16
Applying complex fracture model and integrated workow in unconventional reservoirs Xiaowei Weng n , Olga Kresse, Dimitry Chuprakov, Charles-Edouard Cohen, Romain Prioul, Utpal Ganguly 1 Schlumberger Technology Corporation,110 Schlumberger Drive, MD-2, Sugar Land, TX 77478, USA article info Article history: Received 26 August 2013 Received in revised form 10 September 2014 Accepted 22 September 2014 Keywords: hydraulic fracturing complex fracture fracture modeling unconventional design workow interaction with natural fractures abstract In this paper we present a comprehensive and yet efcient complex fracture network model that simulates hydraulic fracture networks created during the stimulation treatment and proppant place- ment. The theoretical framework of overall complex fracture modeling is described. The paper then focuses on two critical components of the model that address hydraulic fracturenatural fracture interaction (the crossing model) and interaction between hydraulic fractures (stress shadowing). The details of the model and its validation against experimental data and other numerical simulations are presented. A eld example involving both slick water and crosslinked gel treatment is simulated using the complex fracture model and the results are compared to the microseismic monitoring. Due to the complex fractures generated in stimulation of unconventional reservoirs, proper reservoir characterization is essential to obtain more reliable input to the fracture model and to reduce the uncertainties. Complex fractures also present new challenges for the reservoir simulators to properly model the production through the often partially propped complex fracture networks. To enable efcient development and optimization of the completion strategy and treatment design, the fracture model must be closely integrated in a platform that provides efcient workow to easily build or leverage available geological and geomechanical models as input to the fracture model, calibrate against microseismic measurement, and link to the reservoir simulator for production simulation. This paper presents the integrated workow in which the complex fracture model is built and illustrates the design optimization process through an example. & 2014 Elsevier B.V. All rights reserved. 1. Introduction Economic production from ultra-low permeability unconven- tional reservoirs depends greatly on the effectiveness of hydraulic fracturing stimulation treatment. Microseismic measurements and other evidences suggest that the creation of complex fracture networks during fracturing treatments may be a common occur- rence in unconventional reservoirs (Maxwell et al., 2002; Fisher et al., 2002; Warpinski et al., 2005). It has long been observed in mine-back experiments and core-throughs (Warpinski and Teufel, 1987; Warpinski et al., 1993; Jeffrey et al., 1994; Jeffrey et al., 2009a, 2009b) that hydraulic fracture interaction with natural fractures is likely to result in complex fractures. The created complexity is strongly inuenced by the pre-existing natural fractures and in-situ stresses in the formation. However, due to the lack of industry's modeling capability in simulating complex fractures and lack of proper characterization of key reservoir properties, completion and stimulation design for the unconven- tional reservoirs in the past heavily relied on imprecise estimate of the Stimulated Reservoir Volume (SRV) from microseismic obser- vations and through trial-and-error, a highly inefcient approach. Not being able to accurately simulate complex fractures generated during the fracture treatment presents a major limitation that promotes a cookie-cutter completion and fracture design rather than one that is optimized based on the well conditions and formation properties. Fracture simulation can provide information such as propped vs. unpropped fracture surface area, proppant distribution and conductivity, all of which are critical to the short and long term production from the unconventional reservoir, and cannot be obtained from microseismic measurement alone (Cipolla et al., 2011b). In recent years, new hydraulic fracture models have been developed, or existing geomechanics models adapted, for simulat- ing complex fracture networks in a hydraulic fracture treatment of unconventional reservoir (Xu et al., 2009; Dershowitz et al., 2010; Weng et al., 2011; Meyer and Bazan, 2011; Nagel et al., 2011; Fu et al., 2011; McClure, 2012; Savitski et al., 2013; Wu and Olson, 2013). Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/petrol Journal of Petroleum Science and Engineering http://dx.doi.org/10.1016/j.petrol.2014.09.021 0920-4105/& 2014 Elsevier B.V. All rights reserved. n Corresponding author. Tel.: þ1 281 2858934. E-mail address: [email protected] (X. Weng). 1 Now with Baker Hughes. Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workow in unconventional reservoirs. J. Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i Journal of Petroleum Science and Engineering (∎∎∎∎) ∎∎∎∎∎∎

Applying complex fracture model and integrated workflow in unconventional reservoirs

  • Upload
    utpal

  • View
    214

  • Download
    1

Embed Size (px)

Citation preview

Page 1: Applying complex fracture model and integrated workflow in unconventional reservoirs

Applying complex fracture model and integrated workflowin unconventional reservoirs

Xiaowei Weng n, Olga Kresse, Dimitry Chuprakov, Charles-Edouard Cohen,Romain Prioul, Utpal Ganguly 1

Schlumberger Technology Corporation, 110 Schlumberger Drive, MD-2, Sugar Land, TX 77478, USA

a r t i c l e i n f o

Article history:Received 26 August 2013Received in revised form10 September 2014Accepted 22 September 2014

Keywords:hydraulic fracturingcomplex fracturefracture modelingunconventionaldesign workflowinteraction with natural fractures

a b s t r a c t

In this paper we present a comprehensive and yet efficient complex fracture network model thatsimulates hydraulic fracture networks created during the stimulation treatment and proppant place-ment. The theoretical framework of overall complex fracture modeling is described. The paper thenfocuses on two critical components of the model that address hydraulic fracture–natural fractureinteraction (the crossing model) and interaction between hydraulic fractures (stress shadowing). Thedetails of the model and its validation against experimental data and other numerical simulations arepresented. A field example involving both slick water and crosslinked gel treatment is simulated usingthe complex fracture model and the results are compared to the microseismic monitoring.

Due to the complex fractures generated in stimulation of unconventional reservoirs, proper reservoircharacterization is essential to obtain more reliable input to the fracture model and to reduce theuncertainties. Complex fractures also present new challenges for the reservoir simulators to properlymodel the production through the often partially propped complex fracture networks. To enable efficientdevelopment and optimization of the completion strategy and treatment design, the fracture modelmust be closely integrated in a platform that provides efficient workflow to easily build or leverageavailable geological and geomechanical models as input to the fracture model, calibrate againstmicroseismic measurement, and link to the reservoir simulator for production simulation. This paperpresents the integrated workflow in which the complex fracture model is built and illustrates the designoptimization process through an example.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Economic production from ultra-low permeability unconven-tional reservoirs depends greatly on the effectiveness of hydraulicfracturing stimulation treatment. Microseismic measurements andother evidences suggest that the creation of complex fracturenetworks during fracturing treatments may be a common occur-rence in unconventional reservoirs (Maxwell et al., 2002; Fisheret al., 2002; Warpinski et al., 2005). It has long been observed inmine-back experiments and core-throughs (Warpinski and Teufel,1987; Warpinski et al., 1993; Jeffrey et al., 1994; Jeffrey et al.,2009a, 2009b) that hydraulic fracture interaction with naturalfractures is likely to result in complex fractures. The createdcomplexity is strongly influenced by the pre-existing naturalfractures and in-situ stresses in the formation. However, due tothe lack of industry's modeling capability in simulating complex

fractures and lack of proper characterization of key reservoirproperties, completion and stimulation design for the unconven-tional reservoirs in the past heavily relied on imprecise estimate ofthe Stimulated Reservoir Volume (SRV) from microseismic obser-vations and through trial-and-error, a highly inefficient approach.Not being able to accurately simulate complex fractures generatedduring the fracture treatment presents a major limitation thatpromotes a cookie-cutter completion and fracture design ratherthan one that is optimized based on the well conditions andformation properties. Fracture simulation can provide informationsuch as propped vs. unpropped fracture surface area, proppantdistribution and conductivity, all of which are critical to the shortand long term production from the unconventional reservoir,and cannot be obtained from microseismic measurement alone(Cipolla et al., 2011b).

In recent years, new hydraulic fracture models have beendeveloped, or existing geomechanics models adapted, for simulat-ing complex fracture networks in a hydraulic fracture treatment ofunconventional reservoir (Xu et al., 2009; Dershowitz et al., 2010;Weng et al., 2011; Meyer and Bazan, 2011; Nagel et al., 2011; Fu et al.,2011; McClure, 2012; Savitski et al., 2013; Wu and Olson, 2013).

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/petrol

Journal of Petroleum Science and Engineering

http://dx.doi.org/10.1016/j.petrol.2014.09.0210920-4105/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: þ1 281 2858934.E-mail address: [email protected] (X. Weng).1 Now with Baker Hughes.

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Page 2: Applying complex fracture model and integrated workflow in unconventional reservoirs

However, the process of hydraulic fracture propagation in a forma-tion with preexisting natural fractures is very complex. Realisticsimulation of this process requires proper consideration of the keyphysical elements governing the process that are important forultimate reservoir production, including rock deformation, fracturepropagation, fluid flow in the complex fracture networks, interactionbetween the hydraulic fractures and natural fractures, interactionamong different hydraulic fractures, fracture height growth, andproppant transport in the fracture networks. Although completeand rigorous simulation of all the key underlying processes istechnically very challenging and most models have simplifyingassumptions, it is important that the models capture the mostessential elements so that simulation reasonably represents the realprocess. Today many complex fracture models are still evolving andare applicable to the limited conditions where the model assump-tions are valid, or missing important elements to fully simulate thecomplete fracturing process.

