Steam Drive Correlation and Prediction.pdf

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Steam Drive Correlation and Prediction

N.

A. Myhill,

SPE-AIME, Shell Oil Co.

G. L. Stegemeier,

SPE-AIME, Shell Development Co.

Introduction

During the past

15

years, steam-injection processes have

become an important means of exploiting heavy oil re

serves. Traditionally, these processes have been clas

sified

as

either steam soaks·or steam drives. With combi

nations, such

as

presoaking drive wells and partially

driving steam soaks, the distinction is not always appli

cable. Furthermore our experience suggests that

oil/steam ratios from most mature processes converge to

a value determined only by reservoir and steam properties

and time.

To date, the steam-soak process has proven the more

attractive, partly because the immediate response allows

an early evaluation

of

a reservoir and partly because oil

rates from initial soak cycles tend to be better than later

cycles. Successful steam soaks are limited to reservoirs

where natural recovery mechanisms gravity drainage,

pressure depletion, and solution gas drive) are ineffective

because of the low oil mobilities.

Successful steam drives require

1)

good confor

mance, 2) a means of starting the process because high

oil saturations can limit injectivity severely and prevent

effective initial reservoir heating, and 3) sustained high

injectivity throughout the process life. Unlike steam

soaks, steam drives do not respond until built-up oil

banks and heat reach the production wells. Because peak

production rates may not be observed for several years

after the start of injection, piloting

is

expensive and

expansion to full scale

is

somewhat hazardous. For these

0149-2136/78/0002-5572 00.25

© 1978 Society o Petroleum Engineers of AIME

reasons

screening

methods that predict ultimate

oil/steam ratio are useful in planning new projects or in

modifying existing ones.

n

the past, steam injection has been applied to a wide

spectrum of reservoir conditions, many of which have

proven unsuitable. n retrospect, we can explain the var

ied response with a simple mathematical model that

incorporates reservoir and steam properties in the pre

diction. This paper describes the model and compares

predictions from it with laboratory and field results.

Comparison o Model and Field Results

With a Theoretical Model

At this time, we have experience from many field

steam-drive projects

1

-

11

and laboratory physical model

experiments to help screen and design new projects.

From these results, there appears to be a unifying princi

ple that applies

to

long-term, fieldwide, steam-injection

processes. That is, the oil ultimately produced from

steam soaks and steam drives is proportional to the

steam-zone volume that in turn

is

a function

of

reservoir

and steam properties and injection policies. Maximum

deviation from this behavior occurs when a small amount

of heat is applied to reservoirs in which a substantial

amount of primary oil remains, or when initial oil satura

tion is low and banked oil is not recovered efficiently. 12

To compare our past experience with physical models,

a simple energy balance described later)

is

used to esti

mate the oil/steam ratio. Parameters used are given in

Table 1 and comparisons

of

physical model values with

A mathematical model based on a simple energy balance is developed

t

predict ultimate

oil/steam ratio for field steam injection projects _Data includes basic reservoir fluid and

rock properties and injected steam conditions. The model correlates well with results

of

field steam drive projects nd laboratory model experiments.

FEBRUARY, 1978

173


2/10

TABLE 2-COMPARISON OF MODEL RESULTS

Calculated

Model

Quantity of Steam- Equivalent

Equivalent

Steam Zone Oil/Steam

Oil/Steam

Injected

Size Ratio

Ratio

Model

VpD)

VpsD)

(vol/vol) (vol/vol)

Coalinga

2.6 1.20

0.175 0.15

~ I U

U)

Midway-Sunset

1.0 0.75 0.459 0.40

...... c t S ~

( \ J

0)

0>

co

U)

co

0

~ ~

(\J

Mt. Poso

0.72 0.88 0.535 0.57

(Low pressure)

=ai

f?

3: U)

0

0

0

0

U)

Mt. Poso 1.02 0.76 0.323 0.29

.

~ I ~

co

co

~

~

oil/steam ratios are reduced to account for the limited

I

.c

0 .

~

0

0

amount of oil available for recovery from the designated

n

e

~

Qi volume.

z

a..

-21

U)

0

U)

U)

(\J

0 co 0

In addition, oil/steam ratios for field steam-drive proj-

N ~ (')

0>

I -

I -

co co

ii:

U)

co

0

0 0

U)

U)

0

ects also are calculated, using the reported or estimated

w

~ co

0>

0

I -

co

field conditions given in Table 3. These calculated values

,

><

are compared with actual oil/steam ratios from the field

~

..I

projects

in

Table 4 and Fig.

2.

Comparisons are based on

w

0

N. c

I -

"

I -

"

I -

C ?

I -

"

the additional oil production above an estimated pri -

0

~

:: i=

0 0

0

0

mary production.

'

J)

:J

W

@.

Oil saturation at the start of the steam drive has been

~

.

1::

a:

Q)

corrected for the estimated primary oil that would have

0

0 .

::E

e

~

been produced during the steam drive. Cases in which oil

a..

