Analysis of unsaturated clayey materials hydration incorporating the effect of thermo-osmotic flow

Document available in extended abstract form only. The hydraulic gradient is the main physical phenomenon influencing the movement of water in permeable porous media. It is, however, not the only one. Figure 1 presents the main kinds of flow that can occur in a porous media alongside with the corresponding gradient responsible for the movements. The word 'law' is generally used for the diagonal terms associated with the direct flow phenomena, and the name 'effect' is reserved to the non-diagonal ones, called also 'coupled processes'. Lippmann (1907) discovered and named the phenomenon of thermo-osmosis. He discovered it experimentally by separating a volume of water into two parts by means of a membrane. Different temperatures were held in the two regions of the system. The thermal gradient caused a flow of water through the membrane from the cold to the hot side. In permeable reservoirs, the non-diagonal coefficients are relatively small and negligible compared to the diagonal terms. That is the reason why the coupled processes are generally ignored when analyzing problems in aquifers. However, in non-isothermal problems involving low permeability media and/or low hydraulic gradients thermo-osmosis may play a more influential role. Srivastava and Avasthi (1975) and Horseman and McEwen (1996) showed that water flux due to thermo-osmosis can easily exceed Darcy flux in low permeability clays. The 'phenomenological coefficient' that links each flow with the corresponding driving gradient must be measured experimentally. Accounting for thermo-osmosis is assuming that the transport of heat may modify the transport of fluids. The counterpart phenomenon of thermo-osmosis is thermo-filtration, which reflects the influence of a pressure gradient on heat flow. Thermo-osmosis and thermo-filtration are generally formulated as reciprocal relations, so that the coupled conductivity terms related to each phenomenon are set equal. Thermo-osmotic effects have been studied in the past, for example Soler (2001) studied the impact of coupled phenomena on the long-term behavior of radioactive waste repositories in saturated argillaceous rock. Bing (2006) proposed an analytical solution in the half-space for the thermal consolidation of layered saturated soils, including the influences of thermo-osmosis and thermal filtration. Chen et al. (2009) recently proposed a coupled Thermo-Hydro-Mechanical (THM) formulation which accounts for the flow of water and air driven by temperature gradients. The aim of this work is to explore the impact of thermo-osmosis on the hydration of clayey soils and rocks generally used in the design of nuclear waste disposals. Both small scale experiments and large scale problems are analyzed. A coupled THM formulation has been extended to deal with thermal osmosis in porous media. Special emphasis is put on the study of thermo-osmotic flow in unsaturated low permeability clays. A simple model was implemented in Theta-Stock program to study thermo-osmotic effects in the performance of a nuclear waste repository. The thermo-osmotic conductivity KfT is assumed to be a scalar (kT). The permeability of the liquid phase in the initial state is around 5*10-13 m.s-1. The thermo-osmotic coefficient kT is taken 100 times higher than the typical permeability of the massif: kT = 5*10-11m.s-1. Containers are assumed to be stored in a 100- meter depth horizontal gallery. The ground water is located at 500 meters depth. The initial saturation degree of the ground mass was 0.15. The response of the unsaturated tuff is studied over 1000 years. The material parameters, related to fluid and temperature effects, are taken from the data given by Pollock (1986). Up to 200 years of heating, the trends of the saturation degree are the same in both models. But the magnitudes are different around the heating source, between 80 meters and 140 meters deep. With the model accounting for thermo-osmotic effects, the saturation degree is approximately twice smaller in this zone than the saturation degree obtained with the reference behavior model. This means that thermo-osmosis originates drying. During the 1000 years of nuclear waste storage, the host rock is thus expected to be subjected to more significant drying if thermo-osmosis is taken into account. This is because the equivalent thermal conductivity of the unsaturated porous medium, computed as a weighted average of the thermal conductivities of all constituents (solid skeleton, liquid, gas), is expected to be lower than in the reference model (due to its lower saturation). Heat flux is mainly controlled by Fourier's law; so if a given heat flux is imposed at the surfaces of the heating source, the decrease of equivalent thermal conductivity has to be compensated by the gradient of temperature. The massif studied with the thermo-osmotic model being dryer than in the reference case, it is thus logical to observe higher temperatures around the heating source in the simulation accounting for thermo-osmotic effects. As it can be observed, the effect of thermo-osmotic flow is relevant in this problem related to nuclear waste disposals. (authors)