Time Problem

The minimum time problem is also known as the time optimal control problem. Coward (1967), Hansen and Jorgensen (1986), Robinson (1970), Mayur et al. (1970), Mayur and Jackson (1971), Mujtaba (1989) and Mujtaba and Macchietto (1992, 1993, 1996, 1998) all minimised the batch time to yield a given amount and composition of distillate using conventional batch distillation columns. The time optimal operation is often desirable when the amount of product and its purity are specified a priori and a reduction in batch time can produce either savings in the operating costs of the column itself or permit improved scheduling of other batch operations elsewhere in a process. Mathematically the problem can be written as  

Linear bounds on reflux ratio (inequality constraints) 

In the past researchers, using simple models, reported timesaving for the time optimal solutions of more than 10% compared to constant reflux operations. Mujtaba (1989) reported a batch timesaving of 30 - 45% compared to constant reflux operations for a number of example problems using detailed dynamic column models (Type IV-CMH). 

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When looking at one-time problems, it is important to consider whether this could have directly led to an undesired consequence, such as an accident or incident or a noncompliance situation, or if there is another level of safeguard. If it is concluded that the problem or weakness could have directly led to an undesired consequence, the system design should be reviewed to find a way in which a safeguard can be provided. Systematic issues require a redesign of the system to remove the potential for the problem. 

Time and space integrated, paired-data performance. Spacially and/or temporally integrated data can be compared to analogous model predictions, such as daily or monthly averages or totals. This can circumvent some of the timing problems noted in (J ). 

Figure 7b. Thermometer reading as a function of time, Problem 7.2...

The scope of evolutionary simulation is presently largely limited by the size and time problems. Its force fields are mostly expert systems and are far from a faithful reproduction of real physical effects - think of the wrong description of short-range Coulombic forces resulting from locating formal charges at atomic nuclei,... 

By using the information in TABLE 4-6, it can be determined that engine warmup time problems may result if the percent distilled 158°F (70°C) volume is less than the reported volumes at the given temperatures. 

The main element of the distance = rate x time problems is the distance. You solve for rate or time when given the distance or given the fact that the distances traveled by the participants are equal. Just as important is finding out just how far people have traveled. 

First Passage Time Problems in Chemical Physics (Weiss). .. 13 1... 

The number of coulombs is equal to Ihe area under a curve of current versus time. Problem 17-20 provides an example. 

The purpose of this optimization problem is to determine the optimal temperature profiles to achieve the desired final product concentration in minimum batch time, thus the performance index is the final time whereas the desired production concentration is defined as a terminal constraints. The formulation of the minimum batch time problem can be shown as... 

The ring-opening reaction can be performed either as a bulk polymerization, or in solution, emulsion, or dispersion [15,16]. A catalyst or initiator is necessary to start the polymerization. Under rather mild conditions, high-molecular weight aliphatic polyesters of low polydispersity can be prepared in short periods of time. Problems associated with condensation polymerization, such as the need for exact stoichiometry, high reaction temperatures, and the removal of low molecular weight by-products (e.g., water) are excluded in ROP [17]. 

Particle analysis is the most informative method to date for the identification of FDR particles. It does, however, suffer from several major disadvantages including high cost of instrumentation and lengthy and tedious procedures requiring specialized staff Since its introduction serious attempts have been made to solve the time problem. These include the use of backscattered electron images, automation of the search procedure, and sample manipulation to pre-concentrate the sample prior to SEM examination.145151... 

This is the most obvious solution to the time problem, ffaving fully trained samplers permanently on site, 24 hours a day every day, coupled with all the necessary sampling materials permanently on site, is by far the most sensible and effective way of solving many of the time delays. 

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