Читать книгу Global Approaches to Environmental Management on Military Training Ranges - Tracey Temple - Страница 26

Advection is the most important dissolved chemical migration process active in the subsurface and reflects the migration of dissolved chemicals along with groundwater flow, i.e. the mass of actual mass movement of a fluid through the porous media. In fact, it refers to the passive movement of a solute with flowing water (or other solvent) [111].

In a porous medium, the mass flow through a unit section perpendicular to the flow is equal to equation (1.2).

where Fz = mass flow, [M/L2T]; = average linear velocity, [L/T]; n = effective porosity; c = concentration, [M/L3].

Dispersion is the general term applied to the observed spreading of a solute plume and is generally attributed to hydrodynamic dispersion and molecular diffusion. Hydrodynamic dispersion is a physical process in which macroscopic spreading arises from the multiple variations in flow path velocity and tortuosity. Molecular diffusion is a physicochemical process resulting from the Brownian motion of molecules, resulting in a net migration down a chemical gradient. As a result of the kinetic-chemical activity, contaminants have the tendency to move from the areas of greater concentration to those of less concentration, a process that is known as diffusion. In diffusion, the dissolved substances are moved by a concentration gradient. For its study it is assumed that there is no movement of the fluid. The mass flow by diffusion is governed by the first Fick’s law [112] (1.3).

F=−D(dcdz)(1.3)

where Fz = mass flow, [M/L2T], D = effective diffusion coefficient, [L2/T]; c = concentration, [M/L3]; z = distance over which changes in concentration are considered [L].

The flow expressed in Fick’s first law does not consider time: It expresses a permanent flow as long as the variables on which it depends are constant. If there is a point with a constant concentration of a substance (application of a contaminant) and it is desirable to know how the concentration in another point situated at a distance z varies with time, the second Fick’s law is used equation (1.4).

∂c∂t=D(∂c∂z2)(1.4)

where t = time, [T]; D = effective diffusion coefficient, [L2/T]; c = concentration, [M/L3]; z = distance over which changes in concentration are considered [L].

The effective diffusion coefficient is expressed as follows (1.5):

D=ταD0(1.5)

where D = effective diffusion coefficient, [L2/T]; τα = apparent tortuosity; D0 = aqueous diffusion coefficient for the solutes, [L2/T].

At macroscopic scale, it is the porous medium that regulates the flow rate and its direction. However, at a microscopic scale the porous medium is composed of discrete solid particles and voids. Water does not flow through the interconnected empty spaces, but around it. When encountering solid particles, water must alter its course, repeating this process millions of times. The result is a mixture of the flux known as mechanical dispersion. As a result of the mechanical dispersion, the mass of contaminant expands in a progressively larger volume, facilitating its mixing with water devoid of this substance. This causes a decrease in contaminant concentration, or dilution. In this way, the contaminant is transported essentially by advection, while its concentration varies due to the dispersion [113].

The ability of the porous medium to mechanically disperse a fluid flowing through it is reflected in a coefficient called dynamic dispersivity α (units: L), function of the porosity, tortuosity, grain shape, etc.

The mechanical dispersion is equal to the product of this coefficient by the average linear velocity (units: L2/T) (1.6):

where α = dynamic dispersivity, [L]; D′ = mechanical dispersion, [L2/T]; = average linear velocity, [L/T].

The propagation due to mechanisms of mechanical dispersion and molecular diffusion is known as hydrodynamic dispersion, which is a process in which the transport of contaminants is due to variations in velocity (magnitude and direction) in the porous media.

Both mechanisms are taken into account via the coefficient of hydrodynamic dispersion D, which is written as follows (1.7):

D=D′+D(1.7)

where D = hydrodynamic dispersion, [L2/T]; D′ = mechanical dispersion, [L2/T]; D = effective diffusion coefficient, [L2/T].

As the mechanical dispersion is more pronounced in the longitudinal direction than in the transverse direction, a longitudinal hydrodynamic dispersion coefficient DLi and a transverse hydrodynamic dispersion coefficient DTi are introduced. The hydrodynamic longitudinal (1.8a) and transverse diffusion (1.8b) coefficients are defined as:

where DL, DT = hydrodynamic dispersion (longitudinal, transverse), [L2/T]; , = dynamic dispersivity (longitudinal, transverse), [L]; = average linear velocity, [L/T]; D = effective diffusion coefficient, [L2/T].