Wide microseismic events cloud as often observed in fracturetreatments in shale is a hallmark of complex fractures. Micro-seismic events are mostly attributed to shear failures along naturalfractures or faults surrounding a hydraulic fracture (Rutledge et al.,2004; Williams-Stroud et al., 2012). The events cloud forms a“halo” surrounding the hydraulic fracture. In conventional sand-stone formations, the observed events cloud has a relativelynarrow width, whereas in unconventional reservoirs a muchwider events cloud is observed (Fisher et al., 2002). A widemicroseismic cloud may possibly be explained by either deep fluidpenetration into natural fractures in the shale while the inducedhydraulic fracture remains planar or simple (Savitski et al., 2013),or by the creation of complex hydraulic fracture network.Although deep fluid penetration into a highly permeable andinitially well-connected natural fractures network is certainlypossible (Zhang et al., 2013), many unconventional plays havevery low effective permeability, and observation of cores showsthat most natural fractures in these shales are healed or miner-alized (Gale et al., 2007; Gale and Holder, 2008; Han, 2011;Williams-Stroud et al., 2012). Therefore, in very low permeabilityshale, fluid penetration in the natural fractures network is limited.Fluid penetration into natural fractures can also occur due todilation of natural fractures as a result of shear slippage, but thistypically occurs under the condition of large stress anisotropy andfor natural fractures oriented 30–601 from the principal stressdirections (Murphy and Fehler, 1986). For many shale reservoirswhere the tectonic environment is relaxed and the differencebetween the horizontal stresses is low, a wide microseismic cloudis a strong indication that complex, open hydraulic fracture net-works are being created, although the hydraulic fractures mayfollow the paths of the natural fractures. The field case in Barnettshale presented by Fisher et al. (2002), in which fracturing fluidunexpectedly connected to and brought down the production ofseveral adjacent wells not on the expected fracture plane providedthe supporting evidence of complex hydraulic fracture networks.In the analysis of a field case in Barnett shale, Cipolla et al. (2010)showed that the predicted fracture length from a planar fracturemodel far exceeded the fracture length indicated by the micro-seismic data, unless a very low fluid efficiency (less than 10%) isassumed in the simulation in order for a planar fracture toaccommodate the large volume of fluid injected. Such low effi-ciency is not consistent with the very slow pressure declineobserved during the shut-in in most shale formations. In contrast,complex hydraulic fracture networks can explain the much largerfluid volume stored in fracture networks for the same fracturelength and yet still high fluid efficiency (low leakoff).

A critical consideration of a complex fracture model is theinteraction between the hydraulic fracture and the naturalfracture. For a formation that initially contains a large number of

well-connected natural fractures, fracturing fluid is directlyinjected into and dilates the existing natural fracture network.In this case, the induced hydraulic fractures follow the naturalfracture network, and relatively few new fracture paths arecreated. To simulate this scenario, modeling of fracture propaga-tion is not required, and a static numerical grid properly modelingthe natural fracture system can be used to simulate the problem.A coupled geomechanics-reservoir model that is capable of solvingthe coupled fracture (or joint) deformation and fluid flow in thefracture networks is well suited for this kind of simulation (e.g.,Nagel et al., 2011). In formations that contain a large number ofisolated or poorly connected natural fractures, the natural frac-tures are only hydraulically activated when intersected by hydrau-lic fractures and then can alter the path or cause branching of thehydraulic fractures. The induced hydraulic fracture that travelsalong an isolated natural fracture can change direction when itreaches the ends of the natural fracture or when it intersects othernatural fractures. In the limiting case when no natural fractureexists in the formation, the induced fractures become planarfractures. To properly simulate the fracture treatment in this typeof reservoirs, the model needs to simulate hydraulic fracturepropagation. A general purpose, complex fracture model musthave the capability to simulate both scenarios, (i.e. includingfracture propagation and interaction between hydraulic fractureand natural fracture).

As evidenced in the mineback experiments, a hydraulic fracturecan cross a natural fracture without change of direction undersome conditions, but may be arrested or branch off along thenatural fracture in other situations (Boyer et al., 1986; Jeffrey et al.,2009a, 2009b). To require a complex fracture model be capable ofsimulating the interaction between hydraulic and natural fracturespresents a major technical challenge for commercial fracturemodels. This is because of the fact that fracture interaction isdriven by the highly localized stress field and natural fractureactivation near the hydraulic fracture tip right before and after itintersects the natural fracture. To model this process numericallyrequires a very fine simulation grid and is computationally cost-prohibitive if each fracture intersection point is to be simulatedaccurately in a large complex fracture networks. Using the typicalreservoir-scale numerical grid cannot correctly represent thefracture interaction unless the simulator builds in a separatecrossing model that can predict the crossing behavior accuratelyand efficiently. An analytical or semi-analytical crossing model isan ideal approach for this purpose.

In this paper, we present a general complex fracture model,referred to as UFM unconventional fracture model that is based onthe same construction as the pseudo-3D planar hydraulic fracturemodel but is capable of simulating a complex fracture networkwith a multitude of propagating fracture tips. An analytical sub-model for hydraulic fracture-natural fracture interaction (alsocalled the OpenT crossing model) that evaluates local activationand re-initiation at a contacted fracture is integrated within theUFM model for crossing prediction (Chuprakov et al., 2013a). Thecrossing model takes into account fluid flow and viscosity effectand is validated against the experimental data and independentfine-grid numerical simulations. Integration of the analyticalcrossing model into the reservoir-scale UFM model makes themodel computationally efficient and also properly captures thefracture interaction behaviors. We also discuss the modeling ofinteraction among the hydraulic fractures, the so-called stressshadow effect. A field example involving both slick water andcross-linked gel treatment is simulated using the UFM model andthe results are compared to the microseismic monitoring.

The introduction of complex hydraulic fracture models providesa critical component by which to integrate the completion andstimulation treatment with microseismic interpretation, production

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎2

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 3: Applying complex fracture model and integrated workflow in unconventional reservoirs

evaluation, and subsequent optimization processes. To enable thisworkflow, the fracture model must be integrated within a softwareplatform that can efficiently bring together geological and petro-physical data to build a mechanical earth model for fracturesimulation, and take the predicted fracture geometry and propertiesto build a reservoir model for production simulation. For thispurpose, the complex fracture model is integrated within stimula-tion design software that enables this workflow. A design optimiza-tion example using the integrated workflow is illustrated.

2. UFM model overview

In this paper, we present a complex fracture network model.It simulates the propagation, deformation, and fluid flow in acomplex network of fractures. The model solves the fully coupledproblem of fluid flow in the fracture network and the elasticdeformation of the fractures, and has similar assumptions andgoverning equations as found in conventional pseudo-3D fracturemodels. But instead of solving the problem for a single planarfracture, the UFM model solves the equations for the complexfracture network. Fracture height growth is modeled in the samemanner as in a conventional pseudo-3D model. A three-layerproppant transport model, consisting of a proppant bank at thebottom, a slurry layer in the middle, and clean fluid at the top, isadopted for simulating proppant transport in the fracture network.Transport equations are solved for each component of the fluidsand proppant pumped. A key difference between the UFM modeland the conventional planar fracture model is being able tosimulate the interaction of hydraulic fractures with preexistingnatural fractures, which will be discussed in detail in the followingsection. Additionally, the UFMmodel also considers the interactionamong hydraulic fracture branches by computing the “stressshadow” effect on each fracture exerted by the adjacent fractures.The hydraulic fracture interaction will be discussed in more detailsin a separate section.

The basic governing equations to be solved include the equa-tions governing fluid flow in the fracture network, mass conserva-tion, fracture deformation, and the fracture propagation/interaction criterion. The mass conservation equation is given as

∂q∂s

þ∂ðHf lwÞ∂t

þqL ¼ 0; qL ¼ 2hLuL ð1Þ

where q is the local flow rate inside the hydraulic fracture alongthe length of any fracture branch, w is an average width oropening of the fracture at position s¼s(x,y), Hf l (s,t) is the localheight of the fracture occupied by fluid, and qL is the leakoffvolume rate through the wall of the hydraulic fracture into therock matrix per unit length (leakoff height hL times leakoff velocityuL) which is expressed through Carter's leakoff model. The fracturetips propagate as sharp front and the total length of the entirehydraulic fracture networks at any given time t is defined as L(t).

The rheological behavior of the injected fluids is characterizedas a power-law fluid with power-law index n0 and consistencyindex K0. The fluid flow could be laminar, turbulent, or Darcy flowthrough proppant pack and is described correspondingly bydifferent laws. For fluid flow along any given fracture branch, forlaminar flow,

∂p∂s

¼ �α01

w2n0 þ1

qHf l

qHf l

��������n0 �1

ð2aÞ

and for turbulent flow

∂p∂s

¼ � fρw3

qHf l

qHf l

�������� ð2bÞ

with

α0 ¼2K 0

ϕ n0ð Þn0 U4n0 þ2

n0

� �n0

; ϕ n0ð Þ ¼ 1Hf l

ZHf l

wðzÞw

� �2n0 þ 1n0

dz ð3Þ

Here w(z) represents fracture width as a function of depth z at thecurrent position s(x,y), and f is the Fanning friction factor forturbulent flow.

