
data
and methods currently available in the
literature. A method of calculating decline in
productivity index is discussed, and recoveries
by
internal gas drive, external gas drive and
water drive are estimated.
INTRODUCTION
During the life of a producing oil prop
erty an operator is faced with many per
plexing problems. Any attempt
to
deter
mine proper well spacing, optimum rate of
production, or the desirability of pressure
maintenance requires the evaluation not
only of a host of economic and practical
operating factors
but
also of the future per
formance of the reservoir. Although in
some cases economic
or
operating con
siderations may be of primary importance
in planning a development
or
production
program, the anticipated effect on ultimate
recovery is more likely
to
be the decisive
factor.
The soundest basis for evaluating reser
voir performance is past experience with
oil fields
but
pertinent data are difficult
to
obtain or. apply under conditions normally
encountered in California fields. Many of
these fields are characterized by thick
sections of alternating sands and shales
complicated
by
faulting and rapidly chang
ing lithologic conditions. Further compli-
Manuscript
received
at
the
office
of
the
Iastitute Oct.
23. 1942.
Revised Dec. 21.
1943.
Issued
s
T P
1664 in PETROLEUM TE H-
NOLOGY.
January
1944.
•
Union
Oil
Co •
Santa
Fe
Springs. California.
cations are introduced by haphazard
development and production practices
resulting from competitive conditions,
changing demand for oil, and insufficient
knowledge of structural conditions during
early development. Even in the rare cases
where development has been systematic
and adequate, production policy has usually
been controlled by economic and competi
tive factors rather than a desire to obtain
information for use in future operations.
In
other words, comparable reservoirs in
which development and production prac
tices have been systematically varied are
seldom found.
In the light of these conditions, conclu
sions based on experiences usually lack the
certainty required for decisions involving
large sums of money. Some other method
of attacking these problems is needed to
supplement and orient field experience.
Progress in laboratory investigations of
the flow of oil, gas, and water through
sands has been so rapid in recent years
that
these data may furnish such a sup
plementary approach in the near future.
In order to explore this possibility the
author has attempted
to
predict the be
havior of one type of reservoir by applying
published data and methods.
BASIC DATA
AND ASSUMPTIONS
Calculations outlined in this paper are
dependent upon a detailed knowledge of
the properties
of
oil, gas, and water present
in the reservoir and the portion of the
total pore space originally filled by each.
I t
is also necessary to know how the perme
ability of the sand to oil, gas, and water
varies with the saturations of these fluids
120
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E. C. BABSON 121
in the sand. Furthermore, it has been
necessary to make certain simplifying as
sumptions in order to perform the calcula
tions within a reasonable period of time.
In
making assumptions and choosing data,
the writer has attempted to duplicate as
nearly as possible conditions encountered
in certain California oil fields.
The hypothetical reservoir used in the
calculations was assumed to have a porosity
of
21 per cent,
of
which 25 per cent was
originally filled with water and 7 per cent
with oil containing
7
cu. ft. of dissolved
gas per barrel
of
tank oil. Reservoir tem
perature was 21
0
and original pressure
was
3
lb. per sq. in. abs. Properties
of
the oil and gas were assumed to be similar
to those of Dominguez oil and gas de
scribed by Sage and Lacey.l.2 Volumetric
data for both oil and gas and viscosity
data for the oil phase were taken from these
papers. Viscosity data for a lean natural
gas given by Sage and Lacey in another
paper were used for the gas phase in the
present investigation. These phase data
indicate
that
the bubble point of the
original reservoir contents was 3 lb.
per sq. in. abs. and
that
the initial forma
tion volume factor was
1.42. t
was as
sumed that the oil and gas in the reservoir
maintained phase equilibrium at all times.
This assumption may not be strictly true,
but calculations are almost impossible
without it.
Sand permeability was assumed
to
be
too low to permit appreciable recovery of
oil
by
gravity drainage. Despite this
assumption, it was necessary to use the
data of Leverett and Lewis
4
on the rela
tion between the relative permeabilities to
oil, gas, and water and the. saturat ion of
these fluids. Their
data
seem inappropriate
because an unconsolidated sand of very
high permeability was used in their experi
ments, but no other data on the
flow
of all
three phases through sands have been pub
lished. Botset' obtained data on the flow
1
References
are at
the end
of
the paper.
of mixtures of carbon dioxide and water
through a consolidated sand of
moderate
permeability. An attempt was made to ad
just his data for the presence of a third
phase, but the basis for this adjustment
was not too satisfactory. Furthermore, the
data
of
Krutter
6
on the
flow
of gas through
oil-saturated consolidated sands seem to
agree more closely with Leve rett and Lewis
than with Botset.
