Optimal distribution of temperature driving forces in low‐temperature heat transfer

Abstract

A fairly extensive review of research on optimal distribution of driving forces in heat-transfer processes is provided. Four different guidelines for specifying the temperature profiles in heat exchangers have been compared. Not surprisingly, the irreversibilities due to heat transfer in a heat exchanger of given size were found to be minimized when the temperature difference is proportional to the absolute temperature. Comparing a design with an optimal temperature profile and a design with a uniform temperature difference throughout the heat exchanger, sensitivity analyses illustrated that savings in irreversibilities increase with decreasing temperature level and increasing temperature span for the cooling load. Heat exchanger size was found to be of negligible importance. The results indicated that optimal utilization of heat exchanger area is of little importance for processes operating above ambient temperature, while significant savings can be obtained by optimal distribution of temperature driving forces in processes below ambient temperature. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 2447-2455, 2015 Keywords: process design, heat transfer, driving forces, exergy of heat, heat exchanger IntroductionBesides environmental and social aspects, process plants are designed and operated with the purpose of seeking return on investments.1 Hence, economic criteria are required to evaluate different design options and carry out optimization. 2In an early phase of process design, it is normally not possible to account for all fixed and variable costs.2 When comparing the relative merits of different structural options in a flow sheet and parameter settings, the economic criteria can be simplified by neglecting common items. 2The thermodynamic performance of a heat exchanger and thereby the energy cost related to operation can be improved by reducing its temperature driving forces. This does, however, require increasing the heat exchanger size and thereby the investment cost. In heat exchanger network synthesis and design, this conflict is often accommodated by assigning a minimum temperature difference in the heat exchangers.2,3 The minimum temperature difference is then used as an economic trade-off parameter, balancing the operating cost related to energy use and the investment cost of heat exchangers.This approach has been adopted in many studies for design of cryogenic refrigeration processes such as liquefaction of natural gas. 4 However, as pointed out by Jensen and Skogestad, 4 the use of a minimum temperature difference constraint in optimization of natural gas liquefaction processes leads to nonoptimal utilization of the heat exchanger area. This indicates that a design strategy aiming at uniform temperature difference throughout the heat-transfer process gives nonoptimal distribution of temperature driving forces. This is related to the behavior of exergy of heat, which increases steeply with decreasing temperature below ambient.Different design guidelines for optimal distribution of t...

Impact of problem formulation on LNG process optimization

“…, the irreversibilities associated with heat transfer increase both with increasing temperature difference and decreasing temperature level, indicating the importance of keeping the temperature driving forces small at low temperature levels. This is in line with Austbø and Gundersen, suggesting that optimal distribution of the temperature driving forces is of particular importance when the heat‐transfer process takes place at low temperature levels and/or over a wide temperature range. This is highly relevant for LNG processes, suggesting that the minimum temperature difference constraint frequently used in literature would lead to nonoptimal distribution of heat‐transfer area and therefore not serve as a suitable economic trade‐off parameter.…”

“…As opposed to the simple heat exchanger studied by Austbø and Gundersen, the performance of the heat exchanger in an LNG process must be balanced with the performance of the other unit operations. In the following, the irreversibilities of the different pieces of equipment in the simple PRICO ® process of Figure will be presented as function of the UA.…”

“…For a simple heat exchanger, Austbø and Gundersen compared the irreversibilitites in a design with uniform temperature difference throughout the heat exchanger and a design with the temperature difference being proportional to the temperature level. The results indicated that the energy penalty of the former design was nearly independent of the heat exchanger size (within a reasonable range of values).…”

“…The superiority of the maximum UA constraint is only partly explained by the fact that the temperature difference in heat exchangers should be proportional to the temperature level at which heat is transferred (as illustrated by Austbø and Gundersen). For optimal utilization of the heat exchanger area, the trade‐off parameter should also be able to account for the nonlinearity of the composite curves and the trade‐off between temperature driving forces and heat exchanger cooling load.…”

“…Comparing different strategies for design of heat exchangers, Austbø and Gundersen found that a design where the temperature difference in the heat exchanger is proportional to the temperature level, as suggested by Bejan, Xu, and Chang et al among others, gives the smallest irreversibilities associated with heat transfer. The potential savings in energy use, compared to a design with a uniform temperature difference throughout the heat‐transfer process, were found to increase with decreasing temperature level and/or increasing temperature span.…”