Analysis of the Impact of Selected Fuel Thermochemical Properties on

Apr 20, 2012 - In order to clarify First Law efficiency differences between fuels, as well .... Martin L Wissink , Scott J Curran , Greg Roberts , Mar...
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Analysis of the Impact of Selected Fuel Thermochemical Properties on Internal Combustion Engine Efficiency James P. Szybist,* Kalyana Chakravathy, and C. Stuart Daw Fuels, Engines, and Emissions Research Center, Oak Ridge National Laboratory, NTRC Building, 2360 Cherahala Boulevard, Knoxville, Tennessee 37932, United States ABSTRACT: In this study we model the effects of 23 different fuels on First and Second Law thermodynamic efficiencies of an adiabatic internal combustion engine. First Law efficiency is calculated using the lower heating value (LHV), while Second Law efficiency is calculated with exergy, which represents the inherent chemical energy available to perform work. We find that First Law efficiency can deviate by as much as 9% between fuels while Second Law efficiency exhibits a much smaller degree of variability. We also find that First and Second Law efficiencies can be nearly the same for some fuels (methane and ethane) but differ substantially for other fuels (hydrogen and ethanol). The differences in First and Second Law efficiencies are due to differences in LHV and exergy for a given fuel. In order to clarify First Law efficiency differences between fuels, as well as the differences between LHV and exergy, we introduce a new term, the molar expansion ratio (MER), defined as the ratio of product moles to reactant moles for complete stoichiometric combustion. We find that the MER reflects an important part of the physics behind fuel-specific efficiency differences as well as differences between First and Second Law efficiencies. We also discuss how First and Second Law efficiencies are affected by two other fuel-specific thermochemical properties, the ratio of specific heat and extent of dissociation in the reaction products following combustion.

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INTRODUCTION The Energy Independence and Security Act of 2007 mandates increases in vehicle fuel economy as well as increases in the quantity of alternative bioderived fuels.1 As a result, more demands are being placed on efficient operation at the same time that vehicles must be compatible with alternative fuels. Diversifying fuel sources away from conventional petroleumderived gasoline for spark-ignition engines presents many challenges in terms of materials compatibility and optimizing engine calibrations, but it is also an opportunity to examine potential fuel-specific opportunities for efficiency improvements. In the United States, ethanol is by far the most widely used bioderived fuel. 2010 production of fuel ethanol was over 300 million barrels, or nearly 10% of the volume of the 3.28 billion barrels of petroleum-derived gasoline.2 Fuel ethanol is currently available as blends of 10 vol % ethanol (E10) and 85 vol % ethanol (E85). Of particular interest here, several recent studies have reported higher engine thermal efficiencies for E85 compared to gasoline in both engine dynamometer3−5 and vehicle6,7 studies. However, despite the apparent reproducibility of this observation, it is difficult or impossible to draw fundamental conclusions from applied experiments alone because of the combined influence of a number of factors, some of which are known and some of which are unknown. These include system-specific effects of the fueling system (dependent on port of direct-injection fueling and fuel injection timing), the spark timing of the engine, changes in intake manifold pressure, and changes in cylinder wall temperature. Some previous studies do offer potential clues to these observations. In a thermodynamic modeling study, Caton6 estimated that the thermal efficiencies of a spark-ignition engine fueled by ethanol and methanol could be 0.5 and 1.0% higher, © 2012 American Chemical Society

respectively, than for iso-octane. Caton attributed this mostly to a reduced throttling for the alcohol fuels because of their higher intake manifold pressures. Caton noted that, in his study, the cylinder-wall heat transfer differences between the alcohols and gasoline were small and did not have much impact on efficiency. This result contrasts with the findings of Marriott et al.,7 who concluded from experimental measurements that the higher efficiency of E85 compared to gasoline could be attributed to a reduction in heat losses due to the lower cylinder temperature with alcohol fuels. Datta et al.8 offered still other explanations, attributing the increased ethanol efficiency in 2010 model year vehicles to a combination of faster flame speed, higher octane number, and engine calibration differences. In another thermodynamic engine modeling study, Caton9 evaluated the theoretical efficiency differences among eight different fuels. In his First Law analysis, Caton found that ethanol and methanol had the highest thermal efficiencies, and hydrogen and carbon monoxide had the lowest efficiencies, with nonoxygenated hydrocarbon fuels falling in between. On a Second Law basis, the trend was reversed, with hydrogen having the highest efficiency and ethanol having the lowest efficiency of all fuels except carbon monoxide. From this study, it is clear that fuel-related efficiency differences are very much dependent on the particular thermodynamic metrics being considered and the specific chemical and physical properties used to classify fuels. As fuel sources continue to diversify, having a correct understanding of the inter-relationships among fuel chemistry, Received: December 20, 2011 Revised: April 12, 2012 Published: April 20, 2012 2798

dx.doi.org/10.1021/ef2019879 | Energy Fuels 2012, 26, 2798−2810

2799

(l) (g) (g)

methyl butanoate carbon monoxide hydrogen

C5H10O2 CO H2

CH4O C2H6O C3H8O

C6H6 C7H8 C8H10

C2H4 C3H6 C4H8 C5H10

CH4 C2H6 C3H8 C4H10 C5H12 C6H14 C7H16 C8H18 C9H20 C10H22

26.32 10.10 119.98

19.96 26.81 30.74

40.14 40.52 40.94

2687.99 282.97 241.85

639.47 1235.03 1847.18

3135.55 3733.96 4346.25

1323.12 1925.93 2540.70 3123.78

802.54 1428.59 2043.07 2657.28 3245.23 3855.13 4465.36 5074.85 5685.86 6295.87

50.03 47.51 46.33 45.72 44.98 44.74 44.56 44.43 44.33 44.25

47.16 45.77 45.28 44.54

kJ/molfuel

kJ/gfuel

84.12 83.70 71.53

78.53 80.80 82.36

85.40 85.14 85.22

86.56 85.87 85.92 85.08

26.38 10.06 119.36

20.00 26.86 30.80

40.16 40.55 40.97

47.16 45.80 45.33 44.59

50.03 47.55 46.39 45.78 45.05 44.81 44.64 44.50 44.41 44.33

kJ/gfuel

kJ/ molmix 76.26 80.86 82.35 83.16 83.01 83.38 83.65 83.85 84.03 84.16

−ΔU

−ΔH

All tabulated values from refs 13−15 bBasis of 1 mol of fuel.

