Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source

Abstract

SUMMARYSolutions are presented for the behaviour of a layered porous space which contains a decaying heat source. Such a problem arises when high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins. The geometry of the problem is one dimensional and the porous space is constituted by two layers: a deep low permeability layer which contains the nuclear waste disposal and a superficial layer. The solution is used to examine the effects of contrasts of permeability, thermal conductivity and specific heat capacities between the two layers on the large-scale behaviour of the porous space. Results are presented, using realistic data, for the pore pressure and temperature evolution at the heat source centre, and for the vertical displacement of the ground level. The superficial layer has no significant effects on pore pressure, temperature and stress evolution near the heat source centre. The vertical displacement of the ground level is mainly due to the thermal dilatation of the pore water, so it decreases with an increasing of permeability of the superficial layer. The solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical methods to invert the transformed solutions. Comparisons with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass are presented.

Coupled consolidation and heat flow analysis of layered soils surrounding cylindrical heat sources using a precise integration technique

“…Lu and Lin studied the axial symmetrical thermal consolidation caused by a decaying point heat source in a saturated isotropic poro‐elastic full space. In the light of deposition processes of natural soils, it is necessary to consider the stratification characteristics when analysing the coupled consolidation and heat flow responses, and several solutions for this problem of layered soils are derived utilising the analytical approaches and numerical methods …”

“…Lu and Lin 23 studied the axial symmetrical thermal consolidation caused by a decaying point heat source in a saturated isotropic poro-elastic full space. In the light of deposition processes of natural soils, it is necessary to consider the stratification characteristics when analysing the coupled consolidation and heat flow responses, and several solutions for this problem of layered soils are derived utilising the analytical approaches [24][25][26] and numerical methods. [27][28][29] The aforementioned literatures focused on the thermal performance of soils around a point or a plane heat source, which may fails to accurately describe the near-field responses in the field.…”

A solution around a backfilled cavity in a low‐permeability poroelastic medium with application in in situ heating tests

“…In practical applications, there are many problems in which more than one porous material are involved. For solving a problem with high‐level nuclear waste placed in underground repositories, Giraud et al extended the previous solution of a homogeneous single thermoporoelastic isotropic layer to a double‐layer porous space: a lower low‐permeability layer, which contains a decaying heat source and a superficial layer. In the practice of BHEs, the surrounding empty space between pipes and the ground is filled with grout mix to sustain superior heat transfer.…”

Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium

“…Zimmerman [19] gave brief derivation of the equations of linearized poroelasticity and thermoelasticity. Giraud et al [20] analyzed the case of a heat source that decreases exponentially with time by considering a low permeability clay for nuclear waste disposal. Using the Biot's wave equation and the theory of thermodynamic, Liu et al [21] investigated the dynamic response of saturated porous elastic medium.…”