Because these data
of
Leverett and Lewis
form the keystone of this entire paper, a
brief review of their conclusions seems
appropriate. They concluded that a sand
could be considered
to
have simultaneously
at) effective permeability to oil, an effective
permeability to gas, and an effective
permeability to water, and that variables
other than the oil, gas, and water satura
tions affected these permeabilities only to
a very minor degree. (In this paper the
terms oil saturation, gas saturation,
and water saturatio n
mean the per
centage of the total pore space occupied by
the corresponding phase in the reservoir.)
Effective permeabilities were expressed
not in millidarcys but as percentages
relative to the permeability of the sand
to air. The relative permeability to each
phase was 1 per cent
at
1 per cent
saturation o that phase and decreased as
the saturation decreased.
As oil is produced from a sand, the oil
saturation decreases and the space thus
voided becomes filled with either gas or
water, or both. Thus the permeability of
the sand to oil decreases
and
the permeabil
ity
to
gas or water increases.
In
oil fields
we see the effects of these changes in de
clining productivity indices and rising
gas-oil ratios and cuts. The data of Leverett
and Lewis furnish a means by which pro
ductivity index, gas-oil ratio, and water
cut can be related to stage
of
depletion.
DECLINE IN
PRODUCTIVrry INDEX
One source of great concern to the produc
tion engineer is the decline in productivity
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J2"2 PREDICTION
O.F
RE,SERVOIR BEHAVIOR FROM LABORATORY DATA
index usually observed in depletion-type
fields. Various explanations have been
offered to e x p l ~ i n this
decline-transporta
tion of silt, prc<-ipitation of asphaltenes,
" . u ~ U ; " i · i ~ ~ a ' i n n
of water .lear the well bore,
and plugging of perforations in the liner.
While all these factors may contribute
to
the decline, published
data
on
the
relation
betwcfD permeability to oil and oil satura
l:on indicate
that
the productivity index
must decline as the oil in the neighborhood
of a well is depJeted. Since low productivity
indices can result in early abandonment of
wells,
it
is important to know what causes
the observ<:d decline and what can be dont
about
it.
In
order
to
throw some light on
this problem, an attempt has been made to
determine how the productivity index
:,hould var.v with pressure llud gas-oil ratio
for the 2.3EUmed r e ~ e n o i r conditions. By
checking this theoretical decline against
ll.ctual declines observed in wells producing
from similar reservoirs,
it
may
be possible
to determine whether the observed decline
can be accounted for
by
depletion alone or
whether some other cause must be found.
A method described by Evinger and
Muskat1 has been used in making the
calculations. This method assumes
that
flow through sand is steady with respect
to both mass and composition of
the
Howing
stream. Since
the
present calcula
tions are for the purpos" of estimating the
change in
p r o d u t i v i ~ y
index
rather than
its absolute magnitude, the equation of
~ v i n g e r and Muskat has been modified
tv
give a relative productivity index.
1//
1
= _ p.. 3) fP.K./Kr
p - P K./K I.lP,. . .. 8
dP [1]*
In which 11 is the productivity index
under some standard reservoir conditions
and
at a pressure differential approaching
zero. In this paper the term "pressure
differential" refers
to the
difference be
tween the static
and
producing pressures
*
See
nomenclature on page
131 .
in a well, and this difference is considered
to
be equivalent to the term P. - P ) in
Eq.
1).
Since the choice of standard
conditions is purely a
matter of o)n·
venience, initial conditions in the assumed
reservoir were taken as standard. When
the
corresponding permeabilities and vis
cosities are substituted in Eq. I
the
following equat ion results:
In
order
to
solve this equation
it
is
necessary to know how the relative per
meability to oil
K.IK
varies with pressure.
This can be determined
by
utilizing another
equation of Evinger and Muskat:
The variation
of
the ratio of effective
permeabiHties
to
gas
and
oil,
Kul K
0.
with pressure can be established f C, I ~ l )
produced gas-oil ratio R by O - S S U l l i i ~ ; g
different pressures
I),nd
n'.bstituting appro
priate values for the rer:aining factors.
The
relative permeability
to
oil K.IK
corresponding to any value of Kg K. can
he determined from the data of Leverett
and
Lewis if the water saturation is known.
The expression following the integral
sign in Eq.
2
can then be evaluated as a
function of pressure, and the relative
productivity index can be obtained by
graphical integration.
Results of these calculations for a
series of gas-oil ratios and pressures are
shown in Fig. I .
