experimental investigation of hydraulic fracturing through perforations

8/13/2019 Experimental Investigation of Hydraulic Fracturing Through Perforations

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Experimental Investigation of HydraulicFracturing Through PerforationsAbbas Ali Daneshy, SPE-AIME, Halliburton Services

IntroductionThe majority of hydraulic fracturing treatments inthe oil and gas fields are performed through perfora-tions. These perforations ale usually created byshaped charges, by hydrojets, or occasionally bybullets. They generally penetrate through the casing,through the cement, and several inches into the for-mation. Each perforation has approximately a cylin-drical shape, with a diameter of about to 1/2 in.Most of the known theoretical and experimentalresearch on hydraulic fracturing has been performedin open holes. The reasons for this are that the open-hole situation is easier to handle, and more important,the studies on open holes provide insight into themore complicated problem of fracturing cased holes.This paper appears to be the first known serious ex-amination of hydraulic fracturing through perfora-tions. Because of a lack of knowledge about the stressconcentrations around the borehole and the perfora-tions, the studies reported here are mainly experi-mental and composed of observations of the types,orientations, and breakdown pressures of the inducedfractures. The theoretical examination of the problemis limited to the calculation of the stresses around thecasing and in the formation. However, the experi-mental results are quite interesting and shed new lighton the influence of perforations on the created hy-draulic fractures,Stress Distribution Around Cased BoreholesIt is generally accepted that hydraulic fractures arecreated whenever the maximum tensile stress induced

at the borehole wall exceeds the tensile strength ofthe formation. Thus the study of stress distributionaround the borehole becomes an integral part of theexamination of fracture initiation. Contrary to open-hole situations, it is very difficult to derive analyticalexpressions for the stress distribution around per-forated cased holes, mainly because of the compli-cated geometry. Thus, in examining the fractureinitiation in cased holes, the only two alternativesappear to be experimentation or numerical simula-tion. The results reported here are derived from anexperimental approach.The problem of stress distribution around a casedhole (without perforations) has been solved by Satinfor the generalized plane stress or plane strain condi-tions. Fig. 2 compares the stresses around open andcased holes. The symbcls Ul,, uZZ,and US3denote thethree in-situ principal stresses, and uO,, o,,, and u~eare used for the tangential, radial, and shear stresscomponents around the borehole (Fig. 1), The bore-hole is assumed to be parallel to u,,, The curves inFig. 2 show that the existence of the casing signifi-cantly alters the stresses induced by UI,, uZZ,and U33around the borehole. When one adds to this thechanges caused by the perforations and fluid leak-off,it becomes obvious why the breakdown pressure ofperforated cased holes should be considerably ditler-ent from that of open holes.Experimental ProcedureThe experiments reported here were all conducted

I In this study it was found that breakdown pressures of hydraulic fractures decrease asthe number of perforations increases. The existence of the casing and the perforationsseems to have little influence on the direction of the created fracture which isperpendicular to the least principal stress.OCTOBER, 1973 1201


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in blocks of hydrostone, 6 X 6 X 10 in. The bore-holes joined the centers of the two square faces ofthe sample and were thus 10 in. long. The casingswere made of steel and had an inner diameter of0.238 in. and an outer diameter of 0.312 in. Theouter faces of all the casings were knurled. Nocementing material was used between the casing andthe rock. Instead, the steel casing was placed at theproper position inside the mold and hydrostone wasthen poured around it to form the specimen, Thisarrangement was found to give a better bond betweenthe borehole and the casing as opposed to usingcement. The perforations were molded inside thesample.Before a sample was hydraulically fractured, it wasplaced inside a triaxial load cell and pressurized perpendicular to all its external faces. The magnitudes ofthese pressures were independent of each other butequal on parallel faces. More details of the testingprocedure have been discussed in a previous articleand willnot be elaborated here. The experiments weredivided into two groups. Those in the first groupwere conducted under identical external pressureconditions and were used to study the influence ofperforations on breakdown pressures and fractureorientations, The experiments in the second grouphad similar perforations and were used for examiningthe effectof various external pressures on the break-down pressure and the orientation of the inducedhydraulic fractures.Arrangement of the PerforationsThe experimental results presented here are based ontests conducted on five samples for each perforationarrangement involved. The breakdown pressures ob-tained are averages of each fivetests. The perforationshad a number of characteristics in common. They