00(

( i j

:::

production from primary or other mechanisms are sig-

w

N: J

( )

( )

( )

( )

( )

( ) ( )

(\J

~

§

E o

( )

( ) ( )

( ) ( )

( )

( )

n

'

I

Q)

:J

.c

@.

....

f -

1.0

W

...I

fL

(J)

m

I

z

00(

:::

w

~

;

:J

( ) ( )

( )

( )

( )

( )

U)

a:

0.8

E o

( ) ( )

( )

( )

( )

( )

( )

w

'

Q.

:J

x

@.

0

0

2

:I::

0.6

ci

MT

POSO 0

Q)

I

LOW

PRESS. I

~ ~

E

a:

Qi

I i )

a:

Q)

:J

:J

Q)

al :I::

(J)

(J)

Q)

C

0 .

a:

0

c

(J)

w

~

:J

~

'0

'0

I

0.4

o MIDIIAY-SUNSET

n

00.

~

(J)

al

:>,

00.

Q)

0 0

-

01

(J) 3:

( J ) .c

c

E

(J)

(J)

(J) Q)

o

SCHOONEBEEK

al

00

001

8

§ ~

0

3:

a.. I

:J

o..jjj

0

°MT.POSO

;

0.....1

0

~ ~

.c

0 i i ~

~ ~

I

0

~

~ ~

0

CiS

z

(HIGH PRESS. I


3/10

TABLE 3 STEAM DRIVE FIELD PROJECTS SUMMARY OF CONDITIONS

Thermal

Number

Properties'

Petrophysical Properties Steam Parameters

of

T

f

z

i,

A

t

Field

Reference Injections ( F)

J L

z./z

'

~ · ·

f,d

(psig)

(B/O)

(acres/well) (years)

Brea

10

4 175

300

0.63 0.22

0.40

0.75

0.54

2,000 500

10 8

( B

sand)

Coalinga

4 40

96 35

1.0 0.31

0.37

0.7

0.55 400

500

9.2 4

(Section 27,

Zone 1)

EI Dorado

2 4 70

20

0.85 0.26

0.20

0.75

0.45

500

200

1.6

(Northwest pattem)

Inglewood

1 1 100

43

1.0 0.37 0.40 0.75 0.7 400

1,100

2.6 1

KemRiver

5 85 90 55

1.0 0.32 0.40 0.7

0.5

100

360

2.5 5

Schoonebeek

9

4

100 83

1.0 0.30

0.70

0.85

0.7 600

1,250

15 6

Slocum

8

7

75 40

1.0 0.37 0.34 0.8

0.7

200

1,000 5.65

2.5

(Phase 1)

Smackover

3

1 110

50

0.5 0.36 0.55 1.0

0.8

390

2,500

10

Tatums

7 4

70 66

0.56 0.28 0.55 0.7

0.6

1,300 685

10

5

(Hefner steam

drive)

TiaJuana

6

7 113

200

1.0 0.33 0.50 1.0

0.8 300

1,400

12 5.3

Yorba Linda

2 110 32 1.0 0.30

0.31

0.8

0.7

200

850

35

4.5

( F sand)

M,

35

Btu/eu ft- F, M, 42

Btu/eu

ft_oF,k,,, 1.2 Btu/ft-hr-oF.

i lS

(oil saturation at start of steaming change in oil saturation from estimated primary during steam-drive period) - So after steam drive 0.15 average)

nificant compared with production from steam drive are

not described adequately by this simple model and should

be

applied with caution. Total and additional oil/steam

ratios are shown

in

the correlation offield results in Fig. 2

because primary oil often

is

not well defined. This corre

lation demonstrates lower recoveries in the field compared

with calculated values except for cases such

as Coalinga

where the amount of steam injected results in a steam

zone considerably less than the pore volume and where a

sizeable amount

of

primary production has occurred.

Because pattern boundaries are not well defined in field

cases the correction for calculated steam-zone volumes

greater than 1.0

PV

has not been applied. Therefore cal

culated oil/steam ratios for Kern River Inglewood and

Slocum fields could be reduced as much as 20 percent.

With these exceptions the correlation indicates that the

oil/steam ratios from the field projects range from 70 to

100 percent of the calculated values. Less than the calcu

lated maximum efficiency results from reduced sweep

and other operating problems associated with field proj

ects. Techniques for improving steam drives such as

conversion

to

waterflood use of plugging agents etc .

can increase the field performance toward the expected

maximum oil-steam ratio.

