Isotherm-based Reactive Transport Models

Additional sets of equations that describe additional processes can be coupled and solved together. For example, the conservation of thermal energy and groundwater flow equations are coupled to the ADR equation and chemical mass balance equations in the work of Raffensperger (1995). 

Nearly all reactive transport models used in the regulatory environment, however, are based on empirical isotherms. The models take into account the effects of hydrologic processes due to the movement of groundwater such as advection and dispersion, but the effects of chemical reactions are typically described by an isotherm linking the concentrations of i in solid mass to that in groundwater, 

The isotherms are incorporated into the transport models through the retardation factor R. The one-dimensional ADR equation for saturated media becomes 

Pb denotes the bulk density of the aquifer (M L-3) and 6 the effective porosity (dimensionless). The ADR equation thus becomes more mathematically solvable. 

It is important to note that Equations (10.2) and (10.3) are based on the local equilibrium condition which assumes that reaction rates are fast in relation to groundwater flow rates (Cherry et al., 1984). Other assumptions in Equation (10.2) include the reversibility of reaction and the absence of competing species for the same surface sites. 

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To facilitate the discussion below, we need, once again, to define the terminology first. By our definition, the isotherm-based reactive transport models are not coupled models because only one set of equations, namely partial differential equations for transport, is solved. The chemical processes are simulated according to empirical parameters rather than according to thermodynamics and chemical kinetics. 

Even though the limitations of isotherm-based transport models are well known to academics, and detailed from time to time in the literature (see the references cited above), isotherm-based reactive transport models nevertheless remain the mainstay in everyday environmental practice. Therefore, we feel the need to elucidate the weakness and limitations again. 

Applicability of the Isotherm or Retardation-factor-based Reactive Transport Models... 

While the mechanistic treatment of chemical reactions in the coupled multi-component, multi-species mass transport has obvious advantages over the empirical isotherm-based transport models, we can also easily compile a long list of shortcomings for coupled reactive transport models. We choose a few and list them here. 

Another drawback of most conventional reactive solute transport model is that it only evaluates one solute at a time. To emphasize this, we deliberately used the subscript i in the above equations. The interactions between solutes, i.e., reactions of two solutes to form a solid precipitate, competitive sorption of metals onto mineral surfaces, or coprecipitation, cannot be evaluated. Although some isotherm-based transport codes have included the transport of several components, the chemical modules are nevertheless too simple to allow them to interact. 

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. 

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