Determination of the optimal heat energy targets in heat pinch analysis using a geometry-based approach

Abstract

A simple and direct numerical technique is proposed to determine the optimal heat energy targets in heat pinch analysis. The technique is based on a geometrical approach, i.e., utilization of the horizontal shift between the cold composite curve (CC) and the stationary hot CC. The stream and target temperatures of the streams are a subset of an ordered set to form the overall temperature range ▪. If the temperature subinterval in the overlap region of the CCs is equal to the minimum temperature differential Δ T min, simple formulas that utilize the enthalpy flow values can be used to determine the corresponding horizontal shift (bias) B between the CCs . In the overlap range, Bs are determined at all points on one CC and other points on the other CC using Δ T min to form the set ▪. The maximum value of Bs in set ▪, B*, is used to determine the optimal heat energy targets. If the temperature subinterval in the overlap range is not equal to Δ T min, the conventional temperature shift of the CCs is employed first and the resulting stream and target temperatures of the streams are set ▪. In this case the same algebraic formulas are applicable. Heat pinch locations at end points or on a parallel section on the CCs are discussed. It is shown, again, that the same algebraic formulas are applicable. The proposed technique is different from the conventional one since it starts with the determination of the optimally positioned CCs and then proceeds to determine the optimal heat energy targets, heat pinch point location, and grand composite curve (GCC). In the conventional heat pinch analysis, the problem table algorithm (PTA) is employed first. Furthermore, the present technique is conceptually different from the PTA and the simple problem table algorithm (SPTA) since it is developed based on a geometrical approach not energy cascade over the overlap temperature subintervals. While the PTA and SPTA are only applicable using temperature-shifted data the proposed geometry-based technique is applicable to both shifted- and unshifted-temperature data sets. Moreover, the proposed numerical technique can handle both quasilinear 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.