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Predicting Results of Sandstone Acidizing

J. R. Gatewood, Halliburton Serviees

B. E. Hall, Halliburton Services

L. D. Roberts, HalliburtonServices

R. M. Lasater, SPE-AIME,HalliburtonServices

Introduction

Treatment of sandstone formations by mixed hydro-

fluoric-hydrochloric acids has been used as a means

of removing damage caused by the presence of clays.

The removal of such damage results from the dissolu-

tion of clay by reaction with the hydrofluoric acid:

36 HF + Al,Si,O,,(OH), + 4H,SiF, + 12 H,O

+ 2HAIF,.

The acid will also react with sand and other siliceous

minerals:

6 HF + SiO, ~ H,SiF,, t 2 H,O.

These reactions, though they appear simple, are

itd y very cemp ex. Further reactions may take place

that produce insoluble reaction products. It is for this

reason that excess hydrochloric acid should be main-

tained in the mixture and dilute hydrochloric acid

solutions are used as preflushes ahead of the mixed

acids. A discussion of these reactions and their effect

on productivity has been presented by Smith and

Hendrickson. An awareness of these possible prob-

lems allows us to approach such treatments with

proper design to circumvent undesirable results.

Another equally important aspect of successful acid

application is that of adequately describing the effect

of hydrofluoric acid reaction on depth of acid penetra-

tion. It is this aspect that ultimately determines the

extent of damage removal and subsequent produc-

tivity increase.

Relatively little has been done in the area of in-

vestigating the reaction rates of hydrofluoric acid, or

the mixed acids, on silica and silicates. It has been

t

generally stated that the reaction is faster on clays

than it is on sand, but without quantitative work the

desired calculations have not been possible.

It has long been assumed by some that these acid

systems could be injected into a sandstone formation

to dissolve clay at almost any depth from the wellbore,

and that the reaction on sand is so slow that little

reaction takes place.

It has been our purpose to investigate the reaction

rates of hydrofluoric-hydrochlonc acids on silica,

various clays and mixtures thereof, and then to deter-

mine mathematically the amounts of both sand and

clay removed from formations at various depths, as

a function of acid reaction. Also, theoretical increases

.

.. ..

,.,,]fi,,f t~~ i-m the ha+q of

in pro(lucuvny have bseii La~u,a.tiu, - ._ -_L..

the penetration determinations, for the cases of un-

damaged and mud-damaged formations and for for-

mations naturally damaged by clay.

Reaction Rate Studies

Experimental

The determination of reactant concentrations has

been a problem in following the HF-silica reaction

and probably accounts for the meager data available

in the literature. Development of a specific ion elec-

trode for fluoride ions by the Orion Corp. has enabled

us to obtain much information accurately and rapidly.

The analytical procedure and equipment have been

previously described by Gatewood.

Data

Rate studies of the reaction of hydrofluoric acid on

This work proposes to investigate the reaction rates of hydrofluoric-?~ydroch oric wids

1

on silica and various clays and mixtures thereof, and then mathematically to determine

the amounts of both sand and clay removed from formations at various depths. Also

calculated are theoretical increases in the productivity of undamaged and mud-damaged

formations and of formations naturally damaged by clay.

X-P-I--

693

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TABLE 6-REACTION OF HF - HCI ON SILICA AT 150F

ABLE lDATA

FOR SAMPLES STUDIED

Sample

OklahomaNo. 1 sand

Silica Flour

Kaolinite

Albite

Microcline

Oligoclase

Formula

Sioz

Sioz

A14(OH)4 Sia

OZO

At4(OH)aSi4010

ixaAisi3 88

I(AIsi308

90

penxnt NaAlS$ 08

10 percentC6AIZS1206

SurfaceArea

183 aqcm/g

3,770 w cm/g

750 actm/g

29 aqm/g

?.0emmlu

f-. q ,,,,~

29 aqm/g

29 aqm/g

TABLE2REACTION OF 3 PERCENT HF -12 PERCENT

HCI ON CLAYS AND FELDSPARS

Time

Residual HF (percent)

(rnrni

Montmoril -

IOnite

Kaolinite

Albite

Oligocl.ase

Microcline

.

