Hydro-mechanical behavior of single rock fracture under different confining pressures

Transcription

1 Hydro-mechanical behavior of single rock fracture under different confining pressures Advisor: Prof. Jia-Jyun DONG Presenter: Xuan-Xinh Nguyen Date: 17/4/

2 Outline Introduction Literature review Methodology Results and discussion Conclusion Future work

3 Introduction Fluid flow through rock mass is highly depended on rock fracture. Fracture aperture is important factor effecting the fluid flow through fractured rock. Correlation between hydraulic (e h ) and mechanical (E) aperture under normal stress Stress closure conductivity coupling e h =E e h < E Bandis et al.,

4 Literature review Validity of cubic law for fluid flow in a deformable rock fracture (Witherspoon et al., 198. ) Modify the cubic law with friction factor (f) is valid for mechanic aperture from 4 5 m and f = (not measure directly mechanical aperture) Fundamentals of rock joint deformation. (Bandis et al., 1983). Hydraulic conductivity of rock fracture under normal and shear stress (normal and shear stiffness) Laboratory studies of gas flow though a single natural fracture. (Schrauft et al., 1986). Independently measuring the mechanical aperture from the fracture volume measurements of single granodiorite fracture. On the role of fracture surface roughness in fluid flow and solute transport through fractured rock. (Zhao et al., 15). Fracture network model based on a number of empirical models proposed to relate the reduced hydraulic aperture to the mechanical aperture duo to surface roughness. 4

5 Hydraulic and mechanical aperture definition Hydraulic aperture, e h : Darcy s law q ka dp dx Mechanical aperture, E: E V A f e h =E Cubic law (Snow et al., 1965) q 3 ewdp h 1 dx A = e h w Where q = flow rate = fluid viscosity w = fracture width dp/dx = pressure gradient V = fracture volume A f = fracture area A = cross section area e < <E Literature review 5

6 Normal stiffness of fractured rock (K n ) V m a b Hyperbolic relationship: n 1 V a bv j j K ni 1 a JCS: Joint Compressive Strength JRC: Joint Roughness Coefficient Bandis et al., 1983 Literature review Normal stiffness, Kn: K n K ni VK 1 n m ni n JCS Vm A B( JRC) C a j JCS Kni. JRC 1 a j D 6

7 Fracture flow regime 4 MPa confining pressure Linear Darcy flow zone: P AQ q ka P JRC = 7.1 Non-Darcy flow zone Forchheimer s law P AQ BQ (Forchheimer, 191) 1 P Q Q we w e 3 h h A, B = equaiton coefficients β = non Darcy coefficient Using dimensional analysis (Schrauf and Evans, 1986) P ad Q b 3 D Q Where: 3 ehw ehw Literature review a D = 1, for straight flow a D = 3, for pipe flow The hydraulic test of single granite rock b D = f D / f D = friction factor (roughness and tortuous flow) Chen et al., 15 7

8 Roughness effect Modified Cubic law: q 3 1 ewdp h f 1 dx (Witherspoon et al., 198) Where: q = flow rate e h = hydraulic aperture = fluid viscosity dp/dx = pressure gradient f = fiction factor (roughness and tortuous flow) Mechanic aperture (E): 4 5 m Friction factor, f = 1.4 to 1.65 Walsh (1981) K K 1 K 1 K Where: K = permeability of rough surface K = permeability of smooth surface Zimmerman et al., = the ratio of contact area to total area fracture (1 b) 4b ; b is the aspect ratio of the ellipse. Literature review 8

9 Mechanical and hydraulic aperture correlation Li et al., 13 Barton et al., 1985 E / e 1 Z h.5 E / e 1 Z (.6.4* Z )(Re1) h.5.5 E/e h e h E JRC.5 JRC log Z Rasouli and Hosseinian, 11 eh / E 1.3d.565 mc JRC a 1/3 E (mm) d mc = constant minimum closure distance Z = RMS of the first derivative of the profile JRC a = average joint roughness coefficient Roughness profile, Barton and Choubey (1977) Literature review For higher flow rates and larger apertures e h E (Iwai, 1976) With higher normal stress, e h << E (Cook et al., 199) 9

