Thermodynamic analysis on a Kalina cycle based power and chilling refrigeration cogeneration cycle

Accepted Manuscript Thermodynamic analysis on a Kalina cycle based power and chilling refrigeration cogeneration cycle Shaobo Zhang, Yapin Chen, Jiafeng Wu, Zilong Zhu, Fang Fang PII: DOI: Article Number: Reference:

S1359-4311(18)37355-1 https://doi.org/10.1016/j.applthermaleng.2019.114077 114077 ATE 114077

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

30 November 2018 15 April 2019 2 July 2019

Please cite this article as: S. Zhang, Y. Chen, J. Wu, Z. Zhu, F. Fang, Thermodynamic analysis on a Kalina cycle based power and chilling refrigeration cogeneration cycle, Applied Thermal Engineering (2019), doi: https://doi.org/ 10.1016/j.applthermaleng.2019.114077

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Thermodynamic analysis on a Kalina cycle based power and chilling refrigeration cogeneration cycle Shaobo Zhang, Yapin Chen*, Jiafeng Wu, Zilong Zhu, Fang Fang Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, Jiangsu Provincial Key Laboratory of Solar Energy Science and Technology, School of Energy and Environment, Southeast University, Nanjing 210096, China.

Corresponding author. Tel.: +86(0)13851729402. E-mail address: [email protected] (Y.P. Chen).

Thermodynamic analysis on a Kalina cycle based power and chilling refrigeration cogeneration cycle Shaobo Zhang, Yapin Chen*, Jiafeng Wu, Zilong Zhu, Fang Fang Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, Jiangsu Provincial Key Laboratory of Solar Energy Science and Technology, School of Energy and Environment, Southeast University, Nanjing 210096, China.

Abstract: A cogeneration system of power and refrigeration based on the triplepressure Kalina cycle was proposed and investigated. A parallel branch of work solution is split at the outlet of the mid pressure absorber, and it forms a refrigeration sub-cycle to further utilize the heat source sufficiently and provide chilling water for air-conditioning refrigeration capacity. The split fraction for refrigeration fref which determines the relative percentage of work solution flow rate for refrigeration (against power generation) can be altered according to user′s demand. The refrigerant from the evaporator is normally directed to the mid pressure absorber, and it can also be switched to the low pressure one to make ice for cooling load storage at off-peak time. The parameter analysis and optimization were conducted under temperatures of heat source of 450°C and cooling water of 30°C. The optimum fref for the comprehensive power recovery efficiency rises with the decrease of the work concentration, and the lower work concentration has larger adjustable range of the fref. The comprehensive power recovery efficiency reaches about 27.3±0.05% at work concentrations of 0.474~0.5375 with evaporation temperature of 0.5~12°C.

Keywords: Kalina cycle; parameter optimization; parallel cogeneration; refrigeration temperature; comprehensive power recovery efficiency.

1. Introduction The traditional fossil energy is exhausting in the world, thus the efficient utilizations of mid/low grade heat sources including solar, geothermal and waste heat have been gained more attentions. In the distributed energy system (DES) [1], the mid/low grade heat sources can be effectively recovered or converted to valuable products such as electric power, steam, hot water or chilling water for air conditioning at different seasons, thus to reduce the fuel consumption and emission of pollutants [2]. Since the demand for chilling grows very fast with the urbanization and development which consumes lots of energy, the cogeneration cycle integrating Kalina power cycle and absorption refrigeration cycle deserves special investigation, which can effectively exploit the abundant amount of low grade heat sources. In 1984, Kalina cycle (KC) [3] was proposed with ammonia-water instead of pure water as working fluid for power generation. Since the ammonia-water is zeotropic mixture, the evaporation and condensation processes in KC will occur at varied temperatures with greater variable phase change temperature for evaporation and small one for condensation, resulting in a better match between the working medium and the heat source or cooling water, which will significantly decrease the irreversibility of the system. Thereafter, many modified KC schemes for different heat sources have been proposed by many researchers.

Modi and Haglind [4] investigated on four layouts of the KC, and presented a detailed approach to optimize and compare the four layouts with high turbine inlet temperature and pressure. They found that the placement and the number of recuperators have a big influence on the cycle performance. Hettiarachchi et al. [5] studied the performance of the KC driven by low grade heat source, and concluded that the ammonia fraction has a decisive effect on the cycle efficiency. Marston [6] and Park and Sonntag [7] conducted respectively theoretical studies and showed that the KC bottoming cycle was better than the Rankine cycle in terms of the first law and the second law efficiencies. Zhang et al. [8] made a comprehensive review of the research on the KC, and analyzed some technique concerns on the ammonia-water mixture. The Kalina cycles can be categorized as dual-pressure and triple-pressure ones in general. In the conventional dual-pressure KC, the temperature lift of the heating process of the ammonia-water is usually small, which consists of only sub-cold liquid heating and part of evaporation phase change, therefore, the dual-pressure KC is usually applied for lower grade heat source. Chen [9] proposed a dual-pressure KC with the separator placed before the evaporator with lower temperature of the dilute solution, however, the desorption process has restrictions on the turbine inlet pressure and the heat source temperature [10]. In the triple-pressure KC, the heating process usually consists of sub-cold liquid heating, evaporation and vapor super heating of the working fluid with much greater temperature lift which matches well with the sensible heat source, and higher grade heat source can be utilized with the flexible high pressure of the triple-pressure KC. By integrating the KC and ammonia-water Rankine cycle (RC),

Chen et al. [11] and Zhang et al. [12] proposed a novel cycle which can operate on KC for power generation in non-heating seasons and on ammonia-water RC for cogeneration of power and heating water in winter. Zhu et al. [13] and Guo et al. [14] found that the performance of the KC can be promoted by employing dual-pressure vaporization process to recover heat source. The ammonia-water mixture is not only applying to power generation cycles, but also the working fluid for absorption refrigerators [15]. Therefore, based on the KC, many researchers have attempted to invent power and refrigeration cogeneration cycles using the ammonia-water as the working fluid. The way to modify the KC inside and to build a refrigeration sub-cycle for the power/refrigeration cogeneration can make full utilization of the heat source, thus has better performance than to combine simply the KC with an independent refrigeration cycle. Goswami [16] proposed a power and refrigeration cogeneration cycle system, and some relevant researches have been performed [17-19]. The system can be considered as a dual-pressure KC, and the vapor from the boiler is rectified to produce nearly pure ammonia, which is then sent to the turbine for power generation after superheated. Then the turbine exhaust is sent to a refrigeration heat exchanger to produce cooling capacity before the absorber. Nevertheless, the turbine exhaust usually contains very little liquid with the vapor quality requirement for blade safety, which limits the amount of refrigeration capacity. Zheng et al. [20] proposed a power and chilling cogeneration cycle named APC by modifying the triple-pressure KC. The separator in KC is replaced by a rectifier/reboiler and the nearly pure ammonia vapor from the rectifier is evaporated in an evaporator to

