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Internal Combustion Engine (ICE) bottoming with Organic Rankine Cycles (ORCs)
Energy 35 (2010) 1084–1093
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Internal Combustion Engine (ICE) bottoming with Organic Rankine Cycles (ORCs) Iacopo Vaja*, Agostino Gambarotta University of Parma, Industrial Engineering Department (IED), via G. P. Usberti 180/A, 43100 Parma, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2008 Received in revised form 2 June 2009 Accepted 12 June 2009 Available online 4 July 2009
This paper describes a specific thermodynamic analysis in order to efficiently match a vapour cycle to that of a stationary Internal Combustion Engine (ICE). Three different working fluids are considered to represent the main classes of fluids, with reference to the shape of the vapour lines in the T–s diagram: overhanging, nearly isoentropic and bell shaped. First a parametric analysis is conducted in order to determine optimal evaporating pressures for each fluid. After which three different cycles setups are considered: a simple cycle with the use of only engine exhaust gases as a thermal source, a simple cycle with the use of exhaust gases and engine cooling water and a regenerated cycle. A second law analysis of the cycles is performed, with reference to the available heat sources. This is done in order to determine the best fluid and cycle configuration to be employed, the main parameters of the thermodynamic cycles and the overall efficiency of the combined power system. The analysis demonstrates that a 12% increase in the overall efficiency can be achieved with respect to the engine with no bottoming; nevertheless it has been observed that the Organic Rankine Cycles (ORCs) can recover only a small fraction of the heat released by the engine through the cooling water. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine Cycle Internal Combustion Engine Combined cycle
1. Introduction Organic Rankine Cycles (ORCs) can use different working fluids in order to exploit low grade heat sources to produce useful work. An interesting application of ORCs is to couple them with other prime movers and utilize their wasted heat, thus realizing a combined power unit with the effect of enhancing the overall system efficiency [1–4]. Since the ORC systems generate additional power without requiring extra fuel, the specific pollutant emissions of the combined plant are reduced. Organic fluids are to be preferred to water when the required power is limited and the heat source temperature is low, as these fluids often have lower heat of vaporization and can better follow the heat source to be cooled, thus reducing temperature differences and therefore irreversibilities at the evaporator. Furthermore, turbines for organic cycles can provide higher efficiencies at part loads as well and are usually less complex (1 or 2 stages, for an axial turbine) due to the lower enthalpy drop of the fluid [5,6]. Also ORC systems exhibit great flexibility, high safety and low maintenance
* Corresponding author. Tel.: þ39 0521 905863; fax: þ39 0521 905705. E-mail address: [email protected] (I. Vaja). 0360-5442/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2009.06.001
requirements in recovering low-medium grade waste heat, from industrial processes or power plants [7]. Evaporators for ORCs are usually simple components designed as a heat exchanger with direct use of hot gases released by the thermal source, often without use of intermediary fluids, such as diathermic oils. They also have one level of evaporating pressure [1,4]. Recently many power units based on Internal Combustion Engines (ICEs) are being employed as base components in Distributed Energy Systems (DES), intended as systems where power is generated in small decentralized units. DES are usually appreciated because they could help to reduce emissions, save grid capacity, provide opportunities for renewable energy and increase overall energy generation and distribution efficiency [8]. ICEs are often chosen for their reliability, low specific cost and high electrical efficiency, especially in the power range of hundreds of kW to few MW. It may happen however that many of these engines are fuelled using biomass (such as vegetal oils, biogas or others) and the existence of incentives (such as Green Certificates in Italy) for plants based on Renewable Energy Sources makes the operation of these units a viable solution even if no heat is usefully recovered. Few examples of ORCs coupled to ICEs exist and usually the ORC is conceived to efficiently exploit only the heat released at high
I. Vaja, A. Gambarotta / Energy 35 (2010) 1084–1093
Nomenclature
F
H H_
Subscripts C Condenser P Pump R Regenerated/regenerator T Turbine a Available appr Approach cond Condenser crit Critical dead Dead state e Engine ex Heat exchanger f Fluid fin Final g Gas in Inlet out Outlet w Water
P Q Q_ S S_ T V V_ cp h m _ m p s v
Enthalpy [kJ] Enthalpy flow [kW] Power [kW] Heat [kJ] Heat flow [kW] Entropy [kJ/K] Entropy flow [kJ/s K] Temperature [K] Volume [m3] Volume flow rate [m3/s] Specific heat at constant pressure [kJ/kg K] Specific enthalpy [kJ/kg] Mass [kg] Mass flow rate [kg/s] Pressure [kPa] Specific Entropy [kJ/kg K] Specific volume [m3/kg]
Greek symbols Air fuel ratio [–] Heat exchanger effectiveness [–] Efficiency [–] Organic Rankine Cycle efficiency [–] Global efficiency [–]
a 3 h hORC hg
temperatures such as the engine exhaust gases. In [2,3], for example, a setup is proposed where a low speed two stroke marine turbocharged Diesel engine acts as the topper of a combined cycle with exhaust gases used for a bottoming cycle based on a Rankine cycle. The paper describes a full mathematical model built to evaluate the mutual operation of the Diesel engine as source of power and waste heat and a HRSG with a steam turbine, in the whole power-speed spectrum of the Diesel engine. While very comprehensive and detailed, the papers focus on the issue of offdesign operation of the system, which is not so important for stationary engines that are always operated at rated conditions. Furthermore in the proposed design the vapour cycle is based on a conventional water–steam cycle due to the high thermal power available from the marine engine. In [9] the retrofit with two different ORC system rated about 10 kWe of a small engine with a power of 200 kWe, fuelled with biogas, is considered. The bottomer, based on R134a, in this case is thermally fed using only the engine cooling water. The paper focuses on the application of scroll expanders, that may be advantageous when the power of the ORC is limited. The feasibility of the system is supported by field tests conducted on an experimental unit. The availability of waste heat at two different levels of temperature is usually a problem for the application of ORCs onto ICEs. In [16] for example, a mini-hybrid solar power plant is presented, characterized by a field of solar concentrators and a bioDiesel engine integrated to two superposed ORCs. When the system operates in hybrid mode the heat released by the engine, in series with the heat generated by the solar system, is employed to power two simple ORC cycles, the first based on R123 and the second on R134a. Besides the use of solar thermal power, the design proposes a possible solution when heat is available at different temperature levels, with the second ORC powered both by the heat released by the first ORC and by the heat from the engine cooling network, that may be provided either in series as liquid preheater or parallel to the evaporator. Laboratory tests made with the superposed ORCs
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Heat availability [–]
Abbreviations CC Combined Cycle ICE Internal Combustion Engine ORC Organic Rankine Cycle PP Pinch Point
confirmed adequate operational characteristics with good performances over a broad range of conditions, indicating the feasibility of the design. The assessment of double cascade ORC designs in conjunction to stationary ICEs has been considered [19] and will be presented in future works. The present paper is focused on evaluating the extra power achievable by using an ICE as a heat source for just one vapour power cycle, thus with a rather simplified design of the heat recovering unit, under the hypothesis of operating the engine at full load while considering different cycles based on different organic fluids and configurations. 2. The systems considered in the investigation In the analysis a commercial cogeneration engine is considered as a topping system. The engine is a 12 cylinder 4 stroke supercharged natural gas fired medium speed: the main parameters of the engine are reported in Table 1. From the engine data it has been evaluated that about 1700 kWt is available by cooling the exhaust gases down to 120 C (Tg,min) and about 1000 kWt is available from the engine cooling water. It has been calculated that the air fuel ratio a is 29.2 and the excess air coefficient e is 0.701 at nominal conditions, under the hypothesis of perfect combustion of pure methane. The composition
Table 1 Main engine characteristics. Electrical power output Fuel consumption Rated electrical efficiency Engine speed Exhaust gas temperature Exhaust mass flow Combustion air mass flow Engine jacket temperatures Engine jacket flow
2928 7002 41.8 1000 w470 15,673 15,154 79/90 w90
kW kW – min1 C kg/h kg/h C m3/h
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of the exhaust gases on the basis of mass has been calculated at: CO2 ¼ 9.1%, H2O ¼ 7.4%, N2 ¼ 74.2%, O 2¼ 9.3%. This composition is used to evaluate the gas properties. In the study, the engine is assumed to operate at rated conditions as the aim is to determine which organic cycle would better fit the overall heat available for these conditions. Organic fluids used for power applications may have different characteristics in the T–s diagram and the saturation lines may be bell shaped, nearly isentropic or overhanging depending on the fluid molecule complexity. Typically fluids with simpler molecules are characterized by bell shaped vapour lines and lower critical temperatures and fluids with more complex molecules display a overhanging vapour line and higher critical temperatures [10]. In the paper three fluids commonly adopted for technical applications were chosen to represent these different behaviours in the T–s diagram (Fig. 1): benzene (overhanging), R11 (isentropic) and R134a (bell shaped). They are commonly quoted in literature as possible fluids for ORCs [11,12], even though future work would lead to consider other pure fluids or fluid mixtures [13]. It should be noted that in the proposed analysis only thermodynamic aspects will be considered. It is important to remark however that fluids for ORC applications must not only be favourable from a thermodynamic point of view, but have to satisfy conditions such as [11,14]: -
-
chemical stability at the operating pressures and temperatures; environmental friendliness: low ozone depletion potential (ODP), global warming potential (GWP) and atmospheric lifetime (ALT); non toxic, non corrosive and compatible with engine materials; low flammability and auto-ignition properties.
