24
2. Hydrodynamic Dispersion in Porous Media
be adsorbed by the solid. The mass in the solid mayaiso get into the liquid
by dissolution or ion exchange.
5. Chemical reaction and biological process. There may exist chemical reactions among fluids with different chemical compositions and between
fluids and solid particles. For example, precipitation may cause a certain
change in the solute concentration. Biological processes such as the putridity of organisms and reproduction of bacteria will also change the
concentration.
6. Radioactive decay. The radioactive components within the fluid will decrease in concentration as a result of decay over time.
In a generalized model which describes solute concentration behaviors in a
porous medium, all of the factors mentioned above should be taken into
account. The importance of each factor, however, may difTer from case to
case.
To study the mass transport in porous media, we can follow two major
steps. First, we must clarify the mechanism of solute transport from a microscopic viewpoint and derive the relevant mass conservation and advectiondiffusion equations. Then, we can transfer these equations to the macroscopic
level by means of spatial averaging.
2.3 Mass Conservation and Convection-Diffusion
Equations in a Fluid Continuum
2.3.1 Diffusive Velocities and Fluxes
In a multicomponent fluid, the transport of a component can be resolved into
two parts: one is the transport along with the bulk fluid at its mean flow
velocity, which is called advection; the other is the molecular diffusion, which
is caused by the concentration gradient of the component in the fluid.
The difference between the velocity V" of component IX, and the mean flow
velocity V ofthe fluid, written as (V" - V), is called the mass diffusion velocity
of component IX. The product of the mass diffusion velocity and the density of
component IX, is called the mass diffusion flux, written as J"
J" = piV" - V).
(2.3.1)
According to the famous Fick's Law, mass diffusion obeys the following
equation:
J" = -pDdgrad(p"jp),
(2.3.2)
where p is the density of the fluid. For a binary system containing only a
solvent and a solute, Eq. (2.3.2) can be written as
J = -pDdgrad(Cjp),
(2.3.3)
2. Hydrodynamic Dispersion in Porous Media
be adsorbed by the solid. The mass in the solid mayaiso get into the liquid
by dissolution or ion exchange.
5. Chemical reaction and biological process. There may exist chemical reactions among fluids with different chemical compositions and between
fluids and solid particles. For example, precipitation may cause a certain
change in the solute concentration. Biological processes such as the putridity of organisms and reproduction of bacteria will also change the
concentration.
6. Radioactive decay. The radioactive components within the fluid will decrease in concentration as a result of decay over time.
In a generalized model which describes solute concentration behaviors in a
porous medium, all of the factors mentioned above should be taken into
account. The importance of each factor, however, may difTer from case to
case.
To study the mass transport in porous media, we can follow two major
steps. First, we must clarify the mechanism of solute transport from a microscopic viewpoint and derive the relevant mass conservation and advectiondiffusion equations. Then, we can transfer these equations to the macroscopic
level by means of spatial averaging.
2.3 Mass Conservation and Convection-Diffusion
Equations in a Fluid Continuum
2.3.1 Diffusive Velocities and Fluxes
In a multicomponent fluid, the transport of a component can be resolved into
two parts: one is the transport along with the bulk fluid at its mean flow
velocity, which is called advection; the other is the molecular diffusion, which
is caused by the concentration gradient of the component in the fluid.
The difference between the velocity V" of component IX, and the mean flow
velocity V ofthe fluid, written as (V" - V), is called the mass diffusion velocity
of component IX. The product of the mass diffusion velocity and the density of
component IX, is called the mass diffusion flux, written as J"
J" = piV" - V).
(2.3.1)
According to the famous Fick's Law, mass diffusion obeys the following
equation:
J" = -pDdgrad(p"jp),
(2.3.2)
where p is the density of the fluid. For a binary system containing only a
solvent and a solute, Eq. (2.3.2) can be written as
J = -pDdgrad(Cjp),
(2.3.3)