Lumping strategy

Wei s later work with J. C. Kuo on lumping and that of Li and Rabitz at Princeton [Chem. Eng. Sci. 44,1413, (1959)] also opened up an important area of formal kinetics. See also Bischoff and Coxson, Lumping strategy. l.E.C. Res. 26,1329 2151, (1983). J. E. Bailey [Lumping analysis of reactions in continuous mixtures. Chem. Eng. J. 3, 5261 (1962)]. forged an important link between continuous mixtures and lumps. 

Coxson, R G., and Bishoff, K. B., Lumping strategy. 1, Introductory techniques and applications of cluster analysis. Ind. Eng. Chem. Res. 26,1239 (1987b). 

Ocone, R., and Astarita, G., Lumping nonlinear kinetics in porous catalysts Diffusion-reaction lumping strategy. AIChEJ. 39,288 (1993). 

Boock, L.T. and Klein, M.T. (1993) Lumping strategy for modeling the oxidation of C1-C3 alcohds and acetic acid in high-temperature water Ind. Eng. Chem. Res. 32,2464-2473... 

Selection of an appropriate lumping scheme was one of the most important issues in this modelling exercise. Ten lump kinetic scheme developed by Jacob et al. (1976) and five lump kinetic model proposed by Ancheyta et al. (1999) were examined closely. The virtue of more detailed lumping scheme over other less detailed models is that rate constants is that rate constants are independent of feed composition. But utilisation of these models are limited by two problems i.e. detailed characterisation of streams is not available on a regular basis and elaborate kinetic information is scarcely available. Thus, a balance between kinetic description required and cost of laboratory analysis often decides selection of lumping strategy. 

Nin, Y.-S., Vervisch, L., Tao, P.D. An optimization-based approach to detailed chemistry tabnlatimi antomated progress variable definition. Combust. Flame 160, 776-785 (2013) Octme, R., Astaiita, G. Lumping nonlinear kinetics in porous catalysts diffusion-reaction lumping strategy. AIChE J. 39. 288-293 (1993)... 

At the process level, efficient flowsheet optimization strategies based on lumped parameter models are now widely used in practice (Biegler et al., 1997). At this scale, the PEFC is embedded within a power plant flowsheet model, as shown in Figure 3. The process comprises... 

Because of their structural and conformational complexity, polypeptides, proteins, and their feedstock contaminants thus represent an especially challenging case for the development of reliable adsorption models. Iterative simulation approaches, involving the application of several different isothermal representations8,367 369 enable an efficient strategy to be developed in terms of computational time and cost. Utilizing these iterative strategies, more reliable values of the relevant adsorption parameters, such as q, Kd, or the mass transfer coefficients (the latter often lumped into an apparent axial dispersion coefficient), can be derived, enabling the model simulations to more closely approximate the physical reality of the actual adsorption process. 

Jones (1974) used the moment transformation of the population balance model to obtain a lumped parameter system representation of a batch crystallizer. This transformation facilitates the application of the continuous maximum principle to determine the cooling profile that maximizes the terminal size of the seed crystals. It was experimentally demonstrated that this strategy results in terminal seed size larger than that obtained using natural cooling or controlled cooling at constant nucleation rate. This method is limited in the sense that the objective function is restricted to some combination of the CSD moments. In addition, the moment equations do not close for cases in which the growth rate is more than linearly dependent on the crystal size or when fines destruction is... 

A strategy suggested by Chang (1982) is based on the assumption that the perturbed trajectory is in the vicinity of the nominal trajectory and uses one-step iteration in a gradient search technique to improve the perturbed performance index. This approach assumes that the moments of the CSD (the states of the lumped model resulting from the method of moments) can be measured or estimated. 

Crank-Nicolson or Laasonen, (see Ref (2), 3rd edn. only for details). The point is that the first of the two equations includes terms for both species and the whole system of these equations is thus not amenable to the usual Thomas algorithm for a tridiagonal system (this is in fact not quite true, since a related strategy can be devised in this particular case but the statement is true in general for coupled systems). Rudolph, however, recognized that the two equations can be lumped into a single one in terms of vectors and a matrix, becoming... 

Beginning with fundamentals of fluid dynamics, correlations for the pressure loss in channel elements are presented, which are concatenated to fluidic networks to distribute fluid homogeneously over a certain area. Computational fluid dynamic (CFD) simulations of single elements are exploited for analytical pressure loss correlations. These are employed in lumped element modeling of networks and manifolds, which are too complex for direct simulations. Design strategies and methods are presented for charmel networks, manifolds for parallel channels on a plate and headers for stacked-plate devices. 

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