In the analysis that follows three cycle configurations will be assumed, in order to compare not only the fluids considered but also the different cycle setups and to verify the most feasible application of ORCs coupled with ICEs. The setups assumed are: -
-
-
ORC simple cycle thermally powered by engine exhaust gases (Fig. 2a); ORC simple cycle thermally powered by engine exhaust gases and engine refrigerant water (Fig. 2b); regenerated ORC thermally powered by engine exhaust gases (Fig. 2c).
Fig. 2. Scheme of different ORC cycle configurations assumed for ICE bottoming.
For all the cycles considered the following assumptions are valid: -
-
Fig. 1. Different shapes of coexistence curves in the T–s diagram for the considered fluids.
-
isentropic turbine efficiency: hT ¼ 0.7 (this value is conservatively below usual values that may range between 0.8 and 0.88 [6,14,15]); isentropic pump efficiency: hP ¼ 0.8; working fluid temperature at condensation: Tcond ¼ 308 K; vaporizing pressure varying between condensation pressure pcond and critical pressure pcrit; negligible pressure losses in the heat exchangers and pipes; dry expansion for all fluids;
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The last hypothesis has been introduced assuming that a dry expansion would be preferable for the preservation of the expander. This is to eliminate the impingement of liquid droplets on turbine blades. Therefore a slight superheating will be assumed when the isentropic expansion line crosses the vapour line. In other words, it will be considered just the minimum superheating to keep an isentropic expansion totally in the dry zone of the diagram. Introducing high degrees of superheating, however, is not convenient from a thermodynamic point of view, as the cycle efficiency is a weak function of turbine inlet temperature once the evaporating pressure is chosen. In some cases, the highest cycle efficiencies are obtained when superheating is avoided and the fluid is expanded directly from dew line, as demonstrated in [12]. In [15] it has been also shown, through a comprehensive analysis based on irreversibility calculations, that superheating organic cycles (especially if based on overhanging fluids) increases cycle irreversibility and decreases the second law efficiency. As further assumption the extra costs of building the ORC when the turbine inlet pressure is raised have been neglected [12]. The turbine pressure therefore has been assumed as an independent variable of the problem, the only limitation being the field of fluid stability. Fluid properties have been evaluated using the REFPROPÒ database [16] that has been utilized in MatlabÒ. Specific MatlabÒ functions were defined and compiled to evaluate cycle properties and performance in a parameterized way. This is in order to assess the effects of changes in one or more variables (as, for example, the pressure at the evaporator inlet p2) on the main cycle characteristics.
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It is to be noted that in Eq. (1) the organic fluid enthalpies are function of the evaporating pressure chosen for the ORC and cp;g is calculated with REFPROPÒ according to the exhaust gas composition at the average temperature. A second energy balance allows to determine the exhaust gas temperature at the evaporator outlet:
Tg;fin ¼ Tg;PP
_ f ;1 ðh2 h1 Þ m _ g cp;g m
(2)
If Tg,fin calculated with Eq. (2) is lower than the minimum allowed temperature for the gases, a procedure decreases the _ f ;2 is the organic fluid mass flow rate while Tg,fin is above Tg,min. m fluid mass flow rate that satisfies the imposed condition and represents the new fluid mass flow rate for the cycle. The actual gas Pinch Point temperature can be calculated using:
Tg;PP ¼ Tg;out
_ f ;2 ðh30 h2 Þ m _ g cp;g m
(3)
All the organic fluids (especially at relatively high pressures) considered in the analysis have a specific heat of vaporization lower in comparison to that required to warm up the fluid between point 1 and 2 of Fig. 3. Therefore Tg,fin calculated with Eq. (2) is always smaller than Tg,min,. This means that there are no Pinch Point limitations in the heat exchange process and that which limits the amount of heat introduced to the cycle is the need to avoid overcooling of the engine exhaust gases. The global efficiency of the system can be defined as the net power produced by the cycle referred to the total available heat Q_ a
[17]: 3. The ORC simple cycle
P
In Fig. 3 the heat exchange diagram of the evaporator is proposed for a generic ORC simple cycle with no superheating. Heat needed to vaporize the organic working fluid is provided in this case solely by the engine exhaust gases (according to Fig. 2a). The _ g ) are gas temperature at engine exhaust (Tg,out) and flow rate (m defined and constant. A minimum gas pinch point temperature (Tg,PP) is considered (Tg,PP ¼ T2 þ DTPP, where DTPP ¼ 30 K is the minimum temperature difference at Pinch Point to meet the gas/ fluid heat exchanger performances) and this allows writing a first energy balance referred to complete fluid vaporization:
_ f ;1 ¼ m
_ g cp;g Tg;out Tg;PP m h30 h2
(1)
Fig. 3. T—Q_ diagram of the evaporator for a ORC heated with engine exhaust gases.
hg ¼ ORC ¼ 3$hORC Q_ a
(4)
where 3 is the evaporator effectiveness [18]:
cpg Tg;out Tg;fin 3¼ cpg Tg;out T1
(5)
and hORC the organic Rankine cycle efficiency:
hORC ¼
PORC PORC ¼ h3 h1 cpg Tg;out Tg;fin
(6)
From Eq. (4) it can be observed that not always can the maximum global efficiency be achieved with maximum cycle efficiency (hORC). It could happen that with increasing turbine inlet pressure the cycle efficiency increases but the final gas temperature is also increased, thus determining a decrease in the evaporator effectiveness 3. Combination of these two terms might provide that the turbine inlet pressure that maximizes hORC is not the one that maximizes hg [1,18]. The analysis that follows therefore is a result of determining the optimal pressure at turbine inlet that would maximize hg and in turn, provide the maximum ORC power at a given value of Q_ a . In Fig. 4 the cycle efficiency is plotted for the reference fluids in the range of turbine inlet pressures between pcond and pcrit (where pcrit is the critical pressure of each fluid). As expected benzene displays higher achievable efficiencies. The curves are monotonic for all fluids (solid lines): a consequence of the hypothesis from introducing a minor degree of superheating while the isentropic expansion is not completely dry. For higher pressures, the introduced superheating becomes higher and this slightly rises the cycle efficiency. The corresponding dotted curves are plotted for the saturated Rankine cycle (with no superheating) and in this case the
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Fig. 4. Simple cycle efficiencies for evaporation pressures between pcond and pcrit.
Fig. 6. Relative variation of net cycle power output for simple Rankine cycles at different evaporation pressures.
curves show a maximum value of the cycle efficiencies for pressures not far from critical: in particular a maximum hT value of 0.2146 is achieved with benzene at a pressure of 4470 kPa. _ f ðh30 h4 Þ, The curves in Fig. 5 refer to the net power (PORC ¼ m see Fig. 9 for symbols) achievable from the cycles at different pressures of vaporization. The shape of the plotted curves is similar to that of the efficiency curves (Fig. 4). The curves for all fluids have their maximum value at the critical pressure as a consequence of pattern of the efficiency curves. In the analysis an optimal value of p2 will be chosen (indicated by the * symbol in the figures) as the one that maximizes the efficiency curves referred to saturated Rankine cycle (dotted lines of Fig. 4). Therefore the optimum pressure is chosen as 4470 kPa for benzene which returns a net power output of 376 kW, 3835 kPa for R11, with 290 kW and 3723 kPa for R134a with a net power output of 147 kW. In Fig. 6 the dimensionless cycle power output is plotted in the assumed pressure range with reference to the cycle power output, determined at the optimal pressure for each fluid (* of Fig. 5). It can be noted that not only is benzene the fluid with the highest power output value, but it also shows the smallest variations from the optimal power. For example at pressures of 1700 kPa, a cycle based on benzene provides about 90% of the optimal power output. This characteristic leads to consider cycles with lower expansion ratios, while simultaneously simplifying the compression and expansion phases. Fluids with bell shaped vapour lines display instead higher variability in power output with respect to vaporization pressure.