I Formation (E,,v, ).z7?=TYK?z-Casing (EC,VC)m =---// / \ \ -I Fig. l-Cross-section of the borehole with casing,1202

were all in. in diameter and extended in. intothe hydrostone, They were cylindrical, and had novisiblefractures around them, They were located sym-metrically with respect to the midheight of the casing(Fig. 3).The number and location of these perforationswerechanged according to 16 different patterns, First,there were two general arrangements: perforations ona straight line or on a helix. There were 12 dtierentarrangements for line perforations and four for heli-cal, The line perforations were drilled either on oneline or on two diametrically opposite lines on thecasing. The numbers of line perforations used were10, 6, 5, 3, 2, and 1. The even numbers belong toperforations on two sides of the casing (two lines)(Fig, 3a), whereas the odd numbers indicate perfor-ations on only one line (Fig. 3b). This gave sixdifferent types of samples. These perforations werelocated in the expected fracture plane. Three moretypes of samples were prepared with one perforation,30, 60, and 90 away from the expected fractureorientation (Fig. 3b). Finally, the last three types ofsamples had six line perforations on both sides ofthe borehole (three on each line) that made 30, 60,and 90 angles with the expected fracture orientation.This resulted in 12 different arrangements for lineperforations.Four types of helical perforations were also testedduring this research. These were six perforations ononly one side of the hole (Fig. 3c), 12 perforationson both sides (six each), 12 on one side, and finally24 on both sides (12 each).Vertical FracturesTo study the effect of perforations on breakdownpressures, the three external pressures applied to eachsample were fixed at 1,000 psi vertically (parallel to

u

000000000

Casing 0.0.= 8.625 in. 1.D.=7.725 in,Ec= 31 x 10epsi VC=.33Formation E,= 3 x iOe psi Vr=.15

w,, = 1000 psi Uza=2000 psifig. 2Stress distribution around casedholes and open holes.JOURNAL OF PETROLEUM TECHNOLOGY


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,. .,

the borehole axis) and 500 and 800 psi horizontally(in a plane perpendicular to borehole axis). All per-forations were located in the expected fracture planes.The average breakdown pressures for these tests wereOpen holes = 2,440 psi10 perforations on two lines = 4,500 psi5 perforations on one line = 5,010 psi6 perforations on two lines = 4,710 psi3 perforations on one line = 5,330 psi2 perforations on two lines = 5,090 psi1 perforation on one line = 5,160 psi

These results show that the existence of the casinggreatly affectsthe breakdown pressures. Even the lar-gest number of perforations (10) had almost doublethe breakdown pressure of the open hole, Further-more, these results indicate that with line perforationsit is better to perforate both sides of the casing, Forexample, two perforations on both sides of the casinggave lower breakdown pressure than three on onlyone side. Also, six perforations on both sides hadlower breakdown pressures than five on one side.One important result of these tests is that apparentlyonce the number of perforations per given height ofthe sample falls below a certain number, the break-down pressure stays essentially unchanged. (Note theclose values for 3, 2, and 1 perforations,) We didnot run experiments with more than 10 perforations,since this was felt to be relatively higher than thatused in actual field operations, Such informationwould have academic value, however, since it wouldindicate at what upper limit the perforated hole willbehave like an open hole, In this category all hydrau-lic fractures started at the perlorations and werevertical, although some of them did not extendthrough all perforations.Next, we tried to examine the influence of the per-forations on the fracture orientation. Two groups oftests were run for this purpose, The angle, y, listedhere was measured between the plane of the expectedfracture and the plane of the perforations and bore-

Fig. 3--Three arrangements of the perforations on theborehole wall (borehole diameter exaggerated).