(l) (l) (l)

methanol ethanol propanol

a

(l) (l) (l)

(g) (g) (g) (l)

ethene propene 1-butene 1-pentene

benzene toluene ethylbenzene

(g) (g) (g) (g) (l) (l) (l) (l) (l) (l)

methane ethane n-propane n-butane n-pentane n-hexane n-heptane n-octane n-nonane n-decane

−ΔH

−ΔH

Table 1. Thermodynamic Properties of the Fuelsa

2694.22 281.73 240.60

640.72 1237.52 1850.92

3136.80 3736.46 4349.99

1323.12 1927.17 2543.19 3127.52

802.54 1429.84 2045.56 2661.02 3250.21 3861.37 4472.85 5083.58 5695.84 6307.09

kJ/molfuel

−ΔU

84.32 83.33 71.16

78.68 80.96 82.53

85.44 85.20 85.29

86.56 85.92 86.00 85.19

76.26 80.93 82.45 83.28 83.14 83.51 83.79 83.99 84.17 84.31

kJ/ molmix

−ΔU

Alkanes 50.03 47.51 46.33 45.72 45.05 44.81 44.64 44.50 44.41 44.33 Olefins 47.16 45.77 45.28 44.59 Aromatics 40.16 40.55 40.97 Alcohols 20.00 26.86 30.80 Other 26.38 10.10 119.98

kJ/gfuel

LHV

2694.22 282.97 241.85

640.72 1237.52 1850.92

3136.80 3736.46 4349.99

1323.12 1925.93 2540.70 3127.52

802.54 1428.59 2043.07 2657.28 3250.21 3861.37 4472.85 5083.58 5695.84 6307.09

kJ/molfuel

LHV

84.32 83.70 71.53

78.68 80.96 82.53

85.44 85.20 85.29

86.56 85.87 85.92 85.19

76.26 80.86 82.35 83.16 83.14 83.51 83.79 83.99 84.17 84.31

kJ/ molmix

LHV

27.75 9.23 114.13

21.68 28.56 32.45

40.92 41.40 41.91

47.22 46.27 46.04 45.90

50.44 48.43 47.45 46.94 46.62 46.39 46.22 46.09 45.99 45.91

kJ/gfuel

−ΔB

2834.20 258.62 230.06

694.82 1315.88 1950.02

3196.64 3814.85 4449.27

1324.72 1947.03 2583.15 3219.37

809.16 1456.26 2092.19 2728.27 3363.65 3997.60 4631.35 5264.72 5898.62 6532.44

kJ/molfuel

−ΔB

88.70 76.49 68.05

85.33 86.09 86.94

87.07 86.98 87.24

86.66 86.81 87.35 87.69

76.89 82.43 84.33 85.39 86.04 86.46 86.76 86.99 87.17 87.32

kJ/ molmix

−ΔB

2.5 −0.5 −0.5

0.5 1 1.5

0.5 1 1.5

0 0.5 1 1.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

mol

nP-nRb

1.078 0.852 0.852

1.061 1.065 1.067

1.014 1.023 1.029

1.000 1.022 1.034 1.041

1.000 1.028 1.040 1.047 1.051 1.054 1.056 1.058 1.059 1.060

nP/nR

1.0023 0.9956 0.9948

1.0020 1.0020 1.0020

1.0004 1.0007 1.0009

1.0000 1.0006 1.0010 1.0012

1.0000 1.0009 1.0012 1.0014 1.0015 1.0016 1.0017 1.0017 1.0018 1.0018

1.0520 0.9139 0.9512

1.0844 1.0633 1.0535

1.0191 1.0210 1.0228

1.0012 1.0110 1.0167 1.0294

1.0083 1.0194 1.0240 1.0267 1.0349 1.0353 1.0354 1.0356 1.0356 1.0357

−ΔU/−ΔH −ΔB/LHV

Energy & Fuels Article

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standard metric for comparing fuel energies. Thus, one of our motivations here is to help clarify situations where LHV and exergy differences are important when comparing fuels. We also demonstrate that the differences between exergy and LHV are systematic and can be related to the global combustion stoichiometry by means of the molar expansion ratio. We expect that it should be possible to use the molar expansion ratio as an aid to systematically correlate and/or predict engine efficiency trends for different fuels.

thermodynamic potential, fuel specification standards, and connections to engine design and operation will continue to grow in importance. Two key fuel-specific metrics that have been widely used in thermodynamic studies are heating value (specifically the lower heating value or LHV) and exergy. The former is typically used as the basis for First Law analysis, while the latter is typically used for Second Law analysis. While LHV is a measure of the thermal energy released by burning the fuel, the fuel exergy represents the actual work potential (i.e., the thermodynamic Gibbs energy) available from the fuel. There are some fuels with an exergy-to-LHV ratio greater than unity, and these are capable of performing more work than is indicated by their LHV. Some other fuels have an exergy-toLHV ratio of less than unity, and these are less capable of doing work than one would estimate from the LHV. For any given thermodynamic study, it is very important to recognize which of these bases is assumed, because its selection determines the denominator used to compute the fraction of fuel energy converted to work. In the study mentioned above, Caton9 showed that the exergy-to-LHV ratio for different fuels can deviate substantially from unity, with a value as low as 0.909 for carbon monoxide, values of 1.015−1.025 for nonoxygenated hydrocarbons, and up to 1.056 for ethanol. Thus, regardless of engine design and operation differences (e.g., cylinder-wall heat transfer or throttle positioning), molecular differences among fuels affect their inherent thermodynamic efficiency potential. As we will discuss, these inherent differences are reflected in the exergy-to-LHV ratio and imply that ethanol and methanol should have a noticeable efficiency advantage over many other fuels when LHV is the basis of comparison. We also demonstrate that variations in the exergy-to-LHV ratio are related in a simple way to a molecular fuel property we define as the molar expansion ratio (MER).

