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Research ArticleEffects of Hydraulic Gradient Intersecting AngleAperture and Fracture Length on the Nonlinearityof Fluid Flow in Smooth Intersecting FracturesAn Experimental Investigation

Zhijun Wu1 Lifeng Fan 2 and Shihe Zhao3

1The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province School of Civil EngineeringWuhan University Wuhan 430072 China2College of Architecture and Civil Engineering Beijing University of Technology Beijing 100124 China3Department of Geological Engineering School of Geosciences and Info-Physics Central South UniversityChangsha Hunan 410083 China

Correspondence should be addressed to Lifeng Fan fanlifengbjuteducn

Received 12 September 2017 Revised 23 November 2017 Accepted 11 January 2018 Published 7 March 2018

Academic Editor Yuan Wang

Copyright copy 2018 Zhijun Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study experimentally investigated the nonlinearity of fluid flow in smooth intersecting fractures with a high Reynoldsnumber and high hydraulic gradient A series of fluid flow tests were conducted on one-inlet-two-outlet fracture patterns witha single intersection During the experimental tests the syringe pressure gradient was controlled and varied within the range of020ndash180MPam Since the syringe pump used in the tests provided a stable flow rate for each hydraulic gradient the effectsof hydraulic gradient intersecting angle aperture and fracture length on the nonlinearities of fluid flow have been analysed forboth effluent fractures The results showed that as the hydraulic gradient or aperture increases the nonlinearities of fluid flowin both the effluent fractures and the influent fracture increase However the nonlinearity of fluid flow in one effluent fracturedecreased with increasing intersecting angle or increasing fracture length as the nonlinearity of fluid flow in the other effluentfracture simultaneously increased In addition the nonlinearities of fluid flow in each of the effluent fractures exceed that of theinfluent fracture

1 Introduction

The nonlinear behaviour of fluid flow in natural fracturedrock masses is a critical hotspot in numerous branches ofgeoscience and rock engineering fields such as geologicaldisposal of radioactive waste [1 2] reservoir storage [3 4]undergroundmining [5 6] and geothermal extraction [7 8]Considering that an intact rock matrix in a deep formationhas a very low permeability (which is usually assumed tobe impermeable) [9ndash11] the nonlinear behaviour of fluidflow in fractured rock masses is heavily controlled by theflow behaviour in a single fracture or fracture networkIn recent decades the effects of fracture and hydrauliccharacteristics such as fracture length fracture density aper-ture (or hydraulic aperture) fracture orientation fracture

connectivity ratio hydraulic gradient intersecting anglesurface roughness scale effect and number of intersectionsand dead-ends on the nonlinear behaviour of fluid flowin rock fractures have been extensively and systematicallystudied forming the basis for understanding nonlinear fluidflow behaviour in natural fractured rock masses Howeverdue to the complexity of fracture distribution and fracturecharacteristics in naturally fractured rock masses clearlydetermining the effects of all the fracture and hydraulicparameters on the nonlinear behaviour of fluid flow innaturally fractured rock masses is still challenging

Many researchers have focused on the effects of the frac-ture and hydraulic characteristics on the fluid flow behaviourin a single fracture intersecting fractures and fracturenetworks Long and Billaux [10] presented a fracture network

HindawiGeofluidsVolume 2018 Article ID 9352608 14 pageshttpsdoiorg10115520189352608

2 Geofluids

model that accounted for the observed spatial variability bygenerating a network in subregions where the properties ofeach subregion were predicted through geostatistics Theyfound that approximately 01 of the fractures primarilycontrolled the permeability of the system De Dreuzy etal [11 12] conducted a numerical and theoretical study onthe permeability variation by assuming that the fracturelength obeys a power law distribution and concluded thatthe hydraulic properties of fracture networks with a powerlaw length distribution can be classified into three simplifiedtypesWhen the power law exponent 119886 gt 3 fracture networksessentially consist of very small fractures and the percolationtheory applies On the other hand when 119886 lt 2 flow is mostlychannelled into longer fractures and fracture networks canbe considered as a superposition of long fractures Betweenthese ranges (2 lt 119886 lt 3) fracture length distributionscannot be restricted to a unique length even though thesmaller fractures have a small contribution to flow Olson [13]focused on a nonlinear aperture-to-length relationship andsuggested that fracture apertures scale with their lengths tothe 12 power this result was obtained by using linear elasticfracture mechanics in a homogeneous body with subcriticaland critical (equilibrium law) fracture propagation criteriaIn addition Olson [13] determined that a fracture aspectratio (aperturelength) decreases with increasing fracturelength to the negative 12 power Min and Jing [14] con-ducted a series of numerical simulations of the mechanicaldeformation of fractured rock masses at different scales withmany realizations of Discrete Fracture Networks (DFNs) andconcluded that a representative elementary volume can bedefined and the elastic properties of the fractured rock masscan be approximately represented by the elastic compliancetensor Min et al [15] investigated the stress-dependentpermeability issue in fractured rock masses considering theeffects of nonlinear normal deformation and shear dilationof fractures They found that the permeability of fracturedrocks decreases with increasing stress magnitudes when thestress ratio is not sufficiently large to cause shear dilationof the fractures whereas the permeability increases withincreasing stress when the stress ratio is sufficiently largeIn addition permeability changes at low stress levels aremore substantial than those at high stress levels due to thenonlinear relation between fracture normal stress and dis-placement Based on a newly developed correlation equationBaghbanan and Jing [16] investigated the permeability offractured rocks by considering the correlation between thedistributions of aperture and trace length of the fracturesTheir results showed that there is a significant differencebetween correlated and noncorrelated apertures and fracturelength distributions which demonstrated that the hydrome-chanical behaviour of fractured rocks is considerably scale-and stress-dependent when the aperture and fracture lengthdistributions are correlated By solving the Navier-Stokesequations without linearization using a self-developed 2Dfinite volumemethod Zou et al [17] investigated the effects ofwall surface roughness on fluid flow through rock fracturesTheir results indicated that even with the same total flowrate the flow patterns and velocity fields have significantdifferences which are caused by the secondary roughness and

can even create time-dependent dynamic flow with movingand changing eddies when the Reynolds number (Re) ishigh Furthermore Zou et al [18 19] studied the fluid flowand solute transport in a 3D rock fracture-matrix systemwhich had two rough-walled fractures with an orthogonalintersection Zhou et al [20] experimentally investigatedthe nonlinear flow characteristics of fluid flow throughthe rough-walled fractures subjected to a wide range ofconfining pressures (10ndash300MPam) at low Re They foundthat the obtained critical Reynolds number versus confiningpressure curves generally displays a nonlinear weakeningstage (I) in the early stage of confining pressure loadingwhich is followed by a nonlinear enhancement stage (II) asthe confining pressure further increases Using numericalsimulations based on DFNs Liu et al [21 22] estimated theeffects of fracture intersections and dead-ends on nonlinearflow and particle transport in 2D DFNs and demonstratedthat wider fracture apertures rougher fracture surfaces andgreater numbers of fracture intersections in aDFNmay resultin the onset of nonlinear flow at a lower critical hydraulicgradient In addition they found that the effects of fracturedead-ends on fluid flow are negligible (lt15) howeverfracture dead-ends have a strong impact on the breakthroughcurves of particles in DFNs with a relative time deviationrate in the range of 5ndash35 Based on fluid flow tests andnumerical simulations Li et al [23] found that the nonlineardegree of hydraulic gradient (119869) versus flow rate (119876) increaseswith 119869 and the joint roughness coefficient (JRC) whereasthe nonlinear degree of hydraulic gradient versus flow rateincreases as the radius of the truncating circle decreases (theradius is equivalent to fracture length) In addition theyfound that the intersecting angle affects the effluent fractureflow rate (1199021 and 1199022 stand for two effluent fractures) for threedifferent intersecting angle patterns

Previous studies show that a numerical model based ondiscrete fracture networks (DFNs) which usually consistsof thousands of fracture elements and nodes [14 21 22]was mainly used to investigate the nonlinear fluid flow infractured rock masses However a reasonable description ofthe fluid flow in the basic elements and nodes is the keyprerequisite to ensure the accuracy of the numerical resultsReasonable modelling of nonlinear fluid flow behaviourthrough an entire fractured rock mass depends on realis-tically describing the nonlinear fluid flow in both a singlefracture and an intersecting fracture network However thefluid flow through one-inlet-two-outlet fracture patternswitha single intersection which is a fundamental element ofDFNs has not yet been extensively studied Though a fewstudies have been carried out by numerical modelling [23]to investigate the effects of parameters such as 119869 intersectingangle (120579) aperture (119890) and fracture length (Rr) on thenonlinear behaviour of fluid flow the reliability of thenumerical results is low without experimental validation Inthis study a fluid flow test systemwas built to conduct a seriesof laboratory tests on one-inlet-two-outlet specimens withparticular attention paid to the effects of 119869 120579 119890 and Rr on thenonlinearity of fluid flow in both effluent fractures at largeRe and large 119869 During the tests the syringe pressure gradientwas controlled and varied in the range of 020ndash180MPam

