Overview of CurrentHydraulic FracturingDesign and TreatmentTechnologyPart. 1by R W. Veatch Jr., 8PE

Ralph Vestch is research supervisor of fracturing at Amoco Production Co. ResearchCenter in Tulsa. He holds BS and MS degrses in petrolaum engineering and a PhDdegree in engineering science from the U. of Tulsa. Veatch has worked as apetroleum engineer with Amoco h Louisiana, Mississippi and Texas, and wasassociate professor of petroleum engineering at the U. of Southwestern Louisiana. Hehas worked in weil-completiori, stimulation, and fracturing research for the past 9years, Veatch serves on the Technical Coverage Committee and Is a director of theMid-Continent section and general chairman of the 1984 SPE Enhanced 017 RecoverySymposium. He was an SPE Distinguished Lecturer on massfve hydraulic fracturingduring 1978, Other service includes the Forum Series Committee in 1980, theDeGo/yer Distinguished Service Medal Comm/ttee during 1980-82, and various AnnualMeeting technical program committees. In addition, Veatch served 2 years on a U.S.Nat/. Petroleum Council task group studying U.S. tight.gas re.semoir potential.

Introduction

Hydraulic fracturing has made a significantcontribution to the petroleum industry as a method for

enhancing oil and gas producing rates and rscovemblereserves. Fracturing was introduced to the irrdushy irr1949. Since then it has evolved into a standardopem.ting practice, and more than 800,000 treatmentshave been performed. 1 About 35 to 40 % of sllcurrently drilled wells are hydraulically fractured, and

abont 25 to 30% of total U.S. oil reserves have beenmade economical y producible by the process. It has

increased Nofi Americas oil reserves by anadditional 8 billion bbl.

Over the years the technology associated withfracturing has increased significantly. A host of

fmctnring fluids have been developed for reservoirsranging fmm shallow, low-temperature formations to

those that are deep and hot. ,Many different types ofpropparrts have been developed. These range from

silica sand, the standard, to high-strength materiz?ls foruse in deep formations where fm.cture C1OSUC8 stresses

exceed the ranges of smd capabilities.Fracturing treatments typicslly have varied in size

from 500-gal mini-hydraulic fracturing treatments forcontrolIed, shoct, precise f~cture lengths 2 to deeplypenetrating massive hydraulic fracturing (MHF)treatments that now range up to 1 million gal of

fracturing fluid and more than 3 million Ibm ofprupping agent. Over the past decade MHF trsatmerrts

01 49.2,36/82/0041 -0039$00.25COPy,ight lS&3 Sodetj Of Petroleum Engl,eers of AIME

APRIL 1983

have played a significant rule in developing tight (i.e.,low-permeability) gas fqrrmtions. To date, the onlypruved cconomica! development method for tight

reservoirs has been from MHF treatments. The designdifficulties and high cost of MHF have promoted a,strong awareness of the need to enhance our fiacnrre

design and treatment capabilities.This discussion focuses primarily on fractures that

(1) sm. oriented gore or less in the vemical plane, and(2) propagate outward in opposite directions from awellbore-i. e., verticsl fractures. Other types (e.g.,horizontal fractures) constitute a relatively lowpercentage of the situations experienced to date. Part 1

includes economics and optimization, general design

aspects, potential reservoir response, fracturepropagation simulation, and some ruck mechanics

aspects of fracture propagation. Rut 2 (to appear nextmonth) coverc fracturing materials (fluids, proppingagents, etc.) and field methods to obtain dataapplicable to prdkting and analyzing fracturingbehavior.

Fracture design still involves a considerable amount

of judgment engineering. After more than 30 yearsof fmcturing experience and research, our abilities todetermine in-situ fractnre shapes, dimensions (lengths,widths, heights, etc.), symmetry about the wellbore,azimuths, and fracture condrrctivities a~ still nothighly developed. In addkion, our abilities to measurein-situ rock properties and stress fields, which

significantly affect fracture propagation, are not

677

E!ik

Frao. 1/2 Lmmth

1000s Feet

MD .

Micro

D.rcb

b.4 />

, PQfi

2 %%

+%_

L

. . . .

%! W! COw.ti...l

.0001 .001 .405.01 .05.1 1.0 10.0 lW..? 1 5 10 50100 10QO 10,000 100.000

(n Siti Ge* Per,neabil;ty

Fig. lFracture stimulation design the total concept for Fig. 2-Desired fracture half-lengths for different formationoptimization. oermeabMies.

pdected. Consequently, our abilities to optimize

treatment designs and economics arc sometimes

lacking. However, fracturing technology is advancing

significantly.

Fracture Stimulation Economics and Optimization

The design of fracture treatments, generally speaking,has three basic tequirsments. One is to determine what

oil and/or gas prodncing rates and recoveries might be

expected fYom various fmchye lengths and fractureconductivities for a given reservoir. The second is todetermine the fcactnre treatment design rcqnirements to

achieve the desired fmcturc Iene@s and conductivities.

The tbkd ia to maximize economic returns. Theseconcepts arc illustrated in Fig. 1.

IdealIy, a reservoir performance simulator will

provide predictions of the production rates und

recoveries for various frzcturc lengths andconductivities. From these data, a revenue estimatecan be developed for various fracture lengths. As can

be seen in the upper portion of Fig. i, the revenue

estimate as a timction of fracture length is usually not

a linear relationship. The rate of revenue increase

diminishes with increasing fracture length andeventually reaches a relatively flat slope.

A hydraulic fmfuring simulator usually is required

to compute treatment volumes, types of materials, andpumping schcdulcs necessary to achieve various

fracture lengths and conductivities. WItb tht?se data arelationship between fmctnre length (and conductivity)and treatment cost can be generated. An example ofthk is depicted in the lower portion of Fig. 1. As can

be seen, treatment costs usualIy accelerate withincreasing fractnre length.

The find step is to investigate the total netrevenue-i .e., discounted ~venne minus cost. As

shown on the right side of Fig. 1, the net revenuecurve generally exhbks some optimal point at which

the cost to achieve longer fractnres exceeds therevenue generated by production from the addkional

678

length. Thus, a range uf treatment designs that

maximize economics (i.e., optimal treatments) can be.selected.

A major factor in optimization involves achievingthe appropriate balance between the fracture

characteristics and the formation propeties that govern

reservoir performance. High-permeability reservoirs

rsquirc high frscture conductivities but do not need

deeply penetrating fractnres. Low-permeabilityformations rcquicc deeply penetrating frnctnms hut can

tolerate lower fractom conductivities. Some typicaJlength requirements arc illustrated in Fig. 2, anexample by ElkIns. s It is presumed here that adeqnate

ftzcpme. conductivity exists for all cases. Fig. 2 shows

that fracture half-lengib (i.e., wellbore to tip)requirements typically are. less than 1,000 ft for

conventional permeability reservoirs (k> 1.0 red). Butextmrnely Iow-permeability formations (k= O.0001 md):may require half-lengths as long as 3,500 tO 4,500 fi..Optimal economic design is pafiictdarly important forMHF treatments, which can comprise a large portion

of the total well cost. An example of the relative

treatment cost as a pementage of total well cost intbrce nujor U.S. tight-gas basins is given in Fig. 3.As can be seen, for treatments of 500,000 gaI orlarger, fracturing costs can approach half the total well

cost (includlng fracturing).

GenersJ Treatment Design Considerations

Many factors can influence the effectiveness and costof a fracturing treatment. In essence, we are somewhat

limited in our abfity to controI where and how

fractwcs ultimately will propagate in subsurface strata.Our current effofis are limited to selecting (1) meaPPmPriate types of materials (e.g., fluids, additives,and proppants), (2) the appropriate volumes ofmaterials, (3). the injection rates for pumping thesemateriak, snd (4) the schedule for injecting thematerials. Some success has been achieved in vefiical

growth control with diverting-type additives in the

JOURNAL OF PETROLEUM TECHNOLOGY

rDENVER COTTON

VALLEY TREND

10

.

TREATMENT SIZE -lUWS GAL.

Pig. 3Re[ative MHF costs vs. treatment volumes.

fracturing fluid.