The
correct method of
calculating a relative productivity index
for a given gas-oil ratio
is to
determine
the
area under the appropriate curve between
the static
and
producing pressures and
. divide this area by the pressure differential.
Under most conditions, however, the
curves in Fig. I are almost linear, and for
moderate pressure differential
the
relative
productivity index can be read directly
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E.
C. HABSON
irom the chart by using a pressure midway
betw(en the static and the producing
pressures.
These CUIves show what Evinger and
per sq. in. for several weeks, the saturation
distribution around the well will gradually
adjust itself to this pressure gradient and a
certain productivity index will be a t ~ a i n e d
I
t--
1
- - - - - 1 - - - - - - 1 - - - - - - - - - - - - - - - - - - ~
~ _ _ _ : h _ ~ ~ - ~ I l J
00 1
~ o o
zooo Z5QO 3000
PRESSURE
P.ll. .
ABS.
FIG. I . -RELATION BETWEEN PRODUCTIVITY INDEX GAS-OIL RATIO AND PRESSURE
AT
Z:; En (,1':NT
WATER SATURATION.
Muskat have already stated-that the
productivity index decreases as the pres-
sure differential increases.
At
first thought,
this seems contrary to field experience
because indices of actual wells do not
vary in any predictable manner with
pressure differential. A possible cause of
this discrepancy becomes apparent when
the
matter
is given further consideration.
Pr;>ductivity index is a function of the
average permeability of the sand
to
oil,
'Vhich in turn is a function of the saturation
distribution in the sand.
f
a well is pro-
Juced at a pressure differential of
200
lb.
f the well is then opened' up to a differen-
tial of 1000 lb. per sq. in., the saturation
distribution around the well will tend to
change and the productivity index will
tend to decrease. Since a large volume of
oil must be moved in order to alter the
saturation distribution, the process re-
quires considerable time. f a
t(;3;'
• )
made on the well a day or two alter the
prodil.ction ratt; ha:; been 111':i·easeci.,
i t i
probable that the saturation distribution
will have changed only slightiy
and the
productivity index will be practically the
same as at the lower rate. Because of this
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124 PREDICTION OF RESERVOIR BEHAVIOR FROM LABORATORY DATA
behavior the pressures used in evaluating
a productivity index by means
of
Fig.
should relate t9 the normal production
rate of the well rather than conditions
during a short-time test.
In order to illustrate how these results
can be used in predicting the decline in
productivity index, an illustrative example
will be worked out.
f
a well has a pro
ductivity index of
1.5
when the gas-oil
ratio is 1000 cu. ft. per barrel, the static
pressure is
2500
lb. per sq. in. abs., and
the producing pressure
is 2300
lb. per
sq. in. abs., what will the productivity
index be at a gas-oil ratio of
2500
cu. ft.
per barrel, a static pressure of
1500 lb.
and a producing pressure of 1000 lb. per
sq. in.? From Fig. I it can be determined
that 1 1 for the first set of conditions is
0.523, so is equal to 1.5/0.523, or 2.87.
For
the second set of conditions 1 11 is
0.264 and the productivity index is
0.264
X
2.87,
or
0.76.
Preliminary applica
tion of this method to
data
on several
wells in a depletion-type field of low
permeability has shown
that the produc
tivity indices actually decline somewhat
less than the calculations indicate. As
far as the wells studied are concerned,
depletion
of
the oil can tentatively be
considered the principal cause
of
pro
ductivity-index decline.
INTERNAL GAS
DRIVE
In general, oil can be recovered from a
sand by four methods:
I)
internal gas
drive,
2)
external gas drive, 3) water
drive, and 4) gravity drainage. Internal
gas drive is the normal depletion process
in which oil
is
displaced by originally
dissolved gas. External gas drive is a
process in which a gas front advances
through the sand, displacing oil ahead of
it. Water drive operates by a similar
mechanism with water as the displacing
fluid.
In
sands of high permeability large
quantities
of
oil can be recovered by
gravity drainage. In most reservoirs all
four
of
these processes are operative in
some degree,
but usually only one or two
of them are important from the standpoint
of
recovery.
In this paper gravity flow is considered
to be an unimportant factor in production
on account
of
the low permeability
of
the
sand, and i natural water drive
is
ineffec
tive, the operator is in a position to choose
the method
by
which oil
is
recovered
from the sand. f the operator simply
produces oil from all his wells until they
no longer yield a profit and then abandons
them, the reservoir will have been depleted
by
internal gas drive. This method has
been applied almost universally in the
past, largely because of its simplicity.
