Fuel pyrolysis in a microflow tube reactor–Measurement and modeling uncertainties of ethane, n-butane, and n-dodecane pyrolysis

Combustion and Flame 177 (2017) 10–23

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Fuel pyrolysis in a microflow tube reactor–Measurement and modeling uncertainties of ethane, n-butane, and n-dodecane pyrolysis U. Shrestha1, M.J. Rahimi1, G.P. Simms, H.K. Chelliah∗ Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA

a r t i c l e

i n f o

Article history: Received 17 May 2016 Revised 18 November 2016 Accepted 21 November 2016

Keywords: Microflow tube reactor Ethane n-Butane n-Dodecane Pyrolysis Uncertainty analysis

a b s t r a c t A scaled down flow reactor consisting of 4 mm ID quartz tubing and rapid mixing of fuel with a preheated thermal carrier bath was developed to investigate the pyrolysis of both gaseous and pre-vaporized liquid fuels. Starting from a small mixing volume (less than 0.2 cm3 ), the temperature of the hot section (37 cm long) was controlled within ± 5 K. All species concentrations were measured at the exit plane of the reactor using a GC system while residence time variations were explored by varying the bulk flow velocity. For the atmospheric pressure cases reported here, the temperature and flow residence times explored were in the kinetically controlled regime and ranged from 10 0 0 to 110 0 K and 10–90 ms, respectively. The thermal pyrolysis of fuels investigated included ethane, n-butane, and n-dodecane, all diluted in a nitrogen carrier bath of 98% or higher (to minimize temperature departure from the target value). Because the ratio of the mixing volume compared to the kinetically controlled reactor volume is about 2.5%, the associated finite mixing time is shown to have a negligible effect on the temporal evolution of key C0 –C4 species. As a consequence, no species profiles shifting (zero-time shifting) was required in comparisons with model predictions. Experimental and modeling uncertainty analysis are presented to determine whether the experimental data can be used in future efforts aimed at minimization of chemical kinetic model parameter uncertainties. © 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The importance of hierarchical H2 and C1 –C4 models in predicting large hydrocarbon fuel pyrolysis and oxidation is well recognized [1–4]. Starting from the GRI model for C1 kinetics [5], considerable effort has been devoted to the development of accurate models for relevant C0 –C4 species. Supporting experimental data to advance model optimization and validation have included investigations of shock tubes, stirred reactors, flow reactors, and various types of flames (see Refs. [6–9] for comprehensive reviews). In minimization of uncertainties associated with the predictive models, it is crucial to understand the limitations of each type of experiment used in the analysis, including the small diameter tubular flow reactor as considered here. Flow reactors employed in chemical kinetic pathway analysis can be categorized into two main types, (i) small diameter laminar flow reactors (typically less than 10–mm) where a premixed flow of fuel/oxidizer/inert is rapidly heated to a target temperature, followed by a constant temperature hot section with a nom∗

1

Corresponding author. E-mail address: [email protected] (H.K. Chelliah). Contributed equally.

inal residence time [10–20] (see Fig. 1) or (ii) large diameter turbulent flow reactors (typically greater than 10 cm) where a fuel stream is rapidly mixed with a preheated flow of inert/oxidizer in a diffuser, followed by a constant temperature hot section with the residence time determined by the probing location (see Fig. 2) [9,21–25]. As indicated, in type (i) reactors, the species are probed at the exit plane of the reactor while type (ii) reactors with large diameters allow species probing inside the reactor. To limit temperature variations due to exothermicity or endothermicity of chemical reactions, the reactant mole fractions are typically kept low in both types of reactors (≤ 2%). Two key uncertainties that arise in the analysis of flow reactor data are associated with axial and radial variation of species and temperature, especially in small diameter laminar flow reactors. In large diameter flow reactors, such spatial variations of thermal and mass transport effects are eliminated with high dilution and turbulent mixing, however significant uncertainties arise due to the large mixing region. Often species profile shifting (or zero-time shifting) is used in comparisons between measured and predicted species data [9]. By employing a first-order fuel pyrolysis model (c = c0 exp(−k t )), the effects of mass and thermal transport in small diameter tubular laminar flow reactors have been extensively investigated since the 1950s [10–12,26,27]. In particular, Cutler

http://dx.doi.org/10.1016/j.combustflame.2016.11.019 0010-2180/© 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

U. Shrestha et al. / Combustion and Flame 177 (2017) 10–23

Fig. 1. Illustration of typical temperature and fuel decomposition profiles of a small diameter laminar flow reactor with premixed fuel/inert flow, as a function of (a) imposed bulk flow velocity and (b) target temperature variations.

Fig. 2. Illustration of typical temperature and fuel decomposition profiles of a large diameter turbulent flow reactor with separate introduction of inert and fuel.