Geofluids 3

resulting in a high flow velocity at the inletThe outlet of eacheffluent was open where the discharged fluid was collectedin a bucket and later measured by an electronic balanceBased on the collected fluid weight the flux of each effluentwas calculated at the end of the experiment by dividing theeffluent quantity by the collecting time

2 Methodology

21 Theoretical Background

211 Linear Darcy Flow Zone The simple parallel platemodel is the only fracture model available to calculate thehydraulic conductivity of a fracture This model assumesa steady incompressible Newtonian fluid flow in a singlefracture under a one-dimensional pressure gradient betweentwo smooth parallel plates separated by an aperture 119890 [24 25]At sufficiently low 119876 this calculation yields the well-knownldquocubic lawrdquo [26 27] and ldquoDarcyrsquos lawrdquo [28 29]

119876 = minus1198903119908

12120583nabla119875 = minus119896119860

120583nabla119875 (1)

where 119876 is the total volumetric flow rate which representsthe flow rate of the influent fracture in this study nabla119875 isthe pressure gradient 119908 is the width of the fracture 119890is the uniform aperture of the idealized smooth fracture120583 is the dynamic viscosity k is the intrinsic permeabilitydefined as 119890212[5 27] and 119860 is the cross-sectional areaequal to 119890119908 Equation (1) predicts that 119876 is proportionalto the cube of 119890 and that 119876 is linearly correlated with nabla119875when Re is sufficiently small The cubic law has been widelyapplied to rough-walled fractures in rock however in theseapplications 119890 is replaced by the so-called hydraulic aperture(119890119867) [24 30 31] In this paper 119890119867 is equal to 119890 since the wallsof the fractures in the test specimen are smooth

212 Non-Darcy Flow Zone Darcyrsquos law and the cubic laware only valid when the inertial force is negligible comparedwith the magnitude of the viscous force and this condition isanticipated only when 119876 is low Nonlinear flow occurs whenwith an incremental increase in Re 119876 increases more than aproportional incremental amount [26 32ndash35] Forchheimerrsquoslaw [8 36ndash38] has been most widely used to describe thenonlinear flow in fractures and porous media especially instrong inertial regimes

minusnabla119875 = 1198861015840119876 + 11988710158401198762 (2)

where 1198861015840 and 1198871015840 are coefficients 1198861015840 = 12120583(1199081198903) and 1198871015840 =120573120588(11990821198902)120588 is the fluid density and120573 is called either the non-Darcy coefficient or the inertial resistance [5 39 40]

The hydraulic gradient 119869 is proportional to nabla119875

119869 =ℎ1 minus ℎ2Δ119871=1

120588119892

1198751 minus 1198752Δ119871=1

120588119892

nabla119875

nabla119871=1

120588119892nabla119875 (3)

where ℎ1 and ℎ2 are the hydraulic heads at each end of afracture 1198751 and 1198752 are the pressures at each end of a fracture

and Δ119871 is the effective path under the hydraulic gradientEquation (2) can be written in a Forchheimerrsquos law form asfollows

119869 = 119886119876 + 1198871198762 (4)

The term 119886119876 represents the linear gradient and the term 1198871198762represents the nonlinear gradient

Coefficients 119886 and 119887 in (4) are commonly written asfollows

119886 =120583

120588119892119896119860=12120583

1205881198921199081198903 (5a)

119887 =120573

1198921198602=120573

11989211990821198902 (5b)

Equation (5a) states that 119886 is linearly proportional to thereciprocal of the cube of 119890 If the values of 119908 and 119890 aremeasurable and constant the value of 119886 can be calculateddirectly In addition in some studies the value of 119886 isconsidered the intrinsic permeability of the fractured media[29 41 42] The coefficient 119887 in (5b) is determined fromthe geometrical properties of the fractures and media in theexperiments [34 40 43]

For fluid flow within fractures the ratio of the inertialforce to the viscous force is defined as the Reynolds number(Re) which is expressed as follows [44 45]

Re =120588V119890120583=120588119876

120583119908 (6)

where V is the bulk flow velocity in the fractures Criticalvalues of Re can distinguish between the linear and nonlinearflow conditions [20 22 24 31 46 47]

The vector flow velocity V can be reduced to a one-dimensional flow velocity along a fracture intersection

V =119876

119860 (7)

22 Experimental Setup

221 Specimen Preparation First specimens containing oneinlet and two outlets were designed by AutoCAD whichcan accurately create a regular single intersection of threefractures Based on the control variatemethod the specimenswere designed with 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ 119890 =2 3 5 10 and 20mm and Rr = 40 100 200 300 and400mmThe specimensweremadewith PMMA(polymethylmethacrylate) material which is transparent and easy toprocess Then the specimen design diagrams in EPS formatwere transferred to the computer of the dedicated PMMAmachineNext the specimenswere created at a series of scaleswith a small error plusmn002mm The sizes of 119890 Rr and 119908 wereprecisely measured by a digital Vernier caliper Note that the57mm width 119908 was controlled by the length of the drillemployed to cut the PMMA The error of 119908 was plusmn01mm(ie 119908 = 5648ndash5745mm) because the surface of the initialPMMA slab was not flat Next a high-pressure flame gun was

4 Geofluids

Flow direction(a) 120579 = 30∘

Flow direction(b) 120579 = 60∘

Flow direction(c) 120579 = 90∘

Flow direction(d) 120579 = 120∘

Flow direction(e) 120579 = 150∘

Figure 1 The pictures of specimens for the cases of 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘

High pressuresyringe pumpWater

purifier

Collectorwith a

side hole

Flow direction

Valve

Valve

Valve

Digital pressure gauge

PC

SLR camera

Free jet

Introducing thetap-water aswater supply

Inflow butt joint

Transparent tape

Specimen with fractures

Horizontal platform

Electronic balance

Digital operation panel

(a)

Glue

PVC tubulewhich connected tothe inflow butt joint

Flow direction

Square slot

(b)

Figure 2 (a) The fluid flow test system (b) the connection between the PVC tubule and the inflow tank of the model

used to polish the fracture walls so that the initial conditionof smooth fracture walls was met in this study Figure 1 showsthe pictures of the specimens Finally the specimens wereglued to plates with the same side area as the specimens usingthe PMMA adhesive This procedure was repeated to ensureabsolute sealing of the fractures

222 Test System and Experimental Procedure A schematicview of the fluid flow test system is shown in Figure 2(a)Filtered tap water was introduced into the inlet of thespecimen by a high-pressure syringe pump the syringepressure had an accuracy of plusmn001MPam The syringepressure gradient range of 020ndash180MPam resulted in the

range of 200ndash900 Lmin (333 times 10minus5ndash150 times 10minus4m3s) forthe syringe flow rates A digital pressure gauge with anaccuracy of plusmn01 kPam was used to measure the pressurebetween the inlet and the outlets The specimens wereplaced on a horizontal platform fixed by transparent tapeso that the gravitational pressure difference between theinlet and the outlets was negligible Two buckets each ofwhich had a large hole in the side were employed to collectthe discharged water Electronic scales with an accuracy ofplusmn002 g were used to measure the weight of the effluentFluid flow through the transparent PMMA specimen wasrecorded by a SLR (single lens reflex) camera mounted abovethe experimental setup To connect the tube of the syringe

Geofluids 5

Table 1 The coefficient 119861 of 119869-1199021 1199022 and 119876 for the cases of 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘

Coefficient 119887 120579 = 30∘ 120579 = 60∘ 120579 = 90∘ 120579 = 120∘ 120579 = 150∘

119869-1199021 (times109) 29477 25986 22524 24162 22645

119869-1199022 (times1010) 21500 29410 50517 52248 52181

119869-119876 (times109) 14966 14785 14816 15864 14981

Fracture_1

Flow direction

Fracture_2

Influent fracture

Intersection

Figure 3 Definition of 120579 and fractures

pump to the inflow tank of the model at the end of eachfracture a square slot with a size of 5 times 8 times 8mm was leftto fit to be connected with the pressure-proof PVC tubuleof a 6mm inner diameter and 8mm outer diameter Theconnection between the PVC tubule and the inflow tank ofthe model was then sealed using a hot glue gun as shown inFigure 2(b) in the revised manuscript In addition the otherend of the PVC inlet tubule of the inflow tank was quicklyconnected with the tube of syringe pump via an inflowbutt joint The entire flow path including the connectingtubes inflow butt joint and all three fractures was sealedand watertight Filtered tap water was used as the fluidfor the experiments with a density of 9982 kgm3 and adynamic viscosity 120583 of 0001 Pasdots at a room temperature of20∘C

