Inner Loop Property Models

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. 

Each time the simple model parameters are updated. A, and Kj are calculated on each stage by the rigorous property model. The base component b may either be a component in the feed or a hypothetical reference component whose A-value is calculated as some weighted average of the component A-values on each stage. The relative volatilities are calculated as A /A j and held constant until the next parameter update. The reference component Kj is calculated at two temperatures, such as and Tj, for calculating Aj and 5  

The enthalpies in the simple model are expressed as linear functions of the temperature  

---

As an example of how the approximate thermodynamic-property equations are handled in the inner loop, consider the calculation of K values. The approximate models for nearly ideal hquid solutions are the following empirical Clausius-Clapeyron form of the K value in terms of a base or reference component, b, and the definition of the relative volatility, Ot. 

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). 

Using the results of the converged inner loop, calculate the new /C-values and enthalpies by the rigorous thermodynamic property model. If these property values match the latest values used in the inner loop, the problem is solved. Otherwise, determine new values lor. 4, Bj, Cj, dj, ej,fj, Kji, and ocy using the rigorous thermodynamic property model, calculate new values for Rj,Rj, and Sj, and repeat the inner loop calculations starting at step 2. 

---