et al. [12] have critically evaluated the validity of negligible axial diffusion, Poiseuille flow, and temperature non-uniformity on the basis of characteristic time scales associated with forced convection, species diffusion (axial and radial), thermal diffusion, momentum transport, and first-order chemistry. The species axial diffusion also included the Taylor–Aris dispersion effects [28,29]. As summarized by Cutler et al. [12], the criteria of validity for negligible axial species diffusion and temperature non-uniformity are 2 given by τcon v,R / (τsp−di f f,R τchem ) << 0.1 and τth−di f f /τconv,L << 3.7, respectively, and are generally satisfied in highly diluted reactor experiments (see Table A.1 in the Appendix for definition of characteristic time scales, non-dimensional parameters, and relevant quantitative values corresponding to the small diameter reactor implemented). On the other hand, for a reactor with an ideal operating condition of τ chem ≈ τ conv, L , the criterion for negligible species stratification due to Poiseuille flow is given by τsp−di f f,R /τconv,L ≡ τsp−di f f,R /τchem < 1.0) [12]. Note: in terms of Peclet number for mass transport (Pesp−di f f ), this relationship can be written as Pesp−di f f ∗ R < L (see the Appendix). For high conversion rates, i.e. non-ideal operating conditions, the flow field may lead to local species inhomogeneity effects even though the Pesp−di f f ∗ R < L condition is marginally satisfied. Furthermore, at high conversion, the assumption of first-order kinetics may not hold, requiring a comprehensive 2D analysis with multi-step chemistry. Thus, careful attention is needed before imposing the plug flow assumption in modeling small diameter laminar flow reactors.

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Generalization of the flow reactor analysis to include detailed chemistry with a distribution of chemical kinetic time scales was first explored by Westbrook et al. [30] with numerical integration of coupled species conservation equations assuming plug flow condition. More recently, Lee et al. [31] generalized the analysis to include radial species stratification effects by considering a 2D axisymmetric laminar flow with varying Re and Pe numbers. Their main conclusion was that for the moist CO oxidation case investigated, the dominant CO + OH = CO2 + H reaction with differential species diffusion coefficients can lead to departure from plug flow assumption depending on the selection of Re and Pe numbers. For an intermediate diameter flow reactor with an ID of 3 cm, Roesler and co-workers [32,33] explored a simplified approach of including the flow stratification in their analysis, with comparison to plug flow reactor modeling. The influence of radial stratifications, especially at high pressure conditions, on the axial dispersion of species were analyzed by Rasmussen et al. [18] in the context of Taylor– Aris dispersion formulation. For large Pe numbers for species such as those found in present flow reactor operating conditions, the axial dispersion is found to be negligible in comparison to molecular diffusion. Due to the exponential dependance of rate constants on temperature, and therefore its dominant effects on chemistry, a small diameter tubular flow reactor was developed without the temperature ramp-up effects as shown in Fig. 1. This reactor is identified here as a microflow tube reactor (MFTR) – a term coined by Li et al. [15] based on 105 lower flow rate compared to large diameter Princeton Turbulent Flow Reactor (PTFR). The flow configuration adopted here is a hybrid of the two flow configurations shown in Figs. 1 and 2, with rapid mixing of partially preheated fuel and the inert stream heated to the target temperature (see experimental section for further details). A key feature is that, for fuels and flow conditions investigated here, the small mixing volume has eliminated any need for zero-time shifting. Thermal pyrolysis of ethane and n-butane were selected in this initial investigation because of their importance to C1 –C4 kinetic model development efforts and their relatively well known kinetic parameters [34–49]. Experiments were also performed with pre-vaporized n-dodecane to highlight the versatility of the MFTR developed in exploring the pyrolysis of large hydrocarbon fuel molecules, with comparisons to chemical kinetic models available [34,35,50,51]. Temperature and residence times were selected such that the data represent kinetically controlled regimes, i.e. τ conv, L ≈ τ chem . Two dimensional effects due to fully developed parabolic flow were analyzed computationally using an implementation of OpenFOAM reacting flow code [52,53]. Detailed uncertainty analyses of experiments and chemical kinetic model parameters show that the present ethane pyrolysis data are well within the model bound-to-bound uncertainties while those for n-butane show considerable room for improvement.

2. Experimental methodology 2.1. Microflow tube reactor The quartz tube reactor (4 mm ID) as illustrated in Fig. 3 is heated using six modular heaters placed inside a steel pressure chamber (hydro tested up to 100 atm – see Fig. 4). The main diluent flow is preheated to the target temperature in a 125 cm long helical section. The fuel under investigation is introduced via two side tubes of 1 mm ID immediately downstream of the helical section as shown in Fig. 4. A porous quartz frit placed immediately downstream of the junction between the side tubes and the main diluent flow with a mixing volume of less than 0.2 cm3 facilitates rapid mixing, which has been verified by measurement of species

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U. Shrestha et al. / Combustion and Flame 177 (2017) 10–23 Table 1 Temperature estimated from experimentally measured decomposition rate of cyclohexene at 950 K and 1 atm, for a range of flow reactor residence times. Temperatures reported correspond to rate parameters reported by Uchiyama et al. [54], Stranic et al. [57] and Tsang and Rosado-Reyes [59]. Residence time (ms)

Measured rate (s{−1} )

TUchiyama (K)

TStranic (K)

TTsang (K)

29.5 39.3 48.7 59.2

0.7693 0.7266 0.832 1.0737

945.6 944.0 947.7 954.6

936.2 934.6 938.3 945.4

951.9 950.3 954.0 961.1

Fig. 3. Illustration of key features of scaled down flow reactor with small mixing volume to eliminate temperature ramp-up effects.