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ANALYTICAL METHODOLOGY A total of 23 pure compound fuels are considered in this study: 10 alkanes, 4 olefins, 3 aromatics, 3 alcohols, 1 methyl ester, carbon monoxide, and hydrogen. Thermodynamic data for most of the chemical species were obtained from the NASA chemical equilibrium database.13 Some liquid-phase data were also obtained from Yaw’s Handbook of Thermodynamic and Physical Properties.14 Thermodynamic data for methyl butanoate were obtained from Fisher et al.15 The reference state used for all fuels was their natural state at 300 K and 1 atm. The fuels considered in this study included both liquids and gases under ambient conditions. To be consistent with ASTM measurement methods, the LHV of gaseous fuels was determined from the change in enthalpy upon combustion whereas the LHV for liquid fuels was determined from the change in internal energy. Table 1 summarizes the enthalpy, internal energy, and LHV for each of the fuels included in this study. The change in moles during the reaction does lead to a small difference between the internal energy and enthalpy of reaction, with the maximum difference being just over 0.5%. Thus, the two ASTM methodologies for measuring heating value are thermodynamically different values, but the difference between the two measurements is small. Also included in Table 1 is the Second Law measure of work potential, the exergy of reaction (ΔB) calculated according eq 2, where T0 is the dead-state temperature of 300 K and ΔS is the change in entropy for the combustion reaction. The form of exergy in eq 2 neglects any changes in kinetic energy, potential energy, and concentration differences with the dead-state environment, and is therefore the same as the Gibbs free energy. Physically, exergy represents the maximum amount of work which can be generated from oxidizing the fuel with air, without regard to the type of engine used. Thus, it is a fundamental measure of the maximum work that can be extracted.

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FUEL HEATING VALUE LHV is the most widely used measure of the energy content of fuels because it does not require knowledge of the composition, which is important because commercial petroleum-derived fuels typically include hundreds to thousands of chemical species. The LHV measurement for liquid fuels is performed in a constant volume bomb calorimeter, as specified by ASTM D240,10 and the measurement for gases is performed at a constant pressure, as specified by ASTM D1826.11 The basis of the ASTM LHV measurement for liquids is different than the measurement for gases because a constant volume constraint is applied for the former and a constant pressure constraint for the latter. As noted by Heywood,12 the constant volume heating value is thermodynamically equal to the change in internal energy, −(ΔU)v,T′, whereas the constant pressure heating value is equal to the change in enthalpy, −(ΔH)p,T′. These two quantities are related as shown in eq 1, where R is the universal gas constant, T′ is the reference state temperature, and nP and nR are the number of moles in the products and reactants, respectively. (ΔH )p , T ′ − (ΔU )v , T ′ = R(nP − nR )T ′

−ΔB = −(ΔH − T0·ΔS)

(2)

One other implication of the above definition is relevant to our discussion regarding molar expansion ratio (MER) in combustion. That is, the net entropy change in combustion (ΔS) depends directly on the change in the number of moles due to reaction. An increase in the number of moles produces an increase in ΔS, whereas a decrease in the number of moles produces a decrease in ΔS. Interestingly, the increase in the number of moles also results in additional exergy destruction during combustion, but we will show that this increase in moles is beneficial with respect to piston work during expansion (i.e., in the absence of a bottoming cycle for additional work). Unlike the differences between internal energy and enthalpy, which are small, the differences between exergy and LHV can be substantial. Table 1 includes the ratio of exergy-to-LHV, which indicates the amount of work a fuel is capable of relative to its heating value. For example, methanol has an exergy-to-

(1)

From the point of view of basic thermodynamics, it is more accurate to focus on fuel exergy when evaluating engine efficiency, because exergy explicitly measures the inherent chemical energy in the fuel that is actually available to do work. For practical reasons, however, LHV is likely to remain as the 2800

