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 ...

A new strategy is proposed for the optimum design of chemical plants whose uncertain parameters are expressed as bounded variables. The design is such that the plant specifications will be met for any feasible values of the parameters while optimizing a weighted cost function which reflects the costs over the expected range of operation. The strategy is formulated as a nonlinear programme, and an efficient method of solution is derived for constraints which are monotonic with the parameters, a case which arises frequently in practice. The designs of a pipeline with a pump, of a reactor-separator system, and of a heat exchanger network, all with uncertain technical parameters, illustrate the effectiveness of the strategy for rational overdesign of a chemical plant. uncertainty is present in parameters such as pump efficiencies, friction factors, reaction rate constants, and heat transfer coefficients.

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[1] This paper reviews three modes of natural variability that have been identified in the North Atlantic Ocean, namely, the North Atlantic Oscillation (NAO), the Atlantic Multidecadal Oscillation (AMO) and the Atlantic Meridional Mode (AMM). This manuscript focuses on the multidecadal fluctuations of these three modes. A range of different mechanisms to initiate phase reversals in these modes on multidecadal timescales has been suggested previously. We propose a systematic grouping of these mechanisms into three types that involve, respectively, (1) the dependency of the Atlantic thermohaline circulation (THC) on salinity, (2) the sensitivity of the THC to changes in ocean heat transport and (3) the dependency of the NAO to changes in the Atlantic meridional temperature gradient. Some new density data is also provided, demonstrating physical links between the THC and the AMO.

The question of whether and to what extent global warming may be changing tropical cyclone (TC) activity is of great interest to decision makers. The presence of a possible climate change signal in TC activity is difficult to detect because interannual variability necessitates analysis over longer time periods than available data allow. Projections of future TC activity are hindered by computational limitations and uncertainties about changes in regional climate, large scale patterns, and TC response. This review discusses the state of the field in terms of theory, modeling studies and data. While Atlantic TCs have recently become more intense, evidence for changes in other basins is not persuasive, and changes in the Atlantic cannot be clearly attributed to either natural variability or climate change. However, whatever the actual role of climatic change, these concerns have opened a "policy window" that, if used appropriately, could lead to improved protection against TCs.

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