Formation and Extension of Localized Compaction in Porous Sandstone

Transcription

1 Formation and Extension of Localized Compaction in Porous Sandstone J. W. Rudnicki Dept. of Civil and Env. Eng. and Dept. of Mechanical Eng. Northwestern University June 26, Plenary Talk, ARMA, Chicago, IL

2 Northwestern University O Hare Airport Westin Michigan Ave.

3 Collaborators Bill Olsson, Dave Holcomb (Sandia, Albuquerque) Eric Grueschow (Exxon-Mobil) Kathleen Issen (Clarkson University) Sheryl Tembe, Teng-Fong Wong (SUNY Stony Brook) Kurt Sternlof, Dave Pollard (Stanford) Jose Andrade (NU, now Caltech), Steve Sun (NU, now Sandia Livermore), Nicola Lenoir (NU, now Ecole des Ponts ParisTech) Peter Eichhubl (Texas Bureau of Economic Geology) Anita Torabi (University of Bergen, Center for Integrated Petroleum Research) Support: U.S. Dept of Energy, Office of Basic Energy Sciences

4 Outline What are compaction bands? Why are they important? What do they look like? Why do they form? Models for propagation

5 What are compaction bands? o shear band (fault) o shear-enhanced compaction band compaction band

6 Why are compaction bands important?

7 From Vajdova, Baud and Wong, JGR, 2004 Permeability evolution during localized deformation in Bentheim Sandstone Aydin and Ahmadov, Bed-parallel compaction bands in aeolian sandstone: their identification, characterization and implications, Tectonophysics, (2009)

8 In situ permeability measurements inside compaction bands using X-ray CT and lattice Boltzmann calculations Lenoir, Andrade, Sun and Rudnicki, in GeoX2010: Advances in Computed Tomography for Geomaterials, Proceedings of GEOX 10, 2009/Geox2010: 3^rd International Workshop on X-Ray CT for Geomaterials Outside Inside band 600 microns

9 Sun, W., J. Andrade, J. Rudnicki, and P. Eichhubl, Geophys. Res. Lett., doi: /2011gl047683, (2011), Shortest Flow Path Inside and Outside Compaction Bands INSIDE CB = 0.14 = 2.79 = 2.15 = 2.56 K= 3.4e-13 m 2 K= 5.3e-13 m 2 K= 4.4e-13 m 2 OUTSIDE CB = 0.21 = 1.77 = 1.76 = 1.81 K= 1.3e-12 m 2 K= 1.2e-12 m 2 K= 1.3e-12 m 2

10 Uniform compaction Localized compaction

11 What do compaction bands look like in the field?

12 From Sternlof, Rudnicki and Pollard, JGR, 2005; Sternlof, 2006.

13 Compaction Bands: Earliest Structural Fabric of the Aztec From Kurt Sternlof, Stanford

14 From Sternlof, Rudnicki and Pollard, JGR, 2005

15 From Sternlof, Rudnicki and Pollard, JGR, 2005

16 pocket knife Eichhubl, Hooker, Laubach,J. Struc. Geology, 2010

17 Cathodoluminescence image of Compactive Shear Band with 2.5 cm reverse slip Eichhubl, Hooker, Laubach, J. Struc. Geology, 2010 Outer zone of fractured grains Inner zone of higher grainsize reduction and shear strain Detail of Shear band with 1 cm slip Macroscopic band is composed of multiple parallel bands of more intense grain-size reduction

18 Fossen, Schultz &Torabi J. Structural Geology Volume 33, Issue 10, October 2011,

19 shear enhanced compaction bands shear enhanced compaction bands pure compaction bands thin section, pure compaction band Fossen, Schultz &Torabi J. Structural Geology in press slipped compactional shear band offset equal a few cm shear enhanced compaction bands; note offset at intersection pressure solution

20 What do compaction bands look like in the laboratory?

21 Bentheim sandstone: Pc = 300 MPa 1 cm 1 cm 1 cm 1 cm ax = 1.4 % ax = 3.1 % ax = 4 % ax = 6 % Baud, Klein, and Wong, Compaction localization in porous sandstones:, JSG, 2004; GRL, 2001

22 Ben#12 (300 MPa) A compaction band in the Bentheim sandstone: typically the lateral width extends over 2 grains or so (~ 600 m) 0,5 mm 0.5 mm Baud, Klenn, Wong, Compactional Localization in Sandstones., J. Struct. Geology, 2004.

23 Baud, Klein and Wong,, Compaction localization in porous sandstones: spatial evolution of damage and acoustic emission activity, J. Struct. Geology, MPa 300 MPa Papka and Kyriakides, In-Plane Crushing of a Polycarbonate Honeycomb, Int. J. Solid Struct., 1998.

24 Why do compaction bands form?

25 Homogeneous and homogeneous deformation Continued Homogeneous deformation Stress Shear band or compaction band Strain Rudnicki and Rice, JMPS, 1975

26 1. Kinematic Condition du du g( n x) dε dε ( ng gn) 2 band 0 band Equilibrium condition band o n dσ n dσ Ingredients 3. Material (constitutive) relation) dσ L dε

27 Bésuelle and Rudnicki, Localization: Shear Bands and Compaction Bands, in Mechanics of Fluid Saturated Rocks, e. Guéguen and Boutéca d p d p 0 (dilation) Elastic-plastic rate-independent constitutive model depending on first and second invariants (Drucker Prager type). ( a c) / 3 for standard test d p 1 0 d p yield surface d p 1 elastic response, <0 k 1 (compression) k < k crit for localization ( a 2 c) / 3 for standard test p

28 Axisymmetric Compression 100 Dilation Band crit Compaction Band crit = angle between fault normal and most compressive principal stress.

