Article pubs.acs.org/EF
Thermochemical Characterization of Bio- and Petro-diesel Fuels Using a Novel Laser-Heating Technique Cary Presser,*,† Ashot Nazarian,† Thomas J. Bruno,‡ Jacolin A. Murray,† and John L. Molloy† †
Chemical Sciences Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States ‡ Applied Chemicals and Materials Division, Material Measurement Laboratory, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, United States ABSTRACT: A state-of-the-art, rapid laser-heating technique, referred to as the laser-driven thermal reactor, was used to characterize National Institute of Standards and Technology Standard Reference Material (SRM) diesel and biodiesel fuels, as well as a prototype biodiesel fuel. Also described are the various issues associated with carrying out these measurements under different operating conditions (i.e., temperature, pressure, heating rate, and sample mass). The technique provides measurement of various relevant thermochemical characteristics; for this investigation the focus was on the sample endothermic/exothermic behavior, specific heat release rate, and total specific heat release. The experimental apparatus consists of a copper sphere-shaped reactor mounted within a vacuum chamber, along with integrated optical, gas-supply, and computer-controlled data-acquisition subsystems. At the center of the reactor, the sample and substrate rest on a thermocouple. The reactor is heated from opposing sides by a near-infrared laser to achieve nearly uniform sample temperature. The change in sample temperature with time (i.e., thermogram) is recorded and compared to a baseline (no sample) thermogram obtained prior to the experiment, and then processed (using an equation for thermal energy conservation) for the thermochemical information of interest. Results indicated that the baseline is affected by residue remaining after completion of reactions and a change in the oxide layer of the reactor sphere outer surface. Thus, the sphere must be pre-oxidized in air using the laser prior to any sample or baseline measurement. This investigation provides preliminary evaluation of SRM biodiesel fuels, with the results being consistent with distillation curve work reported in the literature.
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Comparison and Benchmark Database,7 NIST Chemistry WebBook,8 and NIST/EPA/NIH Mass Spectral Database9). Most of the fuel-related information provided in these databases is for single-component fuels and specified gaseous and liquid fuel mixtures (including fuel surrogate mixtures). In addition, NIST has developed several biomass feedstock reference materials and two biodiesel Standard Reference Materials (SRMs), along with values for their composition, physical, and combustion properties. Reliable thermochemical/ thermophysical/chemical kinetics data at heating rates representative of real reactor operating conditions are needed for expanding these databases. Biodiesel fuel is considered as a partial or full replacement for petroleum-based, ultra-low-sulfur diesel (ULSD) fuel.10,11 The major constituents of pure biodiesel fuel are fatty acid methyl esters (FAMEs).12 The advantages of using biodiesel fuels include its sustainability (biodiesel can be prepared from sources such as vegetable oil, animal fats, used cooking oil, and microalgae), the potential to produce it domestically, and increased lubricity compared to low-sulfur petroleum-derived diesel fuels.13 The fluid is noncarcinogenic, nonmutagenic, and biodegradable, and the use of it decreases certain emissions (including carbon monoxide, unburned hydrocarbon, and particulate matter mass) when compared to petroleum-derived
INTRODUCTION One main thrust for development and use of alternative biofuels is to expand the portfolio of fuels and feed stocks, and produce a secured sustainable source of energy.1 Another important goal is to reduce hydrocarbon and carbon dioxide emissions into the atmosphere. Primary commercial entities that are influenced by the need for reliable energy sources include fuel production, transportation (automotive, air, and sea craft), and manufacturing. Data and empirical models of the properties, compatibility, and environmental impact of biofuels, as well as for conventional petroleum fuel/biofuel mixtures, are limited and needed to ensure biofuel implementation, commercialization into the U.S. marketplace, and appropriate government regulation. To ensure