*II < @22q I Ulj

I~. a,..blj-~c b \1 312a

hole axis. The results of these tests were as follows.Angle, y Breakdown Pressure(degrees) (psi)

Sii Perforations 4,71030 4,61060 4,27090 5,360

One Perforation 5,16030 5,45060 5,15090 5,800

The breakdown pressures of the tests on samples withsix perforations are scattered, but show a definite in-crease for y = 90. The tests on one perforation aremore conclusive and indicate an increase in thebreakdown pressures with increasing y, As for theorientation of these fractures, they were all perpen-dicular to the direction of the least externally appliedpressure. The point of fracture initiation was dillicultto identify since the sample had to be cut through aperforation to see if the fracture extended throughit or nog and this was not an easy task. Neverthe-less, a number of samples were successfullycut. Theseshowed that for y = O,fractures started from at leastone perforation, For y = 300 and 60 some fracturesstarted at the perforations and some dld not. Fory = 90, fractures did not intersect the perforations.Therefore, in general, it can be stated that as theperforations further viate from the expected frac-ture plane the chances that fractures will initiate fromthem decreases,Fig, 4 shows a hydraulic fracture that has initiatedfrom the perforations. The sample was cut perpen-dicularly to the fracture and almost tangentially tothe borehole so that it could show both the fractureand the perforations, The darker area indicates howfar the fluid has penetrated into the formation. Ascan be seen, the hydraulic fracture has propagatedthrough all the perforations. This situation was foundto be the most prevalent in those samples in whichthe perforations were in the expected fracture plane.There were a few exceptions, however. Fig. 5 showsa case where the hydraulic fracture did not propagatefrom both perforations. The section shown in the pho-tograph is perpendicular to the borehole and tangentto a pair of perforations visible in the picture. Al-though the hydraulic fracture initiated from one per-foration, it completely ignored the opposite one. Fig.6 shows another cross-section perpendicular to theborehole axis. The specimen shown here had only oneperforation at y = 60 and the hydraulic fractureinhiated from the corner of it. But the other wing ofthe fracture does not pass directly through the perfor-ation, One of the most important findings of ourresearch was that hydraulic fractures do not alwaysinitiate from the perforations. Fig. 7 shows one suchcase. The sample had six perforations on two lines.

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,.

.. -. . . .. .

Fig, 4-Hydraulic fracture start ing lromthe perforations (y = O)..

Fig. 5- iydraulic fracture starting from one of theperforations and ignoring the other one, y = O(cross-section through a petioration andperpendicular to the borehole axis).

Fig. Hydraulic fracture starting from one perforation,y = 60 (cross-section through a perforation andperpendicular to the borehole axis),1204

(Only three of them can be seen in this picture. Theother three are on the other side of the borehole.)They made an angle of 90 with the fracture plane.The hydraulic fracture, as can be seen, has totallyignored the perforations. This photograph also showshow the casing was placed inside the boreholes,Another example of fractures not initiating from per-forations can be seen in Fig. 8. The sample shownhere has been cut at such an angle that the plane ofthe cut has intersected the perforations and the frac-ture, As one can see, the plane of the hydraulicfracture is totally unrelated to the perforations,In general, whether or not the fractures i~tiatedfrom the perforations. depended on the angle, y, be-tween the perforations and the expected fractureplane. For y = O,in a large majority of the cases theydid. For y = 30, the fractures of most of the samplesextended from perforations on both sides of the hole;for y = 60, they usually extended from only oneside and ignored the perforations on the other side(whenever there were any perforations there). Fory = 90, the fracture mostly ignored the perforations.The main disadvantage of the line perforation isthat either all of them lie in the plane of the fractureor they all do not, To overcome this prGb]em,fourtypes of samples were tested with perforations drilledin a helical configuration. This arrangement assuresthat at least two perforations are always very closeto the fracture plane. The average breakdown pres-sures of these tests were as follows:6 perforations on 1 helix (1 side) = 4,980 psi12perforations on 2 helixes (2 sides) = 4,240 psi12perforations on 1 helix (1 side) = 3,680 psi24 perforations on 2 helixes (2 sides) = 3,390 psi(The vertical distance between the perforations of thethird and fourth groups was 0.5 in.) These breakdownpressures indicate that if the fracture orientation isknown it is better to perforate the well along a linein the fracture plane than to perforate helically. Sixline @orations for y = Ohad a breakdown pressureof 4,710, whereas helical perforations yielded 4,980.Among the ditlerent helical arrangements, the onewith the largest number of perforations yielded lowerbreakdown pressures, The results of the two types oftests with 12 perforations show that when helical per-forations are drilled on only one side of the boreholeaxis, they yield lower breakdown pressures. Thisresult is diflerent, therefore, from the correspondingone for line perforations.Horizontal FracturesAll the samples tested for the study of horizontalfractures had 24 perforations on both sides of theborehole axis, The fracture types and the breakdownpressures were examined against open-hole tests. Theresults are listed in Table 1. Each entry representsonly one test.A study of the stress distribution around open holesshows that it is very likely that horizontal fracturesmay begin as vertical and then reorient themselves tobecome horizontal. Experiments, including some con-ducted by Haimsons confirm this point. The samething was found to be true for perforated holes, Table

