Heat exchanger network splitting

Figure B.l shows a pair of composite curves divided into vertical enthalpy intervals. Also shown in Fig. B.l is a heat exchanger network for one of the enthalpy intervals which will satisfy all the heating and cooling requirements. The network shown in Fig. B.l for the enthalpy interval is in grid diagram form. The network arrangement in Fig. B.l has been placed such that each match experiences the ATlm of the interval. The network also uses the minimum number of matches (S - 1). Such a network can be developed for any interval, providing each match within the interval (1) satisfies completely the enthalpy change of a strearh in the interval and (2) achieves the same ratio of CP values as exists between the composite curves (by stream splitting if necessary).

Zamora, J. M. and I. E. Grossmann. A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with No Stream Splits. Comput Chem Eng 22 367-384(1998). 

Combinatorial. Combinatorial methods express the synthesis problem as a traditional optimization problem which can only be solved using powerful techniques that have been known for some time. These may use total network cost diiecdy as an objective function but do not exploit the special characteristics of heat-exchange networks in obtaining a solution. Much of the early work in heat-exchange network synthesis was based on exhaustive search or combinatorial development of networks. This work has not proven useful because for only a typical ten-process-stream example problem the alternative sets of feasible matches are cal.55 x 1025 without stream splitting. 

Heat exchanger network resilience analysis can become nonlinear and nonconvex in the cases of phase change and temperature-dependent heat capacities, varying stream split fractions, or uncertain flow rates or heat transfer coefficients. This section presents resilience tests developed by Saboo et al. (1987a,b) for (1) minimum unit HENs with piecewise constant heat capacities (but no stream splits or flow rate uncertainties), (2) minimum unit HENs with stream splits (but constant heat capacities and no flow rate uncertainties), and (3) minimum unit HENs with flow rate and temperature uncertainties (but constant heat capacities and no stream splits). 

Saboo, A. K., Morari, M., and Colberg, R. D., Resilience analysis of heat exchanger networks—Part II Stream splits and flowrate variations. Comp. Chem. Eng., 11, 457 (1987b). 

Figure 4.53 shows a possible matching between the hot and cold streams starting from the hot utility above the pinch. Based on these matchings, Figure 4.54 shows a heat exchanger network system. As there are a total of four hot and cold streams and a total of two hot and cold utility streams, from Eq. (4.233) we learn that we need a minimum of five heat exchangers. In the network, hot stream H2 is split into two. H2a has 58.1% of the hot stream H2 and heats the cold stream Cl, while H2b heats the cold stream C2. 

Synthesis of heat exchanger network (HEN) for minimum energy requirements and maximum heat recovery. Determine matches in subsystems and generate alternatives. Network optimisation. Reduce redundant elements, as small heat exchangers, or small split streams. Find the trade-off between utility consumption, heat exchange area and number of units. Consider constraints. 

The solution of this optimization problem provides the HEN shown in Fig. 20, where flow rates and temperatures are listed for the three operating periods. The areas of the heat exchangers are given in Table XII. Notice that there is splitting of cold stream Sc2 into two branches. Bypasses are also involved in stream Scl (match Shj—Sc]), stream Shl (match Shl-SC2), and stream Sh2 (match Sh2-Sc2). This network, which is feasible for the three operating periods that are considered, features a minimum investment cost of 196,900 and a minimum utility cost of 1.078/hour for operating period 1, 1.999/hour for period 2, and 0.9943/hour for period 3. 

Note also that the set of constraints (A)-(G) exhibit the nice feature of linearity in the continuous and binary variables. Furthermore, the flow rates do not participate in the formulation at all and hence there is a reduction in the number of continuous variables by the number of flowrates. The penalty that we pay for this desirable feature is threefold (i) we introduce more binary variables since we have possible process matches that are equal to the number of stages times the actual number of potential matches, (ii) we deal with a simplified set of alternatives that excludes a number of desirable structures, and (iii) we need to solve an NLP suboptimization problem to determine the flow rates of the split streams and possible reduce the number of heat exchangers if the resulting network exhibits splitting of the streams. 

In summary, six heat exchangers is the minimum for this network when it is required that the hot and cold utilities be minimized as well. As discussed in Section 10.4, the minimum number of heat exchangers for this system is five, which can be achieved either by breaking heat loops, usually at the price of exceeding the MER targets, or by stream splitting. ... 

Thus loops, utility paths, and stream splits offer the degrees of freedom for manipulating the network cost. The problem is one of multivariable nonlinear optimization. The constraints are only those of feasible heat transfer positive temperature difference and nonnegative heat duty for each exchanger. Furthermore, if stream splits exist, then positive bremch flow rates are additional constraints. 

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