Rigorous valid ranges for optimally reduced kinetic models

Oluwole, Oluwayemisi O.; Bhattacharjee, Binita; Tolsma, John; Barton, Paul I.; Green, William

doi:10.1016/j.combustflame.2006.02.009

Cited by 51 publications

(31 citation statements)

References 13 publications

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“…and we can readily show that the Hessian matrix of G in Equation (24), which represents the curvature matrix of the G contour surfaces in γ ∞ space, is the inverse of the Hessian matrix of F in Equation (20).…”

Section: General Non-equilibrium Problemmentioning

confidence: 97%

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Beretta

Keck

Janbozorgi

et al. 2012

Entropy

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The Rate-Controlled Constrained-Equilibrium (RCCE) method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system's internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.

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Section: General Non-equilibrium Problemmentioning

confidence: 97%

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Beretta

Keck

Janbozorgi

et al. 2012

Entropy

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“…A prerequisite for model inference is the availability of (i) plausible models and (ii) relevant data to discriminate among the models. It is important at this stage to distinguish model inference from the common practice of model reduction in chemical kinetics (Bhattacharjee et al, 2003;Oluwole et al, 2006). Model reduction refers to a systematic reduction in the size of a large kinetic model so as to reproduce model outputs within a specified tolerance.…”

Section: Model Inferencementioning

confidence: 99%

Bayesian inference of chemical kinetic models from proposed reactions

Galagali

Marzouk

2015

Chemical Engineering Science

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Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structuresuch as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.

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“…Strictly, this validity should be ensured by the method. Oluwole et al [27,28], for instance, have developed a reduction technique based on constrained optimization that guarantees the range of validity of the reduced scheme. However, this approach is not applicable directly to the DRGEP method.…”

Section: Sampling Processmentioning

confidence: 99%