U.S. competitiveness with international entities, biofuel standards are required which are based on well-characterized reference biofuel compositions.2,3 In addition to physical and chemical data, reliable data are needed on how harsh reactive environmental and operational conditions may impact fuel quality, chemical reactions, thermal energy/power release, and byproduct emissions. At the National Institute of Standards and Technology (NIST), several relevant Web-accessible databases and computational programs exist that address the need to provide well-characterized reference data and materials with specified uncertainties. Such databases and programs include fuel thermophysical properties (REFPROP 4 and the NIST ThermoData Engine5) and fuel chemical kinetics (NIST Chemical Kinetics Database,6 NIST Computational Chemistry This article not subject to U.S. Copyright. Published 2015 by the American Chemical Society
Received: April 17, 2015 Revised: August 3, 2015 Published: August 4, 2015 5761
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diesel fuel.14 Some disadvantages include increased NOx emissions, oxidative instability, moisture absorption during storage, low gel point, and emission of higher number concentration/smaller diameter particles.12,15,16 Combustion characteristics for unblended biodiesel and petroleum-derived diesel fuels are quite different, since the fluids have different chemical compositions and physical, fluid, and thermal properties, all of which need to be taken in account when blending or substituting fuels.13 These considerations are particularly relevant when fuel specifications stipulate that biofuel blends be treated as identical to unblended fuels after demonstrating conformance (such as with ASTM D7566 Standard Specification for Aviation Turbine Fuel Containing Synthesized Hydrocarbons).17 One important property for fuel performance is its heating value, and thus comparison of petroleum-derived diesel fuel and biodiesel fuels will depend on the accurate determination of the energy released at various physical conditions. Characterization of biodiesel fuel physical, chemical, and thermal properties, and comparison to those of diesel fuel, are becoming more important as biofuel use grows. Bruno and Smith18 developed a composition and enthalpy-explicit distillation curve method to estimate energy content of each distillate fraction released from complex liquid fuels. This was accomplished by using gas chromatography/mass spectrometry to determine the chemical composition at each distillate fraction and using enthalpies available in the archival literature to estimate the change in enthalpy (i.e., enthalpy of combustion) of a particular fuel. The distillation curves and enthalpies of combustion were compared with respect to distillate fraction for four soybean-based biodiesel fuels (produced by transesterification consisting of mainly FAMES) and one petroleum-derived diesel fuel.19 The results indicated that, on a molar basis, the enthalpy of combustion of the four biodiesel fuels increased slightly with increasing distillation temperature. The petroleum-derived ULSD fuel was found to be more volatile than the biodiesel fuels (i.e., its distillation curve was at a lower temperature than for the biodiesel fuels), with the initial boiling point being lower than those of the biodiesel fuels by approximately 120 K.19,20 On a molar basis, the biodiesel fuel enthalpies of combustion were greater (for each distillate fraction) than those for the ULSD fuel. However, on a mass or volume basis, the ULSD fuel sample was more energetic. Smith et al.13 also investigated the distillation features of B20 (where the number indicates the volume percent of biodiesel fuel) and found that the distillation curve was displaced to higher temperatures than the ULSD fuel, but still significantly different than the B100 (i.e., unblended biodiesel fuel) distillation curve (occurring at the highest temperatures). It was reported that thermal discrimination (i.e., the preferential vaporization of the FAME components caused the FAME mass fraction to change with percent distillate volume fraction20) occurred with the FAME fraction in B100 but not in B20 (for which the FAME fraction was only present as a background to the petroleum-derived components). Again, this investigation indicated significant differences in the thermal behavior of biodiesel and diesel fuels. In one recent study by the Coordinating Research Council,21 the physical and chemical properties were analyzed and compared for a variety of renewable diesel fuels and four commercial ULSD fuels. For the renewable diesel fuels, none of the oxygen atoms inherent in the starting feedstock were detected, and thus they were thought to have been hydro-
