One of the key components of chemical plant operability is flexibility-the ability to operate over a range of conditions while satisfying performance specifications. A general framework for analyzing flexibility in chemical process design is presented in this paper. A quantitative index is proposed which measures the size of the parameter space over which feasible steady-state operation of the plant can be attained by proper adjustment of the control variables. The mathematical formulation of this index and a detailed study of its properties are presented. Application of the flexibility in design is illustrated with an example. R. E. SWANEY and E. GROSSMANN Department of Chemical EngineeringCarnegie-Melion University Pittsburgh, PA 15213 SCOPEThe goal in chemical process design is to produce a plant design that is optimal with respect to cost and performance. Plant performance involves a broad range of criteria. A good process design must not only exhibit an optimal balance between capital and operating costs, it must also exhibit operability characteristics which will allow economic performance to be realizable in a practical operating environment. Operability considerations involve flexibility, controllability, reliability, and safety. Although these aspects may appear to be similar, they correspond to different technical concepts. Flexibility is concerned with the problem of insuring feasible steady-state operation over a variety of operating conditions, whereas controllability is concerned with the quality and stability of the dynamic response of the process. Reliability is concerned with the probability of normal operation given that mechanical and electrical failures can occur; safety is concerned with the hazards that are consequences of these failures. Because these operability characteristics are the implicit results of design-stage decisions, they must be given direct attention during the design process if the goal of producing a good design is to be achieved.Most of the previous methods for process synthesis (Nishida et al., 1981) and flowsheet optimization (Edahl et al., 1983; Biegler and Hughes, 1982; Jirapongphan et al., 1980) consider a single nominal operating condition in the design of chemical processes. Although these procedures can often provide useful results, there is still a substantial gap between the designs obtained from such procedures and the designs that are actually implemented in practice. The major reason for this gap is that conventional procedures for synthesis and flowsheet optimization do not explicitly account for those factors which relate to plant operability. Therefore, the common practice is to introduce additional equipment and employ various types of empirical overdesign to improve operability characteristics. However, with this approach it is generally not possible to guarantee either optimality or feasible operation for conditions that are different from the nominal point selected for the design.It is only recently that new tools have begun emerging to simultaneous...

Procedures for the numerical computation of an index for operational flexibility in chemical processes are considered. Two types of algorithms are proposed which rely on the assumption that critical points for feasible operation lie at vertices or extreme values of the uncertain parameters. The first algorithm is a direct search procedure that features a heuristic variant to avoid exhaustive enumeration of all vertices. The second algorithm employs an implicit enumeration scheme based on a lower bound for monotonic constraints. These algorithms are applied to several example problems to demonstrate both the use of the flexibility index in process design and the computational efficiency of the algorithms. R. E. SWANEY and I. E. GROSSMANN Department of Chemical EngineeringCarnegle-Mellon University Pittsburgh, PA 15213 SCOPEIn Part I an index of flexibility was proposed to quantitatively characterize the flexibility of chemical processes. As was shown, this index gives a measure of the size of the region of feasible operation in the space of the uncertain parameters. Determination of this index for a design provides bounds for the uncertain parameters within which feasible operation can be guaranteed by proper manipulation of the control variables. Furthermore, identification of the critical points ("worstcase" conditions) which define the performance limits of the design is also provided.Mathematical formulations were developed in Part I to serve as a basis for computing the index, and their properties were studied. Sufficient conditions for the nature of the constraint functions were established for which the solution is guaranteed to lie at a vertex; i.e., with each parameter assuming an extreme value. Furthermore, a parametric description of the feasible region that is convenient for numerical computation was developed. The corresponding formulation determines the direction of parameter deviations that yield the smallest scaled distance from the nominal parameter point to the constraint boundarv.This second part will deal with the problem of developing efficient computational algorithms to determine the flexibility index. These algorithms assume that critical points lie at vertices. The major challenge lies in how to determine the global solution without having to enumerate and analyze the 2 p vertices, where p is the number of uncertain parameters. The first algorithm that is proposed is based on the direct search of all vertices, and is suitable when the number of parameters is small (say p I 4). A heuristic variant of this algorithm, which can handle a large number of uncertain parameters effectively, avoids total enumeration of all of the vertices. The second algorithm also accomplishes this goal, but it uses a lower bound within an implicit enumeration scheme that is rigorous for monotonic constraints. It is shown that these algorithms can be extended to detect nonvertex critical points, and to perform sensitivity analyses which indicate the rate of change of the flexibility index with proposed changes in ...

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in Wiley InterScience (www.interscience.wiley.com).The annular centrifugal contactor has been developed as the central piece of equipment for advanced liquid-liquid extraction processes for use in recycling spent nuclear fuel. While a sufficient base of experience exists to support successful operation of current contactor technology, a more complete understanding of the fluid flow within the contactor would enable further advancements in design and operation of future units. In particular, an important characteristic of the flow that is not well understood and which significantly complicates computational modeling of the contactor is the complex free surface flow in the annular mixing zone. This study presents the results of time-dependent, multiphase computational fluid dynamics (CFD) modeling using the volume-of-fluid (VOF) interface tracking method to characterize the mixing zone in a model centrifugal contactor. Laser doppler velocimetry (LDV) measurements of the actual flow velocities within the contactor were also performed. The experimental results were compared with simulations using various turbulence modeling schemes. The CFD model predictions using a coarse grid large eddy simulation (LES) method are in good agreement with the experimental measurements and observations. 2007 American Institute of Chemical Engineers AIChE J, 54: 74-85, 2008

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in Wiley InterScience (www.interscience.wiley.com).The annular centrifugal contactor is a compact mixer/centrifuge developed for solvent extraction processes for recycling used nuclear fuel. This research effort couples computational fluid dynamics (CFD) modeling with a variety of experimental observations to provide a valid detailed analysis of the flow within the centrifugal contactor. CFD modeling of the free surface flow in the annular mixing zone using the volumeof-fluid method combined with large eddy simulation of turbulence was found to have very good agreement with the experimental measurements. A detailed comparative analysis of the flow and mixing with different housing vane geometries (four straight vanes, eight straight vanes, and curved vanes) was performed. Two additional variations on the eight straight vane geometry were also simulated. This analysis determined that at the simulated moderate flow rate the four straight mixing vane geometry has greater mixing and fluid residence time as compared to the other mixing vane configurations. V

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