A Nonlinear Creep-damage Constitutive Model of Mudstone Based on the Fractional Calculus Theory

Document Type : Research Paper

Authors

Northeast Petroleum University

Abstract

During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerated creep stage of mudstone. After assuming that the relationships between strain and time can be expressed by the exponential functions, the creep-damage constitutive model to describe the relationship between stress and strain stress of mudstone is established under the condition of accelerated strain rate loading. Furthermore, uniaxial creep tests and conventional triaxial compression tests were carried out to validate the proposed model. It is found that the fractional nonlinear creep-damage model can effectively describe the characteristics of the three stages of mudstone creep; moreover, this model can reduce the number of components and the parameters. Both the fractional nonlinear creep model and the creep-damage constitutive model have a high fitting relationship with the test results. Also, the initial elastic modulus and confining pressure are in a good linear relationship. Finally, the parametric sensitivity analysis of the theoretical model is carried out. The correctness and applicability of models were confirmed from three respects of the derivation process, test results, and the theoretical analysis.

Keywords

References

REFERENCES
Yan X. Z., Yang H. L., and Yang X. J., “The Reason Analysis of Mudstone Creep on Casing Damage,” Drilling & Production Technology, 2003, 26(3), 65-69.
Huang X. L., Yang C. H., Liu J. J., and et al., “Experimental Study on Mudstone Creep Behavior under Different Water Contents and Its Effect on Casing Damage,” Rock Mechanics and Engineering, 2008, 2(2), 3477-3487.
Song Y. J. and Lie S. Y., “Mechanical Model of Rock Nonlinear Creep Damage Based on Fractional Calculus,” Chinese Journal of Underground Space and Engineering, 2013, 9(1), 91-95.
Yang C. H., Daemen J. K., and Yin J. H., “Experimental Investigation of Creep Behavior of Salt Rock,” International Journal of Rock Mechanics and Mining Sciences, 1999, 36(2), 233-242.
Wang G. J., “A New Constitutive Creep-Damage Model for Rock and its Characteristic,” Int. J. Rock Mech. Min. Sci, 2004, 41(1), 61-67.
Shao J. F., Zhu Q. Z., and Su K., “Modeling of Creep in Rock Materials in Terms of Material Degradation,” Computers and Geotechnics, 2003, 30(7), 549-555.
Shao J. F., Chau K. T., and Feng X. T., “Modeling of Anisotropic Damage and Creep Deformation in Brittle Rock,” International Journal of Rock Mechanics and Mining Sciences, 2006, 43(4), 582-592.
Li W. Q. , Li X. D., Han B. , and et al., “Recognition of Creep Model of Layer Composite Rock Mass and Its Application,” Journal of Central South University of Technology, 2007, 17(1), 329-331.
Xu W. Y., Yang S. Q., Xie S. Y., and et al., “Investigation on Triaxial Rheological Mechanical Properties of Green Schist Specimen(II) Model Analysis,” Rock and Soil Mechanics, 2005, 26(5), 693-698.
Zhou H. W., Wang C. P., Han B. B., and et al., “A Creep Constitutive Model for Salt Rock Based on Fractional Derivatives,” Int. J. Rock Mech. Mining Sci., 2011, 48(1), 116-121.
Li Y. L., Yu H. C., and Liu H. D., “Study of Creep Constitutive Model of Silty Mudstone under Triaxial Compression,” Rock and Soil Mechanics, 2011, 33(7), 2035-2040.
Sun H. Z. and Zhang W., “Analysis of Soft Soil with Viscoelastic Fractional Derivative Kelvin Model,” Rock and Soil Mechanics, 2007, 28(9), 1983-1986.
He L. J., Kong L. W., and Wu W. J., “A Description of Creep Model for Soft Soil with Fractional Derivative,” Rock and Soil Mechanics, 2011, 32(2), 239-249.
Xu G. W., He C., Hu X. Y., and Wang S. M., “A Modified Nishihara Model Based on Fractional Calculus Theory and its Parameter Intelligent Identification,” Rock and Soil Mechanics, 2015, 43, 132-147.
Wang J. B., Liu X. R., Rong J. Q., and et al., “Creep Properties of Salt Rock and Its Nonlinear Constitutive Model,” Journal of China Coal Society, 2014, 39(3), 445-451.
Ding J. Y., Zhou H. W., Li C., and et al., “The Fractional Derivative Approach of Creep Constitutive Model of Salt Rock Based on WEIBULL Distribution,” Journal of Solid Mechanics, 2013, 34(5), 675-679.
Yin D. S., Ren J. J., and He C. L., “Stress-stain Relation of Soft Soil Based on Fractional Calculus Operators Theory,” Chinese Journal of Rock Mechanics and Engineering, 2009, 28(1), 2973-2979.
Yin G. Z., Wang D. K., Huang G., Zhang D. M., and et al., “A Triaxial Creep Model for Coal Containing Gas and its Stability Analysis,” 2009, 15(3), 248-251.
Zhou H. W., Wang C. C., Duan Z. Q., and et al., “Time-based Fractional Derivative Approach to Creep Constitutive Model of Salt Rock,” Scientia Sinica Physica, Mechanica & Astronomica, 2012, 42(3), 310-318.
Zhou H. W., Wang C. P., Mishnaevsky J. L., and et al., “A Fractional Derivative Approach to Full Creep Regions in Salt Rock,” Mechanics of Time-Dependent Materials, 2013, 17(3), 413-425.
Yao Z. M., Xu Y., Wang H. L., and Shao W., “Fractional Order Derivative Constitutive of Artificial Frozen Soil,” Journal of Sichuan University of Science and Technology (Natural Science).
Chen L., Chen S. G., Zhang H., and Yang J. S., “A Nonlinear Visco-elasto-Plastic Creep Model Based on Fractional Calculus,” Journal of Sichuan University of Science and Technology (Natural Science), 2013, 45(7), 7-14.
Wu F., Liu J. F., Bian Y., and Zhou Z. W., “Fractional Derivative Creep Model of Salt Rock,” Journal of Sichuan University (Engineering Science Edition), 2014, 46(5), 22-28.
Wu F., Xie H. P., Liu J. F., and et al., “Experimental Study of Fractional Viscoelastic-plastic Creep Model,” Chinese Journal of Rock Mechanics and Engineering, 2014, 33(5), 964-970.
Li R. Z. and Le J. Z., “Nonlinear Rheological Constitute of Soft Soil Based on Fractional Order Derivative Theory,” Journal of Basic Science and Engineering, 2014, 22(5), 856-865.
Kang J. H. , Zhou F. B., Liu C., and Liu Y. K., “A Fractional Non-linear Creep Model for Coal Considering Damage Effect and Experimental Validation,” International Journal of Non-Linear Mechanics, 2015, 76, 20-28.
Journal of Petroleum Science and Technology
Volume 7, Issue 4 - Serial Number 4
November 2017
Pages 54-64

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