processed (resulting in the formation of paraffins). Although this hydroprocessed biofuel (a second-generation biofuel referred to in this study as renewable diesel fuel) was not the same as FAME biodiesel fuel discussed above, this was another example illustrating that biodiesel properties were significantly different than those of diesel fuel. Their analysis of the ULSD fuel (with an estimated vapor pressure of 0.3 kPa22) showed it to contain a mixture of n-paraffin, iso-paraffin, monoparaffin, cycloparaffin, and aromatics. It had the highest concentration of n-paraffin (21.9%) as compared to the other types of investigated petroleum diesel fuels. The renewable diesel fuel was predominantly composed of n-paraffin and iso-paraffin (98.9%) with a ratio of about 1:4, respectively. Note that although the aromatics have higher vapor pressures (e.g., about 9.9 kPa at 293 K for benzene23) than the paraffins (e.g., octane with a vapor pressure of about 1.5 kPa at 293 K24), their mass fraction in the hydroprocessed biodiesel fuel is essentially negligible. The report demonstrates that the renewable diesel fuel had a disproportionally higher mass fraction of volatile isoparaffins (about 72%), as compared to the ULSD fuel (about 14%).25 As a result, the volatility of renewable diesel fuels appears to be significantly different than that of petroleum diesel fuel and warrants further investigation. Investigation Objectives. To describe biodiesel fuel characteristics, both thermochemical and chemical kinetics information is required to provide a functional reference database. The objective of this investigation was to determine biodiesel thermochemical characteristics, i.e., sample endothermic/exothermic behavior, specific heat release rate, and total specific heat release (i.e., gross heating value), using a laserheating technique (referred to as the laser-driven thermal reactor, LDTR). Two biodiesel fuels (NIST SRM 2772 and another commercially available fuel) and an ULSD fuel (NIST SRM 2771) were selected to demonstrate the technique’s capability to uniquely detect biodiesel fuel oxidation. The technique provides temporally resolved sample thermal signatures (i.e., temperature-versus-time thermograms) under a variety of operating conditions. These thermal signatures, along with a theoretical model for the conservation of thermal energy, were used to determine the above-mentioned thermochemical characteristics.
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EXPERIMENTAL SECTION
Brief Facility Description. The LDTR measures the total thermal response (due to both substance thermal and chemical heat release) of a sample. The technique has been used for a variety of applications.26 It provides quantitative information on the thermophysical characteristics (while the substance chemical nature is unchanged, e.g., heat capacity, thermal conductivity, emissivity, and absorptivity), thermochemical characteristics (for which the substance chemical identity is altered, e.g., exothermic and endothermic behavior), and chemical kinetics (e.g., reaction sequence, and rate constants) of multicomponent and multiphase substances. This investigation focused on the thermochemical characteristics of the sample endothermic/ exothermic behavior, specific heat release rate, and total specific heat release (i.e., gross heating value). The LDTR experimental facility and theory of analysis are detailed in Nazarian and Presser27,28 and Presser.29 Some pertinent information is summarized for clarity, along with a description of the current facility modifications for these experiments. The laser-driven thermal reactor consists of a sphere-shaped copper reactor mounted within a vacuum chamber, along with optical, gas-supply, and computercontrolled data-acquisition subsystems (see Figures 1 and 2). The sample (i.e., fuel and aluminum pan substrate) is supported on a customized K-type fine-wire thermocouple, which is stationed at the 5762
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Figure 1. Schematic of the LDTR copper reactor sphere. Figure 3. Schematic of the LDTR thermal analysis protocol using the heating-rate approach.
