Simultaneous HEN synthesis

Mathematical programming for HEN synthesis was developed from the early attempts of e.g. by Kesler and Parker (1969) to solve the HEN synthesis problem as an assignment problem, through the sequential transportation and transhipment models of Cerda and Westerberg (1983) respectively Papoulias and Grossmann (1983) and the three-step model of Floudas et al. (1986), to the simultaneous HEN synthesis model of Yee and Grossmann (1990). 

This chapter focuses on heat exchanger network synthesis approaches based on optimization methods. Sections 8.1 and 8.2 provide the motivation and problem definition of the HEN synthesis problem. Section 8.3 discusses the targets of minimum utility cost and minimum number of matches. Section 8.4 presents synthesis approaches based on decomposition, while section 8.5 discusses simultaneous approaches. 

In this section we will focus on addressing the difficulties arising in the first two tasks of sequential HEN synthesis and we will discuss simultaneous approaches developed in the early 90s. More specifically, in section 8.5.1 we will discuss the simultaneous consideration of minimum number of matches and minimum investment cost network derivation. In section 8.5.2 we will discuss the pseudo-pinch concept and its associated simultaneous synthesis approach. In section 8.5.3, we will present an approach that involves no decomposition and treats HRAT as an explicit optimization variable. Finally, in section 8.5.4, we will discuss the development of alternative simultaneous optimization models for heat integration which address the same single-task HEN problem as the approach of section 8.5.3. 

Simultaneous Optimization Models for HEN Synthesis 8.5.4.1 Problem Statement... 

Remark 1 The problem statement is identical to the problem statement of section 8.5.3.1 for the synthesis of HENs without decomposition (Ciric and Floudas, 1991). Note that as in section 8.5.3.1, there is no specification of any parameters so as to simplify or decompose the original problem into subproblems. In other words, the level of energy recovery (specified by fixing H RAT), the minimum approach temperature (EM AT), and the number of matches are not specified a priori. As a result, there is no decomposition into subnetworks based on the location of the pinch point(s), but instead the pinch point(s) are optimized simultaneously with the matches and the network topology. The approach presented for this problem is from Yee and Grossmann (1990) and is an alternative approach to the one of HEN synthesis without decomposition proposed by Ciric and Floudas (1991), and which was presented in section 8.5.3. 

The basic idea in the simultaneous optimization approach for HEN synthesis of Yee and Grossmann (1990) consists of... 

Most of the existing HEN synthesis methods rely on either heuristic rules (for example, pinch analysis method [2]) or mathematical programming (for example, simultaneous optimization approach [3-6]). And further, to some typical objectives considered in the HEN synthesis such as utility consumption, total number of matches, and total exchanger area, the flexibility of the HENs for feasible operation under possible variation of source-stream temperatures and/or heat-capacity flow rates has been emphasized in some recent articles [6-10]. For HEN synthesis, the analysis of this flexibility, defined as the size of the region of feasible operation in the space of desired or undesired deviations of pa-... 

In this paper, we extend the work of [10] by simultaneously considering minimization of the total utility consumption, maximization of operational flexibility to source-stream temperatures, and even minimum number of matches as multiple design objectives. The flexible HEN synthesis problem is thus formulated as the one of multi-objective mixed-integer linear programming (MO-MILP). This formulation also assumes that the feasible region in the space of uncertain input parameters is convex, so that the optimal solution can thus be explored on the basis of the vertices... 

In this paper, the targeted source-stream temperatures are directly treated as individual design objective, and the multi-criteria optimization approach is adopted for HEN synthesis. The minimizing utility and the maximizing operational flexibility can be simultaneously considered as two conflict objectives for synthesis of the network structure. Furthermore, other targets such as minimizing number of matches can also be considered, such as,... 

Results of HEN synthesis for example 1 using two-phase optimization when simultaneously considering minimal utility and maximal flexibility (cases I-IV), and additional objective of minimal units (cases V and VI) with different preference intervals, and with or without considering restriction on heat loads at vertices (a = ft = 0.6)... 

Due to the interaction of mass and heat in the CHARMEN, one should synthesize the MEN and the HEN simultaneously. This section presents an optimization based method for the synthesis of CHARMEN s". Two key assumptions are invoked ... 

The primary limitation however of sequential synthesis methods is that different costs associated with the design of HENs cannot be optimized simultaneously, and as a result the trade-offs are not taken into account appropriately. Early decisions in the selection of HRAT and partitioning into subnetworks affect the number of units and areas of the units in the HEN configuration. Therefore, sequential synthesis methods can often lead to suboptimal networks. 

Detailed reactor and detailed separator model, modified model for the simultaneous synthesis of heat integrated HEN (Yee and Grossmann, 1990). 

More detailed heat integration with different utilities (cold water, refrigerator, steam), restrictions and forbidden matches was carried out simultaneously with the synthesis of the reactor/separator/HEN network. Reactors were modelled as adiabatic reactors due to practical constraints. 

The steps required to convert mevalonic acid to the active-isoprenoid intermediate have been worked out with some assurance. The initial step involves the phosphorylation of mevalonic acid to mevalonic acid-5-phosphate by an enzyme called mevalonic kinase. This enzyme was found in yeast by Tchen (1958). The properties of the mevalonic kinase of liver have been described in detail by Levy and PopjAK (1960). The kinase is inhibited by p-chloromercuribenzoate but not by iodoacetamide. The enzyme requires Mg++, Mn++, or Ca++ and ATP or inosine triphosphate. The kinase is specific for the (+) form of mevalonic acid. Mevalonic acid-5-phosphate is phosphorylated further to give mevalonic acid-5-pyrophos-phate (de Waard and Popjak, 1959 Henning et al. 1959). The purified enzyme (Bloch et al., 1959) requires a divalent metal ion for activity (Mg++ is preferable) and has no pronounced pH optimum. Mevalonic acid pyrophosphate then undergoes simultaneous dehydration and decarboxylation to yield isopentenylpyro-phosphate (Lynen et al., 1958 Chaykin et al., 1958). The enzyme concerned with the dehydration and decarboxylation has been purified (Bloch et al., 1959) and shown to have a pH optimum between 5.5 and 7.4 and to require a divalent metal ion (Mg++, Mn++, Fe++ or Co++). The series of reactions in which mevalonate is converted to isopentenylpyrophosphate is outlined in Figure 6. Brodie et al. (1963) have established a new pathway for the biosynthesis of mevalonic acid from malonyl CoA. The importance of this particular pathway in the synthesis of sterols is still unknown. 

---