This would result in the Rankine cycle being operated at a pressure as close as possible to the optimal pressure for these fluids. In Fig. 7 the estimated value of working fluid mass flow rates are plotted again with respect to the pressure at turbine inlet. It is possible to observe that benzene requires the lowest fluid mass flow rate as consequence of the highest enthalpy increase between state 3 and 1. The energy balance at the evaporator determines higher masses of fluid for R123 and R134a in order to match the total energy of the flue gasses. Fig. 8 reports, for each fluid, the curves referring to actual volumetric flow rate at the expander inlet ðV_ 3 Þ and the turbine outlet/inlet volume flow ratio (v4/v3). The latter parameter is particularly significant as it shows how much the fluid volume increases through the expansion. Fig. 8a refers to benzene and shows that a high value of the ratio v4/v3 of 374 is produced when the cycle is operated at the optimal pressure of 4470 kPa (*), and V_ 3 ¼ 0:015 m3 =s. Considerations regarding the power curve for benzene (Figs. 5 and 6), suggest that a lower evaporating pressure would allow lower turbine outlet/inlet volume flow ratios, while providing a net power output close to optimal. In this case, the cycle would be better operated if a lower pressure was chosen since a simpler expander could be employed. As a reference for this analysis a new optimal value of evaporating pressure for benzene is selected at 2000 kPa (marked with - in Fig. 8a) even if further and more precise considerations would require matching with an actual
Fig. 5. Simple cycle power output at different evaporation pressures.
Fig. 7. Simple cycle working fluid mass flow rate required at different evaporation pressures.
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The graphs plotted in Fig. 9 show the thermodynamic cycle on the T—S_ diagram for the three considered fluids. The curve referring to the engine exhaust gases is superimposed on the diagrams by properly scaling the entropy axes. It is evident, the lower the critical temperature the greater the temperature difference between gases and organic fluid in the heater/evaporator. This temperature difference induces irreversibilities that are the main cause for low thermodynamic efficiencies with R11 and R134a. Future works will include a detailed exergy analysis where the causes of exergy reduction within each component of the system will be properly quantified and discussed [19]. The proposed representation however allows to observe the entropy generation rate due to the heat transfer process between hot gases and organic fluid:
_ f ðs30 s1 Þ m _ g sg;out sg;fin S_ ex ¼ m
(7)
This value, that can be gathered from Fig. 9a–c, is, as expected, the bigger the higher average temperature difference in the heat exchanging process. Particularly S_ is 0.924, 1.234 and 1.842 kJ/s K for benzene, R11 and R134a respectively. Table 2 reports the main parameters for the three cycles proposed (the values for benzene have been estimated at vaporizing pressure of 2000 kPa). It can be observed that a maximum power output of about 350 kW can be achieved from a benzene based simple cycle (hORC ¼ 0.2) while the power decreases to about 190 kW 150 kW with R11 and R134a respectively (hORC ¼ 0.17 and 0.08). It should be noted that in all cases the heat flow provided to the cycles with the engine exhaust gases is the same as they are cooled down to the minimum allowed temperature Tg,min (there are no Pinch Point limitations). 4. ORC with use of heat available from engine refrigerant A further comparison of the selected cycles has been carried out under the hypothesis of employing the engine cooling water for a partial preheat of the organic fluids upstream the main evaporator (Fig. 2b). The thermodynamic cycles are the same as defined in the previous section (Fig. 9) and the cycle efficiency is unchanged. A new heat source is now considered for preheating the working fluid. In the analysis a heat exchanger with a reasonable efficiency has been assumed for the water/fluid heat exchange process, with a temperature difference of 20 K between water inlet and organic fluid outlet (Tw,PP). The energy balance at the water/fluid heat exchanger gives the _ f 1 is the fluid mass first value of the organic fluid mass flow rate: m flow rate that allows complete exploitation of energy available from the cooling water: Fig. 8. Volume flow rate at turbine inlet ðV_ 3 Þ and turbine outlet/inlet volume flow ratio (v4/v3) for different fluids at different evaporation pressures.
commercial expander. At this new value of evaporating pressure the net power output from the cycle becomes 349 kW, the ratio v4/ v3 decreases to 107 while V_ 3 increases to 0.052 m3/s (Table 2). On the other hand, R11 and R134 show lower turbine outlet/inlet volume flow ratios at the chosen evaporating pressure, suggesting that a simple expander could be employed with these fluids even at optimal pressures. It should be noted that the ratio v4/v3 can change significantly depending on the characteristics of the working fluid. Several fluids can achieve values up to 550 and when v4/v3 is smaller than 50, expansion efficiencies higher than 0.8 can be achieved via a single stage axial turbine [1].
_ f ;1 ¼ m
_ w cp;w Tw;out Tw;in m hA h1
(8)
A new energy balance should be written for the evaporator to match the available energy from the engine exhaust gases and the energy required to fully vaporize and superheat the working fluid (if superheating is considered):
_ f ;2 ¼ m
_ g cp;g Tg;out Tg;PP m h30 h2
(9)
_ f 1 is apparently higher than m _ f 2 . This For the cycles analyzed, m condition would in fact not allow complete exploitation of energy available from the cooling water. A further energy balance would define the final temperature of _ f ;1 ; m _ f ;2 Þ it gives: _ f ;3 ¼ minðm the gases leaving the exchanger. If m
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Table 2 Comparison of ORC cycles for benzene, R11 and R134a.
Benzene R11 R134a
PORC [kW]
hORC [–]
pcond [kPa]
pvap [kPa]
Tvap [K]
_ f [kg/s] m
V_ 3 [m3/s]
v4/v3 [–]
Dh30 4 [kJ/kg]
Dh01 [kJ/kg]
349.3 290.3 147.5
0.1986 0.1658 0.0852
19.6 147.9 883.3
2000 3835.9 3723.4
494.5 461 369.9
2.737 7.487 8.9667
0.052 0.030 0.041
107 32 5
130.5 41.9 19.4
0.286 0.316 0.302
Tg;fin ¼ Tg;PP
_ f ;3 ðh2 hA Þ m _ g cp;g m
(10)
Whenever Tg,fin should be smaller than the rated final gas temperature (Tg,min), the procedure implemented decreases the fluid mass flow rate in order to match this condition. Fig. 10 describes the T—Q_ diagram for the three cycles that have been considered. The heat rate entering the cycle, 0 Q_ in ¼ Q_ g þ DH_ 1A , is represented by the sum of the heat rate from hot exhaust gases ðQ_ g Þ and the heat rate from the cooling water actually used to preheat the working fluid ðDH_ 1A Þ. It is to be noted (see Table 3 and Fig. 10) that the heat rate introduced into the cycles is not the same for all fluids but it increases with decreasing critical temperature of the working fluid. For R134a the heat rate introduced into the cycle from the engine cooling water is about 26.1% of 0 the total heat to the cycle ðDH_ 1A =Q_ in Þ and 57.9% of the total heat _ available from the cooling water ðDH 1A =Q_ w Þ. The same parameters has lower values for R11 (12.7% and 24.2%) and benzene (9.5% and 17.5%). The increased heat rate transferred to working fluid leads to a significant increase in net power output of the cycle for fluids with low critical temperature (since the net efficiency of the cycle is unchanged). Table 3 shows that R134a allows a net increase in power output, calculated with respect to the cycle without heat 0 PORC Þ=PORC Þ, of 34.8%, while recovery from coolant water ððPORC a cycle with benzene and water preheating increases its power output only by about 10%. R11 displays intermediate characteristics with an increase in power output of 14.5%. Under these conditions R11 allows to reach mechanical power outputs close to that of benzene (332.5 vs. 386 kW). The new system layout therefore brings less advantages for cycles designed to utilize fluids with high critical temperatures. Fluids with low critical temperatures and bell shaped vapour lines can significantly increase their capability to produce useful work, but the net power output still remains lower than that achievable by overhanging fluids like benzene even without heat recovery from cooling water. 5. ORC regenerated cycle ORCs modules available in commerce often utilize working fluids with overhanging vapour lines. This condition is favourable as it allows dry expansions without superheating and regenerate the cycle by sub-cooling the vapour at the end of expansion (direct regeneration) without vapour extraction. For the cycles considered in the present work it is apparent that only benzene is suitable for direct regeneration. It is considered that the recuperator is a counterflow type heat exchanger and requires a DTappr,R of 15 K. Under these hypothesis the temperature of the vapour at the heat exchanger outlet can be evaluated, as well as the available energy for the internal heat exchange process ðQ_ R Þ:
Fig. 9. Optimal organic cycles and engine exhaust gases cooling curve plotted on two superimposed T S_ diagrams.