center of the reactor (defining the “sample temperature”). The thermocouple bead is in contact with the pan bottom outer surface. A second thermocouple is in contact with the reactor wall inner surface (defining the “reactor temperature”). The reactor assembly is heated from opposing sides by a near-infrared Nd:YAG laser beam (operating at a wavelength of 1.064 μm) to achieve a nearly uniform sample temperature. The reactor is stationed within the vacuum chamber, allowing for control of the environment (e.g., gas pressure and composition) around the sample. In general, measurements are carried out at reduced pressure, which eliminates thermal convection within the reactor sphere, and thus conduction and radiation are the dominant modes of heat transfer. The system was originally designed to limit effects of a nonuniform temperature distribution in the middle of the sphere. The uniformity in temperature of heating a sample placed within the center of the sphere (for a volume with dimensions of about 10 mm diameter by 5 mm height) is of the order of 1 K.28 Within the sample, heat transfer is by conduction. The lumpedcapacitance approximation30 is invoked, in which the sample is spatially uniform in temperature at any instant of time during the transient process, as long as the Biot number 0, then the behavior is exothermic. Integration of eq 5 with respect to time for the entire experiment (including endothermic and exothermic processes) results in an expression for the total specific heat release (equivalent to the gross heating value), Q = ∫ q(T) dt = −ΔH (where ΔH is the change in enthalpy of the chemical reaction).28 One can then compare the measured change in enthalpy to calculated values, which are derived from the set of possible overall chemical reactions (i.e., as obtained from the literature). The most probable reaction is assumed to be the one with a calculated value of ΔH that is similar to the measured value. As noted earlier, there is the possibility of chemical reaction also occurring on the reactor surface, indicating that the total thermal energy release may not be captured with the above substrate-based analysis of eq 5. To characterize the specific heat release rate from the reactor surface q(Tr), one can consider the absorption/release of thermal energy from the outer reactor surface to the surrounding environment. Thus, all reactions occurring within the reactor volume will influence heat transfer to/from the reactor surface. It is assumed that all heat transfer processes within the sphere are distributed uniformly over the inside sphere surface, and the sphere temporal response is slower than that of the substrate due to its larger mass. The heat transfer from the outer reactor surface then can be expressed by eqs 3 and 4, for which the temperature is that of the reactor thermocouple Tr. Since the heat transfer parameter τ is defined by a referred value of the reactor temperature (see Figure 3), it is only applicable to when sample is positioned at the reactor sphere center. Thus, evaluation of eqs 3 and 4 requires that the heat transfer term F(T,To) be defined by eq 13b in ref 28. Combining eqs 3 and 4, 5767
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the top port or detected in the thermograms (as noise in the temperature rise). This observation may indicate that the biodiesel fuels did not react completely at the beginning of the run while sample temperatures were low, and that reactions may have occurred near the inner surface of the reactor sphere (the reactor temperature is always higher than the sample/ substrate temperature). Thus, one needs to account for reactions on the sphere surface and the loss of fuel vapor through the sphere opening when determining the total heat loss. At the end of each run (i.e., steady-state temperature for which the input thermal energy equals the thermal losses, see eq 1), the sample thermograms should approach the baseline values assuming complete consumption of the sample. The diesel fuel case falls below the baseline at the end of the thermogram (while being above the baseline for most of the run). This result was attributed to some degradation of the reactor sphere by the laser heating and a change in the baseline (see Figure 5). The change in the baseline, as discussed earlier, is attributed to deposition of condensable vapor and unreacted residue on the reactor and substrate surfaces, and a change in the CuO layer on the outer sphere surface to Cu2O. To obtain a better perspective of the subtle changes in the thermograms of Figure 7, results are presented for the sample−baseline temperature difference (Figure 8) and the sample temperature−time derivative (Figure 9), both with respect to time and temperature. Sample−Baseline Temperature Difference. The sample thermal behavior is revealed in Figure 8, which presents the