D I S T I N G U I S H E D A U T H O R S E R I E S

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FRACTURED WELL PERFORMANCE: KEYTO FRACTURE TREATMENT SUCCESSHemanta Mukherjee, SPE, Schlumberger Oilfield Services

SUMMARYBest production practice requires the optimum production ratefrom a well with maximum bottomhole flowing pressure (BHFP).This can be engineered only by reducing pressure losses in thereservoir-flow conduit that comprises the reservoir rock and thenear-wellbore completion at or near the perforation. Under mostproducing conditions, an induced fracture with appropriate geom-etry minimizes near-wellbore pressure losses very efficiently. Thispaper explores this role of the hydraulic fracture, which results inmany applications under different reservoir conditions. Problemsconcerning placement of an optimally designed hydraulic fractureand common solutions also are discussed.

INTRODUCTIONThe basic objectives of hydraulic fracturing are to increase pro-ductivity or injectivity and to improve the efficiency of steaminjection in thermal floods. A more fundamental and alternativeview to explain the role of induced fracturing comes from Prats’1

contention that hydraulic fractures extend the wellbore radius.There are a few ways to explain the profound implications ofextended wellbores.2 The most practical explanation derives fromunderstanding the pressure losses in the area of drainage. Darcy’slaw states that the pressure gradient in the direction of flow isdirectly proportional to the velocity. This is stated mathematical-ly in consistent units by

dp/dx=vµ/k, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where v=q/A. This relationship also implies that the lower thevelocity, the lower the pressure gradient in the path of flow. In radi-al drainage, with constant volumetric rate, the flow velocity in theradial-flow path is maximum at the wellbore. Fig. 1 explains thispoint with real dimensions. The velocity at a wellbore of 6-in.radius is 2,000 times that at the entry into the drainage (1,000 ftfrom the wellbore), assuming negligible fluid entry within thisdrainage. From Darcy’s law, this implies that, at the wellboreperimeter, the pressure gradient is 2,000 times greater than at thedrainage surface 1,000 ft from the wellbore. This also suggests that,if the wellbore diameter is increased to 100 ft from 6 in., the entryvelocity into this wellbore increases 10 times that at drainage. Thistranslates to a substantial net increase in BHFP by effectivelyincreasing the wellbore radius from 6 in. to 100 ft. Such an increasein the BHFP can be used to produce the well at higher rates; at

lower drawdown; or at a combination that considers sand-, water-,or gas-control problems.

For a fixed velocity, Darcy’s law also implies that the pressure gra-dient is inversely proportional to the reservoir permeability: thelower the effective permeability of the flowing phase, the higher thepressure gradient. Near the wellbore, permeability is reducedthrough different radial-damage mechanisms, such as drilling-fluidinvasion and production-induced mechanisms (e.g., condensatedropout from gas, solids/fines deposit, sublimation of sulfur, paraf-fin deposit, and other scale deposits).

Consequently, the pressure gradient at the wellbore increases asa result of both increased velocity and the reduced permeabilitycaused by damage. Induced hydraulic fractures not only reducepressure gradients near the wellbore by increasing the surface areaof fluid entry but also inhibit some production-induced-damagemechanisms by reducing drawdown and physically bypassingthese damaged areas. In many such production-induced-damagemitigations, fracturing can postpone the need for frequent matrixacid treatments.

FRACTURE OPTIMIZATIONA fracture can be idealized as a slot induced in the rock, possiblyopen between acid-etched surfaces or filled with proppant to resistclosure. It can be shown analytically that the permeability of anopen slot is proportional to the square of slot width; this can bepresented as

k=54.4×106 w2, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

where permeability, k, is in darcies and slot width, w, is in inches.The permeability of a 0.01-in.-wide open slot is 5,440 darcies.3

Because permeability is inversely proportional to the pressure lossthrough porous media, the pressure losses at or near the wellborecan be minimized if the fluid flow can be directed through a frac-ture or a high-permeability slot from the reservoir to the wellbore.Consequently, the extent of this pressure-loss control determinesthe major fracture properties, such as its physical dimensions andthe permeability with or without proppant.

