This paper shows how the limiting operating conditions, total reflux and thermodynamically optimum operation, can be used to determine the feasibility of a desired separation by continuous ...distillation. To assess feasibility, so-called pinch point trajectories are established as the limits of separations achievable in each column section. These trajectories may be determined graphically using residue curve maps. The feasibility criterion is generalized to result in a method to establish the ranges of top and bottom product compositions achievable by a single-feed distillation column for a given ternary feed. One particularly interesting application is to reveal where and to what extent distillation boundaries for azeotropic mixtures, derived for total reflux, can be surpassed in columns operated at finite reflux ratios. The authors present a criterion for estimating the maximum reflux for such separations and illustrate process schemes that exploit the possibility of crossing of total reflux boundaries to separate azeotrope-forming mixtures. They then demonstrate how intermediate heat exchangers can be used to improve separations of azeotropic mixtures across total reflux boundaries.
The habitat and dietary preferences of Black Grouse were studied from 1989 to 1991 in a largely treeless habitat within a 17 km
2
area of the Pennine hills of northern England using radiotelemetry. ...Grassland habitats were preferred by 84% of 19 birds for much of the year and heather moorland was selected in winter; the other birds, all females, remained in heather habitats all year. Most females reared broods in damp, rushy grass moorlands, but one of six broods used hay fields. Diet closely reflected seasonal plant availability in selected habitats and the leaves, flowers, fruits and seeds of a wide variety of plants were eaten. Cotton-grass Eriophorum vaginatum was important in spring, grassland herbs, grasses, sedges and rushes in summer and autumn and Ling Heather Calluna vulgaris in late autumn and winter. Males fed substantially more on heather in winter than females which partially replaced heather in their diet with the leaves of grasses and herbs. Young chicks showed considerable preference for Sawfly (Symphyta) larvae. Suggested management recommendations include the regulation of sheep-grazing, encouragement of wet flush areas and the late cutting of hay fields.
Many problems that face a business decision maker are most accurately formulated as multi-objective optimization problems. However, actually solving these problems is a difficult and computationally ...expensive process. In this paper, we develop and use an agent-based optimization system for efficiently generating the non-dominated solution set to a non-convex multi-objective optimization problem. Through simulation, we highlight the benefits that arise from allowing collaboration among agents embodying a diverse set of algorithms. Further, we demonstrate the ability of the agent system to use large-scale parallel resources efficiently. We also propose two new metrics for quantifying the performance of multi-objective optimization systems.
Operating in a changing and uncertain environment, firms must make strategic and operational decisions while trying to satisfy many conflicting goals. For example, in order to maximize expected ...profit and minimize risk, they must periodically decide when and by how much to expand capacity and even more often how much to produce, all in the face of unknown future demands, available technology, and so on. We refer to this class of problem as multi-objective decision processes under uncertainty.
We investigate two major methodologies from different research streams that formulate and solve this class of problem: optimal control and stochastic programming. We introduce an example problem of coordinated capacity planning and production-inventory control to illustrate the issues on formulations and solutions of these two methodological approaches. We show that two methodologies are equivalent in that the decision prescribed by the optimal policy found by optimal control is the same as the corresponding optimal decision found by stochastic programming. Both solution approaches suffer from the “curse of dimensionality” but in different ways: the former approach has an immense state space while the latter a large sample space. They possess distinctive advantages and disadvantages for specific problems, which determine that one approach may be preferably used. We discuss and compare two methods on the example problem in terms of their model formulations, computation efficiency, and handling of multiple objectives. We propose an approximation architecture that combines different approaches to solve large-scale problems. We finally present the numerical results obtained from the example problem to demonstrate that one should tailor solution strategies to specific problems.
Graphical tray‐by‐tray methods for reactive distillation columns we developed previously are extended to study two industrial processes: MTBE production and methyl acetate production. As both ...processes involve four components, projection was used to obtain ternary diagrams by ignoring the inert (n‐butane) for MTBE production and by projecting onto planes of constant acetic acid concentrations for methyl acetate production. These projected methods clearly explain the placing that industry uses for the reaction zones in these processes. Further, it can be visualized why there is an optimum reflux ratio for the methyl acetate process and a value can be quantitatively predicted for it that lies within the range the literature reports.
Background: The nucleus 32Mg (N=20 and Z=12) plays a central role in the so-called “island of inversion,” where in the ground states sd-shell neutrons are promoted to the fp-shell orbitals across the ...shell gap, resulting in the disappearance of the canonical neutron magic number N=20.
Purpose: The primary goals of this work are to extend the level scheme of 32Mg, provide spin-parity assignments to excited states, and discuss the microscopic structure of each state through comparisons with theoretical calculations.
Method: In-beam γ-ray spectroscopy of 32Mg was performed using two direct-reaction probes: one-neutron (two-proton) knockout reactions on 33Mg (34Si). Final-state exclusive cross sections and parallel momentum distributions were extracted from the experimental data and compared with eikonal-based reaction model calculations combined with shell-model overlap functions.
Results: Owing to the remarkable selectivity of the one-neutron and two-proton knockout reactions, a significantly updated level scheme for 32Mg, which exhibits negative-parity intruder and positive-parity normal states, was constructed. The experimental results were confronted with four different nuclear structure models.
Conclusions: In some of these models, different aspects of 32Mg and the transition into the island of inversion are well described. However, unexplained discrepancies remain, and, even with the help of these state-of-the-art theoretical approaches, the structure of this key nucleus is not yet fully captured.
This paper shows how to construct a McCabe-Thiele diagram for binary reactive distillation. We consider two types of reaction that are consistent with binary mixtures: isomerization (R1 ⇔ P1) and ...decomposition (R1 ⇔ 2P1). We can account for reaction by tracking only two features of the diagram while constructing it. First, the intersection point of the operating line with the y = x line can be called the reactive cascade difference point, and it moves in a manner directly determined by the ratio of the molar extent of reaction (or reaction turnover flowrate) to the product flowrate. Second, the heat supplied (removed) by reaction decreases (increases) the slope of the operating line while not changing the location of the reactive cascade difference point. By tracking these two features, one can quickly sketch such a diagram. We also show how to construct a McCabe-Thiele diagram if the reaction zone is only at the feed stage. Finally, we discuss a case in which the reactive cascade difference point moves past the feed composition and the bottom product composition is less pure than the feed composition.
We show how to construct a Ponchon-Savarit diagram for a binary reactive distillation column, illustrating it specifically for isomerization and decomposition reactions. We first show the properties ...needed for points to lie on a straight line in composition/enthalpy space. Then, for the isomerization reaction, we show how to step off the stages using a reactive cascade difference point. In the Ponchon-Savarit diagram, the reactive cascade difference point has two elements. One is the composition coordinate formed as a linear combination of stoichiometric coefficient vectors and the top product composition. The other is the enthalpy coordinate formed by combining the top product molar enthalpy, the condenser molar duty and the molar heat of reaction. Finally, and in a similar manner, we construct the Ponchon-Savarit diagram for a decomposition reaction.
PDF