Physical Model xperiments

Physical model experiments

of

steam soaks drives and

combination processes indicate that the recovery effi

ciency of these thermal processes

is

controlled largely by

the growth of the steam zones. One can conclude that oil

TABLE 4 COMPARISON OF FIELD RESULTS

Calculated Field

Additional Additional

Field Total

Quantity Steam- Equivalent

Equivalent

Equivalent

of Steam

Zone Oil/Steam

Oil/Steam

Oil/Steam

Injected

Size

Ratio Ratio

Ratio

Field

VpD)

PSD

(vol/vol)

(vol/vol)

(vol/vol)

Brea

0.5

0.15 0.13 0.14

0.21

Coalinga 0.94

0.45

0.16 0.18 0.37'

EI

Dorado 1.6

0.315 0.05 0.02

0.02

Inglewood

1.26 1.256 0.41 0.28 0.36

Kern River

1.92

1.139

0.32 0.26

0.26

Schoonebeek

0.95 0.617 0.43

0.35

0.35

Slocum 1.41

1.202 0.29

0.18

0.18

Smackover 1.23 0.756 0.27 0.21

0.28

Tatums

1.54

0.397 0.13

0.10

0.13

TiaJuana 0.47

0.551

0.59 0.37

0.53

Yorba Linda

F

0.54

0.280

0.16

0.17

0.21

*Includes waterflood after steam drive.

FEBRUARY, 1978

175


4/10

1.0 r-------------------------------------,

>

>

ci

I-

0.8

f

lI::

a:

LIJ

:;;

J

0.6

o

I

Z

LIJ

.J

a:

;:: 0.

a

LIJ

I- 0.2

o ADDITIONAL OIL/STEAM RATIO

6 TOTAL

OIL/STEAM RATIO

CALCULATED

ADDITIONAL

EQUIVALENT OIL/STEAM RATIO. v /v )

Fig. 2-Comparison of field steam-drive results with calculated

values.

1.0

r----------------------------------------,

; 0.8

0.6

0 .4

0.2

o _ ~ ______ _________

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

o 10 15 20

TIME Y f

Fig. 3-Cumulative steam injection - Midway-Sunset model

experiments.

0 .5

O. 4

z

i

S

u

6 0.3

0

0:

a.

-

0

w

0.2

cr

-

::J

I:

::J

U

0.1

COLD GRRY lTY ORA 1NAGE

0.0

0

5

10

15

TIME y r s

Fig. 4-Cumulative oil production - Midway-Sunset model

experiments.

176

20

production can be accelerated significantly by increasing

the steam-injection rate.

Selected model experiments on the steeply dipping

Midway-Sunset field, where steam soaking

is

being suc

cessfully applied, illustrate the possibility for such an

acceleration in oil production. Fig. 3 shows that continu

ous steam injection allows higher heating rates than

steam soak with

2Vz-acre

spacing, or even steam soak

with complete infilling to

1lJ

acres. In all steam-soak

experiments, each well received one 1O,OOO-bbl steam

soak per year; therefore, the infill case, with twice

as

many wells, received double the heat per pore volume

each year. Fig. 4 indicates that the oil recovery

is

related

closely to these heating rates. Steam soaks in highly

oil-saturated reservoirs begin with high oil/steam ratios,

but decline with time as thermal efficiencies decrease,

and the development of large hot-oil banks becomes more

difficult. In contrast, steam drives exhibit low oil/steam

ratios initially while oil

is

being banked, but the oil/steam

ratio increases when the oil banks arrive at the production

wells. A significant observation from these model studies

is that over long times, oil/steam ratios converge

to

the

same values for both processes. See Fig. 5.)

For a full pore-volume steam drive applied to a given

reservoir, the oil/steam ratio

is

determined primarily by

injection pressure and rate and by hot-fluid production

after heat breakthrough. Factors are so interrelated that

the improvement in performance resulting from a change

in one parameter often

is

offset by opposing changes in

other parameters. For example, although increased injec

tion rates might be expected to improve thermal efficien

cies, this advantage can be offset by increased injection

pressures and larger heat-production losses. Because of

these interactions, interpretation

of

model experiments

is

\ . 0

0 .9

ci

I

0.6

a:

/STEAM

SOAK

a:

I:

a:

w

0.5

f)

-

..J

0

w

0.4

I

a:

..J

>

I:

0.3

>

J

0.2

0-1

0.0

0

5

10

15

TIME.

yn

Fig.

5-Cumulative

oil/steam ratio as a function of ime from start

of steam drive t = 0 at 4.5 years) - Midway-Sunset model

experiments.

JOURNAL

OF

PETROLEUM TECHNOLOGY


5/10

complex. Nevertheless, it appears that many experiments

follow a regular pattern. At first, high pressures are

required to inject the steam

as

oil is being banked up.

After water and heat breakthrough at production wells,

the pressure drops sharply. At this time injection at high

rates results in excessive heat production with attendant

low thermal efficiency. Often, a more-or-Iess continuous

steam layer then spreads across the reservoir, and heated

oil flows

to

the wells

as

a result

of

gravity drainage and

steam drag. In high-permeability reservoirs, little dip or

sand thickness is required to make gravity drainage the

dominant mechanism.

The early pressure level is determined by the mobility

of the cold oil, and the later pressure level by the

mobilities

of

the hot oil, water, and steam. For all practi

cal purposes, cold-oil mobility is determined largely by

cold-oil viscosity and hot-oil mobility by reservoir per

meability. f the reservoir is sufficiently permeable, a

low-pressure process

is

possible after heat breakthrough.

