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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