Coupling temperature to a double-porosity model of deformable porous media. (English) Zbl 0972.74066
Summary: This paper extends the double porosity deformable model to take into account temperature effects. Unlike the double temperature approach, the model assumes a single representative thermodynamics continuum which includes both conducting and convection heat transfer in a fully saturated porous media. Examples are presented to evaluate the suitability of the model.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76F05 | Isotropic turbulence; homogeneous turbulence |
| 76S05 | Flows in porous media; filtration; seepage |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
conductive heat transfer; finite element method; double porosity deformable model; temperature effects; thermodynamics continuum; convection heat transfer; fully saturated porous mediaReferences:
| [1] | Biot, Journal of Applied Physics 12 pp 155– (1941) |
| [2] | Oda, Geotechnique 35 pp 483– (1985) |
| [3] | Barrenblatt, Journal of Applied Mathematics and Mechanics, USSR 24 pp 1286– (1960) |
| [4] | Warren, Transactions of AIME, SPEJ 228 pp 244– (1963) |
| [5] | Aifantis, Developments Mechanics 9 pp 46– (1985) |
| [6] | Wilson, International Journal of Engineering Science 20 pp 1009– (1982) |
| [7] | Khaled, International Journal for Numerical and Analytical Methods in Geomechanics 8 pp 101– (1984) |
| [8] | Valliappan, International Journal for Numerical Methods in Engineering 29 pp 1079– (1990) |
| [9] | Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs. Paper SPE 38884 presented at SPE Annual Technical Conference and Exhibition, San Antonio, TX, 1997. |
| [10] | Aifantis, Mechanics of Research Communications 7 pp 165– (1980) |
| [11] | Aifantis, Mechanics of Research Communications 67 pp 219– (1980) |
| [12] | Bai, International Journal of Engineering Science 32 pp 1615– (1994) |
| [13] | Ghafouri, International Journal for Numerical and Analytical Methods in Geomechanics 20 pp 831– (1996) |
| [14] | Bai, International Journal of Rock Mechanics and Mining Sciences Geomechanics 30 pp 1185– (1993) |
| [15] | Private discussion during CISM course on Environmental Geomechanics, Udine, Italy, 1999. |
| [16] | Theoretical Soil Mechanics. Wiley: New York, 1943. · doi:10.1002/9780470172766 |
| [17] | The Finite Element Method in the Static and Dynamics Deformation and Consolidation of Porous Media (2nd edn). Wiley: England, 1998. |
| [18] | The Finite Element Method (4th edn), vols. 1, 2. McGraw-Hill: London, 1989. |
| [19] | Booker, International Journal for Numerical and Analytical Methods in Geomechanics 9 pp 173– (1985) |
| [20] | Integrated flow and subsidence simulation for hydrocarbon reservoir. 7th Annual Conference of ACME’99 1999; 175-178. |
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