SPE-166107_65 Years of Fracturing Experience_The Key to Better Productivity is What We Have...

8/18/2019 SPE-166107_65 Years of Fracturing Experience_The Key to Better Productivity is What We Have Forgotten and Fail…

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SPE 166107

65 Years of Fracturing Experience: The Key To Better Productivity Is NotWhat We Have Learned But What We Have Forgotten and Failed To Utilize!Frank E. Syfan, Jr., SPE, GoFrac LLC, Terry T. Palisch, SPE, CARBO Ceramics Inc., and Jeffrey C. Dawson,SPE, Independence Oilfield Chemicals LLC

Copyright 2013, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September–2 October 2013.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Many engineers today do not have the training needed to fully understand the importance of fracture mechanics principlesand are easily overwhelmed in trying to deal with proper proppant and fluid selections, perforation design and strategy, andon-site quality control of the fracturing process. The unfortunate reality is that many fracture designs are improperlyengineered with critical reservoir and hydraulic fracture parameters either ignored or improperly addressed. Manycompletions are either marginally economical or produce at reduced commercial rates. Regardless of reservoir type, it iscritically important to achieve a highly conductive hydraulic fracture that provides connectivity between the reservoir and thewellbore.

Since its inception, fracturing and completion knowledge has expanded exponentially allowing the oil and gas industry todevelop ultra-low permeability unconventional reservoirs. During the 1980’s and 1990’s technology pioneers such as

Holditch, Nolte, Warpinski, Veatch, and others, further developed the principles of fracturing which recognize theimportance of critical fracture parameters and their effect upon initial productivity and ultimate recovery. These gains inexpertise have resulted in unprecedented activity in the Bakken, Eagle Ford, Barnett, Haynesville, and Marcellus withincreasing activity in new reservoirs such as the Utica, Niobrara, and Mississippian. Although each of these reservoirs isunconventional, each is uniquely different with respect to lithology, permeability, and hydrocarbon chemistry and interaction.

This paper will challenge the industry notion that infinitely conductive fractures are being placed in many unconventionalcompletions. It further addresses the critical fracturing parameters required to achieve a high conductivity fracture, why theyare important, and how to achieve proper proppant and fluid treatment designs. The importance of these fundamental principles is documented and illustrated by several case histories which demonstrate the value of achieving high conductivityfractures and the effects of improper design. This paper should be of great value to completion and operations engineers tohelp further their knowledge with regard to the importance of fracture conductivity and connectivity in all hydraulicfracturing applications.

Introduction

In 1947, Stanolind Oil and Gas (Company succession: Stanolind → Pan American → Amoco → BP) introduced its“Hydrafrac” process to the oil and gas industry and in 1949, the first commercial fracturing application was performed in theUnited States. J. B. Clark (1949) of Stanolind Oil & Gas Company introduced the concept to the industry in an article in the Journal of Petroleum Technology in January 1949 in which he identified six certain requirements of the Hydrafrac processwhich must be met to be successful:

The hydraulic fluid selected must be sufficiently viscous that it can be injected into the well at pressure high enoughto cause fracturing.

The hydraulic fluid should carry in suspension a propping agent, such as sand, so that once a fracture is formed, itwill be prevented from closing off and the fracture created will remain to serve as a flow channel for oil and gas.


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The fluid should be an oily one rather than a water-base fluid, because the latter would be harmful to manyformations.

After the fracture is made, it is essential that the fracturing fluid be thin enough to flow back out of the well and notstay in place and plug the crack which it has formed.

Sufficient pump capacity must be available to inject the fluid faster than it will leak away into the porous rockformation.

In many instances, formation packers must be used to confine the fracture to the desired level, and to obtain theadvantages of multiple fracturing.

King (2012) reported at the SPE Hydraulic Fracturing Technology Conference in February 2012 that there have been over2.5 million fracturing treatments pumped worldwide with over one (1) million pumped in the United States. Fortunately forthe oil and gas industry, well stimulation technology has advanced extremely rapidly, especially during the past two decades.Unfortunately, however, most production, completion, and operations engineers have not had enough time to properlyanalyze and apply all the new data, materials and techniques. Many engineers today have been relegated to more of a projectmanagement role and thus, have not been properly trained to understand the principles that govern fracture and rockmechanics. As a result, many fail to properly design optimal fracture treatments which achieve high conductivity and highdimensionless conductivity fractures, resulting in losses not only in initial production rate, but ultimate recovery, Net PresentValue (NPV) and Internal Rate-of-Return (IRR).

Moreover, a great number of designs today are created using spreadsheets which rely on oversimplified rules-of-thumb, suchas pounds proppant per vertical/linear foot and gallons fluid per vertical/linear foot. In efforts to save money, manycompanies lower completion costs without realizing the tremendous losses in deliverability, net income, IRR, and NPVinflicted by improper fracture and completion design.

Rock mechanics have always dictated the pressures, width, length, and height of a created hydraulic fracture. In the early1960’s, over 50 years ago, fracturing pioneers T. K. Perkins and L. R. Kern (Perkins and Kern (1961)) correctly stated thatzones with higher in-situ stress found above and below the initiating zone will cause a vertically limiting effect and that thevertical hydraulic fracture would grow until it reached the bounding higher stress zones which will then restrict verticalheight growth. Without a thorough understanding of rock mechanics, fracture design parameters, and critical fracture parameters, optimization of completions is virtually impossible and many completions achieve very low dimensionlessfracture conductivities. In actuality, lower fracture conductivities can and do reduce both initial production rates and ultimaterecoveries as evidenced by Lehman et al. (2003). Further, the effects of conductivity reductions and the need for maximizingfracture conductivity was presented in a Gas Research Institute (now officially named “Gas Technology Institute”) Report

authored by Peterson et al. (1991), and later detailed by Palisch (2007). Syfan and Anderson (2011) presented work whichquantified the staggering losses in initial production rates, ultimate recovery, and NPV losses in the Eagle Ford and Marcellusformations as a result of improper designs with respect to applications which exceed the recommended individual operatingranges for various Northern White quartz and substandard proppants.

To challenge the notion that infinitely conductive fractures are being placed in many unconventional completions, four (4)case histories were examined to illustrate the benefits of proper fracture design. The four cases include a completion whichachieved only a low-medium dimensionless fracture conductivity (Case A – Marcellus Shale), a properly designedcompletion which achieved high fracture conductivity (Case B – Eagle Ford Shale), and two cases which represent the benefits of improved fracture conductivity in the Bakken (Case C) and Cotton Valley (Case D). Case A was furtherexamined to determine the economic losses associated with the low-medium conductivity and also examined the benefits of proper completion design to achieve a much higher conductivity. The results of each case are presented and discussed whichincludes an economic assessment of the Case A depicting the gains that could have been achieved by proper fracture design.

This paper is intended to give inexperienced engineers a guide to understanding rock mechanics, fracture design, and criticalfracture parameters as they relate to modern completions in an effort to increase the overall effectiveness of the thousands ofwells drilled, completed, and hydraulically fractured annually.

Fracture Propagation Theory

The general equations and constitutive relationships governing fracture propagation are summarized below. These equationsillustrate the importance mechanical properties, injection rate, fluid rheology, and confining stress contrast have on thefracture propagation process. The governing mass, momentum, and energy equations and constitutive relationships are presented below (Meyer (2011)).


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SPE 166107 3

Mass Conservation

The governing mass conservation equation, presented in Eq. 1, for an incompressible slurry in the fracture, states that the

volume of slurry injected into the fracture minus the volume loss by leakoff, ( )lV t , and spurt loss, ( )spV t , must be equal to the

fracture volume, ( ) f

V t .

0

( ) ( ) ( ) ( )t

l sp f q d V t V t V t

Continuity

The governing continuity equation, presented below in Eq, 2, for incompressible slurry in the fracture, in terms of the fluid

velocity, v

, is:

2 0lvw v w t

Where, lv is the fluid leak-off velocity and w is the fracture width at any position.

Momentum Equation

Eq. 3, the momentum equation (equation of motion) for steady state flow, can be written as:

2

12 h

f v pd

Where, f is the Darcy friction factor which is a function of the Reynolds Number, e R , and fracture wall roughness.

Width-Opening Pressure Constitutive Relationship

The crack-opening (aperture) and opening pressure relationship from Meyer (1986, 1989) for fractures in each of the principal planes ( ) is of the form depicted in Eq. 4:

2 ( ) 2( , , )

w w

H p H pw x y z

E E

Where, w is a generalized influence function, H is a characteristic fracture half-height (or length), w is the fracture width,

p is the fracture pressure, 22 1 E E is the effective Young’s modulus, is the confining stress and

p p is the net fracture pressure for each discrete fracture in the three principal planes ( ).