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LHV ratio of 1.0929, meaning that it is capable of performing 9.29% more work than its LHV indicates. Similarly, carbon monoxide has an exergy-to-LHV ratio of 0.9139, meaning that the work it can perform is 8.61% lower than its LHV indicates. It is noteworthy that the exergy-to-LHV ratios calculated in this study differ somewhat from those of Caton.9 The reason for this is that Caton9 considered only the gaseous-phase LHV and exergy for all fuels, whereas in this study we considered both gas- and liquid-phase fuel properties depending on the state of each fuel at ambient conditions. Our reasoning for using the ambient condition LHV and exergy content is to be as consistent as possible with how efficiency is considered on a real-world basis. As discussed previously, the energy content of fuel is measured experimentally using the ASTM methodologies. Experimentalists and real-world systems typically use the “fuel-tank” energy content of the fuel to define the energy consumed and the system efficiency; that is, the air or other oxidizer is not considered to bring any energy into the system and the measured heating value is considered to be the fuel energy and is not adjusted for temperature or the physical state of the fuel when it is combusted. Additionally, since one of the major themes of this study is to compare exergy and LHV, an analogous “fuel tank” definition of exergy was used. To gain insight into the fundamental thermodynamic differences among the selected fuels, we analyzed their equilibrium states following two different idealized combustion processes: (1) adiabatic constant volume combustion of fully vaporized stoichiometric fuel-air mixtures initially at atmospheric pressure; and (2) adiabatic fuel-air engine cycle analysis with compression at a fixed compression ratio, constant volume combustion of precompressed fully vaporized stoichiometric fuel-air mixtures, and adiabatic expansion. The equilibrium states of the combustion products from the first process help clarify differences deriving solely from differences in chemical composition and molecular structure. The equilibrium states from the second process provide additional insight into how fuel-specific thermochemical properties affect the compression and expansion processes as well as the postcombustion thermodynamic states for the different fuels. By including postcombustion gas expansion, it is possible to relate the properties of the equilibrium combustion products to the work potential of an internal combustion engine. First and SecondLaw efficiencies calculated for the fuel-air engine cycle analysis are calculated using the extracted work and the “fuel tank” energy and exergy. Our assumptions for both idealized combustion processes are summarized in Tables 2 and 3, respectively. It should be noted that when specifying fuel LHV and exergy, either a liquid or gaseous phase of the fuel is implied depending on its natural state at 300 K, and 1 atm absolute pressure. However, the idealized combustion engine simulations discussed below assume all the fuels considered to be fully vaporized at a constant temperature before they are compressed, and thus vaporization differences between fuels are not included in our efficiency results. We chose the vaporized fuel basis because our objective is to initially isolate the roles of other fuel-specific thermochemical factors not related to vaporization. Admittedly, fuel vaporization effects are important in practical engines, but these involve complex and systemdependent details (carbureted, port fuel injection, direct fuel injection, injection timing, etc.), which we wanted to avoid at this stage.

Table 2. Process 1 Modeling Assumptions initial conditions T [K] P [atm] equivalence ratio reactant composition nitrogen [moles] oxygen [moles] fuel [moles]

300 1 1.0 0.79 0.21 variable

species a

product species CO product species H2 product species a

N2, O2, O, OH, H, H2, CO, CO2, NO N2, O2, O, CO, CO2, NO N2, O2, O, OH, H, H2, NO

For all fuels except CO and H2

Table 3. Process 2 (Otto and Atkinson Cycle) Modeling Assumptions compression adaibatic initial T [K] initial P [atm] Φ compression ratio combustion and expansion

■

adaibatic product composition product species

343 1 1.0 9.2:1

equilibrium N2, O2, O, OH, H, H2, CO, CO2

RESULTS AND DISCUSSION Exergy and LHV. We first observe general trends in exergyto-LHV ratio for the 23 fuels considered, as depicted in Figure 1, with the fuels separated by chemical class. The exergy-toLHV ratio represents the work potential of a fuel relative to its LHV, where an exergy-to-LHV ratio greater than unity means that the fuel is capable of doing more work than would be predicted by its LHV. Note that this ratio increases with molecular size for the hydrocarbon fuels (alkanes, alkenes, and aromatic), but decreases for the alcohols. For carbon monoxide and hydrogen, the exergy-to-LHV ratio is less than unity. Thus, it can be seen that exergy varies in a systematic way relative to LHV, and is dependent on the chemical class of the fuel as well as the molecule size. We observe that the difference between exergy and LHV tracks with the change in moles that occurs following complete, stoichiometric combustion. This molar expansion effect can be quantified by the ratio (MER), which is defined as the ratio of complete product moles (nP) to reactant moles (nR) as shown in eq 3. n MER = P nR (3) The MER for each fuel is depicted as a function of fuel molecular weight for stoichiometric combustion in Figure 2a. The MER for alcohols and methyl butanoate is largest, followed by alkanes, alkenes, and aromatics, and is less than unity for only hydrogen and carbon monoxide. When MER is less than unity, it corresponds to a net reduction in moles during combustion. Figure 2b depicts MER as a function of molecular weight for alkanes, olefins (one unsaturation), single ring aromatics, alcohols, and esters. While the molecular weight of 2801

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Figure 1. Ratio of exergy-to-LHV for each fuel.

Figure 2. MER as a function of fuel molecular weight for stoichiometric combustion.

Figure 3. Ratio of exergy-to-LHV as a function of (a) molecular weight and (b) the MER.

fuel by combustion. At low molecular weights, the MER of oxygenated fuels is greater than for nonoxygenates because the presence of fuel oxygen means that fewer air moles are needed as reactants to complete combustion. The exergy-to-LHV ratio as a function of molecular weight is presented in Figure 3a and is similar to the MER in Figure 2a. This ratio increases with MW for the hydrocarbon fuels, with

these chemical classes is extrapolated to unrealistic values in the plot, it illustrates that the MER for all of these chemical classes tends to converge with increasing molecular weight and the aliphatic character of the molecules becomes more dominant. Physically, this trend in MER with molecular weight can be understood as the result of the increased number of molecular product molecules (CO2 and H2O) generated per molecule of 2802

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concept because it provides a simple, direct measure of the potential for expansive work relative to the most common measure of fuel energy, the LHV. In the above example of constant-volume combustion, we considered the combustion products after they were fully cooled. It is also useful to consider the peak temperature and pressure of the hot product gases immediately following adiabatic constant volume combustion. One interesting trend in this regard is illustrated in Figure 4. We observe here that the

