SPE-4030-PA Consideration on gravel packing

7/25/2019 SPE-4030-PA Consideration on gravel packing

1/8

onsiderations

in

Gravel

Pack

esign

R. J. Saucier,

SPE-AIME, Shell Oil Co.

Introduction

Gravel packs have been used extensively along the

Louisiana Gulf Coast in an effort to reduce or avoid

sand production from unconsolidated formations.

Statistics show,l however, that through 1966, gravel

packs were only about 70 percent successful.

The early literature on gravel pack design

is

based

primarily on the work of Coberly and Wagner2 and

of Hill.

3

Coberly's work in essence suggested that a

gravel pack having granular particles of diameter 10

times the formation grain size at the IO-percent

cqarse point on a cumulative sieve analysis would

provide effective sand control. Numerous failures of

this criterion were noted, especially in the Gulf Coast

sands. Hill suggested that the ratio of lObe reduced

to 8. Failures were still noted in many applications.

t least one writer suggested concentrating on the

fines end of a cumulative sieve analysis. Winter

bum

4

states that actual experience in the field has

shown that sand entry can virtually be eliminated by

the use of gravel which is approximately 10 times

the grain size of the 10 percentile of the finest sand

to be screened. Clearly a finer gravel will be more

effective in screening formation particles. However,

it must be evaluated in the light of how the finer

gravel affects permeability and reduces production.

Depending upon the writer, recommended ratios

of gravel to the IO-percent-coarse point may range

from 4 to 13. Other suggestions appear in the litera-

Some liberty is taken with Mantooth s statistics; nevertheless,

the

value

is

indicative of the problem.

ture; see, for example, the paper by Tausch and

Corl

ey 5

for a summary of earlier gravel pack in

vestigations.

In more recent literature, Sparlin6 has discussed

gravel placement rate and fluid viscosity in his recom

mendations for a slurry pack. Schwartz

7

recom

mends a size ratio of 6 at the 10-percent-coarse point

and at the 40-percent point for uniform and non

uniform sands, respectively. Williams

8

uses Schwartz's

grain-size ratio of 6 and finer and discusses well pro

ductivityas a function of perforation size and density.

In addition to the apparent disagreement on the

geometrical basis for gravel pack design, a more

subtle lack seems to exist. Few writers have explored

the influence of flow parameters on the functioning

of gravel packs. Sage and Lac

y

9

appear to be the first

authors who attempt to take hydrodynamic (and

other) factors into consideration. We supposed that

under certain conditions, hydrodynamic factors could

possibly outweigh geometric factors in the function

ing of gravel packs. This investigation, begun in 1967,

proceeds from that basic premise.

Laboratory

Test and Evaluation Program

A large number of variables are involved both di

rectly and indirectly in gravel pack behavior. Five

were considered to be most significant and funda

mental to the stUdy Therefore, the study was de

signed to explore the following functional depend

ence:

Tests with physical models have shown that sand production and pack impairment are

minimized when the ratio

of

pack median grain size to formation median grain size is

between 5 and 6. n a study of the inertia and viscosity effects of flow in gravel packed

wells it was found that increasing the size and the density

of

the perforations should

increase productivity

FEBRUARY, 1974 205


2/8

DAMPER

Fig. l Luci te linear flow model and flow schematic.

T

'

,

7 '

CASING

206

INTENSIFIER

ELEVATION

' ' '--+-_+,-F OR.:..::M TI ON

PLAN

Fig. 2-Gravel pack model.

1)

where Y may be sand concentration, C or pack pres

sure drop,

D.p

and

t

= median formation grain size

d

p

= median pack grain size

w

= mass flow rate of fluid

.

w

=

time rate of change of w

P

g

= gas/liquid ratio

The median grain size of the formation, was

selected because in practice this value may be more

readily available than other extreme values e.g., 10-

percent-coarse fraction). The latter are subject to

sand sorting and hence not so readily estimated.

Two physical models were employed to evaluate

the influence of the selected variables on gravel pack

operation. A linear flow model of Lucite was de

signed to simulate a severe limiting case of sand

production through a packed perforated casing. This

model and flow schematic are shown in Fig.