Fig. 4. Illustration of the microflow tube reactor showing modular heating sections, helical preheat section, fuel addition via side feed tubes, and probing at the exit plane. 1 – fuel gas cylinder, 2 – nitrogen gas cylinder; 3 – nitrogen mass flow controllers; 4 – Fuel mass flow controller, 5 – PID controller; 6 – thermocouples; 7 – helical heating coil; 8 – heating elements; 9 – side tubes; 10 – porous quartz frit; 11 – atomizer; 12 – pre-vaporization chamber; 13 – liquid syringe pump; 14 – fuel reservoir; 15 – vented high-pressure enclosure (hydro-tested up to 100 atm); 16 – quartz probe; 17 – valve; 18 – dry ice bath; 19 – GC system ; 20 – pressure gauges; 21 – vacuum pump.

mole fraction radially on a plane just downstream of the frit (prior to fusing the hot section). The hot section (from the frit to the tube exit plane) is 37 cm long and is placed inside a combination of 5 and 10 cm long semicylindrical heating elements from ThermCraft (Model RH212), with a maximum temperature limit of 1573 K. Six PID controllers connected via K-type thermocouples were used to maintain the hot section at the target temperature. Because of the small size and modular nature of the reactor, the hotsection ID and length can be varied if needed. In supporting heater calibration experiments, the temperature inside and outside of the tube were measured under typical flow velocities and showed a difference of less than 5 K with inert gas flow. Endothermic pyrolysis of 2% ethane in nitrogen showed a small drop in temperature (≤ 5 K) compared to the inert case, while exothermic oxidation conditions showed a similarly slight increase in temperature. The variation in temperature due to endothermicity/exothermicity can be minimized by further dilution of the fuel. For example, pre-vaporized n-dodecane was diluted to 0.25% in nitrogen to minimize any temperature departures from target values.

A key challenge in introducing pre-vaporized fuels such as ndodecane is the low fuel flow rates of the order of 20–50 μl/min in a 99.75% inert carrier bath. A liquid syringe pump (Teledyne ISCO Model 500D) with flow and pressure capabilities of 0.001– 204 ml/min and 10–3750 psi, respectively, was used for fuel delivery. As illustrated in Fig. 4, an ultrasonic atomizer generating a fine mist of droplets of the order 10–15 μm mixed with nitrogen carrier gas preheated to 500 K was used to deliver the fuel through the side tubes. A series of mass flow controllers (Sierra 100 series, with 1% accuracy at full scale) were used for all gaseous flows. The typical temperature profile obtained inside the reactor is shown in Fig. 5a with a target wall temperature of 1100 K in the hot section. Because the last 2 cm of the reactor is not heated and is open to the atmosphere, a temperature drop of about 100–150 K is observed near the exit (see Fig. 5). All the other interior temperature measurement points show nearly constant temperature (within ± 5 K), for a range of target wall temperatures and mass flow rates. Numerical simulations with the observed temperature drop in last 2 cm has revealed negligible effects (less than 4%) on the measured species data, as discussed in the results section. As an additional verification of temperature measurement by thermocouples, a reference reaction with a known rate constant was used to estimate the temperature, i.e. a concept known as the chemical thermometer [54–59]. Here, cyclohexene pyrolysis to ethylene and 1,3 butadiene was used as the reference unimolecular reaction with rate constants inferred from shock tube experiments (see supplementary notes for further details). While varying estimates of inferred temperature uncertainties have been reported, for example 20 K [58], the recent work by Tsang and Rosado-Reyes [59] suggested that these uncertainties may be due to ancillary reactions associated with contaminants in the system. By inhibiting the ancillary reactions, they have suggest that the chemical thermometer concept can yield an accuracy of 7 K at 10 0 0 K and have proposed a revised rate constant. Using a mixture of 0.23% cyclohexene and 99.77% nitrogen in the flow reactor and for a hotsection temperature of 950 K, Table 1 shows the inferred temperature from measured ethylene or 1,3 butadiene (see the supplementary notes for further details). The new nominal rate constants proposed by Tsang and Rosado-Reyes [59] agrees closely with the target temperature of the reactor (within 11 K), which is very encouraging, while older models result in an estimated temperature departure of approximately 15 K. Ideally, the inferred temperature should be independent of the residence time of the reactor for the target temperature of 950 K, however, present results show a minor variation about 10 K for residence time variation from 30 to 60 ms. Such variations can be associated with radial stratification effects in the reactor or breakdown of the unimolecular reaction assumption of cyclohexene. Note: models reported by Kiefer and Shah [55] and Tranter et al. [56] resulted in much larger errors as the rate constants were inferred from shock tube experimental data performed at very high pressures and are not listed in the Table 1.

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Fig. 5. Measured temperature inside the tube for set wall temperature, (a) for a target wall temperature of 1100 k at different flow rates corresponding 10–100 ms residence time and (b) for 10 ms residence time with varying wall temperature from 950–1100 K.