Fracture Propagation Models

There are numerous 2-D, Pseudo 3-D and fully 3-D models available to the petroleum industry and are well documented inthe petroleum literature. Other hydraulic fracturing models have been specifically developed for discrete fracture networks(DFN’s). Although many fracturing treatments result in relatively simple bi-wing fractures because they require less energyto propagate, there are natural systems that force the boundary condition to create discrete fractures requiring even lessenergy than a bi-wing. This is most easily understood by examining limited entry designs or by perforating large intervals inhighly deviated wellbores. Both of these are examples of creating multiple fractures as the result of a boundary condition.All of these models are invaluable in understanding fracture propagation modeling and design in formations with spacially

varying mechanical properties.

Understanding 2-D fracture propagation theory is critical to understanding the primary effect of various parameters and in performing parametric studies. The two most famous 2-D models are the Geertsma-de Klerk (1969) and the Perkins-Kern/Nordgren (1961) type geometry models. The Geertsma-de Klerk (GDK) type fracture model is a constant height modelthat assumes horizontal plane strain with the characteristic half-height equal to the fracture length (one-wing or half-length).This model is most applicable for fracture length to half-height ratios less than one (L/H1).

Some of the functional relationships between various fracture parameters and their effect on fracture characteristics and pressure responses are illustrated in Table 1 (Hagel et al. (1992)). Table 1 shows the effect of various parameters on fracture

(1)

(2)

(3)

(4)


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length, width and net pressure for PKN, GDK and Radial type 2-D fracture models for viscous and toughness dominatedfracture propagation. The viscous equations are for laminar flow with negligible toughness and no spurt loss. The toughnessequations are for negligible viscous dissipation. The penny shape model is referred to as the Sneddon model for toughnesscontrolled propagation.

Parameters with the largest exponents have the greatest influence on the specific fracture characteristic. Therefore, moreemphasis should be put on refining these critical parameters. A systematic approach is a good method of determining

parameters which best match the fracture characteristics and response. The proportionality equations in Table 1 can be usedto refine input data and to determine parameter sensitivity for 2-D type models. The parameters which affect net pressure themost are: Young's modulus, fracture height and viscosity for the PKN model. To match the net pressure in a GDK modelonly the fluid rheology or Young's modulus can be varied to get a match assuming negligible toughness. The net pressuresfor the GDK and radial (“penny”) models are shown not to be a function of fracture height.

The connected-cluster simulation assumes that the multi-clusters create a single DFN that interacts with the other clusters.That is, fractures from the separate clusters may coalesce with other secondary fractures created from the individual clusters.This assumption may be the best limiting case in that secondary fractures created by individual clusters can occupy the samesecondary network system rather than assuming separate interacting fractures in the principal planes.

A DFN numerical simulation and pressure match for a Marcellus shale well was presented by Jacot et al. (2010), describingtechnology integration as a methodology to enhance production and economics in horizontal Marcellus shale wells. Fig. 1illustrates the surface and bottomhole treatment pressure match. The dominant fracture characteristics (width contours,height, length, etc.) are shown in Figs. 2 and 3, respectively. This numerical simulation illustrates the effect of fracturegrowth and propagation in complex formations.

Table 1

Two-Dimensional Hydraulic Fracture Parametric Equations

Rock Mechanics

Mineralogy

Knowledge of formation mineralogy and composition is critically important information when designing the fracturingtreatment regardless of whether the formation is predominately sandstone (quartz), fractured shale, limestone or dolomite, or


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Poisson’s ratio. If the material being tested is stretched or compressed along the axial x-direction, the equation for Poisson’sration is then represented by Eq. 5.

x

z

x

y

axial

trans

d

d

d

d

d

d

The effects of slight changes in Poisson’s ratio are well documented in the literature, e.g. Perkins and Kern (1960). In

addition, the values of Poisson’s ratio for most rocks reported in the literature range from about 0.05 – 0.25 (Birch, F.(1942)), (Cleary, J. M. (1959)), (Wuerker, R. G. (1956)). From the existing research it is apparent that the minimum fractureextension pressure is not very sensitive to slight changes in Poisson’s ratio. However, width calculations are highlydependent on values of Poisson's ratio and if incorrectly applied can result in significant errors in calculated width, which willaffect the calculated height, created length, and fracture volume.

Young’s Modulus/Modulus of Elasticity

Modulus of Elasticity, or elastic modulus, is defined as the mathematical description of an object or substance’s tendency to be deformed elastically (i.e., not permanently deformed) when a force is applied to it. The elastic modulus of an object isdefined as the slope of its stress-strain curve in the elastic deformation region. As such, the stiffer the material is, the higher

the elastic modulus. The equation for Elastic Modulus is presented below in Eq.6, where lambda () is the Elastic Modulus,Stress () is the restoring force divided by the area to which the force is applied (for industry applications, psi), and Strain ()is the ratio of the change caused by the stress to the original state of the object. For example, if Stress is measured in pounds-force per square inch (psi) and Strain is a dimensionless quantity, then the units of Elastic Modulus are stated in psi.

E Strain

Stressdef

m

Depending on how Stress and Strain are measured, which includes the stress direction, allows for many types of ElasticModuli to be defined. For instance, Young’s Modulus describes the material’s response to linear stress and strain. The BulkModulus describes a material’s response to uniform pressure and Shear Modulus describes a materials response to shearingstresses and strains. Bulk Modulus, Shear Modulus, and Young’s Modulus are the most common.

Young’s Modulus ( E ), used most commonly in hydraulic fracture simulation models, describes tensile elasticity, or thetendency of an object to deform along an axis when opposing forces are applied along that axis, and therefore is defined as

the ratio of tensile stress to tensile strain (t/ t). Young’s Modulus, also known as the tensile modulus, and Poisson’s Ratio

are two of the most important rock mechanics values used in hydraulic fracturing. They are primary quantities which definewidth calculations and therefore will also dictate calculated fracture length and fracture height. If these values are incorrectlyestimated for a given application, fracture geometry cannot be accurately calculated and again, optimization will not bepossible using predictive modeling.

In-Situ Stress

Gidley et al. (1989) discuss the effects, calculations, and role of in-situ stress in depth in SPE Monograph 12, Chapter 3.3.The authors point out that in-situ stresses are clearly the single most important factor controlling hydraulic fracturing. The

maximum horizontal stress (Hmax), minimum horizontal stress (Hmin), and vertical (V), or overburden, stresses controlfracture azimuth, vertical/horizontal orientation, total and directional height growth, surface treating pressure, bottomholetreating pressure, net closure stress and proppant crushing, embedment and fracture cross-sectional width profiles, just toname a few.

Hubbert and Willis (1957) performed experiments to determine the effects of stresses on the fracturing process and stated thatif fluid pressure is applied to the rock, the pressure will increase to the point that the rock ruptures, or fractures, and the rock

parts. Thus, the formation will always fracture when a force is applied to the rock that exceeds the minimum horizontalstress plus the pore pressure. The fracture will then propagate perpendicular to the least or minimum, horizontal stressazimuth. Since the in-situ stresses are so critical in properly planning for and designing hydraulic fracture stimulations, the

problem has been addressed by many and is well documented in the literature.

Hubbert and Willis (1957) believed that the minimum horizontal stress was between a third and half of the effective stressand therefore the fracture pressure could be determined from the following equation:

PPS F 3/

Where, F is the fracture pressure, S is the overburden stress, and P is the formation pore pressure.

(5)

(6)

(7)


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Eaton (1969) believed that the rocks deformed elastically and thus, introduced Poisson’s ratio into the calculation, presentedin Eq. 8:

PPS F

1

Eaton’s work was then further refined by Daines (1982) to include the variable T as the superimposed tectonic stress.

