Effect of micro‐inhomogeneity on the effective stress coefficients and undrained bulk modulus of a poroelastic medium: a double spherical shell model

References

1. AvsethP., MukerjiT. and MavkoG.2005. Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk. Cambridge University Press, Cambridge, UK, 359 p.
   [Google Scholar]
2. BennethumL.S.2006. Compressibility moduli for porous materials incorporating volume fraction. Journal of Engineering Mechanics132, 1205–1214.
   [Google Scholar]
3. BergeP.A. and BerrymanJ.G.1995. Realizability of negative pore compressibility in poroelastic composites. Journal of Applied Mechanics and Technical Physics62, 1053–1062, doi: 10.1115/1.2896042.
   [Google Scholar]
4. BerrymanJ.G. and MiltonG.W.1991. Exact results for generalized Gassmann's equations in composite porous media with two constituents. Geophysics56, 1950–1960.
   [Google Scholar]
5. BerrymanJ.G.1992. Effective stress for transport properties of inhomogeneous porous rock. Journal of Geophysical Research97, 17409–17424.
   [Google Scholar]
6. BiotM.A. and WillisD.G.1957. The elastic coefficients of the theory of consolidation. Journal of Applied Mechanics24, 594–601.
   [Google Scholar]
7. BrownR.J.S. and KorringaJ.1975. On the dependence of the elastic properties of a porous rocks on the compressibility of the pore fluid. Geophysics40(4), 608–616.
   [Google Scholar]
8. CarrollM.M. and KatsubeN.1983. The role of Terzaghi effective stress in linearly elastic deformation. Journal of Energy Resources Technology105, 509–511.
   [Google Scholar]
9. CizR., SigginsA.F., GurevichB. and DvorkinJ.2008. Influence of heterogeneity on effective stress law for elastic properties of rocks. Geophysics73(1), E7–E14.
   [Google Scholar]
10. C.Fairhurst
    DetournayE. and ChengA.H.D.1993. Fundamentals of poroelasticity. In: Comprehensive Rock Engineering: Principles, Practice and Projects, Vol. II, Analysis and Design Method (ed C.Fairhurst ), pp. 113–117. Pergamon Press, Inc.
    [Google Scholar]
11. DuttaN.C.2002. Geopressure prediction using seismic data: current status and the road ahead. Geophysics67, 2012–2041.
    [Google Scholar]
12. GeertsmaJ. and SmitD.C.1961. Some aspects of elastic wave propagation in fluid‐saturated porous solids. Geophysics26, 169–181.
    [Google Scholar]
13. GurevichB.2004. A simple derivation of the effective stress coefficient for seismic velocities in porous rocks. Geophysics69, 393–397.
    [Google Scholar]
14. HartD.J. and WangH.F.2010. Variation of unjacketed pore compressibility using Gassmann's equation and an overdetermined set of volumetric poroelastic measurements. Geophysics75(1), N9–N18.
    [Google Scholar]
15. HashinZ.1962. The elastic moduli of heterogeneous materials. Journal of Applied Mechanics29, 143–150.
    [Google Scholar]
16. HillR.1963. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids11, 357–372.
    [Google Scholar]
17. LandauL.D. and LifshitzE.M.1959. Theory of Elasticity. Pergamon Press, Inc.
    [Google Scholar]
18. LomakinV.A.1973. Application of the Betti reciprocity theorem in the elasticity theory of inhomogeneous bodies. International Applied Mechanics9(10), 1119–1124.
    [Google Scholar]
19. MakarynskaD., GurevichG. and CizR.2007. Finite element modeling of Gassmann fluid substitution of heterogeneous rocks. 69th Annual International Conference and Exhibition, EAGE, Extended Abstracts, 2152.
20. MavkoG., MukerjiT. and DvorkinJ.1998. The Rock Physics Handbook. Cambridge University Press.
    [Google Scholar]
21. MavkoG. and MukerjiT.2013. Estimating Brown‐Korringa constants for fluid substitution in multimineralic rocks. Geophysics78, L27–L35
    [Google Scholar]
22. MiltonG.W.2002. The Theory of Composites. Cambridge University Press, 719 p.
    [Google Scholar]
23. MüllerT.M. and SahayP.N.2013. Porosity perturbations and poroelastic compressibilities. Geophysics78, A7–A11.
    [Google Scholar]
24. RobinP.‐Y.F.1973. Note on effective pressure. Journal of Geophysical Research78, 2434–2437.
    [Google Scholar]
25. SahayP.N.2013. Biot constitutive relation and porosity perturbation equation. Geophysics78(5), L57–L67.
    [Google Scholar]
26. WeberH.J. and ArfkenG.B.2004. Essential Mathematical Methods for Physicists. Elsevier Academic Press, 932p.
    [Google Scholar]
27. WyllieM.R.J., GregoryA.R. and GardnerG.H.F.1958. An experimental investigation of factors affecting elastic wave velocities in porous media. Geophysics23, 459–493.
    [Google Scholar]
28. ZhangJ.2011. Pore pressure prediction from well logs: methods, modifications and new approaches. Earth Science Reviews108, 50–63.
    [Google Scholar]
29. ZimmermanR.W.1991. Compressibility of Sandstones. Elsevier Science Publishing Company, Inc.
    [Google Scholar]