With todays technology, the complete design proc-

css may employ the following data to aasess reservoir

producing potential and to specify appropriate designinformation pertinent to the fracturing treatment.

1. Well draimge area and drainage configuration.

2. Vertical extent of formation net pay.

3. Formation permeability, porosity, andhydrocarbon satmntion snd the venicrd distribution

profile of these pammetem.

.4. Formation fluid propemies including viscosity,formation volume factors, etc.

5. Static reservoir pressure.

6. Formation temperature.

7. Thermal conductivities of formations penetmtedby the fracture, as well as in the vicinity of thefracture.

8. Parameters for fracture height or vertical growthextent that will occur during treatment.

9. Fracture extension pressure andlor fractmeclosme pressure,

10. Critical net fracturing pressure.

11. Formation effective modulus.

12. Fracturing fluid appsrent viscositfi ortheological n and K values for flow behavior index

and consistency index. It may nlso be necessary tospecify the above values as functions of shear rate and

time, as well as of temperature.

13. Fracturing fluid pipe and perforation frictiondata.

14. Fracturing fluid spun loss and, if necessary, itsfunctional dependence on tempecatire.

15. Fracturing fluid combined leakoff coeftlcient,and if necessa~, behavior as a fmrction of pressuredifferemtinl and tempmmwc.

16. Vefiical extent of net Ieakoff height.

17. Fluid tiermal conductivity.

APRIL 1983

rll I _J-o.a#

= w 1 :mr 0.30.1);L

1.0 10 100 Iwo 10ooo

FuctlmlK L----+ (WI

Fig. 4-PI ratio increase from fracturingsteady-state flow,vertical propped fractures, h,lh = 1.0.

18. Proppant size distribution.19. Proppant density.

20. Proppant fmcturc conductivity as a function of

fracture closure stress, proppant type, proppmt size

distribution, proppsnt concentration in the frschue,

and embedment in the formation.

21. Formation embedment pressure.22. Perforation coniigurntion (intervals, shots per

foot, size of holes).23. Tubular goods and wellhead contigurntion,

sizes, and pressure rntinga.Items I through 4 pertain, primarily to reservoir

performance 5 and 6 to both reservoir performance

and fracturin~ and the remainder primarily to thefmcture treatment design. Although the list appenmqnite comprehensive, it still may not reflect a complete

picture of the many factors that may affect frncture

design.

The sensitivity of the predicted and actual results to

the qnality of the design depends on both the relativecost of tie treatments and the nature of experience in

an individual formation. In some areas, it may betypical for operators to try a number of alternative

fluids, treatment sizes, and injection procedures toarrive at a set of standard treatments that provide

acceptable results. In areaa where fracturing treatmentsconstitute a relatively small poflion of the total drilling

and completion coats (e. g., high-permcablityformations where short fractures arc. adequate), thisapproach often is used to obtsin rdatively quick andeffective results. However, in Iow-permeability

formations where deeply penetmting fractures arerequired, resolution of the necessary fracturingparameters is ve~ important. In areas where MHF

treatments account for about half of the total well

costs, the impmtmce of fracturing is equsl to or

greater thm that of development drilling for increasing

679

Fig. 5Producing-rate type cuwes with propped vertical frac-tures-transient flow, constant wellbore pressure.

recovemble teserves. Here it is essenti~ to take the

necessary steps to determine the required datn with ahigh degree of resolution.

Existing methods for accurately quanti&lng essential

fracturing parameters such as fracture length, width,conductivity. height, azimuth, shape, Or sYmmetW

..-

about the wellbore are still very much in theexperimental stage. Thk makes it extremely difficult

to assess how accurately we can predict fracturingbehavior and effectiveness for a given set of design

conditions. Tbe input data problem is not limited to in-situ formation or rock-fracturing pammetem. Current

laborato~ procedures and data for predicting fracturingfluid and proppant behavior during a tr~tment aresometimes inadequate.

However, industw. is ma@ signifimnt PrO@ss nmuny areas. Recent work presented by severalauthors4-L0 describes programs and approaches toprovide better information for fracture treatment

design. In summary, the capabilities of the industryover the past several years have improvedsignificantly.

Reservoir Response to Fracture Length

and Conductivity

A wide and varied assortment of methods, bothgraphic and computerized, are available to estimate

effects of fm.cture length and fracture conductivity onwell productivity for a particular formation. If the

reservoir has a relatively high permeability wheresteady-state flow is dominant, it is possible to use

information such as that provided by TkMey ef al. 1 [as shown in Fig. 4. For example, in a relatively hlgh-penneability reservoir (e.g., conductivity finctiOn< 1.o) the graph indicates that less than a three-foldproduction increase is achievable regardless of fracturelength. For a lower permeability (i.e., a higherconductivity-function value) the more deeplypenetrating fractures enhance the folds of producing

680

P.ddns k Kem Gewtwrl. & deKlerk

Fig. 6Fracture configurations for theoretical modelsPerkins and Kern vs. Geertsma and DeKlerk.

rate increase. It is also possible to use such curves to

investigate the fmcturc conductivity (k@) requirementsfor a given formation permeability. For example, kfblk(md-ft/md) mtios that yield conductivi~-finctionvalues of 5 or more are required to realiie significant

productivity increases from fmCturing. ~lg. 4, Of

course, does not apply if there is severe near-wellbore

skin damage or t~sient flow.

If the reservoir has low penneabllhy such that

transient flow is a dominant regime throughout muchof a wells life, it is necessary to use a transient-flowmewoir computer simuIator or type curves such as

those pruvided by Agarwul et al., 12 shown in Fig. 5.

Here real-time pruducing rate, q, and $lmenslonlessrate, qD, are related by Eqs. 1 and 2.

1 khAp_= .. . . . . . . . . . . . . . . . . . . . . . . .

qD 141.2 qfl

(1)

for oil, and

1 khA[m(p)]_= . . . . . . . . . . . . . .. . . . . . . . . . . .

(2)

qD 1424 qT

for gas.Real time, t, and dimensionless time, trJXf, am

related by

2.634x 10 4 kf @OUm)tDzf =

. . . . . . . . . . .

(3)+(#cl)ir;

And dimensionless fracture flow capacity, FCD, is

expressed by

kfbFCD=. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(4)

kxf

JOURNAL OF PETROLEUM TECHNOLOGY

TABLE ICOMPARISON OF FRACTURE OESIGN CALCULATIONS FOR DIFFERENT

FRACTURING MODELS

Pad volume, bbl

Proppant-laden fluid volume, bbl

Average sand concentration, Ibm/gal

Total amount of sand, IbmViscosity after pad, cp

Created fracture length, ft

Effective fracture length, ft

Created fracture width, in,

Effective fracture width, in.

Effective fracture height, ft

Average fracture conductivity, darcy-ft

From Fig. 5 we can estimate the producing rate

performance from a given reservoir for differentfracture. half-len=gbs, Xf, and fracture conductivities,k@. Observe that producing rates increase as

dimensionless fracture conductivity, FCD, increases.

Observe dso that the curves fOr VariouS FcD vakIes

tend to converge in the neighborhood of Fw =500.This provides considerable insight into the effects of

length and conductivity as hey relate to formationpermeability during unsteady-state flow. To maximize

producing rate, we wmdd like to achieve a fracturewhere FCD values approach the 100 to 500 range.

For the steady-state case in higher-permeabilityreservoirs, fracture stimulation increases early-lifeproducing rntes (which increases c6sh flow) but haslittle or no impact on ultimate cumulative recOveIY.

However, in low-permeability formations, frsctming

can affect ultimate recove~ significantly. The ovemllbenefits that can be derived from deeply penetratingfractures in Iow-permeability formations were

investi ated in a a?cent U.S. Natl. Petrokwm CounciI?.

study 1 on bght-gas reservoirs. The results assummarized by Baker4 and Veatch 15 indicate that

advanced technology will increase recovemble gasfrom tight formations by 40 to 75%. Advaocedtechnology implies deeper and/or higher-conductivityfractures as required by formation permeability levels

and efficiently patterned wells consistent with theazimuthal trend of long, fractures for effective reservoirdrainage.

