Shortcut Optimization Method

The ratio of Eq. (22) to Eq. (23) provides a direct differential equation between epi-chlorohydrin enantiomer concentrations and the enantioselectivity factor, which is a function of temperature and catalyst concentration as variables (Eq. 25). This equation is readily solved to give the mathematical relation between enantiomeric excess and yield (R) as a function of a (Eq. 26). The maximum obtainable yield for a given ee specification (and vice versa) is provided straightforwardly in Eq. (26). Moreover, this equation shows that the yield-ee pair is independent of the amount of water used (provided the amount is sufficient to reach the desired ee) and of the water addition rate. Thus, the water addition mode will only impact the reaction time necessary to reach the desired yield and ee target. 

192 I 2 Industrialization Studies of the Jacobsen Hydrolytic Kinetic Resolution of Epichlorohydrin 

Utilizing this shortcut method, catalyst concentration and reaction temperature are the critical parameters that impact the selectivity through the enantioselectiv-ity factor. The effect of these two parameters on the yield and ee performance of the HKR is graphically illustrated in Fig. 24. The data clearly indicate that operating at the highest catalyst concentration and the lowest reaction temperature maximizes the difference in the rates of reaction for the two enantiomers, and thereby 

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No single method or algorithm of optimization exists that can be apphed efficiently to all problems. The method chosen for any particular case will depend primarily on (I) the character of the objective function, (2) the nature of the constraints, and (3) the number of independent and dependent variables. Table 8-6 summarizes the six general steps for the analysis and solution of optimization problems (Edgar and Himmelblau, Optimization of Chemical Processes, McGraw-HiU, New York, 1988). You do not have to follow the cited order exac tly, but vou should cover all of the steps eventually. Shortcuts in the procedure are allowable, and the easy steps can be performed first. Steps I, 2, and 3 deal with the mathematical definition of the problem ideutificatiou of variables and specification of the objective function and statement of the constraints. If the process to be optimized is very complex, it may be necessaiy to reformulate the problem so that it can be solved with reasonable effort. Later in this section, we discuss the development of mathematical models for the process and the objec tive function (the economic model). 

All of these variables must be optimized simultaneously to obtain the best design. Some of the variables are continuous and some are discrete (the number of stages in each column section). Such optimizations are far from straightforward if carried out using detailed simulation. It is therefore convenient to carry out some optimization using shortcut methods before proceeding to detailed simulation where the optimization can be fine-tuned. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

Yu H.W. and Ching C.B., Design and Optimization of a Simulated Moving Bed Based on an Approximated Model Using a Novel Shortcut Method, AICHE Journal vol. 48, (2002) No. 10.2240-2246. 

In the first step, the design alternatives are automatically generated using a superstructure. In the second step, the design alternatives are evaluated using the rectification body method (RBM) [5], a nonideal thermodynamic based shortcut method. Unlike simulation studies or MINLP optimization, shortcut methods allow fast evaluation of the single separation task without detailed specification of the distillation column. 

In chemical engineering, several methodologies and procedures are applied for decision making during design processes. Representative examples include design heuristics, shortcut methods, decision analysis methods, and mathematical optimization. 

Such methods are typically not applied independently of each other, but their outcomes may interact an example addressing the combination of shortcut calculations with the rectification body method and rigorous optimization is given in [231]. 

Multi-component batch distillation computation time can be excessive with rigorous methods, especially for problems that require multiple runs, such as optimization, and for online applications. It is desirable to have shortcut alternatives for such situations. 

The problem of extensive computing time typical of batch distillation is compounded with the superimposition of an optimization routine. For this reason batch distillation optimization algorithms are usually built around shortcut batch distillation methods. Possible approaches to formulating the optimization problem are presented, although a detailed mathematical discussion is outside the scope of this book. 

In a departure from continuous steady-state processes that characterize a greater part of the book, the subject of batch distillation is discussed. This process, which is important for the separation of pharmaceuticals and specialty chemicals, is presented, including shortcut and rigorous computation methods, along with various optimization techniques. 

As reference we consider the direct separation scheme. The design of columns was done in Aspen Plus by means of shortcut methods followed by rigorous simulation. The energetic consumption depends on the reflux ratio. We assume that the optimal R/Rmi is 1.3, and column pressures of 2 and 1 bar with 0.2 bar pressure drop. Table 11.2 presents the results. Note that the initial feed temperature is 298 K, and therefore the reboiler duty of the first column includes feed preheating. 

Continuously operated chromatographic processes such as simulated moving beds (SMB) are well established for the purification of hydrocarbons, fine chemicals, and pharmaceuticals. They have proven ability to improve the process performance in terms of productivity, eluent consumption, and product concentration, especially for larger production rates. These advantages, however, are achieved with higher process complexity with respect to operation and layout. A purely empirical optimization is rather difficult and, therefore, the breakthrough for practical applications is linked to the availability of validated SMB models and shortcut methods based on the TMD model as described in Chapter 6. 

Starting with the simplest model, the true moving bed (TMB) model, first it will be demonstrated how to determine parameters for the operation of SMB processes. Based on these TMB shortcut methods, a more detailed optimization of operating... 

Before Varicol, PowerFeed, or Modicon is taken into account for process design make sure that appropriate optimization tools are at your disposal. In contrast to SMB, no shortcut methods such as triangle theory are available for these processes. 

Empirical work by Chopra and Ziembra (1993) demonstrated that the most critical aspect of constructing optimal portfolios is the return forecast For this reason, a shortcut employed by some practitioners is to concentrate on the return forecast and use historical risk emd correlation to construct optimum portfolios. This may prove satisfactory because correlations and risk are more stable than returns tmd are therefore more easily predicted. However, this Une of attack may be ineffective if return forecasts substantially deviate fiom history and are combined with historical risk and correlations. In this case, the optimal aUocations can skew overwhelmingly to the high return assets Whatever method is used to obtain forecasts, once the optimum portfoUo is determined, the memager can momentarily relax and wait. Of course, actual outcomes wUl seldom match expectations. 

The design and optimization of a fully thermally coupled distillation column (FTCDC) are solved by a shortcut method, which uses a three-column model (Triantafyllou and Smith,... 

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