provide chilling load. However, the solution fed to the rectifier/reboiler in APC is the basic solution with relatively low concentration, thus the heat source suitable for APC usually cannot be utilized in series. Zhang et al. [21] also studied a power/cooling cogeneration cycle system, in which the fluids for power generation and refrigeration are from the rectifier and reboiler respectively, thus there is a restriction between the refrigeration and power generation. Liu and Zhang [22] investigated further this kind of refrigeration/power cogeneration system, and they conducted a sensitive analysis and mainly focused on the impact of the split ratio and the concentration of ammonia-water on cycle performance. Wang et al. [23] modified the KCS-34 and proposed a novel power/cooling cogeneration cycle by adding a separator behind the turbine and a subcycle with other components required for the refrigeration. Cao et al. [24] studied an independent absorption refrigeration cycle to reclaim heat of the dilute solution from the separator in the dual-pressure Kalina cycle. Rashidi et al. [25] also proposed a cogeneration cycle based on the dual-pressure KC, the ammonia vapor from the separator is divided into two streams, one is eventually fed to the turbine and the other is used for refrigeration. Hua et al. [26] proposed and investigated a cogeneration cycle based on the triple-pressure KC, the work solution out of mid pressure absorber splits into two streams, one for power generation and one for refrigeration. Nevertheless, since in the refrigeration sub-branch, the refrigerant is exactly the work solution concentration without rectified, and the temperature glide in the evaporator is relatively large which ruins its performance. To overcome the problem of difficulty in adjusting power output and refrigeration

capacity and achieve sufficient utilization of heat source, Zhang et al. (the authors) [27] proposed a cogeneration cycle named PPR-KC (parallel power and refrigeration Kalina cycle), which is a modification of the cycle proposed by Hua et al. [26]. In the PPRKC, the heat source flows in series through the boiler and the generator to make the heat source fully utilized by the power generation and refrigeration sub-cycles. Furthermore, the PPR-KC can adjust the power or refrigeration capacity by adjusting the flow rate of the work solutions introduced to the power and refrigeration sub-cycles. However, the PPR-KC is only able to obtain refrigeration temperature in ice-making range, since the refrigerant is fed to the low pressure absorber. In order to make the PPR-KC provide refrigeration for air-conditioning chilling water, which has greater energy demand sector, the cycle is further modified and a new power/refrigeration cogeneration cycle is proposed in this paper. The exhaust refrigerant has two convertible directions that the normal direction is to the mid pressure absorber providing refrigeration with air-conditioning temperature (this case is abbreviated as PPRA-KC in this paper), while the other direction is to the low pressure absorber (i.e. the same as the configuration of the PPR-KC) providing refrigeration with lower temperature. In this way, the new cogeneration cycle is not only able to supply chilling water for air-conditioning in the normal operation, but also supply cold capacity in icemaking at off-peak time for thermal energy storage. Two evaporators and throttle valves for two purposes should be set in real application, however, only one set is drawn in the Fig. 1 for simplicity. 2. Methods

2.1 Description of the new cogeneration cycle The layout of the new cogeneration cycle is shown in Fig. 1, and the main configuration is basically similar to that of the PPR-KC, except for the flow directions of the exhaust refrigerant. Therefore, the detailed description of the main structure of the new cogeneration cycle can be referred to the Ref. [27], and this paper only gives a brief description as follows: 

Power sub-cycle: One stream of work solution from the mid-pressure absorber A2 (point 9) is pumped to the boiler and extracts energy from the heat source, and the solution is converted to superheated vapor (13) before flows to the turbine. After expansion in the turbine, the exhausted vapor (14) will eventually mix with the other solutions in the mixer M1 and form basic solution in the low-pressure absorber A1; while the work solution (8) is again produced in the mid-pressure absorber A2 mainly by the basic solution, after desorption heating in recuperators R1 and R2 and vapor-liquid separation in the separator S and through the mixer M2.



Refrigeration sub-cycle: The rest part of work solution (17) from the mid pressure absorber A2 enters generator/rectifier column and mixes with the solution from the rectifier (18′), and consequently the mixed solution (25′) is introduced to the generator G to further utilize the heat source. The vapor from the generator G is rectified and partially condensed in the rectifier RF and partial condenser PC to produce nearly pure ammonia vapor as refrigerant. Eventually, the condensed refrigerant (20) is fed to the evaporator E to complete the refrigeration process (22-

23). After evaporation, the vapor refrigerant finally flows to the mixer M2 or M1, and the former case abbreviated as PPRA-KC is able to achieve refrigeration temperature in air-conditioning range; while the latter case is to provide refrigeration capacity with temperature in ice-making range corresponding to the configuration of the PPR-KC. The valves V1 and V3 are not for throttling at design condition, but for regulation in off-design conditions. The cooling water in the low and mid-pressure absorbers is arranged in series with the cooling water is introduced into low-pressure absorber A1 first. Moreover, it should be pointed out that this new cogeneration cycle system is not designed to make chilling-water supply and ice-making processes occur simultaneously but separately at different time. 2.2. Model for the PPRA-KC The PPR-KC case has been already investigated in the Ref. [27], thus this paper only studies the PPRA-KC case. The calculation equations for thermal property data of ammonia-water solution are embedded in the engineering equation solver (EES) software, which shown good agreement with the experimental data [2, 28]. The simulations of the PPRA-KC in this paper were carried out via EES with the following basic thermodynamic assumptions: 

All processes included in the cycle are at steady state.



Pressure drops and thermal dissipation losses within pipes or equipment are negligible, and the flows through the throttle valves are isenthalpic.



The vapor or liquid of solutions at the outlets of the absorbers, condensers,

separator, rectifier and generator is saturated. 

The refrigerant vapor quality at evaporator outlet is set as 95% to avoid the large temperature glide at end section of evaporation with the increase of moisture water content.



The heat exchangers are all of countercurrent type.



The ammonia vapor leaving the generator to the rectifier is considered as the average state of heating initiation and termination in the generator.



In the rectification process, the rectification efficiency is taken as 70%. In the PPRA-KC, four important parameters affecting significantly the

performance of the new cycle are investigated in this paper, i.e. the work concentration xw and basic concentration xb produced by the mid and low pressure absorbers respectively, the dew point temperature t12 in the boiler and the split fraction for refrigeration fref. Besides, the xw, xb and other two main ammonia concentrations acquired by the separator are linked by the fref and the circulation multiple f. The low pressure pl in absorber A1 or mid pressure pm in absorber A2 is determined by the concentration of solution in each absorber when the inlet temperature of cooling water and pinch temperature difference are set. Moreover, the refrigeration pressure in PPRKC is exactly the low pressure pl, while in the new cogeneration cycle system, the refrigeration pressure can be either the low pressure pl or the mid pressure pm. The high pressure ph is determined by the dew point state of the work solution in the boiler, and the ph has a significant effect on the quality of the turbine exhaust vapor and shall be carefully selected to prevent turbine last stage blades from moisture droplets corrosion.

