The nanogranular acoustic signature of shale

A multiscale, micromechanics model has been developed for the prediction of anisotropic acoustic properties of shale. The model is based on the recently identified nanogranular mechanical response of shale through indentation experiments. It recognizes the dominant role of the anisotropic elastic properties of compacted clay in the anisotropic elasticity of shale at different length scales compared to contributions of shape and orientation of particles. Following a thorough validation at multiple length scales using mineral elasticity data, nanoindentation experiment results, and ultrasonic pulse velocity tests, the model predictions compare adequately with measurements on kerogen-free and kerogen-rich shales and shaley sandstones. The acoustic signature of shale thus is found to be controlled by two volumetric parameters that synthesize the porosity and mineralogy information: the clay-packing density and the silt inclusion volume fraction. Through a series of dimensionless isoparametric plots, the micromechanics model predicts trends of increasing elastic anisotropy with increasing clay-packing density (or decreasing porosity), which correspond to the intrinsic mechanical response of unfractured shale, and quantifies the stiffness reduction induced by the presence of kerogen.

[1]  Herbert F. Wang,et al.  Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook , 1971 .

[2]  F. Ulm,et al.  Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters , 2004 .

[3]  J. Sherwood,et al.  LETTER TO THE EDITOR: Packing of spheroids in three-dimensional space by random sequential addition , 1997 .

[4]  Pierre M. Adler,et al.  GEOMETRICAL AND TRANSPORT PROPERTIES OF RANDOM PACKINGS OF SPHERES AND ASPHERICAL PARTICLES , 1997 .

[5]  A model for hydrostatic consolidation of Pierre shale , 1991 .

[6]  L. Thomsen Weak elastic anisotropy , 1986 .

[7]  F. Ulm,et al.  Geomechanics Field and Laboratory Characterization of the Woodford Shale: The Next Gas Play , 2007 .

[8]  Franz-Josef Ulm,et al.  Grid indentation analysis of composite microstructure and mechanics: Principles and validation , 2006 .

[9]  O. Coussy Poromechanics: Coussy/Poromechanics , 2005 .

[10]  Sidney Diamond,et al.  Mercury porosimetry: An inappropriate method for the measurement of pore size distributions in cement-based materials , 2000 .

[11]  S. Derenne,et al.  Morphological and chemical features of a kerogen from the underground Mol laboratory (Boom Clay Formation, Oligocene, Belgium): structure, source organisms and formation pathways , 2001 .

[12]  Boris Gurevich,et al.  A generalized Biot–Gassmann model for the acoustic properties of shaley sandstones1 , 2000 .

[13]  Angus I. Best,et al.  The relationships between the velocities, attenuations and petrophysical properties of reservoir sedimentary rocks1 , 1994 .

[14]  R. Hill A self-consistent mechanics of composite materials , 1965 .

[15]  A. Best,et al.  Seismic attenuation and pore‐fluid viscosity in clay‐rich reservoir sandstones , 1995 .

[16]  S. Y. Lee,et al.  Microstructural and Mineralogical Characterization of Selected Shales in Support of Nuclear Waste Respository Studies , 1991 .

[17]  F. Ulm,et al.  The nano-mechanical morphology of shale , 2008 .

[18]  J. Hudson,et al.  Effective‐medium theories for fluid‐saturated materials with aligned cracks , 2001 .

[19]  L. Vernik,et al.  Velocity anisotropy in shales: A petrophysical study , 1997 .

[20]  L. Pratson,et al.  Predicting seismic velocity and other rock properties from clay content only , 2003 .

[21]  Analysis of Thomsen parameters for finely layered VTI media , 1999 .

[22]  D. Farber,et al.  Aggregate and single-crystalline elasticity of hcp cobalt at high pressure , 2005 .

[23]  Philip H. Nelson,et al.  Well logging for physical properties , 1985 .

[24]  Christian Hellmich,et al.  Drained and Undrained Poroelastic Properties of Healthy and Pathological Bone: A Poro-Micromechanical Investigation , 2005 .

[25]  C. Sayers Seismic anisotropy of shales , 2005 .

[26]  M. Jakobsen,et al.  Effect of grain scale alignment on seismic anisotropy and reflectivity of shales , 2004 .

[27]  Franz-Josef Ulm,et al.  Material invariant poromechanics properties of shales , 2005 .

[28]  N. Laws A note on penny-shaped cracks in transversely isotropic materials , 1985 .

[29]  C. MacBeth,et al.  The stress sensitivity of shaley sandstones , 2007 .

[30]  A. Nur,et al.  Elastic properties of dry clay mineral aggregates, suspensions and sandstones , 2003 .

[31]  A. Nur,et al.  Effects of porosity and clay content on wave velocities in sandstones , 1986 .

[32]  B. Hornby Experimental laboratory determination of the dynamic elastic properties of wet, drained shales , 1998 .

[33]  Zhijing Wang,et al.  Seismic Anisotropy In Sedimentary Rocks , 2001 .

[34]  Herbert F. Wang,et al.  Ultrasonic velocities in Cretaceous shales from the Williston basin , 1981 .

[35]  M. Zoback,et al.  Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone , 1989 .

[36]  R. M. Bradley,et al.  Orientational Order in Amorphous Packings of Ellipsoids , 1994 .

[37]  Franz-Josef Ulm,et al.  The effect of the nanogranular nature of shale on their poroelastic behavior , 2007 .

[38]  G. Mavko,et al.  Estimating grain-scale fluid effects on velocity dispersion in rocks , 1991 .