Fracture width is related to fluid pressure through the elasticityequation. The elastic properties of the rock (considered as isotropiclinear elastic material) are defined by Young's modulus E andPoisson's ratio ν. For a vertical fracture in a layered medium withpiecewise constant normal stress σi in the ith layer, the stressintensity factors at the upper and lower tips KIu and KIl and widthprofile can be determined from an analytical solution given byMack et al. (1992) as

KIu ¼ffiffiffiffiffiffiπh2

rpcp�σnþρf g hcp�

34h

� �� �þ

ffiffiffiffiffiffi2πh

r∑n�1

i ¼ 1ðσiþ1�σiÞ

� h2arccos

h�2hih

� ��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihiðh�hiÞ

p� �ð4Þ

KIl ¼ffiffiffiffiffiffiπh2

rpcp�σnþρf g hcp�h

4

� �� �þ

ffiffiffiffiffiffi2πh

r∑n�1

i ¼ 1ðσiþ1�σiÞ

� h2arccos

h�2hih

� �þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihiðh�hiÞ

p� �

wðzÞ ¼ 4E0

pcp�σnþρf g hcp�h4� z2

� �� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffizðh�zÞ

p

þ 4πE0

∑n�1

i ¼ 1ðσiþ1�σiÞ

ðhi�zÞcosh�1zh� 2hi

h

� þhi

z�hij jþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffizðh�zÞ

parccos h�2hi

h

�2664

3775 ð5Þ

where hi is the distance from top of the ith layer to fracture bottomtip, pcp is the fluid pressure at a reference (entry) depth hcpmeasured from the bottom tip, and ρf is fluid density.

The equilibrium fracture height can be determined at eachposition of the fracture by matching KIu and KIl, given by Eq. (4), tothe fracture toughness of the corresponding layer containing thetips. This can be further extended to non-equilibrium heightgrowth calculation by taking into account the pressure gradientdue to the fluid flow in the tip regions in the vertical direction byadding apparent toughness proportional to the fracture's top andbottom velocities.

In addition to the equations described above, the global volumebalance condition must be satisfiedZ t

0Q ðtÞdt ¼

Z LðtÞ

0hðs; tÞwðs; tÞdsþ

ZHL

Z t

0

Z LðtÞ

02uL ds dt dhL ð6Þ

That is, the total volume of fluid pumped is equal to volume offluid in fracture network and volume leaked from the fracture upto time t. The boundary conditions require the flow rate, netpressure, and fracture width to be zero at all fracture tips. The totalfracture network system consists of not only fractures but also theperforations and wellbore. The fracture networks communicatethrough injection elements to account for perforation friction andperforation clusters are connected through wellbore elements toaccount for the friction in the casing.

The system of equations, Eqs. (1)–(6), together with the initialand boundary conditions, plus the equations governing fluid flowin the wellbore and through the perforations represent a completeset of governing equations. Combining these equations and dis-cretizing the fracture network into small elements leads to anonlinear system of equations in terms of fluid pressure p in eachelement, simplified as f(p)¼0. At each time step, each propagatingfracture tip extends an incremental distance, according to thepropagation criterion based on the local fluid velocity and fracture

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 4: Applying complex fracture model and integrated workflow in unconventional reservoirs

tip stress intensity factor, in the direction of local maximumhorizontal principal stress (accounting for the stress shadow effectas discussed later). The intersection of fracture tip with any naturalfracture is checked, and if intersection with natural fracture occurs,the crossing model is applied to determine whether the tip crossesthe natural fracture or is arrested by it, and adjustment in fracturegrid is applied accordingly. The system equation f(p)¼0 is thensolved by using the damped Newton–Raphson method to obtainthe new pressure and flow distribution in the fracture networks.Proppant transport equations are solved to update the proppantmovement and settling in the fractures, and fracture height andstress shadow are also updated. More detailed description of themodel can be found in Weng et al. (2011).

3. Crossing model

As discussed earlier, the interaction between hydraulic andnatural fractures plays a major role in creating fracture complexityduring hydraulic fracturing treatments in formations with preex-isting natural fractures. The understanding and proper modeling ofthe mechanism of hydraulic–natural fractures interactions arekeys to explain fracture complexity and the microseismic eventsobserved during hydraulic fracturing treatments, and therefore toproperly predict fracture geometry and subsequently the reservoirproduction.

When a hydraulic fracture (HF) intersects a natural fracture(NF) it can cross the NF, be arrested at the NF, or subsequentlyopen (dilate) the NF. If the HF crosses the NF, it remains planar,with the possibility to open the intersected NF if the fluid pressureat the intersection exceeds the effective stress acting on the NF. Ifthe HF does not cross the NF, it can dilate and eventuallypropagate into the NF, which leads to a more complex fracturenetwork. So the crossing criterion, in general, controls the com-plexity of the resulting fracture network.

The interaction between HF and NF depends on the in-situstresses, mechanical properties of the rock, properties of naturalfractures, and the hydraulic fracture treatment parameters, includ-ing fracturing fluid properties and injection rate. During the lastdecades, extensive theoretical and experimental work has beendone to investigate, explain, and develop the rules controllingHF–NF interaction (Blanton, 1982, 1986; Warpinski and Teufel,1987; Renshaw and Pollard, 1995; Beugelsdijk et al., 2000; Potluriet al., 2005; Zhao et al., 2008; Gu and Weng, 2010; Gu et al., 2011)as well as numerical simulations to model fracture behaviors atintersection (Zhang and Jeffrey, 2006, 2008; Thiercelin andMakkhyu, 2007; Zhang et al., 2007a, 2007b, 2009; Zhao andYoung, 2009; Chuprakov et al., 2010; Meng and de Pater, 2010;Dahi-Taleghani and Olson, 2011; Sesetty and Ghassemi, 2012;Chuprakov et al., 2013a).

Based on relatively simple analytical considerations of thestress field at the propagating fracture tip, analytical crossing

criteria had been developed in the past (Blanton, 1986;Warpinski and Teufel, 1987; Renshaw and Pollard, 1995; Gu andWeng, 2010). With their relative simplicity, they do not take intoaccount the influence of the hydraulic fracture itself on the resultof interaction. As a result, these criteria are insensitive to para-meters of fluid injection into the hydraulic fracture and the fluidinfiltration into the natural fracture after contact. These criteriawere designed to capture the effect of the fracture approach angle,the NF friction coefficient and the anisotropy of the in-situstresses. Field and laboratory observations, however, showed thatfluid properties are important and should be accounted for.

The experimental study by Beugelsdijk et al. (2000) showedthat flow rate and fracturing fluid viscosity has strong influence onthe hydraulic fracture complexity in a prefractured block. Withlow value of the product of the injection rate Q and fracturing fluidviscosity μ (Qm) fluid tends to leak into the preexisting disconti-nuities and creates tortuous fracture paths following the disconti-nuities. With large Qm value the hydraulic fracture tends to crossmost discontinuities and overall fracture path is nearly straight.Similar observation is made based on the microseismic monitoringof a treatment using gel fracturing fluid and a treatment usingslick water in the same well in Barnett shale (Warpinski et al.,2005).

To improve the description of HF–NF interaction a new analy-tical model that takes the mechanical influence of the HF openingand the hydraulic permeability of the NF into account, referred inthis paper as the OpenT model, has been developed. The details ofthe model can be found in Chuprakov et al. (2013a). The followingprovides a general description of the model and its validationagainst experimental results and numerical simulations.

The analytical model of the HF–NF interaction (OpenT) solvesthe problem of the elastic perturbation of the NF at the contactwith the blunted HF tip, which is represented by a uniformly openslot (thereby, giving its name OpenT). The opening of the HF at thejunction point wT (blunted tip) develops soon after contact, andapproaches the value of the average opening of the hydraulicfracture w, defined by the injection rate Q and the fluid viscosity m.In a viscosity-dominated regime, the average opening of the KGDfracture with half-length L and height H can be estimated as (Valkoand Economides, 1995)

w¼ 2:53QμL2

E0H

" #1=4ð7Þ

where E0 ¼ E=ð1�ν2Þ, E is Young's modulus, ν is Poisson's ratio. TheOpenT model looks for the solution of the elastic problem for theNF perturbed by the HF, and outputs the profiles and boundaries ofthe opening and sliding zones as a result of the contact (bo and bs,respectively shown in Fig. 1, left).

The solution shows that the spatial extent of the open andsliding zones strongly depends on the fluid pressure inside theactivated part of the NF. The larger the inner fluid pressure, the

y

0 0.5 1 1.5-0.5

0

0.5

1

x

HF

NF

1st SF

2nd SF

Fig. 1. Schematic diagram of the HF–NF interaction (left) and result of the computed HF/NF interaction with the initiation of two secondary fractures (SF) and theirsubsequent propagation (right).

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎4

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 5: Applying complex fracture model and integrated workflow in unconventional reservoirs

larger the open and sliding zones at the NF. Consequently, it isexpected that after the HF contacts the NF, the injected fracturingfluid will gradually penetrate the NF with finite hydraulic perme-ability κ and thus enhances the inner fluid pressure within the NF,pNF.

The average pressure of the fracturing fluid that has penetratedthe NF can be approximated by the following function of thecontact time t (Chuprakov et al., 2013a, 2013b):

pNF ðtÞ ¼ pf tanh

ffiffiffiffiffiffiffiffiffiffiffiffi2κpfμb2s

t

s !ð8Þ

where pf is the fluid pressure at the contacting HF tip and κ is thepermeability of the natural fracture. As a result of the NF activationdue to the fracturing, the fluid penetration becomes very active inhighly permeable NFs or with low viscosity fracturing fluids. Thiscould potentially prevent the HF from propagating across the weakinterfaces.