2.2. Residence time variation In experiments, the residence time can be varied by two methods: (i) by changing the bulk inflow velocity or (ii) by changing the distance between the reactants injection point and the sampling probe location. In the case of small diameter flow reactors without the ability to probe inside the reactor, the latter approach requires changing the length of the hot section of the reactor, which can be expensive. Thus, in this work, the residence time was defined as tres = x/v plug , where vplug is the cross sectional average flow velocity, and was varied by changing plug-flow velocity. For a given reactor length, the hotsection temperature and flow residence time must be selected such that the species exiting the reactor are in the kinetically controlled regime. To determine whether a laminar flow field with mixture stratification could affect the data, an axisymmetric 2D computational experiment was performed (see Section 3 for modeling details). In the first computational experiment, the inflow velocity was kept constant at 4 m/s and allowed to develop to full parabolic flow profile and the species concentrations were extracted at different axial locations (corresponding to varying probe locations as in a large diameter flow reactor experiment). In the second computational experiment, the reactor length was kept constant at 40 cm and the inflow velocity was varied to yield overall residence times of 10, 40, 60, 80, and 100 ms, respectively. The latter experiment is similar to the present experimental sampling approach. Figure 6 shows a comparison of the two 2D computational experiment for ethane pyrolysis at 1100 K and 1 atm, showing negligible effects associated with flow stratifications for residence times down to 10 ms. As indicated in Table A.1 for flow residence times below 27 ms, the criterion for negligible stratification effects, τsp−di f f,R /τconv,L < 1.0, is violated and in theory should lead to slight departure from the ideal solution. However, present 2D computations with detailed chemistry, molecular transport, and fully developed parabolic flow field does not indicate a noticeable influence on species evolution. Perhaps this is due to the broad range of chemical and transport time scales associated with the system at highly diluted and constant temperature conditions. Further investigations are needed to understand under what flow conditions the stratification effects play role and is beyond the scope of the present work. 2.3. Species probing and GC analysis In the present study, ethane (99.95% from Matheson), n-butane (99.9% from Matheson), and n-dodecane (anhydrous with ≥ 99% from Sigma Aldrich) pyrolysis investigations were performed at atmospheric pressure. To ensure that the temperature variation is minimal along the tube, the ethane and n-butane were mixed with 98% nitrogen (99.995% from GTS Welco), while pre-vaporized n-

Fig. 6. 2D computational experiment on residence time variation using two methods, (i) probe location variation with fixed bulk flow velocity of 4 m/s (solid line) and (ii) bulk flow velocity variation with fixed reactor length (symbols). Both cases are with 2% ethane in nitrogen at 1100 K and 1 atm.

dodecane was mixed with 99.75% nitrogen. The combustion products exiting the reactor were continuously extracted using a 75 μm quartz microprobe and analyzed via Shimadzu GC (model 2014) systems as described below. The 75 μm probe diameter was selected such that the pressure before and after the GC sample loop is the same – for example, for larger probe tips with higher mass flow rates can result in a significant pressure differential across the GC sample loop leading to species calibration uncertainties. The columns of GC-2014 and the GC temperature profile was custom designed to analyze O2 , N2 , H2 , CO, CO2 and light hydrocarbons C1 –C4 species in about 20 min. The system was equipped with two sets of sampling lines, with each line consisting of its own valves, a sample loop, and detectors. Line 1, consisting of a 10-port and a 6-port valves, and a combination of Hayesep-N and -T, MolSieve-5A, Propak-N, and QS-BOND columns, is used to separate and quantify O2 , N2 , CO, CO2 , C1 –C4 species via two detectors depending on the concentration of the species, i.e. TCD and methanizer/FID. In particular, Propak-N and QS-BOND columns allow separation of C2 species, while Haysep-T column allows separation of propane and propylene. As discussed in the results section, not all C4 species can be cleanly separated by the above column selection. Line 2, with a 10-port valve, Hayesep-Q, and Molsieve-5A columns, is used to quantify H2 via a second TCD. The above two-line, multiport gas sampling valves system allows switching the samples between the different columns based on

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the retention time, thereby minimizing the analysis period. For large hydrocarbon fuel pyrolysis experiments with significant > C4 species yields, including formation of PAH molecules, the continuously sampled probed volume was sent through a dry ice/ethanol bath held at 195 K to separate the light and heavy components. Although a GC–MS system with dual columns was available for quantification of larger species (C5 and higher), they are not reported here due to numerous technical issues with the MS. In order to verify that most of the product species are quantified accurately, carbon balance investigations were performed in ethane and n-butane pyrolysis experiments. This analysis was performed by sending 10 ppth of ultra-high purity argon from Praxiar (99.999% purity) as an internal standard. Argon was calibrated using mass flow controllers before the actual data collection and was analyzed in TCD. The resulting carbon balance for ethane pyrolysis at T=1100 K and τ res =90 ms was 99.45% and for n-butane pyrolysis at T=1100 K and τ res =70 ms was 92.37%. These values are well within the experimental uncertainty of species measurements in ethane pyrolysis and same order in n-butane pyrolysis (see Table SPM.1). The lower carbon balance for n-butane pyrolysis may be attributed to the formation of larger molecules (larger than C5 ) and will be explored in the future using the GC-MS system available. Furthermore, the measured carbon to hydrogen ratio of products at the reactor exit for ethane and n-butane were 0.33 and 0.394, respectively, compared to inflow values of 0.33 and 0.4, providing another verification of species analysis and uncertainties. Carbon balance analysis for n-dodecane pyrolysis are yet to be quantified due to technical difficulties associated with MS available as discussed in experimental methods section. It should be pointed out that, irrespective of less than perfect carbon balance, the mole fractions reported for all the cases (including n-dodecane pyrolysis) are minimally influenced due to overwhelming nitrogen concentration in the GC sample volume. 3. Flow reactor modeling Three reacting flow modeling approaches were considered in analyzing the hot section of the reactor. These include standard zero-dimensional simulations (using Sandia Senkin code [60]) with transformation of time coordinate to distance based on flow velocity (i.e. reacting fluid elements are advected without mixing, a reasonable assumption under highly diluted conditions), onedimensional simulations with plug flow velocity (using Sandia Premixed code [61] by assuming no radial gradients). In addition, full two-dimensional axisymmetric reacting flow simulations were conducted with both axial and radial dependence as described below. 3.1. Two-dimensional Poiseuille flow simulations To understand the coupled radial and axial transport effects of the main flow in the hot section of the reactor, the multidimensional governing equations for conservation of mass, momentum, species, and energy were integrated numerically. Because of the computational cost associated with a large number of transported species, only appropriate skeletal reaction models with species diffusion velocities estimated using the mixture-averaged formulation were employed. Taylor–Aris dispersion formulation was implemented as discussed in the introduction section to assess the significance of added dispersion due to the fully developed parabolic flow profile. An open-source computational fluid dynamics package, OpenFOAM [52], subjected to inflow and outflow boundary conditions, including specified wall heat transfer boundary conditions was used to integrate the governing equations. The conservation equations were solved in a segregated manner using second-order

