Comparison of combined heat and power systems using an organic Rankine cycle and a low-temperature heat source

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1 *Corresponding author. usherbrooke.ca Comparison of combined heat and power systems using an organic Rankine cycle and a low-temperature heat source... Mohammed Khennich *, Nicolas Galanis and Mikhail Sorin Département de génie mécanique, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1... Abstract Two combined heat and power (CHP) systems using an organic Rankine cycle with R134a and a source at 1008C are modeled. The vapor generator pressure which maximizes the specific (i.e. per unit mass flowrate of the heat source) net power output is determined for different values of the specific heat load and a characteristic temperature difference DT related to the temperature pinch of the heat exchangers. The optimal trade-offs between power and heat outputs are defined and explained for two CHP systems. The results show that both systems generate less mechanical power than the heat delivered to the heating load and that a higher fraction of the heat source is used as the heating load increases. The effects of the specific heat load and of DT on the total thermal conductance, the total exergy destruction and other variables are presented. Keywords: organic Rankine cycle; cogeneration; R134a; optimization Received 10 January 2013; revised 29 March 2013; accepted 7 April INTRODUCTION Two basic configurations of combined heat and power (CHP) systems using various free low-temperature (up to 2008C) heat sources, such as waste heat from various industries or geothermal energy, have been built and analyzed. Practically all of them include a power-generating unit operating according to the subcritical Rankine cycle. In the first one, the heating load is supplied by the heat source via a heat exchanger placed in series with the vapor generator of the power-generating unit [1, 2]. In the second configuration the heating load is supplied by the cooling fluid of the power-generating unit condenser [3, 4]. A variant of this second configuration incorporating a heat pump was recently analyzed by Guo et al. [5]. The choice of working fluid for such power-generating units is the subject of many studies. Water is not suitable at these low temperatures. Therefore, organic fluids or mixtures such as H 2 O/NH 3 have been used in prototypes and commercial systems [2, 6]. Theoretical studies have also considered trans-critical cycles with fluids such as CO 2 [7]. Most recent studies of such units fix the source and sink temperatures and compare the performance of different working fluids [8] or seek to optimize a particular performance indicator (maximize the thermal efficiency, minimize the exergy losses etc.) by varying the evaporation pressure of the working fluid [9]. However, these studies have not addressed the optimization problem when the power-generating unit is part of a CHP system that must satisfy a prescribed heating load. The present study analyzes and compares the performance of these two basic CHP configurations for fixed temperatures of the heat source, the heat sink and the fluid supplying the heating load. The power-generating unit is an organic Rankine cycle (ORC) using R134a. The evaporation pressure (P ev ) that maximizes the net power output is determined for different fixed values of the heating load. Corresponding values of other significant system variables are also determined and compared. 2 DESCRIPTION AND MODELING OF THE CHP SYSTEM Figure 1 shows a schematic representation of the two configurations under consideration. Cycle A, similar to the systems built in Altheim [1] and Husavik [2], comprises three heat exchangers with the heating load heat exchanger in series with the vapor generator of the ORC unit: the heat source supplies some of its energy to the working fluid of the ORC system and therefore its temperature at the exit from the vapor generator is T s*, T s,in ;it then flows through the heat load heat exchanger where its temperature decreases to T s,out while that of the secondary heat # The Author Published by Oxford University Press. All rights reserved. For Permissions, please journals.permissions@oup.com doi: /ijlct/ctt028 Advance Access Publication 12 May 2013 i42

2 Comparison of combined heat and power systems Figure 1. Schematic representation of the cogeneration systems under consideration. Table 1. Inputs and temperature relations used in the model. Cycle A Fixed inputs _M s ; T s,in, x 1, h T, h P,DT,T h,in, T h,out, T p,in,t s,out, Condenser pinch ¼ DT/2 Cycle B _M s ; T s,in, x 1, h T, h P,DT,T h,in, Condenser pinch ¼ DT/2 Variable inputs P ev, Q h P ev, Q h Temperature relations T 3 ¼ T s,in 2 DT, T 1 ¼ T p,in þ DT T 3 ¼ T s,in DT, T 1 ¼ T h,in þ DT transport fluid increases from T h,in to T h,out. Cycle B, similar to the system built in Lienz [4], comprises only two heat exchangers because the heating load is supplied by the condenser of the ORC unit (thus in this case _M p ; _M h and T p,in ; T h,in ). The systems are supposed to operate under steady-state conditions. Heat and pressure losses as well as kinetic and potential energies are neglected. The working fluid is assumed to be saturated