Journal of Asian Earth Sciences 75 (2013) 267–279

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Journal of Asian Earth Sciences

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Fracture development in Paleozoic shale of Chongqing area (SouthChina). Part two: Numerical simulation of tectonic stress fieldand prediction of fractures distribution

1367-9120/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.jseaes.2013.07.015

⇑ Corresponding author at: School of Energy Resources, China University ofGeosciences, Beijing 100083, China. Tel.: +86 10 82320629; fax: +86 10 82326850.

E-mail address: dingwenlong2006@126.com (W. Ding).

Weite Zeng a,b,c, Wenlong Ding a,b,c,⇑, Jinchuan Zhang a,b,c, Yeqian Zhang a,b,c, Ling Guo d, Kai Jiu a,b,c,Yifan Li a,b,c

a School of Energy Resources, China University of Geosciences, Beijing 100083, Chinab Key Laboratory for Marine Reservoir Evolution and Hydrocarbon Abundance Mechanism, Ministry of Education, China University of Geosciences, Beijing 100083, Chinac Key Laboratory for Shale Gas Exploration and Assessment, Ministry of Land and Resources, China University of Geosciences, Beijing 100083, Chinad Department of Geology, Northwest University, Xi’an 710069, China

a r t i c l e i n f o a b s t r a c t

Article history:Available online 19 July 2013

Keywords:Longmaxi ShaleMechanical rock propertiesTectonic stress fieldFractures distributionSoutheast Chongqing

A tectonics sedimentation evolution has been researched in Southeast Chongqing, and the reasonableLongmaxi shale highstand system tract (HST) and transgressive system tract (TST) geological model werebuilt respectively based on the rock mechanical test and acoustic emission experiment which the sam-ples are from field outcrop and the Yuye-1 well. The Longmaxi shale two-dimension tectonic stress fieldduring the Cenozoic was simulated by the finite element method, and the distribution of fractures waspredicted. The research results show that the tectonic stress field and the distribution of fractures werecontrolled by lithology and structure. As a result of Cretaceous movement, there are trough-like folds(wide spaced synclines), battlement-like folds (similar spaces between synclines and anticlines) and ejec-tive folds (wide spaced anticlines), which are regularly distributed from southeast to northwest in thestudy area. Since the strain rate and other physical factors such as the viscosity are not taken intoaccount, and the stress intensity is the main factor that determines the tectonic strength. Therefore,the stronger tectonic strength leads the higher stress intensity in the eastern and southeastern study areathan in the northwest. The fracture zones are mainly concentrated in the fold axis, transition locations offaults and folds, the regions where are adjacent to faults. The fragile mineral contents (such as siliceousrock, carbonate rock and feldspar) in the shelf facies shale from south of the study area are higher than inthe bathyal facies and abyssal facies shale from center of the study area. The shales characterized by lowPoisson’s ratio and high elastic modulus from south of the study area are easily broken during Cenozoicorogenic movement.

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0. Introduction

The southeastern portion of Chongqing is the pilot experimen-tal area in China for the key strategic investigations of shale gas.In 2009, the Yuye-1 well, which was the first Chinese well for thestrategic investigation of shale gas, was drilled in this experimen-tal area. By 2011, the Yuke-1, Youke-1, Pengye-1, and Qianye-1wells had been successively drilled in this area. These five wellsrevealed the existence of two formations of high-quality shalein the region in question, namely, the Lower Silurian LongmaxiShale and the Lower Cambrian Niutitang Shale. In particular, a

maximum total hydrocarbon concentration of 22.50% has beenreached by the Pengye-1 well, which targets a shale layer in theLower Silurian Longmaxi-Upper Ordovician Wufeng Shale, andthe greatest desorption gas content of this field was 2.30 m3/t.Moreover, for the Qianye-1 well, which also targets a shale layerof this formation, after hydraulic fracturing treatment and drain-age tests, a wellhead pressure of 3 MPa was achieved, and theinstantaneous flow rate for the initial shale gas test was308 m3/h; this rate is sufficient for industrial gas operations. Inrecent years, various studies have been conducted to addressshale gas exploration in the marine shale of North America. Mostof these studies on shale gas exploitation have focused onidentifying the most effective approaches for fracturing shale; infact, fractures are a critical determinant of the success of shalegas wells (Hill and Nelson, 2000; Curtis, 2002; Warlick, 2006;Gale et al., 2007; Li et al., 2007, 2009; Nie et al., 2009a;

268 W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279

Tan, 2009). Organic-rich shale with low porosity and permeabilitycan form effective natural gas reservoirs if this shale has devel-oped sufficient natural fractures, microfractures, and nanometer-scale pores and fractures within rocks (Sun et al., 2008) or if frac-turing treatments can generate a fracture system that features alarge number of fractures. The development of natural fracturesystems not only directly affects the mining efficiency of shalegas reservoirs but also determines the quality and production lev-els of these reservoirs (Montgomery et al., 2005; Bowker, 2007;Zhang et al., 2003). Higher levels of fracture development increasethe total gas content of a shale formation by both enlarging thevolume of unbound natural gas that is contained in this formationand promoting the desorption of adsorbed natural gas from theshale (Curtis,2002; Nie et al., 2009b; Zhang et al., 2003, 2004;Chen et al., 2009). Based on a detailed analysis of the tectonicand sedimentary evolution in southeastern Chongqing area thatcombines investigations of rock mechanics and acoustic emis-sions experiments, this study applies the finite element methodto simulate the two-dimensional tectonic stress field that existedduring the development of the fracture in Cenozoic for the LowerSilurian Longmaxi Shale of the study region. This approach al-lowed fracture distributions in this shale to be predicted. Thesefracture distribution predictions can provide an important theo-retical guideline for facilitating the industrial production of shalegas in southeastern Chongqing.

