Thermodynamic analysis of a Carbon Carrier Cycle (CCC) for low temperature heat recovery

. The aim of the paper is to study the thermodynamic behavior of a non-conventional power cycle, named Carbon Carrier Cycle (CCC), which is expected to obtain interesting performance with low temperature heat source. The CCC may be regarded as derived from an absorption machine, where an expander replaces the condenser, the throttling valve and the evaporator. The working fluid is a mixture of CO 2 and a proper absorber. In the paper, the thermodynamic model of this kind of cycles is described, and the results obtained considering Acetone as the absorber are discussed. A first performance comparison is then conducted with a more conventional Organic Rankine Cycle (ORC).


Introduction
In recent years, interest for the total efficiency of complex energy systems has grown considerably. In this perspective, the recovery of waste heat output flows may be quantitatively important and CHP is a wellknown and widely used approach. On the other hand, there are a lot of situations where the low temperature heat cannot be usefully consumed. In these cases, the total efficiency of the system may be improved by adopting a bottom power cycle, which uses the low temperature heat as the input for producing some additional power. An ORC is a possible solution, adopting a proper working fluid. The conversion efficiency of such a bottom cycles is necessary low. If the temperature of the recovered heat and that of the cooling medium in the condenser are considered to be 90°C and 25°C, respectively, the maximum theoretical efficiency (i.e. the Carnot efficiency) is less than 18%, therefore the expected actual efficiency is much lower in any case. The aim of the paper is to evaluate the behavior and the performance expected for a non-conventional kind of cycle, named Carbon Carrier Cycle (CCC) [1]. A CCC may be regarded as derived from an absorption machine, where an expander replaces condenser, throttling valve and evaporator. The working fluid in the expander is pure CO2, or a mixture rich of CO2.

* Corresponding author: taccani@units.it
The CCC may be regarded as a particular case of Absorption Power Cycle (APC), the most famous of which is certainly the Kalina Cycle [2]. These power cycles are characterized by the adoption of a mixture as working fluid, instead of a pure substance, which passes through different concentrations during the energy conversion process, so that absorption-desorption processes are necessary involved.
In a CCC, the CO2 is absorbed into a liquid phase at an equilibrium temperature defined by the cooling fluid and it is released at higher pressure at an equilibrium temperature defined by the thermal level of the recovered heat. In this arrangement, the expansion in the turbine or in the volumetric expander can be extended to the pressure inside the absorber, which corresponds to the equilibrium condition of the mixture (CO2 plus the absorbent), not to the phase change equilibrium pressure of the expander working fluid alone. This feature may positively affect the efficiency of the cycle, with respect to more conventional solutions.
A review of different APC can be found in Novotny et al. [3], [4]. In the CCC the working fluid is a mixture of CO2, as previously said, and some organic compound, like ammines or ketones [5]. In this paper in particular, a binary mixture of Acetone and CO2 is considered, because the former can be mixed in very variable percentages, making it possible to analyze the use of different mixtures from the point of view of the CO2 content.
In the paper the thermodynamic model of a CCC is described, and the results obtained varying the main design parameters are discussed, for different temperature levels of the recovered heat. A first performance comparison is then conducted with an ORC using Acetone as working fluid.

Model of the cycles
In the following, the model of the CCC is described in some details, together with a brief presentation of the ORC model, introduced for performance comparison. They are both simple thermodynamic models, based on the energy balance equation of each component and on the assumption of suitable constant efficiencies values for pumps and expanders. Heat and pressure losses are neglected.
To carry on the comparison between CCC and ORC, common temperature ranges are considered for the heat source and the heat sink, neglecting the parasitic consumptions required for moving the hot and cooling fluids trough the necessary heat exchangers. In this way, the comparison results independent by the specific heat recovery application. In fact, the parasitic consumption may be very different if the low temperature power cycle is applied for the heat recovery from an on board ICE for ship propulsion, with a see water cooled condenser, instead of to the power production of a concentrated solar system, with an air cooled condenser.
The cycle working fluid temperature in the correspondence of the heat sink is considered in the range 15-45°C, whilst those in the correspondence of the heat source varies in the range 90-150°C. The design efficiencies of pumps and expanders have been regarded as not affected by those temperature ranges and are equal to:  pump isentropic efficiency: 0.8;  expander isentropic efficiency: 0.8;  mechanical efficiencies: 0.9;  electric efficiency: 0.95.  Fig.1 shows the scheme of the CCC chosen for the analysis. A liquid mixture at the maximum concentration of solute is pumped to the vapour generator, after being heated in a recuperator. The vapour generator is a desorber, which can be modelled in different ways as better discussed in the following. The desorber generates a vapour flow at high solute concentration and a liquid flow at low solute concentration. The first passes through an expander generating mechanical-electrical power. The second is cooled in the recuperator before being laminated in a pulveriser. The two flows mix at low temperature and pressure in the absorber, and the resulting liquid mixture is sent to the pump suction, thus closing the cycle. Heat is exchanged with the heat source in the desorber and with the heat sink in the absorber.