alkanes > alkenes > aromatics. For alcohols, both the MER and the exergy-to-LHV ratio are higher than alkanes of similar molecular weight, but alcohols experience a decrease in exergyto-LHV ratio rather than the increase that was observed for MER. Rather than this being an inconsistency between the two metrics, we conjecture that it is another reflection of the MER convergence with molecular weight exhibited in Figure 2b. The primary difference is that the MER for methanol (the lowest molecular weight alcohol) is less than the convergent value of MER (∼1.07), whereas the exergy-to-LHV ratio of methanol is greater than the convergent value and experiences an initial decrease, much like esters in Figure 2b. Both carbon monoxide and hydrogen have a MER as well as an exergy-to-LHV ratio that is less than unity. Carbon monoxide and hydrogen are unlike the other fuels in that they do not belong to a larger chemical class (i.e., alkanes, alcohols, etc.); thus, additional information cannot be inferred as was done with the convergent behavior for the other chemical species. There is a strong correlation between the MER and the exergy-to-LHV ratio, as shown in Figure 3b, with the alcohols and hydrogen being notable outliers to the general linear trend. As explained earlier, the fuel exergy represents the amount of work that can theoretically be extracted from a fuel by oxidizing it with air, no matter what kind of conversion engine we use. The exergy-to-LHV ratio thus represents the work potential of a fuel relative to the most common measure of fuel energy, LHV. The strong correlation between MER and exergy-to-LHV ratio depicted above implies that these two fuel characteristics are closely related. Adiabatic Constant Volume Combustion Pressure Rise. The higher work potential associated with higher MER can be understood physically by considering the first constant volume combustion system described above with an initial pressure and temperature equal to those of the surroundings. If the product gases are cooled back to their initial temperature after combustion while constrained to the original volume (assuming all water remains in the gaseous state), the MER determines whether the final pressure will be higher or lower than ambient. For fuels with MER = 1 (e.g., methane and ethene), there is no net change in moles during combustion, and the final pressure is the same as the initial pressure (ambient). For fuels with MER > 1 (e.g., alcohols), there is an increase in the number of moles, and the final pressure will be higher than the initial pressure. In this latter case the system still has potential to do additional expansion work. For fuels with MER < 1 (i.e., hydrogen and carbon monoxide), there is a decrease in the number of moles, and the final pressure will be lower than the initial pressure. In this last case, it is possible to generate work by allowing the system to be compressed by the atmosphere (i.e., undergo negative expansion). It is also clear that the MER alone does not completely explain the exergy-to-LHV ratio trends among different fuels. While the exergy-to-LHV ratio appears to exhibit the same convergent behavior as MER with molecular weight, the MER for the smallest alcohols is less than the convergent value and the exergy-to-LHV ratio is greater than the convergent value. As a result, the MER of alcohol fuels increases with molecular weight whereas the ratio of exergy-to-LHV decreases. Additionally, while carbon monoxide and hydrogen have the same MER, carbon monoxide has a much lower ratio of exergy-toLHV than hydrogen, suggesting that other factors are important also. Nonetheless, MER appears to be a useful

Figure 4. Ratio of adiabatic peak pressure to peak temperature for each fuel normalized to methane following constant volume combustion, as a function of MER and fuel type.

normalized ratio of adiabatic peak combustion pressure to temperature (Pp/Tp) is linearly correlated with MER for all the fuels being considered. This should perhaps not be surprising because, at constant volume, the adiabatic ratio of pressure to temperature is constrained by the ideal gas law to be proportional to the number of moles present. Since MER represents the change in moles with stoichiometric reaction, the linear correlation with adiabatic Pp/Tp is a natural result. However something less obvious is also revealed in this plot: the different fuels are clustered according to their families and associated MER. The fuels with the highest adiabatic Pp/Tp ratios are the oxygenated species (alcohols and esters), while the fuels with the lowest adiabatic Pp/Tp ratios are hydrogen and carbon monoxide. Alkanes, olefins, and aromatics are distributed in between. One expects that higher values of adiabatic Pp/Tp might imply that more of the energy released by combustion is available in the form of pressure, while less thermal energy is present. Presumably energy in the form pressure is more useful for displacing the piston in an engine, and thus, the difference among fuels in terms of the pressure to thermal energy distribution after combustion should be relevant. Oxygenated fuels appear to have an especially high adiabatic Pp/Tp ratios compared to other fuels. Additionally, although heat transfer is not considered here, fuels with lower adiabatic Pp/Tp ratios operate at higher temperatures and are therefore subject to larger heat-transfer losses to their surroundings, ultimately reducing their efficiency. Comparing the pressure rise during combustion is another way to evaluate pressure-related characteristics for each fuel. The best way to quantify pressure rise is not straightforward because both the stoichiometric air-to-fuel ratio and the LHV change with fuel type. Thus, it is appropriate to define a dimensionless pressure rise term that is normalized to the LHV 2803

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Figure 5. Dimensionless pressure rise as a function of MER at starting conditions of 300 K and 1 atm when normalized to (a) LHV energy density and (b) fuel exergy density.

Figure 6. Extent of product dissociation as a function of temperature by showing (a) percent of hydrogen converted to H2O and (b) percentage of carbon converted to CO2 for (red *) n-paraffins, (green ■) alkenes, (blue +) aromatics, (◇) alcohols, (□) methyl-esters, (■) carbon monoxide, and (orange ●) hydrogen.

A linear curve fit of ΔPdimensionless_exergy as a function of MER, depicted in Figure 5b, shows no correlation (R2 = 0.0005). The expected result is that there will be no dependency on MER, but it is observed that there is substantial fuel-specific deviation from the mean pressure rise, with hydrogen, methane, and methanol having the highest ΔPdimensionless_exergy, and carbon monoxide, ethene, and benzene having the lowest. The reason the dimensionless pressure rise parameters in Figure 5 do not exhibit obvious trends as a function of MER, and instead show a high degree of fuel-specific variability, is due to the dissociation of the complete products of combustion. As was discussed earlier, our first idealized combustion model assumes that the products are at thermodynamic equilibrium, and because the constant-volume combustion system is adiabatic, stoichiometric combustion produces very high temperatures. Figure 6 shows the equilibrium percentage of the hydrogen and carbon in each fuel converted to water and carbon dioxide as a function of temperature, where 100% conversion represents complete combustion. Although there are some fuel-specific differences due to competing reactions, dissociation of the major combustion products is primarily a function of temperature. At a given temperature, the extent of water dissociation is significantly less than carbon dioxide dissociation. For example, at a temperature of 2482 K for nheptane, 95.7% of the hydrogen in the fuel has been converted

energy density of a stoichiometric mixture with air (ΔPdimensionless_LHV), according to eq 4. An analogus dimensionless pressure rise normalized to the exergy density of the stoichiometric charge is defined in eq 5 (ΔPdimensionless_exergy). ΔPdimesionless LHV =

