Maximization

If this criterion is based on the maximum-likelihood principle, it leads to those parameter values that make the experimental observations appear most likely when taken as a whole. The likelihood function is defined as the joint probability of the observed values of the variables for any set of true values of the variables, model parameters, and error variances. The best estimates of the model parameters and of the true values of the measured variables are those which maximize this likelihood function with a normal distribution assumed for the experimental errors. 

In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

Multiple reactions in parallel producing byproducts. Once the reactor type is chosen to maximize selectivity, we are in a position to alter selectivity further in parallel reaction systems. Consider the parallel reaction system from Eq. (2.20). To maximize selectivity for this system, we minimize the ratio given by Eq. (2.21) ... 

The secondary reactions are parallel with respect to ethylene oxide but series with respect to monoethanolamine. Monoethanolamine is more valuable than both the di- and triethanolamine. As a first step in the flowsheet synthesis, make an initial choice of reactor which will maximize the production of monoethanolamine relative to di- and triethanolamine. 

Figure 2.10 Choosing the reactor to maximize selectivity for multiple reactions producing byproducts.

It should be emphasized that these recommendations for the initial settings of the reactor conversion will almost certainly change at a later stage, since reactor conversion is an extremely important optimization variable. When dealing with multiple reactions, selectivity is maximized for the chosen conversion. Thus a reactor type, temperature, pressure, and catalyst are chosen to this end. Figure 2.10 summarizes the basic decisions which must be made to maximize selectivity. ... 

After maximizing heat recovery in the heat exchanger network, those heating duties and cooling duties not serviced by heat recovery must be provided by external utilities. The outer-most layer of the onion model is now being addressed, but still dealing with targets. 

A refrigeration system is a heat pump in which heat is absorbed below ambient temperature. Thus the appropriate placement principle for heat pumps applies in exactly the same way as for refrigeration cycles. The appropriate placement for refrigeration cycles is that they also should be across the pinch. As with heat pumps, refrigeration cycles also can be appropriately placed across utility pinches. It is common for refrigeration cycles to be placed across a utility pinch caused by maximizing cooling water duty. 

Optimization of the system can be carried out by minimizing a cost function or maximizing economic potential EP defined by (see App. A)... 

All these variables must be varied in order to minimize the total cost or maximize the economic potential (see App. A). This is a... 

In Chap. 2 the objective set was to maximize selectivity for a given conversion. This also will minimize waste generation in reactors for a given conversion. 

In Chap. 10, modification of the process for reducing process waste was considered in detail. It also was concluded that to minimize utility waste, the single most effective measure would be improved heat recovery. The energy-targeting methods presented in Chaps. 6 and 7 maximize heat recovery for a given set of process conditions. However, the process conditions can be changed to improve the heat recovery further. 

The thermal profile through the reactor will in most circumstances be carefully optimized to maximize selectivity, extend catalyst life, etc. Because of this, direct heat integration with other process streams is almost never carried out. The heat transfer to or from the reactor is instead usually carried out by a heat transfer intermediate. For example, in exothermic reactions, cooling might occur by boiling water to raise steam, which, in turn, can be used to heat cold streams elsewhere in the process. 

Figure 16.5a shows the matches around the pinch from Fig. 16.4a with their duties maximized to tick-oflF streams. It should be emphasized that the tick-off heuristic is only a heuristic and can occasionally penalize the design. Methods will be developed later which allow such penalties to be identified as the design proceeds. 

Turning now to the cold-end design, Fig. 16.6a shows the pinch design with the streams ticked off. If there are any cold streams below the pinch for which the duties eu e not satisfied by the pinch matches, additional process-to-process heat recovery must be used, since hot utility must not be used. Figure 16.66 shows an additional match to satisfy the residual heating of the cold streams below the pinch. Again, the duty on the unit is maximized. Finally, below the pinch the residual cooling duty on the hot streams must be satisfied. Since there are no cold streams left below the pinch, cold utility must be used (Fig. 16.6c). 

Solution Figure 16.8a shows the hot-end design with the CP table. Above the pinch, adjacent to the pinch, CPfjSCPc- The duty on the units has been maximized according to the tick-oflF heuristic. 

Figure 16.22c shows an additional match placed on the other branch for stream 3 with its duty maximized to 3 MW to tick off stream 3. No further process-to-process matches are possible, and it remains to place cold utility. 

If the goal is to maximize profit, NPV is used. If the supply of capital is restricted (which is usual), DCFRR is used to decide which projects will use the capital most efficiently. 

In two stages with recycle to the second stage, the conversion per pass is approximately 50 wt. % and the selectivity to middle distillates is maximal 75 to 80 wt. %. However, the investment is clearly higher and is justified only when feedstocks are difficult to convert and that their content in nitrogen is high. Figure 10.11 represents two variants of the hydrocracking process. 

In the particular framework for lubricating oil bases, the operation takes place batchwise, generally using distillates selected according to the desired base, so as to minimize by-products and to maximize lubricating oils and their qualities. 

In the Maximum Entropy Method (MEM) which proceeds the maximization of the conditional probability P(fl p ) (6) yielding the most probable solution, the probability P(p) introducing the a priory knowledge is issued from so called ergodic situations in many applications for image restoration [1]. That means, that the a priori probabilities of all microscopic configurations p are all the same. It yields to the well known form of the functional 5(/2 ) [9] ... 

The representation of cooccurrence matrix as an image in 256 levels of gray necessitates a law of coefficients values transformation. In order that this law is common to all images, there will be no recodage on the maximum coefficient but on a theoretical maximal value. Thus the rule of conversion is the following ... 

In order to maximize the excitation, precautions have to be taken to avoid cross-talk between excitation and signal. Therefore differential probes are commonly used with a SQUID system Nevertheless, for the discussed defects the SQUID system has a lower excitation field by a factor of about 100 compared with the commereial system This we must keep in mind, when we compare measured signal to noise ratios. There is a potential to improve for small defeets, when eross-talk is managed very well. 

High-current EC-50 betatron with maximal energy of accelerated electrons equaled to 50 MeV and radiation dose power 220 Gr/min on the distance of Im from the target [3] was made for experimental physical researches and activated analysis. 

The theoretical approach consists in having a maximal leakage flux allowing the drawing of the defect edge clearly. 

It is to be taken into account that there is a difference between ultrasonic and radiography defect imaging, so the ultrasonic image recognition knowledge required for the person interpreting the inspection results. The ISONIC postprocessing mode allows to ease sueh interpretation because it s maximally approached to inspection standards. 

Companies have to face the problem of how to be maximize visible, that means how to get many visitors to a Website. Website marketing is a new field that needs to be understood before you invest in an Internet presence - to avoid ineffective and unnecessary expenditure. 

Experimentally, it is common for LEED and Auger capabilities to be combined the basic equipment is the same. For Auger measurements, a grazing angle of incident electrons is needed to maximize the contribution of surface... 

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