Exergetic Temperatures for Exergy Targeting

This work presents a methodology for targeting heat and power consumption in energy intensive processes (such as refrigeration cycles, power plants and heat recovery systems). The methodology uses process integration and exergy analysis as tools to obtain minimum exergy consumption and minimum losses (including exergy destruction). By decomposing the thermo-mechanical (physical) exergy of material streams into their pressure and temperature based exergies, it is possible to independently calculate the targets for power and heating systems. Besides, the identification of exergy sources and sinks becomes evident and easy to calculate. Exergy is neither linear with temperature nor with pressure. Actually, pressure is involved in rather complicated relations with temperature and exergy; however, it can be simplified by assuming ideal gas conditions. Under these circumstances, the decomposition of thermo-mechanical (physical) exergy is sharp and there is no dependency of temperature in the pressure based exergy. The targeting method utilizes this sharp split to independently manipulate the exergy components in order to get a linear relation with the specific heat capacity and an Exergetic Temperature. Therefore, changes from one exergetic temperature to another (i.e. for heat exchange without pressure drop) will be represented by a straight line in an Exergetic Temperature – Exergy diagram (T^e - E). By definition, the exergy of a system is the maximum ability to produce work, thus it measures the thermodynamic quality of energy. Parameters, such as the Carnot factor, give indication of the level of the exergy; large figures indicate high exergy levels and consequently low figures indicate low exergy levels. The Exergetic Temperatures are also indicators of exergy level. Thus, T^e – E diagrams illustrate the level and availability of exergy in material streams, allowing better understanding of the exergy transfer, and this insight can be used to improve process systems.

For processes where heat and power are intimately related, such as Low Temperature Processes (LTPs), exergy seems to be a perfect evaluator for the conceptual design procedure. A new Exergy Transfer Effectiveness (ETE) is proposed for the calculation of a Coefficient of Exergy Performance (CEP) for processes above, below and across ambient temperature. Previous CEPs will be briefly commented. The ETE utilizes the simple concept of sources and sinks; however, due to the special behavior of temperature based exergy in some operating conditions (below and across ambient temperature), the recognition of these sources and sinks can be difficult. A general rule is presented for the identification of exergy sources and sinks in processes, where only thermo-mechanical (physical) exergy is under transformation. For any process stream subject to change in exergy, from state a (T_a, p_a) to state b (T_b, p_b) without crossing ambient temperature, it is established that all negative changes in exergy (ΔE_a-b = E_b − E_a), or in its components, are categorized as exergy sources (except for the change in pressure based exergy due to pressure drop), while positive changes in exergy represent exergy sinks. If the operating conditions of the process or unit are across T₀ (i.e. compressors in refrigeration cycles), an intermediate state i (T₀, p_i) is introduced, resulting in the existence of one source (from state a to i) and one sink (from state i to b) for the change in temperature based exergy.

Two simple case studies are used to illustrate the methodology and its capabilities. The first case is a simple heat recovery system with two hot streams and two cold streams where pressure drop is neglected. The heat exchange takes place above ambient conditions (T₀, p₀). The second case study is a reverse Brayton cycle utilized for the liquefaction of natural gas.