Minimum Utility Targets

Two cold streams. Cl and Cl, are to be heated and two hot streams, HI and H2, are to be cooW without phase change. Their conditions and properties are as follows  

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Minimum Utility Targets Using Mathematical Programming (Optimization)... 

Gupta, A., and Manousiouthakis, V. (1993). Minimum utility cost of mass exchanger networks with variable single component supplies and targets. Ind. Eng. Chem. Res. 32(9). 1937-1950. 

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. 

Target (ii) was addressed rigorously by Cerda and Westerberg (1983) as a Mixed Integer Linear Programming MILP transportation model and by Papoulias and Grossmann (1983) as an MILP transshipment model. Both models determine the minimum number of matches given the minimum utility cost. 

The minimum utility cost target problem of HENs can be stated as ... 

Remark 1 The above-mentioned target can be stated as the minimum utility consumption problem. We have stated it as minimum utility cost so as to distinguish the effect of multiple hot and cold utilities. This way, by assigning a different cost for each type of utility (e.g,. fuel, steam at... 

The target of minimum utility cost in HENs can be formulated as a linear programming LP transshipment model which corresponds to a well known model in operations research (e.g., network problems). The transshipment model is used to determine the optimum network for transporting a commodity (e.g., a product) from sources (e.g., plants) to intermediate nodes (e.g., warehouses) and subsequently to destinations (e.g., markets). 

In the previous section we discussed the minimum utility cost target and its formulation as an LP transshipment model. The solution of the LP transshipment model provides ... 

A useful target postulated so as to distinguish among the many HENs that satisfy the minimum utility cost is the minimum number of matches problem which is stated in the following section. 

Given the information provided from the minimum utility cost target (i.e., loads of hot and cold utilities, location of pinch points, and hence subnetworks), determine for each subnetwork the minimum number of matches (i.e., pairs of hot and cold process streams, pairs of hot utilities and cold process streams, pairs of cold utilities and hot process streams, and pairs of hot-hot or cold-cold process streams exchanging heat), as well as the heat load of each match. 

In section 8.3.2.2 we discussed the MILP transshipment model for the minimum number of matches target. For a given minimum utility cost solution (i.e., given HRAT s, QSi, QWj, location of pinch points and hence subnetworks), the solution of the MILP transshipment model, which is applied to each subnetwork provides ... 

The key question that arises at this point is how we can determine a HEN configuration that satisfies the criterion of minimum investment cost subject to the information provided by the targets of minimum utility cost and minimum number of matches applied in sequence. 

Applying the LP transshipment model for the minimum utility cost target yields ... 

Remark 1 The above statement corresponds to the simultaneous consideration of all steps shown in Figure 8.20, including the optimization loop of the HRAT. We do not decompose based on the artificial pinch-point which provides the minimum utility loads required, but instead allow for the appropriate trade-offs between the operating cost (i.e., utility loads) and the investment cost (i.e., cost of heat exchangers) to be determined. Since the target of minimum utility cost is not used as heuristic to determine the utility loads with the LP transshipment model, but the utility loads are treated as unknown variables, then the above problem statement eliminates the last part of decomposition imposed in the simultaneous matches-network optimization presented in section 8.5.1. 

Section 8.4 presents a decomposition-based approach for the HEN synthesis. Section 8.4.1 discusses an approach for the automatic generation of minimum investment cost HENs that satisfy the targets of minimum utility cost and minimum matches, and section 8.4.2 outlines the decomposition-based synthesis strategy. Further reading in this subject can be found in the suggested references. 

A.E.S. Konukman, M.C. Camurdan, U. Akman, Simultaneous flexibility targeting and synthesis of minimum-utility heat exchanger networks with superstructure-based MILP formulation, Chem. Eng. Processing 41 (2002) 501-518. 

The other feature to note regarding the cascade in Fig. IIB is the point where the heat flow becomes zero. This is at an interval temperature of 75°C. This corresponds to the location of the pinch. Given that the interval temperature for the pinch is 75°C, the hot stream pinch temperature is therefore 80° C and the cold stream pinch temperature 70° C. This agrees with the location of the pinch from the composite curves. Thus, the problem table algorithm provides the information required for minimum hot and cold utility targets and the location of the pinch that is critical in the next step, which is to design to achieve the targets. 

Minimum Energy Requirements (MER) as utility targets for heat recovery. 

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