The elasticity model of the fracture interaction enables thecomputation of the stress field in the vicinity of the activated NF.The analysis of the generated stress field gives the positions ofsufficient tensile stress concentration where the new fractures canbe nucleated. In the absence of preexisting defects in the rock nearthe NF, these positions correspond to the two opposite tips of theNF open zone (see Fig. 1, right). In order to decide on thepossibility of a secondary fracture (SF) re-initiation at these points,a criterion of fracture initiation that combines both stress criterionand energy release rate has been employed. The stress criterionrequires that the maximum tensile hoop stress σθθ at a smalldistance of r from the stress concentration point xj having direc-tion θj with respect to the orientation of the NF must exceed thetensile strength of the rock T0 along a certain distance δTσθθðxj; r;θjÞroδT r�T0 ð9ÞThe additional energy criterion states that the elastic energyrelease rate ℑinc due to the incremental initiation of a fracture oflength δl within the critical distance δT must overcome the criticalenergy release rate ℑ1C for the given rock

ℑincðδlÞ4ℑ1C ; δloδT ð10ÞThe length of the fracture must not exceed the critical stress zone,δT. The mixed stress–energy criterion has been verified experi-mentally (Leguillon, 2002).

The model of HF–NF reinitiation has been validated against theresults of various laboratory block tests (Blanton, 1982; Warpinskiand Teufel, 1987; Gu et al., 2011). The predictions of the analyticalmodel for crossing and arresting behavior agree with the experi-mental results for various fracture intersection angles, stresscontrasts and fluid injection conditions used in different experi-mental groups. Fig. 2 shows the comparison between differentanalytical models by Blanton (1986), Gu and Weng (2010) (alsoreferred to as extended Renshaw and Pollard, or the eRP model inthis paper), the OpenT model (Chuprakov et al., 2013a), and theexperimental results from Gu et al. (2011) and numerical simula-tion using the MineHF2D code (Zhang and Jeffrey, 2006, 2008;Zhang et al., 2007b).

The experiments clearly show that the new model agrees withthe experiments as well as other analytical models as it capturesthe first-order crossing-arresting behavior. We note that thediscrimination between the different models would require addi-tional data points in the transition zone, unfortunately notavailable here.

Additionally, it should be noted that the injection rate andviscosity were not changed in this series of experiments; so it wasnot possible to assess their effect on the fracture interactionoutcome. To compensate for this lack of lab experiments, numer-ical experiments were conducted using MineHF2D code to assess

the sensitivity of the injection rate on fracture crossing. The resultsfor one set of parametric runs are shown in Fig. 3; the OpenTmodel agrees well with the numerical results in the sense that itcaptures the crossing-arresting transition as flow rate changes.

It should be mentioned that the OpenT criterion incorporatesthe influence of rock properties (local horizontal stresses, rocktensile strength, toughness, pore pressure, Young's modulus,Poisson's ratio), natural fracture properties (friction coefficient,toughness, cohesion, permeability), intersection angle betweenhydraulic and natural fractures, fracturing fluid properties (visc-osity, tip pressure), and injection rate to define crossing rules. TheeRP criterion accounts for the local stress field, pore pressure,crossing angle, rock tensile strength and frictional properties ofthe natural fractures.

This new OpenT model has been implemented in the UFMmodel. Comparison of different cases showing the impact of fluidviscosity and pump rate can be found in Kresse et al. (2013). A fieldexample illustrating the effect of fluid viscosity on fracture com-plexity will be presented later in this paper.

4. Hydraulic fracture interaction

Fracture network growth pattern is affected by the mechanicalinteraction among the adjacent fractures. Generally known as“stress shadow” effect, the stress field of one fracture is perturbedby the opening and shearing displacements of other nearbyfractures. In a 2D plane-strain displacement discontinuity solution,Crouch and Starfield (1983) describe the normal and shear stresses(σn and σs) acting on one fracture element induced by the openingand shearing displacement discontinuities (Dn and Ds) from allfracture elements as follows:

σin ¼ ∑

N

j ¼ 1AijCij

nsDjsþ ∑

N

j ¼ 1AijCij

nnDjn

σis ¼ ∑

N

j ¼ 1AijCij

ssDjsþ ∑

N

j ¼ 1AijCij

snDjn ð11Þ

where Cij are the 2D, plane-strain elastic influence coefficients.This method, referred to as the 2D Displacement DiscontinuityMethod (2D DDM) is used in our model to compute the additionalstress induced on each fracture element from the displacements ofadjacent elements. In addition, a 3D correction factor Aij suggestedby Olson (2008) (referred to as enhanced 2D DDM) was furtherintroduced to modify the influence coefficients (Cij in the above

Fig. 2. Comparison of laboratory “crossing-arresting” data with previous analyticalmodels (Blanton, eRP), new analytical model OpenT, and MineHF2D simulations.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 5

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 6: Applying complex fracture model and integrated workflow in unconventional reservoirs

equation) to account for the 3D effect due to finite fracture heightthat leads to decaying of interaction between any two fractureelements when the distance increases. This additional normalstress due to the stress shadow effects is computed at each timestep in the UFM model and is then added to the initial in-situstress field on each fracture element during pressure and widthiteration. The effect of stress shadow, including the shear stress, onthe directional change of propagating fracture tips is essential forproper modeling of fracture network propagation pattern.

The UFM model that incorporates the enhanced 2D DDMapproach is validated against full 2D DDM simulator incorporatinga full solution of coupled elasticity and fluid flow equations byCSIRO (Zhang et al., 2007a, 2007b) in the limiting case of very largefracture height (because 2D DDM approach does not consider 3Deffect of finite fracture height). The comparison of influence of twoclosely propagating fractures on each other's propagation pathshas been provided. The propagation of two hydraulic fracturesinitiated parallel to each other (propagating along local maximumstress direction) has been simulated for two configurations, withinitiation points aligned along the y-axis and offset from eachother for isotropic and anisotropic far-field stresses. The fracturepropagation path and pressure inside each fracture has beencompared for the UFM model and CSIRO code for the input datagiven in Table 1.

When two fractures are initiated parallel to each other withinitiation points separated by dx¼0, dy¼10 m (maximum hori-zontal stress field is oriented in the x-direction), they turn awayfrom each other due to the stress shadow effect. The propagationpaths for isotropic and anisotropic stress fields are shown in Fig. 4.

When compared with the isotropic case, the curvatures of thefractures in the case of stress anisotropy are smaller. This is due tothe competition between the stress shadow effect, which tends toturn fractures away from each other, and far-field stresses thatforce fractures to propagate in the direction of maximum hor-izontal stress (x-direction). The influence of far-field stressbecomes dominant as the distance between the fracturesincreases, in which case the fractures would tend to propagateparallel to the maximum horizontal stress direction (as in Fig. 4(right)).

The same conclusion about far-field stresses is applicable forthe case when two fractures are initiated parallel to each otherwith initiation points separated by dx¼10 m, dy¼10 m (Fig. 5).In this situation, due to the offset of the initial positions, the insidetips of the two fractures attract toward each other due to thetensile stress field ahead of the tips. The UFM model correctly

captures the expected behavior and agrees with the predictionfrom CSIRO code.

The numerical study presented above shows that the enhanced2D DDM approach implemented in the UFM model is able toproperly simulate fracture interaction and propagation directionchange, while being computationally efficient. Validation of the 3Deffect due to finite fracture height was also evaluated against 3Dsimulation results under static conditions (Kresse et al., 2012).

The effect of stress shadowing on fracture propagation can beillustrated through a simple example of five parallel fracturesinitiated from a horizontal wellbore. The input parameters for thebase case are given in Table 2.

For this simple case, the results of the UFM model with stressshadow are compared with results of a conventional Perkins–Kern–Nordgren (PKN) model modified by incorporating the stressshadow calculation based on the analytical expression given byWarpinski and Branagan (1989) for a constant height fracture.Note that the simplistic PKN model does not simulate the fractureturning due to the stress shadow effect. The results from thissimple model are compared to the results from the UFM modelthat incorporates point-by-point stress shadow calculation alongthe entire fracture paths as well as fracture turning.

Fig. 6 shows the simulation results of lengths of the fivefractures, computed from both models. Fracture 3 is the centerfracture, and fractures 1 and 5 are the outermost ones. Sincefractures 2, 3, and 4 have smaller widths than the outer ones dueto the stress shadow effect, they have larger flow resistance,receive less flow rate, and have shorter length. Therefore, thestress shadow affects not only fracture width but also fracturelength under dynamic conditions.

Fig. 3. Comparison between numerical crossing-arresting HF–NF behavior using MineHF2D code. The red crosses and squares respectively indicate crossing and arrestingbehavior from MineHF2D code, solid green curves correspond to analytical predictions using OpenT criterion, dash yellow curve corresponds to Blanton criterion, and eRPcriterion is given by dash blue lines. The interaction is studied for various injection rate and relative stress difference for two different HF–NF contact angles, β¼901 (left) andβ¼601 (right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1Input data for validation against the CSIRO model.

