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A coupled finite element model for the consolidation of nonisothermal elastoplastic porous media

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Abstract

A coupled finite element model for the analysis of the deformation of elastoplastic porous media due to fluid and heat flow is presented. A displacement-pressure temperature formulation is used for this purpose. This formulation results in an unsymmetric coefficient matrix, even in the case of associated plasticity. A partitioned solution procedure is applied to restore the symmetry of the coefficient matrix. The partitioning procedure is an algebraic one which is carried out after integration in the time domain. For this integration, a two-point recurrence scheme is used. The finite element model is applied to the investigation of nonisothermal consolidation in various situations.

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References

  1. Borsetto, M., Carradori, G., and Ribacchi, R., 1981, Coupled seepage, heat transfer and stress analysis with applications to geothermal problems, R. W. Lewis, K. Morgan, and O. C. Zienkiewicz (eds.),Numerical Heat Transfer, Wiley, Chichester.

    Google Scholar 

  2. Booker, J. R., and Savvidou, C., 1985, Consolidation around a heat source,Int. J. Num. Anal. Methods Geom. 9, 173–184.

    Google Scholar 

  3. Corapcioglu, M. Y. and Karahanoglu, N., 1980, Simulation of geothermal production, in T. Nejat Verizoglu (ed.),Alternative Energy Sources II, Vol. 5, Hemisphere Publ. Co., N.Y., pp. 1895–1918.

    Google Scholar 

  4. Lippmann, M. J., Narasimhan, T. N., and Witherspoon, P. A., 1976, Numerical simulation of reservoir compaction in liquid dominated geothermal systems,Proc. 2nd. Int. Symp. Land Subsidence, International Association of Hydrological Sciences, Anaheim, Calif., Pub. No. 121, pp. 179–189.

    Google Scholar 

  5. Brownell, D. H., Garg, S. K., and Pritchett, J. W., 1977, Governing equations for geothermal reservoirs,Water Resour. Res. 12, 929–934.

    Google Scholar 

  6. Pritchett, J. W., Garg, S. K., Brownell, D. H., Rice, L. F., Rice, M. H., Riney, T. D., and Hendrickson, R. R., 1976, Geohydrological environmental effects of geothermal power production Phase IIa, Systems, Science and Software, Report SSS-R-77-2998, La Jolla, Calif.

    Google Scholar 

  7. Garg, S. K., Pritchett, J. W., Rice, M. H., and Riney, T. D., 1977, U.S. Gulf Coast geopressure geothermal reservoir simulation, Final Report Systems, Science and Software, Rep. SSS-R-77-3147, La Jolla, Calif.

    Google Scholar 

  8. Aktan, T. and Farouq Ali, S. M., 1978, Finite element analysis of temperature and thermal stresses induced by hot water injection,Soc. Pet. Eng. J., 457–469.

  9. Ertekin, T., 1978, Numerical simulation of the compaction-subsidence phenomena in a reservoir for two-phase non-isothermal flow, PhD Thesis, The Pennsylvania State Univ., Penn.

    Google Scholar 

  10. Bear, J. and Corapcioglu, M. Y., 1981, A mathematical model for consolidation in a thermoelastic aquifer due to hot water injection or pumping,Water Resour. Res. 17, 723–736.

    Google Scholar 

  11. Schrefler, B. A., 1985, A partitioned solution procedure for geothermal reservoir analysis,C.A.N.M.,1, 53–56.

    Google Scholar 

  12. Borsetto, M., Cricchi, D., Hueckel, T., and Peano, A., 1984, On numerical models for the analysis of nuclear waste disposal in geological clay formations, in R. W. Lewis, E. Hinton, P. Bettes, and B. A. Schrefler, (eds.),Numerical Methods for Transient and Coupled Problems, Pineridge Press, Swansea, pp. 603–618.