When making reservoir response studies, we mudconsider how well a given reservoir model IepRSentS

imsitu formation conditions. Some complex reserv0ir3

may require equslly complex reservoir simulators or

methods for analyzing and/or predicting petfonmmce.Improved techniques are emerging to cope with themore complex problems. Many authors 16-23 recentlyhave contributed to improving analysis and modeling

well-flow paformance in hydraulically fracturedformations.

Fracture Design Models

There me cunently two basic approaches commonlyused in ftacmre propagation simulatom. One,

APRIL 1983

Ref. 26 Refs, 30 and 31 Ref. 24 Ref. 32. -

750 320 1,350 1,650

1,250 1,680 650 350

3 2,5 2.5 3.5

157,500 176,000 68,000 51,000

36 36 36

698 670 6%4 845

466 453 240 185

0.22 0.43 0.17 0.16

0.20 0.31 0.16 0.16

9a 97 94 85

7.1 9.8 6.5 6.5

presented by Perkins and Kern, 24 involves premises

published by Sneddon. 2s The other is credhed to

Geertsma and DeKlerk,26 who published an approach

based on earlier work by Khristianovitch andZheltov27 and Barenblatt.2g As depicted in Fig. 6, the

two approaches basically differ in that the Perkins-

Kem model is developed from the premise that thecross section of the fracture in the verticaf plane,

petpendimlar to the long axis of the fracture, generallymsintains an elliptical contigmation. The Geensma-

DeKferk approach presumes an approximately elliptical

configuration in the horizontal pIane and a rectangular

shape in the vertical plane.Development of the Perkins-Kern model begins with

fracture width expressed in terms of fracture height,such that

@b-=. . . . . . . . . . . . . . . . . . . . . . . . . ..s . . . . ...(5)

The Geertsma-DeKlerk development is based onwidth expressed in relation to fracture Iengtlx

b-~: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(6)

Incorpomting Newtonian flow equations that relate

fracture pressure to injection rate and fluid viscosityyields

@3ww)x ,,,,,.,,,P-

hf.-.::;.., . . . . . ...(7)

for the Perkins-Kern approach and yields

(E3#qi) %P-

hf Axf%. . . . . . . . . . . . . . . . . . . . . ... . ...(8)

for the Geertsma-DeKlerk model

6S 1

I

I

Thus, for a given set of condhions the Perkins-Kernmodel predicts wellbote fracturing pressures increasing

proportionally with fmcture length raised to

aPPmximately the one-fourth power, and theGeertsma-DeKlerk method indkates pressures

decreasing propofiionally to fractme length raised to

about the one-half power.

Widths calculated from the Perkins-Kern model

generally are smaller than those computed by theGeettsma-DeKlerk model; hence, the Perkins-Kern

results will prcdkt a significantly longer fracturelength for a given amount of injected fluid at a givenrate, all other ammeters bckrg the same. Geertsma

$and Haafkens 9 presented a study comparing the two

theories. The study included results computed by the

two approaches as well as results of two other

modified ap roaches. One was a method proposed by2Daneshy 30. I that IS similar to the Geertsma-DeKlerk

method. The other was developed by Nordgren32 from

a Perkins-Kern type approach. The msuks are

summarized in Table 1.

The data in Table 1 mise a number of questionsabout differeiic& in results computed by the various

methods. Many arc addressed in Ref. 29 and are not

discussed in detail here. The point is that differences

do exist as a result of the basic premises used to

develop the models. These premises should beconsidered so as to tit the most appropriate model to

the in-situ fracturing conditions.There has been some conjecture as to which of the

two approaches is most appropriate. I think the

selection ~uires some a priori knowledge and

experience of how fracturing behavior occurs undervariqus subsurface conditions of stresses and rockproperties. Such information may be gained by

observing downhole treating pressures during

fracturing treatment. As Pmt 2 will discuss, yeassume that if the vertical growti of fra.cturcs is

relatively well contained, has no slippage at the top orbottom bounda~, and fracture length grows at a

significantly faster rate than fracture height, thenpressure at the wellbore will continue to increase. Thk

is what wotdd be predicted using the Perkins-Kernmodel. However, a contitmdly declining pressure may

indicate either that there is slippage at a boundary orthat the fracture is tending to grow vertically and

laterally at about the same rate-i. e., in a radialfashion. If slippage occurs, the Geertsma-DeKlerk

model may be more. appropriate. Ekher model wouldbe appropriate for purs radial growth.

Computerized Fracturing Simulators. These modelsare in common use throughout the industry today. The

complexities of the models WY from rsther simple

schemes that handle only constant fracture height andconstant fluid propefiies to ve~ sophisticated methods

that account for vertical growth during trcatmen~variations in fluid theological propefiies withtemperature, shear rate, and time; variations in fluid

682

loss with pressure and temperature, etc. Higher

degrees of sophktication, of course, usuaIly require amore comprehensive set of input data on formationproperties, fluid behavior, etc.

Most models use classical procedums33 for

determining pipe frictionlosses, fractnrc width due to

friction losses, and hydraulic horsepower requi~ments.

Many of todays fracturing fluids are non-Newtonian.For these, it is common pm.ctice to substitute an

aPPa~nt viscosity, pa, value for the NewtonianvmcosKy term, p, in the classical flow expressions.

Here apparent viscosity is computed by

47800 KPa=-. . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

In Eq. 9, p=, i, and K am e~rca$ed in cP,seconds -1, and lbf-sec/sq fG n is dimensionless. Thepipe and fracture fluid flow rheology are discussed in

more detail in Part 2.

Perforation friction normally is computed by

0.2369 q:pPfp=~3 . . . . . . . . . . . . . . .

czNpf

(lo)

where pti, qf, p, and dpf am expressed iD Psi,

bbI/min, Ibm/gal, and inches, respectively. Usualpractice employs a values rsnging from 0.8 to 0.9.

l?hdd Temperature Profiles. Many mndelsincorporate computations to prdct fluid temperature

profdes in the fracture during treatment. A variety ofmethods have been presented to accomplish thk. Someof the more commonly used approaches are covered bySettari 34 in a discussion of methods by Sinclair, 35

Barrington et al., 36 Wheeler, 37 and Whhsitt andDysti. 3s The results are shown in Fig. 7.

Sinclair characterizes leakoff in terms of fluidefficiency (defined as the volume of the fracturedivided by the total injected volume at the end ofinjection). At low fluid efficiency, the fluidtempemture in the fmcture, Tf, remains clOse tO the

injection temperature, Ti, and, with incrcnsinget%ciency, the temperature along the fracture tendsexponentially to the reservoir tempemture, T. The

numerical solution gives faster heatup at the entmnce

than both analytical models and falls between the twotoward the fracture tip. These diffe~nces result mainlyfrom coupled leakoff calculation as opposed toassumed leakoff rate dktribution (constant for Wheelerand linearly increasing for Whhaitt and Dysart).

Proppant Transport Models that include proppanttransport predictions genemlly employ expressions

developed fmm Stokes law for laminar flow ofNewtonian fluids and Newtons law for turbulent flow.

Clark and @adlr39 present a comprehensive reviewof the various approaches propoacd to compute patticle

JOURNAL OF PETROLEUM TECHNOLOGY

Length of+ cc To Stress

Oimm,i.!m%

T.mpwatur.

D

1,0

.777/--

wheel., ,--%clai,0.8

/7 Whi,, i,,

0.6& D,m

/

0,4,.

Tf - TiTD=

0,2T-Ti

/

Fig. 7Fluid temperature profile predictions in fractures dur-ing treatment.

settling velocities. They present expressions develop::

by Novotny, 4 Swanson

Bamea and Mednick, 43 ;:$yle;g:::::y

al.,s and GOvier and Aziz. 46 Wkb the exception Of

Ref. 45, the expressions in general pertain to

Newtonian or power-law fluids.For Newtonian fluids, settIing velocities mea

function of the gravitational accele~tion, density of

me flnid and the pardcIe, dinmeter of the particIe,fluid viscosity, and surface roughness. If we assumesingle uniform sphericaJ particles that do not exhibit

electrostatic interactions, Ref. 46 indicates that the

settling velocily v, for the laminar (Stokes law),transition, and turbulent (Newtons law) regions are

= dpp ddz (lamimm), . . . .