1.

A

full-scale gravel pack model representing a section

of 7-in. casing, a packed perforation, and a forma

tion segment was used to verify the results from the

linear flow model. This model is shown in Fig. 2.

Fluids used in the tests were I-micron filtered de

ionized water and CO

2

to simulate gas evolution from

the liquid. The gravel was from commercial stocks

sieved to size and the formation sands were taken

from recent Miocene sands of the Brazos River. The

river sands were washed clean of clay particles as

well as particles 10 microns) and blended in appro

priate proportions to reflect typical formation-grain

size distributions.

The models were packed mechanically in small

I

85 9

Fig. 3-Concentration vs time-l inear model.

JOURNAL OF PETROLEUM TECHNOLOGY


3/8

increments, and the cells were tamped and tapped

until the material reached an apparent minimum vol

ume. During flow through the models, sand was col

lected from the gravel effluent over 5- to 10-minute

intervals, samples were weighed, and average sand

concentrations (C) were computed by weight. Flow

rates were 16 cc/sec

(r- 8.7

B/D/perforation or 26

cc/sec (r- 13.5 B/D/perforation).

Typical examples of test results are shown in Fig.

3 for the linear flow model with 3 in. of pack length.

Both a sharp increase and a sharp decrease in

flow

rate

(w)

caused a temporary increase in sand pro

duction.

I f

the rate was held uniform after the change,

the concentration of outflowing sand decreased con

tinuously.

Controlled surges in the flow were generated to

simulate artificial lift. Surge was on the order to 70

psi and noticeable increases in sand production were

observed; a tenfold increase for

F

p

= 6.7 and a

hundred-fold increase for

F

p

= 9.4.

Gas evolution from the flowing fluid had the most

significant effect on sand production. For F

p

=

6.7,

sand production increased about 60 times as a result

of gas evolution in the pack.

For F

p

= 9.4, gas evol

ution caused a 2,000-fold increase in sand produc

tion. I t was also noted that by reducing the fluid rate

and thus allowing the gas/liquid ratio

F9L

to become

very large, sand production decreased. I t should be

noted that virtually the same results were obtained

using consolidated packs and hence this behavior

was not the result of pack fluidization.

From the preceding, it appears that rate changes

affect pack behavior more significantly than. does the

magnitude of the

flow

rate. Generally,

flow

distur

bances caused by rate changes, surging, and gas evol

ution all have a pronounced effect on gravel pack

behavior and could be grouped as w the principal

distinctions among these three causes are the a lpli

tude and the frequency of the disturbances. Thus, it

appears that for a given flow condition, primary and

secondary sand bridges form that are stable for the

existing geometries and hydrodynamic forces. As fluid

forces are altered, instabilities occur, bridges break

down, and more sand

is

produced until, if possible,

new bridges form under new conditions of stability.

Further evidence of the effects of grain-size ratios

under such disturbed (but realistic) flow conditions

is given in Table 1. As illustrated, previously advo

cated grain-size ratios (for example, 10.7 and 7.4)

failed to constrain formation sands under disturbed

flow conditions.

The

final body of test results indicated that under

the tested conditions of operation, F

p

must be less

than 6 to minimize sand production under disturbed

flow conditions. Because the ratio of pack grain size

to pore size for hexagonal packing of spherical par

ticles is 6.46, this result suggests an absolute stoppage

criterion rather than a bridging criterion for gravel

pack design.

Other notable observations from the test data: (1)

'These results

were

similar to

the

results

of verification

tests

in the

fullscale model and hence were typical.

Eposand consolidation.