0

3.0

3.0

G 3.0

3.0

5

0.90 0.31

0.86 0.85

0.88

10

0.88 0.30

0.84

0.86

0.85

15 0.85

0.25

0.84

0.86

0.85

20

0.85

0.20

0.84

0.86

0.86

25 0.85

0.26

0.84

0.86

0.86

30

0.85

0.22

0.84

0.86

0.86

TABLE 3-REACTION OF 6 PERCENT HF -9 PERCENT

Hcl ON CLAYSAND Fmixmm

Time

(min-

utes)

0

5

10

15

20

25

30

Residual HF (parcent)

6.0

1.24

1.20

1.18

1.18

1.18

1.20

Kaolinite

Albite

6.0 G

0.24

1.15

0.23 1.14

0.22 1.14

0.22

1.14

0.22 1.16

0.21 1.14

Oligoclase

6.0

1.23

1.23

1.16

1.16

1.16

1.19

Microcline

6.0

0.99

1.02

0.87

0.92

0.96

0.90

TABLE

4-REACTION OF 9 PERCENT

HF -6 PERCENT

HCI ON CLAYSAND FELDSPARS

Time

(min.

Utes)

a

5

10

15

20

25

30

Residual HF (rmment)

9.0

1.15

1s3

1.13

1.13

0.99

~aa:~~~ee

9.0

0.17

0.15

0.15

0.15

0.15

0.15

~ ~ : :

-iF

1.47

L47

1.48

1.51

1.49

1.48

Illiundsm

. . .. . . . . . .

9.0

1.53

1.49

1.51

L47

1.48

1.51

Microcline

9.0

1.35

1.27

1.35

1.24

1.27

1.22

TABLE 5-REACTION OF HF - HCI ON SILICA AT 75F

Residual HF (percent)

-.1- B1. I ~; ~=

0 12. b 1

Silica

Crkl;a:;. 1 y;

me U.l;a:;. .

Flour

Sand

Flour

.

0 min.

3.0 3.0 6.0 G.o

9.0 9.0

30

min.

2.91

1.92 5.46

2.46 8.55

4.93

1 hr. 2.88

1.59 5.21

1.50 8.28 1.98

2 hr. 2.76 L48 4.55

1.26

7.30 1.80

3 hr. 2.43

4 hr. 2.35 L24 4.26 1.16 5.86 1.(%

8 hr. L77 1.08

2.94

1.08

3.58 1.03

694

Residual HF (percent)

Okl:a::. 1

;/:: Okl:a:: 1

Silica

Time

Okl a .1

Flour

O min. 3.0 3.0 6.0 6.0 9.o

5 min.

15 min.

30 min.

1 hr.

l~z hr.

2 hr.

4 hr.

8 hr.

1.80

5.94

3.36

2.51 1.42

5.47

2.70

8.46

2.47 L24

1

77

5.18 *.J J

~.~~

2.34 1.12 4.44

1.26 6.93

2.22 1.06 6.19

2.10 1.04

3.36

1.17 5.22

1.71 1.02 2.76

3.24

1.27 0.96

1.41

silica and selected silicates were conducted

mixed solutions of hydrofluoric-hydrochloric

The solutions

were

reacted on samples of Oklahoma

No, 1 sand, silica flour, kaolinite, montmorillotite,

and the three feldspars: albite, microcline and oligo-

clase. Table 1 shows pertinent information concern-

ing the samples used in these studies. Data for the

reaction of mixed 3 to 12 percent, 6 to 9 percent and

9 to 6 percent HF-HC1 on clay and feldspar samples

at 75 F are shown in Tables 2,3 and 4, respectively.

Tables 5 and 6 show the reaction data for 3 to 12

percent, 6 to 9 percent and 9 to 6 percent HF-HC1

systems reacting on Oklahoma No. 1 sand and siIica

flour at 750 and 15UF, respectively. Figs. ]

thiO@h

----- -

3 illustrate these data in graphical form.

Silica

Flour

K

4.88

3.80

~=fj5

1.62

1.41

1.30

1.23

0.95

using

acid.