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TABLE l-BREAKDOWN PRESSURES AND FRACTURE nPES FOR U* < u,,, AND u],

Open holePerforatedPerforated*Open holePerforatedPerforated *Open holePerforatedPerforatedPerforatedPerforatedPerforatedPerforatedPerforatedPerforated

Breakdown Pressure (psi)01;500 1S 3 ass500 1,000 500 3,440500 l,oaa 500 2,530

1,500 2,000 5oa 3,9001,500 2,0ao 500 4,9001,500 2,000 500 4,6702,500 3,000 500 4,7302,500 3,000 500 6,S001,500 2,00a o 5,3501,500 2,000 200 5,6501,500 2,000 3aa 4,9001,500 2,000 500 4,920l,WO 2,0aa 1,000 5,0001,500 2,000 1,500 5,1501,500 2,000 2,000 5,200

Fracture TypeInitiation Extension

Vertical VerticalVertical VerticalVertical VerticalVertical HorizontalVertical HorizontalVertical HorizontalHorizontal HorizontalVertical HorizontalHorizontal HorizontalVetilcal HorizontalVertical HorizontalVertical HorizontalVertical HorizontalVetiical VerticalVertical Vertical

+In these tests, 2,000. psi fluid pressure was maintained inside the borehole for 10 minutes before fracturing was attempted.1 shows that of the 12 experiments through perfora-tions onlyone fracture began as horizontal. The break-down pressures of the perforated holes were greaterthan those of the open holes, Most horizontal frac-tures began as vertical and then reoriented themselvesto become perpendicular to the least principal stress.In two experiments, 2,000 psi fluid pressure wasmaintained inside the perforated hole before it wasfractured. Contra~ to the opinion of some, this wasfound to have no influence on the fracture orienta-tion. The breakdown pressures, as expected, werelower ior these tests (Table 1).Vertical fractures are usually started by the tan-gential component of stress on the borehole wall, u,,.Theoretical considerations show m, to be indepen-dent of u,,, but rocks seldom behave in the simplemanner assumed by theory. To show the influence ofass on the breakdown pressures, a number of testswererun at constant u,, (1,500 psi) and u,, (2,000 psi)with variable U33.Although the breakdown pressuresinclude the stresses developed due to the fluid pene-tration into the rock, a,, induced this way is a func-

;,.

.... k ~..+.. .?.>..-... .,,L. perforationsFIE.7Hydraulic fracture ignoring the perforations,

Y = 90 (the photograph shows fracture face withthree perforations on the casing wall),OCTOBER, 1973

tion of fluidpresure only. Thus, a comparison of thebreakdown pressures should show the influence ofu,,, Fig. 9 shows the variations of the breakdownpressures with u,S for the fixed values of u,, and u,,reported earlier. As it can be seen, except for verysmall values of U,3,the breakdown pressure increasesas U8~ncreases. Further tests are needed to positivelyverify the high breakdown pressures observed forsmall U33.Discussion of Experimental ResultsAnd ConclusionsThe experimental results discussed in this paper indi-

. ./ F+dtd

I~g. 8-Hyd~aulic fracture ignoring the perforations,y = 90 (In this cross.section, the cut intersectsthe fracture and the perforations).

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,.

5800.-

P0: 5600-.

