Retracted: Subloading Surface Plasticity Model Algorithm for 3D Subsidence Analyses above Gas Reservoirs
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Volume 12, Issue 4
Abstract
The coupled hydromechanical state in soils coming from consolidation/subsidence processes and undergoing plasticity phenomena is evaluated by means of the subloading surface model. The most important feature of this theory is the abolition of the distinction between the elastic and plastic domains, as in conventional elastoplastic models. This means that plastic deformations are generated whenever there is a change in stress and a smoother elastoplastic transition is produced. The plasticity algorithm has been implemented in the PLASCON3D FE code, coupling hydromechanical fields within a saturated porous medium (locally partially saturated at the reservoir level owing to the possible presence of a gas phase) subjected to external loads and water/gas withdrawals from deep layers (aquifers/reservoirs). The three-dimensional (3D) model is first calibrated and validated against examples taken from the literature and then subsidence analyses at regional scales owing to gas extractions are developed to predict the evolution of settlements and the pore pressure in soils for long-term scenarios.
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References
Aifantis, E. C. (1984). “On the microstructural origin of certain inelastic models.” J. Eng. Mater. Technol.JEMTA8, 106(4), 326–334.
Alonso, E. E., Gens, A., and Josa, A. (1990). “A constitutive model for partially saturated soils.” GeotechniqueGTNQA8, 40(3), 405–430.
Azienda Generale Italiana Petroli (AGIP). (1996). Progetto alto adriatico—studio di impatto ambientale, AGIP, San Donato, Italy (in Italian).
Baù, D., Ferronato, M., Gambolati, G., and Teatini, P. (2001). “Land subsidence spreading factor of the northern Adriatic gas fields, Italy.” Int. J. Geomech.IJGNAI, 1(4), 459–475.
Baù, D., Gambolati, G., and Teatini, P. (2000). “Residual land subsidence near abandoned gas fields raises concern over northern Adriatic coastland.” EOS Trans. AGUEOSTAJ, 81(22), 245–249.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures, Oxford University Press, New York.
Bažant, Z. P., and Lin, F.-B. (1988). “Non-local yield limit degradation.” Int. J. Numer. Methods Eng.IJNMBH, 26(8), 1805–1823.
Bishop, A. V. (1959). “The principle of effective stress.” Tek. Ukeblad, 106(39), 859–863.
Carbognin, L., Gatto, P., Mozzi, G., and Gambolati, G. (1978). “Land subsidence of Ravenna and its similarities with the Venice case.” Evaluation and prediction of subsidence, Saxena, S. K., ed., ASCE, New York, 254–266.
Chin, L. Y., and Nagel, N. B. (2004). “Modeling of subsidence and reservoir compaction under waterflood operations.” Int. J. Geomech.IJGNAI, 4(1), 28–34.
Collin, F., Cui, Y. J., Schroeder, C., and Charlier, R. (2003). “Mechanical behaviour of chalk reservoir: Numerical modeling of water sensitivity and time dependence effects.” Proc., 10th Int. Society for Rock Mechanics Congress Technology Roadmap for Rock Mechanics (ISRM 2003), South African Institute of Mining and Metallurgy, Johannesburg, South Africa, 219–224.
Comerlati, A., Ferronato, M., Gambolati, G., Putti, M., and Teatini, P. (2006). “Fluid-dynamic and geomechanical effects of sequestration below the Venice Lagoon.” Environ. Eng. Geosci., 12(3), 211–226.
Craft, B. C., and Hawkins, M. F. (1969). Applied petroleum reservoir engineering, Prentice-Hall, Englewood Cliffs, NJ.
De Borst, R., and Mühlhaus, H. B. (1992). “Gradient dependent plasticity: Formulation and algorithmic aspects.” Int. J. Numer. Methods Eng.IJNMBH, 35(3), 521–539.
De Borst, R., Sluys, L. J., Mühlhaus, H. B., and Pamin, J. (1993). “Fundamental issues in finite element analyses of localization of deformation.” Eng. Comput.ENGCE7, 10(2), 99–121.