1. Regional geological setting

The faults in the southern portion of the study area mainly arisefrom stress or stress-shear interactions; therefore, the majorities offaults in this region are thrust-nappe and thrust faults, which typ-ically develop on the two wings of anticlines in a staggered en ech-elon arrangement. The central portion of the study area isdominated by normal faults that are generally inclined towardsthe northwest; these faults have largely developed along the axesof anticlines. The faults in the northern portion of the study areaare predominantly distributed along the wings of anticlines and

Fig. 1. Tectonic map of Sou

include many types of faults, which are mainly inclined to thenorthwest and southwest (Zhang et al., 2010). As a result of thesubduction of the Pacific plate under the Asian plate in the Creta-ceous, the compressive strain transfers and the energy decays inthe SE–NW direction sequentially produced Jura-type folds. Latein the Cretaceous movement, the direction of regional stresstwisted in a counterclockwise direction, altering the morphologyof the existing fold structure by causing S-shaped or arc-like foldsto form in the axial plane. The tectonic stresses of folds formed inthe Cretaceous underwent relaxation or release in the Cenozoic,leading to the creation of a series of large-scale NNE-trending nor-mal faults along anticlinal axes and wings that consisted of horstand graben fault systems; these processes ultimately created themodern tectonic landscape of the study area (see Figs. 1 and 2).

The graptolite Longmaxi Shale in southeastern Chongqing (i.e.,the lower strata of the Longmaxi Formation) was created duringa brief large-scale transgression that occurred early in the Silurianand provided important hydrocarbon source rocks of the Yangtzeplate, particularly in the Sichuan Basin and its surrounding regions(Wo et al., 2007; Zhang et al., 1987). There is a lack of applicablelogging data and seismic data in the research area; therefore,cross-sectional analyses of local outcrops and core facies of theYuye-1 well were performed. Comparative assessments of thestratigraphic sequence framework in the region and of single andmultiple cross-sections of facies from outcrops and wells wereused to examine the sedimentary system in the lower LongmaxiFormation of the research area. Based on these assessments, thebottom strata of the Longmaxi Formation were recognized as onethird-order sequence that included a transgressive system tract(TST) and a highstand system tract (HST) (Figs. 3 and 4). Duringthe TST, water levels were relatively deep and sediments primarilycame from the south. The TST mainly featured the development ofblack carbonaceous shale and small quantities of gray mudstoneand gray siltstone shale. The sedimentation and subsidence centerof the TST was located in the north-central and northwesternregions of the study area, which predominantly experienced bath-yal and deep-water shelf environments. The chief rock types that

theast Chongqing area.

Fig. 2. Tectonic cross-section of southeastern Chongqing area.

Fig. 3. Paleo-geographic reconstruction of the transgressive system tract (TST) for the Longmaxi Shale.

Fig. 4. Paleo-geographic reconstruction of the highstand system tract (HST) for the Longmaxi Shale.

W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279 269

270 W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279

were deposited in this region were black carbonaceous shale, darkgray shale, dark gray silty shale, and siliceous shale. The northeastregion of the study area was likely affected by the ‘Hunan-HubeiUnderwater Plateau’ (Fan et al., 2012; Chen et al., 2004), and there-fore largely featured a shallow-water shelf sedimentary environ-ment. The major rock types that were deposited in this regionwere gray shale, black shale, and calcareous shale. The south regionof the study area was mostly a shallow-water shelf during the TST,although portions of this region consisted of sandy shelf. The rocktypes that were deposited in this region were primarily gray siltymudstone, calcareous shale, and gray siltstone. The HST featuredlower sea levels than the TST; therefore, shale deposition occurredin shallower water during the HST than during the TST. During theHST, the subsidence center was located in the northern and north-western portions of the research area, and sediments primarilycame from the south. In the southern portion of the study region,the area of sandy sediments increased during the HST, and sandyshelf depositions primarily occurred at this time; the major rocktypes that were deposited in this region were calcareous shale,gray argillaceous siltstone, and light gray siltstone. During theHST, the north-central region of the study area is represented bydeep-water shelf and bathyal deposits, but the extend of thesetypes of deposits decreased significantly during the HST relativeto the TST. The main rock types deposited in this region were blackcarbonaceous shale, dark gray shale, and gray argillaceous silt-stone. The scope of the shallow-water shelf depositional area inthe examined region increased in the HST compared with theTST, and the primary rock types deposited in this area were calcar-eous shale and silty shale.

2. Methods for tectonic stress field simulation and fracturedistribution prediction

2.1. Tectonic stress field simulation

The tectonic stress field typically refers to the crustal stress fieldthat causes tectonic movements. The purpose of tectonic stressfield simulation is to model the distribution of stress inside a rockblock through the application of boundary forces, using first inver-sion and forward modeling approaches (Ye, 2011; Li, 2010; Liu,2009). In this study, the finite element method and ANSYS com-puter software were employed to produce a two-dimensional sim-ulation of the stress field of the Longmaxi Shale in southeasternChongqing area.

The simulation of a tectonic stress field includes the followingsteps: (1) the establishment of a geological model; (2) the estab-lishment of a mechanical model; (3) the establishment of a math-ematical model; and (4) computer calculations and analyses of thesimulation results.

Fig. 5. Curve of paleostress measurements based on initial pressures of acousticemissions for shale samples from the Yuye-1 well.

