14-17 May 2018
New Orleans
US/Central timezone

Quaternions Formulation of Linear Thermoporoelasticity

16 May 2018, 17:04
New Orleans

New Orleans

Poster + 3 Minute Pitch GS 1: Fundamental theories of porous media Parallel 8-G


Mario-Cesar Suarez-Arriaga (International Geothermal Association - Asociacion Geotermica Mexicana)


This paper introduces an original application of the hypercomplex numbers known as Quaternions to model non-isothermal processes in porous rocks. The general thermoporoelastic linear theory is introduced in four dimensions and reformulated as a set of quaternions. The need of the fourth dimension appears naturally because of the pores presence. It is shown that a minimum set of four independent experimental coefficients are necessary for the coupling of four strain tensors: two for the bulk porous medium, one for the fluid and one for the total thermal expansion. Once a basic set of parameters are defined, any other coefficient can be deduced algebraically. This formulation could become a new mathematical tool to represent thermoporoelastic phenomena because includes both, the fluid pressure changes and the temperature changes.


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Biot, M. A. and Willis, D. G. (1957) “The Elastic Coefficients of the Theory of Consolidation, J. of Applied Mechanics, 24, 594-601.
Bundschuh, J. and Suárez-Arriaga, M. C. (2010) Introduction to the Numerical Modeling of Groundwater and Geothermal Systems: Fundamentals of Mass, Energy and Solute Transport in Poroelastic Rocks, 525 pp. CRC Press, Taylor & Francis Group.
Coussy, O. (2004) Poro mechanics, John Wiley & Sons, New York, NY.

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Mario-Cesar Suarez-Arriaga (International Geothermal Association - Asociacion Geotermica Mexicana)

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