Delage, P., Schroeder, C., and Cui, Y. J. (1996). “Subsidence and capillary effects in chalks.” Proc., Eurock’96, Balkema, Rotterdam, Netherlands, 1291–1298.
Drucker, D. C. (1988). “Conventional and unconventional plastic response and representation.” Appl. Mech. Rev.AMREAD, 41(4), 151–167.
Eringen, A. C. (1965). “Theory of micropolar continuum.” Proc., 9th Midwestern Mechanical Conf., Univ. of Wisconsin–Madison, Madison, WI, 23–40.
Ferronato, M., Gambolati, G., and Teatini, P. (2004). “On the role of reservoir geometry in waterdrive hydrodynamics.” J. Pet. Sci. Eng.JPSEE6, 44(3-4), 205–221.
Finol, A., and Farouq Ali, S. M. (1975). “Numerical simulation of oil production with simultaneous round subsidence.” Soc. Pet. Eng. J.SPTJAJ, 15(5), 411–424.
Fredrich, J. T., Arguello, J. G., Deitrick, G. L., and de Rouffignac, E. P. (2000). “Geomechanical modeling of reservoir compaction, surface subsidence and casing damage at the Belridge diatomite field.” Soc. Pet. Eng. J., 3(4), 348–359.
Galavi, V., and Schweiger, H. F. (2010). “Nonlocal multilaminate model for strain softening analysis.” Int. J. Geomech.IJGNAI, 10(1), 30–44.
Gambolati, G. (1973). “Equation for one-dimensional vertical flow of groundwater: 2. Validity range of the diffusion equation.” Water Resour. Res.WRERAQ, 9(5), 1385–1395.
Gambolati, G., Ricceri, G., Bertoni, W., Brighenti, G., and Vuillermin, E. (1991). “Mathematical simulation of the subsidence of Ravenna.” Water Resour. Res.WRERAQ, 27(11), 2899–2918.
Garikipati, K., and Hughes, T. J. R. (1998). “A study of strain localization in a multiple scale framework—the one-dimensional problem.” Comput. Methods Appl. Mech. Eng.CMMECC, 159(3-4), 193–222.
Gibson, R. E., Schiffman, R. L., and Pu, S. L. (1970). “Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base.” Q. J. Mech. Appl. Math.QJMMAV, 23(4), 505–520.
Giliberto, J. (2008). “Sull’Adriatico il veto della Lega.” Il Sole 24 Ore, 195, 18 (in Italian).
Grammatikopoulou, A., Zdravkovic, L., and Potts, D. M. (2006). “General formulation of two kinematic hardening constitutive models with a smooth elastoplastic transition.” Int. J. Geomech.IJGNAI, 6(5), 291–302.
Hashiguchi, K. (1980). “Constitutive equations of elastoplastic materials with elastic-plastic transitions.” J. Appl. Mech.JAMCAV, 47(2), 266–272.
Hashiguchi, K. (1989). “Subloading surface model in unconventional plasticity.” Int. J. Solids Struct.IJSOAD, 25(8), 917–945.
Hashiguchi, K. (1993). “Mechanical requirements and structures of cyclic plasticity models.” Int. J. Plast.IJPLER, 9(6), 721–748.
Hashiguchi, K. (1997). “The extended flow rule in plasticity.” Int. J. Plast.IJPLER, 13(1-2), 37–58.
Hashiguchi, K. (2000). “Fundamentals in constitutive equation: Continuity and smoothness conditions and loading criterion.” Soils Found.SOIFBE, 40(4), 155–161.
Hashiguchi, K. (2009). Elastoplasticity theory: Lecture notes in applied and computational mechanics, 42, Pfeiffer, F. and Wriggers, P., eds., Springer, Berlin.
Hashiguchi, K., Saitoh, K., Okayasu, T., and Tsutsumi, S. (2002). “Evaluation of typical conventional and unconventional plasticity models for prediction of softening behaviour of soils.” GeotechniqueGTNQA8, 52(8), 561–578.