Discussion

These data reveal that the reaction of mixed HF-HC1

on clays and feldspars is complete within 5 minutes

at 75F. The surface-area: volume ratio used in these

tests was 108 sq cm/cu cm for montmorillonite. If

this is translated to a sandstone formation containing

10 Percent clay, the surface-areavolume ratio is aP-

pro~mately 10 sq cm/cu cm. Thus, the reaction

r&e

would be increased bv a factor of 10, and spending

would then take plac; in a maximum of 30 seconds

(no data were taken at corresponding times less than

this). The conclusion is drawn that the reaction of

HF on clays and feldspars is virtually instantaneous

7

1

. .

6

/ 5t-

~.... -

-

54

-

..*. _L

--- -

- -

OKLA. NO.I SANO

g

SILICA FLcuR

z

:

$2

TIME [HCURS)

Fig.

lReaction of 3 percent HF-12 percent HCI on

Oklahoma No. 1 sand and silica flour.

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at such surface-area: volume ratios, even at low tem-

peratures. As a result of the extremely fast reaction

at 75 F, tests at higher temperatures were not con-

ducted with clay and feldspar.

Reaction rate constants were calculated for silica

from the foregoing data, assuming first-order kinetics

as determined by Blumberg.4 The average reaction

rate constant at 75 F, when corrected for surface-

area:volume ratio of the test conditions was

K,,. = 3.89 X 10- ~ .

When units are converted for comparison, we see

that

K,,. = 3.89 X 10-

= 6.6 x 10-

This latter figure agrees

rate constant

Z& = 5.4

x

10-

as reported by Blumberg

g SiO,

sec-sq cm HF molality

very well with the reaction

P SiO.

-..

sec-sq cm HF molality

and &rivrinOU.5

The reacfion rate constant determined in the

present work can now be modified for the surface-

area: volume ratio of the formation by utilization of

the Kozeny -Carman Eq. 6.

s=

d

+

- %

(1)

.

,.. L

I : I Jt i r

r.m

1~ ~ =

9.869

wnere ~ E. me permGdulllLy .U .q . .. . ,.

x 10- sq cm). Therefore the experimental rate con-

stant,

K,,

corrected to the surface-area: volume ratio

of the formation is:

K, = 3.89 X 10-

d

4

4.934 X 10-lk(md)

. . . . . . . . . . .

(2)

It is now possible to extrapolate the corrected reac-

0:--+- .~ -~ -Q-

+44

TIME (HOURS)

,Fig. 2Reaction of 6 percent HF-9 percent HCI on

Oklahoma No. 1 sand and silica flour.

tion rate constant to formation temperature using the

Arrhenius equation.

(3)

where the value of E, the activation energy, is taken

as 5.21 Kcal/mol.

Method for Determining Amount of Sand

and Clay Dissolved by I-IFas a Function

of Depth of Penetration

Sandstone with No Clay

By using the reaction rate constants for the reaction

of HF-HC1 mixtures on sand, the following deriva-

tion is used to determine the amount of formation

dissolved as a function of depth of penetration.

Consider acid being pumped into a formation ma-

trix. The amount of sandstone dissolved at a specific

depth of penetration will depend on two conditions.

1. The volume of acid passing a specific increment

and its change in concentration while flowing across

that increment.

~ ~-

=mqyt of ~c~d

remaining static ill that

. Ll,ti Lb... .-. -

increment at the conclusion of pumping and its change

in concentration.

The volume of acid that passes across the nth incre-

ment (vn) is given by

V. = 7.481 ~ mh(r. r.) , . . . (4)

Vn=vtvn+l. . . . . . . . (5)

Therefore, the volume of acid that occupies the nth

element is

iivn=

Vm+]

Yi

n...=....

(6)

The change in concentration of HF being pumped

through a specific increment of formation is depend-

ent upon the amount of time the acid is in contact

with the formation and the initial concentration of the

acid. The amount of time the acid is in contact with

the nth increment (At) can be related to the distance

to the nth increment and the acid pump rate by the

following equations.

Fig. 3--Reaction of 9 percent HF-6 percent HCI on

Oklahoma No. 1 sand and silica flour.

6 35

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t. =

~ h(r~ r02)/i , . . . . . (7)

tn+l

= + IT h[(r. + Ar)

r~2]/i , . . (8)

At =

fnfn+l . . . . . . . .