In the distillation process, the actual reflux ratio which affects the concentration of refrigerant and partial condensation load can be obtained by assuming reasonable rectification efficiency. The thermodynamic model of PPRA-KC is presented in Table 1. 2.3 Cycle evaluation indexes The energy quality grade of chilling load is not equal to the power output, thus the refrigeration capacity should be converted to the electrical power equivalent to generate the same temperature refrigeration capacity by conventional compression refrigeration cycle [19] in the evaluation of the performance of the cogeneration cycle. The refrigeration capacity in this paper is converted by using COPc of conventional compression refrigeration cycle [28, 29], and the COPc can be calculated by Eq. (67)(69). COPc = COPrev·ηref COPrev =

Te

(67) (68)

T20 - Te

Te = (T22 + T23)/2

(69)

In the above three equations, ηref stands for the second law efficiency for the conventional vapor compression refrigeration cycle, and the value of ηref is taken as 40% in this paper [17-19 and 21]; and COPrev is the coefficient of performance in a reversible refrigeration system; Considering the temperature glide, sink temperature Te is taken as the average value of inlet and outlet temperatures in the evaporator; T20 is the temperature of refrigerant at the condenser outlet. Therefore, the performance of the new cogeneration cycle driven by a sensible heat source can be evaluated in a proper

way by employing the comprehensive thermal efficiency given by Eq. (70). ηth,c =

Wnet + Qref/COPc QB + QG

=

Wnet + Qref/COPc

(70)

Ghcph(th1 - th5)

The comprehensive thermal efficiency ηth,c is not a complete criterion when recovering energy from the industrial wasted flue gas, for a high value of ηth,c might not mean a sufficient utilization of the waste heat source if the exhaust temperature is high. To better evaluate the performance of the cogeneration cycle, the comprehensive power recovery efficiency η0,c is suggested which is the product of the comprehensive thermal efficiency and the waste heat recovery ratio ηwh, as shown in the Eq. (71). η0,c = ηth,c ∙ ηwh =

Wnet + Qref/COPc (th1 - th5) Wnet + Qref/COPc = ∙ Ghcph(th1 - th5) (th1 - th0) Ghcph(th1 - th0)

(71)

2.4 Simulation method validation By using the same conditions of a Kalina cycle power plant built in the Iceland [30], with the inlet and outlet temperatures of geothermal heat source of 122°C and 80°C respectively, the comparison was performed with the simulation results of the model established in this paper and those by Ogriseck [30]. The results of the parameters and cycle indexes are comparable that the relative errors of the power output and the thermal efficiency are 3.654% and 4.626% respectively, indicating the reliability of the simulation method used in this work. The validation was also performed with satisfactory agreement for the results of refrigeration sub-cycle with those presented by Barkhordarian [31], which have been validated by many other literatures. 3. Results and discussion

Since the boiler and generator are in series arrangement, the share of each sector should be considered. In most literatures about power/refrigeration cogeneration cycles, power generation is regarded as the primary purposes, thus the parameters for boiler are first set, that is, the pinch temperature difference in the boiler (for power generation) is kept at a minimum value. However, in a distributed energy system (DES) the electricity is easier to be regulated from grids, while the refrigeration capacity should be secured locally. In this paper the refrigeration requirement is considered as the dominant aim, and the pinch temperature difference in the generator is maintained at the minimum restrictive value when other parameters change. In order to make PPRA-KC achieve refrigeration temperature in air-conditioning range, the refrigeration pressure (i.e. the mid-pressure) should be properly maintained. When the work concentration is fixed, the refrigeration pressure is determined by the temperature of work solution at the mid-pressure absorber. In order to avoid the midpressure is too low, the cooling water is arranged in series through the low and mid pressure absorbers. The work concentrations xw are taken as 0.45, 0.475, 0.5 and 0.525 in the following analyzing or optimizing the basic concentration xb, the dew point temperature in the boiler t12 and the split fraction for refrigeration fref of the cogeneration system, and also the xw with broader range is investigated in the Fig. 4. The new cycle is driven by the waste flue gas, and the lowest possible utilization temperature is set as 90°C and the quality of turbine exhaust vapor is more than 88% for the safety of turbine blades [14, 26 and 29]. In addition, the parameters such as flow rate of heat source Gh and the

temperature of dilute solution at the generator outlet t25 are set as 10 kg·s-1 and 130°C respectively, and other operation conditions or restrictions are shown in Table 2. 3.1 Dew point temperature in the boiler The high pressure ph of the cycle, i.e. the turbine inlet pressure, has a significant impact on the heat transfer in the boiler, and consequently influences the performance of the whole cogeneration cycle. When the inlet pressure of turbine is too high, the strength and material requirements of the turbine, boiler and other devices will also upgrade accordingly, thus an upper limit of high pressure of 20 MPa is set in this paper. For the convenience, the dew point temperature t12 is used instead of ph as the variable to show the influences on the cogeneration cycle. As the dew point temperature t12 increases with the split fraction for refrigeration fref of 0.4, the heat consumption in the boiler with a fixed work concentration xw will increase, and thus the pinch temperature difference tp,B in the boiler at the bubble point of the solution will decrease as shown in Fig. 2(a). In the figure, by adding the minimum restriction value of 20 K of the tp,B in the boiler, the highest t12 for each xw are shown by the vertical dash lines. The simulation indicates that the highest t12 is 266.4°C, 272.4°C, 280.5°C or 301.4°C for the work concentrations of 0.45, 0.475, 0.5 or 0.525, respectively. Fig. 2(a) also shows that the final exhaust temperature of heat source th5 decreases with the increase of t12, and higher xw obtains lower th5. The minimum restriction value of th5 (90°C) is also plotted on the figure, and it is clear that the curve of the th5 for each xw is always above the limit value within the discussion scope. When the dew point temperature t12 changes (the degree of superheat changes),

the state of solution at turbine outlet (point 14) will also change, which will affect the heat transfer in the recuperator R1. Hence, when the t12 changes, the basic concentration xb is checked and adjusted accordingly to ensure the restriction of pinch temperature difference (5 K) in R1. Fig. 2(b) shows that the optimum xb increases slightly with the increase of the t12, and higher work concentration xw corresponds to higher xb. Fig. 2(b) also shows that as the t12 increases, the vapor quality at turbine outlet Y14 declines, while within the discussion scope of the t12, the values of Y14 are all higher than the restriction value of 0.88. Fig. 2(c) shows that as the dew point temperature t12 increases, the high pressure ph of the three work concentrations increase, and with fixed t12, higher work concentration xw is corresponding to higher ph. The upper limit of the ph (20 MPa) is also plotted on the figure. Fig. 2(c) also indicates that the t12 has no impact on the mid pressures in the mid pressure absorber A2, and the basic concentration xb is the decisive factor for the low pressure pl, thus the optimized pl shows a slightly increasing trend as the t12 increases. Fig. 2(d) shows the impacts of dew point temperature t12 on the flow rates to the boiler G9 and to the refrigeration sub-cycle G17 and the specific enthalpy drop hT in the turbine. It can be seen that as the t12 increases, more solutions will be introduced into the boiler and the refrigeration sub-cycle simultaneously, since the t12 will influence the temperature of heat source at the boiler outlet, and more solution shall be fed to the refrigeration sub-cycle to meet the minimum pinch temperature difference (20 K) in the generator. The figure also reveals that the hT with a fixed work