2.1.1. Establishment of a geological modelThe geological model considers petrography structural geology.

The finite geometry of active structure will be influenced by the suc-cessive tectonic stress fields during multiple periods. Thus, this his-tory constitutes a comprehensive picture of the impact of multipletectonic stress fields over time. However, the structure is often af-fected by the most recent tectonic stress field (in this situation,the Cenozoic movement). In the absence of seismic and logging datain the study region, the targeted layers to be simulated were sepa-rated from their surrounding rock block based not only on the struc-ture and the historical sedimentary evolution of the research areabut also on the outcrop data and drilling core data from this area.This approach allowed for the establishment of two-dimensionalgeological models of the TST and HST for the Longmaxi Shale beforethe Cenozoic (Figs. 3 and 4).

2.1.2. Establishment of a mechanical modelThe establishment of a mechanical model includes the follow-

ing tasks: (1) to determine the loading regime for geological bodiesand constraints on types and methods of geological loading (i.e.,determine the boundary conditions); (2) to determine the mechan-ical parameters for different rock units of the studied layers; and(3) to determine the mechanical parameters for faults and folds,which will directly affect the simulation results.

(1) Determination of the loading regime for geological bodiesand constraints on the types and methods of geological load-ing (i.e., the determination of the boundary conditions).

To begin with examinations of macroscopic effects, geologicalbodies were assumed to be homogeneous blocks or slices of rockbodies and were simulated as pieces of uniformly elastic material.The boundary conditions included displacement boundary condi-tions and stress boundary conditions. It was assumed that the forceon a boundary is a set of determined values and that this force isuniformly distributed across the boundary of interest. The acousticemission experiments on rock samples were performed at the Geo-stress Measurement Laboratory of the Chinese Institute of Geome-chanics. In particular, the experimental setup utilized a 4010Acoustic Emission instrument, a 300 kN universal press, strain sen-sors, and a computer (Figs. 5 and 6). This device can assess stressesfrom paleostress periods and reveal the maximum effective paleo-stress that have been experienced by the examined strata (Dingand Shao, 2001). This study focused on measuring the maximumprincipal stress r1 of Longmaxi Shale from the Yuye-1 well duringtectonic movements of different periods (Table 1). The experimen-tal samples were obtained from the Yuye-1 well; in particular, 15standard 25 mm � 50 mm cylindrical samples were acquired bydrilling in the core column, perpendicularly to the bedding planeof core.

The most intense tectonic movement in the research area wasthe Cretaceous movement, followed by the Cenozoic movement.Therefore, it is reasonable to believe that the maximum tectonicstress that was experienced by the Longmaxi Shale of the Yuye-1well would have been 148.8 MPa in the Cretaceous and122.5 MPa in the Cenozoic. During the Cenozoic, the research areaas a whole experienced a compressional stress field in the north-west–southeast direction. Given that the Yuye-1 well is locatedon the axis of the Guochangba anticline of the city of Lianhu, itcould be predicted that the stress simulation results for this sitewould 4indicate that larger stresses were experienced at this loca-tion than in nearby ordinary continuous strata. After debugging theabove approach, the following displacement boundary conditionsfor the established geological model were established: a maximumprincipal stress of 80 MPa was applied to the upper left and thelower right boundary; a minimum principal stress of 30 MPa was

Fig. 6. Curve of paleostress measurements based on repeated pressures of acousticemissions for shale samples from the Yuye-1 well.

Table 1The results of tectonic stress measurements from acoustic emissions for shalesamples from the Yuye-1 well.

Well # Depth(m)

Formation Effective tectonicstress r1 duringvarious periods(MPa)

Major stages ofknown tectonicmovement(episode)

Yuye-1 0–325.5 Longmaxi 23.1, 40.8, 57.4,91.0, 122.5, 148.8

6

Fig. 7. Mechanical model of the Longmaxi Shale in southeast Chongqing during theCenozoic.

W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279 271

applied to the upper right and lower left boundary; constraintswere placed on displacement in the X and Y directions for thenodes at the right corner and the left corner of the model, allowingall other units to move freely; and a set of 25 MPa pull tensionswere applied in parallel in the direction of maximum principalstress at the nodes of the upper left and the lower right corner tosimulate the sinistral shear stress that was experienced in theCenozoic (Fig. 7).

(2) Determination of mechanical parameters for various rockunits of the studied layers.

The geological model of this study divided the examined unitsinto the following major unit types (Table 2): fault zones, foldzones, and zones of ordinary sedimentary strata. Based on faultsize, fault zones were subclassified into first-order, second-order,and third-order faults. The only first-order fault in the researcharea is the Qiyao Mountain basement fault, and other faults inthe region were divided into second-order and third-order faultsbased on morphological scale and extension range. Fold zones,which have been produced by southeast-northwest energy trans-fers and energy decays, were divided into trough-like folds (widespaced synclines), battlement-like folds(similar spaces betweensynclines and anticlines) and ejective folds(wide spaced anti-clines). Lithological differences were utilized to subdivide theexamined sedimentary layers into various unit types, includingcarbonaceous shale, siliceous shale, black shale, calcareous shale,and argillaceous siltstone.