ΔP [Pa] LHV Energy Density [J/m 3]

(4)

ΔP [Pa] Exergy Density [J/m 3]

(5)

ΔPdim ensionless exergy =

Based on the assumption that MER is directly related to the differences between exergy and LHV, we expect ΔPdimensionless_LHV to increase with MER because LHV does not include the MER effect, whereas we expect ΔPdimensionless_exergy to exhibit no change with MER because fuel exergy includes the MER effect. Figure 5a depicts ΔPdimensionless_LHV as a function of MER, and it is observed that the alcohols have the highest ΔPdimensionless_LHV whereas carbon monoxide has the lowest. Further, it is observed that, with certain types of hydrocarbons, namely olefins and aromatics, there is a linear trend of increasing ΔPdimensionless_LHV with MER. However, the ensemble linear curve fit produces a poor correlation (R2 = 0.59), with hydrogen, carbon monoxide, and methane being notable outliers. 2804

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Figure 7. Percent of the fuel LHV remaining unreleased at equilibrium due to chemical energy in the form of unoxidized hydrogen and carbon monoxide after constant volume combustion.

Figure 8. Dimensionless pressure rise as a function of MER at starting conditions of 300 K and 1 atm when normalized to the dissociation-adjusted (a) LHV energy density and (b) fuel exergy density.

demonstrates that the expected trend of increasing ΔPdimensionless_LHV with MER is present once product dissociation has been properly taken into account. In a similar manner, the fuel-specific variability of ΔPdimensionless_exergy as a function of MER is substantially reduced once the dissociated chemical exergy has been accounted for, as shown in Figure 8b. We observed that ΔPdimensionless_exergy for hydrogen and carbon monoxide exhibit only negligible differences, whereas there was a substantial difference for these in Figure 5b. Figure 8b, however, shows a declining pressure rise with the MER, whereas it was expected that all fuels would produce the same pressure rise on the basis that exergy includes the MER effect. The reason for the declining pressure rise is associated with another molecular property of the product gases, the ratio of specific heats (γ), and is discussed in more detail below. Real internal combustion engines have a substantial amount of heat loss, so the maximum temperatures are significantly lower than what is reached under adiabatic equilibrium. As a result, fuel-specific differences associated with complete product dissociation are diminished in real engines. This illustrates some of the challenges associated with extrapolating simplified thermodynamic models directly to real-world systems. Nevertheless, simplified thermodynamic analyses such as the above are still useful for understanding broad

to water, whereas only 86.2% of the carbon has been converted to carbon dioxide. The concentrations of dissociated species remaining after adiabatic combustion depend on the relative amounts of carbon and hydrogen present as well as the equilibrium temperature. The majority of the dissociated species are hydrogen and carbon monoxide, which are in equilibrium with water and carbon dioxide. Figure 7 depicts the percentage of fuel LHV remaining in the form of dissociated hydrogen and carbon monoxide in the postcombustion equilibrium state. Product dissociation is significant for all fuels, with carbon monoxide accounting for a much larger fraction of the unavailable fuel LHV. The fuels with the highest H/C ratio have the smallest amount of dissociated fuel energy: methane, ethane, methanol, and hydrogen. The fuels with the lowest H/C ratio are the fuels with the highest dissociated fuel energy: benzene and carbon monoxide. The dimensionless pressure rise terms shown in Figure 5 can be recalculated to discount the unavailable chemical energy associated with dissociation, as in Figure 8a, and the unavailable exergy, as in Figure 8b. The main outliers from Figure 5a, particularly hydrogen, carbon monoxide, and methane, exhibit much less fuel-specific variability in Figure 8a, and as a result, ΔPdimensionless_LHV shows a much stronger correlation as a function of MER than was seen previously (R2 = 0.85). This 2805

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Figure 9. First Law Otto cycle efficiency for stoichiometric combustion as a function of (a) the MER and (b) the exergy-to-LHV ratio.

Figure 10. Second Law Otto Cycle efficiency for stoichiometric combustion as a function of (a) the MER and (b) the amount of unavailable exergy due to product dissociation after combustion.

trends, such as the role of MER in explaining fuel performance differences. MER and Otto Cycle Efficiency. We now consider the second type of combustion process, which is the basis for the ideal Otto cycle. Following adiabatic precompressed constant volume combustion, the equilibrium combustion products are expanded to their original precompressed volume. The resulting expansion work is then compared to the original fuel heating value and exergy to determine the First and Second Law efficiencies. It should be noted that the modeled efficiencies are for highly ideal conditions and do not include friction, heat losses, or finite combustion duration, and are therefore not directly comparable to real engines. Figure 9 shows that the First Law Otto cycle efficiency increases with both the MER and the exergy-to-LHV ratio. Large efficiency differences exist between fuels, with an overall efficiency variation of 37.6% to 47.1%. The efficiencies of hydrocarbon fuels are similar, varying only from 43.5% for ethene to 45.4% for n-decane. Methanol produces the highest efficiency, followed by ethanol and propanol, while carbon monoxide produces the lowest efficiency. Both carbon monoxide and hydrogen are ranked lower than the others, with carbon monoxide lowest of all. This general ranking