Injection rate 0.1 m3/sStress anisotropy 0.9 MPaYoung's modulus 3�1010 PaPoisson's ratio 0.35Fluid viscosity 0.001Pa sFluid specific gravity 1.0Minimum horizontal stress 46.7 MPaMaximum horizontal stress 47.6 MPaFracture toughness 1 MPa m0.5

Fracture height 120 m

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎6

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 7: Applying complex fracture model and integrated workflow in unconventional reservoirs

Note that the “half length” from the UFM model as shown inFig. 6 actually represents the half distance between the fracturetips along the maximum horizontal stress direction, rather thanthe true fracture length along the curved fracture path. Therefore,the half lengths from the UFM model for the two outermostfractures, which have the greatest curvature, are shorter than thecorresponding PKN fractures that are assumed straight. But thelengths of inner fractures (almost straight) are in good agreementfor both models.

The effect of stress shadow on fracture geometry is highlyinfluenced by many parameters. Fig. 7, for example, shows thefracture geometry predicted by the UFM model for three cases of

Fig. 4. Comparison of propagation paths for two initially parallel fractures in isotropic and anisotropic stress fields.

Fig. 5. Comparison of propagation paths for two initially offset fractures in isotropic and anisotropic stress fields.

Table 2Input parameters for the case of five parallelfractures.

Young's modulus 4.5�1010 PaPoisson's ratio 0.35Rate 0.032 m3/sViscosity 0.001 Pa sHeight 30 mLeakoff coefficient 3.9�10�2 m/s1/2

Stress anisotropy 1.4 MPaFracture spacing 20 mNo. of perfs per frac 100

Fig. 6. Half-length of five parallel fractures during injection (Note: the curves withmarkers are calculated from the simplistic PKN model and the curves withoutmarkers are from the UFM model. xfi refers to the fracture half-length for ithfracture in the order from toe to heel.).

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 7

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 8: Applying complex fracture model and integrated workflow in unconventional reservoirs

different fracture spacing (10 m, 20 m, and 40 m). When fracturespacing is large (larger than fracture height), the effect of stressshadow dissipates, and fractures have approximately the samedimensions; as the distance between fractures is reduced, theeffect of stress shadow becomes greater and is noticeably observedin the reduced width and length for the inner fractures.

The UFM model also considers the stress shadow contributionfrom the still open or propped fractures generated in the previouspumping stages on the current treatment stage. In the case ofcomplex fractures, the existing fractures not only affect the currenttreatment stage through the stress shadow effect, they alsopresent as open fracture planes that can terminate and commu-nicate with the newly created fractures in the current stage.Examples of stress shadow effect on complex fractures can befound in Kresse et al. (2012).

5. Field example

Warpinski et al. (2005) presented a field case of a wellin Barnett shale first treated with a crosslinked gel, and thenre-fractured with slick water. The wellbore is approximatelyaligned with the direction of maximum horizontal stress (which

favors longitudinal fractures, untypical of most current transversestimulation orientations). The microseismic events of the twotreatments are shown in Fig. 8. A total volume of 11,600 bbl ofcross-linked gel and 700,000 lbm of sand were pumped at a rate of70 bbl/min for about 3 h with sand concentration ramped up to3 lbm/gal. Most of the microseismic activity suggests longitudinalfracturing with only modest activation of natural fractures, result-ing in a narrow stimulated network (less than 500 ft from thewellbore in many sections of the lateral), as seen in Fig. 8a, withresulting SRV equal to 430 million ft3. During the full re-fracturingconducted several months later, 60,000 bbl of slick water and385,000 lbm of sand was pumped at 125–130 bbl/min for most ofthe treatment that lasted 6.5 h. The stimulated network wasapproximately 1500 ft wide and 3000 ft long (Fig. 8b) withconsiderable height growth and SRV of 1450 million ft3. Clearly,the re-fracturing treatment stimulated a much larger volume ofrock than the initial gel treatment (1450 million ft3 vs. 430 mil-lion ft3), and showed patterns of development that suggested theopening of both northeast and northwest-trending fractures.

This field example indicates the importance of proper consid-eration of fluid properties when modeling the interaction ofhydraulic fractures with preexisting natural fractures. In generalit is observed that for the same field conditions, more viscous fluid

Fig. 7. Fracture geometry and fluid pressure for the cases when distance between injection points is equal to 10 m, 20 m, and 40 m.

Fig. 8. Single-well microseismic event locations for XL gel stimulation and water-frac re-fracturing treatment, horizontal Barnett Shale well (Warpinski et al., 2005). (a) XLgel fracturing and (b) water-frac re-fracturing treatment.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎8

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 9: Applying complex fracture model and integrated workflow in unconventional reservoirs

tends to cross the natural fractures more easily than slick water,which tends to penetrate into the natural fractures more easily andopen them without crossing. Pumping rate as well as rock proper-ties should also be taken into account.

To validate the UFM model in a realistic field condition, weexamine a synthetic case that mimics this field case by Warpinskiet al. (2005) as shown in Fig. 8. Though the details of the well andformation data and pumping schedule are not exactly replicated,the synthetic case is created using the data that is available inWarpinski et al. (2005), so the well and formation configurationsare very close to the real case.

Some of the critical information for fracture simulation, includ-ing Young's modulus and description of the natural fractures, isprescribed based on the work by Gale et al. (2007). According toGale et al. (2007), Young's modulus for Barnett Shale is approxi-mately 33 GPa (4.8�106 psi). The natural fractures contain adominant set trending west-northwest (approximately North 701West). There is also another set trending north–south. Thehydraulic fractures in Barnett trend in the northeast–southwest.The natural fractures are mostly sealed and filled with calcite. Onlythe largest fractures may be open and the largest fracture clustersare expected to be spaced a couple of 100 ft apart. To construct thenatural fractures for UFM model simulation, we assume that onlythe largest natural fractures contribute to the complex fracturenetwork development. The exact values of fracture spacing andfracture length are difficult to determine. We make the assump-tion that the average fracture spacing is 100 ft and average fracturelength is 200 ft. Only the dominant set of fractures is assumed.Fig. 9 shows the top view of the well configuration, perforationclusters and the 2D traces of the generated natural fractures. Thewell geometry closely mimics the field case as shown in Fig. 8.

For the complex fracture simulation, detailed vertical stressprofile is not available fromWarpinski et al. (2005). Instead a fixedheight model is used based on the microseismic measurements.It is assumed that the fracture height is 310 ft, covering LowerBarnett for the case of crosslinked gel treatment, and 360 ft for the

slick water treatment. For the simulation of slick water refrac, anypotential effect of the previous crosslinked treatment and thesmall slick water treatment prior to the main treatment is notconsidered. There is no information on the stress anisotropy givenin the paper. For Barnett shale the difference between maximumand minimum horizontal stresses is considered low, but it can varysignificantly fromwell to well, or even from stage to stage. Danielset al. (2007) estimated the maximum horizontal stress from thesonic measurement in a Barnett well; the stress anisotropy is onthe order of 200–500 psi. For this study, a difference betweenmaximum and minimum horizontal stress is assumed to be200 psi. Table 3 shows the main parameters used for the fracturesimulations.

Fig. 10 shows the simulated fracture geometry and width forboth gel and slick water fracs at the end of the treatments. Planar

Fig. 9. Top view of the wellbore, perforations and the natural fractures used for the Barnett simulations.

Table 3Input data for Barnett shale simulation.

Parameters Crosslinked geltreatment

Slick watertreatment

Young's modulus 4.8�106 psiNatural fracture direction Average N701W, standard deviation 51Natural fracture length Average 200 ft, standard deviation 40 ftNatural fracture spacing Average 100 ft, standard deviation 20 ftCoefficient of friction Average 0.8Hydraulic fracturedirection

N401E

Minimum horizontal stress 5324 psiMaximum horizontalstress

5524 psi

Fracture height 310 ft 360 ftFluid rheology n0 ¼0.42, 1 cp

k0 ¼0.002 lb s/ft2

Injection rate: Q 70 bbl/min 125 bbl/minPump time 174 min 386 minProppant volume 715,000 lbm 600,000 lbm

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 9

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 10: Applying complex fracture model and integrated workflow in unconventional reservoirs

hydraulic fractures first initiate from the perforations. Thesefractures propagate as longitudinal fractures because the wellboredirection is closely aligned with the maximum horizontal stressdirection. For the crosslinked gel treatment, as these initiallongitudinal fractures intersect the natural fractures that are

approximately orthogonal to the fracture direction, the OpenTcrossing model mostly predicts crossing through the naturalfractures. Only when the fluid pressure is sufficiently high toexceed the normal stress acting on the natural fractures, do thenatural fractures open and accept fracturing fluid. The overall

Fig. 10. UFM model simulation results for the Barnett case. (a) Cross-linked gel treatment and (b) slick water treatment.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎10

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 11: Applying complex fracture model and integrated workflow in unconventional reservoirs

geometry predicted by the UFM model shows a strong planartrend along the well with very narrow network width, consistentwith the microseismic observation shown in Fig. 8a.

For the slick water treatment, the OpenT crossing model mostlypredicts non-crossing condition when a hydraulic fracture inter-cepts a natural fracture. This results in a much wider fracturenetwork width as the fractures branch out as shown in Fig. 10b.The width of the network is approximately 1700 ft, approximatelythe same width as indicated by the microseismic data as shown inFig. 8b.

The example presented in Fig. 10 showing the difference ininduced fracture networks from two treatments with differenttypes of fluid matches microseismic cloud trend observed inWarpinski et al. (2005) and shows that the UFM simulator withthe OpenT crossing model is able to correctly replicate theobserved hydraulic fracture patterns.

Additional field examples that use the UFM model to simulatecomplex fractures in unconventional reservoirs can be found inCipolla et al. (2011b), Kennaganti et al. (2013) and Liu et al. (2013).