T4R ¼ T1 þ DTappr
(11)
_ f ;R ðh4 h4R Þ Q_ R ¼ m
(12)
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possible to see that, unlike Fig. 9a, hot engine exhaust gases should be used to vaporize a fluid at a higher temperature than T1; this condition decreases the entropy generation rate, that now accounts for 0.869 kJ/s K, lower than the value calculated for the same fluid in the simple cycle case. Also, in analogy with the engine cooling water case, the mass flow rate of the working fluid will be higher, thus providing a higher power output (the cycle efficiency is also increased in this case). Table 4 reports the main figures of the regenerated cycle and it can be observed that the working fluid mass flow rate is 3.076 kg/s (compared to 2.737 kg/s of the simple cycle and 3.024 kg/s with preheating). The net power output is thus increased by 12.4% with 00 PORC Þ=PORC Þ and is now rated at respect to the simple cycle ððPORC 392.6 kW, with a net cycle efficiency of 22.3%. From Table 4 it can also be observed that the internal heat exchange provides 218 kWt, which is about 10% of the total intro00 duced heat rate ðQ_ R =Q_ in Þ. Fig. 12 describes the T—Q_ diagram for the regenerated cycle, while Fig. 13 shows the cycle power output vs. turbine inlet pressure. It is evident that a maximum power of about 430 kW can be achieved if the regenerated cycle were operated at a pressure of 4180 kPa, resulting in a cycle efficiency of 0.246. In Fig. 14 the three configurations assumed for benzene are compared at varying expander efficiencies. In particular hT has been assumed in the range of 0.4 (accounting for expanders with very low performance) to 1 (assuming ideal expansion). The expander efficiency of hT ¼ 0.7 assumed in the analysis presented in this paper, is in the middle of this range. It can be observed that the simple cycle thermally powered only by engine exhaust gases always displays lower power output values than the other two configurations. Also observed that an expander efficiency value of about 0.75 marks the break even between a regenerated and water cooling cycle. Therefore turbines with low adiabatic efficiency should be employed in cycles that adopt the regenerated design. In fact a low efficiency expander leads to a temperature and
Fig. 10. T Q_ diagrams for benzene, R11 and R134a with preheating using engine coolant.
The state of the liquid at the recuperator outlet can be calculated, since:
_ f ;R h2R ¼ h1 þ Q_ R =m
(13)
The T—S_ regenerated cycle is presented in Fig. 11, with the superimposed line referring to engine exhaust gas cooling. It is
Fig. 11. Optimal benzene regenerated cycle and engine exhaust gases cooling curve plotted on two superimposed T S_ diagrams.
Table 3 Comparison of ORC cycles for benzene, R11 and R134a with preheating using engine coolant.
Benzene R11 R134a
0 [kW] PORC
0 Q_ in [kW]
Dh30A [–]
DH_ 1A =Q_ in [–]
0
DH_ 1A =Q_ w [–]
_ 0f [kg/s] m
0 V_ 3 [m3/s]
0 ððPORC PORC Þ=PORC Þ [–]
386.0 332.5 199.5
1943.1 2005.6 2342.5
581.6 204.3 142.8
0.095 0.127 0.261
0.175 0.242 0.579
3.024 8.573 12.129
0.058 0.035 0.056
0.099 0.145 0.348
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Table 4 Main parameters of benzene regenerated cycle.
Benzene
00 [kW] PORC
h00ORC [–]
Q_ R [kW]
00 Q_ R =Q_ in [–]
pvap [kPa]
_ 00f [kg/s] m
00 V_ 3 [m3/s]
00 ððPORC PORC Þ=PORC Þ [–]
392.6
0.223
218
0.099
2000
3.076
0.059
0.124
Table 5 Combined ICE–ORC efficiencies.
hCC
Fig. 12. T Q_ diagrams for regenerated benzene cycle.
Simple cycle
Simple cycle with preheat
Reg. cycle
Benzene R11 R134a
0.466 0.458 0.438
0.471 0.463 0.445
0.471 – –
Benzene R11 R134a
0.114 0.095 0.048
(hCC he)/he 0.126 0.108 0.065
0.128 – –
enthalpy increase of the superheated vapour at the turbine outlet and this energy is partly recovered in the recuperator. If performing expanders with efficiencies higher than 0.75 were employed, the design with water preheating should be preferred. It can be observed that when hT / 1 the overall power achieved by the benzene regenerated cycle approximates the power generation capability of a simple cycle with no preheating. At very high expander efficiencies, direct thermal regeneration is almost fruitless as the vapour state at the expander outlet nears saturation. 6. Conclusions
Fig. 13. Regenerated benzene cycle power output at different evaporation pressures.
Fig. 14. Cycle power versus turbine efficiency for the three cycle configurations assumed for benzene.
Table 5 summarizes the net efficiency estimated for the combined ICE–ORC cycle (hCC). These values have been calculated assuming 95% efficiency of the electric generator coupled to ORC expander. It is possible to appreciate a significant increase in efficiency from the rated value for the engine (he ¼ 0.418, see Table 1). The highest values are achieved with benzene cycles and interestingly the value is nearly the same in the regenerated and preheated cases, with hCC ¼ 0.47. This is because the value of hT adopted in the analysis is close to the values that makes indifferent the adoption of the water preheating or regeneration in the design of the cycle (Fig. 14). The increase of the efficiency is about 12.5% with respect to engine with no bottoming ((hCC he)/he) in both cases. It has to be considered that the regenerative preheating requires a liquid-gas heat exchanger and furthermore it has been assumed a quite low temperature difference at the exchanger outlet (DTappr,R). This requires very complex heat exchangers with high exchange surfaces, which leads to a component that needs a critical design. When engine coolant is used for preheating instead, a liquid–liquid exchange process is performed and the high availability of fluid at high temperatures makes it possible to use simpler components. Therefore, if expanders with average performances are available (as hT ¼ 0.7 assumed in the analysis) and the heat released through the engine refrigerant is not otherwise utilized, it could be preferable to employ the scheme proposed in Fig. 2b, thus simplifying the design of the heat exchanger required. While cycles based on R134a give small contributions in both configurations (the increase of engine efficiency may reach 6.5%), R11 can provide good performances especially when water preheating is adopted. In this case the increase in engine efficiency is almost 11% and hCC ¼ 0.46. R11 or similar fluids may therefore be preferable than overhanging fluids like benzene for the smaller turbine outlet/inlet
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volume flow ratio. From Fig. 8 in fact it can be observed that v4/v3 is always smaller than 50, which would allow the use of simple expanders such as single stage turbines. In conclusion the use of ORC has been assessed in conjunction with ICEs and it has been shown how interesting thermodynamic advantages can be achieved (when heat released from an ICE is not used for cogeneration purposes). Further ORC cycle solutions will be analysed in future works as well as dynamical model will be introduced to evaluate the behaviour of the system in off-design conditions. The effects of using diathermic oils as heat transfer media between engine gases and organic fluid will also be considered in order to reduce risks related to the flammability of some of the fluids that may be employed and to ensure higher stability for the operation of the ORC due to the oil thermal inertia. This design would however introduce further irreversibilities in the main heat exchange process that are cause for a reduction in the global ORC system efficiency. A detailed exergy analysis will numerically quantify the entity of these losses.