concentration xw increases with the increase of the t12, and higher xw is corresponding to lower hT. Fig. 2(e) shows the curves of net power output Wnet, refrigeration capacity Qref and heat consumption Qin of the PPRA-KC versus the dew point temperature t12 at different work concentrations. It is clear from the figure that as the t12 increases, both Qref and Wnet increase, and when t12 is fixed, higher xw obtains higher Qref but slightly lower Wnet. When t12 increases with a fixed xw, the total heat consumption Qin increases slightly with the heat consumption in the boiler B and generator G decreases and increases respectively. Fig. 2(f) shows the effect of the dew point temperature t12 on the comprehensive thermal efficiency th,c, the comprehensive power recovery efficiency 0,c and the waste heat recovery ratio wh. The figure indicates that as the t12 increases, wh increases slightly, and the higher xw, the higher wh will be. Moreover, th,c shows an increasing trend as t12 increases, and lower xw will obtain higher th,c when t12 is fixed. Combining the trends of th,c and wh, the 0,c also shows an increasing trend with the increase of t12 or decrease of xw. The 0,c is considered as the ultimate criterion of the PPRA-KC, thus the maximum 0,c is corresponding to the optimum dew point temperature t12 of each xw. According to Fig. 2 (c) and (a), it is obvious that for each xw, the optimum t12 can be obtained when the greatest high pressure ph is reached in the boiler, limited by either the pinch temperature difference or high pressure limit (20 MPa). The maximum

0,c of each xw are also indicated by the vertical dash lines in Fig. 2(f). 3.2 Split fraction for refrigeration

In the PPRA-KC, the work solution at the outlet of mid pressure absorber A2 is divided into two streams as shown in Fig. 1, one (point 9) is sent to the boiler to absorb energy from the waste flue gas and finally to fulfill the power generation process in the turbine, while the other one (17) is fed to the generator/rectifier column to absorb heat from the waste flue gas further and to produce nearly pure ammonia vapor as refrigerant. It is noteworthy that the flow rate and inlet temperature of heat source are unchanged when other parameters change. Fig. 3(a) depicts the change trends of the optimum basic concentration xb and the high pressure ph versus the split fraction for refrigeration fref. It can be seen that the optimum xb of each work concentration xw changes slightly with variation of fref, and higher xw is corresponding to higher optimum xb. Since more energy from the heat source will be extracted to work solution in the boiler with the decrease of the fref, the ph of each xw shall be reduced accordingly, otherwise the pinch temperature difference in the boiler will be lower than the minimum restriction value of 20 K. Since the temperature of dilute solution at the outlet of generator G is set as 130°C, the exhaust temperature th4 shall be higher than or equal to 150°C to guarantee the minimum pinch temperature difference in the G (20 K). Fig.3(b) shows that as the split fraction fref decreases, the exhaust temperature th4 for each work concentration xw will be equal to 150 °C at a certain fref, which means that the minimum pinch temperature difference in the G has shifted to the outlet of G (Δth4-25). If continuously reduce the fref to obtain less refrigeration capacity, the high pressure ph shall be properly maintained to ensure that th4 is always 150 °C. Simulations indicate that the certain fref for xw of

0.525, 0.5, 0.475 and 0.45 are 0.3835, 0.3885, 0.394 and 0.4 respectively. Moreover, the maximum fref of each xw is corresponding to the th5 of 90°C as the vertical dash lines indicate, and the maximum fref for xw of 0.525, 0.5, 0.475 and 0.45 are 0.407, 0.451, 0.488 and 0.525 respectively. Comparing the Fig. 3(a) and (b), it is clear that as the fref changes, the temperature difference between the heat source and the work solution at bubble point tp,B is equal to or larger than the minimum limit of 20 K, while the high pressure ph is equal to or lower than the upper limit of 20 MPa. In the conventional triple pressure KC or PPR-KC, the work solution (point 8) is a mixture of the basic solution (2′′) and ammonia-rich vapor from the separator (4′′), while in the PPRA-KC, the refrigerant (24) also plays an important role in the concentration production of work solution. Fig. 3(c) shows that as the fref increases, the relative flow rate of the ammonia-rich vapor solution from the separator m4′′ (G4′′/G8) declines and the curve of higher xw is steeper than that of the lower one, while the relative flow rate of refrigerant m24 (G24/G8) for each xw increases. Fig. 3(c) also indicates that as the fref increases for each xw, the specific enthalpy drop in the turbine hT at fixed xw increases first and then is nearly unchanged, and the simulations indicate that the turning point is exactly the fref corresponding to the minimum pinch temperature difference of 20 K and the greatest high pressure ph of 20 MPa in the boiler. Fig. 3(d) indicates that both the ratio of transferring heat of the second recuperator to that of the first recuperator RR2/R1 and the ratio of transferring heat of the generator to that of the boiler RG/B rise as the fref increases, and higher work concentration xw has lower RR2/R1 but higher RG/B in the common valid range of the fref. Fig. 3(d) also shows that the

temperatures at the evaporator inlet and outlet (t22, t23) are steady with a fixed xw, and higher xw is corresponding to higher refrigeration temperatures. Fig. 3(e) shows the curves of the refrigeration capacity Qref, the net power output Wnet and the heat input Qin versus the split fraction for refrigeration fref at different work concentrations xw. It can be seen from the figure that the Qref increases with the increase of the fref at a given xw, and declines with the decrease of the xw in the common valid range of fref. Relative to the solution flows into the refrigeration sub-cycle, higher fref means less solution flows into the boiler, however, combining the change trend of the specific enthalpy drop in the turbine hT shown in Fig. 3(c), the Wnet increases at first and then decrease with the augment of the fref. Moreover, in the valid range of each xw, lower xw is capable of obtaining greater Qref but less Wnet. Therefore, by adjusting the fref, the users′ demand for different refrigeration load can be met. As previously discussed, for each xw at a fixed fref, the highest comprehensive power recovery efficiency 0,c is obtained with the greatest high pressure ph that can be achieved in the boiler, limited by the pinch temperature difference or upper higher pressure limit (20 MPa). Fig. 3(f) shows the impacts of split fraction for refrigeration fref on the comprehensive thermal efficiency th,c, power recovery efficiency 0,c and the waste heat recovery ratio ηwh. The change trend of ηwh is consistent with the trend of heat consumption Qin in Fig. 3(e). The ηth,c increases and then drops with the increase of the fref, and higher xw obtains higher ηth,c with fixed fref in the common valid range of the fref. Within the valid range of the fref for each xw, combining the trends of the ηwh and ηth,c, the comprehensive power recovery efficiency η0,c also increase and then