    Google Scholar 

  13. Dawson, P. R. and Chavez, P. F., 1980, Thermomechanically coupled creeping flow of saturated cohesive porous media,Proc. 3rd. Int. Conf. Finite Elements in Flow Problems, Banff, pp. 268–279.

  14. Aboustit, B. L., Advani, S. H., and Lee, J. K., 1985, Variational principles and finite element simulations for thermo-elastic consolidation,Int. J. Num. Anal. Methods Geom. 9, 49–69.

    Google Scholar 

  15. Sauty, J. P., Gringarten, A. C., Menjoz, A., and Landel, P. A., 1982,Sensiible energy storage in aquifers 1. Theoretical study,Water Resour. Res. 18, 245–252.

    Google Scholar 

  16. Doughty, C., Hellström, G., Tsang, C. F., and Claesson, J., 1982, A dimensionless parameter approach to the thermal behaviour of an aquifer thermal energy storage system,Water Resour. Res. 18, 571–587.

    Google Scholar 

  17. Lewis, R. W. and Karahanoglu, N., 1981, Simulation of subsidence in geothermal reservoirs, in R. W. Lewis, K. Morgan, and B. A. Schrefler, (eds.),Numerical Methods in Thermal Problems, Vol. II, Pineridge Press, Swansea, pp. 326–335.

    Google Scholar 

  18. Zienkiewicz, O. C., Norris, V. A., Winnicki, L. A., Naylor, A. J., and Lewis, R. W., 1978, A unified approach to the soil mechanics problems of offshore foundations, in O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, (eds.),Numerical Methods in Offshore Engineering, Wiley, Chichester, Ch. 12, pp. 361–412.

    Google Scholar 

  19. Lewis, R. W. and Schrefler, B. A., 1982, A finite element simulation of the subsidence of a gas reservoir undergoing a waterdrive, in R. H. Gallagher, D. H. Norrie, J. T. Oden, and O. C. Zienkiewicz,Finite Elements in Fluids, Vol. 4, Wiley, Chichester, pp. 179–199.

    Google Scholar 

  20. Schrefler, B. A., 1984, The finite element method in soil consolidation (with applications to surface subsidence), PhD Thesis, University College of Swansea.

  21. Zienkiewicz, O. C., 1977,The Finite Element Method, McGraw-Hill, London.

    Google Scholar 

  22. Combarnous, N. A. and Bories, S. A., 1975, Hydrothermal convection in saturated porous media, V. T. Chow, (ed.), inAdvances in Hydroscience, Vol. 10, Academic Press, New York, pp. 231–307.

    Google Scholar 

  23. Schrefler, B. A. and Vitaliani, R., 1985, Partitioned solution procedure for educational software on microcomputers: the case of a coupled consolidation analysis,Proc. Int. Conf. Education, Practice and Promotion of Computational Methods in Engineering Using Small Computers (EPMESC), Macao, 5–9 August.

  24. Park, K. C., 1985, Stabilization of partitioned solution procedure for pore fluid soil interaction analysis,I.J.N.M.E. 19, 1669–1673.

    Google Scholar 

  25. Schrefler, B. A., Majorana, C. E., and Lewis, R. W., A comparison between different simulators for geothermal reservoirs (to be published).

  26. Siriwardane, H. J. and Desai, C. S., 1981, Two numerical schemes for nonlinear consolidation,I.J.N.M.E. 17, 405–426.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Numerical Methods in Engineering, University College of Swansea, SA2 8PP, Swansea, Wales, UK

    R. W. Lewis

  2. Istituto di Costruzioni, University of Padua, Padua, Italy

    C. E. Majorana & B. A. Schrefler

Authors
  1. R. W. Lewis
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  2. C. E. Majorana
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  3. B. A. Schrefler
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Lewis, R.W., Majorana, C.E. & Schrefler, B.A. A coupled finite element model for the consolidation of nonisothermal elastoplastic porous media. Transp Porous Med 1, 155–178 (1986). https://doi.org/10.1007/BF00714690

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  • DOI: https://doi.org/10.1007/BF00714690

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