[5] [6] [7]
[8] [9]
[10] [11] [12] [13] [14]
References [1] Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Appl Ther Eng 2007;27:100–10. [2] Danov SN, Gupta AK. Modeling the performance characteristics of diesel engine based combined-cycle power plants – part I: mathematical model. J Eng Gas Turbines Power 2004;126:28–34. [3] Danov SN, Gupta AK. Modeling the performance characteristics of diesel engine based combined-cycle power plants – part II: results and applications. J Eng Gas Turbines Power 2004;126:35–9. [4] Micheli D, Reini M. On bottoming a micro turbine with a micro ORC section: part b) micro-combine cycle plant performance evaluation. In: Mirandola A,
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Arnas O, Lazzaretto A, editors. ECOS 2007 Conference; Padova, Italy, vol. 2; 2007. pp. 1035–41. Larjola J. Electricity from industrial waste heat using high speed organic Rankine cycle (ORC). Int J Prod Econ 1995;41:227–35. Drescher U, Bruggermann D. Fluid selection for the organic Rankine cycle (ORC) in biomass power and heat plants. Appl Therm Eng 2007;27:223–8. Wei D, Lu X, Lu Z, Gu J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Management 2007;48:1113–9. Pehnt M. Environmental impact of distributed energy systems – the case of micro cogeneration. Environ Sci Policy 2008;2:25–37. Kane M, Favrat D, Gay B, Andrei O. Scroll expandre organic Rankine cycle (ORC) efficiency boost of biogas engines. In: Mirandola A, Arnas O, Lazzaretto A, editors. ECOS 2007 Conference, Padova, Italy, vol. 2; 2007. pp. 1017–24. Macchi E. Cicli di potenza per impianti solari. La Termotecnica 1979;23:309–27 [in italian]. Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210–21. Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661–7. Angelino G, Colonna P. Multicomponent working fluids for organic Rankine cycles (ORCs). Energy 1997;23:449–63. Maizza V, Maizza A. Unconventional working fluids in organic Rankine cycles for waste heat recovery systems. Appl Therm Eng 2001;21:381–90. Mago PJ, Charma LM, Srinivasan K, Somayaji C. An examination of regenerative organic Rankine cycles using dry fluids. Appl Therm Eng 2008;28:998–1007. Lemmon EW, Huber ML, McLinden MO. NIST REFPROP Standard reference database 23, Version 8.0, User’s Guide; 2007. Liu B-T, Chien K-H, Wang C-C. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207–17. Incroprera FP, De Witt DP. Fundamentals of heat and mass transfer. John Wiley & Sons; 2001. Vaja I. Definition of an Object Oriented Library for the Dynamic Simulation of Advanced Energy Systems: Methodologies, Tools and Application to Combined ICE–ORC Power Plants, Ph.D. Thesis in Industrial Engineering, University of Parma, Italy, 2009.
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Internal Combustion Engine (ICE) bottoming with Organic Rankine Cycles (ORCs) Iacopo Vaja*, Agostino Gambarotta University of Parma, Industrial Engineering Department (IED), via G. P. Usberti 180/A, 43100 Parma, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2008 Received in revised form 2 June 2009 Accepted 12 June 2009 Available online 4 July 2009
This paper describes a specific thermodynamic analysis in order to efficiently match a vapour cycle to that of a stationary Internal Combustion Engine (ICE). Three different working fluids are considered to represent the main classes of fluids, with reference to the shape of the vapour lines in the T–s diagram: overhanging, nearly isoentropic and bell shaped. First a parametric analysis is conducted in order to determine optimal evaporating pressures for each fluid. After which three different cycles setups are considered: a simple cycle with the use of only engine exhaust gases as a thermal source, a simple cycle with the use of exhaust gases and engine cooling water and a regenerated cycle. A second law analysis of the cycles is performed, with reference to the available heat sources. This is done in order to determine the best fluid and cycle configuration to be employed, the main parameters of the thermodynamic cycles and the overall efficiency of the combined power system. The analysis demonstrates that a 12% increase in the overall efficiency can be achieved with respect to the engine with no bottoming; nevertheless it has been observed that the Organic Rankine Cycles (ORCs) can recover only a small fraction of the heat released by the engine through the cooling water. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine Cycle Internal Combustion Engine Combined cycle
1. Introduction Organic Rankine Cycles (ORCs) can use different working fluids in order to exploit low grade heat sources to produce useful work. An interesting application of ORCs is to couple them with other prime movers and utilize their wasted heat, thus realizing a combined power unit with the effect of enhancing the overall system efficiency [1–4]. Since the ORC systems generate additional power without requiring extra fuel, the specific pollutant emissions of the combined plant are reduced. Organic fluids are to be preferred to water when the required power is limited and the heat source temperature is low, as these fluids often have lower heat of vaporization and can better follow the heat source to be cooled, thus reducing temperature differences and therefore irreversibilities at the evaporator. Furthermore, turbines for organic cycles can provide higher efficiencies at part loads as well and are usually less complex (1 or 2 stages, for an axial turbine) due to the lower enthalpy drop of the fluid [5,6]. Also ORC systems exhibit great flexibility, high safety and low maintenance
* Corresponding author. Tel.: þ39 0521 905863; fax: þ39 0521 905705. E-mail address: [email protected] (I. Vaja). 0360-5442/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2009.06.001
requirements in recovering low-medium grade waste heat, from industrial processes or power plants [7]. Evaporators for ORCs are usually simple components designed as a heat exchanger with direct use of hot gases released by the thermal source, often without use of intermediary fluids, such as diathermic oils. They also have one level of evaporating pressure [1,4]. Recently many power units based on Internal Combustion Engines (ICEs) are being employed as base components in Distributed Energy Systems (DES), intended as systems where power is generated in small decentralized units. DES are usually appreciated because they could help to reduce emissions, save grid capacity, provide opportunities for renewable energy and increase overall energy generation and distribution efficiency [8]. ICEs are often chosen for their reliability, low specific cost and high electrical efficiency, especially in the power range of hundreds of kW to few MW. It may happen however that many of these engines are fuelled using biomass (such as vegetal oils, biogas or others) and the existence of incentives (such as Green Certificates in Italy) for plants based on Renewable Energy Sources makes the operation of these units a viable solution even if no heat is usefully recovered. Few examples of ORCs coupled to ICEs exist and usually the ORC is conceived to efficiently exploit only the heat released at high
I. Vaja, A. Gambarotta / Energy 35 (2010) 1084–1093
Nomenclature
F
H H_
Subscripts C Condenser P Pump R Regenerated/regenerator T Turbine a Available appr Approach cond Condenser crit Critical dead Dead state e Engine ex Heat exchanger f Fluid fin Final g Gas in Inlet out Outlet w Water
P Q Q_ S S_ T V V_ cp h m _ m p s v
Enthalpy [kJ] Enthalpy flow [kW] Power [kW] Heat [kJ] Heat flow [kW] Entropy [kJ/K] Entropy flow [kJ/s K] Temperature [K] Volume [m3] Volume flow rate [m3/s] Specific heat at constant pressure [kJ/kg K] Specific enthalpy [kJ/kg] Mass [kg] Mass flow rate [kg/s] Pressure [kPa] Specific Entropy [kJ/kg K] Specific volume [m3/kg]
Greek symbols Air fuel ratio [–] Heat exchanger effectiveness [–] Efficiency [–] Organic Rankine Cycle efficiency [–] Global efficiency [–]
a 3 h hORC hg
temperatures such as the engine exhaust gases. In [2,3], for example, a setup is proposed where a low speed two stroke marine turbocharged Diesel engine acts as the topper of a combined cycle with exhaust gases used for a bottoming cycle based on a Rankine cycle. The paper describes a full mathematical model built to evaluate the mutual operation of the Diesel engine as source of power and waste heat and a HRSG with a steam turbine, in the whole power-speed spectrum of the Diesel engine. While very comprehensive and detailed, the papers focus on the issue of offdesign operation of the system, which is not so important for stationary engines that are always operated at rated conditions. Furthermore in the proposed design the vapour cycle is based on a conventional water–steam cycle due to the high thermal power available from the marine engine. In [9] the retrofit with two different ORC system rated about 10 kWe of a small engine with a power of 200 kWe, fuelled with biogas, is considered. The bottomer, based on R134a, in this case is thermally fed using only the engine cooling water. The paper focuses on the application of scroll expanders, that may be advantageous when the power of the ORC is limited. The feasibility of the system is supported by field tests conducted on an experimental unit. The availability of waste heat at two different levels of temperature is usually a problem for the application of ORCs onto ICEs. In [16] for example, a mini-hybrid solar power plant is presented, characterized by a field of solar concentrators and a bioDiesel engine integrated to two superposed ORCs. When the system operates in hybrid mode the heat released by the engine, in series with the heat generated by the solar system, is employed to power two simple ORC cycles, the first based on R123 and the second on R134a. Besides the use of solar thermal power, the design proposes a possible solution when heat is available at different temperature levels, with the second ORC powered both by the heat released by the first ORC and by the heat from the engine cooling network, that may be provided either in series as liquid preheater or parallel to the evaporator. Laboratory tests made with the superposed ORCs
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Heat availability [–]
Abbreviations CC Combined Cycle ICE Internal Combustion Engine ORC Organic Rankine Cycle PP Pinch Point
confirmed adequate operational characteristics with good performances over a broad range of conditions, indicating the feasibility of the design. The assessment of double cascade ORC designs in conjunction to stationary ICEs has been considered [19] and will be presented in future works. The present paper is focused on evaluating the extra power achievable by using an ICE as a heat source for just one vapour power cycle, thus with a rather simplified design of the heat recovering unit, under the hypothesis of operating the engine at full load while considering different cycles based on different organic fluids and configurations. 2. The systems considered in the investigation In the analysis a commercial cogeneration engine is considered as a topping system. The engine is a 12 cylinder 4 stroke supercharged natural gas fired medium speed: the main parameters of the engine are reported in Table 1. From the engine data it has been evaluated that about 1700 kWt is available by cooling the exhaust gases down to 120 C (Tg,min) and about 1000 kWt is available from the engine cooling water. It has been calculated that the air fuel ratio a is 29.2 and the excess air coefficient e is 0.701 at nominal conditions, under the hypothesis of perfect combustion of pure methane. The composition
Table 1 Main engine characteristics. Electrical power output Fuel consumption Rated electrical efficiency Engine speed Exhaust gas temperature Exhaust mass flow Combustion air mass flow Engine jacket temperatures Engine jacket flow
2928 7002 41.8 1000 w470 15,673 15,154 79/90 w90
kW kW – min1 C kg/h kg/h C m3/h
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of the exhaust gases on the basis of mass has been calculated at: CO2 ¼ 9.1%, H2O ¼ 7.4%, N2 ¼ 74.2%, O 2¼ 9.3%. This composition is used to evaluate the gas properties. In the study, the engine is assumed to operate at rated conditions as the aim is to determine which organic cycle would better fit the overall heat available for these conditions. Organic fluids used for power applications may have different characteristics in the T–s diagram and the saturation lines may be bell shaped, nearly isentropic or overhanging depending on the fluid molecule complexity. Typically fluids with simpler molecules are characterized by bell shaped vapour lines and lower critical temperatures and fluids with more complex molecules display a overhanging vapour line and higher critical temperatures [10]. In the paper three fluids commonly adopted for technical applications were chosen to represent these different behaviours in the T–s diagram (Fig. 1): benzene (overhanging), R11 (isentropic) and R134a (bell shaped). They are commonly quoted in literature as possible fluids for ORCs [11,12], even though future work would lead to consider other pure fluids or fluid mixtures [13]. It should be noted that in the proposed analysis only thermodynamic aspects will be considered. It is important to remark however that fluids for ORC applications must not only be favourable from a thermodynamic point of view, but have to satisfy conditions such as [11,14]: -
-
chemical stability at the operating pressures and temperatures; environmental friendliness: low ozone depletion potential (ODP), global warming potential (GWP) and atmospheric lifetime (ALT); non toxic, non corrosive and compatible with engine materials; low flammability and auto-ignition properties.
