effect of gas-oil ratio on the behavior of fractured limestone reservoirs

7/17/2019 Effect of Gas-Oil Ratio on the Behavior of Fractured Limestone Reservoirs

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Effect of Gas-Oil Ratio

on

the Behavior of Fractured

Limestone Reservoirs

JUAN JONES-PARRA, h.

MEMBER

AIME

RAFAEL SEIJAS

R VTOR

AB S T R C T

The

porosities

of

fractured limestone reservoirs can

be divided into

two

broad types in accordance with their

effects on fluid distribution

and

fluid flow.

In

the coarse

porosity, gravity segregaNon takes place freely and the

resistance to fluid flow is very small.

In

the fine porosity

there is no segregation and a high resistance to flow,

and

it has relative permeability characteristics similar to

tight sandstones.

By analyzing the affect of the two porosities it is con

cluded that in some cases to recover the maximum

amount of

oil it is necessary to remove large quantities

of

gas from the reservoir by producing at high gas-oil

ratios.

In

this manner the fine porosity is drained of its

oil and the gas-oil contact drops slowly permitting higher

production rates from the oil leg. Since this conclusion

is

contrary to widely accepted principles

of

conserva

tion, a mathematical model Fig. 1 was constructed to

duplicate the conditions desired.

The behavior of the model indicates that under cer

tain conditions it is possible to recover more oil by pro

ducing

at

high gas-oil ratios than by production at low

gas-oil ratios, and that the rate of production is affected

more by

gas shut-offs than by the decrease in pressure

Figs.

2, 3, 4 and

5).

I N T R O D U C T I O N

t

has been noted that certain limestone reservoirs be

have in such a way as to indicate that there are two

distinct types

of

porous spaces available for fluid storage

and fluid flow. Regardless

of

the nature

of

these porous

spaces the distinguishing characteristic is that in one

type of porous space there is definite gravity segrega

tion between the oil and the gas; while in the other, the

gas evolved tends to remain distributed equally through

out the reservoir. For the sake of simplicity the porosity

in which gravity segregation takes place at a fast enough

rate to affect the behavior will be called coarse po-

Original manuscript

received

in

Society

of Petroleum Engineers

office Nov. 19, 1957. Revised manuscript received March 23, 1959.

Paper presented at Second Annual Regional

Meeting

of Venezuela

Petroleum Sections in Caracas, Nov.

6-9, 1957.

SPE 990-G

68

1

ESCUELA TECNICA INDUSTRIAL

MINISTRY

OF

MINES HYDROCARBONS

CARACAS VENEZUELA

rosity , while that in which this

is

not so will e termed

fine porosity .

The behavior

of

a reservoir of this type would be

different than that of a sandstone reservoir, especially

if most of the oil is in the fine porosity. t has been ob

served that fluid flow to the wells takes place mostly

through the coarse porosity. The large fractures which

r---

I

-

I

f

r

I

fAS

So

s

s

l

Pll

rID r N 8 .

FIG.

I-RESERVOIR

MODEL

13

0.74

II 7

9 9 0 026

1 <

T

5 0 5 8

/2

0 014

4 o 12 16

lOO:

24 28

5

1 0

FIG.

2-BA SIC INFORMATION

FOR SOLVING

EQUATIONS.

JO U RN A L

O F

P E T R O L E U M T E C H N O L O G Y



make up this porosity have such a high fluid carrying

capacity as to make unimportant

that

of the rest of the

rock in contact with the well. Hence, in these reser

voirs, the fine porosity produces into the coarse porosity

which produces into the wells. This being the case, most

of the gas

that

flows from the fine porosity into the

coarse porosity wiII migrate upwards; and,

if

there is

vertical continuity in the coarse porosity, it will accumu

late up-dip creating a secondary gas cap in the coarse

porosity.

Since the normal tendency is to produce

at

reason

ably low gas-oil ratios, gas shut-offs are usually made

to isolate the up-dip fractures which are filled with mi

grating gas, isolating at the same time large quantities

of

oil in the fine porosity and reducing considerably the

production rate of the wells. Since most of the gas

which is produced from the fine porosity flows up-dip

instead

of

flowing towards the well, in these reservoirs

it is possible to produce at very low gas-oil ratios as

long as gas-filled fractures are isolated. However, the

high pressure of the fluids in the coarse porosity pre

vents the production from the fine porosity into the

coarse porosity so

that

the higher the pressure at which

the gas cap occupies all the coarse porosity the less oil

from the fine porosity which would have been produced.

n

other

words, a relatively small volume

of

oil in the

coarse porosity could be produced very efficiently

at

the

expense

of

the oil in the fine porosity.