10 Methodology Roughness profile measurement. Fracture volume and permeability tests using YOKO system. Using steel sample for the beginning study. Apply study results for rock material 1

11 Steel sample YOKO system V (mm 3 ) A f (mm ) mm Joint wall 6. mm First test: Fracture volume test: 3 8 MPa Fracture permeability test: 3 6 MPa Second test: Fracture volume test: 1 17 MPa Fracture permeability test: 5 3 MPa Methodology 11

12 Fracture volume test Effective stress (MPa) Effective stress (MPa) Pressure gauge Frist test Second test Fracture volume: V P P V V i1 f p s l Pf P i. Mechanic aperture: Mechanic aperture, E (mm) Joint closure (mm) E V A p f Result and discussion 1

13 ) P d L ) P d L Fracture permeability test Linear Darcy zone: 4L By using dimensional analysis (Ward, 1964) 4L LbD P Q Q P Q 3 P Q 3 m eh oew h f m 3 m m oehw f oehw f 3 a bq Hydraulic aperture: 4L Qm W P e h o f m 4LP Q W P P d m f ( u d ) o P P u Pd P u Pd The first test.e+.e-6 4.E-6 6.E-6 Volumetric flow rate, Q (m 3 /s) The second test.e+ 5.E-6 1.E-5 1.5E-5 Volumetric flow rate, Q (m 3 /s) 6 MPa 5 MPa 4 MPa 3 MPa MPa 15 MPa 1 MPa 8 MPa 5 MPa 3 MPa 3 MPa 5 MPa MPa 15 MPa 1 MPa 5 MPa Result and discussion The plot of pressure versus discharge of two tests 13

14 Correlation between hydraulic and mechanic aperture Hydraulic aperture, eh (m) 1.E-3 1.E-4 1.E-5 1.E-6 1.E-6 1.E-5 1.E-4 1.E-3 Mechanical aperture, E (m) Result and discussion Marble fracture (Witherspoon et al., 198) 14

15 E/e JRCn Compare the results with a numerical of critical models e E e JRCn.1.5 1/ JRC Mechanic aperture (E). 1 cm cm 3 cm 4 cm 5 cm 6 cm 1 cm cm 5 cm JRC =.8 JRC =.7 JRC =.6 JRC =.5 JRC =.4 JRC =.3 First test Second test JRC with considering the scale effect L JRC JRC L n n.jrc where JRC n = JRC value at n length JRC = JRC value at length of 1 cm L n = sample length L = 1 cm Result and discussion 15

16 E/e Hydraulic aperture, e (m) Relationship between mechanical and hydraulic aperture Rasouli and Hosseinian (11) Li and Jiang (13) Rasouli and Hosseinian, 11 3 eh 1.3d E.565 mc JRC a Mechanical aperture, E (m) Mechanical, E (m) First test Second test Relation ship between mechanical aperture and the ratio of mechanical aperture to hydraulic aperture Result and discussion Rasouli and Hosseinian (11) Li and Jiang (13) First test Second test Li and Jiang, 13 eh E eh E 1 Z (Re<1).5 1 Z (.6.4* Z )(Re1) (Re>1) Assumed:.5.5 d mc =.3 mm JRC a =.5 Z =.17 for JRC = - 16

17 Conclusion The steel sample used to test is identical sample with the results similar for the first and second test. The gas flow through single steel fracture is in linear Darcy zone. Because the fracture surface is smooth surface. Mechanic aperture is greater than hydraulic aperture due to the small holes on the fracture surface. More test with different roughness surfaces need to be experimented. 17

18 Future work Use cooper sample to do next test with rougher fracture surface. Predict fracture surface profile using 3D scan laser machine. 18

19 Thank you for your attention! 19