ABSTRACT

Displacement under Relaxation Effect ..................................................................... 414 10.4.3 Summary .................................................................................................................. 417

10.5 Permeability Impairment in Porous Media by Precipitate Deposition ................................. 417 10.5.1 Formulation............................................................................................................... 418 10.5.2 Simulation of Particulate Depositions under Nonequilibrium Relaxation Effects .....424 10.5.3 Summary .................................................................................................................. 426

10.6 Nonequilibrium Modiœcation of the Gradient Transport Laws ........................................... 428 10.6.1 Unsteady Darcy’s Equation for Accelerating Flow through Porous Media ............. 429 10.6.2 Nonequilibrium Transport in Nonhomogeneous Media Expressed by a

Damped-Wave Equation ........................................................................................... 430 10.6.3 Summary .................................................................................................................. 431

Nomenclature ................................................................................................................................. 431 References ...................................................................................................................................... 435

Although the assumption of instantaneous equilibrium conditions is often made in modeling of phenomenological processes of porous media, many natural processes nevertheless undergo a gradual change owing to the requirement of a œnite time for reorganization of the “uid system and species in porous media from one equilibrium state to another. For example, the freezing and thawing of moist soil is a gradual process occurring over a temperature range (Civan and Sliepcevich, 1985; Civan, 2000a) although many previous works casually assumed instantaneous freezing and melting of water at a constant temperature, such as 0°C at 1 atm. In reality, the equilibrium conditions can never be attained during the porous media transport processes when the magnitude of the relaxation time is larger than the governing process time. Einstein (1920) formulated the kinetics of nonequilibrium relaxation processes by a simple linear kinetics relationship, referred to as a constitutive equation. However, more rigorous constitutive relationships may be required for particular processes as described in this chapter.