accurate total variation diminishing (TVD) Van-Leer schemes. The finite volume equations were integrated in time using the first-order implicit, Eulerian method. Each equation was solved by iterating until the L2-norm of the residual to all equations was below 10−9 . Simulations were run for a specific number of time integrations until steady state was reached and confirmed by monitoring solution residuals [53]. 3.2. Chemical kinetic models and uncertainty factors/bounds Several chemical kinetic models reported in the literature were employed to evaluate the experimental speciation data generated from the present MFTR for ethane, n-butane, and n-dodecane pyrolysis. The models considered included: (i) for ethane pyrolysis – Wang et al. (JetSurf 2.0 [35]) with 348 species in 2163 reactions, Naik and Dean [40] with 181 species in 2066 reactions, and Curran and co-workers (AramcoMech 2.0 [36]) with 493 species in 2716 reactions; (ii) for n-butane pyrolysis – JetSurf 2.0, AramcoMech 2.0, plus modified JetsSurf 2.0 by Pyun et al. [49]; and (iii) for n-dodecane pyrolysis – JetSurf 2.0, Banerjee et al. [51] with 196 species in 1478 reactions, Ranzi et al. (CRECK [34]) with 451 species in 17,848 reactions, and Dagaut and co-workers (CNRS [50]) with 1377 species in 6014 reactions. While the predictive capabilities of chemical kinetic models continue to advance due to new experimental data and advanced computational chemistry methods, all model parameters inherently have some known and unknown uncertainties. To assess the chemical kinetic model parameter uncertainties on predicted results in comparison to experimental uncertainties, the bound-to-bound uncertainties [62] were evaluated based on propagated uncertainties of the kinetic model parameters via Monte Carlo (MC) simulations. The present brute force MC calculations were performed by randomly sampling of the parameter space (assuming uniform probability) using quasi-random Sobol sequences [63], which typically achieve excellent convergence with 2N p sampled simulations. Here, Np is the number parameters perturbed in MC simulations. As the number parameters increase, the computational cost can become prohibitively expensive. Thus, only a subset of selected reaction parameters, namely the top 15 reactions based on local sensitivity analysis, were perturbed within parameter uncertainty bounds estimated from the uncertainty factors compiled by Sheen et al. [64] (see Supplementary materials (SPM)). The resulting extreme limits of species mole fractions (from 215 simulations with each simulation having a random selection 15 perturbed rate parameters) is identified here as the bound-to-bound uncertainty and are shown as shaded areas in Figs. 11 and 14 for ethane and n-butane pyrolysis, respectively. While the zero-dimensional and one-dimensional plug-flow equations can be readily integrated with large chemical kinetic models, the multi-dimensional reacting flow simulations with accurate resolution of chemical time scales can become prohibitively expensive. For the purpose of understanding the flow stratification effects, the present 2D simulations were performed with simplified chemical kinetic models, namely skeletal reaction models. A previously developed chemical kinetic model reduction strategy based on principal component analysis with sensitivity (PCAS) of target properties [65] was used to extract required skeletal models for ethane, n-butane, and n-dodecane pyrolysis. For example, for ethane pyrolysis a 29 species skeletal reaction model was extracted from JetSurF 2.0 model [35] for the present multidimensional reacting flow simulations described in the results section. 4. Results and discussion As discussed in the introduction, the purpose of the present flow reactor analysis is to consider pyrolysis of several fuels for

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Fig. 7. Endothermic effects of ethane pyrolysis on (a) temperature and (b) ethane mole fraction, for 2% ethane in nitrogen. (i) dashed-dot line – zero-dimensional model with constant enthalpy and initial temperature of 1100 K, (ii) dashed line – one-dimensional plug-flow model with constant temperature of 1100 K , and (iii) solid line – two-dimensional axi-symmetric model with constant wall temperature of 1100 K.