appears to be similar to that in Figure 8, reinforcing the impression that the pressure rise is a good indicator of the work generating potential of the expanding exhaust gases. The large difference between carbon monoxide and hydrogen in Figure 9 reflects the higher proportion of unavailable dissociated energy for carbon monoxide, similar to the effect on pressure rise in Figure 5. First Law efficiency correlates better with the exergy-to-LHV ratio in Figure 9b than with MER alone, illustrating once again that while MER is closely related to the difference between exergy and LHV, it does not provide a complete basis for explaining fuel-specific trends in work output. Second Law efficiency is calculated on the basis of fuel exergy, so on the basis of the theory that exergy includes the MER effect, we expect that the Second Law efficiency should be constant for all fuels and independent of MER. Figure 10a confirms that the Second Law efficiency does not exhibit a systematic dependence on MER, and also shows that the range of Second Law efficiencies (41.1−44.9%) is much smaller than what is observed for First Law efficiency. Second Law efficiency for hydrocarbons and oxygenates is nearly constant, varying from only 43.1−44.1%. However, it is apparent that the Second Law efficiency is not constant for all fuels, with hydrogen 2806

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Figure 11. Postcompression γ (solid shading) and postcombustion γ (gradient shading) for each fuel.

have similar contributions to the mixture heat capacity ratio. The variability in γ for the compressed reactants and the postcombustion equilibrium products is shown in Figure 11. Our compression process is modeled as an adiabatic nonreacting system, so the amount of work done on the gases, the compressive temperature, and the compressive pressure are dependent only on the value of γ, with high γ leading to more compressive work and higher temperature and pressure. The postcompression temperature and pressure are expected to be closely related to the peak pressure following combustion as discussed above. The effect of the postcompression ratio of specific heats on first law efficiency can be seen in Figure 12 for a select subset of the fuels, where the ratio of

having the highest efficiency and carbon monoxide the lowest. It is noteworthy, though, that Figure 10a closely resembles the trend of ΔPdimensionless_exergy in Figure 5b, prior to correcting it for product dissociation. Figure 10b illustrates that Otto cycle Second Law fuel efficiency differences correlate closely with the degree of reaction product dissociation (represented as unconverted chemical energy) immediately following combustion. Although our analysis allowed for continued equilibrium conversion of the dissociated products at each point during expansion, incomplete reaction at the beginning of expansion reduces the pressure, thus reducing work generation during early stages of expansion. This effect varies with fuel type, with hydrogen having the smallest amount of postcombustion unconverted chemical energy and carbon monoxide the highest. Because the primary dissociating species is CO2, fuels with higher carbon-tohydrogen ratio are more impacted by this effect. Efficiency and Ratio of Specific Heats. Thus far we have discussed the effect of the MER and product dissociation on postcombustion conditions and expansion work in an ideal Otto cycle. However, we have not yet considered how fuelspecific differences also relate to the details of isentropic gas compression and expansion. In particular, we now consider the role of γ, the ratio of specific heats (cp/cv). Traditional analyses of the Otto cycle have typically related cycle efficiency (η) to γ and compression ratio (CR) by eq 6.16 η=1−

⎛ 1 ⎞γ− 1 ⎜ ⎟ ⎝ CR ⎠

(6) Figure 12. First Law Otto cycle efficiency as a function of postcompression γ for equivalence ratios from 0.5 to 1.0 butane, propane, toluene, and ethanol.

In actuality, the ratio of specific heats impacts two distinct parts of the Otto cycle: (1) compression of the air−fuel mixture and (2) expansion of the postcombustion exhaust gases. The ratio of specific heats varies significantly between these two stages and also as temperature varies within each stage, and we have accounted for these variations in our analyses above. Fuelspecific differences in γ are typically much larger during compression due to the large variation in the individual heat capacity ratios of the different fuels. Variations in γ during expansion are smaller since exhaust gas mixtures vary primarily in the relative amounts of H2O and CO2, and both of these

specific heats is altered by manipulating the equivalence ratio (reducing equivalence ratio increases post compression γ). We observe that, for a given fuel, First Law efficiency increases with the ratio of specific heats in a manner consistent with eq 6. We also observe in Figure 12, however, that while propane, butene, and toluene all share a similar relationship between γ and efficiency, the First Law efficiency for ethanol is substantially 2807

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Figure 13. Effect of the ratio of specific heats (γ) on (a) stoichiometric First Law Otto cycle efficiency and (b) stoichiometric Second Law Otto cycle efficiency.

The initial temperature (T0) and the temperature at the end of compression (T1) are then related, as in eq 7.

higher at a constant ratio of specific heats. For example, at a ratio of specific heats of 1.315, all of the hydrocarbon fuels have a calculated efficiency of 47−48%, whereas ethanol has an efficiency of approximately 51%. Thus, this illustrates that there is a fuel-specific effect on efficiency that is separate from the ratio of specific heats and is not accounted for in eq 6. To further clarify the role of γ, Figure 13 shows First and Second Law Otto cycle efficiencies for stoichiometric combustion as a function of the postcompression ratio of specific heat for all the fuels included in this study. Here, changes in postcompression γ are due only to the inherent properties of the fuels themselves, since there is no variation in equivalence ratio. The resulting trends show that First Law efficiency (Figure 13a) decreases with fuel-imposed increases in postcompression γ, which at first glance seemingly contrasts with the well-understood relationship in eq 6. However, we point out that here our focus is on the fuel-imposed differences in postcompression γ, not the γ of the combustion products during expansion, which is typically where emphasis has been placed in previous discussions about the application of eq 6. Instead, we argue that the relationship shown in Figure 13a reflects a complex trade-off between postcompression γ, which by itself serves to increase efficiency, and decreasing fuel MER, which serves to decrease efficiency. As discussed below, these counteracting effects from γ and MER are important because they imply that the net efficiency differences among fuels will tend to be reduced when both are accounted for. In Figure 13b, the Second Law efficiency exhibits a similar fuel-specific variability previously seen in Figure 5b, which can be largely attributed to the large amounts of product dissociation. The reason that eq 6 can be misleading when comparing fuel effects is that eq 6 is based on the assumption that there are a constant number of gas moles throughout the cycle and that γ is constant. We now consider how eq 6 can be modified to better account for fuel-specific differences during each stage of the ideal Otto cycle: adiabatic compression, constant-volume adiabatic combustion, and isentropic expansion. For simplicity we still assume that the specific-heat ratio is constant during each stage but varies among stages. For compression, we approximate the ratio of specific heats of the reactants (γR) by a constant mean value and assume that no reactions occur (therefore, there is no change in moles).