liquid at the exit from the condenser. The heat source is an industrial gas which is modeled as air. The isentropic efficiency of the pump and the expander are fixed (80%). We also fix the temperature of the heat source entering the vapor generator (T s,in ¼ 1008C which corresponds to process waste gases of some metallurgical transformations), of the cooling water entering the condenser (T p,in ¼ 108C which corresponds to the yearly average temperature of the St. Lawrence river) and of the water which supplies the heating load at the inlet of the heat exchanger (T h,in ¼ 558C which is the average of the corresponding temperatures in two operating prototypes [1, 4]). The temperature difference (DT) between the working and external fluids at the inlet of the latter into the vapor generator and the condenser takes one of the three chosen values (5, 10 or 15 K). Two constraints are also imposed on the operating variables. First, we require that at the expander exit the liquid content of the working fluid must be,5%. Secondly, we specify that the temperature pinch in each heat exchanger must be no less than DT/2. In the case of Cycle A, we also fix the temperature of the water which supplies the heating load at the outlet of the heat exchanger (T h,out ¼ 708C which is between the corresponding temperatures of two operating systems [1, 4]) and of the heat source leaving the system (T s,out ¼ 708C). In the case of Cycle B, the temperature of the water at the position of the condenser pinch is equal to (T 1 2 DT/2) ¼ (T h,in þ DT/2). Table 1 recapitulates the inputs and temperature relations for the two systems under study. The model comprises the equations expressing mass and energy conservation for each component of the system, the expressions of the expander and pump isentropic efficiencies in terms of the appropriate thermodynamic properties as well as the expressions of the heat and power transfers in terms of the appropriate mass flowrates and enthalpies. It also includes the expression of each heat transfer rate in terms of the thermal conductance and logarithmic mean temperature difference of each heat exchanger (vapor generator, load heat exchanger and/or condenser). Thus, for example, for the heating load heat exchanger of Cycle A: _M s c p;s ðt s T s;out Þ¼ _M h c p;h ðt h;out T h;in Þ¼UA DT ln ; where _M is the mass flowrate; c p the specific heat; UA the thermal conductance (subscripts in, out, s and p denote inlet, outleft, source and sink, respectively) and DT ln ¼ ½ðT s T h;out Þ ðt s;out T h;in ÞŠ ln½ðt s T h;out Þ=ðT s;out T h;in ÞŠ and for the pump of both cycles _mðp 2 P 1 Þ¼h p _mðh 2 h 1 Þ; where _m is the mass flowrate of working fluid in the ORC (subscripts 1 and 2 denote thermodynamic states of working fluid in the ORC). These equations have been implemented in Engineering Equation Solver (EES [10]), which also includes relations between the thermodynamic properties of R134a and many other pure fluids. The resulting system of nonlinear algebraic i43

3 M. Khennich et al. equations has been validated [11] in the case of a simple ORC generating unit (i.e. which is not part of a CHP system). In the present case, this system of equations involves more variables than equations. We have therefore addressed an optimization problem for different specified values of the heating load Q h. Its objective is to determine the evaporation pressure of the R134a that maximizes the net power output of the ORC and satisfies the specified heating load. This approach is analogous to that in [9, 11] for ORC cycles which are not part of a CHP system. The maximization of the net power output is an important objective since the ORC converts only a small fraction of the source s thermal energy due to its low temperature. The investigated range of evaporation pressures is limited by the two saturation pressures of R134a corresponding to the condensation temperature (T 1 ¼ T p,in þ DT) and to its temperature at the exit from the vapor generator (T 3 ¼ T s,in 2 DT). 3 RESULTS The results for three values of DT (5, 10 and 15 K) and the two studied configurations are presented in Figures 2 4. The extensive quantities (heating load, maximum net power output, total exergy destruction and total thermal conductance of the heat exchangers) are presented per unit mass flowrate of the heat source (indicated as specific quantities). The dead state for exergy calculations is at atmospheric pressure and T DS ¼ 108C (the same as the temperature of the cooling water entering the condenser of Cycle A subscript DS represent dead state temperature). The intensive quantities are the optimum evaporation pressure (determined with the Golden Section Search method available in EES) and the corresponding vapor generator pinch (VGP). The energy utilization factor 1 is equal to the ratio of the total useful effects (heating load plus maximum net power output) to the enthalpy difference between the source inlet and the dead state ( _M s c ps ðt s;in T DS ÞÞ; therefore, 1 is independent of the heat source mass flowrate and its denominator is fixed for the conditions under investigation. It provides a non-dimensional index of the energy performance of the systems under consideration. Figure 2 illustrates the effects of the specific heating load on the maximum net power output per unit mass flowrate of the heat source and the corresponding optimum evaporation pressure (P 2 ¼ P 3 subscripts 2 and 3 denote the thermodynamic states of working fluid in the ORC). For both configurations, Q h is maximum when W n,max (subscript max denotes maximum) is Figure 2. Effects of Q h on W n,max and P ev,op (subscripts ev, h and op denote vapor generator, heat transport fluid and optimum, respectively) for three values of DT. Figure 3. Effects of Q h on UA and 1 for three values of DT. i44

