Hyperstructure

Fig. 12.6. Schematic representation of the first three levels of a dynamical hierarchy, or, to use Baas term ([baas94] see below), hyperstructure. Level-1 is described by microscopic rules level-2 by second-order rules and so on.

Brown, N., Willett, R, and Wilton, D. J. (2003) Generation and display of activity-weighted chemical hyperstructures. J. Chem. Inf. Comput. Sci. 43, 288-297. 

Baas, N. A. (1994). Emergence, hierarchies, and hyperstructures. In Artificial Life 111, Santa Fe Studies in the Science of Complexity, ed. C. G. Langton, vol. XVII Addison-Wesley, pp. 515-537. 

In the next two sections we will present in detail the hyperstructure generation (i.e., step (i)) and the optimization model (i.e., step (ii)). 

The basic idea in postulating a Matches-HEN hyperstructure is to simultaneously embed ... 

Remark 1 The primary difference between the hyperstructure and the superstructure of Floudas et al. (1986) is that the superstructure presented on section 8.4.1.3 involved only the matches selected by the MILP transshipment model which represents the minimum number of matches criterion. In addition to the matches, we also have information on the heat loads of each match which is not the case with the hyperstructure where we do not know the matches, as well as their heat loads. 

As a result, the hyperstructure consists of stream superstructures in which HI has three matches, H2 has three matches, Cl has two matches, C2 has two matches, and CW has two matches. 

The hyperstructure for the illustrative example is shown in Figure 8.21 The variables also shown in Figure 8.21 are the unknown flow rates and temperatures of the streams. Note that the notation is based on capital letters for the hot streams (i.e., F, T) and lower case letters for the cold streams (i.e., /, t), while the superscripts denote the particular hot and cold streams. 

To identify a minimum investment cost configuration out of the many embedded alternatives in the Matches-HEN hyperstructure, we define variables for two major components ... 

The set of constraints for the simultaneous Matches-HEN hyperstructure will then feature ... 

B) The hyperstructure topology model plus the areas definitions, and... 

Part (B) Hyperstructure Topology Model and Area Definitions... 

Having defined variables for the flow rates and temperatures of the streams in the hyperstructure shown in Figure 8.21, we can write part (B) in a similar way to the superstructure model presented... 

The objective function of the simultaneous Matches-HEN hyperstructure problem can be written in two different ways depending on whether we substitute the expressions of the areas. 

Remark 3 For (ii)-(iv), the hyperstructure approach presented in the section of simultaneous matches-network optimization will be utilized. 

Remark 1 The hot and cold utility loads participate linearly in the objective function (i.e., operating cost), and linearly in the pseudo-pinch MILP transshipment model. They also participate linearly in the energy balances of the utility exchangers postulated in the hyperstructure. This linear participation is very important in the MINLP mathematical model. 

The set of constraints consists of the hyperstructure model presented in section 8.5.1.4 for the pseudo-pinch that is,... 

B) Hyperstructure topology model with area definition, and... 

In postulating the hyperstructure representation we will make the assumption only for simplicity of presentation, that the utility matches take place after the process-process matches. 

Remark 3 In the Ph.D. thesis of Ciric (1990), the full hyperstmcture was derived and formulated as an MINLP problem. However, since the part of hyperstructure which corresponds to cold stream Cl involves five matches, then the mathematical model will be complex for presentation purposes. For this reason we will postulate the part of the hyperstmcture of Cl by making the following simplification which eliminates a number of the interconnecting streams. This is only made for simplicity of the presentation, while the synthesis approach of Ciric and Floudas (1991) is for the general case. 

The hyperstructure of the illustration example with the above simplification for Cl is shown in Figure 8.27. 

Based on the hyperstructure presented in Figure 8.27 and the variables for the interconnecting streams (i.e., flow rates and temperatures), constraints (B) are written as follows ... 

Remark 4 The presented optimization model is an MINLP problem. The binary variables select the process stream matches, while the continuous variables represent the utility loads, the heat loads of the heat exchangers, the heat residuals, the flow rates and temperatures of the interconnecting streams in the hyperstructure, and the area of each exchanger. Note that by substituting the areas from the constraints (B) into the objective function we eliminate them from the variable set. The nonlinearities in the in the proposed model arise because of the objective function and the energy balances in the mixers and heat exchangers. As a result we have nonconvexities present in both the objective function and constraints. The solution of the MINLP model will provide simultaneously the... 

The heat integration alternatives consist of only the different matches that may take place and do not include structural alternatives of the heat exchanger network topology presented in the hyperstructure or superstructure sections of HEN synthesis. 

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