Daines formula is still widely used today as it allows fracture pressure to be calculated while drilling and is not dependent on previous data being available from a specific region. In areas or formations where no engineering data is available on in-situstresses it is possible to estimate the horizontal stress which is useful not only in drilling applications but can be used toestimate horizontal stress in fracturing operations and is presented in Eq. 9:

T p pV H PP

1

Closure Pressure

Nolte (1988) defined Closure Pressure as the fluid pressure required to initiate the opening of an existing fracture. Therefore,this Closure Pressure should be equal to and counteract the stress in the rock perpendicular to the fracture plane, which is

known as the minimum principal in-situ horizontal stress min cP . This statement holds true if there is no fluid

movement or residual width. The final Closure Pressure changes in the case of a propped fracture and will be equal to theminimum horizontal stress plus the additional net pressure caused by introducing proppant to the created fracture, thusincreasing width. Many engineers mistakenly use the value of ISIP (Instantaneous Shut-In Pressure) obtained during pre-fractesting or early fracture stimulation (e.g. pad portion of the stage) to represent Closure Pressure. It is important to note that atthe point of ISIP the fracture is still open, and thus, the actual fracture closure pressure (to zero width on an unproppedfracture) will be a value less than the ISIP. Only if the fracture width at the moment of ISIP is, by coincidence, identical tothe width after closure on a proppant pack, can this value be used to estimate the stress on proppant. If the wrong closure

pressure is used during the stimulation treatment, then all calculations and plots, such as a Nolte or net pressure plot, will beincorrect.

Fracture Toughness and Critical Stress (Tensile Strength)

The criteria for fracture propagation is based on the concept of stress intensity factor I K for Mode I failure. In hydraulic

fractures, propagation is assumed to occur once the stress intensity factor reaches a critical value. This critical value is

related to the propagation resistance (or energy balance) and assumed to be a material property and is given the name“fracture toughness” (or critical stress intensity factor). Fracture toughness is not the same as tensile strength, but the two

parameters can be related. The basis for this relationship involves the assumption that pre-existing defects exist and inducehigh stress concentrations in their vicinity. Thus the fracture will propagate when the stress intensity factor equals the

fracture toughness, IC K , or the stress intensity equals the critical stress of the rock: I IC K K or I IC , whichever isgreater, (Vejbæk et al. (2013)).

Thus, the net pressure in the crack (fracture) must overcome this critical value to propagate c IC p K H . Defining

a minimum critical stress as the minimum stress value for failure to occur based on a maximum effective crack length of c H ,

we have minc IC cK H . The critical stress is the minimum stress ( minc ) for the fracture to propagate in the vicinity

of a constant stress field. This parameter may also be thought of as the apparent tensile strength ( minc t ) since it is the

critical stress that must be overcome for the crack to propagate (in a uniform stress field). Fig. 4 illustrates that as the fracturedimensions increase either the maximum of the critical stress (calculated from the fracture toughness) or the minimum criticalstress (i.e., tensile strength) will determine the stress intensity factor.

Fracture Design Parameters

Fluid & Additive Design

Hydraulic fracturing fluids are designed to transmit hydraulic pressure from the surface to the tip of the propagatingfracture(s) and transport proppant from the surface to the fracture. The job design is more complicated than simply using thefluid to transport proppant. The treatment design uses a sophisticated schedule of proppant concentration to optimize

proppant placement in the fracture, promoting high fracture conductivity. Historically, conventional reservoir fracturingrequired well designed, viscous fracturing fluids that could carry high volumes of proppant needed to establish highly

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conductive proppant packs. The shift from conventional to unconventional reservoirs such as coal-beds, tight gas sands and

later gas and liquid-rich shales radically changed the design criteria of the fracturing fluid, particularly a shift from viscous-

based fluids to high-rate capable, non-viscous fluids needed for slick-water fracturing.

Fig. 4 – Critical Stress Propagation Dependence On The Minimum

Critical Stress (Tensile Strength) and Fracture Toughness

As a guide for designing well-defined fracturing fluids, the API RP-39 was established as the industry standard for testing

fracturing fluids. API RP 39 was later upgraded with the following ISO (International Organization for Standardization)

documents.

ISO 13503-1: Measurement of Viscous Properties of Completion Fluids

ISO 13503-3: Testing of Heavy Brines

ISO 13503-4: Procedure of Measuring Stimulation and Gravel Pack Fluid Leakoff Under Static Conditions.

Based on success in the Barnett, fracturing designs and fracturing fluids were radically changed in a number of resource

plays. The primary driver for this shift is the belief that successful stimulation required extensive reservoir contact or fracture

networks in the shale rather than a bi-wing fracture. In addition, the permeability contrast between the fracture and the ultra-

low permeability of the gas shale, normally in nanoDarcy range, is so large that fracture conductivity compromises have been

tolerated. Consequently, part of these compromises included fluid designs that carry much lower proppant loadings,normally maximum capacity ranging from 1-2 lb proppant per gallon treating fluid, as well as smaller size proppant such as

70/140 and 40/70. Based on these drivers, frac designs evolved, using high rate fluids for proppant placement and negating

the need for viscosity. This also required tremendous volumes of fluid to place the proppant and create the desired fracture

network. Fluid designs also shifted from using guar gum based fluids with viscosity that could range from 10’s cP for lineargel to 100’s cP for crosslinked gels, to new fluids based on low concentrations of polyacrylamide (75 to 300 parts per

million) for friction reduction needed when pumping fluids at high rates, creating the term “Slickwater”. In contrast, the

viscosity of slickwater ranges in the 1’s cP. However, as the slickwater fracturing process evolved, late stage pumping beganusing low viscosity fluids to improve the near-wellbore conductivity with more and larger size proppant. This practice

further evolved, using complex crosslinked fluids in the hybrid fracs for the same purpose, to pack more proppant (and larger

diameter proppant) in the fracture in the late stages of the frac. The pumping of these complex fluids, normally borate-

crosslinked guar gums, on the tail-end of each stage did not require long-term gel stability. These fluids were built to provide

some viscosity but also to be easily degraded. Consequently, the fluid formulations were designed without relying on ISO

13503-1 guidelines and normally based on a viscosity profile measured at a single shear rate.

As gas prices deteriorated, emphasis shifted from gas shales to liquids-rich shales, relying on many of the principles

developed for shale gas fracturing. However, oil/condensate, having substantially less mobility than gas, requires the

fractures possess higher conductivity. Crosslinked fluids are commonly used for a larger portion of the treatments targetingoil plays, so that higher concentrations and larger diameter proppants can be placed. Borate crosslinked guar gum is the

preferred fracturing fluid for this application with gel loadings often ranging from 15 to 30 lb per 1000 gal. In order for these

fluids to provide the necessary viscosity needed for shale oil fracturing, the fluid design should be based on ISO 13503-1

guidelines and with particular focus on the Power Law indices, n’ (flow-behavior index) and K’ (consistency index), as a

guide in the rheological assessment of the fluid. In particular, the fluid should be formulated with the n’ range from 0.4 to0.7 and the K’ exceed 0.01 lb-secn’/ft2 through most of the pump time. Without using the Power Law indices as a fluid

formulation guide, borate crosslinked guar gels can appear viscous but exhibit shear thickening behavior with n’ exceeding

1.0, indicating a poorly designed fluid. By utilizing the Power Law indicies, the crosslinking buffer and borate crosslinkerloadings can be adjusted to provide higher-stability fluids, especially since the formulation should also include a breaker

designed to slowly degrade the fluid.


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SPE 166107 9

The breaker schedule and type can be the most critical feature of the fluid design. There are a number of breakers that areavailable including persulfate, encapsulated persulfates, chlorites, organic hydroperoxides, alkaline earth peroxides andenzymes, each having their specific stability and temperature requirements. There is normally a compromise between initialfront-end stability for the fluid to perform its functions and the later degradation of the fluid to allow well clean-up.

Regardless of the fluid design, slickwater or viscosity-based, the fluid will also contain an array of other treatnment additives,each needed to prevent reservoir specific flow impairment after the treatment. Common additives will include a biocide, clay

control additive, scale inhibitor and flow-back surfactant additive, each additive and loading depending on the reservoir beingtreated. Furthermore, the additive application, type and loading are often scaled as a way to adjust the cost of the treatment.To insure that adequate volumes of water are available at low cost, the water quality is often compromised requiring thetreatment to always include a biocide, particularly to control sulfate reducing and acid producing bacteria. The two mainmodes of bacteria control are the use of short-lived oxidizing agents such as chlorine dioxide, peracetic acid or ozone orlonger lasting chemical agents such as dibromonitropropamide (DBNPA), Glutaraldehyde, Glutaraldehyde-surfactant-basedquaternary ammonium chloride mixtures, tetrakis (hydroxymethyl) phosphonium sulfate (THPS) and Dazomet. Theselection of the biocide is often based on previous field success or cost.

The inclusion of the treatment additives in the fracturing fluid was initially done to protect the reservoir from the invasion ofthe fracturing fluid and assist to clean-up after treatment. Since hydraulic fracturing is an opportunity to place these additivesdeep in the reservoir, the additives used today are expected to provide longer-term protection before production chemicalintervention is required. To determine the longevity of the additive, many companies have resorted to post-fracturingsampling and analysis to include, for example, scale inhibitor residuals, bacteria counts, surface tension and general water

analysis. These results are used to drive a continuous improvement of the additive selection.

