Predictive Chemical Kinetic Models

Computer memory limitations usually require that one terminate the iterative process before 106 reactions have been generated. Several criteria have been used for terminating the model-construction process this author prefers the 

Many of the technical issues involved in computer-aided model-construction have previously been reviewed by Tomlin et al. (1997). Several researchers, most notably Bozzelli, have extended Benson s method for estimating molecular thermochemistry using quantum chemistry (Lay and Bozzelli, 1997a, b Lay et al., 1995). Sumathi and Green (2002) have discussed how quantum chemistry can supplement experiments in developing rate estimation. Matheu et al. have shown how to automate the computation of rates of chemically-activated (pressure-dependent) reactions (Matheu, 2003 Matheu et al., 2003a, b). Here we focus on a few issues which have not been so thoroughly discussed in the literature  

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In practical combustion systems, such as CO boilers, the flue gas experiences spatial and temporal variations. Constituent concentration, streamline residence time, and temperature are critical to determining an efficient process design. Computational fluid dynamics (CFD) modeling and chemical kinetic modeling are used to achieve accurate design assessments and NO, reduction predictions based on these parameters. The critical parameters affecting SNCR and eSNCR design are listed in Table 17.4. 

Fig 13.5 Modeling predictions for reaction of a stoichiometric methane-air mixture in a batch reactor at constant temperature (1200 K) and pressure (1 atm) using a detailed chemical kinetic model [31]. 

When the kinetic model has been established, it is tested against data from selected non-reaction-specific or global experiments. These experiments provide information on the behavior of certain reaction systems, for instance mixtures of fuel and oxidizer. They usually require a complex chemical kinetic model for interpretation. The process must be studied either under transport-free conditions, such as in plug-flow or stirred-tank reactors, or under conditions in which the transport phenomena can be modeled very precisely, such as under laminar flow conditions. This way computer predictions become influenced primarily by parameters in the chemical kinetic model. 

Chemical kinetic models require as a minimum thermodynamic and reaction-specific information. If problems involve transport, also proper transport coefficients are necessary. Since the accuracy of a kinetic model is often associated specifically with the chemical reaction mechanism, it is important to note that also the thermodynamic data are essential for the reliability of predictions. Fortunately the quality and quantity of data on thermochemistry of species and on the kinetics and mechanisms of individual elementary reactions have improved significantly over the past two decades, because of advances made in experimental methods. This has facilitated considerably our ability to develop detailed chemical kinetic models [356],... 

The detailed chemistry of hydrogen and carbon monoxide oxidation is well established [152,291,442], and chemical kinetic modeling can be used confidently for these reaction systems to predict behavior over a wide range of conditions. 

A difficult practical problem is the prediction of the octane number of a blend of fuels. As yet, fundamental chemical kinetic modelling has made little contribution to its solution. In general, the octane number of a mixture of fuels is not a linear function of the composition. For example, if two fuels with octane numbers Ni and N2 are mixed in the ratio by volume of fi and (1 - /i) the octane number of the mixture of two fuels, Amix, can be higher or lower than the value given by simple volume weighting, and, in general. 

H. Li, D.H. Miller and N.P. Cernansky, Development of a Reduced Chemical Kinetic Model for Prediction of Preignition Reactivity and Autoignition of Primary Reference fuels, SAE Technical Paper 960498 (1996). 

Of course, chemical kinetic models would be even more useful if they could accurately predict the behavior of reacting systems under conditions significantly different from those that have already been measured. If these extrapolative predictions were accurate enough, chemical kinetic models could become valuable tools in process and product design, and by reducing the need to do so many experiments in order to gain a small amount of information, the models could accelerate the pace of innovation. Reliable predictive kinetic models would be particularly helpful in situations where it is impractical to do the experiments, e.g. in the public policy arena, where a failed experiment could be prohibitively costly, or in situations where the experiment is impossible (e.g. predicting what happens in very slow or very fast processes). 

In recent years, it has become possible to extrapolate accurately using detailed chemical kinetic models to predict quantitatively the behavior of some rather complicated chemical systems. The most famous examples of this success are the detailed atmospheric chemistry models whose predictions underlie the Montreal Protocol on ozone-depleting chemicals. However, these atmospheric chemistry models were developed through a huge international effort over several decades, based heavily on a large number of laboratory experiments. Much more rapid and efficient methods of model development are required for detailed predictive chemical kinetics to become a practical everyday design tool for chemical engineering. 