L G4800 4

622= 2000 s I

A f

3 800 1200 1600 2000U33, psi

Fig, 9-Variations of the breakdown pressure with u3,.

cate that an important aspect of fracturing throughperforations is the increased breakdown pressure. Theamount of increase depends on the arrangement andthe number of perforations. Of the two general ar-rangements examined in this research, the helical wasfound to be considerably superior to line perforations.The reason is that since the direction of the hydraulicfracture is not usually known before fracturing, thereis a chance that line perforations may not be in thefracture plane, whereas in a helical arrangement thisproblem does not exist. It is expected that randomperforation of the borehole wall will yield essentiallythe same behavior as the helical arrangement.It was found that the existence of perforations hadlittle if any influence on the orientation of hydraulicfracture. At times, as reported earlier, hydraulicfractures ignored the perforations completely and ini-tiated on the borehole wall perpendicular to the leastlateral principal stress. In these cases, the fracturingfluid entered the perforations and traveled betweenthe formation and the outer wall of the casing beforeit reached the fracture. If the treatment fluid is mixedwith a propping agent, as in most oil indust~ treat-ments, this fluid path can become the source of manyproblems, the most important of which is sand-off.Regarding horizontal fractures, it was found thatsuch fractures can begin as vertical and then changeto horizontal. In such cases, the vertical fracture willbe perpendicular to the intermediate principal stress.This situation raises a very interesting possibility.Suppose u,, is the intermediate principal stress, If thefluid pressure during the treatment, which must begreater than uSS,is also greater than u,,, it becomespossible to extend a horizontal and a vertical fracturetogether. For example, suppose uSS= 1,000 psi, uZZ= 1,200 psi, and fluid pressure is 1,300 psi, Sincethefluid pressure is greater than u,, and u,,, it can keepopen and extend both fractures perpendicular to u8Sand u,,, This means that under such conditions onemay have a horizontal and a vertical fracture propa-gating simultaneously. The rate of growth of the hori-zontal fracture will obviously be greater than that of1206

the vertical one since between the treatment presstireand ass there exists a larger difference than betweenthe treatment pressure and u,,. Although such caseshave been observed in the laboratory, their existencehas not yet been investigated in the field, but their oc-currence is certainly a possibility worth considering.Although the results of our few experiments on thelength of perforations were inconclusive, it seemslikely that shorter perforations will have a lowerbreakdown pressure than longer ones. The reason isthat shorter perforations will be closer to the stressconcentrations around the borehole and borehols/perforation intersection. The influence of the diameterof the perforation is mainly on the tensile strength ofthe formation; the larger the diameter the lower thetensile strength would be.More research is needed before all the questionsconcerning fracturing of cased holes can be answered,In particular, efforts should be made to perforate lab-oratory samples by the same methods used in industry.This will allow a comparison between, the variousmethods and also make the laboratory research morerepresentative of actual conditions.Nomenclature borehole radiusb = inner diameter of the casingEC, v, = constants of the casingmaterialE v = constants of the formationPc = breakdown pressure of hydraulicfracturesy = angle between the fracture plane andthe plane formed by line perforationsand the borehole axis6 = angle between u,, and a radial linethrough the center of the boreholeand any point in the formationall, uZ9,uSS= three principal stressesUIJev.,, U..e= tangential, radial, and shear stress atany point in the formationAcknowledgmentsI should like to acknowledge the assistance of DavidMeadows in conducting the experiments and of For-rest Pittman in building some of the equipment usedin the course of this research. I should also like tothank the management of Halliburton Services forpermission to publish this paper.References1.Savin, G. N,: Stress Concentration Around Holes Per-gamon Press, New York (1961) (translated from Rus-sian),2.Daneshy, A. A.: Study of Inclined Hydraulic FracturesSot. Pet Eng J (April 1973) 61-68.3.Haimson, B.: Hydraulic Fracturing in Porous and Non-porous Rock and Its Potential for Determining In-situ~tre;es ; PhD thesis , U. of Minnesota, Minneapolis (July

t J P T

paper SPE 4333 was presented at SpE.AIME EurOPean SPrinSMeeting, held in London, April 2-3, 1973.63 Copyright 1973 Ameri-can Institute of Mining, Metallurgical, and Petroleum Engineer Inc.This paper wiil be printed in Trarrsactlons volume 255, whichwili cover 1973,

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experimental investigation of hydraulic fracturing through perforations

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