FEBRUARY, 1974

T BLE

I TYPICAL TEST RESULTS

Ratio

of

Pack

Median Grain Ratio

of

Pack

Size to

10%

Coarse

Formation Point to

Median

Formation

Grain Size,

10% Coarse

F

p1

Point

Results

of

Test

14.3 10.7

Failed

to

constrain

formation

14.3

7.4

Failed

to

constrain

formation

5.7

4.5

Retained formation

5.7

3.2

Retained

formation

pack length or thickness from 1 to 3 in.

had

a negli

gible effect on sand retention; (2) slight increases in

effective stress simulated by mechanical loading on

the sands during tests caused slight decreases in sand

production; (3) high starting rates caused higher initial

quantities of sand production and greater pack

impairment.

ravel Pack Impairment

Pack permeability was noted in all tests. TypicaJ

observations are shown as Fig. 4 for linear model

tests. The test with the median-grain-size ratio of 9.4

had an initial permeability of 600 darcies, and the

test with the median-grain-size ratio of 6.7 had an

initial permeability of 300 darcies. Fig. 4 shows, how

ever, that during the test the finer pack maintained

the highest permeability. Thus, if pack grain size is

too large, formation sand particles may enter the

pack and reduce the effective pack permeability k

e

to a value less than that of a finer gravel pack that

undergoes less impairment. Further evidence of this

is reflected in the perforation pressure drop data from

the wellbore model (Table 2). Perforation pressure

drops for the coarse pack

k

i

c-:::: 700 darcies) are about

10 times those for the fine pack (k

i

c-:::: 150 darcies).

The degree of pack impairment is illustrated

in

Fig. 5, which shows the ratio of effective to initial

pack permeability ke/k

i

vs median-grain-size ratio

F

1

,f).

The data points are average values from multi

ple tests of the linear model at the two rates (8.7 and

13.5 B/D/perforation). For

F

p

less than 6, there is

6 0 0 ~

3 r;j --

Fpf =6.7

250

~ 3 6

--------.

\

~ '

~

/

~

00

33

O ~ o ~ 0 3 3 Fpf =94

6 0

p o_o_o_o_ /0_0_ '0206 Fpf =94

I O O ~ 6

-/o-o__o_

~ \

r

27

--

0 0

___

-027 F

p

f=94

50

I I I I I I I I I I I j .1 .1 I I I

o 5 10 15 20 25 30 35

40

45

50

55 60 65 70 75 80

85

90

t, MINUTES

Fig.

4-Permeabil ity

vs

time-l inear

model.

207


4/8

-

o ~ L - ~ L - T - L - T - L - T - L - ~ , o - L ~ - L - , - L - , ~ - , ~ ~

'pI

Fig.

5-Pack impairment

vs median-grain-size ratio.

100 -- ,

140

130

120

110

.

>

100

:0

:x; 90

80

o

:i 70

o

60

u

o

o

50 -

4

20

10

;

,

___ a-f=O.Z

12

13

p

Fig. 6--Permeability ratio vs median-grain-size ratio.

J O ~ - - - - - - - - - - - - - - - - - - _ _ _ _ _

a 20-40 us MESH SAND

o

OTTAWA FUNT

o ..

GLASS SPHERES

x

TEST

POINTS fROM

PREV.

GRAVEl.

PACK TESTS

k

(dorcies)

Fig.

7-lnert ia

coefficient for sandstone.

208

virtually no impairment. As

F

pf

increases from 6 to

10.5, formation sand enters the pack, reducing the

effective pack permeability significantly.

For

ratios

greater than 10.5, the behavior would be of only aca

demic interest since, as already discussed, the forma

tions sands would not be adequately constrained

Relative pack impairment is not an adequate cri

terion by which to evaluate well performance. In

deed, as will be shown later, if pack grains are the

same size as formation grains, pack impairment will

be negligible, but so will well productivity.

The ratio of the effective pack permeability

to

the

formation permeability is related to production.

To

define this ratio, we consider Krumbein and Monk's'O

expression for permeability*

(2)

where C

is

a function of the particle shape, packing,

and skewedness. Assuming that C for the pack and

formation may be taken as a constant average value

over a range of analysis, then the desired ratio is

a

= ke/k

f

= ~ ; r e

l

(a1>f-

a

fp) Z:), . (3)

where the function

ke/k

i

may be obtained from

Fig.

5_

Using

lI >f

=

0.7 and 0.2, and

lI >p

=

0.2 in Eq. 3

results in Fig. 6. To maintain the highest pack-to

formation permeability ratio and

to

minimize sand

production, the median-grain-size ratio, F

pf

,

should

be between 5 and 6.