[39]  G. Pratt,et al.  Anisotropic parameters of layered media in terms of composite elastic properties , 1995 .

[40]  L. Thomsen Elastic anisotropy due to aligned cracks in porous rock , 1991 .

[41]  J. Hudson,et al.  The mechanical properties of materials with interconnected cracks and pores , 1996 .

[42]  Laurent Molez,et al.  Shale dynamic properties and anisotropy under triaxial loading: experimental and theoretical investigations , 2007 .

[43]  T. Johansen,et al.  Anisotropic approximations for mudrocks : A seismic laboratory study , 2000 .

[44]  K. Nihei,et al.  Preferred orientation and elastic anisotropy of illite-rich shale , 2007 .

[45]  C. Mccann,et al.  Velocity anisotropy and attenuation of shale in under‐ and overpressured conditions , 2002 .

[46]  John A. Hudson,et al.  Elastic properties of hydrate‐bearing sediments using effective medium theory , 2000 .

[47]  Franz-Josef Ulm,et al.  Poromechanics III - Biot Centennial (1905-2005) : Proceedings of the 3rd Biot Conference on Poromechanics, 24-27 May 2005, Norman, Oklahoma, USA , 2005 .

[48]  M. Cates,et al.  Effective elastic properties of solid clays , 2001 .

[49]  J. Berryman,et al.  Realizability of negative pore compressibility in poroelastic composites , 1995 .

[50]  Zhijing Wang Seismic anisotropy in sedimentary rocks, part 1: A single‐plug laboratory method , 2002 .

[51]  John A. Hudson,et al.  Anisotropic effective‐medium modeling of the elastic properties of shales , 1994 .

[52]  Amos Nur,et al.  COMPRESSIONAL VELOCITY AND POROSITY IN SAND-CLAY MIXTURES , 1992 .

[53]  E. Liniger,et al.  Random loose packings of uniform spheres and the dilatancy onset. , 1990, Physical review letters.

[54]  P. L. Hall,et al.  Pore size distribution of shaley rock by small angle neutron scattering , 1983 .

[55]  Christopher Philip Bobko,et al.  Assessing the mechanical microstructure of shale by nanoindentation : the link between mineral composition and mechanical properties , 2008 .

[56]  P. Gaviglio Longitudinal waves propagation in a limestone: The relationship between velocity and density , 1989 .

[57]  J. Castagna,et al.  Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks , 1985 .

[58]  H. Wenk,et al.  Preferred orientation and elastic anisotropy in shales , 2007 .

[59]  K. Katahara Clay Mineral Elastic Properties , 1996 .

[60]  Franz-Josef Ulm,et al.  The nanogranular nature of shale , 2006 .

[61]  Olivier Coussy,et al.  Mechanics of porous continua , 1995 .

[62]  Franz-Josef Ulm,et al.  Microporomechanics: Dormieux/Microporomechanics , 2006 .

[63]  B. Gurevich Elastic properties of saturated porous rocks with aligned fractures , 2003 .

[64]  Christian Hellmich,et al.  Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach , 2004 .

[65]  C. Sayers,et al.  The elastic anisotrophy of shales , 1994 .

[66]  Pierre Suquet,et al.  Continuum Micromechanics , 1997, Encyclopedia of Continuum Mechanics.

[67]  E. Kröner Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[68]  A. Zaoui Continuum Micromechanics: Survey , 2002 .

[69]  Roy E. White,et al.  A new velocity model for clay-sand mixtu res1 , 1995 .

[70]  D. Dewhurst,et al.  Impact of fabric, microcracks and stress field on shale anisotropy , 2006 .

[71]  R. Hill The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[72]  N. Christensen,et al.  Seismic anisotropy of shales , 1995 .

[73]  H. Ledbetter,et al.  Elastic constants of natural quartz. , 2003, The Journal of the Acoustical Society of America.

[74]  D. Schmitt,et al.  Intrinsic elasticity of a textured transversely isotropic muscovite aggregate: Comparisons to the seismic anisotropy of schists and shales , 2006 .

[75]  A. Nur,et al.  Ultrasonic velocity and anisotropy of hydrocarbon source rocks , 1992 .

[76]  Franz-Josef Ulm,et al.  Statistical indentation techniques for hydrated nanocomposites: concrete, bone, and shale , 2007 .

[77]  Alain Molinari,et al.  Micromechanical approach to the behavior of poroelastic materials , 2002 .

[78]  F. Paillet,et al.  Well Logging for Physical Properties: A Handbook for Geophysicists, Geologists, and Engineers , 2000 .

[79]  E. Kroner Self-consistent scheme and graded disorder in polycrystal elasticity , 1978 .

[80]  R. H. Bennett,et al.  Determinants of Clay and Shale Microfabric Signatures: Processes and Mechanisms , 1991 .

[81]  S. Derenne,et al.  Source organisms and formation pathway of the kerogen of the Göynük Oil Shale (Oligocene, Turkey) as revealed by electron microscopy, spectroscopy and pyrolysis , 1996 .

[82]  B. Budiansky On the elastic moduli of some heterogeneous materials , 1965 .

[83]  Luc Dormieux,et al.  Micromechanics of saturated and unsaturated porous media , 2002 .

[84]  A. Bakulin,et al.  Effective anisotropy of layered media , 2003 .

[85]  C. Sayers Seismic anisotropy of shales: What determines the sign of Thomsen's delta parameter? , 2004 .

[86]  John A. Hudson,et al.  T-matrix approach to shale acoustics , 2003 .