T1 = (CR)γR − 1 T0

(7)

During the constant-volume combustion stage in an ideal Otto cycle, the net internal energy is conserved. Thus, the initial and final temperatures can be related as described by eq 8, which can be rearranged to relate the postcombustion and precompression temperatures as in eq 9. nR Cv , R[T1 − T0] + nR Δu = nP Cv , P[T2 − T0]

T2 = T0 +

(8)

nR Δu + nR Cv , RT0[(CR)γR − 1 − 1] nP Cv , P

(9)

Finally, expansion is described by eq 10.

T3 = (CR)1 − γP T2

(10)

By summing the amount of work done during compression and expansion, we can calculate the network in the cycle by eq 11, where substitution yields eq 12. First Law efficiency can then be calculated by dividing the work term by the lower heating value of the fuel, yielding eq 13. W = nR Cv , R(T0 − T1) + nP Cv , P(T2 − T3)

(11)

W = nR Δh[1 − (CR)1 − γP ] + (nP − nR )RT0[1 − (CR)1 − γP ] + [nR Cv , R + nP Cv , P]T0(CR)1 − γP + [nP Cv , P − nR Cv , R(CR)γR − γP ]T0 η = [1 − (CR)1 − γP ] + + + 2808

(12)

(nP − nR )RT0[1 − (CR)1 − γP ] nR Δh

[nR Cv , R + nP Cv , P]T0(CR)1 − γP nR Δh [nP Cv , P − nR Cv , R(CR)γR − γP ]T0 nR Δh

(13)

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same LHV compared to a fuel with a lower MER, thereby producing a higher First Law efficiency. Because exergy already accounts for MER, the explicit dependence of Second Law efficiency on MER is reduced. For the Second Law efficiency, chemical dissociation of the products more effectively correlates with fuel-related differences. Finally, the heat-capacity ratios (γ) for the intake and exhaust species also affect efficiency, with the intake mixture ratio being of greater importance for fuel-related differences. In general, it is beneficial for efficiency to have a higher γ for reactants and products, as well as a higher MER. Coincidentally, however, for all the fuels considered here, there is a strong inverse relationship between γ and the MER, effectively canceling out the benefits of high MER on efficiency. Additional studies are needed to confirm if this is a general property for all fuels and if the effects of heat losses might significantly change the fuelspecific trends. It should also be noted that a number of additional layers of modeling complexity need to be added before the results of this study can be applied to real spark-ignition engines. In real engines the effect of heat transfer can be significant, whereas this study assumed adiabatic conditions. Fuel vaporization effects can also impact in-cylinder temperature and heat transfer. Additionally, real engines do not undergo instantaneous constant volume combustion, but rather have finite combustion duration and ignition kinetics can make a nonideal combustion phasing or low compression ratios necessary to mitigate engine knock.

Thus eq 13 accounts for the change in moles as well as the differing reactant and product ratios of specific heats. We see from eq 13 that efficiency increases with γR, γP, and nP. Despite the large differences in fuel properties considered, the variation in the mean exhaust heat-capacity ratio (γP) is relatively small, with variations from 1.23 to 1.25 after combustion and before expansion. The variability in heatcapacity ratio during compression (γR) is much more significant, however, ranging from 1.28 to 1.36 for the compressed reactants. Thus, we expect that the fuels with both a high MER and a high γR should exhibit the largest First Law efficiencies. Figure 14 depicts the inverse relationship between the MER and γR for the fuels investigated. The fuels with the highest γR

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Figure 14. Compressed reactant specific heat ratio as a function of the MER.

Notes

The authors declare no competing financial interest.

■

are hydrogen and carbon monoxide, which also have the lowest MER. The fuel with the highest MER, methyl butanoate, is the fuel with the lowest γR. In effect, variations in γ and MER tend to counteract each other for all the fuels considered here. Thus, we see that while the effects of individual fuel properties can be considered separately in a theoretical analysis, the properties of real fuels are not independent of one another.

ACKNOWLEDGMENTS The research is sponsored by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program, under Contract No. DE-AC0500OR22725 with UT-Battelle, LLC.

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■

DISCUSSION AND CONCLUSIONS In this study, we explored the effects of fuel chemistry variations on the First and Second Law thermodynamic efficiencies of an ideal adiabatic internal combustion engine in terms of the individual contributions of molar expansion ratio (MER), reaction product dissociation, and heat-capacity ratio (γ). We also demonstrated how seemingly opposite fuelrelated trends in efficiency can arise depending on whether one uses fuel exergy or lower heating value (LHV) as a normalizing basis. Much of the difference between fuel exergy and LHV is associated with the MER. When the MER is greater than unity, there is additional potential to generate more work than is indicated by the LHV. This effect of MER can lead to apparently opposite trends when considering First and Second Law behavior of different fuels. We found that the pressure effect of MER correlates well with the combustion pressure rise, once chemical dissociation is taken into account. It is through this higher pressure rise that a fuel with a high MER is able to produce more work for the

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