Design Criteria. Optimum fracture dimensions, such as fracturelength and width, are designed to provide high conductivity or lowpressure loss in the flow channel from the reservoir to the wellbore.Agarwal et al.4 showed that these fracture dimensions are con-trolled by a dimensionless parameter called dimensionless fractureconductivity, CfD, defined as

CfD=kfwf /(kxf). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

This dimensionless number should be greater than 10 for goodfracture design. Attaining a value this high for CfD is often difficult,especially in high-permeability reservoirs. A dimensional study onthe parameters in Eq. 3 [such as fracture capacity, kfwf, which nor-

Copyright 1999 Society of Petroleum Engineers

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• MARCH 1999 55

mally varies between 100 and 5,000 md-ft for the available prop-pants in hard rocks unless tip-screenout5,6 (TSO) design is adopt-ed] makes the reason for this obvious. In the soft-rock environ-ment with low Young’s modulus that is conducive to TSO, thefracture capacity can be increased by another order of magnitude.Reservoir permeability, on the other hand, can vary over a muchwider range from microdarcy to a couple of darcies (0.001 to10,000 md), a range of seven orders of magnitudes. This widerange makes permeability of a reservoir the single most importantfactor in fracture design that controls and limits the application offracturing. Optimum fracture length depends on permeability,which is also based on the criteria presented on the dimensionlessfracture conductivity.

Design Parameters. It is very important to note that, although thefracture-design criteria are based primarily on such reservoir-flowproperties as permeability, the design parameters are dependent onthe mechanical properties of the rock (such as the minimum prin-cipal stresses and Young’s modulus) in addition to the fluid-leakoffcoefficient (a direct function of rock permeability). Simply stated,the optimum designed fracture geometry is determined from thereservoir properties but the placement to achieve the designedgeometry depends on the mechanical properties of the rock. Thisdiscrepant need for an ideal combination of reservoir-flow andmechanical properties often causes fracture-placement problems,leading to underperformance of fractured wells. This problem isparticularly severe if reasonable estimates of both reservoir androck properties are not used in fracture design.

CAUSES OF UNDERPERFORMANCEThe most common causes of fracture underperformance arisefrom the inability to achieve designed geometry and include thefollowing.

1. Unconfined height growth.2. Inappropriate perforation.3. Creation of a horizontal fracture instead of designed verti-

cal fracture.4. Inadequate conductivity/near-wellbore choke.5. Asymmetric fracture extension in depleted reservoirs.6. Insufficient fracture coverage in multilayered reservoirs.7. Radial damage.

MITIGATION PRACTICES IN HYDRAULICALLY INDUCED FRACTURINGHeight Containment. Fracture length and conductivity in the payzone are the two main fracture parameters that control well per-formance.7,8 These fracture dimensions are determined on thebasis of reservoir properties. However, the geometry of the fractureduring placement depends on the in-situ stress7-10 and the leakoff

coefficient. As Fig. 2 shows, in the absence of adequate stress bar-riers, fractures tend to grow in height at the expense of length.Height growth can be contained under certain stress conditions.High-permeability formations with high leakoff normally shrinkfractures, controlling both height and extension.11 Fortunately, thehigher the permeability is, the lower the fracture-length require-ment.12-15 This helps in the design of high-permeability fracturing,such as frac and pack in the Gulf of Mexico. Because of the smallfracture half-length requirement, these treatments develop verylow net pressure; this is aided by high leakoff and low Young’s mod-ulus. Lower treatment pressures also contain these fractures.

In low-permeability formations, where long fracture length isabsolutely necessary, fracture-height growth is often a problem.This can be partially arrested by placing barriers of dehydratedproppants at the upper and lower tips of the fracture (Fig. 3).16-18

Inappropriate Perforation. Perforation design is a very impor-tant aspect of overall fracture-geometry evolution.19-25

Perforations not only provide communication between the well-bore and the reservoir during production but also provide animportant conduit for fracture-fluid and slurry entry into thegrowing fracture during its placement. The objective of perforat-ing in hydraulically fractured wells is to minimize near-wellborepressure losses caused by near-wellbore effects during fractureplacement. These near-wellbore effects are perforation friction,microannulus pinch points from gun-phasing misalignment, mul-tiple competing fractures, and fracture tortuosity caused by curvedfracture connection to wellbore.20 Cement bond with casing andthe formation can be very weak and vulnerable to fracture-fluidentry, generating microannuli around the wellbore. In such condi-tions or in the absence of cement integrity, perforation phasing

Fig. 1—In radial flow and for fixed flow rates, velocity of fluidentry, v, decreases with increased wellbore radius.