29 , dilatancy angle in tan / 90 in 37 degrees Range of angles for shear enhanced compaction bands by Eichhubl et al. (2010) 53 degrees implies , fault angle crit Bésuelle and Rudnicki, Localization: Shear Bands and Compaction Bands, in Mechanics of Fluid Saturated Rocks, ed. Guéguen and Boutéca

30 No volume change Range of and from data of Baud, Vajdova and Wong (JGR, 2006) for Adamswiller, Bentheim, Berea and Darley Dale sandstones. Typically and and small compaction bands no shear Bésuelle and Rudnicki, Localization: Shear Bands and Compaction Bands, in Mechanics of Fluid Saturated Rocks, e. Guéguen and Boutéca

31 Evaluate for an Elliptic Yield Cap Rudnicki, JGR, 2004 More elaborate yield surface model: Grueschow and Rudnicki, Int. J. Solids Struc., 2005

32 Q (MPa) COMPACTIVE YIELD STRESSES OF 4 SANDSTONES: The critical stress levels C*at the onset of shear-enhanced compaction were fitted with elliptical caps (yield envelopes) Darley Dale 250 Bentheim 200 Berea Rothbach P (MPa)

33 Lines are predictions of Dimaggio Sandler cap model Baud, Vajdova and Wong, Shear-enhanced compaction and strain localization: Inelastic deformation and constitutive modeling of four porous sandstones, J. Geophys. Res., 2006

34 ( c) a 2 2 b ( a/ b) 1.53 to 3.0 from Wong, David & Zhu (JGR, 1997) for Bentheim Sandstone from Klein et al. (Phys. Chem. Earth A, 2001) b 3 axisymmetric compression path c c a

35 increasing k crit k crit 0 (for normality) Shear bands compaction bands Elliptical cap surface increasing k crit increasing confining stress

36 k crit / G Bandangle (degrees) kcritcom1 Mar. 9, :50:46 PM shear band -0.4 compaction band bandangle S ( c)/ a c

37 Tembe, Baud and Wong, JGR, 2008 Shear bands Mixed failure modes Development of an array of discrete compaction bands

38 Open circles, peak stress at brittle failure Solid circles, onset of shear enhanced compaction distributed cataclastic flow, no localization compaction localization, discrete compaction bands

39 How do the bands propagate (extend)?

40 Energy Release Due to Compaction Band Propagation Rudnicki and Sternlof, GRL, 2005 (after J. R. Rice, 1968) energy release rate G W W 1 Mh M p ( M / M ) (1 ) h M h b 2 b p 2

41 p 2 energy release rate G h M ( / h) O( ) net compaction stress= From Sternlof and Rudnicki, GRL, 2005: h p G 40 MPa 0.01 (1 cm thick CB, spaced 1 meter apart) 0.1 (corresponding to 10% porosity reduction) kj/m (10 to 60 kj/m for range of stress estimates) Tembe et al., JGR, 2006 estimate compaction energies (equivalent to energy release rate) of kj/m -2 for Berea and Bentheim sandstones.

42 Midpoint Thickness (mm) Figure 1:Compaction Band Data 10 Sternlof (2006) Hill (1989) M & A (1996) Baud et al. (2004) Tembe et al. (2008) Fortin et al. (2005) Field 1 Lab Linear Fit: Field Data Linear fit: y A Bx Band Half-Length (m) A , B after Tembe, PhD Thesis, SUNY, Stony Brooke

43 Ellipsoidal band with uniform inelastic compactive strain p compactive displacment w 1 p p w p 2 w band width compressive stress ahead of the band is elevated sufficiently to cause compaction For aspect ratios typical of the field,, 10-3 to 10-4, initial thickness can be neglected entirely anti-crack model Fletcher and Pollard Geology, 1981

44 Combined anti-crack and anti-dislocation model uniform compactive displacement, 2 w uniform resistive nomal traction a a L L

45 K w k L a 2 (1 v) L a E( k) (1 k ) K( k) where k 1 ( a / L) 2 2 F( k) (1 ) 2 G G K K 2 (1 ) 2 crit crit crit crit 8 (1 ) G w L F k L a crit 2 ( ), For =0.2, GPa, G 40 kj/m G crit 3 / mm 1/2 1 crit (Sternlof, Rudnicki & Pollard, 2005) 2w L m 2 F( k) for L 3a F( k) for L 5a

46 Midpoint Thickness (mm) Compaction Band Data 10 Sternlof (2006) Hill (1989) M & A (1996) Baud et al. (2004) Tembe et al. (in prep) Fortin et al. (2005) Field 1 Lab Linear Fit: Sternlof (2006) Linear Fit: Field Data Linear Fit: All Data Linear Fit: Model Band Half-Length (m)

47 Conclusions Compaction bands are predicted to occur on portions of the cap surface where they are (roughly) observed to occur. Predictions are roughly consistent with lab data but do not agree very well quantitatively. Need for better constitutive data and modeling and a better understanding of the micromechanical factors affecting macroscopic response. More complex load paths (now being used) should be more useful for constraining constitutive models.

48 Conclusions A simple fracture and dislocation model indicates a (surprising) consistency between lab and field data. Model is, however, speculative since little information is available on the initiation and propagation of bands in the field. Field and laboratory observations of the breakdown process near the tip of bands would be helpful in constructing more elaborate models.

49 Questions How do lab, field and theoretical results fit together? What properties (or factors) other than porosity affect compaction band formation? What is a good physical microstructural model? How do microscale properties and lithology translate to macroscopic material (constitutive) behavior? What controls band thickness (and changes in thickness), spacing and deviations from planarity? If bands formed under saturated conditions how does interaction of fluid flow with deformation affect formation and extension? How do we model the transition from initial band formation to extension of a fully formed band?

50 Thanks! Questions for me?