3 Results and Discussions

As shown in Figure 3 120579 is defined as the intersection anglebetween the effluent fractures in a 2D plane and can varyfrom 0∘ to 180∘ Pictures of the specimens for the cases of120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ are presented in Figure 1The effluent fracture located in the orientation of influentfracture is called fracture 1 while the effluent fracture locatedin the deflected orientation is called fracture 2 Moreoverin this paper in the cases of 120579 = 30∘ 60∘ 90∘ 120∘ and150∘ fracture 1 is called fracture 11 fracture 12 fracture 13fracture 14 and fracture 15 respectively Similarly in thecases of 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ fracture 2 iscalled fracture 21 fracture 22 fracture 23 fracture 24 andfracture 25

31 The Nonlinear Behaviour of Fluid Flow in IntersectingFractures The tests in Figure 4were conducted on specimenswith 119890 = 2mm Rr = 40mm 119908 = 57mm and 120579 = 30∘ 60∘90∘ 120∘ and 150∘ The specimens were full of fluid and flow

was continuous in the influent fracture as well as both effluentfractures The fitting result of the test data in Figure 4(a)shows that 119869119876 is linearly correlated with 119876 which can beexpressed as 119869119876 = 119886 + 119887119876 The relationship between 119869and 119876 agrees with Forchheimerrsquos law In the tests as 119869 variesfrom 1184 to 31270 119876 varies from 3296 times 10minus5 to 1354 times10minus4m3s and Re of the influent fracture varies from 5782456to 23759649 Researchers [5 20 22 23 48] have concludedthat Forchheimerrsquos law applies for the cases in which themagnitude of 119876 is 10minus7ndash10minus6 and the magnitude of Re is101ndash102 In addition in this paper it is demonstrated thatForchheimerrsquos law also applies for larger magnitudes of 119876(10minus5ndash10minus4) and Re (104ndash105)

The variations of 1199021 1199022 and 119876 as well as the cubic law-based 119876 with increasing 119869 for the cases of 120579 = 30∘ 60∘90∘ 120∘ and 150∘ are shown in Figures 4(b)ndash4(f) 119869 isquadratically correlated with 1199021 1199022 and 119876 with a correlationcoefficient1198772 gt 0955When J = 100ndash101 as shown in Figure 4the 119869-1199021 119869-1199022 and 119869-119876 curves deviate from straight lines(cubic law) and the deviations increase with increasing 119869These results agree with the experimental and numericalresults of Koyama et al [49] and Li et al [23 50] As shownin Figures 4(b)ndash4(f) the deviations of the 119869-1199022 119869-1199021 and 119869-119876 curves from cubic law line are all in a decreasing orderIn this group of tests 119890 and 119908 are considered to be constantin (5a) and (5b) therefore the coefficient 119886 of the linearterm in (4) is calculated as the constant value 21465 times 104Table 1 provides the coefficient 119887 of the nonlinear term in(4) for the cases of 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ Thecoefficient 119887 can quantify the deviations of the 119869-1199021 119869-1199022and 119869-119876 curves The coefficient 119887 of fracture 1 decreases withincreasing 120579 especially when 120579 ge 90∘ (ie as 120579 increasesfrom 30∘ to 90∘ 119887 decreases from 29477 times 109 to 22524 times109) In contrast the coefficient 119887 of fracture 2 increases withincreasing 120579 especially when 120579 ge 90∘ (ie as 120579 increasesfrom 30∘ to 90∘ 119887 increases from 21500 times 1010 to 50517times 1010) However the coefficient 119887 of the influent fractureonly slightly changes with increasing 120579 (ie as 120579 increasesfrom 30∘ to 150∘ 119887 varies from 14966 times 109 to 14981 times 109)This emphasizes that the magnitude of the coefficient 119887 offracture 1 (or fracture 2) remains on the order of 109 (or 1010)as 120579 changes 119892 119908 and 119890119867 are measurable and assumed tobe constant in (5a) so that the coefficient 119887 is determined bythe inertial resistance 120573 Ruth and Ma [40] and Cherubini etal [34] suggested that if the structure of a porous medium issuch that microscopic inertial effects are rare (ie essentiallystraight fractures) then 120573 will be small unless V and Re arehigh Furthermore for high values of Re Re and turbulenceare closely connected The direction of the fluid flow within

6 Geofluids

00

00

fracture_1 amp 2fracture_1fracture_2

JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35

fracture_11fracture_21

fracture_11 amp 21Cubic law

00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)

Figure 4 Relationship between 119869119876 and 119876 as well as relationship between 119869 and 119876 (a) relationship between 119869119876 and 119876 (b) relationshipbetween 119869 and 119876 for 120579 = 30∘ (c) relationship between 119869 and 119876 for 120579 = 60∘ (d) relationship between 119869 and 119876 for 120579 = 90∘ (e) relationshipbetween 119869 and 119876 for 120579 = 120∘ (f) relationship between 119869 and 119876 for 120579 = 150∘

Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)

Figure 5 (a) Relationship between 119876119869 and 120579 for 119869 = 7 12 17 and 22 (b) relationship between 120575 and 120579 for 119869 = 7 12 17 and 22

fracture 2 sharply changes because orientation of fracture 2diverges from that of the influent fracture Thus the inertialresistance 120573 of fracture 2 has a significant influence on theinertial force of the fluid flow Additionally the inertialresistance 120573 of fracture 1 also affects the inertial force of thefluid flow due to the expansion of the fracture cross-sectionalarea at the intersectionThe inertial resistance 120573 of fracture 2is always greater than that of fracture 1 In addition theinertial resistance 120573 of both fracture 2 and fracture 1 exceedsthat of the influent fracture As 120579 increases from 0∘ to 180∘the inertial resistance 120573 of fracture 2 intensifies becausefracture 2 turns away from direction of the influent fractureand thus the direction of fluid flow Due to the limit ofthe syringe pump used in the tests the influent flow rate isfixed for an equivalent 119869 with different specimens Hencefor test cases with different 120579 the 119869119876-119876 curves overlapeach other as demonstrated in Figure 4(a) The fixed 119876provides a constant inertial force of the fluid flow at the inletTherefore the inertial resistance120573of fracture 2 and fracture 1has different effects on the inertial forcewith increasing 119869120573offracture 2 increases with increasing J whereas 120573 of fracture 1decreases As 119869 varies the change in 120573 is clearly similar to thatof 119887

32 Effects of 120579 on the Nonlinearity of Fluid Flow When fluidflow is in a linear regime in this group of tests the predictedvalue of 119876119869 based on (1) is a constant value of 4637 times 10minus5On the other hand in a nonlinear flow regime the predictedvalue of 119876119869 is based on (4) and declines with increasing119869 Furthermore the change in 119876119869 represents the degree ofnonlinearity Therefore as 119869 increases 119876119869 changes froma constant value to decreasing values which indicates thetransition of fluid flow from the linear regime to the nonlinearregime Liu et al [22] using numerical simulation presentedthat the critical value of 119869 is between 10minus3 and 10minus2 for the caseof e = 2mm In this paper the fluid flow within the fractures

is certainly in the nonlinear regime since J = 101ndash102 Therelative change in 119876119869 120575 is defined as follows

120575 =(119876119869)cubic minus (119876119869)experiment

(119876119869)cubictimes 100 (8)

where (119876119869)cubic is the value of 119876119869 calculated by solvingthe cubic law (119876119869)experiment is the value of 119876119869 calculatedby analysing data from the experiments and 120575 expresseshow the true value of 119876119869 ((119876119869)experiment) deviates from theprediction made by the cubic law ((119876119869)cubic) Similarly 1205751and 1205752 the relative discrepancies of fracture 1 and fracture 2respectively are calculated as follows


(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)

where 1199021 and 1199022 are the volumetric flow rateswithin fracture 1and fracture 2 respectively In this fluid flow test system

119876 = 1199021 + 1199022 (10)

By substituting (10) into (8) (9a) and (9b) the relationshipamong 1205751 1205752 and 120575 can be expressed as follows

120575 + 1 = 1205751 + 1205752 (11)