difference between the sample and baseline thermogram temperatures with time and temperature, respectively, for the three fuels. Figure 8C presents the variation in the reactor− baseline temperature difference with time. The thermal behavior of the three fuels was essentially exothermic. For the two biodiesel fuels, the temperature difference increased with time and temperature, with the initial rise attributed to fuel evaporation. There is a significant increase in the temperature difference (for ΔT = T − Tbaseline > 10 K) at ∼11 s (Figure 8A) and ∼520 K (Figure 8B), which is attributed to initiation of reactions and the release of thermal energy. The values peak at ∼640 K (SRM 2772) to ∼650 K (B100) and ∼13 s, which is near the aforementioned FAME boiling points, and then begin to decrease, indicating consumption of reactants and reduction in the heat release rate. At about 700 K and ∼14 s (minimum) the values increase again, indicating the initiation of further reactions (and increase in the heat release rate), and finally peak at ∼880 K (∼16 s) for which reactions terminate. The total specific heat release, Q (as detailed earlier), was determined from both eqs 5 and 6 for the peaks present in the sample−baseline temperature difference profile (Figure 8A). The equations were evaluated according to the following criteria: (1) Δm was set to increase with time from an initially small value to the initial total mass, reaching the maximum value at the second peak (where reactions were expected to reach completion), (2) only portions of the temperature difference profile related to the two peaks were considered for analysis, (3) the minimum between the two peaks indicated the end of the first peak and the start of the second peak, and a tangent line drawn from the minimum outward to intersect the base of the profile defined the start of the first peak and end of the second peak, and (4) results from only one of the two data sets for each fuel are presented so no uncertainties are included with the reported values of Q. In addition, for eq 6, the thermal
temperature was small for the fuels (not knowing the temperature dependency), especially in light of the fact that the bulk of the mass was the aluminum pan. The value for τ was 1.15, which was determined from several baseline experiments at different laser fluences, substituting into eq 2 using the baseline thermograms, and averaging the results. For eq 6, κg(Tg) was 0.024 W·m−1·K−1 (in air)45 and ε(Tr,λ) was 0.45 for CuO.28 Other variables in eqs 5 and 6 are provided above. Finally, sample−baseline temperature difference profiles (as discussed below) were used to estimate over which time intervals the fuel behavior was exothermic, and provide limits for integrating (using the trapezoidal rule) and determining a value for Q. For eq 6, the thermal losses through the opening in the top of the reactor sphere were accounted for by determining the surface area of the opening to the total sphere surface area and adjusting the result for this effect.
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RESULTS AND DISCUSSION Sample Thermograms. In this study, a NIST SRM diesel fuel (2771), NIST SRM biodiesel fuel (2772), and B100 fuel were evaluated using the LDTR. Figure 7 presents the variation
Figure 7. Comparison of the sample and baseline thermograms (sample temperature) for SRM 2771 diesel fuel, SRM 2772 biodiesel fuel, and B100 fuel.
of the sample temperature with time for these fuels. The two biodiesel fuels appear to behave in a similar fashion. The boiling point range for the five FAMEs was estimated to be (605−634) K,25,36 while the range for diesel fuel was estimated to be (436− 660) K.19 At about 520 K, the two biodiesel fuels depart from the baseline, indicating the transition from vaporizing fuel to the onset of chemical reactions. The initial rise in diesel fuel temperature, however, appears to be more rapid than for the biodiesel fuels, departing significantly from the baseline at ∼320 K (initiation of reactions) until ∼670 K, where the temperature changes to that of the biodiesel fuels. Steady-state heating occurs at ∼940 K. For all three fuels, no visible residue was observed in the pan after each measurement with the mass of the substrate remaining unchanged. However, visible fuel residue (reaction byproducts) coating the chamber top window inner surface (i.e., the transport of fuel vapor through the top opening in the reactor sphere) was observed after the biodiesel fuel experiments (also a vapor odor was apparent when the vacuum chamber was opened). No flame was observed through 5768
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Figure 9. Comparison of the sample and baseline derivative profiles (sample temperature) with (A) time and (B) sample temperature for SRM 2771 diesel fuel, SRM 2772 biodiesel fuel, and B100 fuel.
