On the Minimum Number of Units in Heat Exchanger Networks

Abstract

The minimum number of units in a network has been proposed to be obtained using a very simple formula using graph theory ( HohmannE. C. Hohmann, E. C. Ph.D. Thesis, University of Southern California, Los Angeles, CA, 1971.; LinnhoffB. Linnhoff, B. Comput. Chem. Eng.19793295). This is done, usually, assuming that thermodynamic feasibility holds, especially in Pinch technology, where it is applied above and below the pinch, but also for cases where the pinch is ignored. While the failure of this formula is informally known in the community, to our knowledge no realistic counterexample was presented before. We provide such an industrial counterexample. In addition, we propose to use a recently developed MILP model (BarbaroA.BagajewiczM. Barbaro, A. Bagajewicz, M. Comput. Chem. Eng.2005291945) that guarantees finding the global minimum number of exchangers. Finally, we point out the large number of alternative solutions that real industrial problems may exhibit.

Globally optimal synthesis of heat exchanger networks. Part I: Minimal networks

“…Such definition almost always leads to a total number of units that is larger than N min (as defined above), and consequently these structures are rarely MSTR structures. Similarly, structures with nonisothermal mixing and with bypasses that cannot be represented by the staged superstructure have been studied and rendered values given by N min that are virtually impossible using other limited superstructures.Remark There have been several studies in the literature regarding the a‐priori calculation of the minimum number of units, sometimes referred to as minimum number of matches . Letsios et al presented a proof that the minimum number is N min = NH + NC + NHU + NCU‐L , where NHU and NCU are the number of hot and cold utilities types respectively and L ∈ [1, Min { NH + NHU , NC + NCU }].…”

“…Even after this limitation is introduced, they cannot obtain a solution directly, and have to rely on “approximation” algorithms.Remark We believe that the aforementioned works identify the problem as NP‐hard correctly, but only because of their incomplete formulation when multiple intervals are introduced. Bagajewicz and Valtinson showed that linear constraints can be added to solve the problem rigorously and globally using small computational time. The proposed procedure is a simplified version on an earlier MILP model and avoids the aforementioned NP‐Hardness by using a different modeling.Remark The above formula (Equation ) is a formula that does not consider thermodynamic constraints.…”

“…The proposed procedure is a simplified version on an earlier MILP model and avoids the aforementioned NP‐Hardness by using a different modeling.Remark The above formula (Equation ) is a formula that does not consider thermodynamic constraints. Bagajewicz and Valtinson discussed the issue and showed that there are structures that can accomplish this number of units. Moreover, as stated above, there are always uninteresting structures featuring no heat recovery.…”

“…Such cycles consist of path of vertices connected by edges in such a way that the path ends in the first vertex. In Pinch Design Technology language, these simple cycles are called energy “loops.” Q.E.D .Remark For E fixed, the value of EMAT used has no impact in the answer when a solution sought is a MSTR network. This is true regardless of the superstructure model used.…”

Synthesis of large‐scale heat exchanger networks using a T‐Q diagram method

“…Results show that their method can obtain a HEN with a minimum number of heat exchangers. Significant contributions made to improve the pinchbased method also include the revised rules for the unit targeting [8] and utility targeting, [9] the modified and extended problem tables, [10] and the advanced grand composite curves. [11] The pinch technology has been treated as a standard method for synthesis of HENs owing to its great success in industrial practice.…”