Given the relation between oil saturation
and the relative permeabilities to oil and
gas, it is possible to calculate future trends
of static pressure, productivity index, and
gas-oil ratio for wells producing from a
reservoir of this character
by
considering
flow through the sand as a succession
of
steady states.
f
the wells are produced
at appreciable pressure differentials the
area around a well should be divided into
rings and the flow between these rings
investigated in detail in order properly
to evaluate saturation gradients. t is
entirely feasible
by
this method to cal
culate future trends
of
pressure and
productivity for the entire producing
life of a reservoir, but, unfortunately,
the task
is
an extremely laborious one
and has, therefore, not been attempted.
This is regrettable, for such calculations
might furnish information useful in deter
mining optimum well spacing and optimum
rate
of
production, providing that data
pertinent to
the
actual sand in the reservoir
could be used.
Since time was not available for the
more detailed calculations, future trends
for the hypothetical reservoir have been
estimated
by
assuming that the oil is
produced
at
negligible individual well
pressure differentials.
t is
realized
that
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E. C. BABSON
12
5
calculations for high-pressure differentials
would probably indicate more rapidly
rising gas-oil ratios together with a more
rapid pressure decline, but it seems likely
meability ratio K
g
K obtained from the
data of Leverett and Lewis. This per
meability ratio is next converted to free
gas-oil ratio
by
adjusting for the vis-
I
ASSUMlpTIONS I
\
l
POROSITY
21 I.
NTERSTITIAL WATER
2S1
r--
GAS-OIL
RATIO IN PLACE 700 CU. FT/BIIL
'
;::-
4000
/
\
UBBLE POINT
3000
P S I
AilS.
:;
v
0
zoo
a
(3
V
'
1
o
2
OJ
a:
'
1000
Go
o
.8
--...
i
'
r ...
.............
r--
0
50
100
150
200
Z50 DBL.,AC.I T.
o
5.8
11 6
IU ZU n.o 1 Of
OIL
III PU E
CUMULATIVE
OIL PRODUCTION
FIG. 2.-DEPLETION HISTORY
OF
A
RESERVOIR
PRODUCED AT VERY LOW DRAWDOWNS.
that the recovery calculated for the case
of negligible pressure differential is an
upper limit which would be approached
at
small
but
finite differentials. The method
is illustrated by the sample calculation
in Table I. The method is a trial and error
process in which small quantities of oil
and gas are assumed to be withdrawn
from the reservoir and the resultant
pressure is estimated
by
materials-balance
methods. Since the amount of remaining
oil and the reservoir pressure are now
known, the remaining oil saturation can
be calculated and the gas-to-oil per-
cosities and densities of the gas and oil
phases. The total gas-oil ratio is equal to
the free gas-oil ratio plus the gas in solution
in the oil under reservoir conditions.
If this calculated gas-oil ratio does not
agree with the assumed ratio, the calcula
tion is repeated using a different assumed
ratio. When a satisfactory solution has
been obtained for one step, additional
oil and gas are withdrawn from the reser
voir and the calculations repeated. This
stepwise method is followed throughout
the life of the reservoir.
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ResUlts
of
these cakulations art: shown
in Fig.
2,
in which gas'0il
ratio, pre55i.lri:,
and
productivity
InJeA.
alt:
~ ) l o t t t d
agaiu t
cecovely.
In an
effort to apptoXlmll.tt. at
70
._-
1 - - - - - -
bS
I , , --
v
60
I/
a:
0
55
--
0
>
0
~
50
I
z
0
-
45
.:
ct
:>
r
.:
V
0
40
~
35
the
dcccca.<.ing quantity of &&.3
J 1 3 s v ~ V t d
in the
produced oil as
the pressure
drops.
In
other
words, I lO"t
of the
ga i . h & . ~
,.ome.'
O.lt
of
solution Juring the early stagt:s vi
,
-
= ~ ~ ~ ~ ~
I ~ : m ~ : ~
~
. /
GAS-OIL RATIO
600
OILPROOUC
ION
PER
WE 98
..
\
RESERVOIR PRESSURE 1950
~
PRODUCING
PRESSURE
~ ~
A S - ~ Q .
I
0
I
OIL PRODUC
ION PER WE
92
RESERVOIR
PRESSURE 1000
~ ~ ~ D _ U : ; \ ~ 6
1 ~ ~ E ' ; ' 7 . . U R E
I < ~ ~ l .
I
I ulLPRODUC
II,, PERWEU
52
RESERVOIR
-;t--
PRFSSURE 335
. . ~
m ~ ~ ; ~
PRESSURE
5 cig
ATIO
~
OILPROCvC
ION PERWEL
Z6
.-
I - -
~ l
0
100
150 200 250
300
D I S T A N ~ E FROM WELL - FT.
