(185ad) Design of Optimal Multistage Heat Exchange Networks

N.N. Ziyatdinov, I.I. Emelyanov, A.N. Bezrukov, and D.V. Kubanov

Kazan National Research Technological University, Kazan, Russia

nnziat@yandex.ru

Development of an optimal heat exchange system is a complex combinatorial problem with a large number of dimensions due to multiple heat sources and outputs in technological units. The studies in the last several decades resulted in the development of a series of approaches and methods of heat integration which provide significant decrease in the value of the sum of capital and energy costs. We offer a series of modifications of a classic decomposition approach of the mathematic programming which is related to the “assignment” problem. It should be considered as a multilevel iteration procedure with the method of fixing of intermediate variables. The lower level activities are the search and optimization of structurally interconnected units which cool the “hot” flows and heat the “cold” flows to the given temperatures. To formalize the heat exchange optimal economy problem, each pair of technological flows is offered to be related to a certain superstructure of heat exchangers with a set of structural subunits – elementary blocks of a heat exchange system [1]. An elementary block is a structural subunit allowing transfer of a certain given amount of heat to the j-th “cold” flow and the extraction of a certain given amount of heat from the i-th “hot flow”. The problem of optimization of elementary blocks of a heat exchange system can be solved by nonlinear mathematic programming models with the limitations to an admissible force of a heat exchange process.

The second solution level of the discrete linear programming “assignment” problem is finding the single stage heat exchange system structure. A single stage heat-exchange system as a system with a single j-th “cold” flow assigned to the each i-th “hot” flow. The optimal structures of elementary blocks of a heat exchange system and control variables are found for a set of such systems. The input data for such a problem are the matrix of economic evaluations obtained at the lower level. A multistage heat exchange system can be represented by a sequence of single stage heat exchange systems with each i-th “hot” flow able to transfer its thermal energy to several “cold” flows, while each j-th “cold” flow is able to accept thermal energy several “hot” flows. To solve the problem of synthesis of optimal multistage heat exchange systems, we offer to develop an iteration procedure with such search variables as the amount of heat taken from the i-th “hot” flow and transferred to the j-th “cold” flow at the each stage. The third level will be dedicated to the optimization of the heat exchange system with the structure obtained at the previous step. The result will be the determination of new approximations by the search variables.

Let’s install splitters at a heat exchange system inputs at each i-th “hot” and j-th “cold” flows and mixers at its output. We will obtain a heat exchange system with the division of process flows. The optimal synthesis problem statement will in this case be reduced to the previous one by the structural modification and expansion of a single stage heat exchange system. The “assignment” problem is offered to be supplemented by the estimations including or excluding the recuperating heat exchange for the each set of the l-th part of the i-th “hot” flow and the k-th part of the j-th “cold” flow. Such an approach will obviously increase the heat transfer moving force.

The efficiency of the proposed method is compared to the results obtained with SYNHEAT software [2] by the method of integral synthesis of heat exchange systems.

[1] Ziyatdinov N.N., Ostrovskii G.M., Emel’yanov I.I. Designing a Heat-Exchange System upon the Reconstruction and Synthesis of Optimal Systems of Distillation Columns // Theoretical Foundations of Chemical Engineering. 2016. V. 50. № 2. P. 178.

[2] Ponce-Ortega, J. Optimal synthesis of heat exchanger networks involving isothermal process streams / J. Ponce-Ortega, A. Jimenez-Gutierrez, I. Grossmann // Comput. Chem. Eng. 2008. № 32. Р. 1918.