:=!:%] + mnsitin),(11)

. . . . . . . . . (12)

and

.(13)

Eqs. 11 through 13 are for single particles. In slurries,

settling hchaves somewhat differently because ofpatitle interf&ence snd/or clumping. Ref. 42, which

expresses the work of Zanker47 in explicit form, and

Clark and Guler48 address psuticle transport inslurries.

For particle settling in non-Newtonisn fluids, the

Newtonian viscosity, K, is commonly replaced by a

APR2L 1983

VW,:.,( F,,. VsfliC# F,HC Po,,;ble Ho,;mntal

P.,pedkul. r r. confined By Two Frac Whera Vefiical

Laa,t Stress Higher Swe,, Bed, stress (We;ght ofO,erburdml 1, Less

Thao Lateral S,,8,s

Fig. 8Effect of stress fields on fracture propagation.

computed value of apparent viscosity, IL.. Ref. 46

suggests that in some cases for uncrosslinked fluids,this may be an adequate approximation. Ref. 45suggests that it may not be applicable for crosslinked

fluids. There. is a significant need for better prnppant

transport pndiction methods for the crosslinked fluids

commonly in use today.

Rock Mechanics Aspects of

Fracture Propagation and Modeling

There appear to be an infinite number of possible

fracture configurations that can result from a hydmdic

fracturing treatment. As previously stated, onr currentconcepts indicate that most fractures are oriented moreor less in a vertical pkme and propagate outward in

opposite directions from a wellbore. Typically,fractures are thought to propagate either in a radial

fashion (i.e., penny-shaped) or predominantly in thelateral direction of the natural fotination beds and less

dominantly in the vertical direction across beddingplanes.

Many factors can affect fracture propagation. A few

of the theoretically identified factors include (1)variations of in-situ stresses existing in dfferent layers

of rock (2) relative bed thickness of formations in thevicinity of the fracturq (3) bonding betweenformations; (4) variations in mechanical rockproperties (including elastic moduhts, toughness, orductility); (5) fluid pressuce gradients in the fracture;and (6) variations in pore pressure from one zone tothe next.

LocaI stress fields and variations in st~sses between

adjacent formations are thought to have dominanteffects in controlling fracture orientation and vettical

fmctme growth tendencies. Regional stresses may

affect the azimuthal trend of fracture resulting from afmcturitzg stimulation.

Fig. 8 shows how differences in horizontal and

vertical suesses can affect the plsne of orientation of a

683

. .-

Theory Actual ?

Fig. 9Theoretics fracture propagation models vs. possiblo

aotual in-situ behavior.

,,200, I

bFractureLw!th

1,000 500F!.

800

,,000 F!,

.00

4001,500 F.

200 /

w00 200 400

I600 SOD 1,0C4 1.200 1.400

F,.. Flu!d Volume, (ThOUS4nd, of 0.!!.s1

tig. 10Simulation model fracture length and height

calculations.

fracture. Here the stresses are proportional to the

arrow sizes. At shallow depths, horizontal fm.ctures

have been repofied33 such as might result from a

condhion depicted in FLg. 8c. At depths below 1,000

to 2,000 ff experience indicates that most fractures areoriented vertically as in Fig. 8a. Control of verticalfracture growth may be dominated by higher lateral

stresses existing in the formations above and below the

fractnre-initiation zone as showu in Fig. 8b.

CommonIy used theoretical fracture propagationequations presume a rather simple fm.cturs

configuration as shown on the left side of Fig. 9.Experience with MHF treatments indicates thatcomplicated fracture configurations as shown on the

right side of FIg. 9 are probably more common.

684

tDG DERIVED

STRESS, psi DEPTH, ft

F

6055-9470

6S45 II

l!!-

-9495

6550 Ill :~,,, ,.

.......... . ,, -9525

6150

,V ,,,:

Y

-,,K .,.,:f:;: .

6365-9595

t R*:R.-

~wl -3 EFFECTIVZS7RESS MOOIFIED

? IN SHALE ZONES (1,11, fll, V).

m CORRELATE WITH MEAsuREO

~- 6W - TREATING PRESSURES

a

:

E

~ w

e

2

E~m

z

7~

FRAcTURE HEIGHT, ~

Fig. 11-in-situ tire~profi[es and fmcture height vs. pressure.

Knowledge of the vefiical height is extremelyimpo~ntto design. Fracture heigM has asigtificant

effect on fracture. length. Fig. 10 shows results of

fracture Iengti calculations for a number of differentfracmre heights. Here height inconstant throughoutd?e

treatment. Forthese data, fracture length is~sentidlyinversely proportional to fm.cture height. Thk

emphasizes the need forreliabl+ fracture height

information when designing treatment.$. Currently themost common methods for investigating veflicalgrowth are post-treatment tempemture decay profiles

and/or radioactive tracer profiles.

Zn many cases fmcturc heights may grow instead ofremaining constant throughout the treatment. Where

this occurs, methods to estimate the growth profile

JOURNAL OF PETROLEUM TECHNOLOGY

must be developed. This &quires conducting spetial

in-situ stress and fmcture mechanics stndles such asthose discussed in Refs. 4, 8, 49, and 50 to arcive at

profiles such as that shown in Fig. 11.50 This graph

shows a fractuie-heightiffactum-pressure relationahlp

developed for the in-situ stress profile depicted in fhe

upper portion of Fig. 11. Data such as these are usedto Improve fracturing tfeatment effectiveness in

formations known to have undesirable vertical fracture.

growth tendencies.

At this time it is quite difficult 10 infer subsurfacein-situ stress profiles. Curcent modeling capabilhiea are

still not totally adequate. Many investigatorss 1-65

rccefitly have published work addressing the problems,

and we are beginning to improve our capabilities inthese areas.

References

1. Waters, A. B.: cHydra.lic Fmct.ring-What Is It?,+> J. Per.

Tech. (Aug. 1981) 1416,2. Smifh, M.B.: Simulation Design for Short Precise Hydmulk

Fractures-mHF.,, !rmer SPE 10313 Dresmded at the SPE 19S1

Annual Technical Cb;ference and Ex

tions,,, paper SPE 9866 presented at the 1981 SPE/DOE LowPernmbilify Gas Reservoirs Symposium, Denver, May 27-2%

,accepted for publication i. SOC. Pet. E.g. J.

40, Novotny, E. J.: Proppant Transport,> paperSPE6813 presentedat the 1977 SPE Annual Technical Con fetwms and Exhibition,

Denver, Oct. 9-12.

41, Swanson, V. F,: &The Development of Formula for JJirect Deter-mimticm of Free Settling Velocity of Any Size Particle, S, Trans.,

SME (June 1967) 16&66,42. Zigr.mg, D.J. and Sylvester, N. D.: An Explicit Equation for

Parficke Settling Velocities in Solid-Liquid Systems,,, AIChE J.

(No,, 1981) 27, 1043-4443. Bamea, E, and M.dnick, R. L.: Correladom for Minimum

F1.idizatim Velocify,, S Trans., Jnst. Chem. E.grs. (1975) 53,278-81.

44. Daneshy, ,A.A.: Numerical Solution of Sand Trampmf in

Hydraulic Fracturing,,, 3. Prz. Tech. (Jan, 1978) 13240,45. Hmd:gton, L. J,, Hannah, R. R., and Williams, D.: , Dynamic

Expenmmfs and Pmppant Settling i Cmsslinked FracturingFluids,, S paper SpE 8342 presented at ~e 1979 SpE A..U,ITechnical Conference and Exhibition, Las Vegas, Sept. 23-26;

accepted for p.blicakm in SOc, Pet. E.g. J..

46. Govier, G. W. and Aziz, K.: 3% Flow of c%mpleJ M.M.IW inPipes, Van Nostrand Reinhold Co., New York City (1972),

47. Za.ker, A.: Nomography Dctermim Setdig Velocities forSolid-Liquid Systems,x, Chem. E.g. (May 19, 1980) 147,

48. Clwk, P.E. and Guler, N.: Pmppant Transpofi in Vertical Frac-twex Setting Velocity Correlations,- paper SPE 11636 piesented

at the 1983 SPEIDOE Low-ParneabiIity Gas Reservoirs Sym-

posium, Drover, March 13-16.

