Optimization utility paths

Given a network structure, it is possible to identify loops and paths for it, as discussed in Chap. 7. Within the context of optimization, it is only necessary to consider those paths which connect two different utilities. This could be a path from steam to cooling water or a path from high-pressure steam used as a hot utility to low-pressure steam also used as a hot utility. These paths between two different utilities will be designated utility paths. Loops and utility paths both provide degrees of freedom in the optimization. ... 

Thus loops, utility paths, and stream splits offer the degrees of freedom for manipulating the network cost. The problem is one of multivariable nonlinear optimization. The constraints are only those of feasible heat transfer positive temperature difference and nonnegative heat duty for each exchanger. Furthermore, if stream splits exist, then positive bremch flow rates are additional constraints. 

Figure 16.25 The utility paths which can he exploited for optimization of the design from Fig. 16.7.

If the network is optimized at fixed energy consumption, then only loops and stream splits are used. When energy consumption is allowed to vary, utility paths also must he included. As the network energy consumption increases, the overall capital cost decreases. 

Figure 18.26 The utility paths that can be exploited for the optimization of the design from Figure 18.7.

In a network, some of the duties on the matches will not be able to be varied because they are not in a loop or a utility path. This simplifies the optimization. The problem is one of multivariable nonlinear continuous optimization6. 

Thus the hot and cold utility consumption both need to be increased by 1.6 MW to restore the Arm to the original 10°C. In fact there is no justification to restore the Arm back to the original 10°C. The amount of additional energy shifted along the utility path is a degree of freedom that should be set by cost optimization. However, the example illustrates how the degrees of freedom can be manipulated in network optimization. 

Once the initial network structure has been defined, then loops, utility paths and stream splits offer the degrees of freedom for manipulating network cost in multivariable continuous optimization. When the design is optimized, any constraint that temperature differences should be larger than A Tmin or that there should not be heat transfer across the pinch no longer applies. The objective is simply to design for minimum total cost. 

In an infinite-horizon model with stationary instantaneous utilities, TCs and naifs both follow a stationary strategy, wherein behavior depends only on the current addiction level and not the specific period t. In any period, both TCs and naifs choose today s behavior by determining their optimal lifetime path of behavior beginning from today. Given an infinite horizon, stationary instantaneous utilities, and our assumption that people hit when indifferent, for any t there is a unique optimal Lifetime path of behavior, and this path depends on the current addiction level but not the current period t. This logic is summarized in the following lemma ... 

The framework was evaluated with a case study focusing on design of a lignocellulosic biorefmery. The results showed that the tool could find new optimal processing paths for different scenarios (objective functions) which provide a better, more efficient production process and less utility, waste, investment, and operating costs using the expanded biorefinery network. The optimal biorefmery pathways were further analyzed with respect to sustainability and environmental impact, which revealed further options for sustainability... 

Optimization of the flow paths of the multiplex head resulted in an additional reserve of capacity. The layout of the inlet angle of the extmders and the arrangement of the flow channels were made in such a way that necessitates the pressure loss to a miniumum. The benefit of this can be clearly seen in a reduced stock temperature. This lower temperature can be utilized to increase the throughput capacity. 

In the majority of fixed-bed reactors for industrial synthesis reactions, direct or indirect supply or removal of heat in the catalyst bed is utilized to adapt the temperature profile over the flow path as far as possible to the requirements of an optimal reaction pathway. Here a clear developmental trend can be observed. 

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