FIG.
3.·····SATURA rION DISTRIBUTION AT VARIOUS SrAGES OJ ' DEPLETION HISTORY SHOWN IN
FIGt:RE
2.
least some of the effects
of
finite pressure
differentiai, the productivity index has
been corrected for small differentials,
starting with 100 lb. per sq. in. initially
and gradually increasing to
320
lb. per
sq. in.
at
a static
prebSUle of 335
lb. per
sq. in. According to Fig. 2 the gas-oil
ratio first decreases from 700 to
55
cu. ft.
per barrel, then rises to a peak
of 59
cu.
ft. per barrel, and finally drops
off
rapidly.
The decrease in ratio during the early
stages
of
production is caused by the
almost negligible permeability
to
free
gas at low gas saturations together with
production is stored in the sand. The final
decrease in gas-oil ra.tio is the result
of
the
increased volume occupied
by
gas
at
low pressures: The volume 'ratIo'(jf' gas to
oil in the formation is continuously increas
ing
but
the standard cubic feet
of
g a ~
per barrel
of
oil decrease. When
293
bbJ
per acre-foot have been recovered, the
reservoir pressure is
145
lb. per sq. in. and,
if the original productivity index is
assumed to be
1.0
the current productivity
index will be 0.06. This corresponds to a
maximum productive capacity of about
8 bbl. per day, which probably is close
to
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E.
C.
BAbSUN
the economic limit. Thus lhe recovery
by
internal gas drive is approximately 293 bbl.
per
acre-.£oot,
or 34 per cent
of
the oiiginc.:
oil in place.
In
comparison with tield performance,
lhe gas-oil ratio curve of F'ig. 2 seems to
remain
at
a low level for an unusually
long period. These low gas-oil ratios
re5u]t in a flatter pressure-decline curve
and greater ultimate recovery than is
generally obtained in pools
of
this char
acter.
t
is difficult to determine how
much
of
this discrepancy is due to the
effects
of
high pressure differentials and
how much is caused by differences between
California producing sands and the sand
used by Leverett and Lewis. Since the
discrepancies introduced by tinite differen
tials would be reflected in saturation
gradients in the sand, the saturation
distribution in the sand was calculated
at
four stages
of
the depletion history
shown in Fig.
2
using a well radius
of
4
in., a drainage radius
of 400
ft., and the
draw downs assumed in correcting the
productivity indices
of
Fig.
2.
The results
of
these calculations are shown in Fig. 3,
together with the pertinent data.
It
can be seen
that
the saturation gradients
arc very flat except in the very early and
very late stages
of
depletion. These
results indicate that at the
low
rates
of
production assumed, reservoir performance
might approach
that
shown in Fig.
2.
This evidence, however, is far from positive
proof even for low rates, and
at
the high
pressure differentials often encountered
in field practice, important discrepancies
may be introduced.
EXTERNAL GAS DRIVE
Oil is recovered
by
external gas drive
if
a gas front is caused to advance through
the sand, displacing oil ahead
of
it. Partial
gas-drive recovery can be attained by
allowing a gas cap to expand
but
complete
recovery by external gas drive
requires-1:irc
injection
of
gas to maintain pressures above
. ,.
the bubble point.
In
a
r e ~ e t v o i r
produc.tc:
by internal gas drive the entire reservoir L
depleted more or
Ie""
gradually. f thl
oil is displaced entirely by external
ga.
drive,
however-,
the portion
of
dle e ~ e r v o l j
behind the gas froIlt is a l i l l o ~ fully ueplete(J
while the portion ahead
of
the front
undepleted. Thus wells ahead
of
the front
produce without decline, while tho ,:
behind the front may suffer an a l m c ~
complete loss
of
oil productivity.
T) L
problem
of
estimating the recovery aheal'
of
a gas front can be reduced to an estima·
tion
of
the distribution
of oil s 6 . t u r a t i o l ~
behind the gas front. Once the average
oil saturation behind the front has been
determined, the calculation
of
recovery is
simple.
A method proposed by Buckley and
Leverett
8
has been used in this paper.
Their method is based upon the assumptiun
that
flow is steady with respect to the
total volume flowing. This assumption
requires, in turn, either
that
the flui<i,:
in the reservoir be il1LOmpress
i
blc or tha
the pressure be
COl stant
over the
entin
system. For the case
of
linear flow the:;
basic equation is
flu
= dig 4)
¢A
dS
where flu is the distance moved by
d
plane of fixed gas saturation during the
time
that
a total volume
of
gas Qg enters
the system. The relation between the per
centage of free gas in the flowing stream,
fg
and the gas saturation,
SQ
can be
established from the following equ tion:
f
-
1
• - +
K Il
I
KgfJ
[5]
since the gas-to-oil permeability ratie,
K /K is a function
of
the
oil
and gas
saturations only.
