Outer Loop Property Models

These are rigorous, composition-dependent methods, generally based on equations of state and liquid activity coefficients (Chapter 1). The /f-values and enthalpies are ultimately functions of temperature, pressure, and composition  

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For each outer loop function and gradient evaluation 4 and 14 inner loop problems were solved respectively (a total of 124 inner loop problems). For the inner loop problems 12-14 iterations for Tasks 1 and 3 and 5-7 iterations for Tasks 2 and 4 were usually required. For this problem size and detail of dynamic and physical properties models the computation time of slightly over 5 hrs (using SPARC-1 Workstation) is acceptable. It is to note that the optimum number of plates and optimum recovery for Task 1 (Table 7.2) are very close to initial number of plates and recovery (Table 7.1). This is merely a coincidence. However, during function evaluation step the optimisation algorithm hit lower and upper bounds of the variables (shown in Table 7.1) a number of times. Note that the choices of variable bounds were done through physical reasoning as explained in detail in Chapter 6 and Mujtaba and Macchietto (1993). 

These are methods for calculating A -values and enthalpies in the inner loop. They are simple functions that use parameters derived from the rigorous property models. The parameters are updated at each outer loop iteration. 

Cj, dj, ej,fj, Kj, and from property values computed by the rigorous thermodynamic property model. This step marks the beginning of the outer loop. 

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