Equation (11) suggests that if 120575 remains a constant value 1205751and 1205752 are negatively correlated In other words if the fluidflow in the influent fracture is nonlinear the decrease in thenonlinearity of fluid flow in one of the two effluent fractureswill be offset by an increase in the other

The tests in Figure 5 were conducted on the specimenswith 119890= 2mmRr = 40mm119908= 57mm and 120579= 30∘ 60∘ 90∘

8 Geofluids

Table 2 Experimental results of 119876119869 and 120575 in influent fracture for the cases of 120579 = 30∘ 60∘ 90∘ and 120∘ with 119869 = 7 12 17 and 22

120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866

120∘ and 150∘ There was a full flow in the influent fractureand both effluent fractures As 119869 increases the variations in119876119869 and 120575 for the cases of 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘are indicated in Figure 5 As provided in Table 2 119876119869 and 120575vary within only a small range as 120579 varies over a large range(0∘ lt 120579 lt 180∘) for the cases of J = 7 12 17 and 22 For J= 7 with 120579 increasing from 30∘ to 150∘ 119876119869 of the influentfracture varies from 9449 times 10minus6 to 9267 times 10minus6 and 120575 variesfrom 79719 to 80108 The nearly stable values of 119876119869and 120575 indicate the nearly invariable nonlinearity of the fluidflow within the influent fracture for the cases of 120579 = 30∘ 60∘90∘ 120∘ and 150∘ As shown in Figures 5(a) and 5(b) forthe cases of 7 le J le 22 1199022119869 decreases and 1205752 increases withincreasing 120579 especially when 120579 lt 90∘ as 120579 increases 1199021119869 and1205751 have opposite changes in magnitude compared with thoseof 1199022119869 and 1205752 1199021119869 and 1199022119869 are negatively and symmetricallycorrelated similar to 1205751 and 1205752 Thus increasing 120579 enhancesthe nonlinearity of the fluid flow in fracture 2 and decreasesthat of fracture 1 Note that 1205752 gt 1205751 gt 120575 Clearly thenonlinearity of fluid flow in fracture 2 is greatest while thatof the influent fracture is the least of the three fractures As120579 increases for J = 7 1205751 decreases from 85300 to 83235and 1205752 increases from 94518 to 96336 for J = 22 1205751decreases from 91993 to 90913 and 1205752 increases from96979 to 97967 In fact 1199021119869 1199022119869 1205751 and 1205752 only slightlyvarywith varying 120579Thefluid flownonlinearities in fracture 2and fracture 1 are considerably greater because 1205752 and 1205751 areboth approaching 100 for the cases of J = 101ndash102 Moreoverthe changes in 1205752 and 1205751 diminish when 120579 gt 90∘ (ie when J =7 for 120579= 90∘ 1205751 = 83335 and 1205752 = 96368 for 120579= 120∘ 1205751 =83638 and 1205752 = 96368 and for 120579 = 150∘ 1205751 = 83235 and1205752 = 96336) The inertial resistance caused by the fractureintersection changes considerably before the direction of fluidflow in fracture 2 is at a right angle to that in the influentfracture when the fluid flow direction changes more (iefluid flow turns back) the inertial resistance is constant

33 Effects of 119869 on the Nonlinearity of Fluid Flow The tests inFigure 6 were conducted on the specimens with 119890 = 2mm Rr=40mm119908=57mm and 120579=30∘ 60∘ 90∘ 120∘ and 150∘Thefluid flow among the influent fractures and effluent fracturesfilled the fractures In this group of tests the predicted valueof 119876119869 based on (1) is a constant value of 4637 times 10minus5 Withthe changes of 119869 119876119869 and 120575 for the cases of 120579 = 30∘ 60∘90∘ 120∘ and 150∘ are shown in Figure 6 Figures 6(a) and6(b) show the trendlines of 119876119869-J and 120575-J for the cases of J= 10minus5ndash100 from Li et al [23] For the cases of J = 2ndash32 the

changes in the 119876119869-J and 120575-J curves are exactly equal to thetrendlines of Li et al and the trendlines of 119876119869-J and 120575-J areextended to the cases of J = 100ndash101 As shown in Figures 6(a)and 6(b) when 2le 119869 le 35 and 119869 increases119876119869 1199021119869 and 1199022119869decrease whereas 1205752 1205751 and 120575 increaseTherefore increasing119869 strengthens the nonlinearity of fluid flow in all fracturesAn increase in 119869 would increase the number and volume ofeddies in the fractures narrowing the effective flowpaths andconsequently enhance the nonlinearity of fluid flow [22] Alarge magnitude of the change in the nonlinearity arises forthe especial cases of 100 lt J lt 101 However the magnitudeof the change decreases when J gt 101 For example for thecase of 120579 = 120∘ when 100 lt J lt 101 120575 increases from 65959to 81557 as 119869 increases from 2736 to 8167 when J gt 101 120575increases from 85872 to 91061 as 119869 increases from 13512 to34201 As indicated in the enlarged views of Figures 6(a) and6(b) as 119869 increases 1199021119869 increases (or 1199022119869 decreases) and 1205751decreases (or 1205752 increases) Note that 1205752 gt 1205751 gt 120575 Accordingto 32 when 120579 ge 90∘ varying 120579 has a negligible effect on thenonlinearity of fluid flow in fracture 1 and fracture 2 Thusthe119876119869-J or 120575-J curves of fracture 1 and fracture 2 overlap for120579=90∘ 120∘ and 150∘ Furthermore varying 120579has a negligibleeffect on the nonlinearity of fluid flow in the influent fractureresulting in the overlapping 119876119869-J or 120575-J influent fracturecurves with different 120579

34 Effects of 119890 on the Nonlinearity of Fluid Flow The testsin Figure 7 were conducted on the specimens with e = 2 35 10 and 20mm Rr = 100mm 119908 = 57mm and 120579 = 60∘90∘ and 120∘ There was a full flow within all fractures forthe cases with e = 2 3 and 5mm However for the casesof e = 10 and 20mm the fluid flow in fracture 2 did notcompletely fill the open fracture space For the case of e= 10mm in fracture 2 there were many bubbles that haddiameters greater than 1mm For the case of J asymp 10 as 120579increases from 60∘ to 120∘ 1199022 decreased from 2831 times 10minus5 to1930 times 10minus5m3s V of fracture 2 decreased to 0412ms (for120579 = 60∘) 0301ms (for 120579 = 90∘) and 0189ms (for 120579 = 120∘)although V of the influent fracture was 1442ms (for 120579 = 60∘)1409ms (for 120579 = 90∘) and 1424ms (for 120579 = 120∘) For thecase of 119890 = 20mm when 120579 = 60∘ and 90∘ there were morebubbles with diameters greater than 15mm in fracture 2 (seeFigures 8(a) and 8(b)) when 120579 = 120∘ there was only a smallvolume of fluid flow through fracture 2 (see Figure 8(c)) Forthe case of 119890 = 20mm V of fracture 2 decreased to 0141ms(for 120579 = 60∘) 0054ms (for 120579 = 90∘) and 0001ms (for 120579= 120∘) although V of influent fracture was 0723ms (for

Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)

Influent fracturefracture_1fracture_2

= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘

Li et alrsquos trendline for the

(Li et al 2016)cases of J = 10minus5ndash100

(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)

Li et alrsquos trendline for thecases of J = 10minus5ndash100

(b)

Figure 6 (a) Relationship between 119876119869 and 119869 for 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ (b) relationship between 120575 and 119869 for 120579 = 30∘ 60∘ 90∘ 120∘and 150∘

10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)

Figure 7 (a) Relationship between 119876119869 and 119890 for 120579 = 60∘ 90∘ and 120∘ (b) relationship between 120575 and 119890 for 120579 = 60∘ 90∘ and 120∘

fracture_1

fracture_2

Influent fracture

Flow directioneddy_1

Curvilinear boundary

(a)

fracture_2

Influent fracture Fracture_1fracture_1

eddy_2

(b)

fracture_1Influent fracture

fracture_2

eddy_3

(c)

Figure 8 The experimental phenomena for the cases of (a) 119890 = 20mm J = 10701 and 120579 = 60∘ (b) 119890 = 20mm J = 10529 and 120579 = 90∘ and (c)119890 = 20mm J = 10046 and 120579 = 120∘