In
order to illustrate the method,
calculations for external gas drive at
3 lb. per sq. in. abs., will be outlined in
sOme detail. First I is calculated for
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128 PREDICTION OF RESERVOIR BEHAVIOR
FROM LABORATORY DATA
several values
of Sg by
using the
data
of
Leverett and Lewis in Eq. 5. These values
of ig are plotted against the corresponding
values of
Sg
as shown in Fig. 4. The slope
6
{ \
\
1
I
/
/
'
II
/
I
l /
h
ig
.
F
f
h
t e
dS
g
curve
mig .
4 except or a c ange
of scale. Since
it
is impossible for two
different gas saturations to exist
at
the
I
~
\
\
0
o
w
60
s, GAS SATURATION
-10
OF TOTAL
PORE
SPACE
FIG.
4.-PRELIMINARY STEPS
IN CALCULATION
OF
SATURATION
DIsTRmUTION BEHIND
AN ADVANCING
GAS
FRONT
AT A PRESSURE
OF 3000 POUNDS
PER SQUARE
INCH
ABSOLUTE.
of this curve is then plotted as a function
of Sg giving the peaked curve of Fig. 4.
f it
is now assumed
that
some arbitrary
volume of gas is injected, say
21
cu. ft.
at
reservoir conditions)
per
square foot
of cross-sectional area, Eq. 4 states
that
the distance moved by a plane of given
gas saturation can be found
by
multiplying
h
1
f
ig
h
t e va ue 0 dS
g
at t e given saturation
by 21/0.21, or 100. As the original gas
saturation of the reservoir was zero, each
of these calculated distances is measured
from the plane of entry of the gas.
Application of this procedure results in
the curve of Fig. 5, which is the same as
same point, and since the total area
under the curve must equal the total
volume of gas entering the system, divided
by
the porosity and the cross-sectional
area, the dotted portion of the curve is
considered to be imaginary, and a hori
zontal line representing the gas front is
drawn
at
such a position
that
the shaded
area in Fig. 5 is equal to
21/0.21
or
100.
The average gas saturation behind the
front is 36.6 per cent, which corresponds
to a recovery of 420 bbl. per acre-foot
from the area swept
by
the front. f a
larger quantity of gas
is
injected, all
the
values of 1f are multiplied by a new
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E. C. BABSON
12
9
constant so
the
curve of saturation as a
function of distance will be identical
with the curve of Fig. 5 except for a change
of scale.
Thus
the average gas saturation
.00
- \
\
I
500
I
l
I
I
• 00
injection pressures it is obvious that
recirculation of gas will not be economically
feasible and wells must be shut in soon
after
the
gas front passes them. I f no gas
o
~ ~ ~ ~ ~ ~ ~ W ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ = ~ ~ ~
G S
S TUR TION
-
7
OF
TOT L PORE SPACE
FIG. 5.-SATURATION DISTRIBUTION
BEHIND AN ADVANCING GAS FRONT AT A PRESSURE OF
3
000
POUNDS PER SQUARE INCH ABSOLUTE.
behind
the
front iJ independent of
the
distance
the
front may have traveled.
Furthermore it can be shown that
the
average saturation will be
the
same for
the
radial flow case.
Capillary forces will cause
an
actual
gas front to be somewhat less abrupt than
that shown in Fig.
5 but the
error involved
is probably small. As the
front passes a
well
the
gas-oil ratio will rise rapidly
from
700 to 8800
cu. ft.
per
barrel
and
will then rise more slowly as the front
continues its advance. The average gas-oil
ratio of all wells
in
the area swept will be
approximately 20 000 cu.
ft.
per barrel.
Because
of
high gas-oil ratios
and
high
is recirculated full pressure maint enance
requires
the
injection of
1370
cu. ft. of gas
per barrel of oil produced. After
the
gas
front has passed all
the
wells
the
reservoir
will contain
800
M cu. ft. of
h i g h p r e s s u r ~
gas
per
acre-foot most of which can then
be produced
and
sold. Oil recovery during
this period can be estimated
by
the method
illustrated
in
Table
I . I f
all
the
wells
are produced recovery from this phase
of production is estimated to be
15
bbl.
per acre-foot while if most of the produc
tion is taken from wells
last
passed by
the
gas front the recovery might approach
5
bbl. per acre-foot. This gives a total
recovery of 435 to 445 bbl.
per
acre-foot
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130
PREDICTION OF RESERVOIR BEHAVIOR FROM LABORATORY DATA
all of which should be obtainable by flowing
or straight gas lift.
