A pore-network study of bubble growth in porous media driven by heat transfer

We present experimental and theoretical investigations of vapor phase growth in pore-network models of porous media. Visualization experiments of boiling of ethyl alcohol in horizontal etched-glass micromodels were conducted. The vapor phase was observed to grow into a disordered pattern foUowing a sequence of pressurization and pore-filling steps. At sufficiently small cluster sizes, growth occurred "one pore at a time," leading to invasion percolation patterns. Single-bubble (cluster) growth was next simulated with a pore-network simulator that includes heat transfer (convec- tion and conduction), and capillary and viscous forces, although not gravity. A boundary in the parameter space was delineated that separates patterns of growth dictated solely by capillarity (invasion percolation) from other patterns. The region of validity of invasion percolation was found to decrease as the supersaturation (heat flux), the capillary number, the thermal diffusivity, and the vapor cluster size increase. Implications to continuum models are discussed. Introduction Flows in porous media that involve liquid-to-gas phase change occur in many problems of interest. The phase change can be brought about by solute diffusion, where the supersatura- tion is supplied by pressure reduction (see Li and Yortsos, 1994, 1995a, b), or by heat conduction, where the phase growth is controlled by the rate of heat supply. The latter include problems in enhanced boiling heat transfer (Thome, 1990), flows in geo- thermal systems (Schubert and Straus, 1979; Straus and Schu- bert, 1981 ), heat pipes (Ogniewicz and Tien, 1979; Udell, 1983, 1985), and severe nuclear reactor accident scenarios (Dhir and Catton, 1977). In this paper we consider the second problem with particular emphasis on single-bubble growth. As with other porous media processes, this problem can be studied at three different levels: ( 1 ) the single-pore level, where the emphasis is on the mechanics of gas-phase nucleation, film and comer flows, wetting phenomena, and the distribution of phases within single pores; (2) the pore-network level, where the emphasis is on the integration of events in an interacting ensemble of pores, where pore network topology is predomi- nant; (3) the continuum level, where the emphasis is on the average behavior of the system in terms of variables such as heat fluxes, temperature, and saturation levels. Most of past efforts have addressed the continuum level, where the pore-space dynamics are lumped into relative perme- ability and capillary pressure functions imported from the iso- thermal, immiscible displacement literature (Bau and Torrance, 1982; Udell, 1985; Stubos et al., 1993; see also Epstein, 1994). This approach has certain shortcomings: ( 1 ) In enhanced boil- ing experiments, the porous layers might not be extensive enough for the volume-averaging implicit in the continuum ap- proach to be valid; (2) the relative permeability and capillary pressure functions are taken to be independent of the rates of heat transfer. This assumption may not be valid. Experimental investigations also focused on macroscale quantities (Sondergeld and Turcotte, 1977; Straus and Schubert,