Modular-based optimization

Comparison of the results of equation-based and simultaneous modular-based optimization for two connected distillation columns... 

Wolbert et al. in 1991 proposed a method of obtaining accurate analytical first-order partial derivatives for use in modular-based optimization. Wolbert (1994) showed how to implement the method. They represented a module by a set of algebraic equations comprising the mass balances, energy balance, and phase relations ... 

PLOW 1 RAN was made available in 1974 by Monsanto Co. for steady-state simulation of chemical processes based on sequential modular technology. It requires specification of feed streams and topology of the system. In 1987, an optimization enhancement was added. 

The most common chiral auxiliaries are diphosphines (biphep, binap and analogues, DuPhos, ferrocenyl-based ligands, etc.) and cinchona and tartaric acid-derived compounds. It is clear that the optimal chiral auxiliary is determined not only by the chiral backbone (type or family) but also by the substituents of the coordinating groups. Therefore, modular ligands with substituents that can easily be varied and tuned to the needs of a specific transformation have an inherent advantage (principle of modularity). 

Finally, we should mention that in addition to solving an optimization problem with the aid of a process simulator, you frequently need to find the sensitivity of the variables and functions at the optimal solution to changes in fixed parameters, such as thermodynamic, transport and kinetic coefficients, and changes in variables such as feed rates, and in costs and prices used in the objective function. Fiacco in 1976 showed how to develop the sensitivity relations based on the Kuhn-Tucker conditions (refer to Chapter 8). For optimization using equation-based simulators, the sensitivity coefficients such as (dhi/dxi) and (dxi/dxj) can be obtained directly from the equations in the process model. For optimization based on modular process simulators, refer to Section 15.3. In general, sensitivity analysis relies on linearization of functions, and the sensitivity coefficients may not be valid for large changes in parameters or variables from the optimal solution. 

Before leaving this section we consider a slightly different optimization problem that may also be expensive to solve. In flowsheet optimization, the process simulator is based almost entirely on equilibrium concepts. Separation units are described by equilibrium stage models, and reactors are frequently represented by fixed conversion or equilibrium models. More complex reactor models usually need to be developed and added to the simulator by the engineer. Here the modular nature of the simulator requires the reactor model to be solved for every flowsheet pass, a potentially expensive calculation. For simulation, if the reactor is relatively insensitive to the flowsheet, a simpler model can often be substituted. For process optimization, a simpler, insensitive model will necessarily lead to suboptimal (or even infeasible) results. The reactor and flowsheet models must therefore be considered simultaneously in the optimization. 

As the follow up to our studies in connection to the development of Ti-cat-alyzed cyanide additions to meso epoxides [4], we developed the corresponding catalytic enantioselective additions to imines [5]. A representative example is shown in Scheme 1 chiral non-racemic products maybe readily converted to the derived cx-amino acids (not available through catalytic asymmetric hydrogenation methods). In these studies, we further developed and utilized the positional optimization approach effected by examination of parallel libraries of amino acid-based chiral ligands (e.g., 1 and 2). Thus, the facile modularity of these ligands and their ease of synthesis were further exploited towards the development of a new catalytic enantioselective method that delivers various ar-... 

Yamamoto has used the modularity of another type of oc-amino acid-based chiral ligand to promote enantioselective epoxidations of allylic alcohols [21]. Thus, as illustrated in Eq. (8), parallel libraries of various ligand candidates were prepared and the identity of the optimal ligand 13 was established through positional optimization. 

With the above considerations in mind, we prepared and examined a myriad of chiral Mo-based catalysts for both asymmetric RCM (ARCM) and ROM (AROM) transformations [5]. In this article, several efficient and enantioselec-tive reactions that are catalyzed by these chiral complexes are discussed [6]. The structural modularity inherent to the Mo-based systems allows screening of catalyst pools, so that optimal reactivity and selectivity levels are identified expeditiously. 

In 2001, the SRS announced its choice of CSSX as the baseline cesium-removal technology over small-tank precipitation (a small-scale version of the ITP process) and ion exchange with CST for its Salt Waste Processing Facility (SWPF) to go into operation in 2010 [22], An optimized solvent system, model, and flowsheet were developed and demonstrated in 2001 and 2002 [37,49], and a modular concept was developed by ORNL in 2003 [68], Thus, the past decade has seen the emergence and maturation of a powerful new technology based on a macrocyclic cation receptor designed to function in solvent extraction to meet the critical need of the USDOE for a means of cleanly separating Cs from alkaline tank waste. 

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