Dispersion in Modeling Multiphase Transport through Heterogeneous Geological Media

340 Numerical modeling approaches for multiphase fl ow and tracer or chemical transport in porous media are generally based on methodologies developed for reservoir simulation and groundwater modeling. They involve solving coupled massconservation equations that govern the transport processes of all chemical components in isothermal and nonisothermal subsurface systems using fi nite-difference or fi nite-element schemes. Since the 1960s, in parallel with rapid advances in multiphase fl ow simulation and groundwater modeling, signifi cant progress has been made in understanding and modeling solute transport through porous and fractured media (Scheidegger, 1961; Bear, 1972; Huyakorn et al., 1983; Istok, 1989; Falta et al., 1992; Unger et al., 1996; Forsyth et al., 1998; Wu and Pruess, 2000). Since the 1970s, transport problems involving solute and contaminant migration in porous and fractured formations have received increasing attention in the groundwater and soil science literature. As demanded by site characterization, remediation, and other environmental concerns, many quantitative modeling approaches have been developed and applied (van Genuchten and Alves, 1982; Abriola and Pinder, 1985; Corapcioglu and Baehr, 1987; Adenekan et al., 1993; Forsyth, 1994). More recently, suitability evaluation of storing high-level radioactive wastes in underground, unsaturated fractured rock has generated renewed interest in investigating tracer or radionuclide transport in a nonisothermal, multiphase fractured geological system (e.g., Viswanathan et al., 1998; Robinson et al., 2003; Moridis et al., 2003). In addition, the application of tracer tests, including environmental and manmade tracers, has become an important technique for characterizing subsurface porous-medium systems. Even with the continual progress in both computational algorithms and computer hardware made in the past few decades, modeling the coupled processes involved in multiphase fl uid fl ow and chemical migration in porous and fractured media remains a mathematical challenge. Many unresolved issues and limitations with current numerical approaches still exist. One concern is that severe numerical dispersion often occurs when using a multidimensional control-volume–type numerical grid in fi eld-scale modeling studies. The problem becomes even greater when dealing with tracer transport, in which a general three-dimensional, coarse, irregular grid is used to solve advection–dispersion–type governing equations for handling tracer transport. To overcome these numerical diffi culties, scientists have investigated a number of TVD or fl ux-limiter schemes and applied them in transport modeling, with varying success (Sweby, 1984; Liu et al., 1994; Unger et al., 1996; Forsyth et al., 1998; Oldenburg and Pruess, Effi cient Schemes for Reducing Numerical Dispersion in Modeling Multiphase Transport through Heterogeneous Geological Media