decrease. Moreover, for each xw, the curves of th,c and η0,c are much closer at higher fref, since the value of the ηwh is close to 1. Simulations indicate that when the pinch temperature difference in the boiler tp,B is 20 K and the high pressure ph is 20 MPa, respectively, the PPRA-KC will obtain the highest η0,c. Fig. 3(f) also indicates that the cogeneration cycle is perfectly operating in the optimal work concentration with different fref or the demand of Qref, then the performance curve could be the envelop line of all summit of the power recovery efficiency curves at different xw, which could be implemented with a solution concentration regulation system [32] by using an cylindrical solution tank with two I/O nozzles at both ends accommodating either work solution from mid pressure absorber or basic solution from low pressure absorber, respectively. The formal connected to the outlet of the mid pressure absorber and the latter has two lines connected to both inlet and outlet of the low pressure pump via valves. 3.3 Work concentration As previously discussed, when the work concentration xw is given, the cycle can achieve the highest comprehensive power recovery η0,c with the high pressure of 20MPa and a certain split fraction for refrigeration fref. When the PPRA-KC always reaches the highest η0,c, Fig. 4 shows the change trends of various parameters with the change of work concentration xw. Fig. 4(a) reveals that with the increase of the xw, the mid pressure (i.e. the refrigeration pressure) will increase, resulting in the increases of t22 and t23. Simultaneously with the increase of refrigeration temperature, the optimum split fraction for refrigeration fref will also be lower with higher xw, and the

corresponding optimum basic concentration xb will increase accordingly. The figure also depicts the change trend of the corresponding COPc, it can be seen that the COPc will reach higher value with higher xw, since the COPc is determined by the evaporation temperature in the evaporator. Fig. 4(b) shows that with the increase of the xw, both the exhaust temperatures th4 and th5 of heat source decrease, and when the xw is 0.5375, the th5 will be 90°C. Opposite to the change trends of th4 and th5, the temperature t18 of solution at the outlet of the second preheater PH2 shows an increase trend with the increase of xw. The figure also shows that the turbine exhaust vapor quality Y14 will lower than the minimum restriction value of 0.88 when the xw decreases to 0.454. Therefore, to keep the cycle always in the optimum performance, the applicable range of the xw is 0.454 to 0.5375, and the corresponding range of evaporation temperature at the inlet of the evaporator is about 0.5°C to 12°C as shown in Fig. 4(a). Fig. 4(c) reveals the impact of work concentration xw on the net power output Wnet, refrigeration capacity Qref and the total heat consumption Qin, it can be seen from the figure that as the xw increases, the Wnet and Qin will increase, while the Qref declines slightly. Fig. 4(d) shows the change curves of the comprehensive thermal and power recovery efficiencies th,c and 0,c and the waste heat recovery ratio ηwh versus the xw. The figure shows that the ηwh increases mildly first and then steeper when the xw increases. Fig. 4(d) also indicates that both ηth,c and 0,c decrease with the increase of the xw, and the difference between the highest and lowest 0,c with work concentrations

of 0.454 and 0.5375 is only 0.00153. Therefore, the system will maintain a stable performance, when changing the xw to obtain different refrigeration temperatures and capacities. 3.4 Performances When the highest comprehensive power recovery efficiencies 0,c are obtained with work concentration xw of 0.475, 0.5 and 0.525, the heat transfer curves of the solutions and waste flue gas in the boiler B and generator G of the PPRA-KC are shown in t-Q diagram of Fig. 5. It is clear from the figure that the solution with higher xw will match the heat source better, and extract more energy in the B while less in the G. Moreover, Fig. 5 also indicates that lower xw will consumes more energy in the G to heat the solution to the saturation state. Therefore, the exhaust temperatures of the flue gas with these three xw are relatively close. By adopting the work concentration of 0.5 and when the highest 0,c is obtained , the corresponding thermodynamic parameters of each status point in Fig. 1 are listed in Table 3. It should be pointed out that the refrigeration temperature lower than about 0.5°C is also able to be obtained by adopting lower inlet temperature or larger volume of cooling water to decrease the temperature rise in the low pressure absorber. When decrease the refrigeration temperature by utilizing lower work concentration, the highest pressure in the boiler may need to be lower than 20 MPa to meet the restriction of vapor quality at the turbine outlet. Moreover, if the split fraction fref is 0, the cycle will be exactly the conventional triple pressure Kalina cycle with only power generation, and the cogeneration cycle will achieve its lowest comprehensive power recovery

efficiency. As previously described, when switching the valve V3 to introduce the refrigerant to the low pressure absorber, the new cogeneration cycle will be exactly the configuration of the PPR-KC. By adopting the same work concentration xw of 0.5 and other given conditions as shown in Table 2, with the pinch temperatures in all the heat exchangers are of the minimum restriction values, the performances of the PPRA-KC and PPR-KC are shown in Table 4. It can be seen that with the same xw, the optimum basic concentration and the corresponding back pressure of turbine in PPRA-KC are lower than that in PPR-KC, and the net power and the refrigeration capacity are slightly higher in PPRA-KC. Table 4 also reveals that the heat source can be utilized more thoroughly in PPRA-KC. However, the refrigeration temperature in PPR-KC is much lower than that in PPRA-KC, resulting in lower corresponding COPc and higher comprehensive efficiencies for the PPR-KC case. 4. Conclusion A new cogeneration cycle for electric power and refrigeration was proposed based on the Kalina cycle. The refrigerant has two convertible flow directions, one is to the low pressure absorber to achieve refrigeration temperature in ice-making range (PPRKC case), while the other one is to the mid pressure absorber to obtain refrigeration temperature in air-conditioning range (PPRA-KC case). The effect of some key parameters such as dew point temperature in the boiler t12, work concentration xw, basic concentration xb, and split fraction for refrigeration fref on the PPRA-KC case have been investigated and discussed. Results shown that when the xw is fixed and the t12 is

optimum obtained with the pinch temperature differences in all heat exchangers are of the minimum restriction values (20 K for heat source involved or 5 K for others) and the high pressure is 20 MPa, the PPRA-KC will achieve the highest comprehensive power recovery efficiency η0,c, which is considered as the ultimate evaluation criterion of the PPRA-KC. To maintain the highest η0,c, simulation outputs indicate that the available range of the xw is from 0.454 to 0.5375, which are limited by the restrictions of vapor quality at the turbine outlet and the discharged temperature of heat source respectively. And within the available range of the xw, the highest η0,c can reach about 27.3±0.05% with refrigeration temperatures from 0.5°C to 12°C. With the xw of 0.5 and under the conditions of the temperatures of heat source and cooling water are 450°C and 30°C respectively, the η0,c of the PPRA-KC is 27.27%, and the thermal efficiencies of both power generation and refrigeration are 30.83% and 50.57%, respectively.

Acknowledgement

This work is supported by the National Natural Science Foundations of China (51776035).