Fig. 2—Uncontained fracture-height growth results in decreasedfracture half-length.

Fig. 3—Height containment through barrier placement as a pre-treatment.

Upper Barrier

Lower Barrier

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does not make too much difference in fracture initiation andgrowth. However, perforation-tunnel diameter and shot densityshould be high enough to minimize treatment pressure losses.

In wells with good cement bond, perforation phasing, shot den-sity, length of perforated interval, tunnel diameter, and other suchfactors become very important for proper fracture placement.Fractures extend perpendicular to the minimum-principal-stressdirection. If the minimum-principal-stress direction is horizontal,the preferred fracture plane (PFP) is vertical. If vertical wells ornear-vertical wells (generally deviations less than 30°20) are perfo-rated properly, created fractures should be in contact with thewellbore throughout the perforated interval. In this case, the bestcommunication between the fracture and the perforations is estab-lished when the perforations are phased 180° and are orientedwithin 30° of the PFP.20,21,23 As the angle between perforation toPFP increases, the fracture-initiation pressure increases because ofhorizontal-stress difference. In vertical wells with good cementbond, the following perforation criteria should be used.

1. If the PFP is known with reasonable accuracy, oriented 180°phased perforation in alignment with PFP is preferred. In this case,all the holes should communicate with the fracture. Adequate shotdensity and tunnel diameter should minimize the pressure loss.The tunnel length should be such that it creates at least a 1- or 2-in. hole in the reservoir rock to help fracture initiation.

2. If the PFP is unknown, a 60° phased gun and three times theshot density of 180° phasing (because of limitations in direct linksto the fracture) are recommended.23 In this case, 90° and 120°phasing guns are also preferred over 0° and 180° phasing guns.

Another important aspect of perforation design is determinationof the perforation interval. To achieve optimum fracture dimen-sions, the perforation interval should be selected with due consid-eration of the lithology, the stress profile, and the leakoff profile(high-permeability streaks). This is done by consulting appropriatewell logs. The actual field data presented in the log in Fig. 4 illus-trate this point. The log shows the carbonate pay zones in the6,000- to 6,100-ft depth interval. The stress profile shows higherstress in most of the pay zone overlain by very shaly carbonateswith substantially lower stress. The lower pay zones in the 6,080-to 6,090-ft interval are naturally fractured and have higher perme-ability. Note that high permeability with high leakoff shrinks frac-tures. If this well is perforated in the whole pay zone and treated atan adequate rate to create fracture, the fluid entering through theupper sets of perforations creates a fracture that grows above thepay zone, resulting in very poor well performance. If the 5-ft inter-val of high permeability above the depth of 6,084 ft is perforatedand treated at a high enough rate, the fracture grows upward fromthe lower part of the pay to cover more of the pay zone with theoptimum fracture half-length. Coverage of this zone with high per-meability results in high fluid loss and thus requires higher treat-ment rates to keep the fracture open and growing upward into thetighter pay zones. Fracturing high-permeability pay also ensuresimproved well performance. In this case, initiation of the fracturein this lower zone is certainly preferable to perforating the wholepay zone or the upper part of it to initiate the fracture.

Horizontal Fractures. Before any fracture is designed, it is veryimportant to know the general orientation of the induced fracture.Perforation design for horizontal- and vertical-fracture placement istotally different. If well-performance calculations and the fracturenet present value are based on vertical-fracture orientation and thePFP is horizontal, well-performance results can be catastrophic. Inthis case, there are two reasons for underperformance.

1. Vertical fractures are fed by horizontal flow streams from thereservoir that are perpendicular to the fracture surface. In sedi-mentary deposits, horizontal permeability is at least an order of

magnitude higher than vertical permeability. Consequently, the ver-tical fractures perform better.

2. Horizontal fractures in sedimentary rock produce through thelower vertical permeability, resulting in lower production. If thewhole vertical interval is perforated with the expectation of plac-ing a vertical fracture, it tends to create very-low-radius horizon-tal fractures through each perforation tunnel. These tiny pancake-shaped fractures normally lose fluid at accelerated rates, causingearly screenouts. The result is a number of very poorly placed hor-izontal fractures with very poor well performance. In this case, aselect number of good horizontal fractures should be placedthrough high-density perforations located in very short intervals(no more than 1 ft each).

