Hua Kailing, Li Yourun, Hu Shanying, Shen Jingzhu
(Department of Chemical Engineering, Tsinghua University, Beijing, 100084)

Received Oct. 20, 2000; Supported by the National Natural Science Foundation of China (29836140).

Abstract Based on the three-distribution-parameter general model for reactor network synthesis proposed earlier by the author, waste minimization target is included to realize source reduction in reactor network. The profit maximization design with waste minimization target can be formulated as a multi-objective optimization problem and e constraint technique is applied to convert it into a single objective optimization problem. After optimization, not only the reactor type and configurations can be directly decided according to the optimal solution of distribution parameters, but also the non-inferior curve can be attained. Two examples are studied and discussed.
Keywords three-distribution-parameter general model, reactor network synthesis, waste minimization

Reaction system is the most crucial part in the whole process integration for profit benefit and waste minimization. Due to the inherent complexity of the problem itself, the development of reactor network synthesis is still insufficient. Strategies exploited are chiefly heuristic and mathematical optimization approach. The later is more fitted in solving large-scale problems and become the main strategy.
    Two main branches of mathematical optimization approaches are superstructure approach and targeting approach. Superstructure approach is to propose an initial superstructure and to find a subsystem that produces the best result. Its advantages include the easiness in adding additional constraints and modifying objectives in the optimization calculation and the ability of simultaneous achievement of optimal objective and network. But global optimal solution is always available. Targeting approach is originated from attainable region concept suggested by Horn in 1964. Ever since then, two main branches have been developed: geometric approach and constructive targeting approach. Geometric region approach can provide physical insight into the problem to be studied but has serious dimension limitation. In constructive targeting, no initial networks are predetermined and instead a bound on the performance index is tried to find out. The optimal solutions are formed during a series calculation procedure.
    In this paper, based on the three-distribution-parameter general model proposed in an earlier paper (Hua et. al, 2000), multi-objective optimization strategy is exploited for the developed optimization framework to solve the waste minimization problem. Two case studies will be demonstrated on this approach.

1. GENERAL MODEL BASED OPTIMIZATION APPROACH
1.1 New general model for reactor network synthesis   
The importance of the influence of concentration profile and residence time distribution on reaction results demands on appropriate controlling ways. Three flow streams are chosen to define the macro mixing state and the connection ways in the reactor network. Each of them represents some specific characteristic of reactor network and further more give the comprehensive reflection of optimal network. For example, the side feeding strategy has great impact on concentration and resident time distribution; the recycling can represent different back mixing extent so as to decide the reactor type and the bypassing represents resident time distribution in the network and realizes parallel structure. But the boundaries between them are not clearly cut and they all can effectively increase conversion and reduce wastes. So the general model represented by them is capable of efficient expression for optimal concentration profile and residence time distribution. Figure 1 shows a schematic diagram for this general model. And it can also be called DRDSR, which is differential-recycling DSR.

Figure 1. Schematic diagram of new general model

Figure 2. Schematic diagram of ith discretized model

Above is just an ideal situation and results attained from it can not be directly realized. Then one possible discretized reactor network model can be is derived, as Figure 2 shows. Theoretically speaking, the discretized model can infinitely approach the primal model when segment number goes to infinite.

1.2 Optimization problem developed             
Based on above general model, an optimization model P1 to solve reactor network synthesis problem is built. The objectives are generally the function of exit concentrations and mean residence time. The Constraints consist of material balances and logical constraints on distribution parameters. In P1, equation (1) is differential mass balance expression. Equation (2) is initial feed condition. Equation (3) is exit concentration expression. Equation (4) and (5) is normalization of  f(t) and q(t). Equation (6) is expression for mean residence time.

P2
     

In P2, Equations (1) to (3) are expression for concentrations at knots. Equation (4) is expression for temporary mixed concentration. Equation (5) is the exit concentration expression. Equation (6) to (7) is normalization expression Equation (8) is expression for mean residence time. Inequality constraints (9) to (10) are constraints on distribution parameters.

3. EXAMPLE PROBLEMS
3.1 Williams-Otto reaction system            
Reactions and reaction rate expression for A, B, C, P, E and G is given as:

Table 1. Two limiting points of the noninferior curve

Figure 3. Noninferior curve for Williams-Otto

Figure 4. Noninferior curve for Van-de-Vusse

Reaction equations and reaction rate expression for A, B and C is given as:

B is product and D is assumed to be waste because it has great impact on the conversion of A to B as important reaction. Following the same procedure with the maximization of B we can attain the noninferior curve as figure 4 shows. From the results it can be seen that when the D upper level decreases, the global recycling ratio increase accordingly. Unlike the complex situation in example 1, the change of noninferior curve is quite smooth.

4. CONCLUSION
From the results, it can be concluded that since the side feeding, recycling and bypassing strategy can give a comprehensive reflection of optimal characteristic of the reactor network and the source reduction measure within the reactor network, it can be effectively applied into waste minimization targeted design. The waste minimization objective is stressed especially in this paper, which shows in two aspects: outer multi-objective optimization to minimize waste level and inner source reduction realization by two distribution side streams of side feed, recycling. So they can effectively reduce the waste and provide good start point to realize source reduction. Then multiobjective optimization is used to realize source reduction and yield maximization at the same time to promote the profitability and environmental acceptability of reactor network. In a conclusion, the three-distribution-parameters general model can provide an effective tool to realize source reduction design to clean process.