Reactive mass transport

In the previous part of the book chemical interactions were described without any consideration of transport processes in aqueous systems. Models for reactive mass transport combine these chemical interactions with convective and dispersive transport, so that they can model the spatial distribution coupled to the chemical behavior. Requirement for every transport model is a flow model as accurate as possible. 

Particularly sophisticated models deal with reactive mass transport, including both the accurate description of the convective and dispersive transport of species, as well as the modeling of interactions of species in water, with solid and gaseous phases (precipitation, dissolution, ion exchange, sorption). 

An extremely simplified application of the described approach is already implemented in the PHREEQC program. Reactive mass transport can be modeled for the one-dimensional case at constant flow rates considering diffusion and dispersion. 

Aquifers with double porosity (e.g. sandstones with fractures and pore volume) require special considerations with regard to transport modeling even if no reactive mass transport in its proper sense is taken into account. This problem is demonstrated with the following example of an aquifer regeneration in an uranium mine. The ore was leached in this mine by in-situ leaching (ISL) using sulfuric acid. The hydrochemical composition of the water that is in the aquifer after this in-situ leaching process is shown as ISL in Table 40 ... 

Freedman V. L. and Ibaraki M. (2003) Coupled reactive mass transport and fluid flow issues in model verification. Adv. Water Resour. 26, 117-127. 

In general, geochemical models can be divided according to their levels of complexity (Figure 2.3). Speciation-solubility models contain no spatial or temporal information and are sometimes called zero-dimension models. Reaction path models simulate the successive reaction steps of a system in response to the mass or energy flux. Some temporal information is included in terms of reaction progress, f, but no spatial information is contained. Coupled reactive mass transport models contain both temporal and spatial information about chemical reactions, a complexity that is desired for environmental applications, but these models are complex and expensive to use. 

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,... 

In this chapter we shall limit our discussion of the codes to speciation-solubility and reaction path modeling codes. Coupled reactive mass transport codes are much more mathematically and computationally complex. The readers can find recent discussions in Lichtner (1996) and Steefel and MacQuarrie (1996). 

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-... 

Figure2 Ohnishi et al. (1985) and Chijimatsu et al. (2000)) and reactive-mass transport model (inside the box named Chemical in Figure 2). This is a system of governing equations composed of Equations (l)-(9), which couple heat flow, fluid flow, deformation, mass transport and geochemical reaction in terms of following primary variables temperature T, pressure head y/, displacement u total dissolved concentration of the n master species C< > and total dissolved and precipitated concentration of the n" master species T,. Here we set master species as the linear independent basis for geochemical reactions, and speciation in solution and dissolution/precipitation of minerals are calculated by a series of governing equations for geochemical reaction. Now we adopt equilibrium model for geochemical reaction (Parkhurst et al. (1980)), mainly because of reliability and abundance of thermodynamic data for geochemical reaction.

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. 

In general, the substrate temperature will remain unchanged, while pressure, power, and gas flow rates have to be adjusted so that the plasma chemistry is not affected significantly. Grill [117] conceptualizes plasma processing as two consecutive processes the formation of reactive species, and the mass transport of these species to surfaces to be processed. If the dissociation of precursor molecules can be described by a single electron collision process, the electron impact reaction rates depend only on the ratio of electric field to pressure, E/p, because the electron temperature is determined mainly by this ratio. 

Since the dependence of the i/i o6) ratio on d and the tip geometry can be calculated theoretically [8], simple current measurements with mediators which do not interact at the interface can be used to determine d. When either the solution species of interest, or electrolysis product(s), interact with the target interface, the hindered mass transport picture of Fig. 1(b) is modified. The effect is manifested in a change in the tip current, which is the basis of using SECM to investigate interfacial reactivity. 