The possibility

that

the higher pressures available

would maintain production rates high enough to shorten

the period required to produce the oil to the extent that

the shorter pay-out would compensate for the oil left be

hind is eliminated by the fact

that

the reduction in pro

duction due

to

gas shut-off is much more significant than

that due to the decrease in pressure. In some reservoirs

it

might be possible

to

recover the oil left behind in the

reservoir by producing the gas in the coarse porosity;

however, the only place to

establish continuity in the

lOOO

.-----r---,----,----,---,

1.3

1100 - - - - - t - - - t - - - - t - - ~ ± _ _ - _ _ 1

6

1000 ------ --- ---- --- ----

o

0 1

04

0 6

0 8

10

H

FIG.

3 - RELATIONSHIP BETWEEN FRACTION OF

COARSE

POROSITY

OCCUPIED

BY

GAS

AND

PRESSURE.

MAY

1959

oil from the fine porosity to the coarse porosity to the

well would only be at the bottom of the reservoir, so

that before the oil can be produced it is necessary that

it drain by gravity all the way down-dip.

The

production mechanism which is proposed is logi

cal. but the main conclusion

is

contrary to firmly es

tablished concepts. Hence, equations are derived for a

model reservoir having the required characteristics

which, when solved, indicate that under certain condi

tions the higher the cumulative produced gas-oil ratio

the more oil

that

can be recovered from it at a faster

rate.

DERIVATION OF THE EQUATIONS

Fig. 1 shows a model

of

the reservoir under con

sideration. Its total pore volume

is composed of two

zones. The j zone is

that

in which gravity drainage does

not take place and the reservoir behaves in the same

manner as a tight sandstone reservoir producing by so

lution gas. This is the fine porosity zone.

In

the coarse

porosity zone 1 - f ) gravity segregation takes place

subdividing it into a gas-filled zone H) and an oil-filled

zone 1 -

H).

Zone

j

contains oil

(So),

gas

(So)

and

connate water

(S ,).

From Fig. 1 it

can

be seen that the free gas in the

reservoir

at

any pressure and at reservoir conditions is

given by

NB;

[H 1

- f)

Sgj]

.

1)

o iT

This volume

of

gas can also

be

obtained by subtract

ing from the original gas

that

which has been produced

and that which is still in solution and converting to

reservoir conditions.

v[Nr,

-

nrp

- N -

n r ]

2)

Combining these equations the following expression

is obtained for the ratio

of

produced oil

to

oil initially

in place.

lOOO , - - , - - - - - - - , , - - , - - - - - , - - - - - - , , - - - - - , - - - - ,

1800

f . 1 . \ \ - - - - - - f - - - - - - - I - - - - - - _ _ _ 1

1600 H f f i \ - - + - - - - - ' ~ - - + - - - f - - - _ + _ - _ _ _ 1

1400 _ _ _ - \ l W ~ - H , _ _ _ _ _ _ _ _ + _ - - I - - - _ + _ - _ _ _ 1

1100 _ _ _ - - - j \ \ r t - - ' ~ _ _ _ _ _ _ \ _ + _ - - I - - - _ + _ - _ _ _ 1

1000 f - - - _ + _ - \ - - \ - ' < ~ ~ - + \ , _ _ _ _ _ _ _ _ _ 1 - - _ + _ - _ _ _ 1

nl

FIG.

4 RELATIONSHIP

BETWEEN n/N AND

PRESSURE.

0.14

69



n/N = B,[H(1 - I) + sun _ r, - r

SOiTV r - rp)

r

- rp

(3)

This ratio can also be obtained from the following

equation'.

B, B

n/N = = -

So iT

B

but since the figure indicates that

SoT = l

-

H) l

-

f + ISo

then

n/N = 1 _ ISoB,I_ (1 - H) (1 -

j)B,

SOiTBI

So TB

Combining Eqs. 3

and

6 and

s o l ~ i n g

for H,

rp A

-

B

H= _r_

rpC +

D

where

A = r,v [ - I

+

ISo _

B :'T]

B =

vr( 1 -

I + ISo) + ISgB

_ B v r ~ ~ O T

C

=

r,v(1

-

j )

D = (1

-

I) B - vr)

(4)

(5)

(6)

(7)

With the value

of

H thus obtained, the ratio

n/N

can

be obtained from Eqs.