Nomenclature Latin letters

l

low or liquid

f

circulation multiple (G1/G8)

m

mid

fb

basic fluid solution portion (G2″/G8)

net

net power

p

pinch point

split

fraction

fref (G18/G9)

for

refrigeration

fr

refrigeration portion (G19/G18)

r

refrigerant

G

mass flow (kg∙s-1)

ref

refrigeration

h

specific enthalpy (kJ∙kg-1)

rev

reversible

relative mass flow rate in contrast to m

total work solution at mid pressure w

work (concentration)

absorber p

pressure (MPa)

number

Q

heat (kJ∙kg-1)

Abbreviations

R

reflux ratio, ratio of transferring heat

A

absorber

T, t

temperature (K, °C)

B

boiler

W

power output (kW)

C

condenser

x

ammonia concentration

E

evaporator

Y

vapor quality

G

generator

Greek letters

M

mixer

Δ

difference

P

pump

ηR

rectification efficiency

PC

partial condenser

ηth,c

comprehensive thermal efficiency

PH

preheater

ηwh

waste heat recovery ratio

R

recuperator/ ratio

RF

rectifier

Subscript

S

separator

b

SC

subcooler

comprehensive

power

η0,c

state points of the cycle

recovery

efficiency

basic (concentration)

c

cooling water

T

turbine

digit

status point in Fig. 1

V

valve

h

high, heat source

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Tables: Table 1 Basic mathematic model. Equipment/ Item

Formulas

Work solution

p8(or h8, s8) = f (t8, xw)

(1)

Basic solution

p1(or h1, s1) = f (t1, xb)

(2)

Saturate vapor

p12(or h12, s12) = f (xw, t12)

(3)

Superheating vapor

h13(or s13) = f (t13, xw, p12)

(4)

Saturate solution

t11(or h11, s11) = f (xw, p12)

(5)

Saturate solution

p20(or h20) = f (t20, x20)

(6)

Saturate solution

x25(or h25) = f (t25, p20)

(7)

Saturate vapor

t19(or h19) = f (x19, p20)

(8)

Circulation multiple

Basic solution portion Split fraction for refrigeration Relative flow rate of refrigerant Relative flow rate for power generation Refrigerant portion Relative flow rate of ammonia-rich vapor Boiler B

f = G1/G8 = (xw - x4')/(xb - x4')+ fref ∙ fr ∙ (x4' - x19)/ (xb - x4') fb = G2''/G8 = (𝑥w - 𝑥4")/(xb - x4") + fref ∙ fr ∙ (x4" - x19)/(xb - x4")

No.

(9)

(10)

fref = G17/G8

(11)

m24 = G24/G8 = fref ∙ fr

(12)

G9/G8 = 1 - fref

(13)

fr = G19/G17 = (xw - x25)/(x19 - x25)

(14)

m4'' = G4''/G8 = 1 - fb - m24

(15)

Gh ∙ cph(th1 - th2) = G9(h13 - h12)

(16)

Gh ∙ cph(th2 - th3) = G9(h12 - h11)

(17)

Gh ∙ cph(th3 - th4) = G9(h11 - h10)

(18)

∆tp,B = th3 + 273.15 - T11

(19)

QB = Gh ∙ cph(th1 - th4)

(20)

fref ∙ xw = fref ∙ fr ∙ x19 + (fref - fref ∙ fr) ∙ x25

(21)

G18 ∙ h18 + QG = G19 ∙ h19 + G25 ∙ h25 + QPC

(22)

Rmin = (x19 - x18'') (x18'' - x18,l)

(23)

x18,l(or h18,l) = f (p20, t18'' )

(24)

R = Rmin/ηRF = (x19 - x18'')/(x18'' - x18')

(25)

G19 ∙ x19 = G18'' ∙ x18'' - G18' ∙ x18'

(26)

G19 = G18'' - G18'

(27)

h18'(or t18') = f( p20, x18')

(28)

G25'x25' = G18'x18' + G17xw

(29)

G25'h25' = G18'h18' + G17h18

(30)

G25' = G18' + G17

(31)

h25,l(or t25,l) = f( p20, x25')

(32)

h18''(x18''or t18'') = f( p20, (t25' + t25)/2)

(33)

QPC/G19 = ℎ18'' - ℎ19 + R ∙ (h18'' - h18')

(34)

G25x25 = G25'x25' - G18''x18''

(35)

G25 = G25' - G18''

(36)

G25h25 = G25'h25' + QG - G18''h18''

(37)

QG = Gh ∙ cph(th4 - th5)

(38)

Partial condenser PC

QPC = Gc2cpc(tc6 - tc5)

(39)

Evaporator E

t22(or h22) = f (x20, h21, p8)

(40)

h23(or s23) = f ( x20, p8,Y23)

(41)

h14s = f (p1, xw, s13)

(42)

h14 = h13 - ηT(h13 - h14s)

(43)

WT = G9(h13 - h14)

(44)

Rectifier RF and generator G

Minimal reflux ratio

Actual reflux ratio

Turbine T

1st Recuperator R1

QR1 = (1 - fref) ∙ (ℎ14 - ℎ15) = (f - fb) ∙ (h3' - h2')

(1 - 𝑓ref) ∙ (h14 - h14') = (f - fb) ∙ (h3' - h3)

(45) (46)

2nd Recuperator R2

Separator S

QR2 = fref ∙ (1 - fr) ∙ (h25 - h26) = (f - fb) ∙ (h4 - h3')

(47)

h3'(or p3', s3') = f (t3', p8, xb)

(48)

x4'(or x4'', h4', h4'') = f (p8, t4)

(49)

(f - fb) ∙ xb = (1 - fb - fref ∙ fr)x4'' + (50)

(f - 1 + fref ∙ fr)x4' 1st preheater PH1

(f - 1 + fref ∙ fr) ∙ (h4' - h5) = (1 - fref) ∙ (h10 - h9)

(51)

2nd preheater PH2

(1 - fb - fref ∙ fr) ∙ (h4'' - h7) = fref ∙ (h18 - h17)

(52)

Condenser C

Gc3cpc(tc8 - tc7) = G19(h20 - h19)

(53)

Subcooler

h20 - h21 = h24 - h23

(54)

1st mixer M1

f ∙ h16 = fref ∙ (1 - fr) ∙ h27 + (1 - fref)h15 + ( f - 1 + fref ∙ fr)h6

(55)

f ∙ x16(or xb) = fref ∙ (1 - fr) ∙ x27 + (1 - fref) ∙ xw + (56) ( f - 1 + fref ∙ fr) ∙ x6 2nd mixer M2

x7'(or xw) = (1 - fb - fref ∙ fr)x4'' + fbxb + fref ∙ fr ∙ x19

(57)

h7' = (1 - fb - fref ∙ fr)h7 + fbh2'' + fref ∙ fr ∙ h24

(58)

Low-p absorber A1

Gc1cpc(tc2 - tc1) = G1(h16 - h1)

(59)

Mid-p absorber A2

Gc1cpc(tc4 - tc3) = G8(h7' - h8); tc3 = tc2

(60)

Pumps

WP1 = G1(h2 - h1)/ηP

(61)

WP2 = G9(h9 - h8)/ηP

(62)

WP3 = G17(h17 - h8)/ηP

(63)

Throttle valves

h5 = h6; h26 = h27; h21 = h22

(64)

Net power output

Wnet = WT - WP1 - WP2 - WP3

(65)

Refrigeration capacity

Qref = G19(h23 - h22)

(66)

Where f() stands for function; the subscript h and c represent respectively the heat source and cooling water; the subscript number stands for the state point shown in Fig. 1; the subscript s stands for the isentropic process of turbine or pumps; x18,l stands for

the concentration of solution at the bottom of the rectifier with the minimal reflux ratio Rmin; the subscript 25,l is corresponding to the saturate liquid solution in the generator; and RF is the rectification efficiency.