A word
of
caution is necessary
at
this
point. Even if all the calculations in this
paper are applicable without modification
to California oil sands, the additional
recovery due to pressure maintenance
is obtained only from that portion of the
sand actually swept by the gas front.
The remainder of the sand will not produce
more than 293 bbl. per acre-foot and may
conceivably produce somewhat less. For
this reason the gas front must sweep
out a major portion of the reservoir in
order to ensure an appreciable increase in
recovery.
t
is not within the province
of this paper to discuss the difficulties
involved in pressure maintenance opera
tions, but adequate control of gas fronts
in a typical California oil field is an
engineering problem
of
major proportions.
If
the gas-drive operation is conducted
after the reservoir pressure has been
allowed to fall to
2000
lb. per sq. in., the
average gas saturation behind the gas
front is
35.1
per cent, which gives a total
recovery
of
336 bbl. per acre-foot from the
area swept. f the operation is conducted
a pressures lower than
1500
lb. per
sq. in., the gas saturation resulting from
normal depletion will be so high that there
will be no true gas front. Producing gas-oil
ratios will begin to rise almost immediately
and recirculation
of
gas will be necessary.
t is extremely difficult to estimate the
additional recovery to be obtained in
this manner, because of a most com
plex interrelation between physical and
economic factors in this lower pressure
range,
but it seems unlikely that large
quantities of oil could be recovered from
the assumed reservoir by this method.
The low recovery from external gas
drive at low pressure in this reservoir
probably is due to the relatively efficient
primary recovery
by
internal gas drive.
If the primary recovery operation had
been less efficient, owing either to lower
original pressures or to wasteful production
practices, important quantities of oil
might be recoverable by low-pressure
gas drive.
WATER DRIVE
Recovery by water drive has been
estimated by a method similar to that
used for gas drive.
If
the water drive
is
operated at the original reservoir pressure
of
3000
lb. per sq. in., the recovery ahead
of the water front is estimated to be 545
barrels.
TABLE I. Sample Calculation of Depletion
History by Internal as Drive at Very Low
Drawdowns
Given: Porosity, 21
per
cent
Total
pore volume
- 0.21
X
0.7758 -
X630
bbl. per acre-foot
InterstItial water - 2S per cent
Net pore volume - x - 0.25) 1630 = 1223
bbl. per acre-foot
Initial formation volume factor = 1.42
Oil
in
place = = 860 bbl per acre-foot
1·42
Initial
pressure - 3000
lb. per
sq. in. abs.
=
bubble point
Temperature - 210 °F.
Initial gas-oil ratio - 700 cu. ft per barrel
Calculation: A B
I. Assumed oil production, bbl.
per acre-ft
20 20
2. Assumed average gas-oil
ratio,
cu.
ft. per
bbl. 680 662
3.
Remaining
o il 860 - x ),
bbl. per acre-f t. 840 840
4. Calculated pressure, lb. per
sq. in. abs. 2,775 2,785
5. Formation
volume
factor of
liquid
X.365 1.367
6. Oil
saturation
3) X 5) /
1630, per cent of
total
pores
70.4
70.5
7
K./K. after Leverett and
Lewis) 0.0005
0.00045
8. Conversion factor pfI,../
II ,
cu. ft. per
bbl.
32,500 32,600
o. Free gas-oil ratio 7) X 8),
cu. ft. per bbl. 16 IS
10. Dissolved gas-oil ratio, cu.
ft. per bbl. 607 612
n .
Total gas-oil ratio 0)
10), cu.
ft. per bbl.
623 627
12. Average gas-oil ratio 700
n) /2 661.5 663.5
In calculation B the calculated gas-oil ratio is 663.5
while the assumed ratio is 662.
This is a
satisfactory
solution.
per acre-foot from the area swept. The
production from a well passed
by
the
front will contain 84 per cent water, and
if production is continued, an additional
35 bbl. per acre-foot can be recovered
before the water content
of
the
well
effluent reaches 90 per cent. The method
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E. C. BABSON
used in this paper is not rigorously appli
cable to a water drive at any pressure
below the bubble point because
of
the
complications introduced
by
variable gas
saturation.
In
order to approximate the
recovery to be expected
at 400
lb. per
sq. in.
it
was assumed
that
the gas satura
tion behind the front would be constant
at
5 per cent. Recovery ahead
of
the front
then becomes 405 bbl. per acre-foot and
the recovery to
90
per cent water in the
well
effluent is
472
bbl. per acre-foot.
