Model AIChE efficiency

Individual component efficiencies can vary as much as they do in this example only when the diffusion coefficients of the three binary pairs that exist in this system differ significantly For ideal or nearly ideal systems, all models lead to essentially the same results. This example demonstrates the importance of mass-transfer models for nonideal systems, especially when trace components are a concern. For further discussion of this example, see Doherty and Malone (op. cit.) and Baur et al. [AIChE J. 51,854 (2005)]. It is worth noting that there exists extensive experimental evidence for mass-transfer effects for this system, and it is known that nonequilibrium models accurately describe the behavior of this system, whereas equilibrium models (and equal-efficiency models) sometime... 

Gogate PR, Shirgaonkar IZ, Sivakumar M, Senthilkumar P, Vichare NP, Pandit AB (2001) Cavitation reactors Efficiency assessment using a model reaction. AIChE J 47 2526-2538... 

Theoretical Efficiency Prediction Theoretical tray efficiency prediction is based on the two-film theory and the sequence of steps in Fig. 14-41. Almost all methods evolved from the AIChE model (AIChE Research Committee, Bubble Tray Design Manual, New York, 1958). This model was developed over 5 years in the late 1950s in three universities. Since then, several aspects of the AIChE model have been criticized, corrected, and modified. Reviews are given by Lockett (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986) and Chan and Fair [Ind. Eng. Chem. Proc. 

The Chan and Fair correlation generally gave good predictions when tested against a wide data bank, but its authors also observed some deviations. Its authors described it as "tentative until more data become available. The Chan and Fair correlation is considered the most reliable fundamental correlation for tray efficiency, but even this correlation has been unable to rectify several theoretical and practical limitations inherited from the AIChE correlation (see Kister, Disfiliation Design, McGraw-Hill, New York, 1992). Recently, Garcia and Fair (Ind. Eng. Chem. Res. 39, 1818, 2000) proposed a more fundamental and accurate model that is also more complicated to apply. 

High Viscosity and Surface Tension Bravo (Paper presented at the AIChE Spring National Meeting, Houston, Tex., 1995) studied a system that had 425-cP viscosity, 350 mN/m surface tension, and a high foaming tendency. He found that efficiencies were liquid-phase-controlled and could be estimated from theoretical HTU models. Capacity was less than predicted by conventional methods which do not account for the high viscosity. Design equations for orifice distributors extended well to the system once the orifice coefficient was calculated as a function of the low Reynolds number and the surface tension head was taken into account. 

Shilkin, A., Kenig, E.Y., Olujic, Z. A hydrodynamic-analogy-based model for efficiency of structured packing columns. AIChE Journal, Vol. 52,... 

In order to convert point efficiencies to Murphree tray efficiencies, the Chan and Fair correlation uses the same general mixing model as the AIChE model (125). This model uses Lewis case 1 (Sec. 7.1.3), i.e., mixed vapor and plug flow of liquid. In addition, some liquid back-mixing is assumed and correlated via an eddy diffusion coefficient. The model gives... 

Vapor maldistribution. Most popular theoretical models (such as the AIChE and the Chan and Fair models, Sec. 7.2.1) postulate perfectly mixed vapor flow. In larga-diameter columns, vapor is more likely to rise in plug flow. Modeling work showed (143,179,180) that in the absence of stagnant zones on the tray, vapor flow pattern has generally little effect on tray efficiency. When column efficiency exceeds 30 percent (143), or when stagnant liquid zones exist (171,173,180), vapor plug flow reduces tray efficiency. 

Downcomer mixing. The AIChE model assumes that liquid along the downcomer length is perfectly mixed. A recent study using a tracer injection technique (174) showed that in large trays, the downcomer liquid is unmixed. A computational analysis (174) showed that efficiency reduction due to an unmixed downcomer is relatively small, but will intensify in the presence of liquid stagnant regions on the tray. 

The mass-transfer efficiencies of various MHF contactors have been studied by many researchers. Dahuron and Cussler [AlChE 34(1), pp. 130-136 (1988)] developed a membrane mass-transfer coefficient model (k ) Yang and Cussler [AIChE /., 32(11), pp. 1910-1916 (1986)] developed a shell-side mass-transfer coefficient model (ks) for flow directed radially into the fibers and Prasad and Sirkar [AIChE /., 34(2), pp. 177-188 (1988)] developed a tube-side mass-transfer coefficient model (k,). Additional studies have been published by Prasad and Sirkar [ Membrane-Based Solvent Extraction, in Membrane Handbook, Ho and Sirkar, eds. (Chapman Hall, 1992)] by Reed, Semmens, and Cussler [ Membrane Contactors, Membrane Separations Technology Principle. and Applications, Noble and Stern, eds. (Elsevier, 1995)] by Qin and Cabral [MChE 43(8), pp. 1975-1988 (1997)] by Baudot, Floury, and Smorenburg [AIChE ]., 47(8), pp. 1780-1793 (2001)] by GonzSlez-Munoz et al. [/. Memhane Sci., 213(1-2), pp. 181-193 (2003) and J. Membrane Sci., 255(1-2), pp. 133-140 (2005)] by Saikia, Dutta, and Dass [/. Membrane Sci., 225(1-2), pp. 1-13 (2003)] by Bocquet et al. [AIChE... 

Krishnamurthy, R. and Taylor, R., A Nonequilibrium Stage Model of Multicomponent Separation Processes. Ill—The Influence of Unequal Component Efficiencies in Design, AIChE J, 31, 1973-1985 (1985c). 

Lee and Dudukovic [18] described an NEQ model for homogeneous RD in tray columns. The Maxwell-Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell-Stefan) mass-transfer coefficients. Newton s method and homotopy continuation are used to solve the model equations. Close agreement between the predictions of EQ and NEQ models were found only when the tray efficiency could correctly be predicted for the EQ model. In a subsequent paper Lee and Dudukovic [19] presented a dynamic NEQ model of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy continuation. Murphree efficiencies calculated from the results of an NEQ simulation of the production of ethyl acetate were not constant with time. 

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