Applied reaction modeling

PEP theory has also been applied to modelling the free energy profiles of reactions in solution. An important example is the solvent effect on the SN2 reaction... 

Tliis interpretation is based only upon the structural and electronic properties of the pyridinium cations. Tire calculation of relative activation Ijarri-ers for the competing substitution reactions will give more reliable results —especially if solvent effects are included in the calculations. In order to assess the reliability of actual theoretical methods as applied to model sys-... 

Termination scheme 11 applies to the geometric mean and phi factor models and scheme 12 Is required for the penultimate effect model. All the above reaction models were used In attempts to simulate kinetic data. 

Chemical vapor deposition (CVD) of carbon from propane is the main reaction in the fabrication of the C/C composites [1,2] and the C-SiC functionally graded material [3,4,5]. The carbon deposition rate from propane is high compared with those from other aliphatic hydrocarbons [4]. Propane is rapidly decomposed in the gas phase and various hydrocarbons are formed independently of the film growth in the CVD reactor. The propane concentration distribution is determined by the gas-phase kinetics. The gas-phase reaction model, in addition to the film growth reaction model, is required for the numerical simulation of the CVD reactor for designing and controlling purposes. Therefore, a compact gas-phase reaction model is preferred. The authors proposed the procedure to reduce an elementary reaction model consisting of hundreds of reactions to a compact model objectively [6]. In this study, the procedure is applied to propane pyrolysis for carbon CVD and a compact gas-phase reaction model is built by the proposed procedure and the kinetic parameters are determined from the experimental results. 

This chapter has outlined specifically how quantitative data on somewhat idealized reaction systems can be used as a basis for demonstrating the validity of our empirical electronic models in the field of reactivity. The multiparameter statistical models derived for the systems studied (PA, acidity, etc.) have limited direct application in EROS themselves. The next section develops the theme of applying the models in a much more general way, leading up to general reactivity prediction in EROS itself. 

An approximate analysis of polymer adsorption as a set of sequential reactions leads to a simple equation for the adsorption isotherm expressed in terms of three parameters. Comparison of the model with recently published statistical theories reveals remarkable agreement in both the general shape of the isotherms and the predicted effects of molecular weight. The problems of applying such models to experimental data are discussed. 

Reaction models, despite their simple conceptual basis (Fig. 2.1), can be configured in a number of ways to represent a variety of geochemical processes. Each type of model imposes on the system some variant of equilibrium, as described in the previous section, but differs from others in the manner in which mass and heat transfer are specified. This section summarizes the configurations that are commonly applied in geochemical modeling. 

Polythermal reaction models (Section 14.1), however, are commonly applied to closed systems, as in studies of groundwater geothermometry (Chapter 23), and interpretations of laboratory experiments. In hydrothermal experiments, for example, researchers sample and analyze fluids from runs conducted at high temperature, but can determine pH only at room temperature (Fig. 2.2). To reconstruct the original pH (e.g., Reed and Spycher, 1984), assuming that gas did not escape from the fluid before it was analyzed, an experimentalist can calculate the equilibrium state at room temperature and follow a polythermal path to estimate the fluid chemistry at high temperature. 

The /f( approach, as strictly defined, implies but does not specify a chemical reaction. A variant of the approach known as the reaction Kci model (or activity Kd model) based on a specific chemical reaction is commonly applied in reaction modeling. For example, the sorption and desorption of Cd++ might be taken to occur according to the reaction,... 

Fig. 15.4. Use of reaction modeling to derive a fluid s carbonate concentration from its titration alkalinity, as applied to an analysis of Mono Lake water. When the correct HCO3 total concentration (in this case, 25 100 mg kg-1) is set, the final pH matches the titration endpoint.

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

According to Hardie and Eugster s (1970) model and its later variants (see discussions in Eugster and Jones, 1979 Drever, 1988, pp. 232-250 and Jankowski and Jacobson, 1989), a natural water, as it evaporates, encounters a series of chemical divides that controls the sequence of minerals that precipitate. The reaction pathway specific to the evaporation of a water of any initial composition can be traced in detail using a reaction model like the one applied in this section to Sierra spring water. 

In a series of papers, Harvie and Weare (1980), Harvie el al. (1980), and Eugster et al (1980) attacked this problem by presenting a virial method for computing activity coefficients in complex solutions (see Chapter 8) and applying it to construct a reaction model of seawater evaporation. Their calculations provided the first quantitative description of this process that accounted for all of the abundant components in seawater. 