The model of the CCC
The main design variables are the temperature of the vapour flow exiting the desorber, Tvap, and the temperature of the saturated liquid in the absorber, indicated in the following as Tass, which stay in thermodynamic analogy with the condensation temperature of the best-known Rankine cycle.
Tvap is a function of the desorber pressure and of the degree of completion of the evaporation of the mixed fluid entering the desorber. Such a degree is defined as (Tvap-Tsl)/(Tsv-Tsl), where Tsl and Tsv are the saturated liquid and saturated vapour temperatures, respectively, of the mixed fluid at the desorber pressure.
Tass is a function of the absorber pressure and of the mixed fluid composition, i.e. of the molar fraction of the solvent or of the solute.
As previously said, the desorber may be designed in different ways. The basic design may be regarded as directly derived by the standard arrangement adopted for absorption cooling cycles. In this arrangement, the vapour-liquid phase separation is obtained with a single step in a drum, at the temperature Tvap and at the desorber pressure.
With this arrangement, at high degrees of completion of the evaporation, i.e. at high Tvap values, correspond the production of vapour in saturated condition with a poor solute concentration. Such a concentration could be successively incremented with a vapour rectification process, but the final mass flow rate of solute in the expander it would still be very low. On the contrary, at low Tvap values correspond the production of vapour in saturated condition with a high solute concentration but, again, the final mass flow rate of solute in the expander would be very low.
A different arrangement is considered in this paper, where the liquid mixture entering the desorber is continuously heated in counter-current with the heat source thermal vector, starting from the temperature Tsl up to the temperature Tvap, as shown in the scheme of Fig.2 and in the equilibrium diagram of Fig.3. The phase separation starts at the points indicated in Fig.3 by the lower temperature markers (blue circle for the liquid and red circle for the vapour phase) with the initial production of high solute concentration vapour, and proceeds up to the higher temperature markers, with a high level of completion of the evaporation process. In the meantime, the progressively produced vapour is continuously collected, and superheated at the temperature Tvap. The result is a final high mass flow rate of solute rich and superheated vapour, at the thermodynamic condition shown with a x blue marker in Fig.3. The proposed arrangement is, in the authors' opinion, in agreement with the scheme found in a patent of the Climeon Company [6], and reported in Fig.4.   In the thermodynamic model of the CCC cycle, the calculation has been arranged, according to the scheme of Fig.5, as a series of phase separators operating at increasing temperature. The division into 40 steps proved to be sufficient to simulate the real continuous process.
The considered working fluids are binary mixtures of Acetone as absorber (solvent) and CO2 as solute, at various molar concentrations, XAc and XCO2, where is obviously XCO2=1-XAc.
The thermodynamic properties of the mixtures and the enthalpy of mixing values, in every significant point of the cycle, have been obtained by means of REFPROP. The calculations employ a model that applies mixing rules to the Helmholtz energy of the components. The departure function from ideal mixing is consistent with the GERG model [7].

The model of the ORC
The simulated ORC is a simple single pressure level cycle, as reported in Fig.6. The main design variables, chosen in order to facilitate the comparison with the CCC cycle with reference to the same heat and sink sources, are the evaporation temperature Tvap and the condensing temperature Tcon. The possible working fluids must be pure substances, having thermodynamic properties compatible with the design variables. In the present analysis, the working fluid is Acetone, which is the solvent of the binary mixture taken in to account for the CCC cycle. As shown in the T-s diagram of Fig. 7, the minimum condensing temperature of 15°C correspond to a pressure of 0.2 bar while the maximum vapour temperature of 150°C correspond to a pressure of 13 bar. The critical point is at 235°C and 47 bar. The saturated vapour line is almost isentropic but, at the lowest pressure, it assumes a wet fluid behavior, for which a small superheating degree of 5°C has been assumed to avoid excessive condensation at the expander exit. The cycle can be simple or regenerative. In the last case, the effectiveness of the regenerative heat exchanger is equal to 0.85. The properties of Acetone are calculated with REFPROP. Fig. 7. T-s diagram of pure Acetone.