Hashiguchi, K., and Ueno, M. (1977). “Elastoplastic constitutive laws of granular materials.” Proc., 9th Int. Conf. on Soil Mechanics and Foundations Engineering, Special Session 9, Murayama, S. and Schefield, A. N., eds., Japanese Society of Soil Mechanics and Foundation Engineering (JSSMFE), Tokyo, 73–82.
Kohler, R., and Hofstetter, G. (2008). “A cap model for partially saturated soils.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 32(8), 981–1004.
Kroner, E. (1967). “Elasticity theory of material with long-range cohesive forces.” Int. J. Solids Struct.IJSOAD, 3(5), 731–742.
Lewis, R. W., Roberts, G. K., and Zienkiewicz, O. C. (1976). “A nonlinear flow and deformation analysis of consolidation problems.” Proc., 2nd Int. Conf. on Numerical Methods in Geomechanics, Desai, C. S., ed., ASCE, Reston, VA, 1106–1118.
Lewis, R. W., and Schrefler, B. A. (1982). “A finite element simulation of the subsidence of gas reservoirs undergoing a waterdrive.” Finite element in fluids, 4, Gallagher, R. H., Norrie, D. H., Oden, J. T., and Zienkiewicz, O. C., eds., Wiley, Chichester, U.K., 179–199.
Lewis, R. W., and Schrefler, B. A. (1987). The finite element method in the deformation and consolidation of porous media, Wiley, Chichester, U.K.
Lewis, R. W., and Schrefler, B. A. (1998). The finite element method in the static and dynamic deformation and consolidation of porous media, Wiley, Chichester, U.K.
Majorana, C. E. (1987). “Two-dimensional non-linear thermo-elastoplastic consolidation program Plascon.” 9, The finite element method in the deformation and consolidation of porous media, Lewis, R. W. and Schrefler, B. A., eds., Wiley, Chichester, U.K.
Marotti de Sciarra, F. (2008). “A general theory for nonlocal softening plasticity of integral-type.” Int. J. Plast.IJPLER, 24(8), 1411–1439.
Menin, A., Salomoni, V. A., Santagiuliana, R., Simoni, L., Gens, A., and Schrefler, B. A. (2008). “A mechanism contributing to subsidence above gas reservoirs.” Int. J. Comput. Methods Eng. Sci. Mech., 9(5), 270–287.
Monte, J. L., and Kritzen, R. J. (1976). “One-dimensional mathematical model for large-strain consolidation.” GeotechniqueGTNQA8, 26(3), 495–510.
Mühlhaus, H. B., and Aifantis, E. C. (1991). “A variational principle for gradient plasticity.” Int. J. Solids Struct.IJSOAD, 28(7), 845–857.
Mühlhaus, H. B., and Vardoulakis, I. (1987). “The thickness of shear bands in granular materials.” GeotechniqueGTNQA8, 37(3), 271–283.
Needleman, A. (1988). “Material rate dependence and mesh sensitivity in localization problems.” Comput. Methods Appl. Mech. Eng.CMMECC, 67(1), 69–86.
Nuth, M., and Laloui, L. (2008). “Effective stress concept in unsaturated soils: Clarification and validation of a unified framework.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 32(7), 771–801.
Pietruszczak, S., and Mroz, Z. (1981). “Finite element analysis of deformation of strain-softening materials.” Int. J. Numer. Methods Eng.IJNMBH, 17(3), 327–334.
Pijaudier-Cabot, G., and Bažant, Z. P. (1987). “Nonlocal damage theory.” J. Eng. Mech.JENMDT, 113(10), 1512–1533.
Poland, J. F., ed. (1984). Guidebook to studies of land subsidence due to groundwater withdrawal, UNESCO, Paris.
Salomoni, V. A., and Schrefler, B. A. (2005). “A CBS-type stabilizing algorithm for the consolidation of saturated porous media.” Int. J. Numer. Methods Eng.IJNMBH, 63(4), 502–527.