Because this study primarily seeks to provide two-dimensionalsimulations of tectonic stress fields, the major mechanical param-eters of rocks that are required are the elastic modulus and Pois-son’s ratio. Experiments to examine rock mechanics wereperformed in the Rock Mechanics Testing Laboratory of the Univer-sity of Science and Technology Beijing. In particular, these experi-ments used not only a uniaxial rock mechanical testing platformthat consisted of a WGE-600 universal testing machine, 100-tonpressure sensors, 7V14 program-controlled recorder, and anE4800 computer but also used a triaxial rock mechanical testingplatform that consisted of a TYS-500 triaxial rock testing machine,

100-ton pressure sensors, a 7V14 program-controlled recorder, andan E4800 computer. The experiment was performed in accordancewith the protocols specified by Chinese standard SL264-2001,‘‘Specifications for Rock Tests in Water Conservancy and Hydro-electric Engineering’’. In accordance with the burial depth of theLongmaxi Shale in the study area and the actual number of sam-ples that were examined, the confining pressures that were uti-lized in the triaxial rock mechanics experiments were 0, 5, 10,and 15 MPa, and the influence of ground temperature was not con-sidered. The uniaxial rock mechanics experiment was primarily de-signed to measure the parameters of rock density, uniaxialcompressive strength, elastic modulus, Poisson’s ratio, and tensilestrength, although other parameters were also examined. In thetriaxial rock mechanics experiment, measurements of axial rupturestress, elastic modulus, and Poisson’s ratio of samples at differentconfining pressures were used to calculate cohesion and internalfriction angle, and other shear strength parameters (Table 2). TheLongmaxi Shale samples for rock mechanics measurements werecollected from the Yuye-1 well and outcrops in the field. In partic-ular, for each examined lithology, the samples were obtained bydrilling vertically to the bedding plane; these samples were thenprocessed into 19 standard 25 mm � 50 mm cylindrical samplesfor each examined lithology.

(3) Determination of mechanical parameters for faults andfolds.

In this study, to address fault zones and fold zones (Table 3),fault zones were defined as ‘weak zones’. The elastic modulus ofa fault zone is typically smaller than the elastic modulus of a nor-mal stratum; in particular, this modulus is generally 50–70% of themodulus of a corresponding normal stratum. The Poisson’s ratio ofa fault zone is larger than the Poisson’s ratio of a correspondingnormal sedimentary rock stratum, and the difference betweenthese two ratios is typically between 0.02 and 0.1. Fold zones aredefined as ‘‘hard zones’’. The elastic modulus of a fold zone is typ-ically larger than the elastic modulus of a normal stratum; in par-ticular, this modulus is generally 150–300% of the elastic modulusof a corresponding normal stratum. The Poisson’s ratio of a foldzone is smaller than the Poisson’s ratio of a corresponding normalsedimentary rock stratum, and the difference between these tworatios is typically between 0.01 and 0.15.

Table 2A calculation table for the uniaxial compression test of various rock types.

Lithology Natural density, qo

(g cm�3)Tensile strength, rt

(MPa)Compressive strength,rc (MPa)

Elastic modulus, E(GPa)

Poisson’sratio, l

Cohesion, C(MPa)

Internal frictionangle, u (�)

Carbonaceousshale

2.715 16.67 100.95 52.83 0.266 22.33 34.53

Black shale 2.657 5.95 149.60 59.75 0.255 27.71 34.56Argillaceous

siltstone2.688 12.23 102.75 65.82 0.286 3.84 56.36

Calcareousshale

2.655 6.79 132.87 42.87 0.205 16.42 49.01

Siliceous shale 2.747 9.06 101.83 54.06 0.261 12.42 58.11

272 W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279

2.1.3. Establishment of the mathematical modelA geological model was constructed in the form of a triangular

mesh that was subdivided into a series of node and element grids.The geological model of the HST strata included 9965 nodes and19,670 elements, whereas the geological model of the TST strataincluded 8270 nodes and 16,330 elements. After the model bound-ary conditions and the applied load had been determined, the finiteelement method was applied to solve the model. The fundamentalnotion underlying the finite element method involves dividing thedomain of a continuous field function that must be solved into aseries of elements that are only connected at nodes, allowing foran unknown function value at an element to be obtained throughinterpolation of known values from the selected function. In gen-eral, finer elemental divisions produce more accurately computedresults. We divided the geological model into a number of planar,triangular mesh elements. For an arbitrary triangular mesh ele-ment, the displacement u and v of an arbitrary point (x,y) in theelement can be expressed in matrix form as follows:

½f �e ¼u

v

� �¼

Niui þ Njuj þ Nmum

Niv i þ Njv j þ Nmvm

� �

¼Ni 0 Nj 0 Nm 00 Ni 0 Nj 0 Nm

� �ui v i uj v j um vm½ �T

¼ ½N�½d�e ð1Þ

where Ni, Nj, Nm are the shape functions describing the element’sdisplacement; [N] is the shape function matrix; and [d]e is the ma-trix of node displacement components.

To determine the displacement function and express the dis-placement of an element in terms of the nodal displacement, thestrain of the element must be calculated; the following geometricequation was utilized to accomplish this task:

½e� ¼ex

ey

exy

264

375 ¼

@@x 00 @

@y

@@y

@@x

264

375 u

v

� �ð2Þ

By substituting Eq. (1) into Eq. (2), the strain matrix of the ele-ment may be obtained:

½e� ¼ ½B�½d�e ð3Þ

where the conversion matrix [B] is a geometric matrix.

Table 3The mechanical properties of different types of rock units.