Table 2 Operation conditions and constraints. Items

Unit

Values

Circulation multiple f

/

3.5

Isentropic efficiency of turbine ηT

%

85

Isentropic efficiency of Pump ηP

%

70

Concentration of refrigerant

%

99.9

Inlet temperature of waste flue gas

°C

450

Turbine inlet temperature

°C

430

Inlet temperature of cooling water

°C

30

Temperature-rise of cooling water in low-p absorber

°C

8

Pinch temperature difference (one side is flue gas)

K

 20

Pinch temperature difference

K

5

Table 3 Parameters of a case for the PPRA-KC. State points

Temperature

Pressure

Concentration Enthalpy

Relative

(°C)

(MPa)

(kg·kg-1)

(kJ·kg-1)

flow rate

1

35

0.1427

0.3173

-46.35

3.5

2

35.07

0.553

0.3173

-45.68

3.5

2'

35.07

0.553

0.3173

-45.68

2.781

2''

35.07

0.553

0.3173

-45.68

0.719

3

76.76

0.553

0.3173

136.1

2.781

3'

82.28

0.553

0.3173

255

2.781

4

83.5

0.553

0.3173

244.6

2.781

4'

83.5

0.553

0.2858

178.2

2.645

4''

83.5

0.553

0.9308

1540

0.136

5

76.79

0.553

0.2858

148.3

2.645

6

50.09

0.1427

0.2858

148.3

2.645

7

48.17

0.553

0.9308

1221

0.136

7'

62.27

0.553

0.5

310

1

8

43

0.553

0.5

-47

1

9

47.34

20

0.5

-12.93

0.5702

10

78.5

20

0.5

125.6

0.5702

11

256.7

20

0.5

1146

0.5702

12

304.7

20

0.5

2153

0.5702

13

430

20

0.5

2648

0.5702

14

88.69

0.1427

0.5

1831

0.5702

14'

81.77

0.1427

0.5

1397

0.5702

15

45.3

0.1427

0.5

510.4

0.5702

16

50.09

0.1427

0.3173

212.7

3.5

17

43.17

1.35

0.5

-45.6

0.4297

18

65.43

1.35

0.5

55.42

0.4297

18'

66.75

1.35

0.5575

68.72

0.01464

18''

97.75

1.35

0.9584

1513

0.1603

19

43.93

1.35

0.999

1303

0.1456

20

35

1.35

0.999

165.6

0.1456

21

12.51

1.35

0.999

57.75

0.1456

22

6.986

0.553

0.999

57.75

0.1456

23

7.508

0.553

0.999

1214

0.1456

24

24.94

0.553

0.999

1322

0.1456

25

130

1.35

0.2442

405.2

0.284

25'

65.5

1.35

0.5019

55.85

0.4444

26

87.28

1.35

0.2442

213.9

0.284

27

59

0.1427

0.2442

213.9

0.284

Table 4 Comparison of the PPR-KC and the PPRA-KC. (th1=450℃, tc1=30℃, xw=0.5) Item

Unit

PPRA-KC

PPR-KC

Split fraction for refrigeration fref

/

0.4297

0.416

Optimum basic concentration xb

/

0.3173

0.3575

Inlet pressure of turbine

MPa

20

20

Back pressure of turbine

MPa

0.1427

0.1879

Absorbers heat rejection (A1 and A2)

kW

-2840

-2842

Condensers heat rejection (C and PC)

kW

-489

-481.4

Pumps work, input WP

kW

-50.3

-46.3

Turbine enthalpy drop hT

kJ·kg-1

816.6

802.3

Net power output Wnet

kW

996.3

981.9

Refrigeration capacity Qref

kW

378.4

369.1

Inlet/outlet temperature of evaporator

°C

6.99/7.51

-20.24/-19.81

Refrigeration COPc

/

4.04

1.831

Heat source exhaust temperatures th4 and th5

°C

158.8/91.4

157.2/95.46

Boiler heat input

kW

3232

3251

Generator heat input

kW

748.3

684.6

Power generation thermal efficiency ηth,e

%

30.83

30.20

Refrigeration thermal efficiency ηth,ref

%

50.57

53.91

Comprehensive thermal efficiency ηth,c

%

27.38

30.07

Waste heat recovery ratio ηwh

%

99.61

98.48

Comprehensive power recovery efficiency η0,c

%

27.27

29.62

(P1, P2 and P3)

Figure Captions Fig. 1. Schematic diagram of the new cogeneration cycle. Fig. 2. Influences of dew point temperature t12. (t13 = 430°C, tcl = 30°C, f=3.5 and fref = 0.4). (a) Pinch temperature difference in boiler and exhaust temperature of heat source, (b) optimum basic concentration and vapor quality of turbine exhaust, (c) low, mid and high pressures, (d) flow rates of work solution for both power and refrigeration and turbine enthalpy drop, (e) refrigeration capacity, net power output and heat consumption, and (f) comprehensive thermal and power recovery efficiencies and waste heat recovery ratio. Fig. 3. Influences of split fraction for refrigeration fref. (t13 = 430°C, tcl = 30°C and f = 3.5). (a) Optimum basic concentration, high pressure, (b) exhaust temperatures of the waste heat source at the boiler and generator outlets, pinch temperature differences in boiler, (c) relative flow rates of the refrigerant and the ammonia vapor from the separator, and the specific enthalpy drop in the turbine, (d) the ratios of transferring heat in R2 to that in R1 and in generator G to that in boiler B, and the temperatures at the evaporator inlet and outlet, (e) refrigeration capacity, net power output and heat consumption, and (f) comprehensive thermal and power recovery efficiencies and waste heat recovery ratio. Fig. 4. Influences of work concentration xw. (t13 = 430°C, tcl = 30°C and f = 3.5). (a) optimum split fraction for refrigeration, optimum basic concentration, inlet and outlet temperatures in the evaporator and the COPc, (b) exhaust temperatures at boiler and generator outlets, temperature at the generator/rectifier inlet and the turbine exhaust vapor quality, (c) refrigeration capacity, net power output and heat consumption, and (d) comprehensive thermal and power recovery efficiencies and waste heat recovery ratio. Fig. 5. Heat exchange diagram t-Q/Qh0. (f = 3.5, fref =opt., t13 = 430°C and tcl = 30°C).

Figures:

Fig. 1. Schematic diagram of the new cogeneration cycle.