Results
The equilibrium diagram of the just cited Fig.3, the T-s diagram of Fig.8  The corresponding design temperatures are Tass = -4.8 °C and Tvap= 145.6 °C. The net efficiency of the cycle is 0.14.
As reported in Fig.3, the liquid mixture with XAc=0.45 pumped into the desorber is splitted in a vapour flow with XAc=0.087 and in a liquid flow with XAc=0.878. In the figure, the red and blue vertical lines show the evolution along the cycle of the vapour and liquid flows, respectively, while the magenta line refers to the pumped mixture (colours have the same meaning also in Fig.8 and Fig.9). The resulting mass flow rate distribution is 48.63% vapour and 51.37% liquid. Then, as can be seen in Fig.8 and Fig.9, the vapour flow expands adiabatically while the pumped mixture cools the liquid flow. The dotted lines in these figures represent schematically the desorbing and adsorbing processes. In particular, the magenta dash-point line in Fig.8 shows, in a simplified way, the progressive evaporation in the desorber described in the previous paragraph.
Again, in Fig.8 the green curves are the saturated liquid and vapour lines of the mixtures in the various phases of the cycle while the black lines refer to the pure carbon dioxide.
The pressures in the absorber and in the desorber of this example have been selected because they could allow operating in the chosen temperature range of heat source and sinking, as can be appreciated in Fig.3. The maximum net efficiency is achieved, however, for the cited values of XAc and (Tvap-Tsl)/(Tsv-Tsl), to which correspond the previously seen high value of Tvap and low value of Tass, the last one, in particular, completely out of the desired range.   Acetone values (Tvap-Tsl)/(Tsv-Tsl) the adsorbed power of the pump is greater than the positive power produced by the expander and the efficiency falls below zero. The maximum efficiency is reached at the maximum obtainable values of (Tvap-Tsl)/(Tsv-Tsl) and for intermediate values of XAc, that corresponds to the optimal balance between the pump and the expander flows, as shown in Fig.11.   Fig. 11. Flow rate ratio in the expander and in the pump of the CCC -Pass=15 bar, Pvap=35 bar.  The corresponding values of Tvap are reported in Fig.12, where it can be seen that values compatible with the chosen lower bound temperatures of the heat source are obtainable only at very low XAc values, with a sensible but still acceptable reduction of efficiency. The vapour quality at the expander exit, given in Fig.13, is always sufficiently high to avoid operating problems with almost all kinds of expander.
Obviously, the maximum efficiency increases with higher Pvap values and lower Pass values. Fig.14     The curves of Tvap show that, with an accurate choice of the pressures, it is possible to reach good efficiencies at almost all the considered range of the heat source temperatures, but such a good result is also due to the corresponding optimal values of Tass, which falls in the range of cold or criogenic temperatures.
The most significant limit to the use of the CCC cycle considered in this analysis is then the very low temperature in the absorber, which do not allow considering the environment as the heat sink.
The discussion of this topic can be carried on with reference to the Fig.17, which reports the equilibrium temperatures of the saturated liquid of the Acetone-CO2 mixtures at absorber pressures in the range 0.2 -40 bar. The two vertical blue dotted lines indicate the values of XAc corresponding to the best efficiency conditions in the various considered cycle arrangements, while the two horizontal red dotted lines indicate the range of ambient temperature between 15°C and 25°C. It can be observed that for operating with Tass in the ambient range it is necessary to choose XAc values higher than that of the optimal range, and the higher the lower is the absorber pressure.   .95, close to the optimal value for maximum efficiency, as shown in Fig. 10. As a whole, it can be concluded that, although the reduction in efficiency is quite high, the results could be still acceptable. The net efficiency values obtained with the ORC model, where pure Acetone is considered as working fluid, are shown in Fig.21 as a function of the superheated vapor temperature Tsh, equal to Tvap+5°C and variable from 90°C to 150°C, for three values of Tcon, i.e. 15, 20 and 25°C. Only non-recuperated cycles are considered, because the wet characteristic of Acetone implies that a very poor internal regeneration effect could be obtained in the considered temperature range. By comparing these values with those discussed for the CCC, it is observed that, while the maximum values are comparable, those obtainable with the same minimum cycle temperature are always higher in the case of the ORC.
These results are not in accordance with what is stated in the technical documentation of groups such as those produced by Climeon, which refer to the patent [6], but the available technical information is limited, avoiding to mention the composition of the mixture, apart from the presence in it of CO2, and the details of the absorption and desorption processes.

CONCLUSIONS
The modelization of an Acetone-CO2 cycle, which is a possible realization of a generic CCC, has allowed to evaluate the influence on the cycle performance of the most important thermodynamic design variables and related constraints. While the validity of the obtained quantitative results is limited to the choices made in the definition of the model, in particular to the choice of the solvent, the mutual qualitative influence of the variables on the performance can be extended to a wider range of cases, to be explored in the continuation of the research.
The main thermodynamic limit seems to be the low temperature required in the absorber to reach the maximum efficiencies, due to the correlations amongst mixture composition, absorber pressure, composition and mass flow rate of the solute rich vapor flow in the expander.
These features could make it interesting to study the adoption of the considered cycle in applications of WHR where the heat sink has temperature lower than the environmental one, as in the case of the regasification of liquefied gases.