Advection, Dispersion, and Diffusion

The physical transport of dissolved organic compounds through the subsurface occurs by three processes advection, hydrodynamic dispersion, and molecular diffusion. Together, these three cause the spread of dissolved chemicals into the familiar plume distribution. Advection is the most important dissolved chemical migration process active in the subsurface, and reflects the migration of dissolved chemicals 

Typical Residual Saturation Data for Various LNAPL and DNAPL Types 

Diesel and light fuel oil Light oil and gasoline Lube and heavy fuel oils 

Coarse gravel Coarse sand and gravel Medium to coarse sand Fine to medium sand Silt to fine sand Coarse sand Medium sand Fine to coarse sand Stone, coarse sand Gravel, coarse sand Coarse to medium sand Fine to medium sand Fine sand and silt Soil Soil Soil 

---

Aqueous phase migration — Dissolved in groundwater and soil moisture, advection, dispersion, and diffusion and... 

Modelling. Transport and reaction models consider advective, dispersive and diffusive transport mechanisms as well as ad- and desorption processes (Fritsche et al., 2007 Jacoub and Westrich, 2007 Kamahl and Westrich, 2007). 

In addition to the mass transfer and transformation mechanisms that occur during air sparging, VOC transport mechanisms play a role in ensuring remediation. The important transport mechanisms that occur during air sparging include advection, dispersion, and diffusion. 

The contours of log(req) describe a hyperbolic surface, shown in three dimensions in Figure 3.5. Thus there is a region where the time and distance to equilibrium is dependent only on Da (reaction dominated), and there is another region where they are independent of Da (transport or advection dominated). Local equilibrium can occur in both domains. Most natural environments with elevated temperatures fall in the reaction dominated domain, where the effects of dispersion and diffusion can safely be ignored. 

Figure 10.1. An example of the reactive transport capabilities of phreeqc. Pure advection (plug flow ADVECTION option) are shown in (a)-(d) advection plus dispersion and diffusion (TRANSPORT option) are shown in (e)-(h).

In this equation, D represents the molecular diffusion coefficient (L2.T ), C represents the solute concentration (M.L 3), V represents the interstitial velocity (L.T1), R represents the retardation factor due the sorption phenomena. The component dispersive and diffusive is represented by d2C/dx2, the advection is represented by V dC/dx and the concentration gradient is represented by dC/dx. 

Acar and coworkers (46] and Shapiro et al. [52] have presented general models based on the first of these two approaches. These models predict that the contaminant and the electrolysis products at inert electrodes will be transported and dispersed by advection, migration, and diffusion. Modelling in this manner provides only a first-order, mathematical framework to examine the flow patterns and chemistry generated in the process adsorption/desorption kinetics, acld/base chemical reactions, complex equilibria, and precipitatlon/solubility factors may heavily influence the model accuracy and outcome of any site remediation. Two approaches for mathematic modelling are the use of analytical solutions or numerical, finite element methods (FEM). Both models require adequate definitions for the boundary conditions (nature of electrolyses, flow behaviour). 

The solute flow process includes advection (or convection), dispersion and diffusion. The equation for the process can be written as... 

Solute transport by advection alone yields a sharp solute concentration front as shown in Figure 23.1.1. In reality, the advancing front spreads out due to the processes of dispersion and diffusion as shown in Figure 23.1.1, and is retarded by sorption (Figure 23.1.2) and biodegradation. 

The parameter kg-out must account for diffusion/dispersion and advection losses at the lower boundary of a soil compartment. Advection with water that infiltrates through the soil is typically a unidirectional process, which removes chemicals with the effective velocity obtained in Equation 8.11. However, dispersion and diffusion processes such as molecular diffusion and bioturbation move chemicals both up and down within the soil, making it difficult to define a net loss factor applicable to the bulk soil. However, with a single well mixed compartment receiving chemical input at is surface, we can assume that the net diffusion is in the downward direction and proportional to the concentration gradient in the penetration depth z. In this case the parameter kg-out is obtained from a simple model for mass loss at the lower boundary of the soil compartment ... 

The relative contribution of mechanical dispersion and diffusion to solute transport is evaluated using Peclet numbers. A Peclet number is a dimensionless number that relates the effectiveness of mass transport by advection to the effectiveness of mass transport by diffusion or dispersion. Peclet numbers have the general form... 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

While the advection-dispersion equation has been used widely over the last half century, there is now widespread recognition that this equation has serious limitations. As noted previously, laboratory and field-scale application of the advection-dispersion equation is based on the assumption that dispersion behaves macroscopically as a Fickian diffusive process, with the dispersivity being assumed constant in space and time. However, it has been observed consistently through field, laboratory, and Monte Carlo analyses that the dispersivity is not constant but, rather, dependent on the time or length scale of measurement (Gelhar et al. 1992),... 

To quantify such transport, the advection-dispersion equation, which requires a narrow pore-size distribution, often is used in a modified framework. Van Genuchten and Wierenga (1976) discuss a conceptualization of preferential solute transport throngh mobile and immobile regions. In this framework, contaminants advance mostly through macropores containing mobile water and diffuse into and out of relatively immobile water resident in micropores. The mobile-immobile model involves two coupled equations (in one-dimensional form) ... 

In this situation, transport equations similar to those discussed previously can be applied. For example, by assuming sorption to be essentially instantaneous, the advective-dispersion equation with a reaction term (Saiers and Hornberger 1996) can be considered. Alternatively, CTRW transport equations with a single ti/Ci, t) can be applied or two different time spectra (for the dispersive transport and for the distribution of transfer times between mobile and immobile—diffusion, sorption— states can be treated Berkowitz et al. 2008). 

Table 22.1 Scheme to Describe Flux and Temporal Concentration Change Due to Advection and Diffusion (or Dispersion)...

Explain the difference between the dispersion coefficient, dis, in a river and in the atmosphere. How is dis related to the mean advection velocity and to lateral turbulent diffusivity in each case ... 

---