Well Productivity

The

nature of the flow through gravel packed per

foration tunnels (casing and cement thickness) is of

primary importance in the performance of gravel

packed wells. The pressure drop through gravel

packed perforations may often be considerably

greater than that predicted by Darcy's law.

The limit of applicability of Darcy's law is for

Reynolds number

(N

Re

= ud

p

/ f-t

less than

or

equal

to 10.** For N

Re

>

10, inertia effects

as

well as vis

cous effects of

flow

must be accounted for.

For

one

dimensional

flow,

Greenberg

et

l

l

suggest the fol

lowing relationship between pressure gradient and

volumetric

flow

rate:

- dp/dx =

Sf-t q/

A)

+ 3p q/A)

.

4)

(viscous) (inertia)

On integrating Eq. 4, equating the first term with

Darcy's law, and using convenient units, we obtain

for one-dimensional flow through a perforation,

t lPpf

=

0.888 L: + 9.1 X

1O-

,3

/1Lp( )"

(5)

Values of the inertia coefficient,

/1,

extrapolated

from data by Tek

et

l

l3

are shown in Fig. 7, along

This

relationship is oversimplified

but

is

nevertheless assumed

to

be valid.

Apparently. transit ion from laminar f low in porous

media

may

occur for NRE between 1

and

10 (see, for example, Ref. 11).

JOURNAL

OF

PETROLEUM TECHNOLOGY


5/8

with coefficients calculated from the previously dis

cussed test data. The multicycle extrapolation

is

suf

ficient cause for the lack of complete agreement.

Fig. 8 is a graphical display of Eq. 5 for typical

values of perforation size. The significant difference

between Darcy's law and actual perforation pressure

drop is evident. Fig. 8 also illustrates how great the

pressure drop can be across formation-filled perfora

tions; this emphasizes the necessity of placing gravel

in the perforations.

From

the foregoing, the productivity from gravel

packed wells compared with that from open holes

may now be calculated. For unconsolidated sands,

the perforation depth into the formation is assumed

to be negligibly small. I f we further assume that the

pressure drops in a gravel packed well are due only

to the packed perforations ( ~ P p f ) and the formation

( ~ P f m ) then the productivity ratio is

l

- / -

~ P f m ~ P f m

1 0 -

fac tua l l open

hole

-

A + Ap

=

~

UP m U pf up

6)

where

~ P p f

is from Eq. 5 and

_

q,u

In re/re)

Pfm - 7.08 k

f

h

Fig. 9 shows 1 1 vs

p

for typical production in

terval data and various perforation sizes and densi

ties.

I t

is evident that increases in perforation size or

density should result in substantial increases in pro

ductivity. From Fig. 9 for the conditions assumed

we

see that for a drawdown of 500 psi and four -in.

diameter perforations per foot only 46 percent of

open-hole productivity is available. Increasing the

perforation size to lh-in. diameter provides 63 per

cent of open-hole well productivity, and increasing

it

to -in. diameter provides 86 percent. Assuming no

casing or cement damage would result, 95 percent of

open-hole productivity could be obtained with eight

-in.-diameter perforations per foot.

A previous evaluation by Muskat

14

has indicated

that the flow resistance through perforated casing is

greater than the flow resistance of an open-hole com

pletion. Thus, if in addition to

~ P p f

and ~ P f m we

assume the perforated casing resistance of Muskat,

then Fig. 10 may be generated.

I t

must

be

pointed

out that Muskat's relation for perforated casing is a

function of the perforation radius, whereas our analy

sis includes radius to the second power (area) hence

it is not completely consistent to combine the two.

However, it illustrates possibly the relative influence

of gravel packs on well productivity, assuming there

is some reduction due to perforated casing.

In

the preceding examples, typical values were

used. I t should be pointed out that for increasing

formation permeability (i.e., permeability greater than

the 0.5 darcies used) the curves of 1

o

indicate a

lower percentage of open-hole productivity available.

Nevertheless, this still may be overcome to a large

degree by increasing perforation size and density, and

From the

tests, pressure

drops through the

gravel

annulus

and

the

screen are

indeed

negligibly small.