6. Integrated design workflow and production optimization

A complex fracture model presents a powerful tool to evaluatehydraulic fracture network propagation under the specified fieldpumping conditions and completion configuration. It can be usedto predict the developed hydraulic fracture network and match itwith the observed microseismic event cloud and provide properunderstanding of the fracture footprint as well as propped fracturesurface estimation which is important input for the productionevaluation. By linking the completion and treatment to theproduction, operators can evaluate how various completion andtreatment design parameters impact the production, and optimizewell spacing, completion and treatment designs to maximize theproduction.

To enable this design optimization process, there must be a wayto communicate and pass data from one component to the next.Some of the key components include the construction of thegeological model and detailed earth model with the geomechani-cal and reservoir properties, completion design, simulation of

Fig. 11. Integration of the UFM complex fracture model in an integrated workflow (DFN is discrete fracture network).

Table 4Additional input data for Barnett shale production example.

Parameters

Treating fluid Slick water (1 cp)Injection rate 80 bbl/minTotal fluid volume (all stages) 105,700 bblTotal proppant (all stages) 2,280,000 lbm (100 mesh and 40/70 mesh sands)Reservoir fluid Dry gas, connate water saturation 22%Permeability 0.0001 mdPorosity 3%Reservoir pressure 3600 psiBottomhole flowing pressure 500 psiNo. of perf clusters/stage 4No. of stages 6–12Unpropped frac conductivity 0.3 md ftProduction time 10 years

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 11

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 12: Applying complex fracture model and integrated workflow in unconventional reservoirs

Fig. 12. Simulated complex fractures and conductivity distribution (in md ft) in the fracture network for the eight-stage completion.

Fig. 13. Unstructured grids in the near-well region for the first three stages.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎12

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 13: Applying complex fracture model and integrated workflow in unconventional reservoirs

fracturing treatment, calibration of the fracture model againstmicroseismic observation, generation of the reservoir grid model,and production simulation. Additionally, these components needto be seamlessly integrated in a software platform so this optimi-zation process can be executed efficiently.

To integrate a complex fracture model with a reservoir simu-lator, the reservoir simulator must be able to properly simulate theproduction from the generated complex fracture networks. Typi-cally there are two approaches toward simulating the productionfrom a complex fracture network. One is based on the dual-porosity–dual-permeability concept which upscales the fracturesinto equivalent anisotropic permeabilities in the regular reservoirgrids. The other approach is based on the single-porosity conceptto directly simulate the reservoir flow into the discrete highpermeability fracture network. Although single-porosity simula-tion with discrete fracture networks is numerically quite challen-ging, it provides more accurate results for ultra-tight formationsthan the dual-porosity approach.

Cohen et al. (2013) presented examples of using a semi-analytical production model integrated with the UFM model toanalyze and optimize fracturing parameters such as fluid viscosity

and proppant size. However, simpler production models arelimited in terms of their ability to accurately account for theeffects of multiphase flow and cleanup of fracturing fluid, highlyuneven vertical proppant distribution due to proppant settling,fracture conductivity change over the life of production, gasdesorption, etc. For accurate production simulation, a full 3Dnumerical reservoir simulator is needed and accurate simulationrequires fine gridding near the fractures. Due to the complexfracture patterns predicted by the fracture simulator, manuallygenerating the reservoir grid is practically impossible. Therefore, akey enabler for this process is an automated grid generator thatcan deal with arbitrary complex fracture geometry. Cipolla et al.(2011a) presented an auto-gridding algorithm and an example inwhich the auto-gridder is used to generate the unstructured grid,taking the UFM model output as the input to the auto-gridder. Thegenerated unstructured grid was then used by a reservoir simu-lator to simulate long-term production.

To support well completion design and production optimiza-tion workflow for unconventional reservoirs, the UFM fracturesimulator has been integrated in a software platform that fullysupports the “seismic-to-simulation” workflow and seamlessly

Fig. 14. Simulated pressure distribution in reservoir for the eight-stage completion after producing for 1, 3 and 10 years. (a) 1-year production, (b) 3 years production,(c) 10 years production.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 13

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 14: Applying complex fracture model and integrated workflow in unconventional reservoirs

integrates the above-mentioned key components (Cipolla et al.,2011a). The integrated workflow is schematically illustrated inFig. 11.

This integrated workflow allows operators to build the geome-chanical and reservoir model that represents as accurately aspossible the unconventional reservoir being developed, analyzethe fracture treatments and production of existing wells tocalibrate the reservoir model, and investigate “what-if” scenarios

to optimize the fracturing treatment, completion design, wellplacement and pad development plans.

Field case studies illustrating the complete integrated workfloware out of the scope of this paper. Previous field case studies byEjofodomi et al. (2011), Cipolla et al. (2011a), Walker et al. (2012),Kennaganti et al. (2013), and Liu et al. (2013) demonstrated someparts of the workflow or the complete workflow, involvingdetailed reservoir characterization, completion design based onreservoir and completion quality, fracture simulation and calibra-tion against microseismic, and production matching and simula-tion. In the following, we present an example to illustrate howintegrated complex fracture modeling and reservoir modeling canbe used to optimize the completion design, more specifically thenumber of stages in a horizontal well in an unconventionalreservoir. The example is based on the generic data for the Barnettshale presented in the earlier example (Fig. 10) and a hypotheticalwell drilled in approximately the direction of the minimumprincipal stress (northwest–southeast direction). A set of simula-tions are run for different numbers of stages in the well withlateral length of 4000 ft. The total amount of fluid and proppantvolume for the whole well is fixed. That is, when the number ofstages increases, the fluid and proppant volume decrease propor-tionally. Parameters used for production simulation in addition tothe formation parameters given in Table 3 are given in Table 4.

Fig. 12 shows the top view of the simulated complex hydraulicfracture planes and conductivity distribution of all stages of aneight-stage completion along with line traces of the preexistingnatural fractures as the input to model simulation. Fig. 13 showsthe unstructured grid generated by the auto-gridder, zoomed intothe first three stages in the near-well region, for one layer of thegrid in the vertical direction. Note that the fracture permeabilitycan vary drastically vertically due to highly uneven proppantdistribution as a result of proppant settling as shown in Fig. 12.Fig. 14 shows the snapshots of pressure distribution in thereservoir after 1, 3 and 10 years of production.

As is seen in Fig. 14, pressure depletion primarily occurssurrounding the fractures in the region close to wellbore. Theouter region covered by the hydraulic fractures remains largelyundepleted after 10 years of production. This is primarily due tothe poor proppant transport by slick water and the larger prop-pant (40/70 mesh) does not reach the outer region of thegenerated hydraulic fracture network (as shown in the conductiv-ity and permeability distribution in Figs. 12 and 13).

The fracture network also shows pockets of reservoirs that arenot well covered by the induced fractures. This is resulted from acombination of the influence of the natural fractures and the stressshadow effect. As the number of stages increases, the distancebetween stages decreases, which causes the fractures generatedfrom the previous stages that remain open (due to the very slowleakoff) to cast a stress shadow on the current pumping stage. Thesimulation often shows that if fracture network becomes asym-metric with respect to the wellbore (influenced by natural fracturedistribution), there is a tendency for the fractures in the next stageto preferentially grow towards the opposite side of the wellboredue to a lesser stress shadowing effect there. As can be seen inFigs. 12 and 14, the fracture asymmetry swings from one side ofthe well to the other side, and from one stage to the next from thetoe to the heel. As the number of stages increases, there is alsogreater overlap of fracture surface area between the adjacentstages. Due to the spread of the fracture network, as a result ofthe natural fractures, the fractures generated in the subsequentstage connect into the existing fracture network and this reducesthe generation of new fracture surface area.

Fig. 15 shows the simulated production rate and cumulativeproduction for 6–10 and 12 stages. Fig. 16 shows the 10-yearcumulative production vs. the number of stages. The highest

Fig. 15. Simulated production rate and cumulative production for different stages.

Fig. 16. Simulated 10-year cumulative production vs. number of stages.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎14

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 15: Applying complex fracture model and integrated workflow in unconventional reservoirs

production is achieved with seven stages. As the number of stagesfurther increases, the production decreases, presumably due to theeffect of stress shadow and communication between the adjacentstages.

The simulation in this example is based on the single-wellanalysis. Completion optimization may be further analyzed byconsidering multiple wells in a development block. The optimalnumber of stages could be different when considering the differ-ence in effective fracture network length resulting from thedifference in job size per stage. The above analysis is based onthe assumption of fixed material cost. Optimization can be donebased on other criteria, in other words, by applying differentobjective functions such as the Net Present Value, or by applyingdifferent constraints, and then the optimal number of stages canbe different depending on the objective function selected.

7. Conclusions

The complex fracture model provides a critical element neededto link formation parameters and completion design to the wellproduction performance in an unconventional reservoir. By inte-grating the fracture model with the production model within asoftware platform that enables easy data and user workflowamong various components, engineers can evaluate various for-mation and design parameters that potentially impact the wellperformance and economics and make decisions based on morequantitative analyses using formation or even well-specific data,rather than relying on the long learning cycle that is based on thetrial-and-error approach.