In the analysis that follows three cycle configurations will be assumed, in order to compare not only the fluids considered but also the different cycle setups and to verify the most feasible application of ORCs coupled with ICEs. The setups assumed are: -
-
-
ORC simple cycle thermally powered by engine exhaust gases (Fig. 2a); ORC simple cycle thermally powered by engine exhaust gases and engine refrigerant water (Fig. 2b); regenerated ORC thermally powered by engine exhaust gases (Fig. 2c).
Fig. 2. Scheme of different ORC cycle configurations assumed for ICE bottoming.
For all the cycles considered the following assumptions are valid: -
-
Fig. 1. Different shapes of coexistence curves in the T–s diagram for the considered fluids.
-
isentropic turbine efficiency: hT ¼ 0.7 (this value is conservatively below usual values that may range between 0.8 and 0.88 [6,14,15]); isentropic pump efficiency: hP ¼ 0.8; working fluid temperature at condensation: Tcond ¼ 308 K; vaporizing pressure varying between condensation pressure pcond and critical pressure pcrit; negligible pressure losses in the heat exchangers and pipes; dry expansion for all fluids;
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The last hypothesis has been introduced assuming that a dry expansion would be preferable for the preservation of the expander. This is to eliminate the impingement of liquid droplets on turbine blades. Therefore a slight superheating will be assumed when the isentropic expansion line crosses the vapour line. In other words, it will be considered just the minimum superheating to keep an isentropic expansion totally in the dry zone of the diagram. Introducing high degrees of superheating, however, is not convenient from a thermodynamic point of view, as the cycle efficiency is a weak function of turbine inlet temperature once the evaporating pressure is chosen. In some cases, the highest cycle efficiencies are obtained when superheating is avoided and the fluid is expanded directly from dew line, as demonstrated in [12]. In [15] it has been also shown, through a comprehensive analysis based on irreversibility calculations, that superheating organic cycles (especially if based on overhanging fluids) increases cycle irreversibility and decreases the second law efficiency. As further assumption the extra costs of building the ORC when the turbine inlet pressure is raised have been neglected [12]. The turbine pressure therefore has been assumed as an independent variable of the problem, the only limitation being the field of fluid stability. Fluid properties have been evaluated using the REFPROPÒ database [16] that has been utilized in MatlabÒ. Specific MatlabÒ functions were defined and compiled to evaluate cycle properties and performance in a parameterized way. This is in order to assess the effects of changes in one or more variables (as, for example, the pressure at the evaporator inlet p2) on the main cycle characteristics.
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It is to be noted that in Eq. (1) the organic fluid enthalpies are function of the evaporating pressure chosen for the ORC and cp;g is calculated with REFPROPÒ according to the exhaust gas composition at the average temperature. A second energy balance allows to determine the exhaust gas temperature at the evaporator outlet:
Tg;fin ¼ Tg;PP
_ f ;1 ðh2 h1 Þ m _ g cp;g m
(2)
If Tg,fin calculated with Eq. (2) is lower than the minimum allowed temperature for the gases, a procedure decreases the _ f ;2 is the organic fluid mass flow rate while Tg,fin is above Tg,min. m fluid mass flow rate that satisfies the imposed condition and represents the new fluid mass flow rate for the cycle. The actual gas Pinch Point temperature can be calculated using:
Tg;PP ¼ Tg;out
_ f ;2 ðh30 h2 Þ m _ g cp;g m
(3)
All the organic fluids (especially at relatively high pressures) considered in the analysis have a specific heat of vaporization lower in comparison to that required to warm up the fluid between point 1 and 2 of Fig. 3. Therefore Tg,fin calculated with Eq. (2) is always smaller than Tg,min,. This means that there are no Pinch Point limitations in the heat exchange process and that which limits the amount of heat introduced to the cycle is the need to avoid overcooling of the engine exhaust gases. The global efficiency of the system can be defined as the net power produced by the cycle referred to the total available heat Q_ a
[17]: 3. The ORC simple cycle
P
In Fig. 3 the heat exchange diagram of the evaporator is proposed for a generic ORC simple cycle with no superheating. Heat needed to vaporize the organic working fluid is provided in this case solely by the engine exhaust gases (according to Fig. 2a). The _ g ) are gas temperature at engine exhaust (Tg,out) and flow rate (m defined and constant. A minimum gas pinch point temperature (Tg,PP) is considered (Tg,PP ¼ T2 þ DTPP, where DTPP ¼ 30 K is the minimum temperature difference at Pinch Point to meet the gas/ fluid heat exchanger performances) and this allows writing a first energy balance referred to complete fluid vaporization:
_ f ;1 ¼ m
_ g cp;g Tg;out Tg;PP m h30 h2
(1)
Fig. 3. T—Q_ diagram of the evaporator for a ORC heated with engine exhaust gases.
hg ¼ ORC ¼ 3$hORC Q_ a
(4)
where 3 is the evaporator effectiveness [18]:
cpg Tg;out Tg;fin 3¼ cpg Tg;out T1
(5)
and hORC the organic Rankine cycle efficiency:
hORC ¼
PORC PORC ¼ h3 h1 cpg Tg;out Tg;fin
(6)
From Eq. (4) it can be observed that not always can the maximum global efficiency be achieved with maximum cycle efficiency (hORC). It could happen that with increasing turbine inlet pressure the cycle efficiency increases but the final gas temperature is also increased, thus determining a decrease in the evaporator effectiveness 3. Combination of these two terms might provide that the turbine inlet pressure that maximizes hORC is not the one that maximizes hg [1,18]. The analysis that follows therefore is a result of determining the optimal pressure at turbine inlet that would maximize hg and in turn, provide the maximum ORC power at a given value of Q_ a . In Fig. 4 the cycle efficiency is plotted for the reference fluids in the range of turbine inlet pressures between pcond and pcrit (where pcrit is the critical pressure of each fluid). As expected benzene displays higher achievable efficiencies. The curves are monotonic for all fluids (solid lines): a consequence of the hypothesis from introducing a minor degree of superheating while the isentropic expansion is not completely dry. For higher pressures, the introduced superheating becomes higher and this slightly rises the cycle efficiency. The corresponding dotted curves are plotted for the saturated Rankine cycle (with no superheating) and in this case the
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Fig. 4. Simple cycle efficiencies for evaporation pressures between pcond and pcrit.