49. Rosepilm, M. H.: CDelermimdion of Primipal Stresses imd the

Con fimrmnt of Hydraulic Fractures in Cotfcm Vane y,,, paper

SPE 8405 presented at the 1979 SPE Anmal Technical Co-

f.wence sndExhibitio, Las Vegas, Sept. 23-26.

50. Nolte, K.G. md Smiti, M. B.: Interpretation of Fracturing

Pressures,3 J. Pet. Tech. (Sept. 19S1) 1767-75.51, Hanson, M. E., Andemm, G. D., Shaffer, R. J., and Thor$m,

L. D,, C .%.. Pet. Eg. J. (J.m 1982) 321-32.52. Warpimki, N.R. et .1,: Laborato~ Investigation o tie Effect of

In-situ Stresses o Hydraulic Fracture Coma.iormnt,,. S... PaE.g. J. (J.. 1982) 333-4o.

53. Teufel, L. W. and Clark, J. A.: Hydraulic Fracture Propagation

in Layered Rock: Expwimeotal Studies of Fracture Comain-

merit, Dater SPE 9878 mesented at the 1981 SPEIDOE LOW.Permeab;liiy Gas Resewo~rs Symposium, Demmr, May 27-29.

54. Cliftcm, R.J. and Abau-Sayed, A. S.: .A Variational Approach tothe Predktion of the Three-Dimensional Gmmetty of Hydrmdk

FrattnEs,, paper SpE 987g p=senf~ at tie 1981 SpE/DOELow-Permeability Gas Reservoirs Symposium, Denver, May

27-29.55. Cleary, MB:: Amlysis of Mechmkms and Procedures for Pr-

oducing Favorable Shapes of Hydraulic Fracmres,,, paper SPE

9260 presented at the 1980 SPE Amwa[ Technical Conference andExhibiticm, Dallas, Sept. 21-24,

56. Danesby, A A.: ; paper SPE

11626 presemed at the 1983 SPE/DOE Low-Permeability Gas

Reservoirs Sympmium, Denver, March 13-16.

61, Pahmw, I.D. md card, H.B. Jr.: Numerical Solution for

Height of Elomgated Hydraulic Fractures with Leakoff,,x paper

SPE 11627 presented at fhe .1983 SPEIDOE Low-Permeability

Gas Reservoirs Symposium, Denver, March 13-16.

62. SetWi, A.:< Quantitative Analysis of Factors Commlling VerticalFracture Growth (Containment),,9 peper SPE 11629 presented atthe 1983 SPEiDOE Low-Pcnneability Gas Resewoin Sym-

posium, Denver, March 13-16.

63. CIeaIY, M. P., Kavvadas, M., and Lam, K. Y.: A Fully Three-

Dimensional Hydraulic Fracture Sinwlator, paper SPE 11631

wesented ac the 1983 SPEJDOE Law-Penneabilitv Gas Resewoim~ymposiwn, Denver, March 13-16.

64. Ahmed, U., Wilsm, M. D., and Straw., J.: Effect of Stress

Distribution on Hydraulic FtackIre G.omem A laboratory

Simulation Study on One-Meter Cubic Blocks,,, paper SPE 11637

presented at the 1983 SPWDOE Low-Permeability Gas Resavoim

Symposium, Demw, March 1316.

65, Teufel, L. W.: , Determination of In-Situ SUt?sses Fmm Anebtic

Strain Recovery Measurements of Oriented Corm Applications toHydra.Jic Fractwing Treahnem Design,,, p~per SPE 11649

presented at the 1983 SPEIDOE Low-Permeahd!ty Gas ReservoirsSymposium, Denver, March 13-16.

Nomenclature

b = fracture width, ft (m)B = formation voluine factor

ct = total system compressibility, psi ] (kPa 1)d = pmticle diameter, in. (cm)

dpf = perforation diameter, in. (cm)

ti = shesr rate, seconds-1

E = Youngs modulus of elasticity

FCD = dimensionless fractuti flow capacityg = gravitational acceleration, fflsec (mIs)

h = formation net pay, ft (m)hf = fixture height, ft (m)

k = formation permeability, md

if = fracture permeability, md

K = Consistency index, lbf-sec/sq ft (Pa.s)

m(p) = msJ gas pseudopmssurc, psi2/cp(kPaz/Pa.s)

J Pd

= J NJJ)z(p)Pb

~ = flo..xj b~h~vio~ incje~ (&,~~@&s~)

N = number of perforations

p = pressure, psi (IJ%)pb = base pressure, psi (kPa)

Pfi = friction 10ss across petiorations

p= = fracture closure strew

,Ap = pressure drop, psi/ft (kPa/m)q = flOw Me, STBID or Mcf/D (stock-tank

m3/d or 103 m3/d)qzJ = $rnensionless flow rate

qf = mJection rate, bblhnin (m3/s)re = resewoir drainage mdius, fI (m)rw = wellbore radius, ft (m)

S = weIl spacing, acres (mz)

686 JOURNAL OF PETROLEUM TECHNOLOGY

t = producing time, hours

t~, = dimensionless time based on .rf

$= fmntaticm temperature, RTD = dimensionless

temperuhrrc=(Tf- T~)/(T-Ti)Ti = injection tempe~NO% RTf = fluid temperature in tie fracture at point of

interest, R

v, = settling velocity, fdsec (m/s).x = distance from tbe wellbore to some point irr

a fracture

Xf = fracture half length, ft (m)z = real gas deviation factor

a = perforation coefficient

~ =. viscosity, cp (Pa .s)v. = appment viscosi~, cp (Pa.s)

@cr)i = viscosity-compressibility prnduct at initialreservoir conditions

p = fluid density, g/mL. @crrr3)

PP = Paficle density, g/err ft (g/m3)$ = fomration porosity, fraction

S1 Metric Conversion Factors

bbl X 1.589873 E01 = m3

q x I.OCKI* E-03 = Pas

ft X 3.048* E-01 = m

gal X 3.785412 E-03 = m3

in. x 2.540* E+OO = cm

lbf X 4.448222 E+OO = N

Ibm x 4.535924 E01 = kg

psi x 6.894757 E-03 = MPa

sq ft X 9.290304 E-02 = mz

Co.vmim factor is exact. JPfD!wng.lshed Author series articles are general, uescriPfive Presentations ma

SUmmarim the stale .[ the art i. an area 01 :echno[ogy by desccibinq recantdevelopm.m,, for readers who are not ,Peci.4isls in the toPics tiscu,%d. Wriiten by

intividuds recognized as expwt$ in me areas, these articles prmide key mference$!. mote de fi.iWE work and present specific dewls only to illustrate tie technology,

Purpose To inform the general read.amhip of recent ad.ancm in various areas of

,oelrolewn .ngineerMg. The serlm is a project of !he Technical Cmwe Cmnmiuee.

APa3L 19s3 687

10039 Ralph W, Veatch, Jr, 13

to =

tSD =

t =SDO

Dxf =

T=

TD =

T=i

f =

Tr =

v.

f =

v=o

w=

f =

x =

f =

z =

$=

$6 =

i=

P =

IJ=

Pa =

(pct)i =

p=

Pp =

4=

post frac

post fracAt/to

referenceences

shut-in time

dimensionlessshut-in time =

shut-in time for pressure differ-

dimensionlesstime based on

reservoirtemperature,R

dimensionlesstemperature=

injection temperature,R

f

(Tf-Tr)/(Ti-Tr)

temperaturein the fracture, R

reservoirtemperature,or

pipe fluid velocity, ft/sec

fluid velocity in a fracture, ft/sec

settling velocity, m/see

fracturewidth, ft

fracturewidth, it

distance from the wellbore to some point ina fracture

fracturehalf length, ft

real gas tieviationfactor

foratationvoltuaefactor

ratio of average and wellbore pressureswhile shut-in

-1shear rate, sec

viscosity, cp

Poissons ratio

apparent viscosity, cp

viscosity-compressibilityproduct at ini-tial reservoirconditions

fluid density

particle density

formationporosity, fraction

REFERENCES

1. Waters, A. B.: HydraulicFracturing - What IsIt?, TIC Facts JPT, V. 33, August, 1981,pp. 1416.

2. Smith, M. B.: StimulationDesign for ShortPrecise Hydraulic Fractures - mHF, SPE 1013,presented at 56th Annual SPE Fall Tech. Conf.,San Antonio, Texas, Oct. 5-7, 1981.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

Elkins, Lloyd E.: Presented at May, 1980 GasResearch Conf,

Tinsley, J. N., Williams, J. R., Tiner, R, L.,and Nalone, W. T.: VerticalFracture Height -Its Effect on Steady State ProductionIncrease,SPE 1900, J. Pet. Tech., May, 1969,p. 633.