Fracture-Conductivity Control. Because of the limitations inproppant permeability, fracture-width manipulation provides thebest control of fracture conductivity. TSO design is the best way tocontrol fracture width.5,6 This requires sizing the pad volume onthe basis of injection rate, leakoff coefficient, and slurry schedule tocreate the designed fracture length with dehydrated proppantsbridging the tip. Once TSO is achieved, more slurry at higher prop-pant concentration is pumped to open the fracture and simultane-ously fill it up with proppant; this leaves a minimum volume offluid in the created fracture. Minimum fluid in the fracture at theend of treatment ensures faster closure and allows minimum prop-pant movement during closure. At the end of such treatments, thefracture is completely filled with proppant.

In many low-permeability reservoirs, fracture length becomesvery important. Large pads are pumped to create the long fracturesrequired. Because of the high fracture-fluid efficiency in these sys-tems, fracture-closure times can be very long, which allows theproppant slurry to settle in the fracture. If the fracture grows belowthe pay, such a phenomenon tends to deprive the pay of adequateproppant conductivity. The proppant-pack movement during clo-sure normally moves proppant away from the perforations (Fig. 5),creating a choked fracture that does not have the needed connec-tion to the wellbore. Depending on fracture geometry, in this case,a quick flowback often helps maintain fracture conductivity.26-27

Fig. 4—To fracture, perforate on the basis of vertical-stress andleakoff profiles.

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This is a good practice that helps in most cases and seldom dam-ages fracture conductivity.

Asymmetric Fracture. Induced vertical hydraulic fractures areassumed to grow symmetrically around the wellbore in two sym-metric wings. Under ideal stress conditions in a homogeneousreservoir at static-pore-pressure condition, this assumption seemsto be valid and performance calculations based on it usually areaccurate. However, in mature producing fields where infill wells arefractured, the pore-pressure distribution around active wells mayalter the natural stress profiles, causing asymmetric fracture growthand underperformance.

Hydraulic fractures grow in the path of least resistance, whichnormally is in the direction of the maximum principal stress. In adepleting reservoir, the pore-pressure distribution changes with thedynamics of fluid flow in the reservoir because of production andinjection streamlines. Unlike in static reservoirs, pore-pressure dis-tribution in producing or actively flooded reservoirs can causereorientation of the fracture azimuth (Fig. 6).28

Insufficient Fracture Coverage in Multilayered Reservoirs.Multilayered formations often are fractured in single-stage treat-ments. A common problem in such treatments is nonuniform cov-erage by fractures in all the layers. If every layer is perforated withsimilar guns with the same shot density, either the higher-perme-ability layers take most of the fluid, depriving the low-permeabili-ty layers, or the low-closure-stress layers fracture and take fluidsbefore the high-stress layers. A combination of permeability, thick-ness, and closure stress of individual layers determines the cover-age of layers. To avoid incomplete coverage of layers, multilayered-

fracture models should be used to design the perforation in eachlayer to cover all the zones. These multilayered models considerindividual layer thickness, layer permeabilities, and closure stress-es to allocate fluid entries into each layer. Sensitizing on the num-ber of perforations in each layer, these models allow proper designof fractures with adequate coverage of all layers.

Fig. 7 shows a sample application of multilayered fracturingmodels for coverage of four different layers. The actual case pre-sented in Fig. 7 is a poorly fractured well with perforated inter-vals in each layer and with designed fracture half-lengths in theselayers from a shot density of 4 shots/ft. These perforated intervalsare also the pay thicknesses of these layers. In this case, the lowertwo layers with higher productivity indices are deprived of frac-ture coverage.

The design, with the same pump schedule and same shot densi-ty, is improved by altering only the number of perforations in eachlayer like in the equivalent new perforation intervals shown for themultilayer case in Fig. 7. The lower two layers in this designreceived more perforations than the upper two layers, as dictatedby the multilayer model. For example, according to the model, thelowest zone needed 120 perforations (equivalent of a 30-ft perfora-tion interval with 4 shots/ft) compared with only 80 holes in theactual case. As Fig. 7 shows, the result is more uniform coverage offractures in all four layers and a corresponding improvement inwell performance of more than 40% at the end of 1 year.