which reasonably well established kinetic models are available, such as ethane, n-butane, and n-dodecane. The speciation data collected together with detailed model analysis is expected to provide better understanding on (i) any need for zero time shifting, (ii) the ability to control temperature and flow residence time, (iii) effects of radial stratification, (iv) effects of species probing and quantification approach, and (v) effects of higher surface area to volume in small diameter reactors. The fuels considered here offered distinct advantages and challenges. For example, due to the low vapor pressure of n-butane, it was at the verge of condensing at room temperature for a fuel feed line pressure of 20–30 psig, which required maintaining the fuel vapor feed lines at elevated temperatures. On the other hand, n-dodecane clearly required prevaporization, which was especially challenging because of the very small flow rates (20–50 μl/min) associated with the scaled down flow reactor. Thus, the experimental uncertainties reported here for fuels have varying contributing factors not common to the flow reactor itself, with gaseous ethane data offering the lowest experimental uncertainty. 4.1. Selection of fuel/inert composition and reacting flow model assumptions The maximum mole fraction of fuel that can be delivered through the reactor without introducing significant temperature change due to endothermic pyrolysis was established by performing numerical analysis. Here, the governing equations were integrated assuming: (i) zero-dimensional constant temperature (the ideal case for chemical kinetic model analysis with no mass transfer across the advected reacting fluid element boundary), (ii) zerodimensional constant enthalpy case (adiabatic) with significant temperature drop, (iii) one-dimensional constant temperature case (identical to zero-dimensional constant temperature case due to high dilution and negligible axial diffusion), and (iv) axisymmetric two-dimensional case with constant wall temperature (most realistic case if radial stratification is important). For 2% ethane in nitrogen at 1100 K with a flow residence time of 100 ms, Fig. 7 shows the predicted temperature and ethane mole fraction as a function of the axial distance along the hot section. The 0D constant temperature case (item (i) above) is not shown here as it is identically equal to the 1D constant temperature case. The most realistic 2D axisymmetric laminar flow case shows that the maximum temperature departure from the target value of 1100 K is less than 5 K. Furthermore, the ethane decomposition plot (see Fig. 7(b)) shows that the difference between full 2D axisymmetric case and 1D con-

stant temperature (or 0D constant temperature) are well below the 2σ experimental measurement uncertainty of 8–10% (see Table SPM.1 in supplementary materials). These results are consistent with criterion for negligible radial species variations in a Poissuille flow, given by τsp−di f f,R /τconv,L = 0.27 < 1.0, for a flow residence time of 100 ms (see Table A.1 in the Appendix for relevant values). Additional comparisons of species yield predicted by 2D axisymmetric and 1D constant temperature approximations are shown in Fig. 8. This supports the idea that for highly diluted flows, if the condition τsp−di f f,R /τconv,L < 1.0 is satisfied then either 1D or 0D simulations with constant temperature approximation can predict the species evolution in small scale tubular flow reactors. Furthermore, if ethane mole fraction is halved from 2% to 1%, then the observed differences become even more negligible. For n-dodecane, a similar level of accuracy between 1D constant temperature and 0D constant enthalpy is retained by reducing the inflow fuel mole fraction to 0.25%. In present experiments, as shown in Fig. 5, the temperature is nearly constant in about 95% of the hot section, with drop in temperature near the exit. As the flow velocity is increased to explore short residence times, owing to the momentum of the flow, the temperature drop at the exit in fact becomes negligible. Instead of using constant temperature approximation, 1D calculations were also performed with the temperature profile that includes such temperature departure at the exit of the reactor (note: a heat transfer model constructed based on experimentally measured temperature data was used to generate the temperature profile for the simulations). The results indicated that, for residence times and temperatures explored, namely 10–90 ms and 10 0 0– 1100 K, the observed exit temperature variation had less than 4% effect on the species mole fractions exiting the reactor and well within the experimental species measurements uncertainties reported in Table SPM.1. Thus, in the remainder of this paper, all flow modeling is performed by temporal integration of 0D governing equations assuming constant temperature, which is the ideal situation for investigations on chemical kinetic model performance and associated uncertainties, a key objective of present experimental design. 4.2. Ethane pyrolysis – dependance on residence time and temperature Based on the above flow reactor analysis, the hotsection temperatures and residence times were selected that generated species data in kinetically controlled regimes. The maximum temperature

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Fig. 8. Several predicted C0 –C2 species yield from ethane pyrolsis, for 2% ethane in nitrogen at 1 atm and 100 ms residence time: (i) dashed line – one-dimensional plug-flow model with constant temperature of 1100 K , and (ii) solid line – two-dimensional model with constant wall temperature of 1100 K.

Fig. 9. Comparison of (a) ethylene and (b) acetylene mole fractions (normalized by initial ethane mole fraction) vs. ethane conversion level, from present flow reactor  experiments ranging from 10 0 0–110 0 K and 10–90 ms (), shock tube data from Tranter et al. [41] at 340 bar (+) and at 10 0 0 bar ( ), and Hidaka et al. [37] at 50 Torr (). Also shown are the normalized computed (a) ethylene and (b) acetylene mole fractions at iso-conversion levels of ethane, for several flow reactor temperatures and residence times considered here.

explored was limited to 1100 K with a maximum ethane conversion of about 40% in 90 ms. For temperatures above 1100 K, the characteristic chemical reaction layer length can become smaller than the physical length of the reactor, leading to non-ideal reactor operating conditions. Irrespective of this upper temperature limit of 1100 K, the present ethane pyrolysis results can be compared with shock tube data reported in the literature for temperatures as high as 1450 K and much shorter residence times by considering iso-conversion levels as shown in Fig. 9. In particular, ethylene data from ethane pyrolysis is seen to be minimally affected by the temperature/residence time combinations at iso-conversion levels, similar to previous findings by Dente et al. [66]. This insensitivity of ethylene yield to initial conditions is verified by using JetSurf kinetic model [35] predictions for several flow reactor temperatures and residence times (see Fig. 9(a)). Since the shock tube speciation data are not influenced by mixing effects, the reasonable comparison between flow reactor and shock tube data suggests that the mixing effects in the present microflow tube reactor is indeed negligible. Figure 9(b) shows a similar comparison of acetylene yield during ethane conversion. Unlike ethylene, the model predicts that the acetylene yield is sensitive to combined effects of temperature and residence time, consistent with the experimental data from flow reactors and shock tubes with varying temperatures and residence times. This implies that, in general, any comparison of