The general criteria for an experimental investigation of the kinetics of reactions at liquid-liquid interfaces may be summarized as follows known interfacial area and well-defined interfacial contact are essential controlled, variable, and calculable mass transport rates are required to allow the transport and interfacial kinetic contributions to the overall rate to be quantified direct interfacial contact is preferred, since the use of a membrane to support the interface adds further resistances to the overall rate of the reaction [14,15] a renewable interface is useful, as the accumulation of products at the interface is possible. Finally, direct measurements of reactive fluxes at the interface of interest are desirable. 

The modeling of mass transport from the bulk fluid to the interface in capillary flow typically applies an empirical mass transfer coefficient approach. The mass transfer coefficient is defined in terms of the flux and driving force J = kc(cbuik-c). For non-reactive steady state laminar flow in a square conduit with constant molecular diffusion D, the mass balance in the fluid takes the form... 

The possible mechanisms which one might invoke for the activation of these transition metal slurries include (1) creation of extremely reactive dispersions, (2) improved mass transport between solution and surface,... 

Enhanced chemical reactivity of solid surfaces are associated with these processes. The cavitational erosion generates unpassivated, highly reactive surfaces it causes short-lived high temperatures and pressures at the surface it produces surface defects and deformations it forms fines and increases the surface area of friable solid supports and it ejects material in unknown form into solution. Finally, the local turbulent flow associated with acoustic streaming improves mass transport between the liquid phase and the surface, thus increasing observed reaction rates. In general, all of these effects are likely to be occurring simultaneously. 

The possible mechanisms which one might invoke for the activation of these transition metal slurries include (1) creation of extremely reactive dispersions, (2) improved mass transport between solution and surface, (3) generation of surface hot-spots due to cavitational micro-jets, and (4) direct trapping with CO of reactive metallic species formed during the reduction of the metal halide. The first three mechanisms can be eliminated, since complete reduction of transition metal halides by Na with ultrasonic irradiation under Ar, followed by exposure to CO in the absence or presence of ultrasound, yielded no metal carbonyl. In the case of the reduction of WClfc, sonication under CO showed the initial formation of tungsten carbonyl halides, followed by conversion of W(C0) , and finally its further reduction to W2(CO)io Thus, the reduction process appears to be sequential reactive species formed upon partial reduction are trapped by CO. 

However, ultrasonic rate enhancements of heterogeneous catalysis have usually been relatively modest (less than tenfold). The effect of irradiating operating catalysts is often simply due to improved mass transport (58). In addition, increased dispersion during the formation of catalysts under ultrasound (59) will enhance reactivity, as will the fracture of friable solids (e.g., noble metals on C or silica (60),(62),(62) or malleable metals (63)). 

Beginning in the late 1980s, a number of groups have worked to develop reactive transport models of geochemical reaction in systems open to groundwater flow. As models of this class have become more sophisticated, reliable, and accessible, they have assumed increased importance in the geosciences (e.g., Steefel et al., 2005). The models are a natural marriage (Rubin, 1983 Bahr and Rubin, 1987) of the local equilibrium and kinetic models already discussed with the mass transport... 

Such models are known as reactive transport models and are the subject of the next chapter (Chapter 21). We treat the preliminaries in this chapter, introducing the subjects of groundwater flow and mass transport, how flow and transport are described mathematically, and how transport can be modeled in a quantitative sense. We formalize our discussion for the most part in two dimensions, keeping in mind the equations we use can be simplified quickly to account for transport in one dimension, or generalized to three dimensions. 

Equation 20.24 can be solved analytically to give closed-formed answers to simple problems. Many mass transport problems, however, including all but the most straightforward in reactive transport, require the equation to be evaluated numerically (e.g., Phillips, 1991). There are a variety of methods for doing so, including... 

At the same time, reaction modeling is now commonly coupled to the problem of mass transport in groundwater flows, producing a subfield known as reactive transport modeling. Whereas a decade ago such modeling was the domain of specialists, improvements in mathematical formulations and the development of more accessible software codes have thrust it squarely into the mainstream. 

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