The primary goal of chemical kinetic modeling is to make predictions given our current understanding of chemistry, what do we expect to happen in a particular reacting mixture under specified reaction conditions If desired, these... 

To the extent that we have confidence in the predictions of chemical kinetic models, we could then use these models to design new products, processes, and reactors to plan new experiments, to design model-based control systems and safety systems, and to inform critical business and public policy decisions. However, to develop the required level of confidence in the model predictions, the loop in Fig. 1 must be functioning effectively. 

There is more than just scientific progress at stake. Predictions based on chemical kinetic models are increasingly used to inform major policy and business decisions, often with large impacts on society, so it is critical that the uncertainties and assumptions associated with these predictions be clearly enunciated and understood. Clarity about our current level of ignorance is essential both to avoid misleading decision makers and to facilitate future work to test the assumptions and reduce the uncertainties in the predictions. 

When one begins to construct a chemical kinetic model, there are several different types of required input information, Fig. 4. Obviously, one needs some specification of the initial concentrations of the reactants, and of the reaction conditions (e.g. T, P, timescale) of interest. Normally one wants to numerically solve the kinetic model to predict species and/or temperature profiles, so the inputs must also include some specification of numerical tolerances on these outputs, and options for the differential equation solver. The most complicated input information required to construct a kinetic model is the chemistry what species, reactions, or reaction types will be considered How will all the thermochemical and rate parameters be estimated ... 

The methods described in Section II carry out the first step in Fig. 1, constructing a detailed chemical kinetic model from our current understanding of chemistry. However, this step is only useful if we can numerically solve the chemical kinetic simulation to obtain quantitative predictions. In many cases, solving the model is even more challenging than constructing it. 

Frequently, the next step after numerically solving a chemical kinetic simulation is to compare the model predictions with some experimental data, to check whether it is consistent with reality at least in one case. This is called validating the model. In the 20th century, it was a common practice to plot chemical kinetic model predictions with some experimental data, without any attempt to indicate the uncertainties in either. The reader then had to make his or her own judgment about whether the model and the data were close enough to be considered consistent , or whether the data had disproved the model. 

With laser augmentation at 1 atm, HMX will exhibit a dark zone temperature plateau similar to NC/NG at 1300 to 1500 K. In this case, the single-step gas reaction can be applied to the primary flame the secondary flame will have no appreciable effect on steady burning rate, as in NC/NG. If it is desired to simulate the secondary flame, a more complex kinetic mechanism (at least two-step) must be considered. Complex chemical kinetics models have shown the ability to simulate the two-stage gas flame structure of RDX under laser irradiation. (However, complex chemistry models still have difficulty in predicting the correct temperature sensitivity of HMX, as noted below.)... 

In chemical kinetics modeling, we have seen artificial controversies arise between research groups solely due to the limited maimer in which research is reported and information is shared (e.g., concise, derived conclusions in archival journals). This has led to imprecise and inaccurate extraction of the information truly contained in the community s experimental data records. A typical situation in chemical kinetics goes as follows. In order to improve a complex model s predictive capability, scientist 1 devises an experiment Ei whose outcome should be dominantly... 

The methodology to answering these parameter estimation and set-based questions relies on different mathematical approaches. In principle, the parameter identification of chemical kinetic models can be posed as classical statistical inference [17,19-21] given a mathematical model and a set of experimental observations for the model responses, determine the best-fit parameter values, usually those that produce the smallest deviations of the model predictions from the measurements. The validity of the model and the identification of outliers are then determined using analysis of variance. The general optimizations are computationally intensive even for well-behaved, well-parameterized algebraic functions. Further complications arise from the highly ill-structured character... 

We have formulated a chemical kinetic model for the Thermal De-NOx process that satisfactorily predicts the NO removed and the N2O and NO2 produced by the process over a range of temperatures and initial oxygen concentrations. The new feature of the mechanism is that NO2 appears as an essential intermediate in the reaction scheme. It is formed as a consequence of NNH reacting with molecular oxygen,... 

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