In this chapter we consider how reaction modeling applied to open systems might be used to study the nature of diagenetic alteration. We develop examples in which modeling of this type can aid in interpreting the diagenetic reactions observed to have occurred in sedimentary rocks. 

The effectiveness of alkali flooding, and, in fact, most reservoir treatments, varies widely from formation to formation in a manner that is often difficult to predict. Quantitative techniques have been applied to model the migration and consumption of alkali as it moves through a reservoir (e.g., Bunge and Radke, 1982 Zabala et al., 1982 Dria et al., 1988). There have been fewer attempts, however, to predict the specific chemical reactions that might occur in a reservoir or the effects of the initial mineralogy of the reservoir and the composition of the flood on those reactions (Bethke et al., 1992). 

Laboratory studies are very important for providing basic knowledge to scale-up of batch reactions. Modeling a batch system is very important as well. When the batch reaction and system are well understood, a large scale-up factor may be applied while still maintaining safe operations. 

Before applying any model it is essential to have confidence that the input data is valid. There are repeated warnings in the literature of data being invalid because it is obtained at such accelerated levels of the degradation agent that reactions occur which are not seen at lower levels. 

The relative importance of the EDL for reactions other than adsorption is not well understood. Surface complexation models have recently been applied to processes in which adsorption represents the first step in a sequence of reactions. For example, Stumm et al. (22) have applied a model with an EDL component in their studies of the role of adsorption in dissolution and precipitation reactions. The effect of surface charge and potential on precipitation and the... 

An alternative to evaluating the KIE and the rate constants from the above equations is to apply nonlinear least-squares fitting to the complete kinetic set of a and t values. This latter procedure has the advantage that errors in the reaction model, e.g. an incorrect mechanism, or extraneous data points are more easily discovered. This method was applied by Bergson et al. (1977) and Matsson (1985) in the determination of both the primary deuterium and secondary a-deuterium KIEs in the 1-methylindene rearrangement to 3-methylindene (reaction (67)). For example, a secondary /3-deuterium KIE of 1.103 0.001 was determined very accurately in toluene at 20°C using this method (Bergson et al., 1977). 

Many of the models encountered in reaction modeling are not linear in the parameters, as was assumed previously through Eq. (20). Although the principles involved are very similar to those of the previous subsections, the parameter-estimation procedure must now be iteratively applied to a nonlinear surface. This brings up numerous complications, such as initial estimates of parameters, efficiency and effectiveness of convergence algorithms, multiple minima in the least-squares surface, and poor surface conditioning. 

The authors applied this model to the situation of dissolving and deposited interfaces, involving chemically interacting species, and included rate kinetics to model mass transfer as a result of chemical reactions [60]. The use of a stochastic weighting function, based on solutions of differential equations for particle motion, may be a useful method to model stochastic processes at solid-liquid interfaces, especially where chemical interactions between the surface and the liquid are involved. 

Kapoor and Frohberg (1973) applied this model to the ternary system CaO-FeO-Si02. They envisaged that mixing occurred by formation of three asymmetric cells obtained by a reaction between symmetric cells of the metallic oxides and silica. For Ca0-Si02, the formation energy for the asymmetric cell is denoted Wis, where the subscripts I and S denote the combination of symmetric cells from CaO and Si02. In addition interactions between the various symmetric and asynunetric cell. were considered such that... 

Unfortunately the ab initio workers are not always cautious enough as is exemplified by Ref. [55]. In it a wide set of experimental data on catalytic reactions taking place in the presence of Pd complexes with substituted phosphine ligands PR3 is modelled by ab initio methods applied to models where the whole variety of the ligands is represented by the unsubstituted phosphine PH3 molecule. The main problem with such an approach is that the sensitivity of the processes under study to the number and nature of organic substituents at the phosphorous atom is well known in the literature. 

This paper provides an example of how accurate continuum models can open the door to the modeling of condensed-phase processes where solvation free energies have a very large influence on reaction energetics. It additionally offers a case study of how to first choose a model on the basis of experimental/tlieoretical comparisons over a relevant data set, and then apply tliat model with a greater expectation for its utility. The generality of this approach to other (equilibrium) electrochemical reactions seems promising. 

---