Reaction path modeling

It can do this not by trying to consider states of disequilibrium, but by being applied to a succession of states of metastable equilibrium. So in the K-feldspar case, a tiny amount of KAlSigOs is conceptually added to pure water, and the resulting aqueous species are calculated.2 We have a new metastable state K-feldspar and a very dilute solution 0fKAlSi3O8 in water.3 Then another tiny increment of KAlSisOs is added to 

2The increments don t always have to be tiny. They do in this case because K-feldspar is very insoluble, and many phase changes are involved. 

3We call this a metastable state in the sense used in 3.1.1 and 3.1.2, that is, a state in a conceptual or model system, where the K-feldspar is separated from, or constrained from reacting with, the K-feldspar 

In this succession of equilibrium states, a surprising amount of precipitation and dissolution of phases is found to be involved, the details of which can be found in many geochemistry textbooks. But the question arises - is this succession of calculated states what would be observed if K-feldspar was really dissolved into water Well, probably not. So why do the calculation This is a crucial point which must be understood. 

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Fast P L and Truhlar D G 1998 Variational reaction path algorithm J. Chem. Phys. 109 3721 Billing G D 1992 Quantum classical reaction-path model for chemical reactions Chem. Phys. 161 245... 

In a reactive transport model, the domain of interest is divided into nodal blocks, as shown in Figure 2.11. Fluid enters the domain across one boundary, reacts with the medium, and discharges at another boundary. In many cases, reaction occurs along fronts that migrate through the medium until they either traverse it or assume a steady-state position (Lichtner, 1988). As noted by Lichtner (1988), models of this nature predict that reactions occur in the same sequence in space and time as they do in simple reaction path models. The reactive transport models, however, predict how the positions of reaction fronts migrate through time, provided that reliable input is available about flow rates, the permeability and dispersivity of the medium, and reaction rate constants. 

Plumlee, G. S., M. B. Goldhaber and E. L. Rowan, 1995, The potential role of magmatic gases in the genesis of Illinois-Kentucky fluorspar deposits, implications from chemical reaction path modeling. Economic Geology 90,999-1011. 

The reaction modeling techniques described so far (transition structure optimization, adiabatic mapping, and reaction path modeling) rely on the assumption that a single protein structure... 

Cleverley, J.S., Benning, L.G. and Mountain, B.W. (2003) Reaction path modelling in the As-S system a case study for geothermal As transport. Applied Geochemistry, 18(9), 1325-45. 

Further reduction of the constrained reaction path model is possible. Here we adopt a system-bath model in which the reaction path coordinate defines the system and all other coordinates constitute the bath. The use of this representation permits the elimination of the bath coordinates, which then increases the efficiency of calculation of the motion along the reaction coordinate. In particular. Miller showed that a canonical transformation of the reaction path Hamiltonian T + V) yields [38]... 

Figure 1. Reaction path model of singlet ( A ) and triplet ( A and A") potential energy surfaces associated with the 0( P/ D) + H2 reaction. The curves refer to the potential along ininiinuin cnergt- path of the triplet reaction for slightly bent O-H-H geometries in (a) diabatic and (b) adiabatic representation. Note that idthough there are only three diabats, the adiabats are derived from the four state basis defined in the text.

Our quantum scattering calculations refer to the reduced dimensional (reaction path) model of O + H2 dci)ictcd in Figure f. As mentioned above, the four states that we include are one singlet = 0)), and three triplets ( A. Mn —... 

Chemical reaction path modeling of ore deposition in Mississippi VaUey-type Pb-Zn deposits of the Ozark region, U.S. Midcontinent reply Economic Geology, v. 90, no. 5, p. 1346-1349. 

Observations The mass transfer models can predict the overall geochemical behavior of a contaminant and whether reactions go to equilibrium within a system. They are often used in reaction path modeling. 

Wolery, T. J., and S. A. Daveler. 1992. EQ6, A computer program for reaction path modeling of aqueous geochemical systems Theoretical manual, user s guide, and related documentation (Ver. 7.0). UCRL-MA-11066 Pt IV. Lawrence Livermore Natl. Lab. 

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. 

Reaction path models calculate a sequence of equilibrium states involving incremental or step-wise mass transfer between the phases within a system, or incremental addition or subtraction of a reactant from the system, possibly accompanied by an increase or decrease of temperature and pressure (Helgeson, 1968, 1969). The calculated mass transfer is based on the principles of mass balance and thermodynamic equilibrium. Unlike speciation-solubility calculations, which deal with the equilibrium state of a system, the reaction path model simulates processes, in which the masses of the phases play a role. 

Although all reaction path models are based on the principle of mass balance and thermodynamic equilibrium, various configurations of the mass transfer models have been constructed to simulate different processes. 

Flush The flush reaction path model is analogous to the perfectly mixed-flow reactor or the continuously stirred tank reactor in chemical engineering (Figure 2.5). Conceptually, the model tracks the chemical evolution of a solid mass through which fresh, unreacted fluid passes through incrementally. In a flush model, the initial conditions include a set of minerals and a fluid that is at equilibrium with the minerals. At each step of reaction progress, an increment of unreacted fluid is added into the system. An equal amount of water mass and the solutes it contains is displaced out of the system. Environmental applications of the flush model can be found in simulations of sequential batch tests. In the experiments, a volume of rock reacts each time with a packet of fresh, unreacted fluids. Additionally, this type of model can also be used to simulate mineral carbonation experiments. 

It should be noted that the flush model, other reaction path models, such as the fluid-centered reaction path model, and models with the dump option (see Wol-ery, 1992), have become less useful for their originally intended uses in simulating reactive transport. Although the extent of reactions is often monitored by the reaction progress variable (f), no temporal information is included in the model. Additionally,... 

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). 

The mathematical formulation of equilibrium speciation-solubility models and the numerical methods to solve the algebraic equations are described elsewhere, and we shall not repeat them here. The reader can consult Anderson and Crerar (1993), Bethke (1996), and Westall et al. (1976). Mathematical formulations for the reaction path models are described in detail in Anderson and Crerar (1993) and Bethke (1996). 

The results from speciation models are relatively simple. A common problem in reaction path models is their voluminous output, often amounting to tens of pages, depending on how many time-steps have been taken and what the print interval is. With so much data, it can be a problem to find exactly what is necessary, especially to get a graphical representation of just those variables which the user is interested. 

On the other hand, many investigations have shown that Saturation Indices are a reasonably good guide to certain phases, such as some carbonate and sulfate minerals. Saturation Indices are also quite useful in reaction path modeling (Chapter 8) and inverse mass balance modeling (Chapter 9) in the sense that they indicate (within the accuracy of the data) which processes are possible (e.g., precipitation of a phase having an SI > 0), and which are impossible (e.g., dissolution of a phase having an SI > 0). 

In the first step, acidic water of about pH 4.5 was first neutralized to a pH of 6.6 by titrating calcite using phreeqc (see 8.3). Neutralization of the acid water caused the precipitation of gypsum, and A1 and Fe hydroxides. This kind of reaction path modeling will be discussed in Chapter 8. Here, we only present the resulting compositions of the neutralized water and precipitated solids in Table 7.8. 

Figure 8.1. A possible conceptualization of the reaction path model for the dissolution of K-feldspar in water. (From Anderson, 1996, Chap. 12.)...

As we discussed in 6.2, the samples from the monitoring wells at the Bear Creek Uranium site are observed to fall into four fairly well defined pH zones (Figure 6.2). Compositional zones such as this are often produced by mineral buffering of the solutions. This process can be illustrated by using reaction path modeling. 

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