Unit type Elastic modulus (MPa) Poisson’s ratio

Fault zoneFirst-order fault 21,435 0.332Second-order fault 32,436 0.317Third-order fault 36,981 0.305

Fold zoneTrough-like fold 102,180–137,460 0.200–0.211Battlement-like fold 85,660–102,180 0.211–0.248Ejective fold 65,740–85,660 0.248–0.256

From elasticity equations, stress and strain exhibit the followingrelationship:

½r� ¼ ½D�½e� ð4Þ

By substituting Eq. (3) into Eq. (4), the stress matrix for the ele-ment may be derived as follows:

½r� ¼ ½D�½B�½d�e ¼ ½S�½d�e ð5Þ

where [S] is the stress matrix.As illustrated above, the nodal force for a triangular element in-

volves a total of six components, as follows:

½P�e ¼ ½Ui Vi Uj Vj Um Vm �T ð6Þ

The stress that is caused by this nodal force on the element maybe expressed as follows:

½r� ¼ ½rx ry txy �T ð7Þ

According to the principles of virtual displacement and virtualwork, the following stiffness matrix for the element may be de-rived as follows:

½P�e ¼ ½K�e½d�e ð8Þ

where [K]e is the element stiffness matrix, which expresses the rela-tionship between nodal force and nodal displacement.

A transformation of the element stiffness matrix can be imple-mented to derive the integral stiffness matrix. The boundary con-ditions may then be introduced into the equation, and theintegral stiffness matrix may be transformed to derive the follow-ing overall stiffness equation:

½P� ¼ ½K�½d� ð9Þ

where [K] is the integral stiffness matrix, [P] is the integral nodalload matrix, and [d] is the nodal displacement matrix for the inte-gral structure of the examined elemental array.

By solving the linear equation (9), [d], the nodal displacementvector for the integral structure, may be obtained; therefore, thenodal displacement of each element may be derived. The substitu-tion of this displacement into the element equations (2)–(5), canthen be performed to determine the displacement, strain, andstress of each individual element in the structure.

For every element, the maximum principal stress was typicallyderived through a coordinate transformation that involved solvingthe following eigenvalue problem:

rx � r syx

syx ry � r

�������� ¼ 0 ð10Þ

The solving of the above equation allows the maximum princi-pal stress r1 and the minimum principal stress r3 to be determined(and no r2 exists for a two-dimensional simulation of the tectonicstress field).

W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279 273

2.1.4. Calculation of solutionsThe ANSYS software package was utilized to simulate the tec-

tonic stress field in the two-dimensional plane for the LongmaxiShale in southeastern Chongqing area. The simulation results indi-cated the distributions of the maximum principal stress, shearstress, and stress intensity. These parameters were primarily se-lected for the following two reasons. First, the maximum principalstress is the main factor that determines tectonic deformation andthe formation and distribution of faults, whereas the stress inten-sity determines the tectonic strength and the density of faults andfolds in an area. The shear stress significantly affects the crackingand distortion that are produced by faults and folds.

2.2. Methods for simulating and predicting fractures

There are two major types of fractures in rocks that occur due tostress: shear fractures and tension fractures. Shear fractures weregenerally predicted using the combined Mohr–Coulomb shear rup-ture criterion, whereas tension fractures were predicted using theGriffith criterion.

2.2.1. Griffith criterionGriffith proposed a strength theory that addressed the ruptur-

ing of brittle materials (Griffith, 1921). In particular, Griffith sug-gested that for brittle materials with a large number of fine andelliptical cracks that are influenced by stress field, tangential ten-sile stresses will be concentrated around the periphery of theseoval cracks. Once the concentration of tangential tensile stress ata point near the peripheral edge of a crack reaches the intramolec-ular cohesive strength of the examined material, the material willbegin to undergo brittle rupturing in this area; this fracture will ex-tend in a particular direction that may be determined. In the Grif-fith strength theory, the following expressions exist for the planarrupture criterion.

If r1 + 3r3 P 0, the rupture criterion may be expressed asfollows:

ðr1 � r3Þ2 � 8ðr1 þ r3ÞrT ¼ 0 ð11Þ

If r1 + 3r3 < 0, the rupture criterion may be expressed asfollows,

r3 þ rT ¼ 0 ð12Þ

where r1 is the maximum principal stress of a rock, r2 is the min-imum principal stress of this rock, and rT is the tensile stress of therock in question.

2.2.2. The Mohr–Coulomb shear fracture criterionThe Mohr–Coulomb criterion suggests that the shear fracture of

rocks along a fault plane depends not only on s, the magnitude ofshear stress on the fault plane, but also on r, the normal stress onthe plane of interest. In other words, the shear fracture on a planeis related to the combination of the normal stress r and the shearstress s that are acting on the plane. The Coulomb–Navier shearfracture criterion may be written as follows:

jsj ¼ C þ rNtgu ð13Þ

where |s| is the shear strength of the rock; rN is the normal stress; Cis cohesion, which is the shear strength of the rock if the normalstress is zero; u is the internal friction angle; and tgu is the internalfriction coefficient.

2.2.3. Determination of tectonic fracturesTectonic stress field simulations of fracture formation periods

may be used to calculate the tensile stress and shear stress of rocksduring these periods. The aforementioned fracture criterion may

then be employed to compare these tensile and shear stresses withthe tension and shear strengths, respectively, of the examinedrocks, allowing for the determination of whether ruptures will oc-cur in these rocks.

To facilitate computer processing and quantitative analyses, thetension rupture rate of fractures, It, is introduced:

It ¼ rT=rt ð14Þ

where rT is the effective tensile stress and rt is the tensile strengthof the rock. If It P 1, a tension rupture will occur in an examinedrock.

Similarly, to facilitate computational processing and quantita-tive analyses, the shear rupture rate, In is also introduced:

In ¼ sn=jsj ð15Þ

where sn is the effective shear stress and |s| is the shear strength ofthe rock. If In P 1, a shear rupture will occur in an examined rock.

