Wave propagation in porous media is of interest in various diversified areas of science and engineering. The theory of the phenomenon has been studied extensively in soil mechanics, seismology, acoustics, earthquake engineering, ocean engineering, geophysics, and many other disciplines. This review presents a general survey of the literature within the context of porous media mechanics. Following a review of the Biot's theory of wave propagation in linear, elastic, fluid saturated porous media which has been the basis of many analyses, we present various analytical and numerical solutions obtained by several researchers. Biot found that there are two dilatational waves and one rotational wave in a saturated porous medium. It has been noted that the second kind of dilatational wave is highly attenuated and is associated with a diffusion type process. The influence of coupling between two phases has a decreasing effect on the first kind wave and an increasing effect on the second wave. Procedures to predict the liquefaction of soils due to earthquakes have been reviewed in detail. Extension of Biot's theory to unsaturated soils has been discussed, and it was noted that, in general, equations developed for saturated media were employed for unsaturated media by replacing the density and compressibility terms with modified values for a water-air mixture. Various approaches to determine the permeability of porous media from attenuation of dilatational waves have been described in detail. Since the prediction of acoustic wave speeds and attenuations in marine sediments has been extensively studied in geophysics, these studies have been reviewed along with the studies on dissipation of water waves at ocean bottoms. The mixture theory which has been employed by various researchers in continuum mechanics is also discussed within the context of this review. Then, we present an alternative approach to obtain governing equations of wave propagation in porous media from macroscopic balance equations. Finally, we present an analysis of wave propagation in fractured porous media saturated by two immiscible fluids.

Cementitious solidification/stabilization (s/s) treatment processes combine Portland cement or lime/pozzolan mixtures with waste materials or contaminated soils to immobilize contaminants by physical and chemical mechanisms. It is a low cost remedial alternative and is commonly used at Superfund sites for treatment of soils, sludges and debris. Although widely utilized, s/s processes do not preclude migration of contaminants, but they can substantially reduce the rates of release to the environment. Evaluation of the impact of these releases requires appropriate application of risk assessment techniques. Problems associated with accurate prediction of leach rates are exacerbated in stabilized soil/waste matrices by (1) reactions between soil components and cement hydration or pozzolanic reaction products and (2) interactions between stabilized soil/waste matrices and adjacent media. This paper assesses effects of soil/cement reactions and environmental interactions on solid and solution phase characteristics of stabilized soil/waste matrices. First, available information on soil S/S applications will be evaluated to ascertain plausible disposal scenarios for stabilized soil/waste matrices. Second, cement hydration reactions, soil/cement reactions and environmental interactions that affect solid and solution phase characteristics of stabilized soil/waste matrices and, consequently, long-term leach rates will be delineated. Finally, techniques for predicting long-term leach rates will be evaluated.

Sedimentary basins represent large-scale porous media, are important hosts to a significant portion of the world's economic energy and mineral resources. Processes occurring in sedimentary basins include groundwater flow, heat transport, and reactive mass transport. Quantitative models of flow and transport in these settings can provide insight into the processes that control the evolution of sedimentary basins by enabling the examination of processes that may occur too slowly to be observed in the field or laboratory. In many cases, such models may be the only available tool for studying processes occurring over geological time and space scales. In addition, it is important to consider the behavior of the processes occurring in sedimentary basins simultaneously, since they are generally coupled. Groundwater flow is controlled by the boundary conditions and the distribution of hydraulic conductivity; as a result, flow velocities vary spatially and temporally. This circulation is capable of transporting thermal energy and dissolved mass. In general, flow rates will be sufficiently small that the water will reach approximate equilibrium with each lithology along the flow path at the ambient temperature and pressure. These successive equilibria produce changes in the chemical composition of the fluid, resulting in reactions with the medium (i.e., precipitation, dissolution), which in turn modify the porosity and permeability. This modification may be insignificant at a human time scale, but very significant at the geological time scale. The hydrogeological flow field then is a coupled hydrological-thermal-geochemical system, requiring solution to three sets of coupled partial differential equations. This paper reviews developments over the past several years in numerical simulation of these coupled processes. The governing conservation equations are presented, and solution procedures discussed; the finite element equations are developed for the case where local chemical equilibrium is assumed. Application of coupled models to a variety of geological problems is discussed, such as the propagation of mineral reaction fronts in one spatial dimension. These studies have noted the importance of hydrodynamic dispersion and its control on the spatial distribution of reaction rates and products. Relatively few two-dimensional simulations are available in the literature, but these few are reviewed, including the formation of uranium ore deposits, mixing-zone reactions in carbonate aquifers, and sandstone diagenesis. These studies note the importance of transport-controlled reaction-front propagation, fluid mixing, and gradient reactions, which all occur to varying degrees in a heterogeneous sedimentary basin. Future developments will require greater computer capability, and are likely to focus on application to well-documented field problems and greater inclusion of natural geological heterogeneity, but results presented to date show promise of enabling quantitative study of coupled hydrological, geochemical, and thermal processes in evolving sedimentary basins.

Flow of non-Newtonian fluids through porous media occurs in many subsurface systems and has found applications in certain technological areas. Previous studies of the flow of fluids through porous media were focusing for the most part on Newtonian fluids. Since the 1950s, the flow of non-Newtonian fluids through porous media has received a significant amount of attention because of its important industrial applications, and considerable progress has been made. However, our understanding of non-Newtonian flow in porous media is very limited when compared with that of Newtonian flow. This work presents a comprehensive theoretical study of single and multiple phase flow of non-Newtonian fluids through porous media. The emphasis in this study is in obtaining some physical insights into the flow of power-law and Bingham fluids. Therefore, this work is divided into three parts: (1) review of the laboratory and theoretical research on non-Newtonian flow, (2) development of new numerical and analytical solutions, (3) theoretical studies of transient flow of non-Newtonian fluids in porous media, and (4) demonstration of applying a new method of well test analysis and displacement efficiency evaluation to field problems.

Subsurface biodegradation of non-aqueous phase liquid (NAPL) compounds is extremely complex. Understanding of the interaction of physical, chemical and biological phenomena is still primitive, and much experimental and investigative work is needed in order to elucidate the important factors. Mathematical modeling of subsurface biodegradation can help us to understand the factors that are likely to be most important in harnessing the restorative power of this technology. The literature contains many mathematical models that describe subsurface biodegradation. These models approach the subject from many different perspective, and each contribute something to our understanding of the phenomena. This report describes the methods by which researchers have modeled subsurface NAPL biodegradation, describes several models in detail to illustrate different approaches, and recommends how subsurface biodegradation modeling can be further developed.