The

effects

of

per

forated casing alone on well productivity is discussed in the

followi ng pa ragra

phs.

FEBRUARY,

1974

T BLE 2 PERFORATION PRESSURE DROP

Median-

Grain-

Perforation

Size

Flow Rate

Pressure

Ratio,

Drop,

Test

p

,

cc/sec

B/D/perforation

t.p

p

, (psi)

Fine

Pack 6 0

15.5

8.2

k

i

:::::;

150 darcies

27.0 14.0

15.6 8.2

Fine

Pack 6.0

15.5

8.2

(Repeat)

26.6

13.8

15.5 8.2

Intermediate Pack

8.5 14.8

7.7

k

i

:::::; 270 darcies

25. l3.

14.8

7.7

Coarse Pack

12.8 15.7

8.3

k, ; 700 darcies

21.6 11.2

15.5

8.2

900 --------------------

i

800i


6/8

10 ,

40


7/8

also were installed improperly (that is, they were cir

culated in place instead of being squeezed into the

interval).

Fig. 12 shows the probability of failure

vs

median

grain-size ratio based upon the uncorrected sidewall

cores and also after

an

empirically defined correction

was applied. No failures occurred for F

pf

less than 6,

with the probability of failure increasing with increas

ing

F

pf

These data support the laboratory findings

that the median-grain-size ratio should be less than 6

to prevent gravel pack failure.

t

has also been noted that the productivity indices

of more recent wells are greater than those of wells

completed with the older conventional techniques.

However, gravel pack productivity still needs to be

improved, and increased perforation size and density

as well as improved gravel placement techniques are

being used toward that end.

Conclusions

From the preceding, we conclude the following:

1

To

minimize sand prosuction, the ratio of pack

median grain size to formation median grain size

should

be

between 5 and 6 where there is severe

flow disturbance.

2 Bridging, though satisfactory for uniform un

disturbed flow, is unsatisfactory for severe (but realis

tic) flow conditions.

3. Pack permeability impairment is minimized and

hence production is maximized if the median-grain

size ratio is 6 under severe flow conditions and with

given perforations.

4. Rounded grains appear to be better than angu

lar grains for gravel packing.

5. Well productivity may be increased with in

creased perforation size or density.

6. Perforation tunnels must be tightly packed with

gravel to minimize impairment; therefore, squeeze

packing must be employed.

7. Before packing, perforation debris must be re

moved by backsurging or some equivalent method.

8.

t

is mandatory that completions be clean and

that packing fluids be compatible with the formation.

9. Crossover tools should be used in gravel place

ment.

Nomenclature

A =

cross-sectional area of a perforation

C = function of particle shape, packing and

skewed ness

C = concentrat ion of jets per foot

C

=

average sand concentration in gravel

pack effluent in time increment t1t

C

max

= maximum C value during test period

dp

f dx

= pressure gradient

d

= mean particle diameter (general)

d

f

= median formation grain size

d

p

=

median pack grain size

F

g

= gas-liquid ratio

F

pf

ratio f f

rnpd;afJ err;:,; ,,;71'

nf

Dack

to

median grain size of formation

h

= net pertoratlon helgat

FEBRUARY, 1974

J = productivity index

of

gravel pack in per

forated casing assuming flow resistance

due to packed perforations only

J

CSg

= productivity index in perforated casing

after Muskaf1

4

J

g

= productivity index of gravel pack in per

forated casing (J) plus added resistance

of perforated casing (JCSg)

J

o

= productivity index of open-hole interval

k = permeability (general)

k

=

effective total permeability of the gravel

k

f

=

permeability of formation

k

i

= initial unimpaired total permeability of

the gravel

L

=

length

NRe = Reynolds number

pi

= perforation

fi

= probability of failure

t1p

=

pressure drop

t1pcsg = pressure drop due to open perforations

in casing (after Muskat

14

)

t1Pfn = pressure drop in formation

t1Ppf

=

pressure drop through gravel packed

perforation

t1pwf

=

drawdown

q

=

volumetric flow rate

r

= casing radius

r

=

reservoir radius

u = average pore velocity

w

= mass

flow

rate of fluid

IV = time rate of change of mass flow rate of

fluid

Y

=

general response as sand concentration

or pack pressure drop

a

= permeability ratio

kef

k

f

f =

inertia coefficient

y = fluid specific gravity

S = constant assumed to be a function of the

medium matrix

f = fluid viscosity

p = fluid density

O rj>j = logarithmic standard deviation (sorting)

of granular material j

< > =

units used to measure sorting -

< > =

log2

diameter (in mm)

cknowledgment

I express my appreciation to Shell Oil Co.