In present situations, tension fracture systems and shear frac-ture systems do not exist alone in fractured reservoirs; instead,both types of fractures develop concurrently. The level of rock rup-ture is a comprehensive reflection of both fracture rates. Therefore,we introduce the comprehensive rupture rate, In:

Iz ¼ ðaIt þ bInÞ=2 ð16Þ

where a and b are the proportions of tension fractures (includingtension shear fractures) and shear fractures observed in the core,respectively. Investigations and statistical analyses of fractures inthe core of the Yuye-1 well and relevant data from the research areaproduced the result that the ratio of the number of tension fracturesto the number shear fractures in the research area during the Ceno-zoic was 6:4. In the equation above, for Iz P 1, the rock ruptures,and higher values of the comprehensive rupture rate correspondto greater degrees of rupture.

2.2.4. Determination of tectonic fracturesUsing the comprehensive rupture rate of fractures as an indica-

tor, we evaluated the degree of fracture development for two sys-tem tracts, the HST and TST, of the Longmaxi Formation in theresearch area. The degrees of fracture development in the exam-ined tracts were divided into three grades: developed zones, sec-ondary developed zones, and undeveloped zones (Table 4).

3. Results and interpretations

3.1. Stress field simulation results for the Longmaxi Shale insoutheastern Chongqing during the Cenozoic

As illustrated in Fig. 8, the maximum principal stress in the TSTstrata of the Longmaxi Shale in southeastern Chongqing was gen-erally distributed between �217.404 MPa and �4.109 MPa. In thissituation, a positive sign indicates tensile stress, whereas a nega-tive sign indicates compressive stress. The interiors of fault zoneswere defined to be ‘weak zones’; higher levels of rock fragmenta-tion and lower levels of maximum principal stress (ranging from�46.768 MPa to �4.109 MPa) were observed in these fault zonesthan in ordinary strata. Compared with the fault zones, zones withcontinuous strata exhibited stable lithologies, and the magnitudesof maximum principal stress for these zones of continuous strataranged between �103.647 MPa and �46.768 MPa. This range ofmaximum principal stress magnitudes encompassed the widestdistribution of rocks in the research area. The interiors of foldzones were defined as ‘hard zones’. There, rocks experienced fold-ing deformations without rupturing or reaching critical states offracture. Thus, these zones featured highly concentrated stressand were therefore found in regions with high levels of stress; in

Table 4Determination criteria of the degree of fracture development.

Fracture development level I II III

Comprehensive rupture rateof fractures

Iz P 1.4 1.0 6 Iz < 1.4 Iz < 1.0

Degree of fracturedevelopment

Developed Secondarydeveloped

Undeveloped

274 W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279

particular, the maximum principal stresses in these zones rangedbetween �217.404 MPa and �103.647 MPa.

As presented in Fig. 9, the maximum principal stresses in theHST strata of the Longmaxi Shale in the research area were distrib-uted between �173.063 MPa and �17.715 MPa; thus, these maxi-mum principal stresses reflected states of compression stress. Theinteriors of fault zones were regions with low stress levels; in thesezones, the magnitudes of maximum principal stresses were largelybetween �48.784 MPa and �17.715 MPa. The magnitudes of max-imum principal stresses in continuous strata ranged from�90.211 MPa to 48.784 MPa. The most severe deformation wasexperienced by rocks inside folds, particularly along the centralaxis and the transitional portions of these folds. In these locations,if no fault had developed to relieve stress, highly concentratedstresses were observed. Moreover, increased stress intensitieswere evident if folds were either clamped by thrust faults (whichoccurred in various locations, such as southwest of Huayuan andwest of Pengshui) or located close to faults (such as folds in theLongshan and Xiushan areas); variations in the stress gradient be-came more evident as the distances between folds and faultsdiminished. In addition to the fold zones that have been discussedabove, the ends of fault zones and the turning points of faults werealso regions with high magnitudes of stress. These areas repre-sented transitional regions between fractured rocks and continu-ous strata inside fault zones; rocks in these regions were on thecusp of rupture and therefore demonstrated enhanced levels ofstress. The values of the maximum principal stresses in theseaforementioned high-stress regions were mainly distributed be-tween �173.063 MPa and �90.211 MPa.

In southeastern Chongqing, the shear stresses in the TST strataof the Longmaxi Shale ranged from �4.707 MPa to 49.222 MPa

Fig. 8. Distribution of maximum principal stress intensity for the transgressive

(Fig. 10), and the shear stresses in the HST strata of this formationranged from 5.72 MPa to 58.206 MPa (Fig. 11). In this case, positivevalues of shear stress represented stresses in the sinistral direction,whereas negative values of shear stress represented stresses in thedextral direction. The research area includes north-northeast-ori-ented S-shaped faults and folds that generally demonstrate coun-terclockwise twisting; during the formation of the Neocathaysianstructual system (the main tectonics are large-scale NNE-trendingfolds and shearing compressive fault belt, distributing in left eche-lon), the combined tectonic activities of nearly north-south-trend-ing compression and continued counter-clockwise twisting wereobserved, and fault zones with distinct strike-slip characteristicswere produced. As illustrated in Figs. 10 and 11, the research areapredominantly featured counterclockwise sinistral shear stresses;therefore, the simulation results for the shear stress distributionwere consistent with the known characteristics of Himalayan tec-tonic stress in the examined area.