4 Comparison of combined heat and power systems Figure 4. Effects of Q h on VGP and E d for three values of DT. nil (for this condition T s* ¼ T s,in ). The maximum value of Q h for Cycle A is independent of DT (approximately equal to 30 kj/kg) since the ORC unit is not operating under these conditions. This value is approximately the same as that for Cycle B with DT ¼ 10 K. The maximum value of Q h for Cycle B increases monotonically with DT. It should be noted that for most combinations of Q h and DT, Cycle A produces a higher net power output per unit mass flowrate of the heat source; Cycle B produces a higher W n,max only when DT ¼ 5 K and Q h kj/kg. Furthermore, it is important to note that for both cycles the value of W n,max is always much smaller than the corresponding value of Q h. Figure 2 also shows that in the case of Cycle A the quantity W n,max decreases monotonically as Q h increases. Qualitatively this behavior could have been predicted from the operating conditions of Cycle A. It is due to the fact that the enthalpy drop of the source, c ps.(t s,in 2 T s,out ), is constant since both T s,in and T s,out are fixed for this configuration. Therefore, the increase of Q h causes an increase of the intermediate source temperature T s* (see Figure 1) and a decrease of the heat supplied to the ORC unit which results in a decrease of the net power output. On the other hand, in the case of Cycle B the variation in W n,max with Q h is not monotonic. For low values of Q h, W n,max increases with Q h but for high values of Q h the trend is reversed while T s,out decreases monotonically as Q h increases. This behavior of W n,max is due to the fact that, for low values of the heating load, as Q h increases the decrease in the source outlet temperature is such that the source supplies to the system more energy than the increase in Q h. As a result, the ORC produces more net energy. On the other hand, for high values of Q h, as the heating load increases, the decrease in the source outlet temperature is small and thus the source supplies to the system less energy than the increase of Q h. As a result the ORC produces less energy under these conditions. The effect of the DT on W n,max is the same for both configurations: W n,max decreases when DT increases because the maximum temperature of the cycle (T 3 ) decreases while its minimum temperature (T 1 ) increases. Finally, Figure 2 shows that the effect of Q h on the optimum evaporation pressure is not the same for cycles A and B. In the first case, it increases with Q h while in the second one it decreases as Q h increases. This behavior is due to the fact that as Q h increases the average temperature of the heat source in the vapor generator increases in the case of Cycle A (since T s* increases with Q h ) but it decreases in the case of Cycle B (since T s,out decreases as Q h increases). The only exceptions are for Cycle A at high values of Q h and for Cycle B at very small values of Q h (and DT ¼ 158C); for these conditions, the evaporation pressure is equal to the saturation pressure corresponding to T 3 and remains therefore constant. Furthermore, Figure 2 shows that for both configurations the optimum evaporation pressure decreases as DT increases. The effect of DT on the optimum evaporation pressure is more pronounced in the case of Cycle B. For values of Q h smaller than 11 kj/kg the optimum evaporation pressure for Cycle A is lower than the corresponding value for Cycle B. For higher values of Q h, the optimum evaporation pressure for Cycle A is higher. Figure 3 shows the effects of Q h on the total thermal conductance UA of the heat exchangers and on the energy utilization factor 1. The latter decreases as DT increases but this effect is small, especially for large values of Q h ; therefore, only the results for DT ¼ 5 K are shown. For both cycles, the energy utilization factor increases with Q h since, as noted before, its denominator is constant while its numerator increases because Q h varies more rapidly than W n,max. The values of 1 are higher in the case of Cycle A when Q h is smaller than 23 kj/kg; on the other hand, when Q h is bigger 1 for Cycle B is slightly higher. Cycle B is particularly appropriate for heating loads exceeding 30 kj/kg for which Cycle A is inoperative (for higher heating loads T s,out must be lower than the imposed value of 708C). As shown in Figure 3 the qualitative effect of Q h on the total thermal conductance UA of the heat exchangers is strikingly different for the two configurations under consideration. As Q h increases, UA decreases for Cycle A while it increases for Cycle B. In the first case, this behavior is due to the progressive decrease of the size of the ORC unit which in the limit (T s* ¼ T s,in or equivalently W n,max ¼ 0) leads to the elimination of the vapor generator and condenser. On the other hand, in the case of Cycle B, the increase in Q h necessitates a bigger vapor i45

