prediction of reservoir behavior from laboratory data

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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



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



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



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



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



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.



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



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



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



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



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



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



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.

prediction of reservoir behavior from laboratory data

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