Difference points in reactive and extractive cascades. III—Properties of column section profiles with arbitrary reaction distribution

The behavior of reactive column section profiles under arbitrary reaction distribution policies is addressed through the use of difference points. We develop a method to capture the effects of reaction distribution and show how the placement of reaction within a section controls the path of the profile. We also investigate the relationship between reaction distribution and sectional flow rates and compositions which leads to a set of feasibility criteria that must be maintained as profiles proceed from stage-to-stage. Finally, the termination conditions for reactive profiles are identified, and fixed point techniques are developed to predict where profiles pinch in composition space. The first two papers in this series derived and analyzed the fundamental mathematical and geometric properties of difference points for cascade sections (Chem. Eng. Sci. 55(16), 3145) and developed a lever rule to facilitate discovery of full column design alternatives (Chem. Eng. Sci. 55(16), 3161). This third paper provides the analytical basis for identifying reachable feed compositions of reactive cascades.     

Difference points in reactive and extractive cascades, V: Determining reaction distribution from separatrix manifolds

The effect of reaction distribution policy on a reactive column profiles is analyzed. We find that the extent reaction on a single reactive stage can greatly influence the feasibility and termination of subsequent non-reactive stages. We develop a method to quantitatively predict when perturbing the amount of reaction on a single stage will subsequently force the column profile to become infeasible or otherwise fail to meet global design targets. To predict such behavior we rely on the map of stable invariant manifolds over the saddle branch of an isoreflux pinch point curve. We show how this method can be used to select reactive stages and distribute reaction over a column section profile to meet certain design criteria. We also show how this method can be used to find limits on overall extent reaction within a column or extent reaction on a single stage.     

A fundamental principle and systematic procedures for process intensification in reactive distillation columns

A fundamental principle is developed for process intensification through internal mass and energy integration in reactive distillation columns and three systematic procedures are devised for process synthesis and design. For reactive distillation columns involving reactions with highly thermal effect, process intensification can be achieved with an exclusive consideration of internal energy integration between the reaction operation and separation operation involved. However, in the case of a highly endothermic reaction with an extremely low reaction rate and/or small chemical equilibrium constant, internal mass integration has also to be considered between the reactive section and stripping section. For reactive distillation columns involving reactions with negligibly or no thermal effect, process intensification can be performed with an exclusive consideration of internal mass integration. For reactive distillation columns involving reactions with moderately thermal effect, process intensification must be conducted with a careful trade-off between internal mass and energy integration. Five hypothetical and two real reactive distillation systems are employed to evaluate the principle and procedures proposed. It is demonstrated that intensifying internal mass and energy integration is really effective for process intensification. Not only can the thermodynamic efficiency be improved substantially, but also the capital investment can be further reduced.     

Esterification of acetic acid with ethanol: Reaction kinetics and operation in a packed bed reactive distillation column

The reaction kinetics of the esterification of acetic acid with ethanol, catalyzed both homogeneously by the acetic acid, and heterogeneously by Amberlyst 15, have been investigated. The reactions were carried out at several temperatures between 303.15 and 353.15 K and at various starting reactant compositions. Homogeneous and heterogeneous reactions have been described using the models proposed by Pöpken et al. [T. Pöpken, L. Götze, J. Gmehling, Reaction kinetics and chemical equilibrium of homogenously and heterogeneously catalyzed acetic acid esterification with methanol and methyl acetate hydrolysis, Ind. Eng. Chem. Res. 39 (2000) 2601–2611]. These models use activities instead of mole fractions. Activity coefficients have been calculated using ASOG [K. Kojima, K. Tochigi, Prediction of Vapor–liquid Equilibria by the ASOG Method, Elsevier, Tokyo, 1979] and UNIFAC (Aa. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–liquid Equilibria Using UNIFAC. A Group Contribution Method, Elsevier, Amsterdam, 1977] methods.

A packed bed reactive distillation column filled with Amberlyst 15 has been employed to obtain ethyl acetate. The influence of feed composition and reflux ratio have been analyzed.     

Epoxidation of soybean oil in toluene with peroxoacetic and peroxoformic acids — kinetics and side reactions

The kinetics of the epoxidation of soybean oil and the extent of side reactions were studied at 40, 60, and 80 °C. Epoxidation was carried out in toluene with “in situ” formed peroxoacetic and peroxoformic acid and in the presence of an ion exchange resin as the catalyst. The reaction was found to be first‐order with respect to the double bond concentration. At higher temperatures and at higher conversions a deviation from the first‐order kinetics was observed. The rate constants for the epoxidation with peroxoacetic acid were 0.118 (h⁻¹) at 40 °C, 0.451 (h⁻¹) at 60 °C and 1.278 (h⁻¹) at 80 °C, while those for peroxoformic acid were 0.264, 0.734, and 1.250 (h⁻¹). The activation energy was found to be 54.7 kJ/mol for the epoxidation with peroxoacetic acid and 35.9 kJ/mol for that with peroxoformic acid. Three factors indicated that side reactions did not occur on a large scale: The absence of an OH band in the IR spectra, the formation of less than 2% of higher molecular weight products from gel permeation chromatography and the selectivity values between 0.9 and 1.     

Changes in contrast thresholds with mean luminance for chromatic and luminance gratings: A reexamination of the transition from the DeVries–Rose to Weber regions

We have examined the influence of the mean luminance level on the detection thresholds for luminance and red–green chromatic gratings for three different spatial frequencies. The changes in detection thresholds according to the mean luminance level reflect the two different regions, the DeVries–Rose and Weber ranges, found in previous studies. The results for luminance gratings suggest that the transition luminance is proportional to the spatial frequency of the grating. Predictions based on the constant‐flux hypothesis indicate, however, that the transition luminance is proportional to the square of the spatial frequency of the grating and so do not describe the distributions of luminance contrast thresholds adequately. For chromatic gratings, we obtained the same transition luminance for the two lowest spatial frequencies, showing that luminance and chromatic mechanisms behave differently as far as the dependence of the transition luminance on spatial frequency is concerned. Our results suggest that the transition luminance is related to the peak spatial frequency of visual mechanisms that respond to luminance and chromatic gratings. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 177–182, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20003