Thus, heat can be stored in the reservoir at high pressures

and redistributed later to

indude

more of the reservoir by

blowing the pressure down. Because

of

this redistribution

and because heat can be recovered from cap and base

rock, it appears that the final process pressure largely

determines the heat requirements.

Mathematical Model Studies

Description and ssumptions

The mathematical model used to predict oil/steam ratios

is

the commonly accepted energy balance between in

jected heat, hea t loss to cap and base rock, heat stored in

the steam zone, and heat produced through the condensa

tion front.

The

steam-zone growth

is

calculated using a

slightly modified version of Eq.

56 of

Mandl and

VolekP The oil/steam ratio is calculated assuming oil

produced is equal to steam-zone pore volume times the

change in oil saturation. An additional correction for oil

displaced from a heated region not at steam temperature

is

available; however , it was not used because its effect

is

negligible at the end of a steam-drive process where the

steam zone occupies most

of

the reservoir volume. In

addition, the delay resulting from oil-bank formation

1

and the effects of allowing steam injection rates to vary14

are not

induded

in this simple model.

Fig. 6 shows schematically the geometric configuration

assumed and the reservoir and steam properties used.

Although the steam zone is presumed vertical, the as

sumptions made in the heat-balance equations

of

Mandl

and Volek are not so restrictive.

Two

unknowns in these

equations are the steam-zone volume and the combined

contact area of cap and base rock. For vertical fronts, the

volume is equal to the product of the height and the

combined areas divided by a factor

of

2.

(V

=

Ah/2.

However, other geometrical shapes also give an identical

relationship. Examples are (1) a linearly advancing in

dined

linear front, (2) an inclined linear front advancing

only at the top, and (3) cylindrical fronts. For conical

shapes the volume varies, depending on the amount

of

truncation, from Ah/3 (cone) to

Ah/2

(cylinder).

The

squares of these proportionality constants determine the

values of dimensionless time so that t for the conical

shapes differs by a factor

of

4:9. Inspection

of

Fig. 7

reveals that for this uncertainty in dimensionless time, the

steam-zone thermal efficiencies seldom differ by more

FEBRUARY, 1978

than 25 percent. Even curved shapes, representative of

severe steam layover, will not introduce significantly

greater differences. It

is

likely that the relative insensitiv-.

ity

of

the calculation to the shape of the steam front

accounts for the good correlation observed between ac

tual and predicted results.

In summary, the basic assumptions for the calculation

are

as

follow.

1 The reservoir contains a uniform amount of oil per

unit bulk volume

as

defined by the product of porosity,

net to gross thickness, and oil saturation in the net pay.

Gross thickness and area per injector are also constant

throughout the reservoir.

2. Thermal properties,

induding

initial formation

temperature, heat capacity

of

reservoir rock, and heat

capacity and conductivity of cap and base rock, are as

sumed constant throughout the zone.

3. Steam is injected at a constant pressure, quality,

and rate per injector.

4.

Vertical temperature gradients in the reservoir are

zero.

5. Heat losses from the steam zone are by conduction

only and occur normal to the reservoir into the cap and

base rock. Heat

is

transferred in the reservoir by convec

tion only, and heat passes through the condensation front

only after Mandl and Volek s critical time.

~

p

v

0 .

o •

o •

S

TEAM

Z NE

T ~

j ~

o

ig.

6 Geometrical configuration for energy balance

calculations .

0. 0 L L L - - - - - - L , - - L L i ~ _ = = = ± E ~ ~ ~

01 I 10 l

OG

0

Fig.

7 Steam zone thermal efficiency as a functi

on

of

dimens ionless parameters.

177


6/10

Applicable equations for the calculations are given in

the Appendix. Fig. 7

is

a graphical representation

of

the

steam-zone heat efficiency functions .15 The ratio of heat

in

the steam zone to total heat injection is plotted

vs

a

dimensionless function

of

time

tD)

for various values

of

a

dimensionless function of steam quality hD). The func

tion

h is

the ratio of the latent heat content of the steam

divided by the sensible heat. The magnitude of the differ

ence between solutions with and without heat flow

through the condensation front is shown in Fig. S. As

shown

in

Fig. 9 for a typical formation temperature and

steam-zone heat capacity/unit volume, the value of

h

for

most steam drives ranges from 1.0 to 2.5.

'

Also, the oil/steam ratio divided by the moveable oil

o.

,

o.s

no

a

0.1

0 .5

o.

,

0 .2

0 .3

0.3

0 .5

0.2

t.o

o.

t

0.0

0.01

0

Fig.

8 Upper minus lower

bound efficiency as a function of

dimensionless parameters.

4

3

2

0.5

f

5

Fig. Typical dimensionless quality values.