In contrast to distributions of maximum principal stresses, plotsof stress intensity merely indicate the absolute value of the resul-tant stress that is exerted on each element of the geological modeland cannot reflect the compressive and tensile stress states foreach element. From the results that are depicted in Fig. 12, theresultant stress intensities in the TST strata of the Longmaxi Shalein southeastern Chongqing ranged between 4.109 MPa and217.404 MPa, and the stress intensity and maximum principalstress distributions were similar for these strata. In particular,the predicted stress intensities at the site of the Yuye-1 well rangedbetween 117 MPa and 130 MPa; these simulation results wereclose to the stress intensity (122.5 MPa) that was determinedthrough acoustic emission experiments, supporting the validityof the simulation results for stress intensity in the examined strata.The southern portion of the study area was dominated by sedi-ments of shallow-water and sandy shelf facies; the main lithologyof this region was calcareous shale, argillaceous siltstone, and silt-stone. These rocks featured high levels of quartz, carbonate, andother brittle minerals; therefore, the mechanical parameters ofthese rocks were characterized by high elastic moduli and lowPoisson’s ratios. By contrast, the north-central and northwest por-tions of the work area were dominated by bathyal and deep-watershelf environments, and the main rock types in this region were

system tract (TST) strata of the Longmaxi Shale in southeastern Chongqing.

Fig. 9. Distribution of maximum principal stress intensity for the highstand system tract (HST) strata of the Longmaxi Shale in southeastern Chongqing.

Fig. 10. Distribution of shear stress magnitudes for the transgressive system tract (TST) strata of the Longmaxi Shale in southeastern Chongqing.

W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279 275

black carbonaceous shale, dark gray shale, and siliceous shale.These rocks featured relatively low elastic moduli and high levelsof Poisson’s ratio. Thus, it was unsurprising that the stress intensityin the continuous strata was lower in the northern and northwest-ern portions of the study area than in the southern and eastern re-gions of this area.

The stress intensities in the HST strata of the Longmaxi Shaleranged between 17.715 MPa and 173.063 MPa (Fig. 13); in partic-ular, the simulated stress intensity at the Yuye-1 well was 121.28–130.78 MPa, which was highly consistent with the stress intensityfinding (122.5 MPa) from acoustic emission experiments in thecore of the Yuye-1 well. In the Cretaceous, southeastern Chongqingexperienced southeast-northwest compressive stress; this stressinduced the formation of a trough-like folds, battlement-like folds,and ejective folds in the southeast-northwest direction sequen-tially that is representative of the ‘Jura-type’ folds that are

observed in southeastern Sichuan. Geologists have extensivelystudied the deformation and formation history of this tectonic belt(Ding et al., 2005,2007; Hu et al., 2009; Huang, 2000; Feng et al.,2003; Li et al., 2002; Liu, 1995; Xu et al., 2004; Zhang et al.,2009). For instance, from an analysis of tectonic deformation, Yanet al. (2000) proposed that ejective folds were first formed at theearly stages of tectonic development but these folds eventuallyevolved into trough-like folds by thrusting movement, meanwhile,the new ejective folds were formed at the front end of the com-pressive nappe stronger deformation would be expected fortrough-like folds at the back end (the southeastern portion of theresearch area) than for ejective folds at the front end (the north-western portion of the study area) of this nappe. Among the foldsof the aforementioned folding pattern, the strongest deformationwould occur in synclines within trough-like folds, whereas theweakest deformation would occur in synclines within ejective

Fig. 11. Distribution of shear stress magnitudes for the highstand system tract (HST) strata of the Longmaxi Shale in southeastern Chongqing.

Fig. 12. Distribution of stress intensities for the TST strata of the Longmaxi Shale in southeastern Chongqing.

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folds. The battlement-like folds should feature deformation levelsthat are between the deformation levels of trough-like folds andejective folds; for these battlement-like folds, synclines and anti-clines should feature similar degrees of deformation. The resultsof the stress field simulation in the research area (Figs. 8, 9, 12and 13) indicated that the stress intensity of trough-like folds inthe southeastern portion of this area was markedly greater thanthe stress intensity of ejective folds in the northwest of the re-search area. Moreover, the stress intensity was higher for the syn-cline than for the anticline for trough-like folds in the southeast ofthe study area, whereas the stress intensity was lower for the syn-cline than for the anticline for ejective folds in the northwest ofthis area. For the intermediate battlement-like folds, similar stressintensities of synclines and anticlines were predicted. Thus, the

simulation results were highly consistent with the actual situationfor the research area.

3.2. Predictions of fracture distributions in the Longmaxi Shale insoutheastern Chongqing during the Cenozoic

Using the contours of the comprehensive rupture rate in the TSTstrata of the Longmaxi Shale in the research area, the fracture dis-tribution during the Himalayan was determined. The most widelydistributed comprehensive rupture rate of favorable areas for LevelI fractures in the eastern portion of the work area (southeast ofLaifeng and Longshan) was 1.4–2.0. Notably, high comprehensiverupture rates that were sometimes greater than 2.0 were observedalong the axis of large trough folds to the north of Huayuan in the

Fig. 13. Distribution of stress intensities for the HST strata of the Longmaxi Shale in southeastern Chongqing.

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study area. Favorable areas for both Level II and Level I fractureswere distributed across the southern (south of Xiushan and Huay-uan) and northwestern (Lianhu area) portions of the examined re-gion, and the comprehensive rupture rate of these regions rangedfrom 1.0 to 1.4. The western portion (Wulong and Pengshui) ofthe research area was primarily a favorable area for Level II frac-tures, and the comprehensive rupture rate in this region wasapproximately 1.0 (Fig. 14).

The fracture distribution in the HST strata of the shale of Long-maxi Shale (Fig. 15) was generally similar to the fracture distribu-tion for the TST strata of this formation. The favorable regions for

Fig. 14. Predicted distribution of favorable areas for fractures in the TST strata o

Level I fractures were mainly distributed across the eastern, south-ern, and northwestern portions of the study area, and the compre-hensive rupture rate for the HST strata in these areas was 1.4–1.6.The most favorable area for Level II fractures in the HST strata wasfound in the central portion of the work area (the Youyang area),and the comprehensive rupture rate in this region was 1.0–1.4.