species yields at iso-conversion levels must be performed at similar temperatures and residence times, while differences in initial reactant concentrations can be normalized (at least at low conversion levels) as shown in Fig. 9. With above excellent comparison of ethylene yields during ethane pyrolysis with shock tube data, Fig. 10 shows a comparison of the the present experimental ethane conversion data with several kinetic models available in the literature, namely JetSurf 2.0 chemical kinetic model by Wang et al. [35], an optimized model for ethane pyrolysis proposed by Naik and Dean [40], and a recent model developed by Curran and co-workers (identified as AramcoMech 2.0 [36]). The results show a reasonable agreement among the ethane conversion trends. Next, for a hot section temperature of 1100 K, Fig. 11 shows the residence time effect on species evolution during ethane pyrolysis. As described in Section 2.2, the residence time variation in experiments was achieved by varying the bulk flow velocity (Note: no zero-time shifting was applied to experimental or predicted data). The three chemical kinetic models implemented show reasonably good agreement on predicted temporal yields of major species, i.e. ethylene, hydrogen, methane, and acetylene, however, significant differences are observed for propene and propane. Recognizing that the current chemical kinetic model parameters are associated with inherent uncertainties due to experimental data used, Fig. 11 also includes the bound-to-bound uncertainty of

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Fig. 10. Ethane conversion as a function temperature, from experiments (symbols) and numerical predictions (lines), for inflow species compositions of XC2 H6 = 0.02, XN2 =0.98, p=1 atm and residence time of 90 ms.

kinetic model parameters (shaded area) based on Monte Carlo calculations by perturbing the top 15 sensitive reactions of the Wang et al. model [35] (see Table SPM.3 Supplementary materials for the list of reactions included in MC analysis). The uncertainty factors were adopted from Sheen et al. [64], with the assumption of uniform probability and implementation of Sobol sampling sequence [67]. Two important conclusions can be drawn from above data, i.e. (i) the present MFTR with less than 0.2 cm3 mixing volume between the quartz-frit and the side fuel injection eliminates any need for applying zero-time shifting and (ii) the lower experimental uncertainty (2σ ) compared to the bound-to-bound model uncertainty implies that the present data can be used to minimize the uncertainty factors of key rate controlling reactions (Note: measured ethane mole fractions indicate a larger uncertainty, ∼ 16%, due to the flow controllers used in generating the calibration gases and 10% uncertainty of ethane standards used - see supplementary materials for further details). Simulations that treat the small mixing volume as a perfectly stirred reactor (PSR), followed by PFR calculations as suggested by Schmidt and Bowman [24] showed no influence on the predicted ethane conversion and species yields, confirming the negligible effects of small mixing volume on major C0 –C4 species of interest in this study. To address any catalytic effects due to quartz surfaces, experiments were also conducted by inserting three 1mm diameter quartz rods of 35 cm length to double the surface area to volume ratio in the hot section of the reactor. For the same flow residence time (taking into account the displaced volume), the measured species data has shown that the differences with and without quartz rods are negligible and are well within the GC measurement uncertainty (see Fig. SPM.1 in Supplementary materials). While ethane pyrolysis predictions with the three chemical kinetic models adopted are within the uncertainty bounds predicted by MC calculations (except for minor species propene and propyne), the excellent agreement of species data gathered with the recently proposed chemical kinetic model by Curran and co-workers (AramcoMech 2.0) [36] is very encouraging. In typical small diameter flow reactor investigations as illustrated in Fig. 1, due to the long temperature ramp-up and rampdown, species yields are typically reported as a function of the hotsection temperature for a nominal flow residence time. While the major focus of this investigation was to explore residence time ef-

Fig. 11. Comparison of species mole fractions in ethane pyrolysis as a function of time, for hot section temperature of 1100 K (experiments (symbols) and predictions (lines)) with models by Wang et al. [35], Naik and Dean [40], and AramcoMech2 [36]. Inflow conditions are XC2 H6 = 0.02, XN2 =0.98 and p=1 atm.

fects, Fig. 12 shows species yield from ethane pyrolysis as a function of temperature, for p=1 atm and at 90 ms. The reaction pathway analyses have highlighted the dominant reactions controlling the ethane pyrolysis for range of residence times up to 100 ms. At peak ethane pyrolysis conditions, the dominant path is the hydrogen abstraction leading to the formation of ethyl radical, followed by the three-body collision reactions forming ethylene (see Fig. SPM. 6 in Supplementary materials). In addition, ethane reaction with methyl contributes to about 1% of ethane destruction at 50 ms and explains the somewhat delayed methane formation by this reaction or large ethylene to methane ratio at low residence times. The reaction pathway analysis for the residence time of 100 ms and 1100 K temperature indicates that 1,3 butadiene leads to formation of allene and propyne and are consistent with the experimental results shown in Figs. 11 and 12. It is well known that stable C3 H4 isomers (allene and propyne)

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ing), with an order of magnitude difference between the rates of Wang et al. [35] and Naik and Dean [40] as seen in Fig. 13(a). The AramcoMech2.0 model [36] with rate parameters for reaction C2 H4 +H(+M) ⇒ C2 H5 (+M) in between the other two models is seen to predict the ethane decomposition in close agreement with present experimental data. Similarly, one can analyze for example the reactions contributing to the differences observed in Fig. 11 in predicting propene formation. The corresponding sensitivity analysis has shown that the reaction CH3 +CH3 (+M) = C2 H6 (+M) has the highest sensitivity for propene (see Fig. SPM.2(b)) and hence the AramcoMech2.0 model [36] with highest rate constant for this reaction (see Fig. 13(b)) yields propene concentration in close agreement with present experimental data. While a combination of reaction uncertainty, sensitivity, and flux analysis as described above can reveal key differences of proposed chemical kinetic models, the focus of the present work is to report well-controlled experimental speciation data. The experimental data and the limited modeling data will be freely available to anyone interested in further analysis. 4.3. n-Butane pyrolysis – dependance on temperature and residence time