Fig. 6. Relative variation of net cycle power output for simple Rankine cycles at different evaporation pressures.
curves show a maximum value of the cycle efficiencies for pressures not far from critical: in particular a maximum hT value of 0.2146 is achieved with benzene at a pressure of 4470 kPa. _ f ðh30 h4 Þ, The curves in Fig. 5 refer to the net power (PORC ¼ m see Fig. 9 for symbols) achievable from the cycles at different pressures of vaporization. The shape of the plotted curves is similar to that of the efficiency curves (Fig. 4). The curves for all fluids have their maximum value at the critical pressure as a consequence of pattern of the efficiency curves. In the analysis an optimal value of p2 will be chosen (indicated by the * symbol in the figures) as the one that maximizes the efficiency curves referred to saturated Rankine cycle (dotted lines of Fig. 4). Therefore the optimum pressure is chosen as 4470 kPa for benzene which returns a net power output of 376 kW, 3835 kPa for R11, with 290 kW and 3723 kPa for R134a with a net power output of 147 kW. In Fig. 6 the dimensionless cycle power output is plotted in the assumed pressure range with reference to the cycle power output, determined at the optimal pressure for each fluid (* of Fig. 5). It can be noted that not only is benzene the fluid with the highest power output value, but it also shows the smallest variations from the optimal power. For example at pressures of 1700 kPa, a cycle based on benzene provides about 90% of the optimal power output. This characteristic leads to consider cycles with lower expansion ratios, while simultaneously simplifying the compression and expansion phases. Fluids with bell shaped vapour lines display instead higher variability in power output with respect to vaporization pressure.
This would result in the Rankine cycle being operated at a pressure as close as possible to the optimal pressure for these fluids. In Fig. 7 the estimated value of working fluid mass flow rates are plotted again with respect to the pressure at turbine inlet. It is possible to observe that benzene requires the lowest fluid mass flow rate as consequence of the highest enthalpy increase between state 3 and 1. The energy balance at the evaporator determines higher masses of fluid for R123 and R134a in order to match the total energy of the flue gasses. Fig. 8 reports, for each fluid, the curves referring to actual volumetric flow rate at the expander inlet ðV_ 3 Þ and the turbine outlet/inlet volume flow ratio (v4/v3). The latter parameter is particularly significant as it shows how much the fluid volume increases through the expansion. Fig. 8a refers to benzene and shows that a high value of the ratio v4/v3 of 374 is produced when the cycle is operated at the optimal pressure of 4470 kPa (*), and V_ 3 ¼ 0:015 m3 =s. Considerations regarding the power curve for benzene (Figs. 5 and 6), suggest that a lower evaporating pressure would allow lower turbine outlet/inlet volume flow ratios, while providing a net power output close to optimal. In this case, the cycle would be better operated if a lower pressure was chosen since a simpler expander could be employed. As a reference for this analysis a new optimal value of evaporating pressure for benzene is selected at 2000 kPa (marked with - in Fig. 8a) even if further and more precise considerations would require matching with an actual
Fig. 5. Simple cycle power output at different evaporation pressures.
Fig. 7. Simple cycle working fluid mass flow rate required at different evaporation pressures.
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The graphs plotted in Fig. 9 show the thermodynamic cycle on the T—S_ diagram for the three considered fluids. The curve referring to the engine exhaust gases is superimposed on the diagrams by properly scaling the entropy axes. It is evident, the lower the critical temperature the greater the temperature difference between gases and organic fluid in the heater/evaporator. This temperature difference induces irreversibilities that are the main cause for low thermodynamic efficiencies with R11 and R134a. Future works will include a detailed exergy analysis where the causes of exergy reduction within each component of the system will be properly quantified and discussed [19]. The proposed representation however allows to observe the entropy generation rate due to the heat transfer process between hot gases and organic fluid:
_ f ðs30 s1 Þ m _ g sg;out sg;fin S_ ex ¼ m
(7)
This value, that can be gathered from Fig. 9a–c, is, as expected, the bigger the higher average temperature difference in the heat exchanging process. Particularly S_ is 0.924, 1.234 and 1.842 kJ/s K for benzene, R11 and R134a respectively. Table 2 reports the main parameters for the three cycles proposed (the values for benzene have been estimated at vaporizing pressure of 2000 kPa). It can be observed that a maximum power output of about 350 kW can be achieved from a benzene based simple cycle (hORC ¼ 0.2) while the power decreases to about 190 kW 150 kW with R11 and R134a respectively (hORC ¼ 0.17 and 0.08). It should be noted that in all cases the heat flow provided to the cycles with the engine exhaust gases is the same as they are cooled down to the minimum allowed temperature Tg,min (there are no Pinch Point limitations). 4. ORC with use of heat available from engine refrigerant A further comparison of the selected cycles has been carried out under the hypothesis of employing the engine cooling water for a partial preheat of the organic fluids upstream the main evaporator (Fig. 2b). The thermodynamic cycles are the same as defined in the previous section (Fig. 9) and the cycle efficiency is unchanged. A new heat source is now considered for preheating the working fluid. In the analysis a heat exchanger with a reasonable efficiency has been assumed for the water/fluid heat exchange process, with a temperature difference of 20 K between water inlet and organic fluid outlet (Tw,PP). The energy balance at the water/fluid heat exchanger gives the _ f 1 is the fluid mass first value of the organic fluid mass flow rate: m flow rate that allows complete exploitation of energy available from the cooling water: Fig. 8. Volume flow rate at turbine inlet ðV_ 3 Þ and turbine outlet/inlet volume flow ratio (v4/v3) for different fluids at different evaporation pressures.
commercial expander. At this new value of evaporating pressure the net power output from the cycle becomes 349 kW, the ratio v4/ v3 decreases to 107 while V_ 3 increases to 0.052 m3/s (Table 2). On the other hand, R11 and R134 show lower turbine outlet/inlet volume flow ratios at the chosen evaporating pressure, suggesting that a simple expander could be employed with these fluids even at optimal pressures. It should be noted that the ratio v4/v3 can change significantly depending on the characteristics of the working fluid. Several fluids can achieve values up to 550 and when v4/v3 is smaller than 50, expansion efficiencies higher than 0.8 can be achieved via a single stage axial turbine [1].
_ f ;1 ¼ m
_ w cp;w Tw;out Tw;in m hA h1
(8)
A new energy balance should be written for the evaporator to match the available energy from the engine exhaust gases and the energy required to fully vaporize and superheat the working fluid (if superheating is considered):
_ f ;2 ¼ m
_ g cp;g Tg;out Tg;PP m h30 h2
(9)
_ f 1 is apparently higher than m _ f 2 . This For the cycles analyzed, m condition would in fact not allow complete exploitation of energy available from the cooling water. A further energy balance would define the final temperature of _ f ;1 ; m _ f ;2 Þ it gives: _ f ;3 ¼ minðm the gases leaving the exchanger. If m
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Table 2 Comparison of ORC cycles for benzene, R11 and R134a.
Benzene R11 R134a
PORC [kW]
hORC [–]
pcond [kPa]
pvap [kPa]
Tvap [K]
_ f [kg/s] m
V_ 3 [m3/s]
v4/v3 [–]
Dh30 4 [kJ/kg]
Dh01 [kJ/kg]
349.3 290.3 147.5
0.1986 0.1658 0.0852
19.6 147.9 883.3
2000 3835.9 3723.4
494.5 461 369.9
2.737 7.487 8.9667
0.052 0.030 0.041
107 32 5
130.5 41.9 19.4
0.286 0.316 0.302
Tg;fin ¼ Tg;PP
_ f ;3 ðh2 hA Þ m _ g cp;g m
(10)
Whenever Tg,fin should be smaller than the rated final gas temperature (Tg,min), the procedure implemented decreases the fluid mass flow rate in order to match this condition. Fig. 10 describes the T—Q_ diagram for the three cycles that have been considered. The heat rate entering the cycle, 0 Q_ in ¼ Q_ g þ DH_ 1A , is represented by the sum of the heat rate from hot exhaust gases ðQ_ g Þ and the heat rate from the cooling water actually used to preheat the working fluid ðDH_ 1A Þ. It is to be noted (see Table 3 and Fig. 10) that the heat rate introduced into the cycles is not the same for all fluids but it increases with decreasing critical temperature of the working fluid. For R134a the heat rate introduced into the cycle from the engine cooling water is about 26.1% of 0 the total heat to the cycle ðDH_ 1A =Q_ in Þ and 57.9% of the total heat _ available from the cooling water ðDH 1A =Q_ w Þ. The same parameters has lower values for R11 (12.7% and 24.2%) and benzene (9.5% and 17.5%). The increased heat rate transferred to working fluid leads to a significant increase in net power output of the cycle for fluids with low critical temperature (since the net efficiency of the cycle is unchanged). Table 3 shows that R134a allows a net increase in power output, calculated with respect to the cycle without heat 0 PORC Þ=PORC Þ, of 34.8%, while recovery from coolant water ððPORC a cycle with benzene and water preheating increases its power output only by about 10%. R11 displays intermediate characteristics with an increase in power output of 14.5%. Under these conditions R11 allows to reach mechanical power outputs close to that of benzene (332.5 vs. 386 kW). The new system layout therefore brings less advantages for cycles designed to utilize fluids with high critical temperatures. Fluids with low critical temperatures and bell shaped vapour lines can significantly increase their capability to produce useful work, but the net power output still remains lower than that achievable by overhanging fluids like benzene even without heat recovery from cooling water. 5. ORC regenerated cycle ORCs modules available in commerce often utilize working fluids with overhanging vapour lines. This condition is favourable as it allows dry expansions without superheating and regenerate the cycle by sub-cooling the vapour at the end of expansion (direct regeneration) without vapour extraction. For the cycles considered in the present work it is apparent that only benzene is suitable for direct regeneration. It is considered that the recuperator is a counterflow type heat exchanger and requires a DTappr,R of 15 K. Under these hypothesis the temperature of the vapour at the heat exchanger outlet can be evaluated, as well as the available energy for the internal heat exchange process ðQ_ R Þ:
Fig. 9. Optimal organic cycles and engine exhaust gases cooling curve plotted on two superimposed T S_ diagrams.