The comparison of the fracture distribution predictions withmodern tectonic plots in southeastern Chongqing revealed thatthe most favorable areas for fracture development are largely dis-tributed along faults and folds. The Cenozoic tectonic movementtransformed the NE-SW trending folds that were formed in the

f the Longmaxi Shale in southeastern Chongqing area during the Cenozoic.

Fig. 15. Predicted distributions of favorable areas for fractures in the HST strata of the Longmaxi Shale in southeastern Chongqing area during the Cenozoic.

278 W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279

Cretaceous. The strata in the most favorable areas for fractures,which were found along anticlines in the northwest, east, and cen-tral regions of the study area, experienced ruptures that led to theformation of normal faults and the development of predominantlytension fractures. In contrast to the axes of anticlines, the axes ofsynclines were locked, inhibiting the formation of normal faults;therefore, these regions primarily developed transtensional shearfractures. Due to the influence of sinistral shear stresses duringthe late Cretaceous and the Cenozoic, the morphology of faultsand folds became S-shaped or arc-shaped, and many strike-slipfaults were formed. During this period, the turning of folds andfaults experienced strong shear deformation and consequentlydeveloped a number of shear fractures. The predictions of fracturedistribution for both the TST strata and the HST strata indicatedthat fractures would be most developed in the eastern and south-ern regions of the study area, especially in regions that were lo-cated near faults and along the axes of wide spaced synclineswith relatively strong deformations. In particular, synclines in theLaifeng area developed normal faults along their axes despite thefact that normal faults do not readily form in this context. Thenorthwestern section of the study area is predicted to have thenext highest degree of fault development. Although the deforma-tion of ejective folds is relatively weak in this area, a number ofnormal faults were formed at the axes of anticlines due to theclamping of folds by Cretaceous thrust faults and the governingrole of the large Qiyao Mountain basement fault. Thus, stress fieldsand degrees of fracture development in southeastern Chongqinghave mainly been controlled by tectonic factors.

Lithology is another important factor that affects fracture distri-bution. Compared with TST strata, HST strata feature a larger areaof bathyal shelf facies in the northern portion of the study area andthe northward extension of the area of sandy shelf facies in thesouthern portion of the study area. In addition, decreased deep-water shelf and bathyal marine depositions and increased contentsof brittle minerals (siliceous and calcareous compounds) in rocksare observed in the HST strata relative to the TST strata. The

lithology of sandy shelf facies is dominated by calcareous shale,gray argillaceous siltstone, and gray siltstone, which are prone torupture under tectonic stress. Therefore, the areas of fracturedevelopment in the south and north of the study area are largerin the HST strata than in the TST strata.

5. Conclusions

(1) The simulation results for stress fields of the Longmaxi Shalein southeastern Chongqing during the Cenozoic indicatedthat the areas with high stress intensities are primarilylocated in the eastern and southern regions of the studyarea. In particular, the highest stress intensities were foundfor the axes of wide spaced synclines, followed by ejectivefolds that were clamped by faults in the northwest regionof the work area. The predicted stress intensities were low-est in the fault zones, followed by continuous strata withoutstrong deformation. The shear stress simulation results indi-cated that during the Himalayan, southeastern Chongqingprimarily experienced sinistral shear stresses that causedthe morphologies of faults and folds to become S-shapedor arc-shaped. The simulation results were consistent withthe characteristics of tectonic stress in southeastern Chongq-ing during the Cenozoic.

(2) In accordance with the simulation results for the tectonicstress field, fractures of the Longmaxi Shale in southeastChongqing during the Cenozoic mainly developed in theeastern and southern portions of the study area. These frac-tures were distributed along folds and faults and were par-ticularly prevalent in areas with relatively large gradientsof stress change, such as the turning and transition zonesof faults; fault junctions; and the top and the steep wingsof anticlines. The deformation of shale was strong in theseareas, and shale fractures were typically well developed inthese regions. In the northwestern region of the study area,high levels of fracture density and fracture development

W. Zeng et al. / Journal of Asian Earth Sciences 75 (2013) 267–279 279

were observed in shale distribution areas that were close tofault zones, whereas low levels of fracture density and frac-ture development were observed in shale distribution areasthat were distant from fault zones. However, fracture devel-opment did not occur near each specific fault; this phenom-enon indicates the complexity of the relationship betweenfaults and fracture development. The high productionregions of shale gas are largely found near the turning of foldstructures and fault zones. Therefore, the Pengye-1 and Qia-nye-1 wells, which are located in favorable areas of frac-tures, appear to be good prospects for shale gasdevelopment.

(3) From the tectonic stress simulation and fracture prediction,the stress field distribution and the regions of fracture devel-opment in the examined region appear to be largely gov-erned by tectonic factors and, to a lesser extent, bylithology. Rocks from sandy shelf facies in the southernregion of the study area and shallow shelf facies in thenorthern region of the study area featured relatively highquartz, carbonate, and feldspar content. The shale in theseregions was therefore highly brittle, with a low Poisson’sratio and a high elastic modulus, and would readily rupturedue to external forces. The degree of fracture development inthe examined shale samples was positively correlated withthe brittle mineral content of these samples.

Acknowledgements

This research was supported by the Important National Scienceand Technology Specific Projects of China (Project No.2011ZX05018-001-002 and 2011ZX05009-002-205) and the Na-tional Natural Science Foundation of China (Project No.41072098, 41272167 and 41002072).

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