Reactive transport model numerical solution

Modelling Reactive Transport of Organic Solutes in Groundwater 7.2.3 Numerical Evaluation of Breakthrough Curves... 

SMART is applicable if integral information on contaminant behaviour in groundwater is sufficient. If point information is needed a conventional FD or FE model has to be used. Although it is obvious that the streamtube approach is not as flexible as real 3D models , decoupling of conservative transport and physico-chemical processes allow to model three-dimensional contaminant transport in a convenient and computationally efficient way, especially if only one representative streamtube must be modelled. Computation times, as observed by Peter et al. (chapter 14) are much lower compared to MT3D simulations. It should also be mentioned, that the streamtube approach possesses some advantages compared to real 3D models even if each and every streamtube has to be modelled by means of a numerical model in order to evaluate F. Since only one dimensional advective-reactive transport must be modelled, numerical solutions based on discrete or mechanistical approaches, free of numerical dispersion, can be applied. In SMART this is done by a so-called parceltracking approach where contaminant transport is described by means of a continuous series of water volumes ( parcels ) as described in Finkel et al. (1998). 

Numerical simulations were carried out using a multicomponent reactive solute transport model to study the migration of four heavy metals (Cd, Pb, Cu, and Zn ) in a sand/bentonite mixture. The leachate pH has a significant effect on the migration of Cd and Pb but has only limited effect on the mobility of and Zn " (Wu and Li, 1998). 

Contaminants with very low water solubilities (e.g. polycyclic aromatic hydrocarbons) play an important role in risk assessment of dangerous wastes and development of soil remediation. The mobility of such hydrophobic substances can be strongly affected by the existence of carriers (e.g. dissolved organic carbon), which can adsorb the contaminant and thereby enhance or reduce its velocity. The numerical simulation of the spreading of these contaminants, requires the solution of reactive transport equations for all involved components, coupled by the contaminant s sorption to the carrier. Our development is based on a model [2], in which all the carrier s influence on the contaminant transport is contained in an effective adsorption isotherm, depending on the carrier concentration and thereby also on space and time. First we shortly summarize the modelling of reactive transport of a single component (carrier, contaminant, carrier bound contaminant) in a porous medium, then in section 3 we combine the two equations for the contaminant components. The properties of the contaminant s effective isotherm and its influence on the transport equation are discussed in section 4. 

The present chapter provides an overview of several numerical techniques that can be used to solve model equations of ordinary and partial differential type, both of which are frequently encountered in multiphase catalytic reactor analysis and design. Brief theories of the ordinary differential equation solution methods are provided. The techniques and software involved in the numerical solution of partial differential equation sets, which allow accurate prediction of nonreactive and reactive transport phenomena in conventional and nonconventional geometries, are explained briefly. The chapter is concluded with two case studies that demonstrate the application of numerical solution techniques in modeling and simulation of hydrocar-bon-to-hydrogen conversions in catalytic packed-bed and heat-exchange integrated microchannel reactors. 

Srivastava, R. and Jim Yeh, T.C., A three-dimensional numerical model for water flow and transport of chemically reactive solute through porous media under variably saturated conditions, Adv. Water Resour., 15, 275, 1992. 

Totsche, K. U. Knabner, P Kogel-Knabner, I. (1996) The modelling of reactive solute transport with sorption to mobile and immobile sorbents. Part II Modell discussion and numerical simulation. Water Resour. Res. 32,1623 1636. 

Modelling is mainly based on the solution of partial differential equations obtained in most cases by numerical methods like Finite Difference Method (FDM), Finite Element Method (FEM) or Boundary Element Method (BEM) describing always a bimetalhc corrosion situation at various scales combining current and potential distribution (Laplace s equation) with the mass transport of reactive species (Nemst-Planck s equation). 

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