3

or 6. Using

Eq.

6

n/N = E

- (1

-

H)F ,

(8)

where

E

=

1 -

ISoB, and

F

= (1

-

j)B, .

So TB SoiTB

Assuming

that

all

the

production rate is due

to

the

coarse porosity, the decline in productivity index (DPI)

would be given by

(1 - H)

DPI = u

o

B)

1

(9)

where (1 -

H)

has been substituted for

ko

in the well

known equation.' Assuming further

that

the pressure

drawdown is a constant fraction

of

the static pressure,

the ratio

of

the production at any pressure and any

value of H to the production capacity at initial condi

tion would be given by

Qo 1 - H) (uoB) iP

Qo.

(10)

uoBP,

APPLICATION

OF

TIlE

EQUATIONS

Fig. 2 shows the basic information used to solve

the equations. A value of I

=

0.95 and a value of S.,

=

0.20 were chosen.

The

relationship between

So

and

pres

sure shown in

the

figure was obtained using the stand

ard material balance equation; with the

Ku/Ko

curves

given by Muskat corrected to a value of Sw of 0.20.

The relationship between

H

and the pressure as a

function of

the

ratio

of

cumulative produced gas-oil

ratio to initial solution gas-oil ratio is given in Fig. 3

and that between n/N and the pressure is shown in Fig.

4;

the

limiting values of

n/N

when

H

= 0 and when

H

=

1 are also shown.

The

curves indicate the behavior

from 3,000 to 1,000 psi.

In

Fig. 5

the

relationship between the production ra

tio as functions

of the

pressure and

H

is indicated. For

70

1.0

0.1

0.

..

,: : .

04

02

02 04 os s to

FIG. 5-RELATIONSHIP BETWEEN

PRODUCTION RATIO

AS

FUNCTIONS OF

PRESSURE AND H

example, if P

=

1,450 and H

=

0.4 then the production

would be 0.23 of the initial production.

C O N C L U S I O N S

The limiting value of n/N shown in Fig. 4, when

the gas occupies all the coarse pore volume (when H

= 1),

clearly indicates that the lower the pressure at

which this occurs the greater the volume of oil which

can be recovered.

That

the productivity depends more

on

the value

of

H

than

on the pressure

is

fairly obvious, but can best

be shown by specific examples.

From

Figs. 3 4 and 5

it is possible to obtain the effect of arriving at any stage

of

depletion

at

different cumulative gas-oil ratios.

From

the figures the following tabulation was obtained:

n/N p/r; P H 00 001

0.10 OT 2,025

0.63

-0:23

0.10 1.0 1,770 0.27 0.38

0.10 1.6 1,.615 0.06 0.42

0.14 0.1 1,840 0.96 0.02

0.14 1.0 1,540 0.61 0.16

0.14

1.6 1,370

0.38 0.22

This tabulation clearly indicates

that

the production

declines less when producing

at

the higher gas-oil ratios

in spite of the fact that at any given stage

of

depletion

the pressures are lower.

N O M E N C L A T U R E

N

=

initial stock-tank oil in place, bbl

n = stock-tank oil produced, bbl

ST = saturation based on total pore volume

S

=

saturation based

on

fine pore volume

H = fraction

of

coarse porosity occupied by gas

I = fraction of total pore volume where gravity

segregation does not take place

v

= volume occupied in barrels in the reservoir

by a standard cubic foot of gas

r1 = cumulative produced gas-oil ratio

r

= gas in solution,

cu

ft/bbl

B = oil formation volume factor

lo = viscosity, cp

k

= relative permeability

P

=

pressure, psi

Q = production rate, STB/D

SUBSCRIPTS

i = initial values

0, g W = oil, gas and water

REFEREN ES

1. Calhoun, J. C.,

Jr.:

Reservoir Engineering Fundamentals ,

Oil and

Gas

Jour.

Series, No. 337 and No. 345.

2.

Muskat, M.:

Physical Principles of Oil Production,

Mc·

Graw-Hill Book Co., Inc., N. Y. (1949).

JOURNAL OF PETROLEUM TECHNOLOGY

effect of gas-oil ratio on the behavior of fractured limestone reservoirs

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