Convection-Dispersion Models

Crane, G., Panofsky, H.,andZeman, O. (1977). A model for dispersion firom area sources in convective turbulence. Atmos. Environ. 11, 893-900. 

Willis, G. E., and Deardorff, J. W. (1978). A laboratory study of dispersion from an elevated source within a modeled convective planetary boundary layer. Atmos. Environ. 12, 1305-1311. 

Mechanistic Multiphase Model for Reactions and Transport of Phosphorus Applied to Soils. Mansell et al. (1977a) presented a mechanistic model for describing transformations and transport of applied phosphorus during water flow through soils. Phosphorus transformations were governed by reaction kinetics, whereas the convective-dispersive theory for mass transport was used to describe P transport in soil. Six of the kinetic reactions—adsorption, desorption, mobilization, immobilization, precipitation, and dissolution—were considered to control phosphorus transformations between solution, adsorbed, immobilized (chemisorbed), and precipitated phases. This mechanistic multistep model is shown in Fig. 9.2. 

Cameron, D. R., and Klute, A. (1977). Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model. Water Res. 13, 183-188. 

The use of convection-dispersion models in oral drug absorption was first proposed in the early 1980s [177, 178]. The small intestine is considered a 1-... 

For absorbable substances, a first-order absorption term can be coupled with the convection-dispersion (6.15) to model both the fluid flow and the absorption process ... 

Recently, a novel convection-dispersion model for the study of drug absorption in the gastrointestinal tract, incorporating spatial heterogeneity, was presented [182]. The intestinal lumen is modeled as a tube (Figure 6.7), where the concentration of the drug is described by a system of convection-dispersion partial differential equations. The model considers ... 

Niro, R., Byers, J., Fournier, R., and Bachmann, K., Application of a convective-dispersion model to predict in vivo hepatic clearance from in vitro measurements utilizing cryopreserved human hepatocytes, Current Drug Metabolism, Vol. 4, No. 5, 2003, pp. 357-369. 

In an effort to describe effluent results obtained from the different soil layers, we utilized various versions of the multireaction model described above. In principle, we based our efforts on the assumption of the miscible displacement approach that describes retention reactions of solutes during transport in porous media (Selim, 1992). Several simplifying assumptions were necessary in order to describe the S04 experimental data based on these models. Briefly, we tested the capability of the convection-dispersion (CD) equation to describe the mobility of applied sulfates in individual soil layers where steady-state conditions were assumed. 

Modeling solute transport requires the convection-dispersion-reaction equation to be used, written as... 

Raats et al. (1982) developed a model for simulating one-dimensional convective-dispersive transport of P in soil, with nonlinear, reversible adsorption and irreversible fixation. The rate of fixation was assumed proportional to the amount of mobile phosphate in solution and to the amount of Al and Fe available for binding P. Therefore the fixation capacity was finite and first-order that differed from traditional first-order expressions assuming an infinite sink for immobilized P (Larsen et al., 1965 Fitter, 1974). 

Barry, D.A., and G. Sposito, 1988. Application of the convection-dispersion model to solute transport in finite soil columns. Soil Sci. Soc. Am. J. 52 3-9. 

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. 

Snow, V.O., B.E. Clothier, D.R. Scotter, and R.E. White. 1994. Solute transport in a layered field soil experiments and modelling using the convection-dispersion approach. J. Contamin. Hydrol. 

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),... 

The sequence of models used in these studies constituted a progression from a simple analytical model of the convection-dispersion type with fixed parameters, associated with the assumption of a semi-infinite homogenous profile, to a convection-dispersion numerical model, which incorporated dynamic water and solute movement through a multilayered profile. In brief, the sequence was as follows (a) one-dimensional analytical model with an upper boundary... 

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. 

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