Proppant Design

Proppant design has been a subject that has been published on numerous occasions, and therefore, this paper will not attemptto repeat the results and experimentation pertaining to that work. This paper will address the factors which are consideredcritical to proper proppant design and references will be cited, to provide the reader with complete information.

If we were to summarize the characteristics associated with an “Ideal Proppant”, i.e. one that will fit all applications, the listwould include high strength and crush resistance, high conductivity, durable conductivity, complete system compatibility, noembedment or flowback, nearly buoyant, plentiful, and low cost. While several of these criteria are extremely important,such as crush resistance & high strength, no flowback, complete system compatibility, and cost effectiveness, the truth is thatthe Ideal Proppant simply does not exist!! There is not a proppant manufactured or mined today, that can accomplish all ofthese items for every application and still be cost effective.

Selecting the proper proppant (-Quartz, Resin Coated (RC) Proppant or Ceramic) cannot be performed by looking at asingle reservoir/formation parameter, such as stress, as this approach will rarely yield the optimal completion. For givenvalues of closure stress and also because of the rock mechanics associated with differing formations, many of the selectionfactors discussed below cannot be eliminated, nor can they be used solely for optimal proppant selection. Consequently,

proper engineering is a critical step in assuring optimal conductivity within the in-situ fracture by minimizing the effects ofthose selection factors over which control is limited.

Infinite vs. Finite Conductivity

The terms “infinite” and “finite” conductivity refer to the relationship between the flow capacity of the fracture to thedeliverability of the formation. Mathematically, this ratio is simply the Dimensionless Fracture Conductivity (see Equation16 below – C f D). As C f D increases, the drawdown pressure effectively transmitted to the fracture face increases and the

reservoir will deliver more hydrocarbons. However, there are diminishing returns, and at some point is C f D so high that thefracture flow capacity “outruns” the deliverability of the formation. When this occurs, the conductivity is considered“infinite” when compared to the formation deliverability. In other words, increasing the conductivity further will not producea significant increase in production. Conversely, a fracture that has “finite” conductivity will see an increase in production ifconductivity is increased.

For many years it was thought that many hydraulic fractures were “infinite” conductivity. Many also mistakenly believe thesame thing about the hydraulic fractures placed in most of today’s ultra-low permeability unconventional reservoirs.However, it is well documented that this simply is not the case. As the industry has come to understand and model thedifference between reference (API/ISO) conductivity measurements, and actual realistic conductivity of the fracture, it is nowapparent that most fractures have “finite” conductivity, or are “conductivity-limited” (Palisch 2007). This means that even inthe unconventional reservoirs, particularly those that produce liquids or condensate, increasing the fracture conductivity willincrease production - the only question is whether it is economic to do so (Palisch 2012).


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Depth/Closure Stress

The vast importance of depth and closure stress and its ultimate effect on conductivity cannot be overlooked whenconsidering proper proppant design. At some point all proppants undergo breakage of the individual grains through naturalstresses and depletion, temperature, induced cyclic stresses due to variable flowing conditions, or workovers executed withless than best practices. Regardless of the source the sudden changes in effective closure stress, the strength of the proppantmaterial can easily be exceeded. Even the highest quality quartz proppant is weaker than most ceramic proppants, but bothcan be seriously damaged by sudden changes in effective stress. This results in lost and unrecoverable flow capacity, i.e.

fracture conductivity. Additional damage to productive capacity occurs due to the movement of very fine broken grains, orfines, which are transported through the pack by higher flow velocities resulting from damaged pack permeability. These

produced fluids are capable of moving fine proppant shards through the pack and further damaging productivity by pluggingadditional conductivity.

In a paper presented by Syfan and Anderson (2011), six well conditions and proppant selection criteria were identified thatinfluence obtainable conductivity. The six factors include closure stress, temperature, proppant concentration, proppantstrength, proppant particle size, and proppant grain shape. A paragraph explaining the importance of proppant durability isalso included. The results of that work are presented below in the following paragraphs and are also explained in furtherdetail in the procedure provided in ISO 13503-5. ISO 13503-5 takes each one of these six factors into account when

performing a conductivity test on a specific proppant.

The number of specific proppant articles that address these six factors is extremely well documented with over 300 specific

articles in the petroleum literature since 1980. For time’s sake, a synopsis of much of the literature is available from Holditchet al. (1989) Anderson and Phillips (1988) and Palisch (2007).

Closure Stress

Natural alpha-quartz (-quartz) Northern White (NW) proppants with roundness and sphericity values (Krumbein factors)greater than 0.6, will begin to fail at as little as 4,000 psi, even when tested under ideal conditions with wide fracturesuniformly loaded with proppant and subjected to stable stresses for short time periods. Brown sands usually tend to fail atmuch lower closure pressures due to the inclusion of additional minerals such as iron and feldspar. The quartz grains willcontinue to break or crush to a point in which the amount of fines generated reaches and exceeds 10% of the original

proppant. This value, documented in ISO 13503-2 guidelines, is referred to as the K-Value.

K-value is determined by performing several crush resistance tests on a proppant sample, with the amount of fines generatedrecorded for each test. Closure stress or load is increased in 1,000 psi increments on subsequent tests until such a load isreached at which the amount of fines generated exceeds 10% by weight of the sample. Verification of the stress at 10% finesis accomplished by lowering the stress by 1,000 psi and repeating the test on a new sample. This process of reducing thestress and repeating the test is continued until the stress at which the fines generated exceeds 10% is bracketed by crush testsat two consecutive stress levels. The k-value is the stress at which the amount of fines generated does not exceed 10%. Forexample, if a 20/40 quartz proppant has 9.3% fines at 7,000 psi closure stress and then at 8,000 psi closure stress has 10.5%fines, the associated K-Value for that proppant would be 7K. It has been observed that certain high quality NW mines

produce 40/70 quartz proppants capable of withstanding loads in the 11,000 psi range before the fines generated numberexceeds 10%, thus a K-Value of 11K.

It is important to clarify however, that a 7K 20/40 ISO Crush DOES NOT mean that these proppants will optimally perform at closure stresses of these magnitudes. K-Value is simply a relative number and can only be used for comparison purposes if the two samples have exactly the same mineralogy and sieve distribution. Coulter and Wells (1972) indicatedthat as little as 5% fines in the proppant pack can reduce flow capacity as much as 60%! In the end, conductivity

requirements and performance at downhole conditions should be the primary tool for optimal proppant selection.

Durability

G. S. Penny (1987) documented that the elements of both time and temperature at closure pressure are major contributors tolong-term conductivity decline. With time, all proppants lose permeability due to proppant pack rearrangement, stresscracking, and solubility. Penny’s research led to the implementation of the “modified API conductivity test”, which (amongother changes) increased the test time at each stress in the API test from 15 minutes to 50 hours. This modification was laterformalized in API RP19D and ISO 13503-5. However, work by several additional authors (Cobb (1986), Hahn (1986),Montgomery (1985)) indicated that while the bulk of the conductivity loss may occur in the first 50 hours, long term theconductivity continues to drop albeit to a much smaller degree. In addition, the severity of this conductivity loss is dependenton many factors, including proppant type. A quality ceramic will be least impacted, followed by quality resin coated sand,with an uncoated sand experiencing the highest conductivity loss due to time (Handren (2007)).


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SPE 166107 11

Temperature

Another consideration when choosing proppants centers on the reservoir temperature. The original API conductivity test wasdesigned to be performed at “room temperature”. However, another modification proposed by Penny (1987) was to increasethe temperature. The current API/ISO test procedure now calls for a temperature of 150° F for uncoated frac sands, and 250°F for resin coated sands and ceramics. Testing performed by the StimLab Consortium indicated that the conductivity ofsand-based proppants (uncoated and coated) is adversely affected once the temperature exceeds 200° F (ceramic proppantswere found to be unaffected by temperature, likely since they are sintered at >2000° F). It is worth noting that the impact can

be severe. As an example, at Eagle Ford conditions of 275° F and 7000 psi stress, uncoated 20/40 white sand will lose over50% of its conductivity compared to the baseline 150° F test (Pope 2009). At Haynesville conditions the impact is evenworse.