\ .0

178

per bulk volume is only a function of the dimensionless

terms

t

and h Fig. 10). This oil/steam ratio is the

volume of oil displaced from the steam zone per volume

of water used

to

generate steam. It is our practice to

stanqardize oil/steam ratio to equivalent steam with a heat

content of 1,000 Btu/lb above average boiler inlet tem

perature. For field pressures from 200

to

1,000 psi, this

is approximately SO-percent quality steam.

Effect of Reservoir

and

Steam Properties on

Oil/Steam Ratio

The effect of individual parameters, including reservoir

thermal, reservoir petrophysical, and steam properties on

equivalent oiVsteam ratio, was calculated from Eqs. A-2,

A-4, A-7, A-12, and A-13. Assumed conditions are

listed in Table 1 under

Mount

Poso, Effect of Parame

ters.

In this study, all values except the one being

examined) were held constant. Results are shown in Figs.

11, 12, and 13. Thermal reservoir properties do not

strongly affect oil/steam ratios in the range of possible

values. As might be expected, the gross reservoir thick

ness is one of the most important parameters. Other

petrophysical properties, including porosity, net- to-gross

thickness, and change in oil saturation, would have had a

linear effect, except that the quantity of steam was ex

pressed on a constant total pore- volume basis, so that the

actual amount of steam varied somewhat. Steam proper

ties greatly affect oil/steam ratio; however, defining

oil/steam ratio as equivalent steam suppresses the quality

effect. The very large dependence on pressure, especially

at low values, is demonstrated. Low pressure may even

be the significant factor contributing

to

good efficiencies

of steam soaks. The steam-injection rate per unit area

determines the length of time and then the thermal effi

ciency of the process; however, for long times, the effi

ciency function changes slowly and injection rates be-

come less important. Pressure and maximum injection

rates are interrelated and constrained by reservoir mobil

ity and by minimum injection-well density.

Conclusions

1. Oil/steam ratios calculated with a simple mathe

matical model correlate well with experience from field

steam-drive projects and laboratory physical-model

experiments. The model, which predicts oil/steam ratio

from average reservoir and steam properties and project

o

I·

S

1

0

0

Fig.

10 0il lsteam

ratio as a function of dimensionless

parameters.

JOURNAL OF PETROLEUM TECHNOLOGY


7/10

life,

is

a fairly accurate screening tool for evaluation

of

steam-injection projects.

2. Conversion from steam soak to steam drive offers

the advantage of increasing the heating rate of the reser

voir and decreasing over-all project life.

3. Improved steam-drive efficiency often can be at

tained initially by heating the reservoir rapidly, by dis

tributing steam over most

of

the reservoir to avoid leaving

cold-oil banks, and then by reducing injection once heat

breakthrough occurs.

4. Model and field studies indicate that eventually all

types of field-wide steam-injection processes are limited

by attainable thermal efficiences. Thus, late in project

life, oil/steam ratios from continuous steam injection and

from steam soaking can approach similar values.

Nomenclature

=

area/injector, acres/well

As

=

area of steam zone, sq ft

C

=

specific heat, Btu/lb;oF

Eb

= boiler efficiency, dimensionless

E =

ratio of energy displaced from steam

zone to energy required to generate

steam (as defined in Eq. A-14),

dimensionless

hs

=

thermal efficiency

of

steam zone (as

defined by Eq. A-2), dimensionless

hs

=

average thermal efficiency of steam

zone (as defined by Eq. A-7),

dimensionless

Fos =

ratio

of

oil displaced from steam zone

to water as steam injected (as

defined in Eq. A-12),

dimensionless

Fose =

ratio of oil displaced from steam zone

to water as steam injected, 1,000

Btu/lb (as defined in Eq. A-13),

dimensionless

i b

=

steam quality, boiler outlet

isd = steam quality, injector bottom-hole,

dimensionless

h

=

ratio of enthalpy of vaporization to

liquid enthalpy (as defined

in

Eq.

A-6), dimensionless

Ho

=

heating value of oil, Btu/lb

i,.

=

injection rate

of

water injected as

steam, bbl/D

kh2 = thermal conductivity of cap and base

rock (Btu/ft-hr-OF)

= heat of vaporization

of

steam, Btu/lb

M 1

= PIC

I

=

average heat capacity

of

steam zone,

Btu/cu ft-OF

M

=

P C

2

=

average heat capacity

of

cap and base

rock, Btu/cu ft-OF

N

p = volume of oil displaced from steam

zone, cu ft

NpD

= pore volume of oil displaced =

N

p

/43 560Az

n

1> dimensionless

p =

steam zone pressure, psia

Q =

rate

of

heat injection, Btu/hr

1S

=

average change

in

oil saturation

during steam process,

dimensionless

t =

time of steam injection, hours

FEBRUARY, 1978

>:

a:

w

>-

>

>

- - 1 -

o

.

.

- 0

ZlL

W •

- - 10

a :

> >

- a :

:::>0:

'

>:

>-,

o .

.

