Convection dispersion equation

The convection-dispersion equation can be written as (see for example Bear [ 1] or Nielsen [2] )... 

This is known as the convective-dispersive equation (CDE) (Scott 2000). For chem-bio agents, Equation (3.4.16) can be written as follows ... 

Soil contaminated by biological and chemical weapons would be a different problem than waters contaminated by biological and chemical weapons. Soils contaminated by transuranic waste from RDDs would be a long-lasting problem. The radioactive particles would travel through the air with the soil particles moved by wind. The radioactive particles would travel within the soil if the particles are moved by water. Biological and chemical materials that are sorbed to the soil would move within the soil by convection-dispersion equation (see Chapter 3) or become retransported with the soil in the air or water. 

Based on Eq. [13-15], Selim et al. (1976b) assumed the reactions between exchangeable and nonexchangeable as well as those between nonexchangeable and primary minerals were first-order kinetic reactions. The authors coupled Eq. [13-15] with the one-dimensional convective-dispersive equation (one-site version of Eq. [6]) to describe the transformation kinetics of K during transport in soil. 

Dyson, J.S., and R.E. White. 1987. A comparison of the convective dispersion equation and transfer function model for predicting chloride leaching through undisturbed structured clay soil. J. Soil. Sci. 38 157-172. 

The convection-dispersion equation (CDE) is the most widely used of the velocity distribution models. For steady state, one-dimensional water flow, the CDE for a nonreactive solute can be written as (Fried Combarnous, 1971),... 

All of the models used in these studies are based upon the convection-dispersion equation for solute transport through porous media and thus are constrained by the inherent limitations of this mathematical representation of actual processes. These limitations, analyzed in some detail in a number of recent papers (9.10.11.12.13). are real for many field conditions. On the other hand, alternative approaches (e.g. stochastic transfer models) are still in an early state of development for solute transport applications. Consequently, we have initiated our modeling efforts with the traditional transport equations. Hopefully, improved approaches will be developed in the near future. 

Thirty-six undisturbed soil columns were taken on a 6 x 6 sampling grid immediately adjacent to the field core locations, and were brought to the laboratory. The columns were leached at 2 cm/d until steady state was reached, at which time a pulse of KC1 and napropamide was added to the inlet end. Affluent breakthrough curves for each chemical were fitted to the convection-dispersion equation by the method of moments (11). The effective retardation factor R, which may be calculated from the ratio of the chloride and napropamide vnap velocity parameters obtained by fitting the convection-dispersion equation, is equal to... 

Simunek, J., van Genuchten, M. Th., Sejna, M., Toride, N., and Leij, F.J. The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of the convection-dispersion equation, Versionl/0 and 2.0. 1999. Colorado, USA, International Ground Water Modeling Center, Colorado School of Mines. 

Pol3rmer is invariably found in the aqueous phase, and its transport equation is usually taken to be a generalised convection dispersion equation of the following form ... 

The main objective of this chapter is to include the above phenomena in a suitable transport equation to describe the flow of polymer species through porous media. It has been found that terms describing these effects may be included in generalised convection-dispersion equations which appear to give a satisfactory macroscopic description of the processes in that they reproduce the main features observed in laboratory core flood experiments. It is these single-phase transport equations which provide the basis for simulation of polymer transport through porous media in the multiphase... 

The convection-dispersion equation for tracer and polymer transport... 

In the following sections, the experimental results which have been found in various studies of single-phase polymer flow in 1-D porous media will be discussed. Results will be referred to the convection-dispersion equation outlined above as a model for the flow. However, when there are deviations from this, the appropriate equations/models will be developed. In addition to discussing the macroscopic fit of the generalised convection-dispersion model for polymer transport in porous media, some aspects of the microscopic or physical basis of the phenomena under consideration will also be discussed. 

From the effluent concentration profile in a polymer or tracer flood, the total core Peclet number is calculated by fitting the analytic form of the convection-dispersion equation as described above. The most direct experimental comparison between the dispersion appropriate for polymer and for an inert tracer should be done in experiments in which both species are present in the injected pulse of labelled polymer solution. This helps to reduce greatly errors that may arise when separate tracer and polymer experiments are carried out. For example, in the study by Sorbie et al (1987d), the dispersion properties of two different xanthans were examined in consolidated outcrop sandstone cores. In all floods, the inert tracer, Cl, was used, thus allowing the dispersion coefficient of the xanthan and tracer to be measured in the same flood. An example of this is shown for a low-concentration (low-... 

Recently, Vossoughi et al (1984) have incorporated Koval s central idea into a generalised convection-dispersion equation to describe both ordinary dispersive transport and viscous fingering. The form of their equation as it... 

In order to model polymer transport phenomena of this type, where polydispersity effects are important, it is not adequate to consider the polymer as a single component of concentration, c, as has been done so far in this chapter. The polymer itself is made up of many components which are different only in their size (although the Mark-Houwink parameters that apply for the polymer will be esentially the same for each of the polymer subcomponents). Thus it is necessary to use a multicomponent representation of the polymer molecular weight distribution in order to model the polymer behaviour adequately in such experiments. Brown and Sorbie (1989) have adopted this approach in order to model the Chauveteau-Lecourtier results quantitatively. They used a multicomponent representation of the MWD based on a Wesslau distribution function (Rodriguez, 1983, p. 134) with 26 discrete fractions being used to represent the xanthan. For this case, a set of convection-dispersion equations including dispersion and surface exclusion... 

A simplified form of the 1-D polymer transport equation in two-phase flow, in which the polymer is found only in the aqueous phase, is given by the following generalised convection-dispersion equation ... 

Equation (35) shows the applied type of convection-dispersion-equation about the transport of a pollutant in the model soil column. The term on the lefthand side describes the change of adsorbate concentration with time at a certain location z. The first term on the righthand side calculates the dispersion, the second term calculates the convection, and the third term the sorption of the transported pollutant at the respective location. 

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