sphere surface area). The value of Q for the SRM 2772 first peak was estimated to be 16 kJ·g−1 and the second about 23 kJ· g−1, as based on the specific heat release rate (q) from the reactor surface eq 6 − the value of Q reported earlier from bomb calorimetry13 was 39 kJ·g−1. When the analysis was based on the pan substrate at the reactor center eq 5, the values were generally found to be much lower, i.e., estimated to be 5 and 5 kJ·g−1, respectively. This is attributed to vaporization of unreacted fuel, which later reacts on the reactor surface. Similarly for B100, the results were estimated to be 18 and 20 kJ·g−1 (reactor surface), and 2 and 13 kJ·g−1 (center of reactor). The value of Q (distillation analysis)24 was reported earlier to be about 37 kJ·g−1. This two-peak behavior is thought to be related to the preferential vaporization and reaction of the five different FAMEs (having different boiling points and enthalpies of combustion, as listed earlier); the more volatile fractions react while the less volatile fractions continue to vaporize until the temperature is high enough to react. Regarding the diesel fuel, the exothermic behavior is similar to that of the biodiesels fuels, but is initiated earlier (comparing the first diesel fuel peak to that of the biodiesel fuels) with a significantly larger temperature difference (appearing to have a
Figure 8. Comparison of the sample−baseline temperature difference profile (sample temperature) with (A) time and (B) sample temperature, and (C) sample−baseline temperature difference profile (reactor temperature) with time for SRM 2771 diesel fuel, SRM 2772 biodiesel fuel, and B100 fuel.
losses through the opening in the top of the reactor sphere were accounted for with a multiplicative correction factor (the opening surface area was estimated to be about 22% of the total 5769
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value of ∼760 K (∼15 s), indicating reaction of the less volatile hydrocarbons. Comparing the sample−baseline temperature difference profile (Figure 8) to the sample derivative profile (Figure 9) indicates that when reactions are initiated (i.e., exothermic release of thermal energy), the temperature difference (as well as the derivative) increases until reactive species are consumed preferentially. The temperature−time derivative will increase (along with the reaction rate) as long as the change in the Arrhenius rate constant (being dependent on temperature) is the dominant term in the reaction rate equation (compared to the term representing the reactants consumption rate). The derivative will reach a maximum (thermogram inflection point) when the term for the reactants consumption rate becomes the dominant term with increased temperature. The temperature difference continues to increase until termination of reactions (near the minimum in the sample derivative profile).
greater release of energy than the biofuels). This result appears to be consistent with the boiling-point distillation curve work described above,13,24,25 for which the vapor-rise temperature of the diesel fuel fractions is significantly lower than for biodiesel fuels (indicating that the diesel fuel fractions vaporize more readily than the biodiesel fuel and are more reactive). The temperature difference (for ΔT > 10 K) increases initially at ∼320 K and ∼6 s (indicative of reaction and the release of thermal energy), peaks at ∼620 K (∼12 s), and then decreases to a minimum (consumption of reactants and reduction in the heat release rate). At about 740 K and ∼14 s (minimum), the temperature difference increases again (initiation of reaction and an increase in the heat release rate) and peaks at ∼900 K (∼17 s), indicating termination of reactions. The second peak is similar to that of the biodiesel fuels, and may indicate that the volatility of the heavier fractions is similar for all of the fuels. This behavior again is attributed to preferential vaporization and reaction of the lighter hydrocarbon fractions in the diesel fuel, while the heavier fractions continue to vaporize and then react at a later time and higher temperature (second peak). Reaction of the lighter fractions would also explain why reactions are initiated at ∼320 K, which is lower than the estimated boiling point for diesel fuel. The values of Q for the SRM 2771 first and second peaks, respectively, were estimated to be 44 kJ·g−1 (reactor surfaceonly the first peak formed, see Figure 8C) and 10 and 3 kJ·g−1 (center of reactor), with the value from the literature46,47 estimated to be about (43−44) kJ· g−1. The endotherm at the end of the experiment, again is attributed to the change in the baseline during the reaction