120579 = 60∘) 0660ms (for 120579 = 90∘) and 0729ms (for 120579 =120∘) Hence V of fracture 2 sharply decreases with increasing120579 especially at 119890 = 20mm Clearly each bubble is causedby an eddy that occurs because of the sudden decrease invelocity of the fluid flow and the retroflex direction of theflow As shown in the experiment diagrams (see Figure 8)there was a curved surface boundary encompassing one ormore eddies (ie eddy 1 eddy 2 and eddy 3) at the fractureintersection which reduced to a curvilinear boundary in the2D diagram The curvilinear boundary is the separatrix ofthe fluid flow which means that only a little fluid flow cancross it In addition as 120579 increases from 60∘ to 120∘ thecurvilinear boundary moves from fracture 2 to fracture 1Therefore with a change in 120579 the flow decreases crosses thecurvilinear boundary andmoves into fracture 2 intensifyingthe non-full-flow state within fracture 2Therefore eddy 2 islarger than eddy 1 and the eddy diminishes in fracture 2 witha small fluid flow for the cases of e = 20mm and 120579 = 120∘ Infact for e = 20mm and 120579 = 120∘ a small volume of fluid turnsback into fracture 2 due to eddy 3 (see Figure 8(c))

In this paper the relationship between 119869 and 1199022 agreeswith the Forchheimerrsquos law though fluid flow in fracture 2

is in a non-full-flow state With changing e 119876119869 and 120575 forthe cases of 120579 = 60∘ 90∘ and 120∘ are shown in Figure 7 Asshown in Figure 7(b) 1205752 1205751 and 120575 increase with increasinge whereas 119876119869 1199021119869 and 1199022119869 vary in different ways (ieas 119890 increases 119876119869 remains constant 1199021119869 increases and1199022119869 decreases) In fact 1199021119869 and 1199022119869 have a negative andsymmetric correlation From the enlarged view given inFigure 7(b) 1205752 is still greater than 1205751 which is still greaterthan 120575 Based on (5a) the coefficient 119886 is linearly proportionalto the reciprocal of the cube of 119890 Thus the coefficient 119886rapidly decreases with widening 119890 causing the broad changesin the cubic law-based 119876119869 Considering that the basic valueof the cubic law-based 119876119869 is not constant in this group oftests the changes in119876119869 1199021119869 and 1199022119869 in Figure 7(a) cannotdescribe the degree of nonlinearity of the fluid flow 1205752 1205751and 120575 approach 100 for 119890 gt 5mm For example when 120579 =60∘ as 119890 widens from 5 to 20mm 1205752 increases from 99668to 99996 1205751 increases from 99008 to 99982 and 120575increases from 98627 to 99977 Note that varying 119890 has anegligible effect on119876119869 because the syringe pump in the testscan provide a stable flow rate for each hydraulic gradientUnfortunately the differences in the 1199021119869-e 1199022119869-e 1205751-e

Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)

Figure 9 (a) Relationship between 119876119869 and Rr for 120579 = 60∘ 90∘ and 120∘ (b) relationship between 120575 and Rr for 120579 = 60∘ 90∘ and 120∘

and 1205752-e curves caused by the varying 120579 have not yet beenpresented and require more attention in future experimentalstudies

35 Effects of Rr on the Nonlinearity of Fluid Flow The tests inFigure 9 were conducted on the specimens with 119890 = 2mm Rr=40 100 200 300 and 400mm119908= 57mm and 120579=60∘ 90∘and 120∘ There was a full flow in the influent fracture as wellas both effluent fractures In this group of tests the predictedvalue of 119876119869 based on (1) is still the constant value 4637 times10minus5 As Rr increases the changes in 119876119869 and 120575 for all threefractures for the cases of 120579 = 60∘ 90∘ and 120∘ are shownin Figure 9 As shown in Figures 9(a) and 9(b) when J = 101199022119869 increases and 1205752 declines with increasing Rr especiallyfor Rr lt 100mm However the magnitudes of 1199021119869 and 1205751have different responses as Rr increases as one parameterincreases the other decreases In fact 1199021119869 and 1199022119869 havea negative and symmetric correlation similar to 1205751 and 1205752Thus increasing Rr enhances the nonlinearity of fluid flow infracture 1 but decreases that in fracture 2The consequence isthat themagnitude of these changes in 1199022119869 and 1205752 diminisheswhen Rr gt 100mm similar to the result obtained by Li

et al [23] Therefore if the fracture length is long thedisturbance on the fluid flow resulting from the intersectionwould become negligibly small Furthermore the on-wayresistance resulting from the long effluent fractures decreasesthe dominant effect of the intersection As Rr increases theinertial resistances of fracture 1 and fracture 2 caused by thefracture length and the intersection decrease In additionas the on the way resistance becomes more dominant thenonlinearity of fluid flow approaches a constant value Notethat the nonlinearity of fluid flow in fracture 2 is still greaterthan fracture 1 which is still greater than that in the influentfracture As indicated in the enlarged views of Figures 9(a)and 9(b) as 120579 increases 1199021119869 increases (or 1199022119869 decreases)and 1205751 decreases (or 1205752 increases) In addition varying Rrand 120579 have a negligible effect on the nonlinearity of fluidflow in the influent fracture resulting in a constant valueof 120575

4 Conclusions

In this study a series of tests including on 182 one-inlet-two-outlet specimens that including different fracture patternswith 120579 = 30∘ 60∘ 90∘ 120∘ and 150∘ 119890 = 2 3 5 10 and

12 Geofluids

20mm Rr = 40 100 200 300 and 400mm and 119908 = 57mmwere carried out with a fluid flow testing system Since thesyringe pump in the tests provided a stable flow rate for eachhydraulic gradient the inertial force of fluid flow at the inletremained constant and the nonlinearity of the fluid flow inthe influent fracture was fixed when 119890 was stable As a resultthe effects of 119869 120579 119890 and Rr on the nonlinearities of fluidflow in effluent fracture 1 and fracture 2 were independentlyinvestigated with one-inlet-two-outlet specimens containinga single fracture intersection The main conclusions are asfollows

(1)The hydraulic gradient 119869 intersecting angle 120579 aperture119890 and fracture length Rr significantly affect the nonlinearityof fluid flow through the fracture specimens with a singleintersection

(2) Forchheimerrsquos law also applies for large magnitudes of119876 (10minus5ndash10minus4) and large Re (104ndash105)

(3) The inertial resistance 120573 of fracture 2 increases withincreasing J whereas 120573 of fracture 1 decreases

(4) The nonlinearity of fluid flow in fracture 1 decreaseswith the increase in 120579 whereas that of fracture 2 increasesThe nonlinearities of fluid flow in fracture 1 and fracture 2have a negative and symmetric correlation

(5) As 119869 increases the nonlinearities of fluid flow infracture 1 fracture 2 and the influent fracture all increaseespecially for the cases of 100 lt 119869 lt 101 However when J gt101 the increase in nonlinearity stops

(6) The nonlinearities of fluid flow in fracture 1fracture 2 and the influent fracture sharply increase as 119890widens especially for 119890 lt 5mm

(7) As Rr increases the nonlinearity of fluid flow infracture 1 increases whereas that of fracture 2 decreases

(8) With an increase in 120579 J 119890 or Rr the nonlinearity offluid flow in fracture 2 is always greater than fracture 1 whichis always greater than that of the influent fracture

However in this study only one-inlet-two-outlet speci-mens were tested with particular attention paid to the effectsof 119869 120579 119890 and Rr on the nonlinearity of fluid flow at largeRe and large 119869 To clearly figure out the mechanism of thenonlinear fluid flow behaviour through an entire fracturedrock mass further experimental tests on other fundamentalelements of DFNs especially the two inlets and two outletstype and two inlets and one outlet type are needed tobe carried out In addition since the specific geometriescaused by the real intersection shapes with round bulgesand corners can also strongly affect the nonlinear flowbehaviour further experimental studies on a broad spectrumof intersection geometries are required to fully elucidate thenonlinear flow behaviour through a fractured intersectionBased on the test results obtained from fundamental elementsof DFNs numerical model which can more realisticallyreflect the nonlinear fluid flow behaviour through an entirefractured rock mass by reasonably realizing the fracturesystem information with DFNs can then be developed in thefuture

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] M Souley F Homand S Pepa and D Hoxha ldquoDamage-induced permeability changes in granite a case example at theURL in Canadardquo International Journal of Rock Mechanics andMining Sciences vol 38 no 2 pp 297ndash310 2001

[2] Y Liu J Wang L G Tham and M Cai ldquoBasic physico-mechanical properties and time-temperature effect of deepintact rock from Beishan preselected area for high-levelradioactive waste disposalrdquo Yanshilixue Yu Gongcheng Xue-baoChinese Journal of RockMechanics and Engineering vol 26no 10 pp 2034ndash2042 2007