Agarwal, R. G., Carter, R. D., and Pollock,C.B Evaluationand PerformancePredictionofL;;-PermeabilityGas Wells Stimulatedby Mas-sive Hydraulic Fracturing,SPE Trans.,Vol. 267, 1979, pp. 362-372D.

IJPC- UnconventionalGas Sources - Volume V -Tight Gas Reservoirs - Part I - December,1980, Report by the Tight Gas Reservcir TaskGroup of the UnconventionalGas Committee ofthe National Petroleum Council.

Baker, C. O.: Effect of Price and Technologyon Tight Gas Resources of the United States,paper 819584, ASNE Proc. of the 16th Intersoc.Energy ConversionConf., Atlanta, Aug. 9-!4,19810

Veatch, R. W.: A Brief Survey of the Tech-nology Challenge to improve Recovery from TightGas Reservoirs* PaPer 819582, ASHE proc. ofthe 16th Intersoc.Energy ConversionConf.,Atlanta, August 9-14, 1981.

Veatch, Ralph W., Jr. and Crowell, Ronald F.:Joint Research-Ope]~tions Programs AccelerateMassive Hydraulic Fracturing Technology,SPEPaper 9337 presented at the 55th Annual FallTechnical Conference and Exhibitionof the SPEof AIHE, Dallas, Texas, September 21-2fI,1980.

Abou-Sayed,A. S., Abmed, U., and Jones, A:SystematicApproach to Massive HydraulicFrac-turing Treatment Design, SPE/DOE 9877presented at 1981 SPE/DOE Low Perm. Symp.,Denver, Nay 27-29, 1981.

White, J. L., and Daniel, E. F.: Key Factorsin NHF Design, J. Pet. Tech, V. 33, Aug.,1981, pp. 1501-1512.

Howard, G. C., and Fast, C. R., HydraulicFracturing,SPE Nonograph, Vol. 2, 1970.

Rosepiler, M. H.: Determinationof PrincipalStresses and the Confinementof Hydraulic Frac-tures in Cotton valley, paper SPE 8405 pre-sented at SPE 54th Annual Technical Conference,Las Vegas, September 23-26, 1979.

Nolte, K. G. and Smith, H. Il.: Interpretationof Fracturing Pressures,paper SPIi8297 pre-sented at SPE 54th Annual Technical Conference,Las Vegas, September 23-26, 1979.

Hanson, M. E., Anderson, G. D., Shaffer, R. J.,an~tThorson, L. D.: Some Effects of Stress,Friction and Fluid Flow on Hydraulic Frac-turing, SPE/DOE 9831 presented at the SPESymp. on Low Perm. Gas Reservoirs,Denver,May 27-29, 1981.

317

14 CURRENT HY!RAULIC FRACTURING TREATMENT AND DESIGN TECHNOLOGY 10039

.6. Warpinski,N, R., Clark, J. A., Schmidt, R. A., 30. Williams$ B, B,: ItFluidLOSS from Hydrauli-and Huddle, C. W.: LaboratoryInvestigation tally Induced Fractures,SPE Trans. (1970),on the Effect of In Situ Stresses on Hydraulic V. 249, pp. 882-888.Fracture Containment,SPE/DOE 9834 presented at the SPE Symp. on .LowPerm. Gas Reservoirs, 31. Hall, C. D., Jr. and Dollarhide,F. E,: Frac-Denver, May 27-29, 1981. turing Fluid Loss Agent PerformanceUnder

Dynamic Conditions,J. Pet. Tech. (July, 1968).7. Tuefel, L. W., and Clark, J. A.: Hydraulic 763-768.

Fracture Propagationin Layered Rock: Experi-mental Studies of Fracture Containment, 32. Rogers, R. E., Veatch, R. W., and Nolte, K. G.:SPE/DOE 9878 presented at the SPE Symp. on Low Pipe Viscometer Study of Fracturing FluidPerm. Gas Reservoirs,Denver, May 27-29, 1981. Rheology, SPE 10258 presented at SPE 56th Ann,

Fall Tech. Conf. and Exhib., San Antonio,.8. Clifton, R. J., and Abou-Sayed,A. S.: A Var- Ott. 4-7, 1981.

iationalApproach to the Predictionof theThree-DimensionalGeometry of Hydraulic Frac- 33. Cloud, J. E. and Clark, P. E.: Stimulationtures, SPE/DOE 9879 presented at the SPE Symp, Fluid Rheology 111. Alternativesto the Poweron Low Perm. Gas Reservoirs,Denver, May 27-29, Law Fluid Model for Cross-LinkedGels,1981. SPE 9332 presented at 55th SPE Ann. Fall Tech.

Cori?.and Exhib., Dallas, Sept. 21-24, 1980.19. Cleary, M. B,: Analysisof Mechanisms and

Procedures for Producing Favorable Shapes of 34. Cutler, R. A,, Jones, A. H., Swanson, S. R.,Hydraulic Fractures,SPE 9260 presented at the and Carroll, H. B., New Proppants for Deep GasSPE 55th Ann, Fall Tech. Conf. and Exhib., Well Stimulation,Paper 9869 presented at theDallas, Sept. 21-24, 1980. 1981 SPE/DOE Low PermeabilitySymposium,

Denver, May 27-29, 1981.?0. Daneshy, A. A.: HydraulicFracture Propaga-

tion in Layered Formations,Sot. Pet. Eng. 35. Neal, E. A., Parmley, J. L., and Colpays, P.Jour. V. 18, No. 1, pp. 33-41, 1978. J.: Oxide Ceramic Proppants for Treatment of

Deep Well Fractures,Paper 6816 presented at!1. BJ Hughes, Inc., a subsidiaryof Hughes Tool the SPE 52 Annual Fall Technical Conferenceand

Company, Arlington,Texas - fracturingengi- Exhibition,Denver, October 9-12, 1977.neering and product data.

36. Sinclair,A. R., and Graham, J. W.: A New~2. Dowell Division of Dow Chemical U.S.A., Tulsa, P~oppant for Hydraulic Fracturing,Paper pre-

Oklahoma - fracturingengineeringand productdata,

sented at ASME Energy Technology Conference inHouston, Texas (November5-9, 1978).

23. Dresser-TitanDivision of Dresser Industries, 37. Perkins, T. K. and Kern, L. R.: ;WidthsofHouston Texas - fracturingengineeringand pro- Hydraulic Fractures,Journal of Petroleumduct data. Technology,September, 1961, p. 937.

24. HalliburtonServices, a HalliburtonCompany, 38. Sneddon, I. N.: The Distributionof Stress inDuncan, Oklahoma - fracturingengineeringand the Neighborhoodof a Crack in an Elasticproduct data. Solid, Proc. Royal Sot. (1946) A, vol. 187,

229.25. Smith Energy Services, a Division of Smith

International,Inc., Golden, Colorado - frac-turing engineeringand product data.

39. Geertsma,J. and DeKlerk, F,: A Rapid Method26. The Western Company of North America, Fort

Worth, Texas -of PredictingWidth and Extent of Hydraulically

fracturingengineeringand pro- Induced Fractures,Journal of Petroleum Tech-duct data. nology, December, 1969, p. 1571.

27. RecommendedPractice for Standard Procedure 40. Khristianovitch,S. A and Zheltov, Yu. P.:for the Evaluation of Hydraulic Fracturing Formationof Vertical Fractures by Means ofFluids, RP 39, American Petroleum Institute, Highly Viscous Fluids, Proceedingsof the 4thDallas, Texas. World Petroleum Congress,Vol. II, 1955,

28.p. 579.