Proppant Concentration

Proppant concentration refers to the amount of proppant per unit area of fracture wall as measured on one side only. Incustomary units it is expressed in pounds of proppant per square foot of one wall of the fracture. If proppant settles to the

bottom of a vertical fracture as it enters the fracture, the width will be highly influenced by the hydraulic/dynamic width atthe time of settling, i.e., during pumping. If the proppant is suspended in the fracturing fluid until the fracture closes,concentration will be determined by both the width during pumping and the concentration of proppant in the fluid (Palisch2008). It is well documented that fracture conductivity increases with increasing concentration of proppant in the fracture.

Proppant Strength

It is a truism to state that the strength of proppants is of major concern in the design of propped fractures. Historically, particle strength has been represented in terms of the load required to crush a single grain of proppant. However proppantsdon’t act as single grains nor are they used as single grains, but rather proppants are used in multi-layers. Since the strengthof single grains is essentially meaningless as a measure of proppant load bearing capacity in a fracture, a test procedure wasdeveloped to observe and record the behavior of proppants in confined packs. The technique developed is called CrushResistance (or K-Value discussed in previous paragraphs) and attempts to measure the amount of fine particles observed afterexposing a proppant pack to a known stress or load. Within the last few years a new set of acceptability standards for usewith crush resistance testing has been published in conjunction with the ISO 13503-2. The data can also be found in API RP-19C which replaces the now obsolete API RP-56 procedure.

While useful for comparison, caution must be used when using crush test results alone for selection proppant. There aremany identified nuances with the crush test that can lead one to the wrong proppant when the test results are incorrectly

employed (Palisch 2009). Crush resistance testing finds it’s most redeemable use as a quality control tool to assure end usersthat the quality of the material mined or manufactured today is consistent with past supplies. Sand mines may use them forqualification purposes, and ceramic manufacturers use the results to ensure consistent quality. The crush test procedures have

been discussed at great length in the literature over the last few years and many new ideas have been proposed to bring these procedures into agreement with long-term conductivity performance.

Proppant Particle Size

If nowhere else does size matter, it is in the business of selecting proppant for the long-term productivity of the well at hand(Syfan & Anderson 2011). The adage “bigger is better” is debatably true and is probably more likely. From a flow capacity

point of view “bigger is better” with one caveat, at a sufficiently elevated stress level the long-term conductivity of all sizesof like proppants begin to look the same. For example, at higher stresses, a 20/40, 30/50 and 40/70 sand will eventually havesimilar conductivities, as the proppants are crushed. To achieve the conductivity advantage of larger diameter proppants athigher stresses, one must typically make the change to a stronger proppant type. While most proppants are characterized by a

mesh “distribution” – i.e. 20/40 or 30/50, there still can be a large performance difference even within the same meshdistribution. As an example, a well known 20/40 premium lightweight ceramic is actually a “two-screen” proppant, withover 90% of the particles actually falling between the 20 and 30 Mesh screens, where as a 20/40 standard lightweight ceramic

proppant may have 90% of the particles between the 20 and 35 Mesh screens. The conductivity difference between these twosized proppants is substantial. Furthermore, most premium resin coated sand utilizes a “coarse” distribution (particlesskewed to the large side of the distribution) to ensure premium conductivity.

However, with the tremendous shortage of quality white sand, premium RCS and premium ceramics, many other lowerquality products have filled the void, and in many cases, these products are skewed to the finer end of the distribution toincrease yield and drive down costs. However, this comes at a cost to performance, as just moving from a coarse to a finedistribution can yield a noticeably large drop in conductivity.


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12 SPE 166107

Proppant Grain Shape

Of the various observed properties of proppants, the significance of grain shape is arguably the least appreciated. If weexamine a typical grain of high quality, sintered ceramic proppant, the observed result is a relatively smooth, nearly spherical,and very round particle. There is at least one property of ceramic proppants which should be considered as desirableregardless of the type of proppant selected. The grain shape of high quality man-made ceramic proppants possess roundnessand sphericity values of 0.9 each, much higher values than are typically found in naturally occurring proppants. A near-

perfectly round and spherical particle under load provides the highest sustainable porosity and therefore permeability and

conductivity possible with solid particles.

Minimum Krumbein factors as established in the ISO 13503-2 guidelines are greater than or equal to 0.6. It is noteworthythat proppants with Krumbein factors less than 0.6, may actually exhibit higher conductivity values at very low closurestresses (under 2,000 psi). Due to the angularity of the particles the proppant grains do not pack as well, thus increasing

porosity and permeability. However, proppant grains fail via point-to-point loading. Therefore, as closure stress increases,the proppant grains fail quickly and result in fines in the proppant pack causing severe reductions in permeability andconductivity. It should also be noted that while the above discussion centers on high quality proppants regardless of type,with the rapid increase in demand over the past several years many lower quality proppants have entered the market. These

proppants may exhibit lower shape values than typically expected, dipping into the 0.7-0.8 for low quality ceramics, and lessthan 0.5 for low quality quartz sands.

Formation Ductility/Embedment

The stress or load transmitted to the proppant pack during fracture closure causes shifting or rearrangement of the particle pack as the excess liquid is squeezed into the porosity of the reservoir, or as fluid is returned to surface during flowback. Asthe relative porosity reaches the range of about 30% for spherical or nearly so materials the individual grains begin toexperience mechanical stress or load from the surrounding fracture walls. When the transmitted load exceeds the embedmentstrength of the reservoir rock, which is a function of the Brinell Hardness, the grains begin to embed in the face of the rock.After embedment has gone as far as it can, the proppant grains must bear the full load of the closure stress.

The damage to fracture conductivity is also explained in detail by Penny (1987) in which he states that any embedment willreduce the effective retained width causing a further reduction in fracture conductivity. He further describes an experimentusing 20/40 Intermediate Density Ceramic which indicated that embedment equal to 1.5 grain widths could account forconductivity reductions in excess of 17%.

While embedment may not be avoidable in some formations, it can sometimes be reduced using curable resin coated

proppants if the proppant mass is correctly consolidated within the fracture before full drawdown stresses are applied. Theresin coating, by consolidating the proppant pack, increases the area of contact between the proppant grain and the formationface which reduces the pressure applied to the fracture wall. Embedment can further be compensated for by decreasing the

particle (mesh) size within the fracture resulting in more grains in contact with the fracture face thereby reducing the load ofeach grain. However, while smaller diameter proppants will have less embedment, there will also be a loss in permeability,so it becomes a trade-off.

Cyclic Stress

Research identifying and quantifying the effects of cyclic fatigue failure of proppants is well documented in the industryliterature. Ouabdesselam and Hudson (1991) studied the effects of time-dependent reductions in fracture conductivity andidentified cyclic fatigue failure as a contributing factor to fracture conductivity reduction and impairment. The data fromtheir study concluded that proppant permeability and fracture width gradually decrease with time as the number of pressurecycles increases as the proppant pack and formation face break down. Further, the effects of cyclic stress fatigue failure areincreased in cases where the in-situ proppant concentration is decreased. Palisch et al. (2007) demonstrated the effects ofcyclic stress fatigue failure and documented the fact that ceramic and resin-coated proppants exhibited much better resistanceto fatigue failure than northern white a-quartz proppants, as depicted in Fig. 5.

Multi-Phase Flow

Most experienced fracture design engineers are familiar with the effect of multi-phase treatment fluids on the friction pressure losses encountered when pumping fluids through small internal diameter tubulars. These fluids include nitrogenwith gelled water foams and oil-in-water poly-emulsion fluids. These fluids exhibited higher than average fluid loss control

properties. The same type phenomena occur in propped fractures where two or more immiscible liquid or gas phases aretrying to occupy the same space. As a point of further reference, there are now sufficient correlations in the literature whichenable the calculation of gross effects of multi-phase flow and add it to the very familiar Forchheimer equation as anadditional factor to high rate gas or liquid flow.


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SPE 166107 13

Documented work from the StimLab Proppant Consortium has shown that as little as 10% liquid in the produced gas streamcan increase the pressure drop per unit length within the fracture over 30 times those values measured for 100% gas flow.These effects must be compensated for when correctly selecting a proppant.

Figure 5 – Conductivity Impacts on Proppants due to cyclic loading (courtesy StimLab)

Non-Darcy Effects

Henry Darcy first developed his famous “Darcy” equation (Eq. 10) in the 1800’s while observing fluid flow through a sandcolumn (Frick 1962).

k

v

L

P

Where, P/ L = pressure drop per length of proppant pack, = fluid viscosity, v = superficial fluid velocity (as if porositywere 100%) and k = permeability of porous media. Since the conductivity test flow rates are laminar (2 ml/min), Darcy’sLaw is successfully applied to calculate the conductivity during this test. However, in 1901 Forchheimer also determinedthat if a fluid rate through a porous media were increased, there comes a point where Darcy’s Law does not fully describe the

pressure drop (Forchheimer 1901). Eq. 11 is Forchheimer’s Equation:

2vk v

LP

Where, = coefficient of inertial resistance, v is the fluid velocity, and = fluid density.