[3] A Folch AMencio R Puig A Soler and JMas-Pla ldquoGround-water development effects on different scale hydrogeologicalsystems using head hydrochemical and isotopic data andimplications for water resources management The Selva basin(NE Spain)rdquo Journal of Hydrology vol 403 no 1-2 pp 83ndash1022011

[4] Q Jiang Z Ye and C Zhou ldquoA numerical procedure for tran-sient free surface seepage through fracture networksrdquo Journal ofHydrology vol 519 pp 881ndash891 2014

[5] Y-F Chen J-Q Zhou S-H Hu R Hu and C-B ZhouldquoEvaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fracturesrdquo Journal ofHydrology vol 529 pp 993ndash1006 2015

[6] L Weng L Huang A Taheri and X Li ldquoRockburst character-istics and numerical simulation based on a strain energy densityindex A case study of a roadway in Linglong goldmine ChinardquoTunnelling and Underground Space Technology vol 69 pp 223ndash232 2017

[7] J Schmittbuhl A Steyer L Jouniaux and R Toussaint ldquoFrac-ture morphology and viscous transportrdquo International Journalof Rock Mechanics and Mining Sciences vol 45 no 3 pp 422ndash430 2008

[8] T Babadagli X Ren and K Develi ldquoEffects of fractal surfaceroughness and lithology on single and multiphase flow in asingle fracture an experimental investigationrdquo InternationalJournal of Multiphase Flow vol 68 pp 40ndash58 2015

[9] D Trimmer B Bonner H C Heard and A Duba ldquoEffect ofpressure and stress on water transport in intact and fracturedgabbro and graniterdquo Journal of Geophysical Research Atmo-spheres vol 85 no 12 pp 7059ndash7071 1980

[10] J C S Long and D M Billaux ldquoFrom field data to fracture net-work modeling An example incorporating spatial structurerdquoWater Resources Research vol 23 no 7 pp 1201ndash1216 1987

[11] J-R De Dreuzy P Davy and O Bour ldquoHydraulic propertiesof two-dimensional random fracture networks following apower law length distribution 1 Effective connectivityrdquo WaterResources Research vol 37 no 8 pp 2065ndash2078 2001

[12] J-R De Dreuzy P Davy and O Bour ldquoHydraulic properties oftwo-dimensional random fracture networks following a powerlaw length distribution 2 Permeability of networks based onlognormal distribution of aperturesrdquoWater Resources Researchvol 37 no 8 pp 2079ndash2095 2001

[13] J E Olson ldquoSublinear scaling of fracture aperture versus lengthAn exception or the rulerdquo Journal of Geophysical Research SolidEarth vol 108 no B9 2003

[14] K-B Min and L Jing ldquoNumerical determination of the equiva-lent elastic compliance tensor for fractured rock masses usingthe distinct element methodrdquo International Journal of RockMechanics andMining Sciences vol 40 no 6 pp 795ndash816 2003

Geofluids 13

[15] K B Min J Rutqvist C-F Tsang and L Jing ldquoStress-dependent permeability of fractured rock masses a numericalstudyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 7 pp 1191ndash1210 2004

[16] A Baghbanan and L Jing ldquoHydraulic properties of fracturedrock masses with correlated fracture length and aperturerdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 5 pp 704ndash719 2007

[17] L Zou L Jing and V Cvetkovic ldquoRoughness decompositionand nonlinear fluid flow in a single rock fracturerdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 75 pp 102ndash118 2015

[18] L Zou L Jing and V Cvetkovic ldquoModeling of flow andmixingin 3D rough-walled rock fracture intersectionsrdquo Advances inWater Resources vol 107 pp 1ndash9 2017

[19] L Zou L Jing and V Cvetkovic ldquoModeling of solute transportin a 3D rough-walled fracture-matrix systemrdquo Transport inPorous Media vol 116 no 3 pp 1ndash25 2017

[20] J-Q Zhou S-HHu S Fang Y-F Chen andC-B Zhou ldquoNon-linear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loadingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 80 pp 202ndash218 2015

[21] R Liu Y Jiang and B Li ldquoEffects of intersection and dead-endof fractures on nonlinear flow and particle transport in rockfracture networksrdquo Geosciences Journal vol 20 no 3 pp 415ndash426 2016

[22] R Liu B Li and Y Jiang ldquoCritical hydraulic gradient fornonlinear flow through rock fracture networks The roles ofaperture surface roughness and number of intersectionsrdquoAdvances in Water Resources vol 88 pp 53ndash65 2016

[23] B Li R Liu and Y Jiang ldquoInfluences of hydraulic gradientsurface roughness intersecting angle and scale effect on non-linear flow behavior at single fracture intersectionsrdquo Journal ofHydrology vol 538 pp 440ndash453 2016

[24] R W Zimmerman and G S Bodvarsson ldquoHydraulic conduc-tivity of rock fracturesrdquo Transport in Porous Media vol 23 no1 pp 1ndash30 1996

[25] P G Ranjith and W Darlington ldquoNonlinear single-phase flowin real rock jointsrdquoWater Resources Research vol 43 no 9 pp146ndash156 2007

[26] J Bear Dynamics of Fluids in Porous Media Am Elsevier NewYork NY USA 1972

[27] P AWitherspoon J S YWang K Iwai and J E Gale ldquoValidityof cubic law for fluid flow in a deformable rock fracturerdquoWaterResources Research vol 16 no 6 pp 1016ndash1024 1980

[28] H Darcy Les Fontaines Publiques de la Ville de Dijon DalmontParis France 1856

[29] E Ghane N R Fausey and L C Brown ldquoNon-Darcy flow ofwater through woodchip mediardquo Journal of Hydrology vol 519pp 3400ndash3409 2014

[30] J S Konzuk and B H Kueper ldquoEvaluation of cubic law basedmodels describing single-phase flow through a rough-walledfracturerdquo Water Resources Research vol 40 no 2 pp 389ndash3912004

[31] D J Brush and N R Thomson ldquoFluid flow in synthetic rough-walled fractures Navier-Stokes Stokes and local cubic lawsimulationsrdquoWater Resources Research vol 39 no 4 pp 1037ndash1041 2003

[32] R Jung ldquoHydraulic in situ investigations of an artificial frac-ture in the Falkenberg graniterdquo International Journal of RockMechanics and Mining Sciences vol 26 no 3-4 pp 301ndash3081989

[33] Z Wen G Huang and H Zhan ldquoNon-Darcian flow in a singleconfined vertical fracture toward a wellrdquo Journal of Hydrologyvol 330 no 3-4 pp 698ndash708 2006

[34] C Cherubini C I Giasi and N Pastore ldquoBench scale lab-oratory tests to analyze non-linear flow in fractured mediardquoHydrology and Earth System Sciences vol 9 no 4 pp 5575ndash5609 2012

[35] M Javadi M Sharifzadeh K Shahriar and Y Mitani ldquoCriticalReynolds number for nonlinear flow through rough-walledfractures the role of shear processesrdquoWater Resources Researchvol 50 no 2 pp 1789ndash1804 2014

[36] P Forchheimer Wasserbewegung durch Boden Zeitschrift desVereines Deutscher Ingenieuer Germany 1901

[37] K N Moutsopoulos ldquoExact and approximate analytical solu-tions for unsteady fully developed turbulent flow in porousmedia and fractures for time dependent boundary conditionsrdquoJournal of Hydrology vol 369 no 1-2 pp 78ndash89 2009

[38] P G Ranjith and D R Viete ldquoApplicability of the rsquocubic lawrsquofor non-Darcian fracture flowrdquo Journal of Petroleum Science andEngineering vol 78 no 2 pp 321ndash327 2011

[39] J Geertsma ldquostimating the Coefficient of Inertial Resistancein Fluid Flow Through Porous Mediardquo Society of PetroleumEngineers Journal vol 14 no 14 pp 445ndash450 1974

[40] D Ruth and H Ma ldquoOn the derivation of the Forchheimerequation by means of the averaging theoremrdquo Transport inPorous Media vol 7 no 3 pp 255ndash264 1992

[41] A Nowamooz G Radilla and M Fourar ldquoNon-darcian two-phase flow in a transparent replica of a rough-walled rockfracturerdquo Water Resources Research vol 45 no 7 pp 4542ndash4548 2009

[42] M C Sukop H Huang P F Alvarez E A Variano and K JCunningham ldquoEvaluation of permeability and non-Darcy flowin vuggy macroporous limestone aquifer samples with latticeBoltzmann methodsrdquo Water Resources Research vol 49 no 1pp 216ndash230 2013

[43] Z Zeng and R Grigg ldquoA criterion for non-darcy flow in porousmediardquo Transport in Porous Media vol 63 no 1 pp 57ndash692006