5 M. Khennich et al. generator and a bigger condenser since the heat supplied by the source to the heating load is transferred through the ORC unit. The values of UA are higher in the case of Cycle A when Q h is smaller than 16 kj/kg; on the other hand, when Q h is bigger UA for Cycle B is higher. The effect of DT on UA is the same for both configurations: as DT increases UA decreases since the DT between the two fluid streams in the vapor generator and condenser decreases. For Cycle A, this effect decreases as Q h increases since under these conditions the importance of the vapor generator and condenser of the ORC unit diminishes. In the case of Cycle B, the effect of DT on UA increases as Q h increases since under these conditions the vapor generator and condenser of the ORC unit grow bigger. Figure 4 shows the effects of Q h on the VGP and on the specific total exergy destruction E d for the operating conditions for which the specific net power output is maximum. The qualitative influence of Q h on these two quantities is different for the two cycles. Thus, as Q h increases E d decreases for Cycle A and increases for Cycle B. The reasons for this opposite behavior are the same as those explaining the influence of Q h on UA. The effect of DT on E d is the same for both configurations: as DT increases E d decreases since the temperature difference between the two fluid streams in the vapor generator and condenser decreases. For Cycle A, this effect decreases as Q h increases while the opposite is true in the case of Cycle B. The reasons for this opposite behavior are the same as those explaining the influence of Q h on UA. The VGP shown in Figure 4 increases with DT and remains constant over a fairly large range of Q h values for both cycles. These constant values of VGP are in each case equal to DT/2, the chosen minimum acceptable value. In the case of Cycle A, they occur at low values of Q h ;asq h increases the VGP for this cycle increases. However, this increase is not very important and does not change the decreasing trend of UA and E d despite the fact that it increases the logarithmic mean temperature difference of the vapor generator. It should be noted that for Cycle A with DT ¼ 5 K the VGP for Q h higher than 23 kj/kg is independent of Q h and equal to DT. This indicates that for these conditions the VGP occurs at the source inlet since it is equal to (T s,in 2 T 3 ). In the case of Cycle B, the constant values of VGP occur at high values of Q h ;asq h decreases the VGP for this cycle increases. However, this increase is not very important and does not change the decreasing trend of UA and E d despite the fact that it increases the logarithmic mean temperature difference of the vapor generator. 4 CONCLUSION The effects of the specific heat load Q h on the two CHP cycles under study are very different. Thus, for Cycle A, as Q h increases the maximum specific net power output, the total thermal conductance and the total exergy destruction decrease. On the other hand, for Cycle B, as Q h increases the maximum specific net power output does not vary monotonically (it reaches a maximum value) while the total thermal conductance and the total exergy destruction increase. In general, the maximum value of the specific net power output is higher for Cycle A. For low values of the specific heat load, Cycle A requires a lower optimum evaporation pressure, has a higher energy utilization factor but necessitates larger values of the total thermal conductance. Cycle B is particularly appropriate for high values of the specific heat loads for which Cycle A is inoperative. Both cycles generate considerably less mechanical power than the quantity of heat delivered to the heating load. Furthermore, in both cases a higher fraction of the energy content of the heat source is used as the heating load increases. The presented results indicate that the preliminary design of CHP systems should consider both cycles. For a given specific heat load and fixed values of the external fluids temperature, the choice between Cycles A and B must be based on their respective maximum net power output and the corresponding optimum evaporation pressure as well as on the thermal conductance of the heat exchangers since P ev and UA influence the size, and cost, of the system. REFERENCES [1] Pernecker G, Uhlig S. Low-enthalpy power generation with ORCturbogenerator. The Altheim project, Upper Austria. GHC Bull 2002; 23: [2] Hjartarson H, Maack R, Johannesson S. Husavik energy multiple use of geothermal energy. GHC Bull geoheat.oit.edu/bulletin/bull26-2/art3.pdf. [3] Schuster A, Karellas S, Kakaras E, et al. Energetic and economic investigation of Organic Rankine Cycles applications. 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Engineering Equation Solver (EES), Academic Commercial V McGraw Hill, [11] Khennich M, Galanis N. Thermodynamic analysis and optimization of power cycles using a finite low-temperature heat source. Int J Energy Res DOI: /er i46