In this paper we briefly describe Biot's Poroelasticity classical theory as a first step to introduce a general operational tensorial model to represent the porous rock deformation coupled to fluid and energy flows in geothermal reservoirs. If the geothermal rock is only subjected to small deformations, the Hooke's Law can be used to relate strains and stresses. We formulated the poroelastic model using the Finite Element Method. We also present an analytical formula for the Gibbs free internal energy. With this function the four classic thermoelastic equations can be derived and coupled to isothermal poroelasticity. These results can be useful in the study of enhanced hydrothermal reservoirs, in hot dry rock system

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