Nitrogen Cooling using N2 Refrigerant

Wi is the amount of work required by the compressor and VF,, the amount of work extracted from the i expander. 

The second objective is the minimization of total heat exchanger 

n2 and Pi,n2 represent the refrigerant pressure at the inlet and the exit, respectively, of each of the n expanders. The optimization is subject to the following constraints  

T is the final temperature of the cold product as shown in Fig. 8.9. The cold and hot pinch temperatures represent the temperatures on the cold and hot sides of a heat exchanger where the composite curves are the closest. If the condition in Eq. 8.7 is not true, then it means there is a temperature cross (or internal pinching) within the heat exchanger as shown in Fig. 8.10. When this occurs, the heat exchanger area (or capital cost) becomes infinite. Hence, Eq. 8.7 ensures a finite, positive temperature difference between the hot and cold composite curves (or, in other words, both composite curves are not overlapping as shown in Fig. 8.10). 

The Pareto-optimal solutions for the above optimization problem for nitrogen cooling are shown in Fig. 8.12. These results were obtained with NSGA-II after 400 generations with a population size of 100. The other GA parameters were crossover probability = 0.65, mutation probability = 0.25 and random number seed = 0.8. These values were chosen after around 15 trials with different values of the GA parameters, in order to get a very good spread of the Pareto-optimal solutions. 

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