McDaniel, R. R,, Deysarkar, A. K., and Cal-lanan, M. J.: An Improved Method for Mea- 41. Barenblatt,G. I.: MathematicalTheory ofsuring Fluid Loss at SimulatedFracture EquilibriumCracks, Advances in AppliedConditions,SPE 10259 presented at SPE 56th Mechanics,Vol. III, 1962, p. 55.Ann. Fall Tech. Conf. and Exhib., San Antonio,Oct. 4-7, 1981. 42. Geertsma,J., and Haafkens, R.: A Comparison

29.of Theories for PredictingWidth and Extent of

King, G, E.: Factors Affecting Dynamic Fluid Vertical HydraulicallyInduced Fractures,Leakoff with Foam FracturingFluids, SPE 6817 Trans ASME, V. 101, March 1979, pp. 8-19.presented at SPE 52nd Ann. Fall Tech. Conf. andExhib., Denver, Oct. 9-2.2,1977. 43. Daneshy, A. A.: On the Design of Vertical

Hydraulic Fractures,Journal of PetroleumTechnology,Jan. 1973, p. 83.

10039 Ralph W. Veatch, Jr, 15

h4. Daneshy, A, A,, et al,: Effect of Treatment 59. Govier, G. k. and Aziz, K.: The Flow of Com-Parameterson the Geometry of a Hydraulic Frac-ture, SPE Preprint 3507, presented at the 46th

plex Mixtures in Pipes, van Nostrand Reinholdco,, New York (1972).

Annual Fall Meeting of SPE, New Orleans, 1971.60, Dobkins, Terrel A.: Methods to Better Deter-

\5. Nordgren, R. P.: Propagationof a Verti:al mine Fracture Height, paper SPE 8403 presentedHydraulic Fracture,Society of PetroleumEngi- at SPZ 54th Annual Fall Technical Conference,neering Journal, August, 1972, p, 306, Las Vegas, September 23-26, 1979.

i7. Settari, A.: Simulationof Hydraulic Frac- 61, Smith, R. C., Dobkins, T. A., Smith, M. B., andturing Processes,SPEJ, v. 2

TABLE 1

COMMONLY USED FRACTURINGFLUID SYSTEMS

Water-basedpolymer solutionsof

Natural Guar Gum (Guar)a

HydroxypropylGuar (HPG)a

Hydroxethyl Cellulose (HEC)

CarboxymethylHydroxethylCellulose (CMHEC)a

Polymer Water-in-OilEmulsions

2/3 Hydrocarbonb+ 1/3 Water-Based Polymer Solutionc

Gelled HydrocarbonsPetroleum distillate,diesel, kerosene, crude oil

Gelled Alcohol (Methanol)

Gelled Acid (HC1)

.!queousFoams

abc

TABLE 2

TYPICAL FUNCTIONS OR TYPES OF ADDITIVES

AVAILABLE FOR FRACTURINGFLUID SYSTEMS

Activators,chelating,or cross-linkingagentsAnti-foamingagentsBacteria control agentsBreakers for reducingviscosityBuffersClay stabilizingagentsDefoamersDemulsifyingagentsDispersing agentsEmulsifyingagentsFlow diverting or flow blocking agentsFluid loss control agentsFoaming agentsFriction reducing agentsGyp inhibitorspH control agentsScale inhibitorsSecvxesteringagentsSludge inhibitorsSurfactantsTemperaturestabilizingagentsWater blockage control agents

Sand SizeDesignation

Primary Sizes

12/2020/4040/70

Alternate Sizes

6/128/1616/3030/5070/140

TABLE 3

Typical Fracturing Sand Sizes

Water phase - guar, HPG SolutlonsGas phase - nitrogen, COZ

Can be crosslinkedto increaseviscosity.Petroleum distillate,diesel, kerosene, crude oil..Usually guar or HPG.

CorrespondingSieve ScreenRange of Opening Sizes

850-1700 micrometers425- 850212- 425

1700-33501180-2360600-1180300- 600106- 212

TABLE 4

Comparison of Fracture Design Calculationsfor Different FracturingModels

Results calculatedon the basis offracture dimensions.

Pad Volume (bbl)

Proppant-ladenfluidVolume (bbl)

Average sandConcentration (lb/gal)

Total amount of sand (lb)Viscosity after pad (Cp)Created fracture length (ft)Effective fracture length (ft)Created fracturewidth (inch)Effective fracture width (inch)Effective fracture height (ft)Average fracture cond. (Dft)

different theories for predicting

Geertsma & Perkins &DeKlerk Daneshy Kern Nordgren

750 320 1350 1650

1250 1680 650 350

3 2.5 2.5 3.5

157500 176000 68000 5100036 36 36 36698 670 804 845486 453 240 185,22 ,43 .17 .16.20 .31 .16 ,1698 857.1 9% 6:; 6.5

TABLE 5

COMPARISONOF FLUID LOSS COEFFICIENTVALUESOBTAINED FROM FIELD TESTS VERSUS LABORATORYMEASUREMENTS

Permeability Field Data LaboratoryDataFormation/Area (microdarcies)Fluid Type$ (JJ 3 ft/~min) (10 3 ft/Jmin)

Cotton Valley/Texas

!4uddy-J/Colorado

Frontier/Wyoming

Mesa Verde/Wyoming

Dakota/New Mexico

*Fluid types: 1 =2 ==

:=

1-1oo 1, 2, 4 0,3 - 0.7 0.7 - 1.0

1-1oo 1, 3 0.5 - 0.7 0.3 - 0.7

1-300 1, 2 1.0 - 1.2 1.0 - 1.5

1-1oo 1, 2 1,0 - 6.0 0.5 - 2.0

10-1000 1, 2 0.8 - 1.2 1.0 - 1.5

40# or 50# gel per ?fgalX-linked HPG1 + 5% hydrocarbonpolymer emulsion50# gel per Mgal X-linked cellulosederivative

Propped

Healed

Propped 1}HealedproppedFig. 1- Example One wing of a propped vertical fracture.

B! .a

Fig.

(Length

$ RevenueLess 1/

s cost

kLangth

Fracture Langth

A *

Fracture Fracture ResewoirConductivity Length Permeability

~

costs &Revenues

Fig. 3- Critical factors tooptimum fracture stimulation.

Frac. 1/21000s

LengthFeet

MOMicro

4

3

2

1

xtremelyTight

.0001 .0.1 1

Darcies

VeryTight

NearTight Tight

1Conventional

I!, ,! I 1 !.005 .01 .06.1 1 lo 10.0 100.

5 10hl Situ

60100 1000 Ic),ooo 100,OOO

aBe Permeability

Fig. 4- Desired fracture half:lengths for different formation permeabilities.

10 I ?I11111 I I 1111!1 I I 111111 1 I [11111 I I IlrllrL-=

8 e

6 Folds Of Producing

Rate Increase4

conud#g??ty k w..oo159+(*)vq

++[

Fig. 5- Producing rate folds of increase from fracturing-steady state flow.

10

1

ReciprocalDimensionless 10-

Rate,1

q~

10-:

10-:

DimensionlessFracture CapacityCD

.

-().~-(),5-f

>6/9

/50/~ w

2.624 x104kt *um. 2

kfwCD= ~

1o-m 10-4 10- 10- 10 1Dimensionless Time, tD~

Fig. 6-Producing rate type curves with propped vertical fractures - transient flow,constant wellbore pressure.

80 rFracture Length

Cumulative Production, ~.% Gas In Place

20 -100

00 4 8 12 16 20 24

Producing Time, Years

Fig. 7- Cumulative production vs. fracture length - low permeability (.005 md) case.

SPLithology

Type.

.

~.

.. .* O. O.*l O. .

.=:::~;:.:8*-*.*.,* ;.-*l l-**.*-..

.0.

ll~~llbge~o

l9:,. l ****.*,,

l, .** i: i;;:0,:.;.le***,*:, l,9.:: l.*l l***.***

l@ ~l I :Oy,{{*. j: .,.:,*O;

I l 9.,** ll***;*.,l..***..*,**:.*..,.

-

. - .

. .

.

.

.

-

Permeability Profile.Ooo1 .001 .01 .1

(MD)1.0

This?Or I

This?