[44] R W Zimmerman A Al-Yaarubi C C Pain and C AGrattoni ldquoNon-linear regimes of fluid flow in rock fracturesrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 3 pp 163ndash169 2004

[45] M Javadi M Sharifzadeh and K Shahriar ldquoA new geometricalmodel for non-linear fluid flow through rough fracturesrdquoJournal of Hydrology vol 389 no 1-2 pp 18ndash30 2010

[46] C Louis ldquoA study of groundwater flow in jointed rock andits influence on the stability of rock massesrdquo Rock MechanicsResearch Report vol 10 pp 1ndash90 1969

[47] J Qian H Zhan S Luo and W Zhao ldquoExperimental evidenceof scale-dependent hydraulic conductivity for fully developedturbulent flow in a single fracturerdquo Journal of Hydrology vol339 no 3-4 pp 206ndash215 2007

[48] Z Zhang and J Nemcik ldquoFluid flow regimes and nonlinearflow characteristics in deformable rock fracturesrdquo Journal ofHydrology vol 477 pp 139ndash151 2013

14 Geofluids

[49] T Koyama I Neretnieks and L Jing ldquoA numerical study ondifferences in using Navier-Stokes and Reynolds equations formodeling the fluid flow and particle transport in single rockfractures with shearrdquo International Journal of Rock Mechanicsand Mining Sciences vol 45 no 7 pp 1082ndash1101 2008

[50] B Li Y J Jiang T Koyama L R Jing and Y TanabashildquoExperimental study of the hydro-mechanical behavior of rockjoints using a parallel-plate model containing contact areas andartificial fracturesrdquo International Journal of RockMechanics andMining Sciences vol 45 no 3 pp 362ndash375 2008

Hindawiwwwhindawicom Volume 2018

Journal of

ChemistryArchaeaHindawiwwwhindawicom Volume 2018

Marine BiologyJournal of


BiodiversityInternational Journal of


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2 Geofluids

model that accounted for the observed spatial variability bygenerating a network in subregions where the properties ofeach subregion were predicted through geostatistics Theyfound that approximately 01 of the fractures primarilycontrolled the permeability of the system De Dreuzy etal [11 12] conducted a numerical and theoretical study onthe permeability variation by assuming that the fracturelength obeys a power law distribution and concluded thatthe hydraulic properties of fracture networks with a powerlaw length distribution can be classified into three simplifiedtypesWhen the power law exponent 119886 gt 3 fracture networksessentially consist of very small fractures and the percolationtheory applies On the other hand when 119886 lt 2 flow is mostlychannelled into longer fractures and fracture networks canbe considered as a superposition of long fractures Betweenthese ranges (2 lt 119886 lt 3) fracture length distributionscannot be restricted to a unique length even though thesmaller fractures have a small contribution to flow Olson [13]focused on a nonlinear aperture-to-length relationship andsuggested that fracture apertures scale with their lengths tothe 12 power this result was obtained by using linear elasticfracture mechanics in a homogeneous body with subcriticaland critical (equilibrium law) fracture propagation criteriaIn addition Olson [13] determined that a fracture aspectratio (aperturelength) decreases with increasing fracturelength to the negative 12 power Min and Jing [14] con-ducted a series of numerical simulations of the mechanicaldeformation of fractured rock masses at different scales withmany realizations of Discrete Fracture Networks (DFNs) andconcluded that a representative elementary volume can bedefined and the elastic properties of the fractured rock masscan be approximately represented by the elastic compliancetensor Min et al [15] investigated the stress-dependentpermeability issue in fractured rock masses considering theeffects of nonlinear normal deformation and shear dilationof fractures They found that the permeability of fracturedrocks decreases with increasing stress magnitudes when thestress ratio is not sufficiently large to cause shear dilationof the fractures whereas the permeability increases withincreasing stress when the stress ratio is sufficiently largeIn addition permeability changes at low stress levels aremore substantial than those at high stress levels due to thenonlinear relation between fracture normal stress and dis-placement Based on a newly developed correlation equationBaghbanan and Jing [16] investigated the permeability offractured rocks by considering the correlation between thedistributions of aperture and trace length of the fracturesTheir results showed that there is a significant differencebetween correlated and noncorrelated apertures and fracturelength distributions which demonstrated that the hydrome-chanical behaviour of fractured rocks is considerably scale-and stress-dependent when the aperture and fracture lengthdistributions are correlated By solving the Navier-Stokesequations without linearization using a self-developed 2Dfinite volumemethod Zou et al [17] investigated the effects ofwall surface roughness on fluid flow through rock fracturesTheir results indicated that even with the same total flowrate the flow patterns and velocity fields have significantdifferences which are caused by the secondary roughness and

can even create time-dependent dynamic flow with movingand changing eddies when the Reynolds number (Re) ishigh Furthermore Zou et al [18 19] studied the fluid flowand solute transport in a 3D rock fracture-matrix systemwhich had two rough-walled fractures with an orthogonalintersection Zhou et al [20] experimentally investigatedthe nonlinear flow characteristics of fluid flow throughthe rough-walled fractures subjected to a wide range ofconfining pressures (10ndash300MPam) at low Re They foundthat the obtained critical Reynolds number versus confiningpressure curves generally displays a nonlinear weakeningstage (I) in the early stage of confining pressure loadingwhich is followed by a nonlinear enhancement stage (II) asthe confining pressure further increases Using numericalsimulations based on DFNs Liu et al [21 22] estimated theeffects of fracture intersections and dead-ends on nonlinearflow and particle transport in 2D DFNs and demonstratedthat wider fracture apertures rougher fracture surfaces andgreater numbers of fracture intersections in aDFNmay resultin the onset of nonlinear flow at a lower critical hydraulicgradient In addition they found that the effects of fracturedead-ends on fluid flow are negligible (lt15) howeverfracture dead-ends have a strong impact on the breakthroughcurves of particles in DFNs with a relative time deviationrate in the range of 5ndash35 Based on fluid flow tests andnumerical simulations Li et al [23] found that the nonlineardegree of hydraulic gradient (119869) versus flow rate (119876) increaseswith 119869 and the joint roughness coefficient (JRC) whereasthe nonlinear degree of hydraulic gradient versus flow rateincreases as the radius of the truncating circle decreases (theradius is equivalent to fracture length) In addition theyfound that the intersecting angle affects the effluent fractureflow rate (1199021 and 1199022 stand for two effluent fractures) for threedifferent intersecting angle patterns

Previous studies show that a numerical model based ondiscrete fracture networks (DFNs) which usually consistsof thousands of fracture elements and nodes [14 21 22]was mainly used to investigate the nonlinear fluid flow infractured rock masses However a reasonable description ofthe fluid flow in the basic elements and nodes is the keyprerequisite to ensure the accuracy of the numerical resultsReasonable modelling of nonlinear fluid flow behaviourthrough an entire fractured rock mass depends on realis-tically describing the nonlinear fluid flow in both a singlefracture and an intersecting fracture network However thefluid flow through one-inlet-two-outlet fracture patternswitha single intersection which is a fundamental element ofDFNs has not yet been extensively studied Though a fewstudies have been carried out by numerical modelling [23]to investigate the effects of parameters such as 119869 intersectingangle (120579) aperture (119890) and fracture length (Rr) on thenonlinear behaviour of fluid flow the reliability of thenumerical results is low without experimental validation Inthis study a fluid flow test systemwas built to conduct a seriesof laboratory tests on one-inlet-two-outlet specimens withparticular attention paid to the effects of 119869 120579 119890 and Rr on thenonlinearity of fluid flow in both effluent fractures at largeRe and large 119869 During the tests the syringe pressure gradientwas controlled and varied in the range of 020ndash180MPam

Geofluids 3


2 Methodology



119876 = minus1198903119908

12120583nabla119875 = minus119896119860

120583nabla119875 (1)



minusnabla119875 = 1198861015840119876 + 11988710158401198762 (2)



119869 =ℎ1 minus ℎ2Δ119871=1

120588119892

1198751 minus 1198752Δ119871=1

120588119892

nabla119875

nabla119871=1

120588119892nabla119875 (3)



119869 = 119886119876 + 1198871198762 (4)



119886 =120583

120588119892119896119860=12120583

1205881198921199081198903 (5a)

119887 =120573

1198921198602=120573

11989211990821198902 (5b)



Re =120588V119890120583=120588119876

120583119908 (6)



V =119876

119860 (7)