-

•

cfo

>-

b:

,0:

w

0 4

0 3

M I

0 2

3 ~ 0 4 ~ 1 0 ~ ~ S O

HERT

CAPAC

lTV.

BTU/

cu . f r , 0 F

0 4

0 3

0 . 2 0 . ~ 8 ~ ~ I L . 0 ~ ~ I ~ . ~ 2 ~ I . L 4 ~ I L . 6 ~ 1 I . B

THERMRL CONDUCT V TV.

BTU

If -

h,

, • F

0 4

0 3

0 2

90 100 110 120 130 140

FORMRTION TEMPERRTURE. OF

Fig

11 Effect

of reservoir thermal properties on equivalent

oil/steam ratio.

0 4

,

-

'"

0 3

3

....

a:

a:

"

0 2

;:

0

0 1

z

w

.J

g

::>

0

w

0 .0

0

50

100

FORMATION THICKNESS

fT)

0 4

,

-

.

,0

0 .3

ci

....

a:

a:

"

0 .2

;:

0

0 1

z

j

g

::>

:'.l

0 .0

0

0 .5

1 0

Fig 12 Effect of reservoir petrophysical properties on

equivalent oil/steam ratio.

179


8/10

180

tl = temperature

of

boiler feed water, of

t D

= time of steam injection at onset of

convective heat transport through

the condensation front (as defined

by Eq. A-5), dimensionless

t

= time

of

steam injection (as defined by

Eq. A-3), dimensionless

Tr

=

temperature

of

original formation, of

Ts = temperature

of

injected steam, of

Subscripts

1 = steam zone

2 = cap and base rock

b = boiler

D = dimensionless

d

= bottom-hole

e

= equivalent

Ts

=

TI

= temperature of steam zone, of

f= formation, original conditions

=

oil

s

=

steam

w

=

water

-

>

-

>

-

°

.,

c:i

-

a:

cr

1:

a:

w

f

U

"-

J

a

f

z

w

J

a:

>

:;

a

w

-

>

-

°

.,

0

f

a:

cr

I:

IT

W

f

U

"-

-

-

Z

W

.J

IT

>

::>

C)

L.I

tJ T

=

steam/zone temperature - original

formation temperature,

of

u = integration variable

VI = bulk volume of steam zone, cu ft

Vs = volume

of

water having a mass equal

to that

of

injected steam, cu ft

V

pD

=

pore volume

of

steam injection

=

V

s

/43,560Az

n

1> dimensionless

Zn

= net thickness of reservoir, ft

Zt = gross thickness

of

reservoir, ft

Yo = specific gravity of oil, dimensionless

> = porosity, dimensionless

Pl 2

=

bulk density of formation, lb/cu ft

Pw

= density of water = 62.4, lb/cu ft

O

5

O 4

O

3

O 2

0.1

0.0

0

0.5

O

4

O 3

O 2

0·1

8. 0

0·0

500

PRESSURE. (ps lg l

1.0

CUMULAT I VE

STEAM INJECTED IVpOI

1000

2.0

>

-

cknowledgments

We

wish to express our appreciation to Shell Develop

ment Co. and Shell Oil Co. for permission to publish this

paper. We also acknowledge the contribution

of

P. van

Meurs and C. W. Volek, who developed scaling rules

and supervised the laboratory experimental work.

References

I. Blevins,

T

R., Aseltine, R

J.,

and Kirk,

R

S.: Analysis ofa

Steam Drive Project, Inglewood Field, Californ ia, 1. Pet Tech

(Sept.

1969) 1141-1150. . .

2 Hearn, C L.: The

EI

Dorado Steam Drive - A Pilot Tertiary

0.5

0.5

•

: O 4

0

0.4

>

-

L.,0

0

a:

0.3

a:

1:

a:

w

(JJ

O 2

-

-

a

z

0·1

w

J

a:

>

:;

a

0.0

w

0.0

-

0.5

>

"-

ID

0.4

l J

0

c:i

0:

0.3

a:

1:

0:

W

(JJ

0.2

"-

-

;;

Z

0.1

w

-

0:

>

=>

a

0.0

0

0.5

STEAM QUALITY

1000

I NJECT I ON RATE.

BID

I \JELl

0.3

O

2

0.1

0.0

1.0

2000

0

0

>

-

0

l J

0

0:

a:

1:

0:

w

(JJ

-

J

;;

Fig 13-Effect of steam parameters on equivalent oil/steam

ratio.

JOURNAL

OF PETROLEUM TECHNOLOGY


9/10

Recovery Test,

l.

Pet. Tech. (Nov. 1972) 1377-1384.

3. Smith, R. V., Bertuzzi,

A.

F., Templeton, E. E., and Clampitt,

R L.: Recovery

of

Oil by Steam Injection in the Smackover

Field, Arkansas,

l .

Pet. Tech. (Aug. 1973) 883-889.

4.

Afoeju, B.I.: Convers ion of Steam Injection to Waterflood, East

Coalinga Field,

l.

