Coping with uncertainty in the description of complex kinetic mechanisms
S. Balakrishnan, M. Ierapetritou (Department of Chemical Engineering, Rutgers
University);
P.G. Georgopoulos (EOHSI, UMDNJ - R.W. Johnson Medical School and Rutgers University)
Accurate models that correctly describe chemical processes are often intricate and involve a large number of reacting species and reaction steps. Examples include combustion processes, atmospheric chemistry problems etc. Complex kinetic mechanism reduction is often carried out as a way to overcome the computational burden associated with including all reactions steps. In the case of complex reaction mechanisms, output species concentration profiles can potentially change dramatically based on the set of values chosen for the uncertain inputs (including rate constants, initial conditions etc.). This complicates reaction mechanism reduction because reduction strategies typically condition prediction error (full vs. reduced) to lie below a specified limit. A systematic uncertainty analysis can provide insight into the level of confidence of model estimates and aid mechanism reduction. Conventional techniques of uncertainty propagation however, typically require a large number of model runs that sample various combinations of the inputs resulting in heavy computational demand (eg. Monte Carlo, Latin Hypercube methods). Response surface methods and variants thereof try to address this problem by reducing the number of simulations required for adequate estimation of uncertainty propagation. Stochastic Response Surface Method (SRSM)1 is one such technique which uses computationally efficient instantiation of the random variables responsible for uncertainty in order to capture uncertainty effects. Based primarily on classical response surface methods and Deterministic Equivalent Modeling (DEMM)2, SRSM expresses random outputs in terms of the “polynomial chaos expansion”3 of Hermite polynomials and uses an efficient collocation scheme combined with regression in order to determine the coefficients of the expansion. This polynomial form then engenders many useful properties including straightforward determination of statistics like the mean and variance and computation of first and second sensitivity information. Reaction rate constant uncertainty is focused on (given prior lognormal distributions with known median and uncertainty factors) and SRSM is shown to be very accurate in determination of the uncertainty propagation characteristics while using an orders of magnitude less model simulations than traditional Monte Carlo techniques. In addition, a two stage mechanism reduction process is outlined wherein in stage one, first and second order sensitivity information obtained from SRSM is utilized to create good starting points for stage two, where Branch & Bound is performed4,5. Two case studies are analyzed, a supercritical wet oxidation process6 and a CO/H2/Air combustion process7, which elucidate the application of SRSM to complex kinetic mechanisms. The results presented illustrate how the computational burden associated with mechanism reduction can be eased by application of this two stage method.
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