and

Shell

Development Co. for granting permission to prepare

and publish this paper. I also acknowledge the sub

sequent work by R S Torrest

on

flow through gravel

packed perforations, which expanded this initial effort.

References

1 Mantooth, M. A.: Statistical Analysis of Recent Sand

Control Work,

API

Paper 926-13-G,

API

Committee

on Sand Control

(1968).

2

Coberly, C.

J.,

and Wagner, E. M.: Some Considera

tions in the Selection and Installation of Gravel Packs

for Oil Wells, Pet. Tech. (Aug. 1938) 1-20.

3

Hill,

K.

E.:

Factors

Affecting the Use

of

Gravel in

Oil Wells, Oil Weekly (May 26, 1941) 13-20.

4. Winterburn, Read: Contr ol of Unconsolidated Sands

in Wilmington Oil Field, Drill.

and

Prod. Prac.

API

(1947) 63-79.

211


8/8

5. Tausch, G., and Corley,

C :

Sand Exclusion in Oil

and

Gas

Wells,

Drill. and Prod. Prac.

API (1958)

66-82.

6. Sparlin,

Derry:

Fight Sand With Sand-A Realistic

Approach

to Gravel Packing, paper SPE 2649 pre

sented

at SPE-AIME

44th Annual

Fall

Meeting, Den

ver, Colo., Sept. 28-0ct. 1 1969.

7. Schwartz, D.

H.:

Successful Sand Control Design for

High Rate Oil

and Water

Wells,

1 Pet. Tech.

(Sept.

1968) 1193-1198.

8. Williams, B. B., Elliott, L. S., and Weaver, R. H.:

Productivity

of

Inside Casing

Gravel Pack

Comple

tions,

1 Pet. Tech.

(April 1972) 419-425.

9. Sage, B.,

and Lacy,

W.:

Effectiveness of Gravel

Screens,

Trans.

AIME (1942) 146, 89-106.

10. Krumbein, W., and Monk, G.: Permeability as a

Function of Size Parameters of Unconsolidated Sand,

Trans. AIME

(1943) 151, 153-160.

11. Hassinger, R. C : Transverse Dispersion in

Porous

Media,

PhD

thesis,

Tulane

U., New Orleans (1967) 22.

212

12. Greenberg, D., Cresap, R., and Malone, T.: Intrinsic

Permeability of Hydrological Porous Mediums: Varia

tion With Temperature, Water Resources Res. AGU

(1968) 4, No.4, 791-800.

13. Tek, M. R., Coats, K. H.,

and

Katz, D. L.:

The

Effect

of Turbulence on

Flow

of

Natural

Gas Through Porous

Reservoirs, 1

Pet. Tech.

(July 1962) 799-806;

Trans.

AIME,225.

14. Muskat, Morris:

Physical Principles of Oil Production

McGraw-Hill Book Co., Inc., New

York

(1949) 216-

219.

15. Maly,

G.

P.:

Improper

Formation

Sampling Leads

to

Improper Selection of Gravel Size,

1 Pet. Tech.

(Dec.

1971) 1403-1414.

PT

Paper

SPE 4030 was

presented at

SPEAIME 47th Annual

Fall

Meeting, held

in San Antonio, Tex., Oct. 811, 1972. Copyright

1974 American Institute of Mining, Metallurgical, and Petroleum

Engineers, Inc.

This paper

will

be printed in

ransactions

volume 257, which

will

cover 1974.

JOURNAL

OF

PETROLEUM TECHNOLOGY

SPE-4030-PA Consideration on gravel packing

Documents

Transcript of SPE-4030-PA Consideration on gravel packing