4 Geofluids








purifier

Collectorwith a

side hole

Flow direction

Valve

Valve

Valve


PC

SLR camera

Free jet


Inflow butt joint

Transparent tape


Horizontal platform

Electronic balance


(a)

Glue


Flow direction

Square slot

(b)





Geofluids 5


Coefficient 119887 120579 = 30∘ 120579 = 60∘ 120579 = 90∘ 120579 = 120∘ 120579 = 150∘

119869-1199021 (times109) 29477 25986 22524 24162 22645

119869-1199022 (times1010) 21500 29410 50517 52248 52181

119869-119876 (times109) 14966 14785 14816 15864 14981

Fracture_1

Flow direction

Fracture_2

Influent fracture

Intersection








6 Geofluids

00

00


JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)


Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 3


2 Methodology



119876 = minus1198903119908

12120583nabla119875 = minus119896119860

120583nabla119875 (1)



minusnabla119875 = 1198861015840119876 + 11988710158401198762 (2)



119869 =ℎ1 minus ℎ2Δ119871=1

120588119892

1198751 minus 1198752Δ119871=1

120588119892

nabla119875

nabla119871=1

120588119892nabla119875 (3)



119869 = 119886119876 + 1198871198762 (4)



119886 =120583

120588119892119896119860=12120583

1205881198921199081198903 (5a)

119887 =120573

1198921198602=120573

11989211990821198902 (5b)



Re =120588V119890120583=120588119876

120583119908 (6)



V =119876

119860 (7)



4 Geofluids








purifier

Collectorwith a

side hole

Flow direction

Valve

Valve

Valve


PC

SLR camera

Free jet


Inflow butt joint

Transparent tape


Horizontal platform

Electronic balance


(a)

Glue


Flow direction

Square slot

(b)





Geofluids 5


Coefficient 119887 120579 = 30∘ 120579 = 60∘ 120579 = 90∘ 120579 = 120∘ 120579 = 150∘

119869-1199021 (times109) 29477 25986 22524 24162 22645

119869-1199022 (times1010) 21500 29410 50517 52248 52181

119869-119876 (times109) 14966 14785 14816 15864 14981

Fracture_1

Flow direction

Fracture_2

Influent fracture

Intersection








6 Geofluids

00

00


JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)


Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















4 Geofluids








purifier

Collectorwith a

side hole

Flow direction

Valve

Valve

Valve


PC

SLR camera

Free jet


Inflow butt joint

Transparent tape


Horizontal platform

Electronic balance


(a)

Glue


Flow direction

Square slot

(b)





Geofluids 5


Coefficient 119887 120579 = 30∘ 120579 = 60∘ 120579 = 90∘ 120579 = 120∘ 120579 = 150∘

119869-1199021 (times109) 29477 25986 22524 24162 22645

119869-1199022 (times1010) 21500 29410 50517 52248 52181

119869-119876 (times109) 14966 14785 14816 15864 14981

Fracture_1

Flow direction

Fracture_2

Influent fracture

Intersection








6 Geofluids

00

00


JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)


Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 5


Coefficient 119887 120579 = 30∘ 120579 = 60∘ 120579 = 90∘ 120579 = 120∘ 120579 = 150∘

119869-1199021 (times109) 29477 25986 22524 24162 22645

119869-1199022 (times1010) 21500 29410 50517 52248 52181

119869-119876 (times109) 14966 14785 14816 15864 14981

Fracture_1

Flow direction

Fracture_2

Influent fracture

Intersection








6 Geofluids

00

00


JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)


Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















6 Geofluids

00

00


JQ

(sm

3)

Q (m3s)

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

14E6

12E6

10E6

80E5

60E5

40E5

20E5

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

(a)

0

5

10

15

20

25

30

35



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

J

y=

214

65E+4x

+215

00E+10

x2 R

2=

099

7y=21465E+4x

+29477E+9x

2 R2 =

0991

y=21465E+4x

+14966E+9x

2 R2 =

0991

y = 21465E + 4x

(b)

y=

214

65E+4x

+2941

0E+10

x2 R

2=

0997

y=21465E+4x

+25986E+9x

2 R2 =

0996

y=21465E+4x

+14785E+9x

2 R2 =

0994

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(c)

y=

214

65E+4x

+505

17E+10

x2 R

2=

0999

y=21465E+4x

+22524E+9x

2 R2 =

0996

y=21465E+4x

+14816E+9x

2 R2 =

0996

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(d)

y=

214

65E+4x

+522

48E

+10

x2 R

2=

0955

y=21465E+4x

+24162E+9x

2 R2 =

0964

y=21465E+4x

+15864E+9x

2 R2 =

0970

y = 21465E + 4x



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(e)

y=

214

65E+4x

+521

81E

+10

x2 R

2=

0980

y=21465E+4x

+22645E+9x

2 R2 =

0996

y=21465E+4x

+14981E+9x

2 R2 =

0993

y = 21465E + 4x2



00

Q (m3s)

14Eminus4

12E

minus4

10E

minus4

80E

minus5

60E

minus5

40E

minus5

20E

minus5

0

5

10

15

20

25

30

35

J

(f)


Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 7

20 40 60 80 100 120 140 160


12E minus 5

10E minus 5

80E minus 6

60E minus 6

40E minus 6

20E minus 6

QJ

(m3s

)

(∘)

J = 7

J = 12

J = 17

J = 22

(a)

20 40 60 80 100 120 140 16070

80

90

100

θ (deg)


J = 7

J = 12

J = 17

J = 22

(

)

(b)






(119876119869)cubictimes 100 (8)



(1199021119869)cubictimes 100 (9a)


(1199022119869)cubictimes 100 (9b)


119876 = 1199021 + 1199022 (10)


120575 + 1 = 1205751 + 1205752 (11)



8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















8 Geofluids


120579119876119869 (times10minus6m3s) 120575 ()

119869 = 7 119869 = 12 119869 = 17 119869 = 22 119869 = 7 119869 = 12 119869 = 17 119869 = 22

30∘ 9449 7065 5999 5177 79719 84837 87125 8888960∘ 9424 7117 5973 5221 79771 84723 87180 8879490∘ 9454 7054 5978 5203 79708 84858 87169 88833120∘ 9342 7181 5879 5193 79947 84587 87381 88853150∘ 9267 6979 5943 5187 80108 85019 87243 88866





Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 9

001 0

1

05 1 2 5 10 20 30

J

J

J

15 20 2500

0 5 10 15 20 25 30 3500

1Eminus4

1Eminus3

1Eminus5

10E minus 5

20E minus 5

15E minus 5

50E minus 6

50E minus 6

25E minus 5

30E minus 5

QJ

(m3s

)QJ

(m3s

)

1E minus 04

1E minus 03

1E minus 05

QJ

(m3s

)


= 60∘ = 30∘

= 30∘

= 90∘

= 120∘

= 150∘

= 60∘

= 90∘

= 120∘

= 150∘



(a)

J

15 20 25

0102030405060708090

100

86

88

90

92

94

96

98

0102030405060708090

100

001 0

1

05 1 2 5 10 20

1Eminus4

1Eminus3

J

0 5 10 15 20 25 30 35


= 60∘ = 30∘

= 90∘

= 120∘

= 150∘

30

J

1Eminus5

= 30∘

= 60∘

= 90∘

= 120∘

= 150∘

(

)

()

(

)

(Li et al 2016)


(b)


10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















10 Geofluids

0 2 4 6 8 10 12 14 16 18 2000


20E minus 6

40E minus 6

60E minus 6

80E minus 6QJ

(m3s

)

e (mm)

= 60∘

= 90∘

= 120∘

(a)

0 2 4 6 8 10 12 14 16 18 20

84

86

88

90

92

94

96

98

100

8 10 12

996

998

1000

(

)

e (mm)


= 60∘

= 90∘

= 120∘

(b)


fracture_1

fracture_2

Influent fracture



(a)

fracture_2


eddy_2

(b)


fracture_2

eddy_3

(c)





Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 11

0 50 100 150 200 250 300 350 40000

Rr (mm)

180 200 220 240 260 280 300 320Rr (mm)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

70E minus 6

80E minus 6QJ

(m3s

)

20E minus 6

40E minus 6

60E minus 6

50E minus 6

30E minus 6

10E minus 6

QJ

(m3s

)


= 60∘

= 90∘

= 120∘

(a)

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

Rr (mm)

180 200 220 240 260 280 300 32086

88

90

92

94

96

Rr (mm)


= 60∘

= 90∘

= 120∘

(

)

()

(b)





4 Conclusions


12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















12 Geofluids













References















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















Geofluids 13



































14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















14 Geofluids




Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy
















Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















effects of hydraulic gradient, intersecting angle...

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