Pet. Tech. (Nov. 1974) 1227-1232.

5. Bursell, C. G. : Steam Displacement - Kern River Field.

l. Pet. Tech. (Oct. 1970) 1225-1231.

6. de Haan, H. J. and Schenk, L.: Perform ance Analysis ofa Major

Steam Drive Project in the Tia Juana Field, Western Venezuela,

l .Pet. Tech. (Jan. 1969) 111-119; Trans., AIME,246.

7. French, M. S. and Howard, R. L.:

The

Steamflood Job, Hefner

Sho-Vel-Tum,

Oil

andGasl.

(July 17, 1967) No. 29, 65, 64.

8. Hall,

A.

L. and Bowman, R. W.: Operation and Performance of

the Slocum Thermal Recovery Pro ject,

l.

Pet. Tech. (April 1973)

402-408.

9. van Dijk, C.: Steam-Dr ive Project

in

the Schoonebeek Field, The

Netherlands, l Pet. Tech. (March 1968) 295-302; Trans.,

AIME,243.

10. Volek, C. W. and Pryor,

J.

A.: Steam Distillation Drive - Brea

Field, California, l. Pet. Tech. (Aug. 1972) 899-906.

II. Harmsen, G. J.:

Oil

Recovery by Hot Water and Steam Injec

tion, Proc., Eighth World Pet. Cong., Moscow (1971) 3,

243-251.

12.

Niko, H. and Troost, P.J.P.M.: Experimental Investigation of

Steam Soaking

in

a Depletion-Type Reservoir,

l.

Pet. Tech.

(Aug. 1971) 1006-1014; Trans., AIME, 251.

13.

Mandl, G. and Volek,

C.

W.: Heat and Mass Transport

in

Steam-Drive Processes, Soc. Pet. Eng.

l.

(March 1969) 59-79;

Trans.,

AIME, 246.

14. Prats, M.: The Heat Efficiency of Thermal Recovery Pro

cesses,

l.

Pet. Tech. (March 1969) 323-332; Trans., AIME,

246.

15.

Walsh,

J.

W.: Unpublished correspondence, Shell Development

Co., Houston.

16.

Prats, M. and Vogiatzis,

J.

P.: Personal communication, Shell

Development Co., Houston.

17. Zaba, J. and Doherty, W. T.: Practical Petroleum Engineers

Handbook, Gulf Publishing Co., Houston (1951) 55.

18.

Keenan,

J.

H. and Keyes, F. G.:

Thermodynamic Properties of

Steam, John Wiley Sons, Inc ., London (1936).

19. Ramey,

H.

J.:

How

to Calculate Heat Transmission in Hot

Fluid, Pet. Eng. (Nov. 1964) 110.

PPENDIX

Thermal fficiency Function

The thennal efficiency of a steam-injection process in a

reservoir

is

defined

as

the ratio

of

heat remaining in the

steam zone to the total heat injected.

E

hs

=

VIMILlT (A-I)

Qt

Combining Eq. A-I and Eqs. 53 and 54

of

Mandl and

Volek

l3

results in an expression for the thennal efficiency

of the steam zone before the critical time, teD at which

heat begins to pass through the condensation front.

E

hs

=

_ _ fetD erfc Vt;; + 2 - 1 , ... (A-2)

tD \: 7T

where

tD = 4kh2M2t . .

(A-3)

zlMI2

For times greater than the critical time (tCD)

,

an approx

imate solution for average steam-zone thermal efficiency

has been given,13 using the arithmetic average of two

thermal efficiencies representing the upper and lower

bounds of steam-zone growth. The upper bound is calcu

lated by assuming no heat flow across the condensation

front, which

is

the solution given in Eq. A-2. The lower

bound

is

calculated by assuming heat flow across the

FEBRUARY, 1978

condensation front, but no preheating of the cap and base

rock (see Ref. 13, Eq. 56). Because Mandl and Volek's

solution neglected higher-order tenns, a slight inaccu

racy was introduced. Prats and Vogiatzis

l6

have included

these tenns and obtained the more exact solution for the

lower bound,

E

- 1

2 r-

t

_ 2VtD -

tCD

lower bound - V tD

V-:;t

D

1 + hD

I

tc

e

erfcVu

dU ,

...

(A-4)

o

V t

D

-

U

where

__ _ = etcD erfc' (A 5)

1 +hD VlcD, -

and

hD =

fSdLV

(A-6)

CwLlT

(Note that the denominator in Eq. A-6 presumes a con

stant value for the heat capacity of water,

w

, over the

temperature range. For a more precise calculation, the

differences in enthalpies of liquids at steam and at the

reference temperature should be used.) Prats and Vogiat

zis also suggested a new weighting factor for the average

steam-zone thermal efficiency:

- _ ( 1 )

Ehs-Eupperbound- I+hD LlE, (A-7)

where Eupper

bound

is E

hs

from Eq. A-2 and

LlE

=

Eupper bound - Elower bound ••• • • (A-8)

These relationshigs, shown in Figs. 7 and 8, fulfill the

requirement that

hs

approach zero as the steam quality

becomes small. Although this formulation

is

arbitrary, it

is expected to give reasonable estimates of steam-zone

thermal efficiency for steam qualities greater than about

0.2. Calculation

of

oil/steam ratio for low-quality steam

processes, however,

is

not recommended because the

model described in the next section does not account for

the hot-water drive that would predominate in a low

quality steam drive.