While Darcy’s Law works well in matrix flow in the reservoir, Forchheimer’s equation is necessary to describe the pressuredrop within hydraulic fractures. This is because in typical hydraulic fracture treatments, the fluid velocity is much higherthan that of the matrix, which, since the velocity (v) term is squared, means the Forchheimer pressure drop can quickly makethe Darcy conductivity relatively unimportant. In fact, it has been reported that non-Darcy flow can be of significance in adry gas fracture flowing as little as 50 MCFD (Miskimins 2005).

Critical Fracture Parameters

Fracture SkinFracture Face Skin

Fracture face skin is well documented in the literature from work initially performed by Ramey, Cinco, Gringarten, andMeyer and is represented by Eq. 12:

1

D

r

f

x face

k

k

X

Y Skin

Where, Y x is the depth of the damage along the fracture face, X f is the effective propped fracture half-length, k r is theformation permeability, and k D is the permeability of the damage zone.

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(11)

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14 SPE 166107

Choked Fracture Skin

The choked skin effect as identified by Mukherjee and Economides (1991) due to the radial convergence from a verticalfracture to a horizontal wellbore and can be written as (Meyer et al. (2010)) and presented in Eq. 13:

1ln

2 2ch

f fD w

h hS

x C r

Where, Sch is choked fracture skin, C f D is dimensionless fracture conductivity, h is fracture height, and r w is the wellboreradius. This equation illustrates the parameters affecting choked skin as a result of flow convergence in a vertical fracture tothe horizontal wellbore.

Fracture conductivity does make a significant impact on the productivity index even for high conductivity fractures. This isalso amplified when one considers the radial convergence from a vertical fracture into a horizontal wellbore. The chokedfracture skin given by Eq. 13 is shown to be inversely proportional to the dimensionless conductivity. Thus even forrelatively large fracture conductivities a choked skin will still be present near the wellbore.

Fracture Half-Length and Width

The understanding of proper fracture half-length and width is well documented in the petroleum literature. However, theunderstanding of optimum fracture length and the relationship between fracture fluid production, dimensionless fracture

conductivity, and effective fracture length has not been as well documented (Lolon, Elyezer P. et al. (2003)). Research performed by Lolon et al. (2003) correctly stated that fracturing fluid that remains in the fracture and formation pore spacesafter cleaning up a fracture treatment can reduce productivity by reducing the relative permeability to gas in the regionoccupied by the fracture fluid. They further stated that this invading fluid can damage the formation which results in asignificant reduction in formation permeability at the face of the fracture based on research performed by Tannich (1975) andHolditch (1979).

Their observations and conclusion were based on fractured well simulations which examined the effects of both single phaseand multiphase modeling. In the cases of short fractures, e.g. Lf = 200 ft, the research showed that gas recovery wasapproximately 18% higher for a C fD = 30 than for a C fD = 3, which again is consistent with the topic of this paper. In cases ofmuch longer fractures, e.g. Lf = 800 ft, it becomes apparent that fracture cleanup, and thus longer effective fractures, is muchmore dependent on fracture conductivity. These observations were further substantiated by prior industry research. In theirconclusion, Lolon et al. (2003) stated “Greater dimensionless fracture conductivity results in longer effective fracture lengthsand greater cumulative gas production. This is because fracture fluid recovery increases with increasing fractureconductivity” and “The fracture cleans up faster with higher gas flow rates. However, the effective fracture length is stillaffected more by fracture conductivity than by gas flow rate.”

However, it must be pointed out that increasing fracture lengths past the optimum length, may increase gas recovery but inturn reduce the well’s Net Present Value and Rate-of-Return. Holditch et al. (1978) correctly pointed out that as effective

propped length increases, the initial flow rate and ultimate recovery are usually increased. Holditch also pointed out that the bigger the fracture treatments the better! Summarizing, if the created and effective propped fracture are greater than theeconomic optimum effective length, then while the production and ultimate recovery are better, the economic results from thewell can be reduced.

Gidley et al. (1989) outlined a procedure to calculate the optimum effective fracture length, and thus, optimum economic benefit for a given well. In order to calculate the optimum fracture length and also well spacing for a given well andreservoir, it is necessary to (1) predict the propped fracture lengths for a reservoir as a function of hydraulic fracturing costs,

(2) use appropriate reservoir simulation to predict the well performance as a function of fracture length, and (3) to perform aneconomic assessment of each case considering total drilling and completion costs (which includes fracturing costs for eachscenario), operating expenses, and well performance. Once this is done, graphs comparing NPV to fracture length can beconstructed to determine the optimum length.

Fracture Width

Perkins and Kern (1961) presented classic discussions and calculations dealing with fracture extension pressures andresulting fracture width for Newtonian fluids in laminar and turbulent flow, represented by Eqs. 14 and 15, respectively.Since that time, calculation of width has been researched and published by many authors and is well documented in the

petroleum literature.

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SPE 166107 15

4/1

38.0

E

LQW

Where, W is the maximum crack width, Q is the total pump rate, is the effective fracture fluid viscosity, L is the length of avertical fracture, and E is the Young’s Modulus of the rock.

4/1

2

6.0

H E

LQW

f

Where, f is the specific gravity of the fracturing fluid and H is the height of a restricted, vertical fracture.

Fracture Conductivity

The formula for fracture conductivity is extremely well documented in the petroleum literature and has the universal symbolof w*k f , where “w” is the width of the created fracture in feet multiplied by the permeability (k) of the proppant pack (orfracture, “f”) in millidarcies. Conductivity is arguably the most important with respect to critical fracture parameters. The

permeability-thickness of the formation becomes inconsequential, no matter how high its value, if the conductivity of thecreated fracture is so finite as to limit the well’s productive rate.

The laboratory measurement of long-term fracture conductivity is fraught with difficulties, inconsistencies and otherseemingly insurmountable issues. Among these is conflicting data from different sources, and the stretching of verifiedtechniques to provide answers the procedures were never capable of providing. In order to eliminate these difficulties andinconsistencies, the procedures for measuring long-term fracture conductivity were outlined in detail in ISO 13503-5guidelines.

Dimensionless Conductivity

Laplacian solution methodology for predicting the flow behavior of multiple transverse finite-conductivity vertical fracturesintercepting horizontal wellbores was utilized for the case studies included in this paper. The solution accounts for the highinitial production from multiple transverse fractures and matches the late time production decline as a result of fractureinterference.

The dimensionless fracture conductivity (C fD) is the main parameter that quantifies the hydraulic fracture effectiveness (i.e.,

the reservoir is linked to the wellbore through a finite conductivity vertical fracture). The dimensionless fracture conductivityis given by Eq. 16.

f

f f

fD xk

wk C

In the above equation, f f k w is the fracture conductivity (md-ft), k is the equivalent reservoir permeability (md), and f x is

the propped fracture half-length (ft). The dimensionless pseudosteady-state solution for a finite conductivity vertical fracturein an infinite reservoir from Meyer et al. (2005) is given by Eq. 17 and discussed in the following paragraphs:

1 4

ln2

D Dxf fD p t f C

e

Where, the pseudo-skin function, fD f C and the effective wellbore radius, w f r x , for a uniform finite-conductivityfracture in a homogeneous infinite reservoir are given by and presented in the following equations:

ln 2 fD fD

f C C

and

1

2w

f fD

r

x C

The effective wellbore radius for infinite conductivity fracture fDC is 1 2w f r x . The effective dimensionless

wellbore radius and dimensionless pseudo-skin function as function of the dimensionless fracture conductivity are shown in

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(14)

(15)

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16 SPE 166107

Fig. 6 and Fig. 7, respectively. These figures illustrate that w f r x and fD f C are strong functions of the dimensionless

fracture conductivity (i.e. 10 fDC ). That is, as the conductivity increases w f r x increases and fD f C decreases.

