Optimal assignment of multiple utilities in heat exchange networks

Abstract

Existing numerical geometry-based techniques, developed by [A.I.A. Salama, Numerical techniques for determining heat energy targets in pinch analysis, Computers & Chemical Engineering 29 (2005) 1861–1866; A.I.A. Salama, Determination of the optimal heat energy targets in heat pinch analysis using a geometry-based approach, Computers & Chemical Engineering 30 (2006) 758–764], have been extended to optimally assign multiple utilities in heat exchange network (HEN). These techniques utilize the horizontal shift between the cold composite curve ( CC) and the stationary hot CC to determine the HEN optimal energy targets, grand composite curve ( GCC), and the complement grand composite curve (CGCC). The proposed numerical technique developed in this paper is direct and simultaneously determines the optimal heat-energy targets and optimally assigns multiple utilities as compared with an existing technique based on sequential assignment of multiple utilities. The technique starts by arranging in an ascending order the HEN stream and target temperatures, and the resulting set is labelled T . Furthermore, the temperature sets where multiple utilities are introduced are arranged in an ascending order and are labelled T ic and T ih for the cold and hot sides, respectively. The graphical presentation of the results is facilitated by the insertion at each multiple-utility temperature a perturbed temperature equals the insertion temperature minus a small perturbation. Furthermore, using the heat exchanger network (HEN) minimum temperature-differential approach (Δ T min) and stream heat-capacity flow rates, the presentation is facilitated by using the conventional temperature shift of the HEN CCs. The set of temperature-shifted stream and target temperatures and perturbed temperatures in the overlap range between the CCs is labelled T ol . Using T ol , a simple formula employing enthalpy-flow differences between the hot composite curve CC h and the cold composite curve CC c is used to determine the horizontal shift (bias) B between the CCs. In the overlap range, the Bs are determined at all temperatures in set T ol to generate the bias set B . The maximum value of B’s in set B , B*, is used in an optimization scheme to determine the optimal assignment of multiple utilities, optimal heat- energy targets, grand composite curve ( GCC), and the complement grand composite curve ( CGCC) (Salama, 2009), if needed. It should be pointed out that the optimal heat-energy targets and optimal multiple utilities are needed in heat-pinch analysis. The motivations for the present work is to complement the work of Shenoy [U.V. Shenoy, A. Sinha, S. Bandyopadhyay, Multiple utilities targeting for heat exchanger networks, Trans Institution of Chemical Engineers Part A, 76 (1998) 259–272], by approaching the multiple-utility targeting not sequential but rather in a direct manner. Furthermore, the proposed technique builds on the strengths of the numerical techniques developed by Salama [A.I.A. Salama, Numerical techniques for determining heat energy targets in pinch analysis, Computers & Chemical Engineering 29 (2005)1861–1866; A.I.A. Salama, Determination of the optimal heat energy targets in heat pinch analysis using a geometry-based approach, Computers & Chemical Engineering 30 (2006) 758–764], which are different from the conventional one that starts with the problem table algorithm ( PTA). The proposed technique starts with the determination of the optimally positioned CCs and then proceeds to determine the optimal heat energy targets, heat pinch-point location, grand composite curve ( GCC), complement grand composite curve ( CGCC) [A.I.A. Salama, Numerical construction of HEN composite curves and their attributes, Computers & Chemical Engineering, 33 (2009) 181–190], and optimal assignment of multiple utilities. Moreover, the proposed numerical technique can handle both quasi-linear CCs and CCs exhibiting discontinuities (assuming the critical lower bound on Δ T min , Δ T min c , is known) hence, it is more robust and versatile and avoids the lumping and cascading stages in the PTA. It should be emphasized that the optimal heat loads are determined using the HEN CCs. The associated optimization problems are implemented using Microsoft Excel TM and are solved using the “solver” module embedded in Excel. Published data set has been used to demonstrate the paper results.