T BLE
2. Summary of ecovery
Calculations
Total Recovery
Method of Depletion
Bbl.
per
Per
Acre-ft.
Cent
Normal
depletion
internal gas
drive)
293
34
Full
pressure
maintenance
external
gas
drive
at
3000 lb.
per sq.
in.
plus subsequent depletion)
. . . . . .
435
51
Partial pressure maintenan ce ex-
ternal gas drive
at
2000 lb.
per
sq.
in.
plus
subsequent
depletion) . . .
348
41
Water drive
at
3000 lb.
per sq. in ..
580
68
Normal
depletion plus
water
drive
at 400 lb. per sq.
in
472
55
Although these recoveries seem high
it
must be remembered
that
they apply
only to the area swept by the water.
In
the low-pressure drive normal recovery
was obtained from the reservoir before
the flood started so
that
only the addi
tional recovery from the unswept area
is
lost. In the high-pressure drive however
it
seems unlikely
that
normal recovery
can be obtained from portions of the reser
voir unswept
by
water because dewatering
a flooded sand is a costly operation.
SUMMARY
Results
of
the various recovery cal
culations which are summarized in Table 2
should be regarded as examples
of the
type
of information obtainable from laboratory
data rather than quantitative predictions
of
the behavior of California reservoirs
since the data entering into these cal
culations are applicable only to the
particular sand on which the laboratory
tests were made. Permeability-saturation
relations for California oil sands under
reservoir conditions are not
yet
available
in the literature hence
it
is impossible
at
present to make reliable predictions
of
field performance from laboratory data.
The preliminary investigation reported
in this paper however suggests
that
future application of such information
may furnish workable solutions to some
of
the perplexing problems facing
the
industry.
ACKNOWLEDGMENTS
The author wishes to express his grati
tude to Howard C Pyle for his advice
and guidance and to the management
of
the Union Oil Co. for permission to
publish this paper.
NOMENCLATURE
Productivity
index,
bbl. per
day
per lb. per
sq. in.
P
Pressure lb. per sq. in. abs.
. Viscosity. millipoises.
J
Formation volume
factor of oil
p h a s ~
bbl. per bbl.
K
Permeability. darcys
p Density of gas. std. cu. ft. per bbl. space.
R Total gas-oil ratio. std. cu. ft. per bbl. oil
M Dissolved gas-oil ratio.
std.
cu. ft. pcr bbl.
oil.
o
Total volume. cu. ft.
< >
Porosity. fraction.
A Cross-sectional area. sq.
ft.
f Proportion of displacing fluid in flowing
stream. per cent
by
volume. .
S
Saturation. per cent of total pores.
u
Distance, ft.
Subscripts
o refers
to
oil
phase.
g refers to gas
phase.
e refers to conditions at drainage radius.
w refers to conditions at the well face.
1 refers
to
arbitrarily
chosen standard
conditions.
REFERENCES
I B.
H.
Sage and
W. N. Lacey:
Formation
Volume
and
Viscosity Studies
for
Domin-
guez Field. Amer. Petro Inst. Drill. and
Prod. Practice
I935)
I4I.
2 . B. H. Sage
and
W. N. Lacey:
Thermo-
dynamic Properties of Mixtures of a
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132
PREDICTION OF RESERVOIR BEHAVIOR FROM LABORATORY DATA
Crude
Oil and a
Natural
Gas.
Ind and
Eng Chern Feb. 1936)
28 249;
3. B.
H. Sage and
W. N.
Lacey:
Effect of
Pres
sure upon
Viscosity of
Methane
and
Two
Natural Gases. Trans A.I.M.E.
I93S)
137,
uS
4 M. C.
Leverett and
W.
B.
Lewis:
Steady
Flow of
Gas-oil·water Mixtures through
Unconsolidated Sands. Trans A.I.M.E.
1941) 142, 107· .
5 H. G.
Botset:
Flow of
Gas-liquid
Mixtures
through Consolidated Sand. Trans
A.I.M.E. 1940) 136,91.
6.
H.
K:rutter:
Secondary
Recovery
of
Pe
troleum
by
Air
Drive. Oil Weekly
June
9, 1941) 103, 1),
21.
7
H. H. Evinger
and M.
Muskat: Calculation
of Theoretical Productivity Factor. Trans
A.I.M.E. 1942) 146,126.
S
S.
E. Buckley and M.
C.
Leverett: Mecha
nism of
Fluid
Displacement in
Sands.
Trans A.I.M.E. 1942)
146.
107.