T4R ¼ T1 þ DTappr
(11)
_ f ;R ðh4 h4R Þ Q_ R ¼ m
(12)
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possible to see that, unlike Fig. 9a, hot engine exhaust gases should be used to vaporize a fluid at a higher temperature than T1; this condition decreases the entropy generation rate, that now accounts for 0.869 kJ/s K, lower than the value calculated for the same fluid in the simple cycle case. Also, in analogy with the engine cooling water case, the mass flow rate of the working fluid will be higher, thus providing a higher power output (the cycle efficiency is also increased in this case). Table 4 reports the main figures of the regenerated cycle and it can be observed that the working fluid mass flow rate is 3.076 kg/s (compared to 2.737 kg/s of the simple cycle and 3.024 kg/s with preheating). The net power output is thus increased by 12.4% with 00 PORC Þ=PORC Þ and is now rated at respect to the simple cycle ððPORC 392.6 kW, with a net cycle efficiency of 22.3%. From Table 4 it can also be observed that the internal heat exchange provides 218 kWt, which is about 10% of the total intro00 duced heat rate ðQ_ R =Q_ in Þ. Fig. 12 describes the T—Q_ diagram for the regenerated cycle, while Fig. 13 shows the cycle power output vs. turbine inlet pressure. It is evident that a maximum power of about 430 kW can be achieved if the regenerated cycle were operated at a pressure of 4180 kPa, resulting in a cycle efficiency of 0.246. In Fig. 14 the three configurations assumed for benzene are compared at varying expander efficiencies. In particular hT has been assumed in the range of 0.4 (accounting for expanders with very low performance) to 1 (assuming ideal expansion). The expander efficiency of hT ¼ 0.7 assumed in the analysis presented in this paper, is in the middle of this range. It can be observed that the simple cycle thermally powered only by engine exhaust gases always displays lower power output values than the other two configurations. Also observed that an expander efficiency value of about 0.75 marks the break even between a regenerated and water cooling cycle. Therefore turbines with low adiabatic efficiency should be employed in cycles that adopt the regenerated design. In fact a low efficiency expander leads to a temperature and
Fig. 10. T Q_ diagrams for benzene, R11 and R134a with preheating using engine coolant.
The state of the liquid at the recuperator outlet can be calculated, since:
_ f ;R h2R ¼ h1 þ Q_ R =m
(13)
The T—S_ regenerated cycle is presented in Fig. 11, with the superimposed line referring to engine exhaust gas cooling. It is
Fig. 11. Optimal benzene regenerated cycle and engine exhaust gases cooling curve plotted on two superimposed T S_ diagrams.
Table 3 Comparison of ORC cycles for benzene, R11 and R134a with preheating using engine coolant.
Benzene R11 R134a
0 [kW] PORC
0 Q_ in [kW]
Dh30A [–]
DH_ 1A =Q_ in [–]
0
DH_ 1A =Q_ w [–]
_ 0f [kg/s] m
0 V_ 3 [m3/s]
0 ððPORC PORC Þ=PORC Þ [–]
386.0 332.5 199.5
1943.1 2005.6 2342.5
581.6 204.3 142.8
0.095 0.127 0.261
0.175 0.242 0.579
3.024 8.573 12.129
0.058 0.035 0.056
0.099 0.145 0.348
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Table 4 Main parameters of benzene regenerated cycle.
Benzene
00 [kW] PORC
h00ORC [–]
Q_ R [kW]
00 Q_ R =Q_ in [–]
pvap [kPa]
_ 00f [kg/s] m
00 V_ 3 [m3/s]
00 ððPORC PORC Þ=PORC Þ [–]
392.6
0.223
218
0.099
2000
3.076
0.059
0.124
Table 5 Combined ICE–ORC efficiencies.
hCC
Fig. 12. T Q_ diagrams for regenerated benzene cycle.
Simple cycle
Simple cycle with preheat
Reg. cycle
Benzene R11 R134a
0.466 0.458 0.438
0.471 0.463 0.445
0.471 – –
Benzene R11 R134a
0.114 0.095 0.048
(hCC he)/he 0.126 0.108 0.065
0.128 – –
enthalpy increase of the superheated vapour at the turbine outlet and this energy is partly recovered in the recuperator. If performing expanders with efficiencies higher than 0.75 were employed, the design with water preheating should be preferred. It can be observed that when hT / 1 the overall power achieved by the benzene regenerated cycle approximates the power generation capability of a simple cycle with no preheating. At very high expander efficiencies, direct thermal regeneration is almost fruitless as the vapour state at the expander outlet nears saturation. 6. Conclusions
Fig. 13. Regenerated benzene cycle power output at different evaporation pressures.
Fig. 14. Cycle power versus turbine efficiency for the three cycle configurations assumed for benzene.
Table 5 summarizes the net efficiency estimated for the combined ICE–ORC cycle (hCC). These values have been calculated assuming 95% efficiency of the electric generator coupled to ORC expander. It is possible to appreciate a significant increase in efficiency from the rated value for the engine (he ¼ 0.418, see Table 1). The highest values are achieved with benzene cycles and interestingly the value is nearly the same in the regenerated and preheated cases, with hCC ¼ 0.47. This is because the value of hT adopted in the analysis is close to the values that makes indifferent the adoption of the water preheating or regeneration in the design of the cycle (Fig. 14). The increase of the efficiency is about 12.5% with respect to engine with no bottoming ((hCC he)/he) in both cases. It has to be considered that the regenerative preheating requires a liquid-gas heat exchanger and furthermore it has been assumed a quite low temperature difference at the exchanger outlet (DTappr,R). This requires very complex heat exchangers with high exchange surfaces, which leads to a component that needs a critical design. When engine coolant is used for preheating instead, a liquid–liquid exchange process is performed and the high availability of fluid at high temperatures makes it possible to use simpler components. Therefore, if expanders with average performances are available (as hT ¼ 0.7 assumed in the analysis) and the heat released through the engine refrigerant is not otherwise utilized, it could be preferable to employ the scheme proposed in Fig. 2b, thus simplifying the design of the heat exchanger required. While cycles based on R134a give small contributions in both configurations (the increase of engine efficiency may reach 6.5%), R11 can provide good performances especially when water preheating is adopted. In this case the increase in engine efficiency is almost 11% and hCC ¼ 0.46. R11 or similar fluids may therefore be preferable than overhanging fluids like benzene for the smaller turbine outlet/inlet
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volume flow ratio. From Fig. 8 in fact it can be observed that v4/v3 is always smaller than 50, which would allow the use of simple expanders such as single stage turbines. In conclusion the use of ORC has been assessed in conjunction with ICEs and it has been shown how interesting thermodynamic advantages can be achieved (when heat released from an ICE is not used for cogeneration purposes). Further ORC cycle solutions will be analysed in future works as well as dynamical model will be introduced to evaluate the behaviour of the system in off-design conditions. The effects of using diathermic oils as heat transfer media between engine gases and organic fluid will also be considered in order to reduce risks related to the flammability of some of the fluids that may be employed and to ensure higher stability for the operation of the ORC due to the oil thermal inertia. This design would however introduce further irreversibilities in the main heat exchange process that are cause for a reduction in the global ORC system efficiency. A detailed exergy analysis will numerically quantify the entity of these losses.
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