Fig. 8- Possible tightidentify from logs?

gas reservoir permeability profiles - can we

Length of_ = To Stress

Vertical FracPerpendicular 10

Least Stress

EB 3E

Vertical FracConfined By Two

Higher Stress Beds

cPossible HorizontalFrac Where VerticalStress (Weight Of

Overburden) Is LessThan Lateral Stress

Fig. 9-Effect of stress fields on fracture propagation.

400

Height- ~OoFeet

200

1Oa

c

.

.

~

1000 2000 3000Fracture Length - Ft.

Ffg. 10-Fracture height vs. fracture length-300,000 gallon treatment design.

LOG DERIVEDSTRESS, psi

DEPTH, ft

6055 1-9470

6845 II

~ A

-9495

6550 Ill*.:l,**,,,:;,.,,, ,1,,* S*:, -9525,,~lx ~ - ,V :;;X ,,

: T

:. :,t . ,,.f.,,,., ,.,6855x b

-9595

RA;TUREA

-%35lam

20

EFFECTIVE S-r . MODIFIEDIN SHALE ZONES (I, II, II I,V}TO COPTEIATE WITH MEASUREDTREATING PRESSURES

/&-=FROM LOG ,II : RAPID FRACTUREI , GROWTH ZONE

111+11I

>l

1 1 I 170 100 150 m

FRACTURE HEIGHT, ft

Fig. 11 -in situ stress profiies, and fracture height vs. pressure.

Theory Actual ?

FractureLength(Ft.)

Fig 12- Theoretical fracture propagation models vs.possible actual in situ behavior.

.-

I T/1,500

~~~

Water & Oil1,000 Base Gels

500 150Fracture Height20 BPM

01 1 1 1 1 1 I 1 1 I I I 1 I 120 60 100 140 180 220 260

Volume (1000s Gallons)

Fig. 13- Fluid 10 .s vs. fracture length for low (emulsion) and highloss behavior.

(base gels) fluid

1.0

0.5

Spurt Loss 0,gawtz l

0.05

\90-150 md: Excessive Spurt Loss

\

\~175 F

80 OF

=rmabiitt 0,1-1 md S Zero Spurt Loss

0,01I 1 1 t 1 1 B 1 1 I 10 20 40 60 80 100 # oGuar Concentration-lb/l 000 Gal Water

Fig. 14- Spurt loss vs. Guar conceritratlon(uncrosslinked), temperature, and formationpermeability.

0.01 \ s ! I I 1 I r I I i I I I

0,005 -

C,ll-ft/mh/2 : ~:;m!;:~:

.-

0.OO10 20 40 60 80 100 140

Guar Concentration-lb/l 000 Gal Water

Fig. 15- Clll fluid ioss coefficient VS. Guar concentration (uncrosslinked).

.008

,007

,006

Fluid Loss Coefficient,,Oog

Clll, Ft/Min.12,004

,00:

,00:

.00

1 I I I 1

Without FLA

401 Lb. 60$ Lb,

1/ 40 Lb.

// 0=;, z 60 Lb{/ / With 25 Lbt2000 Gal./ Solid Particulate FLA/ i

I I 1 1 I I100 150 200 250 300 350

Fluid Temperature, F

Fig. 16- Fluid loss additives and temperature effect on Clll fluid loss coefficient-c:osslinked HPG.

1000

Shear Stress, ,0.dyne/cm2

10

4

0A

o

1/4 D TubeRotational Viscometer1/8 D Tube40 Lb/1000 Gal, 149*F

I Jn

1 I I 1 11111 I 1 1 1 1{100

# 10

Shear Rate, sem-

Fig. 17- Flow curve for uncrosslinked 40 lb HPG.

$aa

.Flow Behavior Index n Consistency Index K

}o~

180 240 300I

180 240 300

10.10 =-Y*$ucFluid Temperature, F Fluid Temperature, F

Fig. 18- Typical n and Kshear at temperature).

behavior-crosslinked 40 and 60 lb HPG (2 hours continuous

Apparent Viscosity,pa @ S11 see-l

10

t

0123466 7Timo @ Temperature, Hours

Fig. 19- Temperature and time effects on viscosity-40 lb crosslinked HPG.

m

.1la10 0Apparent Viscosity,Poise@ 51 see-lL

l.O -

0.1A 25

13 1

Crosslinked,Borate IonPolymer Soln,No Crosslinker

/..-

/

A-

*

/

3 17 1 19OR-l ~ 104

Fig. 20-Temperature stabilitycrosslinked versus uncrosslinked HPG.

Shear Stress,dyne/cm2

1000

1oa

1(

1 I I 1 I I If

/

/

,0/ #[d

I I

A Rotational viscometer01/8 D Tubesq l/4 D Tubes

i I i 1 1111 I 1 1 I i 1(-10 100

Shear Rate, see-l

Fig. 21- Flow curves from pipe and rotational viscometer 40 ib crosslinked HPG at176F.

,FrictionPSI Per 1

1

Pressure-000 Feet

Ooov I I 1 I 1 I I II I I I I/1 I800 /600 -

400 -

Lbs/1 000 Gal200 - HEC

@o

100 F*O

80 -60 ~

6040 - /

20 -

102 4 6 810 20 40 6080100

Flow Rate-BBL Par Min.

Fig. 22- Pipe friction vs. flow rate and gel concentration-iiEC fluids.

1O,ooa

MD- 1 ,OocFt. FractureConductivity

1Oc

Range Of FractureConductivity AchievableWith 20-40 Mesh Sand19000- 14,000 Depth Range)

0 2 4 6 8 10 12 14 16

Depth ( 1000s Ft.)

Fig. 23- Expected typical fracture conductivity vs. depth.

100,000

1~,ooo

FractureCo;d;;t~ty

.

1,000

100,

1 1 I 1 I I I I I I I I I 1 1 1 1] I i 1 1 1 I 1 flA

Proppant Concentration - lb. per 1000 sq. ft. of propped area

Fig. 24- Fracture conductivity, closure stress, and proppant concentration-24/40 fracsand.

Perkins & Kern Geertsma & deKlerk

l 8.

1,200

1,000

800

40(1

2oa

a

10

8

6DimensionlessTemperature

T* 4

2

a

I i I i I I

/

200 400 600 800 1,000 1,200 1Frac Fluid Volumes (Thousands of Gallons)

Fig. 26- Simulation model fracture length.

I

Wheeler

. /

.

0 z 4 6 8X@

Fig. 27- Fluid temperature profile predictions in fractures during treatment.

,*

9,500

9,6(X)

9,7(XIi=wwLEa 9,80)wmYo= 9,900

10,OM

10,m

SIMULATED !TEMP. \ (

\PROFILE i ;( L~ f- POSTFRACFRACTURE TOP & T~p.oF,---- . < 0;

.

I\i

1

200 225 250

2900

2930

IA

s3020 z

3050

.0)F

43 108 121 135c

Fig. 28- Temperature profiles: pre.frac (PWC), post-frac (PROFILE), and pre.frac model simulated.

+

POST FRACOST GAMMA RAYRAC

LP c

))

2780

2840 y?

Fig. 29- Warm Nose anomaly temperature profiie and post-frac gammasurveys.

pn:pT+ STAT[CHEAD -Pc

/

.

.

.

.

.

.

.

I -CONFINED HEIGHT;UNRESTRICTED EXTENSION

II -II -

Iv -

P;

STABLE GROWTH,ORFLUID LOSSGROWIH RESTRICTION

UNSTABLE HEIGHT

ill

----- -

Iv

tEXTENSION--

LLOG TIME

Fig. W- Wellbore net fracturing behavior during treatment-verticallyconfined fractures.

f-oT.

I

Iul

r -TUBING

vDFP = PT+ STATIC HEAD

I 1 1 1 1 i 19 12 3

CLOCKTIME (HOURS)

Fig. 31- Injection rates, downhole (tubing) and surface (annulus) fracture pressuresduring MHF.

IFig.type

I- 1 LOGCYCI.E -.

.

P* CHLE &

/H; d

s

.

.

.

32-

~ SDO0.25

1 I I 1 1 1 t= 1

SD- DIMENSIONLESS SHUT-IN TIME

Post-fracturing treatment shut-in pressure master DECLINEcurves.

psimin.Rft

fiiih.