Oil/Steam Ratio Function

The maximum oil/steam ratio (Fos) is defined as the ratio

of volume of oil displaced from the steam zone to the

volume of water having a mass equal to that of the

injected steam. The volume of oil displaced is

N

p

=

AsZncPLlS .

(A-9)

The volume of steam required can be calculated from the

heat in the steam zone, the heat efficiency, and the heat

content of the steam:

VI

=

MIAsztLlT·(l/Ehs)

,

(A-lO)

Pw(CwLlT + fSdLV)

since

Fos = Np/VI

(A-ll)

Fos

=

PwCw .(1 + h ).£ (t h ).

cPLlS(zn/Zt) MI hs D, D

(A-I2)

If the ratio of heat capacities of water and the bulk steam

181


10/10

zone are constant, the oil/steam ratio divided by the

dimensionless petrophysical properties is a function of

only tD and h

D

.

Equivalent Oil/Steam Ratio

To standardize oil/steam ratio to an equivalent 1,000-

Btu/lb steam at boiler outlet, the following correction

is

required.

Fose

= 1,000 ·Fos . . . . . . . . . . (A-13)

Cw(T

l

-

Tb)

+

SbLv

Over-All

Energy

Balance

The equivalent oil/steam ratio can be modified to define

the ratio of energy recovered from the process to energy

required to generate steam.

E

= oil heating value/volume oil

D heat requirement/volume oil

ED =

YoH(;;SO Eb

(A-14)

A simple relationship between specific gravity and heat

ing

value of the oip7 is

Ho = 13,100 + 5,600/yo, . . . . . . . . . . . . . . (A-15)

which further simplifies Eq. 14 to

ED

= (l3.1yo

+5.6 ·Eb·Fos

e

. . . . . . . . . .

(A-16)

Example Calculation

Yorba Linda

F

Sand Drive

Given the parameters listed in Table 3 and values from

standard steam tables,18

Lv = 837.4 Btu/lb(at 215 psia, 387.9°F)

CwTs

= 361.91 Btu/lb (at 215 psia, 387.9°F)

CwTr =

77.94 Btu/lb (at 110°F)

CwTb = 38 Btu/lb (at 70°F)

C

=

CwD.T

=

361.91 - 77.94

w ---;yr- 387.9 -

110

1.022,

Isb

=

0.8.

1. Calculatet

D

from Eq. A-3.

Original manuscript received

in

Society of Petroteum Engineers office Sept. 12.1975.

Paper accepted for publication Feb. 2 1976. Revised manuscript received Dec. 1

1977. Paper SPE 5572) was presented althe SPE-AIME 50th Annual Fall Meeting,

held

in

Dallas, Sept. 28-Oct.

1

1975.

182

tD

35,040kh2M2tyrs

,

. . . . . . . . . . . . .

(A-17)

Z? M12)

35,040( 1.2)(42)(4.5)

(32)2(35)2

= 6.33.

Alternatively, tD can be calculated from steam-injection

rate and pore volume of steam injected:

744,750M

2

k

h

Zn/Zt) cpAV

pD

tD = _--- -

= - c ~ . . . . : . : : . . . . . . . . : . . : . . . . - - - - - - - - - - = - -

(Mlf

Ztis

(A-18)

2. Calculate hD from Eq. A-6 (or read approximately

from Fig. 9). Bottom-hole steam quality, Isd, can be

estimated by subtracting surface-line and injection-well

heat losses1

9

from boiler-exit quality. In this example,

fsd ;;; 0.7.

h = (0.7)(837.4) - 2.064

D (361.91 - 77.94)

3. Using tD andh

D

,

determineE

hs

from Eqs. A-2, A-4,

andA-7(orFig.7).

E

hs

=0.313.

4. CalculateFos fromEq. A-12.

Fos = (0.3)(0.31)(1.0)

(1.022

6i s

4

)

l + 2.064)(0.313)

=

0.162.

(Alternatively,

Fos

could have been obtained using values

of

D

and

hD

in Fig. 10).

5. Calculate Fose from Eq. A-13.

F = 1,000(0.162)

ose (361.91 - 38) + 0.8(837.4)

= 0.163.

6. Calculate

ED

from Eq. A-16, assuming

o =

0.94

andE

b

= 0.8.

E

D

[13.1(0.94) + 5.6](0.8)(0.163)

=

2.3.

That is, even for this case of a fairly low oil/steam ratio,

the oil-heating value equal to 2.3 times the injected heat

is

displaced from the steam zone.

JPT

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