Fig. 6—Asymmetric fracture extension resulting from pore-pres-sure depletion.

Fig. 5—Effect of immediate flowback on fracture conductivitynear the wellbore.

Fig. 7—Effect of perforation on multilayer-fracture extension.

xf

Fig. 8—Radial damage impairing permeability.

PoorConductivity

PoorConductivity

58 MARCH 1999 •

RADIAL DAMAGEIn many high-permeability formations, producing fluids carrysolids toward the wellbore and deposit these solids at or near thewellbore. If this process continues, it results in radial-damage col-lars around the wellbore (Fig. 8). Depending on the depth of thedamage collar, the best way to regain production losses may be tofracture these wells beyond these damage collars. Normally, matrixacidization can be applied commercially to affect less than 3 ft ofdamage from the wellbore owing to cost considerations. If the dam-age extends farther, fracturing becomes a viable alternative andoften results in a more sustained production increase. A method isavailable that predicts the depth of damage collars with corre-sponding permeabilities through a buildup test.29

Depending on the depth of damage collars, the optimum fracture-design parameters, such as length and conductivity, vary significant-ly. The simulation of the productivity ratio vs. fracture half-length inFig. 9 shows the importance in this case of conductivity above a min-imum fracture half-length. The critical fracture half-length in theexample is approximately 10 ft. Depending on the original perme-ability of the reservoir rock and the damage-collar radius beyond thiscritical fracture half-length, well performance (folds of increase inrate) becomes sensitive to the fracture productivity.

CONCLUSIONSThis paper points out some of the common reasons for underperfor-mance of induced hydraulic fractures. Placement of optimum frac-tures depends on rock properties (such as permeability) and fluidproperties (such as stress and leakoff coefficient) that are indepen-dent of the reservoir properties used to optimize fracture geometry(such as length and conductivity). Consequently, placement of opti-mum-design fractures often becomes difficult. This is particularlytrue in very-low-permeability rocks, where long fracture half-lengthsare required for optimum flow. Evolution of such long fracture half-lengths needs precise understanding of the confining parameters,such as stress barriers in adjoining layers. Understanding the para-meters that limit fracture placement discussed in this paper can oftenimprove their placement and at least limits undue expectations fromhydraulic fractures. Acquisition of adequate data through well log-ging, well testing, and minifracturing in key wells before inducing afracture is imperative for optimum fracture design.

NOMENCLATUREA= area, L2

k= permeability, L2, mdp= pressure, m/Lt2, psiaq= rate, L3/t

r= damage-collar radius, L, ftv= velocity, L/tw= width, L, ftx= fracture half-length, L, ftµ= viscosity, m/Ltν= Poisson’s ratio

Subscriptsf= fracture

ACKNOWLEDGMENTSI thank SPE for the invitation to participate in the DistinguishedAuthor Series program. I also thank the many colleagues whocontributed to the building of the present knowledge base used inthis paper. At different times in my career, Schlumberger OilfieldServices provided the unique opportunity to review well prob-lems with the engineers, generating the core content of this paper.

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SI METRIC CONVERSION FACTORS

ft ×3.048* E−01=m

in. ×2.54* E+01=mm

md ×9.869 233 E−04=µm2

psi ×6.894 757 E−03=MPa

*Conversion factor is exact.

Hemanta Mukherjee is Manager, Production Enhancementfor West and South Africa, with Schlumberger OilfieldServices, currently posted to Luanda, Angola. His previouspositions within Schlumberger were as Manager, ProductionEnhancement Gulf Coast, with Schlumberger OilfieldServices in New Orleans; as an area stimulation engineerwith Dowell in Englewood, Colorado; and as a senior devel-opment engineer with Johnston-Macco Schlumberger inSugarland, Texas. Before joining Schlumberger, he was withGulf R&D Co. He holds a BS degree from the Indian Schoolof Mines, Dhanbad, India, and MS and PhD degrees fromthe U. of Tulsa, all in petroleum engineering. Mukherjee iscoauthor of the upcoming SPE Monograph Multiphase Flowin Wells. He has served as a member of the Editorial ReviewCommittee, on Annual Meeting Technical Committees, andas Program Chairman of the 1993 Rocky MountainRegional/Low Permeability Reservoirs Symposium.

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