(9)

The change in concentration for acid being pumped

through the nth increment (ACJ is given by the fol-

lowing relation:

c

n+l

ce-kAt, . . . . . . . . (10)

Acn =

Cnen+, . . . . . . . 11)

The static HF concentration in the nth increment is:

,.

(12)

Therefore, the amount of sandstone dissolved by

the HF in the nth increment (AWfi)is

Awl =

0.083527 V*

AC. , . . . .

(13)

Aw, =

0.624963 C.

A~n , . . . . (14)

Awn =

Aw~+Aw, , . . . . . .

(15)

where A

Wf is the

weight of sandstone dissolved by

flowing acid (lb) and

AW, is the

weight of sandstone

dissolved by static acid (lb).

In this method it is assumed that the surface-area:

volume ratio remains constant, which implies that the

rate of reaction on sandstone is always the same from

the first pore volume to the last pore volume, and it

is also assumed that there is always formation present

for the HF to react on. This method further assumes

that the Kozeny

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DR =

]o/jdOr k./&, . . . . . . (29)

.,

. ..

.- ....~.mmm=d

frwmati~~

where JOn proaucnon from all U~u~,,,~6-- . . . . . . . . .

i.

--A.-:- m

and Jd is

prcmlddl

.ra ------- ~

dam a~etj

formation. Pro-

duction resulting from complete removal of damage

is equal to l..

Jo =

(DR)(td) . . . . . , . . (30

The theoretical production increase is therefore equal

to the damage ratio.

PI={./~~=DR . . . . . . . (~i)

If acid is used to remove clay damage, an additional

production increase is usually obtained because of

the improvement in formation permeability resulting

from the reaction of HF on that part of the formation

not contributing to damage (sand, feldspars, etc.).

Damaged formations resulting from the presence

of clays can be classified into two basic types, depend-

ing upon the factors contributing to the cause of the

damage. We have classified these as mud-damaged

formations and naturally damaged formations.

Mud-Damaged Formations

Mud damage is most commoniy the resuit of d~fiiifig

mu

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I

3

///

f Kd

K.

/i

~kd

Re

DAMAGED

ZONE

Fig. S-Naturally damaged wellbore.

8.0

T - ~fi~ DAMAGED F~MATION

DAMAGE RATIO = 6.0

~

r 6.0

%

< WL1.ME OF 3 /oHF =200 GALLON / FOOT

g

5.0

g

~ 4.0

c

g> o

a

0

E 2.o-

1

I

I

10

Is

20

25

OEPTH OF HF ACIO PENETRATION IIN

Fig. 6-Effect of depth of penetration of 3 percent HF

.4 -- -- .-I. ...*.... ;f...a=ea

~CiU WI

pioUUb LIUIl 11,-, =-s.,.

15 -

r

------~

I I

OR 2.0

1

f

I [

I

1

,L-

1 I I

1

10

30

m

5(SI

I000

VOLUME OF 3% HF (GALLONS/ FOOT OF FORMATION

Fig. 7M~d-damaged formation, 2 percent clay,

3 percent i-i F-i2 pereent HCX.

38

36~

I

~

se~ -- --

c 32(

: 30+

28

$26

~ 24,

$22

E 20

a

: 1,s

u

14

12

I9,0

34

100

VOLUME OF 3% HF (GALLONS/ FCUF OF FORMATION

Fig. 8-Naturally damaged formation, 2 percent clay,

3 percent HF-12 percent HCI.

.,,.

The permeability of the damaged zone can be de-

termined by solving Eq. 33 for k?.

kd =

b rdr.

(41)

l/~a in r,/ro I/k. in re/rd . .

Since

the damage was assumed to have resulted

from the swelling or migration of natural formation

clays and no new clay was introduced into the forma-

tion, the depth of penetration of live acid will be the

same as that in an undamaged formation. Also, all the

damage caused by the clay will be removed for the

entire depth of penetration of live acid because of

the assumed instantaneous reaction of HF on clay.

Therefore, the same amount of sandstone and clay

will be dissolved by equal volumes and concentrations

of acid in both undamaged and naturally damaged

formations, and the improvement of virgin perme-

ability resulting from acidiziig will be the same for

undamaged and naturally damaged formations. The

production increase ratio for stimulation of a naturally

damaged formation can now be expressed as

J/Jo = in rdr~ +

{

& i~o [(~ rn/ro) l ki

(ln rd/rn) 1/kcl]

}

+ (hI r./rd) l/ko , . . . .