This paper presents a comprehensive, efficient complex frac-ture model that effectively simulates the hydraulic fracture net-works created during stimulation treatment and proppantplacement. The model simulation results show that it capturesthe fracture behaviors observed from microseismic monitoring forgel and slick water treatments. The presented example illustratesthe model's utility as an application for completion optimizationthrough integration with a comprehensive numerical reservoirsimulator.

Acknowledgments

The authors would like to thank Schlumberger for permissionto publish this paper. They would also like to acknowledge theircolleagues Tarik Itibrout and Hitoshi Onda for their advices inproduction simulations shown in this paper and the members ofMangrove project team who had made the integrated workflowinvolving complex fracture modeling and production simulation areality.

References

Blanton, T.L., 1982. An Experimental Study of Interaction between HydraulicallyInduced and Pre-existing Fractures. SPE 10847 Presented at the SPE/DOEUnconventional Gas Recovery Symposium. Pittsburgh, PA, May 16–18.

Blanton, T.L., 1986. Propagation of Hydraulically and Dynamically Induced Fracturesin Naturally Fractured Reservoirs. SPE Unconventional Gas Technology Sympo-sium. Louisville, Kentucky; 1st January 1986.

Beugelsdijk, L.J.L., de Pater, C.J., Sato, K., 2000. Experimental Hydraulic FracturePropagation in a Multi-Fractured Medium. SPE 59419 Presented at the SPE AsiaPacific Conference in Integrated Modeling for Asset Management. Yokohama,Japan, April 25–26.

Boyer II, C.M., Stubbs, P.B., Scherer, F.C., 1986. Measurement of Coalbed Propertiesfor Hydraulic Fracture Design and Methane Production. Paper Presented at theSPE Unconventional Gas Technology Symposium. Louisville, Kentucky.

Chuprakov, D.S., Akulich, A.V., Siebrits, E., Thiercelin, M., 2010. Hydraulic FracturePropagation in a Naturally Fractured Reservoir. SPE 128715 Presented at theSPE Oil and Gas India Conference and Exhibition held in Mumbai, India, January20–22.

Chuprakov, D., Melchaeva, O., Prioul, R., 2013a. Injection-Sensitive Mechanics ofHydraulic Fracture Interaction with Discontinuities. ARMA Symposium. SanFrancisco, CA.

Chuprakov, D., Melchaeva, O., Prioul, R., 2013b. Hydraulic fracture propagationacross a weak discontinuity controlled by fluid injection. In: Bunger, A.P.,McLennan, J.D., Jeffrey, R.G. (Eds.), Effective and Sustainable Hydraulic Fractur-ing. InTechhttp://dx.doi.org/10.5772/55941 (ISBN: 978-953-51–1137-5).

Cipolla, C.L., Williams, M.J., Weng, X., Mack, M., Maxwell, S., 2010. HydraulicFracture Monitoring to Reservoir Simulation: Maximizing Value. Paper SPE133877 Presented at SPE Annual Technical Conference and Exhibition. Florence,Italy, September 19–22.

Cipolla, C.L., Fitzpatrick, T., Williams, M.J., Ganguly, U.K., 2011a. Seismic-to-Simulation for Unconventional Reservoir Development. Paper SPE 146876Presented at SPE Reservoir Characterization and Simulation Conference andExhibition. Abu Dhabi, UDA, October 9–11.

Cipolla, C.L., Weng, X., Mack, M., Ganguly, U., Gu, H., Kresse, O., Cohen, C., 2011b.Integrating Microseismic Mapping and Complex Fracture Modeling to Char-acterize Fracture Complexity. Paper SPE 140185 Presented at the SPE HydraulicFracturing Technology Conference and Exhibition in The Woodlands, Texas,USA, January 24–26.

Cohen, C.E., Abad, C., Weng, X., England, K., Phatak, A., Kresse, O., Nevvonen, O.,Lafitte, V., Abivin, P., 2013. Analysis on the Impact of Fracturing TreatmentDesign and Reservoir Properties on Production from Shale Gas Reservoirs. IPTC16400 Presented at the International Petroleum Technology Conference. Beij-ing, China, March 26–28.

Crouch, S.L., Starfield, A.M., 1983. Boundary Element Methods in Solid Mechanics,1st ed. George Allen & Unwin Ltd, London.

Dahi-Taleghani, A., Olson, J.E., 2011. Numerical modeling of multistrand hydraulic-fracture propagation: accounting for the interaction between induced andnatural fractures. SPE J. September, 575–581.

Daniels, J., Waters, G., Le Calvez, J., Lassek, J., Bentley, D., 2007. Contacting More ofthe Barnett Shale Through an Integration of Real-Time Microseismic Monitor-ing, Petrophysics, and Hydraulic Fracture Design. Paper SPE 110562 Presentedat the 2007 SPE Annual Technical Conference and Exhibition. Anaheim,California, USA, October 12–14.

Dershowitz, W.S., Cottrell, M.G., Lim, D.H., Doe, T.W., 2010. A Discrete FractureNetwork Approach for Evaluation of Hydraulic Fracture Stimulation of NaturallyFractured Reservoirs. ARMA10-475. Presented at 44th US Rock MechanicsSymposium. Salt Lake City, Utah, June 27–30.

Ejofodomi, E., Baihly, J., Malpani, R., Altman, R., Huchton, T., Welch, D., Zieche, J.,2011. Integrating All Available Data to Improve Production in the MarcellusShale, Paper SPE 144321 Presented at SPE North American Unconventional GasConference. Woodlands, TX, June 14–16.

Fisher, M.K., Davidson, B.M., Goodwin, A.K., Fielder, E.O., Buckler, W.S., Steinberger, N.P., 2002. Integrating Fracture Mapping Technologies to Optimize Stimulations inthe Barnett Shale. Paper SPE 77411 Presented at the 2002 SPE Annual TechnicalConference and Exhibition. San Antonio, Texas, USA, September 29–October 2.

Fu, P., Johnson, S.M., Carrigan, C.R., 2011. Simulating Complex Fracture Systems inGeothermal Reservoirs using an Explicitly Coupled Hydro-Mechanical Model.ARMA 11-244 Presented at 45 US Rock Mechanics Symposium. San Francisco,CA, June 26–29.

Gale, J.F.W., Reed, R.M., Holder, J., 2007. Natural fractures in the Barnett Shaleand their importance for hydraulic fracture treatment. AAPG Bull. 91 (4),603–622.

Gale, J.F.W., Holder, J., 2008. Natural Fractures in the Barnett Shale: Constraints onSpatial Organization and Tensile Strength with Implications for HydraulicFracture Treatment in Shale-Gas Reservoirs. ARMA 08-096 Presented at 42ndUS Rock Mechanics Symposium and 2nd Canada Rock Mechanics Symposium.San Francisco, June 29–July 2.

Gu, H., Weng, X., 2010. Criterion for Fractures Crossing Frictional Interfaces at Non-orthogonal Angles. 44th US Rock Mechanics Symposium and 5th US–CanadaRock Mechanics Symposium; Salt Lake City, Utah: American Rock MechanicsAssociation, 1st January.

Gu, H., Weng, X., Lund, J.B., Mack, M., Ganguly, U., Suarez-Rivera R., 2011. HydraulicFracture Crossing Natural Fracture at Non-Orthogonal Angles, a Criterion, itsValidation and Applications. Paper SPE 139984 Presented at the SPE HydraulicFracturing Conference and Exhibition. Woodlands, Texas, January 24–26.

Han, G., 2011. Natural Fractures in Unconventional Reservoir Rocks: Identification,Characterization, and its Impact to Engineering Design. ARMA Paper 11-509Presented at 45th US Rock Mechanics/Geomechanics Symposium. San Fran-cisco, CA, June 26–29.

Jeffrey, R.G., Bunger, A., Lecampion, B., Zhang, X., Chen, Z., As, A., Mainguy, M.,2009a. Measuring Hydraulic Fracture Growth in Naturally Fractured Rock.Paper Presented at the SPE Annual Technical Conference and Exhibition. NewOrleans, Louisiana.

Jeffrey, R.G., Weber, C.R., Vlahovic, W., Enever, J.R., 1994. Hydraulic FracturingExperiments in the Great Northern Coal Seam. Paper SPE 28779 Presented atSPE Asia Pacific Oil & Gas Conference. Melbourne, Australia, November 7–10.

Jeffrey, R.G., Zhang, X., Thiercelin, M., 2009b. Hydraulic Fracture Offsetting inNaturally Fractured Reservoirs: Quantifying a Long-Recognized Process. PaperSPE 119351 Presented at SPE Hydraulic Fracturing Technology Conference.Woodlands, TX, January 19–21.

Kennaganti, K.T., Grant, D., Oussoltsev, D., Ball, N., Offenberger, R.M., 2013.Application of Stress Shadow Effect in Completion Optimization Using aReservoir-Centric Stimulation Design Tool. Paper SPE 164526 Presented at SPEUnconventional Resources Conference USA. The Woodlands, TX, April 10–12.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 15

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i

Page 16: Applying complex fracture model and integrated workflow in unconventional reservoirs

Kresse, O., Weng, X., Wu, R., Gu, H., 2012. Numerical Modeling of HydraulicFractures Interaction in Complex Naturally Fractured Formations. ARMA-292Presented at 46th US Rock Mechanics/Geomechanics Symposium. Chicago, Il,USA, June 24–27.

Kresse, O., Weng, X., Chuprakov, D., Prioul R., Cohen, C., 2013. Effect of flow rate andviscosity on complex fracture development in UFM model. In: Proceedings ofthe International Conference for Effective and Sustainable Hydraulic Fracturing.Brisbane, Australia, May 20–22.