105 100

40

95

35

90 tp,B xw 0.45 0.475 0.5 0.525

30 25

th5

80 75 70

20 15

85

Exhaust temperature th5 /C

Pinch temperature dif. tp, 

45

65 270

260

250

280

290

300

310

60

Dew point temperature t12 /C (a) 0.50

1.00

Basic concentration xb

0.40

xw xb 0.45 0.475 0.5 0.525

Y14

0.92 0.88

0.35

0.84

0.30 0.25

0.80 0.76

250

260

270

280

290

300

Dew point temperature t12 /C

(b)

310

Vapor quality Y14

0.96

0.45

28

0.56

24

0.48

20

0.40

16 xw pl 0.45 0.475 0.5 0.525

0.32 0.24

pm

ph

8

0.16 0.08

12

High pressure ph /MPa

Low and mid pressures pl, pm /MPa

0.64

4

250

260

270

280

310

300

290

0

Dew point temperature t12 /C (c)

1.35

Flow rate G17, G9 /Kgs-1

825

1.20 800 xw G17 0.45 0.475 0.5 0.525

1.05

0.90

G9

hT

775 750 725

0.75

250

260

270

280

290

300

Dew point temperature t12 /C (d)

310

700

Specific enthalpy drop hT /kJkg-1

850

1100

4500 4200

Outputs Qref, Wnet /kW

900 800 700

3900

xw Qref Wnet Qin 0.45 0.475 0.5 0.525

600 500 400

3600 3300

Heat consumption Qin /kW

1000

300 200

250

260

270

280

290

300

310

3000

Dew point temperature t12 /C

(e) 0.285

Efficiencies th,c, 0,c

0.280

0.95

0.275

0.90

0.270

0.85

0.265

xw th,c 0,c wh 0.45 0.475 0.5 0.525

0.260 0.255 0.250 0.245

250

260

270

280

290

300

310

0.80 0.75 0.70 0.65

Waste heat recovery ratio wh

1.00

0.60

Dew point temperature t12 /C

(f) Fig. 2. Influences of dew point temperature t12. (t13 = 430°C, tcl = 30°C, f=3.5 and fref = 0.4). (a) Pinch temperature difference in boiler and exhaust temperature of heat source, (b) optimum basic concentration and vapor quality of turbine exhaust, (c) low, mid and high pressures, (d) flow rates of work solution for both power and refrigeration and turbine enthalpy drop, (e) refrigeration capacity, net power output and heat consumption, and (f) comprehensive thermal and power recovery efficiencies and waste heat recovery ratio.

Basic concentration xb

0.44 0.40 0.36 0.32 0.28 0.375

22 20 18 16 14 xw xb ph 12 0.45 0.475 10 0.5 8 0.525 6 4 2 0 0.400 0.425 0.450 0.475 0.500 0.525 Split fraction for refrigeration fref ph, max= 20 MPa

High pressure ph /MPa

0.48

(a)

35

Exhaust temperatures th4, th5 /C

170

30

160

25

150 140 xw th4 0.45 0.475 0.5 0.525

130 120 110 100

th5 tp,B

15 10 5

90 80 0.375

20

0.400 0.425 0.450 0.475 0.500 Split fraction for refrigeration fref (b)

0 0.525

Pinch temperature dif. tp,B /K

180

0.28

840 830

0.24

820

xw hT 0.45 0.475 0.5 0.525

810 800 790

m24

m4''

780

0.20 0.16

770 0.12

760

Relative flow rates m24, m4''

Specific enthalpy drop in turbine hT /kJkg-1

850

750 740 0.375

0.400 0.425 0.450 0.475 0.500 Split fraction for refrigeration fref

0.08 0.525

0.8

12

0.7

8

0.6

4

0.5 0.4 0.3

xw RG/B RR2/R1 t22 0.45 0.475 0.5 0.525

t23

-4 -8 -12

0.2

-16

0.1 0.0 0.375

0

-20

0.400 0.425 0.450 0.475 0.500 Split fraction for refrigeration fref (d)

0.525

Temperatures t22, t23 /C

Ratios of transferring heat RG/B, RR2/R1

(c)

1100

4200

1000

Outputs Wnet, Qref /kW

900

4000

800 700 600 500

xw Qref Wnet Qin 0.45 0.475 0.5 0.525

400

3800 3700 3600

300 200 0.375

3900

0.400 0.425 0.450 0.475 0.500 Split fraction for refrigeration fref

Heat consumption Qin /kW

4100

3500 0.525

(e)

1.00

0.280

0.98

0.276

0.96

0.272

0.94

0.268 0.264 0.260 0.256 0.375

0.92 xw th,c 0,c wh 0.45 0.475 0.5 0.525

0.400 0.425 0.450 0.475 0.500 Split fraction for refrigeration fref

0.90 0.88 0.86

Waste heat recovery ratio wh

Comprehensive efficiencies c,th c,0

0.284

0.84 0.525

(f) Fig. 3. Influences of split fraction for refrigeration fref. (t13 = 430°C, tcl = 30°C and f = 3.5). (a) Optimum basic concentration, high pressure, (b) exhaust temperatures of the waste heat source at the boiler and generator outlets, pinch temperature differences in boiler, (c) relative flow rates of the refrigerant and the ammonia vapor from the separator, and the specific enthalpy drop in the turbine, (d) the ratios of transferring heat in R2 to that in R1 and in generator G to that in boiler B, and the temperatures at the evaporator inlet and outlet, (e) refrigeration capacity, net power output and heat consumption, and (f) comprehensive thermal and power recovery efficiencies and

waste heat recovery ratio.

Optimum fref and xb

1.2 1.0

15

fref xb t22 t 23 COPc

10 5

0.8 0

0.6

-5

0.4

Temperatures t22, t23 /C and COPc

1.4

-10 0.2 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 Work concentration xw (a)

1.00

160 140 120

th4 th5 t18 Y14

0.95 0.90 Y14=0.88

100 80

0.85 th5=90C

0.80

60

0.75 40 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 Work concentration xw (b)

Vapor quality Y14

Temperatures th4, th5 and t18 /C

180

Heat consumption Qin /kW

Outputs Qref, Wnet /kW

1400 4500 1300 4000 1200 3500 1100 1000 3000 900 2500 Qref 800 2000 Wnet 700 Qin 600 1500 500 1000 400 500 300 0 200 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 Work concentration xw

(c)

wh=1

1.00

0.276 0.275 0.274 0.273 0,c=0.00153

th,c 0,c wh

0.99 0.98 0.97 0.96

Waste heat recovery ratio wh

Comprehensive efficiencies th,c, 0,c

0.277

0.272 0.95 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 Work concentration xw

(d) Fig. 4. Influences of work concentration xw. (t13 = 430°C, tcl = 30°C and f = 3.5). (a) optimum split fraction for refrigeration, optimum basic concentration, inlet and outlet temperatures in the evaporator and the COPc, (b) exhaust temperatures at boiler and generator outlets, temperature at the generator/rectifier inlet and the turbine exhaust vapor quality, (c) refrigeration capacity, net power output and heat consumption, and (d) comprehensive thermal and power recovery efficiencies and waste heat recovery ratio.

450 400 Heating flue gas (10 kg/s)

Temperature t /C

350

tp,B

300 250 200 150

xw=0.475 xw=0.5 xw=0.525

100 50 tp,G 0 0.0

0.1

0.2

0.3

0.4

0.5 0.6 Q/Qh0

0.7

0.8

Fig. 5. Heat exchange diagram t-Q/Qh0. (f = 3.5, fref =opt., t13 = 430°C and tcl = 30°C).

0.9

1.0

Highlights Kalina cycle based power and refrigeration cogeneration cycle (PPRA-KC) was studied. Refrigeration sub-branch is parallel to the power loop from outlet of mid-p absorber. To provide chilling water or ice making, refrigerant leads to mid or low-p absorbers. Factors impacting on comprehensive power recovery efficiency of PPRA-KC were studied. Optimal work concentration envelop line for regulating split fraction is presented.