(42)

where ki is calculated in the same manner as for un-

damaged formations.

~~ .A - Tk.a.dballw ~dssrslinrs

lmlect

d 1 U=um=Lmw-~J - -.-= -e

HF-HC1Mmtures

The effect of depth of penetration of live acid on the

production increase obtained for undamaged, mud-

damaged and naturally damaged formations is shown

in Fig. 6. It is apparent from these data that the treat-

ment of an undamaged sandstone formation with HF

is not highly beneficial. HF is, however, effective for

treatment of damaged formations.

When removing clay damage with HF, the most

efficient treatment should be obtained by the smallest

volume of acid that will entirely penetrate the dam-

n.A 7nnP

u~u .-.

h Lhe case of mud-damaged formations

(1 in. depth), t.hk volume is about 25 gal of acid per

foot of zone to be treated @lg. 7); however, if addi-

,.

I... ,.- --a heeallce Of rn-u~ fi trates

uorid damage llds w-d. l.-

...- . . . .

contacting natural clays, a larger volume of acid may

be required. For naturally damaged formations, where

the depth of damage is assumed to be 3 ft, an ex-

.-

tremely large volume of acid will be required to pene-

trate the damaged zone (Fig, 8).

From Fig. 9 we can determine the effect of clay

concentration on the penetration depth of live acid.

As clay concentration is increased, the depth of pene-

tration of live acid is significantly decreased. Conse-

quently, for naturaiiy damaged formations or fmma-

tions with damage resulting from mud filtrate, a high

concentration of clay will usually prevent the acid

from completely penetrating the damaged zone. Those

..

. - ...zAI-. _ h:-h~~+ eln., rnnrpntratinn d]

formanons

WIUI t.hG LU511V=C .-J -w..-+______

probably have the most severe natural damage, and

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in these formations the distance that live acid can be

pumped into the wellbore will be the shortest.

Since clay is the mineral that causes most of the

damage in sandstone formations, the most efficient

treaf@ system would be one in which the reaction

is only with clays. This system can be approached by

retarding the rate of reaction of HF on sandstone,

thereby allowing more of the acid to be used for clay

removal. Fig. 10 shows the effect of retarding 3 per-

cent HF-12 percent HCI for the stimulation of a

naturally damaged formation containing 2 percent

clay and having a damage ratio of 6. A treatment of

1,000 gal of 3 percent HF-12 percent HC1 per ft of

zone will be improved 234 percent by retarding the

rate of reaction tenfold. Consequently, while the un-

retarded acid will give a theoretical production in-

crease of 3.2, retarding the acid will improve the

theoretical production increase to 7.5. This additional

theoretical production increase is accomplished with-

out any increase in acid volume.

Conclusions

From calculations made with the derivations pre-

sented in this paper, the following conclusions can

be drawn.

~. Production increases are most significant for

interstitial acidizing of damaged formations. Produc-

tion increases resuiting from EIF treatnwnt of i,iiidain-

aged formations would not in most cases be significant

enough to justify the cost of the stimulation treatment.

2. In formations with drilling-mud damage result-

ing from clay-particle invasion, volumes of acid suffi-

cient to remove only the clay contained within a l-in.

radius of the wellbore should yield the most economi-

cal production increases. This applies only if no

natural damage has occurred as a result of mud

filtrates contacting water-sensitive clays.

3. When treating formations with natural clay

damage, the production increase realized is directly

dependent upon the distance which live HF can be

pumped into the formation, The penetration of this

live HF is dependent upon the foiiowhig factors:

(a) clay concentration, (b) formation temperature,

I

I I

I I

I 1

1 I

I I

I

I

i

I

I

I

I

I

I I

I I

1

L-

0024661012 1416 820

CLAY CONCENTRATION (WT. PERCENTI

Fig. 9-Penetration radius of live acid

vs clay concentration.

(c) inhial HF concentration, (d) rate ot HF reaction,

and (e) pump rate.

4. As the clay concentration is increased, the

penetration radius of live acid is decreased.

5. As the formation temperature is increased the

penetration radius of tinspect acid is decreased.