Leguillon, D., 2002. Strength or toughness? A criterion for crack onset at a notch.Eur. J. Mech. A-Solid 21 (1), 61–72 (Jan–Feb).

Liu, H., Luo, Y., Zhang, N., Yang, D., Dong, W., Qi, D., Gao, Y., 2013. Unlock Shale OilReserves Using Advanced Fracturing Techniques: A Case Study in China. IPTC16522 Presented at IPTC. Beijing, China, March 26–28.

Mack, M.G., Elbel, J.L., Piggott, A.R., 1992. Numerical Representation of MultilayerHydraulic Fracturing. ARMA Paper 92-0335 Presented at 33rd U.S. Symposiumon Rock Mechanics. Santa Fe, NM, June 3–5.

Maxwell, S.C., Urbancic, T.I., Steinsberger, N.P., Zinno, R., 2002. MicroseismicImaging of Hydraulic Fracture Complexity in the Barnett Shale. Paper SPE77440 Presented at the SPE Annual Technical Conference and Exhibition. SanAntonio, Texas, September 29–October 2.

McClure, M.W., 2012. Modeling and Characterization of Hydraulic Stimulation andInduced Seismicity in Geothermal and Shale Gas Reservoirs. Stanford University(Ph.D. dissertation).

Meng, C., de Pater, C.J., 2010. Hydraulic Fracture Propagation in Pre-FracturedNatural Rocks. ARMA 10-318 Presented at 44th US Rock Mechanics Symposiumand 5th US–Canada Rock Mechanics Symposium. Salt Lake City, UT, June 27–30.

Meyer, B.R., Bazan, L.W., 2011. A Discrete Fracture Network Model for HydraulicallyInduced Fractures: Theory, Parametric and Case Studies. Paper SPE 140514Presented at the SPE Hydraulic Fracturing Conference and Exhibition. Wood-lands, Texas, USA, January 24–25.

Murphy, H.D., Fehler, M.C., 1986. Hydraulic Fracturing of Jointed Formations. PaperSPE 14088 Presented at the SPE 1986 International Meeting on PetroleumEngineering. Beijing, China, March 17–20.

Nagel, N., Gil, I., Sanchez-Nagel, M., 2011. Simulating Hydraulic Fracturing in RealFractured Rock – Overcoming the Limits of Pseudo 3D Models. Paper SPE140480 Presented at the SPE Hydraulic Fracturing Conference and Exhibition.Woodlands, Texas, USA, January 24–26.

Olson, J.E., 2008. Multi-Fracture Propagation Modeling: Applications to HydraulicFracturing in Shales and Tight Sands. 42nd US Rock Mechanics Symposium and2nd US–Canada Rock Mechanics Symposium. San Francisco, CA, June 29–July 2.

Potluri, N., Zhu, D., Hill, A.D., 2005. Effect of Natural Fractures on Hydraulic FracturePropagation. Paper SPE 94568 Presented at SPE European Formation DamageConference. Scheveningen, Netherlands, May 25–27.

Renshaw, C.E., Pollard, D.D., 1995. An experimentally verified criterion for propaga-tion across unbounded frictional interfaces in brittle, linear elastic-materials.Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 32 (3), 237–249.

Rutledge, J.T., Phillips, W.S., Meyerhofer, M.J., 2004. Faulting induced by forced fluidinjection and fluid flow forced by faulting: an interpretation of hydraulic-fracture microseismicity, Carthage Cotton Valley Gas Field, Texas. Bull. Seismol.Soc. Am. 94, 1817–1830.

Savitski, A.A., Lin, M., Riahi, A., Damjanac, B., Nagel, N.B., 2013. Explicit Modeling ofHydraulic Fracture Propagation in Fractured Shales. IPTC 17073 Presented atIPTC. Beijing, China, March 26–28.

Sesetty, V. Ghassemi, A., 2012. Simulation of Hydraulic Fractures and TheirInteractions with Natural Fractures. ARMA 12-331 Presented at 46th US RockMechanics/Geomechanics Symposium. Chicago, IL, June 24–27.

Thiercelin, M., Makkhyu, E., 2007. Stress field in the vicinity of a natural faultactivated by the propagation of an induced hydraulic fracture. In: Proceedingsof the 1st Canada–US Rock Mechanics Symposium; vol. 2, pp. 1617–1624.

Valko, P., Economides, M.J., 1995. Hydraulic Fracture Mechanics. John Wiley & Sons.Walker, K., Wutherich, K., Terry, J., Shreves, J., Caplan, J., 2012. Improving Production

in the Marcellus Shale Using an Engineered Completion Design: A case Study.Paper SPE 159666 Presented at SPE Annual Technical Conference and TechnicalExhibition. San Antonio, TX, October 8–10.

Warpinski, N.R., Branagan, P.T., 1989. Altered-Stress Fracturing. SPE 17533, JPT,September, pp. 990–997.

Warpinski, N.R., Teufel, L.W., 1987. Influence of geologic discontinuities onhydraulic fracture propagation (includes associated papers 17011 and 17074).SPE J. Pet. Technol. 39 (2), 209–220.

Warpinski, N.R., Lorenz, J.C., Branagan, P.T., Myal, F.R., Gall, B.L., 1993. Examinationof a cored hydraulic fracture in a deep gas well. J. SPE Prod. Facil. August,150–164.

Warpinski, N.R., Kramm, R.C., Heinze, J.R., Waltman, C.K., 2005. Comparison ofSingle- and Dual-Array Microseismic Mapping Techniques in the Barnett Shale.Paper SPE 95568 Presented at the 2005 SPE Annual Technical Conference andExhibition. Dallas, Texas, October 9–12.

Weng, X., Kresse, O., Cohen, C., Wu, R., Gu, H., 2011. Modeling of Hydraulic FractureNetwork Propagation in a Naturally Fractured Formation. Paper SPE 140253Presented at the SPE Hydraulic Fracturing Conference and Exhibition. Wood-lands, Texas, USA, January 24–26.

Williams-Stroud, S.C., Barker, W.B., Smith, K.L., 2012. Induced Hydraulic Fractures orReactivated Natural Fractures? Modeling the Response of Natural FractureNetworks to Stimulation Treatments. ARMA 12-667 Presented at 46th US RockMechanics/Geomechanics Symposium. Chicago, IL, June 24–27.

Wu, K., Olson, J.E., 2013. Investigation of Critical In Situ and Injection Factors inMulti-Frac Treatments: Guidelines for Controlling Fracture Complexity. PaperSPE 163821 Presented at SPE Hydraulic Fracturing Conference. Woodlands, TX,February 4–6.

Xu, W., Calvez, J.L., Thiercelin, M., 2009. Characterization of Hydraulically-InducedFracture Network using Treatment and Microseismic Data in a Tight-GasFormation: A Geomechanical Approach. Paper SPE 125237 Presented at the2009 SPE Tight Gas Completions Conference. San Antonio, Texas, USA, June 15–17.

Zhang, F., Nagel, N., Lee, B., Sanchez-Nagel, M., 2013. The Influence of FractureNetwork Connectivity on Hydraulic Fracture Effectiveness and MicroseismicityGeneration. Paper ARMA 13-199 Presented at the 47th American RockMechanics Symposium. San Francisco, CA, USA, June 23–26.

Zhang, X., Jeffrey, R.G., 2006. The role of friction and secondary flaws on deflectionand re-initiation of hydraulic fractures at orthogonal pre-existing fractures.Geophys. J. Int. 166 (3), 1454–1465.

Zhang, X., Jeffrey, R.G., 2008. Reinitiation or termination of fluid-driven fractures atfrictional bedding interfaces. J. Geophys. Res. Solid Earth 113 (B8), B08416.

Zhang, X., Jeffrey, R.G., Thiercelin, M., 2007a. Effects of Frictional GeologicalDiscontinuities on Hydraulic Fracture Propagation. SPE 106111 Presented atthe SPE Hydraulic Fracturing Technology Conference, College Station. Texas,January 29–31.

Zhang, X., Jeffrey, R.G., Thiercelin, M., 2007b. Deflection and propagation of fluid-driven fractures as frictional bedding interfaces: a numerical investigation.J. Struct. Geol. 29, 390–410.

Zhang, X., Jeffrey, R.G., Thiercelin, M., 2009. Mechanics of fluid-driven fracturegrowth in naturally fractured reservoirs with simple network geometries.J. Geophys. Res. 114, B12406.

Zhao, J., Chen, M., Jin, Y., Zhang, G., 2008. Analysis of fracture propagation behaviorand fracture geometry using tri-axial fracturing system in naturally fracturedreservoirs. Int. J. Rock Mech. Min. Sci. 45, 1143–1152.

Zhao, X.P., Young, R.P., 2009. Numerical Simulation of Seismicity Induced byHydraulic Fracturing in Naturally Fractured Reservoirs. Paper SPE 124690Presented at SPE Annual Technical Conference and Exhibition. New Orleans,LA, October 4–7.

X. Weng et al. / Journal of Petroleum Science and Engineering ∎ (∎∎∎∎) ∎∎∎–∎∎∎16

Please cite this article as: Weng, X., et al., Applying complex fracture model and integrated workflow in unconventional reservoirs. J.Petrol. Sci. Eng. (2014), http://dx.doi.org/10.1016/j.petrol.2014.09.021i