The dimensionless pseudosteady-state solution for finite conductivity vertical fracture in a closed reservoir is shown in Eq.18:

2 1 D DA D p t J

Where,

1 ln e D xe fD f

x J f C

x

,

ln fD x

fD

f C I C g

, and f

w f r x e

McGuire and Sikora (1960) published an iconic paper on "The Effect of Vertical Fractures on Well Productivity" that

demonstrated the productivity benefits from hydraulic fracturing as a function of fracture penetration ( x f e I x x ) and

relative fracture conductivity. Figs. 8 and 9 present a comparison of work referenced in a paper presented by Syfan andAnderson (2011) with the published data of various authors including McGuire and Sikora as a function of fracture

penetration and dimensionless conductivity. These figures clearly indicate that as conductivity and penetration increase so

does the dimensionless productivity index. Also for full penetrating fractures ( 1 x I ), the productivity index does not

asymptote to a maximum value until the fracture conductivity approaches approximately one-hundred (i.e. 100 fDC ) for a

drainage area aspect ratio of unity ( 1 ) and approximately one-thousand ( 1000 fDC ) for an aspect ratio of ten ( 10 ).

The role of fracture conductivity as an important design criterion is often overlooked in shale plays. Even for low permeability formations the dimensionless fracture conductivity is often much greater than the optimum value as initially proposed by Prats et al. (1961) and later by Economides et al. (2002). The optimum dimensionless conductivity for various

penetrations and fracture drainage aspect ratios is given by 4 1 1 fDopt

C which for a square drainage area ( 1 )

is 2 fDopt

C .

Figure 6 - Dimensionless effective wellbore radius for a finite-

conductivity vertical fracture - Comparison with the work of

Economides, Barker, Cinco-Ley, and Riley et al.

Figure 7 – Pseudo-skin function versus dimensionless

conductivity – Comparison with the work of Economides,Barker, Cinco-Ley, and Riley et al .

Case Histories

The case histories chosen to illustrate the points discussed in this paper are further documented in SPE 131732. Case A is aMarcellus Shale example showing history matched production and an economic analysis. Case B is an Eagle Ford Shaleexample discussing the history matched production and the effects of varying fracture conductivities. Cases C and Drepresent the Bakken and Cotton Valley, respectively, where production rates and cumulative production volumes are

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SPE 166107 17

calculated from known reservoir values and characterize changes in ultimate recovery and initial production rate from variousdimensionless fracture conductivities. The economic parameters used to calculate economic results are presented in Table 3.

Figure 8 - Dimensionless productivity index as a function of

dimensionless conductivity and penetration for a squarereservoir - Comparison with the work of Holditch, McGuire &

Sikora, and Valko et al.

Figure 9 - Dimensionless productivity index as a function of

dimensionless conductivity and penetration for a rectangularreservoir with an aspect ratio of ten - Comparison with the

work of Valko and Economides (1998).

The values presented in Table 3 are the actual values used in the analysis of the well. The authors freely acknowledge thatwhile some of the values presented may have changed in today’s economic conditions, but the trends that they represent areaccurate.

Table 3 – Economic Parameters

Parameter Value

Fracture Fluid Unit Cost, $/U.S. Gal. 0.30

Proppant Unit Cost, $/Lb. 0.28

Other Well Drill & Complete Cost, $K 2,000Gas Price, $/Mscf 3.75

Working Interest, % 100.0

Revenue Interest, % 80.0

Case A – Marcellus Shale

The Marcellus Shale may arguably be the largest shale in the continental United States with an aerial extend of approximately54,000 sq. miles and extends through Pennsylvania, New York, Ohio, Maryland, and West Virginia. Engelder (2009)

predicted that the Marcellus Shale may ultimately hold 489 Tcf of natural gas reserves.

Case A references a Marcellus Shale completion that was completed with seven (7) hydraulic fracture stages containing five(5) perforation clusters per stage over a horizontal lateral length of 2,100 ft. The reservoir and hydraulic fracture parametersfor Case A are presented in Table 4. The production data for the well in Case A were history matched using a single-phase,analytical reservoir simulator for multiple transverse finite-conductivity fractures including a choked fracture skin. Thehistory matched parameters are given in Table 5.

While the history matched production only covers a period of 201 days, the predicted values for these parameters seems to bereasonable with respect to the fracture treatment, fracture fluid efficiency, and expected reservoir permeability for this type ofreservoir. The reservoir permeability predicted from the history match is 583 nD (0.583 microdarcies) which yields areservoir capacity (permeability-thickness) equal to 0.094 md-ft. The propped effective fracture length was calculated to be320 ft with a fracture conductivity of 3.77 md-ft. These values are also believed to be reasonable based on the fracturetreatment pumped. The choked fracture skin was calculated to be +0.096 which is not unreasonable considering that thesefracture treatments are over-flushed and are subjected to further over-flushing from composite plug pump downs.


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18 SPE 166107

The dimensionless fracture conductivity (C f D) calculated from the history match is equal to 20.2, which represents a mediumfinite-conductivity fracture. To illustrate the points made earlier in this paper, the C f D was plotted using values of 2, 20, and200. The production rate and cumulative gas production for Case A are presented in Figs. 10 and 11.

Table 4 – Case A: Marcellus Reservoir and Fracture Parameters

Description Value

Reservoir Depth, ft 7,876

Reservoir Thickness, ft 162

Hydrocarbon Porosity, % 4.2

Reservoir Pore Pressure, psi 4,726

Reservoir Temperature, oF 175

Drainage Area, acres 80

Aspect Ratio (xe/ye), dimensionless ¼

BHFP, psi 1,450 – 530

Wellbore Radius, ft 0.3646

Lateral Length, ft 2,100

Number of Stages 7

Number of Clusters/Stage 5

Table 5 – Case A: Fracture and Reservoir History Matched ParametersDescription Value

Reservoir Permeability, nD 583.0

Reservoir Capacity (kh), md-ft 0.94

Effective Propped Length, ft 320

Fracture Conductivity, md-ft 3.77

Dimensionless Conductivity 20.2

Choked Skin, dimensionless +0.096

Number of Equivalent Fracs 6

Diffusivity, md-psi/cp 4000

Figure 10 – Case A: Predicted Gas Production Rate Figure 11 – Case B: Predicted Cumulative Gas Production

The figures point out that a lower achieved value for dimensionless fracture conductivity equal to 2 or a much higher valueequal to 200 yield significant variances in gas rate and cumulative production. Initial production rates varied from just over3.0 MMscf/day for the high conductivity case to 330 Mscf/day for the low conductivity case which yields 10-year cumulative

production equal to 2.9 Bscf and 0.9 Bscf, respectively, for the high and low conductivity cases.

The economic evaluation of Case A is based on an analysis assuming that the proppant cost is a linear function of fracture

conductivity ( f f k w ). Although this may be a very simplistic assumption it illustrates that increased proppant conductivity

does increase the total job cost. The proppant cost was taken from the actual job cost based on a history matched fracture


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SPE 166107 19

conductivity of 3.47 f f k w mD-ft (i.e. 20 fDC ) (Jacot et al. (2010)). The economic analyses are based on the Net

Present Value (NPV = DWR – CF) and Discounted Return on Investment (DROI = DWR/CF) where DWR is the DiscountedWell Rate and CF is the fracture treatment cost.

The fracture Net Present Value (NPV) and Discounted Return on Investment (DROI) as a function of fracture conductivityand producing time are shown in Fig. 12 and Fig. 13, respectively. The NPV and DROI are shown to increase with time butreach maximum values as a function of fracture conductivity. At five years, the optimum conductivity to maximize the NPV

($5MM) and DROI (1.5) are about 5 f f k w mD-ft ( 29 fDC ) and 4 f f k w mD-ft ( 23 fDC ), respectively. Figs. 12 and

13 also illustrate that for an economic period of five years, the NPV and DROI for a conductivity of 0.347 ( 2 fDC ) are

negative and less than one, respectively. The NPV and DROI for the same period but at a high conductivity of 8.68 md-ft (

50 fDC ) are about $2MM and 1.3, respectively. Fig. 14 and Fig. 15 also illustrate for full penetration fractures designed

with the traditional rule of thumb dimensionless fracture conductivity of about two (i.e. 2 fDC ) may not be economical.

Figure 12 – Case A: Fracture NPV vs. Conductivity Figure 13 – Case A: Fracture DROI vs. Conductivity

Case B – Eagle Ford Shale Example

The Eagle Ford formation is a widespread Upper Cretaceous deposit in the Gulf Coast region of South-Central Texas longknown as a source rock for other plays. Only recently has it been recognized as an unconventional oil and gas play. In SouthTexas, where it has hydrocarbon potential, the Eagle Ford formation is between 5,000' and 13,000' below the surface andranges in thickness from 50' to 300'. Although the Eagle Ford is described as a “shale” formation, the reservoir is actuallycomposed of organic-rich calcareous mudstones and chalks that were deposited during two transgressive sequences (theUpper and Lower Eagle Ford). Total organic carbon (TOC) in the Eagle Ford formation ranges from 1-7%. The organicrichness in the Eagle Ford typically increases with depth. As such, the Lower Eagle Ford tends to be more organically richand produces more hydrocarbons.