portion of the run and thus the initial portion of the baseline is more certain than the end (see Figure 5). As a result, this effects the estimation of Q. Sample Temperature−Time Derivatives. Figure 9 presents the variation of the sample temperature−time derivative with time and temperature, respectively, for the three fuels. The derivative was determined by taking the difference between two adjacent data points per time interval at each measured temperature for the sample and baseline thermograms. Again, the curves for the two biodiesel fuels are similar, while there is a significant departure for the diesel fuel. The first maximum is reached for the two biodiesel fuels at ∼570 K (SRM 2772) to ∼590 K (B100) and ∼12 s. The departure of the derivative from the baseline is attributed to initiation of reactions and the release of thermal energy of the more volatile FAME (associated with the rapid rise in temperature, see Figure 7), until the peak value. At this point, the heat release rate decreases, along with the continued consumption of reactants, and results in a decrease in the derivative. Note that the peak in the derivative corresponds to the inflection point in the sample thermograms of Figure 7 and sample−baseline temperature difference profiles (Figure 8). Termination of the volatile-FAME reaction occurs when the derivative decreases back to the baseline at ∼640 K for SRM 2772 and ∼660 K for B100 (minimum at ∼13 s). The derivative then rises again until it peaks at about ∼760 K (∼14 s), indicating reaction of the less volatile FAME. The derivative for the diesel fuel initiates reactions at ∼320 K and ∼6 s (dT/dt ≈ 20 K/s) and peaks at ∼590 K (∼11 s), but at a smaller value of the derivative than for the biodiesel fuels. The derivative reaches a minimum at ∼650 K (∼13 s), indicating reaction termination of the volatile hydrocarbon fractions. The derivative again rises (as do the biodiesel fuels) to a peak
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CONCLUSIONS A laser-heating technique was used to investigate the thermochemical behavior of two soybean-based biodiesel fuels and an ultra-low-sulfur diesel fuel. The results indicated that the LDTR thermograms were different for the fuels investigated, as well as their exothermic behavior. The thermal behavior and energy release of each fuel were dependent on the preferential vaporization of the volatile fuel fractions. A change in the baseline (after reaction of the sample) was attributed to deposition of condensable vapor and unreacted residue on the reactor and substrate surfaces, and a change in the oxide layer on the reactor sphere outer surface, which affected measurement uncertainty. Nevertheless, the results remained consistent with distillation curve work reported in the literature. This study demonstrates that the LDTR can provide useful information regarding biodiesel fuel thermochemical behavior at different temperatures.
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AUTHOR INFORMATION
Corresponding Author
*Telephone: 301-975-2612. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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NOMENCLATURE A = sample geometric cross-sectional area [m2] cp(T) = specific heat capacity [kJ·kg−1·K−1] (dT/dt) = sample temperature−time derivatives [K·s−1] F(T,To) = heat transfer term [W] II = intensity of the laser beam that heats the sample [W· m−2] kc = coverage factor m = sample total initial mass [g] n = number of samples Nu = Nusselt number q(T) = specific heat release rate due to chemical reaction [W·g−1] Pr = Prandtl number Q = total specific heat release (or absorption) [kJ·g−1] Ra = Rayleigh number Rlh = laser heating rate [K·s−1] s = standard deviation t = time [s] DOI: 10.1021/acs.energyfuels.5b00835 Energy Fuels 2015, 29, 5761−5772
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t1, t2 = time corresponding to the sample temperatures T1 and T2, respectively [s] T = sample temperature [K] Tg = gas temperature [K] Tr = reactor temperature [K] To = sample temperature of the baseline [K] T1, T2 = sample temperatures at two different laser fluences [K] uc = combined uncertainty Greek Symbols
β(T) = absorptivity ΔH = change in enthalpy [kJ·g−1] Δm = mass of the reactive portion of the sample, mass loss [g] Δt = change in time [s] ΔT = change in temperature [K] ε(Tr,λ) = emissivity of copper oxide κg(Tg) = gas thermal conductivity [W·m−1·K−1] λ = laser wavelength [m] σ = Stefan−Boltzmann constant (5.670373 × 10−8 W·m−2· K−4) τ(T) = temperature-dependent relaxation time [s] Subscripts
r = reactor sas = sample and substrate so = substrate only
■
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