ON INTRINSIC EXERGY EFFICIENCY AND HEAT PUMPS J. LABIDI, E. BOULET and J. PARIS Chemical Engineering Department, Ecole Polytechnique, Montre Âal, Que Âbec, Canada E xergy analysis provides an assessment of the degree of thermodynamic perfection of a process. Several exergy ef®ciency de®nitions have been proposed among which is the intrinsic ef®ciency which is based on the concept of transiting exergy. This method of analysis has been applied to absorption heat pumps and the results are presented. It is shown that when the analysis is limited to heat ¯uxes, the intrinsic exergy ef®ciency becomes equivalent to a particular case of the well known thermodynamic ef®ciency based on the second law analysis, which is simpler computationally and conceptually, and has a broader scope. Keywords: exergy analysis; heat pumps; intrinsic ef®ciency; transiting exergy; thermodynamic coef®cient; absorption heat pumps BACKGROUND The exergy ef®ciency of a process, g e , sometimes named after Grassman who ®rst introduced it 1 , is a simple and direct indicator of the degree of irreversibility of a process. It is de®ned as the ratio of exergy output, E 00 , to the exergy input, E 0 , to the system: g e = E 00 E 0 = 1 ê D int E 0 (1) The term D int is the exergy destroyed because of thermo- dynamic irreversibility in the process, also called the internal exergy losses. For example, in a process consisting of a single non reversible chemical reaction, the internal exergy losses increase as more matter is transformed, and the Grassman ef®ciency is a decreasing function of the chemical conversion 2 , as illustrated by curve I on Figure 1. Ideal, totally reversible processes are of little practical engineering interest. Attempts have been made recently to formulate an exergy ef®ciency coef®cient, which could be of more practical use to the design engineer. In this perspective, the intrinsic exergy ef®ciency, g i , was proposed by Brodyansky et al. 3 ; it expresses the ratio of the exergy which is actually produced by the system, E p , to the exergy actually consumed, E c , by taking into account the transiting exergy, E tr g i = E p E c = E 00 ê E tr E 0 ê E tr (2) The transiting exergy is the part of the exergy entering a system, which traverses it without taking part in any transformation. It was ®rst introduced by Kostenko 4 ; the concept is schematically illustrated in Figure 2. The intrinsic ef®ciency represents the capability of a system to actually utilize exergy to accomplish a given purpose. Equation (2) can be re-written in terms of the exergy losses: g i = 1 ê D int E c = 1 ê E 0 ê E 00 E 0 ê E tr = 1 ê D int E 0 ê E tr (3) If the transiting exergy decreases in a system, both Grassman and intrinsic ef®ciencies tend toward a common value, as illustrated in Figure 1. Since the intrinsic ef®ciency is a decreasing function of the exergy losses and an increasing function of the transiting exergy, it can exhibit an extremum. This happens in the case of a chemical system consisting of two competing reactions, as illustrated in Figure 3 5 . It should be noted, however, that there is no relationship between the intrinsic ef®ciency maximum and an engineering optimum based on techno-economic considerations. The transiting exergy can be computed for each type of exergy involved, i.e., chemical, thermomechanical, heat and work, following rigorous algorithms developed by Bro- dyanski et al. 3 . The method has been illustrated in a number of recent publications concerning primarily reaction or separation systems 2,3,5,6,7 . It has also been used to evaluate the thermodynamic ef®ciency of a chemical heat pump used as a chiller-heater 8,9,10 . For speci®c applications to heat cycles in which only heat ¯uxes are considered (i.e., when the mechanisms by which energy is transformed are not taken into account), the only form of exergy involved is thermal exergy. In this particular case, the analysis based on transiting exergy reduces to conventional entropy analysis, a fact that does not seem to have been observed in previous studies. This point is illustrated in the next section. INTRINSIC EXERGY EFFICIENCY OF HEAT PUMPS The transiting thermal exergy associated with a transfor- mation of heat ¯uxes (Q) between two temperature levels (T 0 and T 00 ) is given by the following equations 6 , depending on the relative positions of T 0 , T 00 and the temperature of the environment T 0 : T 00 $ T 0 ; T 0 $ T 0 , T min = min(T 0 , T 00 ), E tr = Q 1 ê T 0 T min = Qu min (4a) T 00 # T 0 ; T 0 # T 0 , T max = max(T 0 , T 00 ), E tr = Q 1 ê T 0 T max = Qu max (4b) 180 0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 78, Part A, March 2000