The calcareous makeup of this rock makes this play significantly different than other well-known unconventional plays suchas the Barnett Shale, Haynesville Shale, and Marcellus Shale (all of which are found in primarily siliceous environments).

Case B references an Eagle Ford Shale completion that was completed with ten (10) hydraulic fracture stages containing four(4) perforation clusters per stage over a horizontal lateral length of 4,000 ft. The reservoir and hydraulic fracture parametersfor Case B are presented in Table 6. As with the previous case, the production data for the well in Case B were historymatched using a single-phase, analytical reservoir simulator for multiple transverse finite-conductivity fractures including achoked fracture skin. The history matched parameters are given in Table 7.

The Case B well was designed to yield high dimensionless fracture conductivity, as shown in Table 7. The Eagle Ford wellwas completed with a ten stage stimulation using slickwater, linear gel, and ceramic proppant in a 4,000 foot lateral.Composite flow through bridge plugs was used for isolation and four two-foot clusters were perforated per stage (40 clusterstotal). The first and last intervals were shot at six (6) shots per foot (spf) and the middle two intervals were shot at 12 spf.The average treating rate and pressure was about 50 bpm and 8,900 psi, respectively. The proppant concentration for eachstage increased from 0.25 to 1.5 lbm/gallon without any slickwater sweeps. Linear gel was used to place 0.75 to 1.5 pound


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concentration of proppant. Average proppant placed per stage was ~250,000 lbm and 11,300 gallons of water. Productionlogs and chemical traces in the flowback samples indicated that all clusters have somewhat variable production rates;however, the total production from each fracture treatment stage is producing approximately equal volumes. As such, the

production data history matched used forty (40) multiple transverse fractures (ten stages with four clusters per stage).

Table 6 – Case B: Eagle Ford Shale Reservoir and Fracture Parameters

Description Value



Hydrocarbon Porosity, % 5.76

Reservoir Pore Pressure, psi 8,350



Aspect Ratio (xe/ye), dimensionless ¼

BHFP, psi 3,900 – 1,500


Number of Stages 10

Number of Clusters/Stage 4

Table 7 – Case B: Fracture and Reservoir History Matched ParametersDescription Value

Reservoir Permeability, nD 17.2

Reservoir Capacity (kh), md-ft 0.0049

Effective Propped Length, ft 131

Fracture Conductivity, md-ft 0.86

Dimensionless Conductivity 382

Choked Skin, dimensionless +0.0254

Number of Equivalent Fracs 40

Diffusivity, md-psi/cp 153

While the history matched production only covers a period of approximately 93 days, the predicted values for these parameters seems to be reasonable with respect to the fracture treatment, fracture fluid efficiency, and expected reservoir permeability for this type of reservoir. The reservoir permeability predicted from the history match is 17.2 nD which yields areservoir capacity (permeability-thickness) equal to 0.0049 md-ft. The propped effective fracture length was calculated to be131 ft with a fracture conductivity of 0.86 md-ft. These values are also believed to be reasonable based on the fracturetreatment pumped. The choked fracture skin was calculated to be +0.0254 which is considered reasonable based on flushvolumes.

The dimensionless fracture conductivity (C f D) calculated from the history match is equal to 382, which represents a highconductivity fracture. The C f D was plotted using values of 4, 40, and 400. The production rate and cumulative gas

production for Case B are presented in Figs. 14 and 15.

The fracture stimulation treatments pumped on the Eagle Ford Shale in Case B were designed using accurate reservoir andcore data and achieved a high value of dimensionless fracture conductivity. Figures 14 and 15 illustrate this fact and indicatethat a much higher achieved value for dimensionless fracture conductivity equal to 400 yields significant increases in gas rate

and cumulative production. Initial production rates varied from just over 5.0 MMscf/day for the properly designed highconductivity case. This is apparently due to the 250,000 lbs. of ceramic proppant placed per stage, which equates to 2.5MMlbs for the 10 stages pumped. Lower proppant concentrations or lower conductivity proppants pumped into the wellwould result in much lower fracture conductivities and initial production rates. Fig. 14 shows that much lower values ofdimensionless conductivity equal to 40 and 4 result in initial production rates of approximately 940 Mscf/day and 140Mscf/day, greatly reducing ultimate recovery and significantly reduce the NPV and IRR of the well.

Case C – Bakken Example

The Bakken is a rock formation from the Late Devonian – Early Mississippian age. The play covers much of the WillistonBasin in parts of Montana and North Dakota and extends into the Canadian provinces of Saskatchewan and Manitoba. TheBakken formation consists of three layers: an upper black shale layer, middle silty-dolomite, and a lower black layer of shale.The shale layers are petroleum source rocks as well as seals for oil reservoirs in the middle dolomite layer and in the


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Figure 16 – Case C: Bakken Oil Production Rate Figure 17 – Case C: Bakken Cumulative Oil Production

Table 9 – Case D: Cotton Valley Reservoir and Fracture Parameters

Description Value



Reservoir Permeability, D 0.001Porosity, % 7.0

Reservoir Pore Pressure, psi 6.000



BHFP, psi 1,500

Effective Fracture Length, ft 1,500

Fracture Conductivity, md-ft 114

Dimensionless Conductivity 76


Number of Transverse Fractures 7

Figs. 18 and 19 illustrate the fact that increasing values for dimensionless fracture conductivity yield higher initial production

rates and ultimate recoveries in sandstone formations. As with the previous three (3) cases, initial production rate andultimate gas recovery increases as dimensionless fracture conductivity increases from 0.76 to 76. A slight increase in ratesand recoveries is also illustrated as dimensionless conductivity increases from 76 to 760. Again, the Cotton Valley formationshows significant increases in productivity and ultimate recovery again supporting the work presented by McGuire andSikora (1960).

Figure 18 – Case D: CV Gas Production Rate Figure 19 – Case D: CV Cumulative Gas Production


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SPE 166107 23

Summary

It is apparent from the provided technical information and the case histories that proper fracture design and ultimately,fracture optimization, cannot and will not happen without sound engineering practices and an understanding of the manytechnical factors involved in optimum fracture design. Furthermore, without optimum fracture design, it is a truism thatinitial production rates, ultimate recovery, NPV, and rate-of-return will be compromised. The bottom line is that unlesscurrent practices and procedures are changed, highly conductive fractures will not be achieved in a high percentage of the

stimulations pumped !

The importance of this paper centers around this key point: At the end of the day, the horsepower on location is going to rigdown, leave location and head to the next job. The fluid that was injected during the stimulation will be broken, flowed back,removed from location and discarded. The only remaining item is the proppant pack which, depending upon design, may ormay not provide conductivity high enough to maximize initial rate and ultimate recovery. However, if the proppant pack is

properly designed, it can and will last the life of the well.

Conclusions

1. Understanding the rock mechanics associated with the primary zone of interest, in addition to the zones above and belowthe primary zone, is essential to achieving high conductivity fractures.

2. The research presented by McGuire and Sikora (1960) holds true regardless of reservoir type and ultimately dictates

reservoir and production performance.3. Fracture conductivity and dimensionless fracture conductivity ultimately govern the initial production rates and ultimate

recoveries regardless of the type of reservoir lithology.

4. The history matches of the production data from Case A (Marcellus Shale) and Case B (Eagle Ford Shale) illustrate theimportance of achieving high conductivity transverse fractures in a horizontal wellbores.

5. Increasing fracture conductivity, regardless of reservoir type, results in a significant positive impact on IRR and NPV,

Acknowledgements

The authors wish to thank the management of GoFrac LLC, CARBO Ceramics Inc., and Independence Oilfield ChemicalsLLC for the opportunity to perform this research and publish the findings. The authors would also like to thank Bruce R.Meyer for his help and discussions on the theory of fracture propagation and production simulation analysis. The authorswould also like to acknowledge Gerald R. Coulter and James E. Briscoe for their contributions in reviewing and editing this

paper.

Nomenclature

axial = Axial StrainBHFP = Bottonhole Flowing PressureF = FahrenheitC fD = Dimensionless Fracture ConductivityoF = Degrees Fahrenheit

m = Elastic Modulusw = Fracture Widthmd = Milli-Darcy

D = Micro-DarcynD = Nano-Darcy

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