Multi-component Reactive Transport Models

Consider advective-dispersive-reactive (ADR) transport in one-dimensional saturated porous media, the transport equation is (Bear, 1972), 

Equation (10.1) is a statement of mass balance on a per volume of groundwater basis for a given component i. The first two terms on the right hand side of the equation refer to the net influxes of mass due to dispersive and advective transport in groundwater. 

The reaction term Rj describes the loss or gain of component i in groundwater due to the mass transfer between groundwater and immobile solid phases. From the transport point of view, mass transfer reactions between aquifer matrix and groundwater represent possible sinks and sources for the contaminants so that this term is sometimes called the source/sink term. 

As discussed in Chapter 2, we reserve the term coupled transport model to multiple component-multiple species reactive mass transport models such as phreeqc described above. In coupled models, two set of equations are solved together through some coupling schemes. In the case of coupled reactive transport models, two sets of mathe- 

---

Hunter et al. (1998) used a kinetic model to simulate reactive transport and ground-water evolution upon the intrusion of landfill leachate into an oxic aquifer. Most interestingly, they found that the patterns of redox fronts are similar to what have been seen in marine sediments. Hunter et al. (1998) first developed a one-dimensional multi-component reactive transport model biorxntrn and then conducted a numerical experiment using this code. The actual model is quite complex we describe here the essentials of it so that we can see what can be done. 

Zhu, C., Hu, F. Q., and Burden, D. S., 2001a, Multi-component reactive transport modeling of natural attenuation of an acid ground water plume at a uranium mill tailings site. J. Contaminant Hydrology, v. 52, pp. 85-108. 

Regnier, P., Wollast, R., and Steefel, C.I. (1997) Long term fluxes of reactive species in macrotidal estuaries Estuaries from a fully transient, multi-component reaction transport model. Mar. Chem. 58, 127-145. 

The SPH method has been also used to simulate pore-scale dissolution of the trapped non-aqueous phase liquids, pore-scale miscible non-reactive flows (Tartakovsky and Meakin, 2005 Zhu et al, 2002), and single- and multi-component reactive transport and precipitation (Tartakovsky et al, 2007). Recently, Jiang et al. (2008) developed a meso-scale SPH model for... 

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. 

Yeh, G. T. and V. S. Tripathi, 1989, A critical evaluation of recent developments in hydrogeochemical transport models of reactive multi-chemical components. Water Resources Research 25, 93-108. 

In this book, we use the term coupled model to describe models in which two sets of equations that describe two types of processes are solved together. For example, multi-component, multi-species coupled reactive mass transport models (this is a mouthful,... 

Reactive distillation occurs in multiphase fluid systems, with an important role of the interfacial transport phenomena. It is an inherently multicomponent process with much more complexity than similar binary processes. Multi-component thermodynamic and diffusional coupling in the phases and at the interface is accompanied by complex hydrodynamics and chemical reactions [4, 42, 43]. As a consequence, an adequate process description has to be based on specially developed mathematical models. However, sophisticated RD models are hardly applicable for plant design, model-based control and online process optimization. For such cases, a reasonable model reduction should be applied [44],... 

Steefel et al. ([23] and references therein) noted that the approach does not account for pH, competitive ion effects or oxidation-reduction reactions. As a consequence, values may vary by orders of magnitude from one set of conditions to another. Chen [25] also highlighted these limitations by comparing numerical modeling results of contaminant transport using a multi-component coupled reactive mass transport model and a based transport model. The conclusion from this work was that values vary with location and time and this variation could not be accounted for in the model. 

---