6. Greater depths of penetration will be obtained

by increasing the initial HF concentration.

7. Retarding the rate of reaction of HF on silicates

will facilitate greater penetration of live acid into the

formation. With greater depths of penetration, a

higher production increase for formations with natural

clay damage will be achieved. Undamaged forma-

tions or formations with damage resulting from mud

invasion will not benefit from acidizing with retarded

HF as much as will a naturally damaged formation.

8. As the depth of damage increases, the need for

a retarded acid system becomes more desirable.

9. Increasing the pump rate will slightly increase

the penetration radius of live acid.

Nomenclature

C =

initial HF concentration (mol/liter)

AC. = amount of acid used to dissolve clay

under flowing condhions in the nth

increment

ACno= amount of acid used to dissoive sand

n _.-.: --- -

-~+: -c ;ri the .q~h

under m w IIIg

Volld Llch= -. ....

increment (formation initially con-

tained clay)

C., = concentration of HF acid in contact with

sand under static conditions in the

nth increment (formation initially con-

tained clay)

AC. = amount of acid used to dissolve sand

under flowing conditions in the nth

increment (formation contained no

clay)

C* = concentration of HF acid in contact with

sand under static conditions in the

nth increment (formation contained

no clay)

7.0

g

~ 60

r

~ 5.0

g

f

z

4.

0

0

~

g ~,

o

E ~- ;MP RATE =O. ./

---- ~

4.

FORMATION TEMP : 150- F

DAMAGE RATIO = 60

I

II

I

I

~

01.0

5.0

10

RETARDATION FOLD

Fig. 10-Effect of retarding 3 percent HF-12 percent HCI

acid for treatmant of naturally damaged formations.

699

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amount of acid used to remove damage

due to clay particle invasion

damage ratio

activation energy, Kcal/mol

height of formation, ft

pump rate, bbl/minute

improved production

]d =

damaged production

.TO

k

=

kd =

Ed =

b=

,.~

k. =

K, =

Ki =

p~ =

rd =

r~ =

rn =

rO=

R=

Ar =

t. =

T, =

At =

v. =

V$=

v., =

Avn =

undamaged production

permeability, md

permeability of damaged zone, md

permeability of damaged formation, md

~em.eabfi~ty Ofnth increment after acid-

iziig, md

undamaged permeability, md

rate constant at temperature Tf

rate constant at temperature T]

....fi~,le+;fim

nrrfqce ratin

pluuutiu.. . ..... -.4.-...

depth from formation face to end of

damaged zone

drainage radius of well

depth from formation face to nth incre-

ment

wellbore radius

gas constant, Kcal/mol-K

size of increments

time to reach rzthincrement

formation temperature, K

amount of time acid is in contact with

the Mb increment, minutes

volume of acid that passes through nth

increment, gai

total volume of acid, gal

volume of clay and sand removed in nth

increment, cu ft

pore volume of nth increment, gal

Awf = weight of sand dissolved by flowing acid,

lb

A W, = weight of sand dissolved by static acid,

lb

A Wn = total weight of sand dissolved, lb

Awf2 = weight of sand dksolved by flowing acid

information containing clay, lb

A W,z = weight of sand dissolved by static acid in

formation containing clay, lb

A

W.z = total

weight of sand dissolved by acid in

formation containing clay for nth in-

~~~m-@ lb

Awn =

total weight of clay removed in nth incre-

ment, lb

Wm = weight of drilling mud that invades for-

mation, lb

@= weight percent of clay in the formation

p = density of formation, gin/cc

4 = porosity, fraction

~d = damaged porosity, fraction

~~ =

po::ctyo:nth

increment after treatment,

~. = undamaged porosity, fraction

= porosity occupied by mud damage, frac-

tion

Acknowledgments

We wish to thank the management of Halliburton

Services for permission to publish this paper and also

those of this organization who made helpful sugges-

tions and comments.

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PT

Original manuscript received in Society of petroleum Engineers

office July 7, 1969. Paper (SPE 2622) waa praaented at SPE 44th

Annual Fall Meeting, held in Denver, COIO.. SePt. Zs-oct. 1? 1969.

0 Copyright 1970 American Institute of Mining, Metallurgical, and

Petroleum Engineers, Inc.