Partial saturation, porous media

The traditional, continuum-based approach uses Darcy s law, modified for partially saturated porous media, to quantify the flux of water ... 

In this chapter, we examine the various mechanisms that influence chemical redistribution in the subsurface and the means to quantify these mechanisms. The same basic principles can be applied to both saturated and partially saturated porous media in the latter case, the volumetric water content (and, if relevant, volatilization of NAPL constiments into the air phase) must be taken into account. Also, such treatments must assume that the partially saturated zone is subject to an equilibrium (steady-state) flow pattern otherwise, for example, under periods of heavy infiltration, the volumetric water content is both highly space and time dependent. When dealing with contaminant transport associated with unstable water infiltration processes, other quantification methods (e.g., using network... 

Gray, W.G. and Schrefler, B.A. (2001) Thermodynamic approach to effective stress in partially saturated porous media, Eur. J. Mech. A/Solids 20, 521-538... 

Kim, H., P.S.C. Rao, and M.D. Annable. 1997. Determination of effective air-water interfacial area in partially saturated porous media using surfactant adsorption. Water Resour. Res. 32 2705-2711. 

We present now the extension of the constitutive equation (7) to partially saturated porous media. The material is assumed to be saturated by a liquid phase (noted by index w) and a gas mixture (noted by index g ). The gas mixture is a perfect mixture of dry air (noted by index da) and vapour (noted by index va). Based on most experimental data of unsaturated rocks and soils (Fredlund and Rahardjo 1993), and on the theoretical background of micromechanical analysis (Chateau and Dormieux 1998), the poroelastic behaviour of unsaturated material should be non-linear and depends on the water saturation degree. We consider here the particular case of spherical pores which are dried or wetted under a capillary pressure equal to the superficial tension on the air-solid interface. By adapting the macroscopic non-linear poroelastic model proposed by Coussy al. (1998) to unsaturated damaged porous media, the incremental constitutive equations in isothermal conditions are expressed as follows ... 

The main processes are electrochemical reactions at electrified metal-electrolyte interfaces reactant diffusion through porous networks proton transport in water and at aggregates of ionomer molecules electron transport in electronic support materials water transport by gasous diffusion, hydraulic permeation, and electro-osmotic drag in partially saturated porous media and vaporization/condensation of water at interfaces between liquid water and gas phase in pores. 

Richards equation (Richards 1931), based on a mass conservation balance, together with Eq. 9.1, can be used to describe the transient flow of water through a partially saturated porous medium. In one dimension (vertically), Richards equation is given as... 

Knowledge of detailed liquid-vapor configurations enables separation of capillary and adsorptive contributions to the interfacial area as shown in Fig. 1-1 la (note the log-log scale). We denote liquid-vapor interfacial areas associated with menisci (curved interfaces at pore comers) as capillary contributions, and those associated with films as adsorptive contributions. The results in Fig. 1-1 la illustrate the dominant contribution of liquid films to the total liquid-vapor interfacial area of a partially saturated porous medium (Millville silt loam). Note that the flat region in Fig. 1-1 la (changes in SA with no change in p) reflects pore snap-off processes. 

The pore scale model and the associated unitary approach were upscaled to represent a sample of partially saturated porous medium. 

A numerical model was developed to simulate MeBr movement in soil and volatilization into the atmosphere. The model simultaneously solves partial differential equations for nonlinear transport of water, heat, and solute in a variably saturated porous medium. Henry s Law is used to express partitioning between the liquid and gas phases and both liquid and vapor diffusion are included in the simulation. Soil degradation is simulated using a first-order decay reaction and the rate coefficients may differ in each of the three phases (i.e., liquid, solid, or gaseous). 

The COj concentration in the subsurface may be different in small and large pores and vary as a function of the aerobic or anaerobic activity of the microbial population. Paul and Clark (1989) showed that a change from aerobic to anaerobic metabolism occurs at an concentration of less than 1% (by volume). The overall aeration of the soil layer is not as important as that of individual aggregates. Calculations show that water-saturated aggregates larger than 3 mm in radius have no in their center (Harris 1981). This means that aerobic and anaerobic zones may coexist in a porous medium even under partially saturated conditions. 

The extent of trapping is determined primarily by the physical properties of the vadose zone. If the organic liquids are characterized by a low vapor pressure and a low solubility in water, they remain trapped in the partially saturated zone. In this particular case, the porous medium behaves like an inert material and the behavior of the organic liquids depends only on their own properties, with no interaction between the liquid and the solid phases. 

Soils, typically, are not fully saturated by water the soil layer and the region reaching to the water table contain water contents below full saturation. These regions usually are referred to as the vadose zone and said to be unsaturated, but they are more correctly considered partially saturated. The degree of saturation is the ratio of the volume of water to the pore volume within the porous medium. Saturation levels usually are a few percent at land surface (or even zero in perpemaUy dry arid zones) and increase slowly with depth until the region of the capillary fringe (water table), where it increases rapidly to 100%. 

The transient contaminant transport from a dissolving DNAPL pool in a water saturated, three-dimensional, homogeneous porous medium under steady-state uniform flow, assuming that the dissolved organic sorption is linear and instantaneous, is governed by the following partial differential equation ... 

In the previous discussion of Darcy s Law only homogeneous fluid flow was considered. If the porous medium is only partially saturated with a fluid the permeability of the porous medium to the fluid will be less than the permeability obtained when the medium is 100% saturated. The permeability at less than 100% saturation is known as the effective permeability. Values of the effective penneability range between 0 and K where K represents the permeability at 100% saturation. The symbols Kg, Kg, and are used to represent the effective permeabilities to oil, gas, and water, respectively. 

Effective permeability is used in Darcy s Law in place of the permeability at 100% saturation when two or more fluids are present in a porous medium. Thus, if oil partially saturates a porous medium, Darcy s Law may be written... 

Similarly for a porous medium partially saturated with gas the quantity of gas flowing is... 

Abstract This contribution deals with the modeling of coupled thermal (T), hydraulic (H) and mechanical (M) processes in subsurface structures or barrier systems. We assume a system of three phases a deformable fractured porous medium fully or partially saturated with liquid and a gas which remains at atmospheric pressure. Consideration of the thermal flow problem leads to an extensively coupled problem consisting of an elliptic and parabolic-hyperbolic set of partial differential equations. The resulting initial boundary value problems are outlined. Their finite element representation and the required solving algorithms and control options for the coupled processes are implemented using object-oriented programming in the finite element code RockFlow/RockMech. 

Typical examples of percolation systems are (i) random mixtures of electronically conducting metallic spheres in an insulating host medium, for example, a polymer electrolyte, (ii) a network of gas pores providing high diffusivity in a porous matrix of a gas-tight material, or (iii) a porous electrode partially saturated with a liquid electrolyte. 

---