Schlumberger-GeoQuest. (2003). Eclipse simulator, version 2003A, Technical Description, Houston, TX.
Schrefler, B. A., Lewis, R. W., and Majorana, C. E. (1981). “Subsidence above volumetric and waterdrive gas reservoirs.” Int. J. Numer. Methods FluidsIJNFDW, 1(2), 101–115.
Schrefler, B. A. G., Salomoni, V., Simoni, L., and Maier, G.(1997). “On compaction in gas reservoirs.” Rend. Acad. Naz. LinceiAANLAW, 8(4), 235–248.
Schrefler, B. A., Wang, X., Salomoni, V., and Zuccolo, G. (1999). “An efficient parallel algorithm for three-dimensional analysis of subsidence above gas reservoirs.” Int. J. Numer. Methods FluidsIJNFDW, 31(1), 247–260.
Shafiqu, Q. S. M. (2008). “Finite element analysis of consolidation problems in several types of cohesive soils using the bounding surface model.” J. Eng. Appl. Sci.JOASDI, 3(6), 51–57.
Shandhu, R. S., Liu, H., and Singh, K. J. (1977). “Numerical performance of some finite element schemes for analysis of seepage in porous elastic media.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 1(2), 177–194.
Simoni, L., Salomoni, V., and Schrefler, B. A. (1999). “Elastoplastic subsidence models with and without capillary effects.” Comput. Methods Appl. Mech. Eng.CMMECC, 171(3-4), 491–502.
Siriwardane, H. J., and Desai, C. S. (1981). “Two numerical schemes for nonlinear consolidation.” Int. J. Numer. Methods Eng.IJNMBH, 17(3), 405–426.
Society of Petroleum Engineers. (1998). Proc., SPE/ISRM Rock Mechanics in Petroleum Engineering (Eurock98), Allen, TX.
Society of Petroleum Engineers. (2002). Proc., SPE/ISRM Rock Mechanics Conf., Allen, TX.
Supangkat, H. (1994). “On finite element analysis of nonlinear consolidation.” M.S. thesis, Dept. of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 〈http://hdl.handle.net/1721.1/37795〉 (May 8, 2012).
Taylor, D. W. (1948). Fundamental of soil mechanics, Wiley, New York.
Terzaghi, K. (1923). “Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen.” Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt 2A., 132(3-4), 125–138.
Terzaghi, K., and Peck, R. B. (1951). Soil mechanics in engineering practice, Wiley, New York.
Thomas, L. K., Chin, L. Y., Pierson, R. G., and Sylte, J. E. (2003). “Coupled geomechanics and reservoir simulation.” Soc. Pet. Eng. J., 4(8), SPTJAJ350–358.
Wiborg, R., and Jewhurst, J. (1986). “Ekofisk subsidence detailed and solution assessed.” Oil Gas J.OIGJAV, 84(7), 47–52.
Willam, K. (1984). “Experimental and computational aspects of concrete failure.” Computer aided analysis and design of concrete failure, Damjanic, F., ed., Pineridge, Swansea, U.K., 33–70.
Yale, D. P. (2002). “Coupled geomechanics-fluid flow modelling: Effects of plasticity and permeability alteration.” Proc., SPE/ISRM Rock Mechanics Conf., SPE/ISRM, Allen, TX.
Yamakawa, Y., Hashiguchi, K., and Ikeda, K. (2010). “Implicit stress-update algorithm for isotropic Cam-clay model based on the subloading surface concept at finite strains.” Int. J. Plast.IJPLER, 26(5), 634–658.
Zhou, H., and Randolph, M. F. (2007). “Computational techniques and shear band development for cylindrical and spherical penetrometers in strain-softening clay.” Int. J. Geomech.IJGNAI, 7(4), 287–295.
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Published In
International Journal of Geomechanics
Volume 12 • Issue 4 • August 2012
Pages: 414 - 427
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© 2012. American Society of Civil Engineers.
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Received: Mar 4, 2010
Accepted: Mar 4, 2011
Published online: Mar 7, 2011
Published in print: Aug 1, 2012
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