Fig. 12. Comparison of species mole fractions in ethane pyrolysis as a function of temperature, for residence time of 90 ms (experiments (symbols) and predictions (lines)) with models by Wang et al. [35], Naik and Dean [40], and AramcoMech 2.0 [36]. Inflow species compositions are XC2 H6 = 0.02, XN2 =0.98 and p=1 atm.

play an important role in soot formation pathways [68,69], especially via C3 H3 radical chemistry [70,71]. In more recent work [72], both C3 H3 and C3 H4 isomers have been quantified in laminar premixed propanol–air flames using molecular beam mass spectrometry, including an extensive list of stable and radical species that leads to formation of PAH molecules. The objective here is to construct a similar set of species using the present flow reactor for fuel pyrolysis investigations and subsequent chemical model development work. As seen from Fig. 11, the three models adopted show significant variation (within the uncertainty bounds) in predicting many of the species reported. While the rate of most sensitive reaction (C2 H6 + H = C2 H5 + H2 ) is found to be nearly identical for all three models, the key underlying differences in predicting C2 H6 and C2 H4 can be attributed to the second most sensitive reaction C2 H4 + H(+M) = C2 H5 (+M) (see Fig. SPM.2(a) for sensitivity list-

The finite-rate kinetics of n-butane has also been extensively investigated as it is one of the simplest hydrocarbon molecules that exhibit higher-order hydrocarbon combustion characteristics, namely the negative-temperature coefficient, two-stage ignition, and low temperature pyrolysis. Consequently, several detailed chemical kinetic models have been developed on the basis of shock-tubes, rapid compression machines, jet-stirred reactors, flow reactors, and flame experiments (see for example [42–46,48]). In this work, three recently proposed models for n-butane chemistry [35,36,49] were implemented to assess the speciation data generated by the MFTR. The model proposed by Pyun et al. [49] is in fact an update of the JetSurf2.0 chemical kinetic model based on recent shock tube data, while AramcoMech 2.0 [36] is a more recent updated model based on broad range of experiments. The composition and temperature conditions explored in nbutane pyrolysis experiments were similar to ethane, i.e. 2% nbutane in N2 , for temperatures of 1050 and 1100 K and a pressure of 1 atm. Unlike ethane, which has high vapor pressure, n-butane at room temperature has a vapor pressure of 32 psi. Thus, the fuel line had to be kept warm in order to assure no condensation occurred until mixing with the nitrogen diluent. Consequently, experimental repeatability uncertainty of n-butane was slightly higher when compared with ethane. Figure 14 shows a comparison of major pyrolysis product yields from n-butane cracking, with those trends predicted using the models by Wang et al. [35], Pyun et al. [49], and Curran and co-workers [36]. The reasonable agreement between the experimental data and model predictions give confidence that the small scale MFTR can be used to investigate fuel pyrolysis of more complex molecules without any profile shifting. To understand the n-butane species measurement uncertainties with respect to the model parameter uncertainties, MC simulations similar to that of ethane were performed by perturbing the top 15 reactions (see Table SPM.4 in Supplementary materials for a list of reactions and uncertainty factors used). The bound-to-bound uncertainties from the model predictions show that experimental data for C2 H4 , H2 , CH4 , C2 H2 , C3 H6 , pC3 H4 , and n-C4 H10 have much lower uncertainty bounds compared to current model uncertainty factors, except for C2 H6 . As mentioned before, the unusually large ethane mole fraction uncertainty is due to a combination of flow controllers used to generate calibration standards and unusually high uncertainty of ethane standards in the GC analysis. As mentioned above, sensitivity and flux path analysis have been performed to identify the key reactions contributing to the

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Fig. 13. Differences in reaction rates (a) C2 H4 + H(+M) = C2 H5 (+M) and (b) CH3 + CH3 (+M) ⇒ C2 H6 (+M) for the three models adopted [35,36,40].

differences observed between predictive models. The n-butane sensitivity analysis shown in Fig. SPM.3(a) indicates that the dominant reactions controlling the major species evolution is 2C2 H5 (+M) = C4 H10 (+M). Specifically, at 1100 K a factor of two difference between the two models by Wang et al. [35] and Pyun et al. [49] of this reaction C4 H10 (+M) ⇒ 2C2 H5 (+M) and a factor of six difference of reaction C4 H10 (+M) ⇒ nC3 H7 + CH3 (+M) (see Fig. 15) can explain the predicted species yields shown in Fig. 14. Interestingly, the model by Curran and co-workers [36] with an in-between value for this rate constant leads to prediction of nbutane and ethylene profiles in close agreement with the present MFTR experimental data. However, the predicted temporal profiles of hydrogen and acetylene defies the order based on the rate constants of above two reactions. Further examination of sensitivity analysis of acetylene formation listed in Table SPM.3(b) reveals that the second most sensitive reaction C2 H4 + CH3 = C2 H3 + CH4 with a factor of five lower rate constant at 1100 K in AramcoMech2 model [36] compared to that of Wang et al. [35] or Pyun et al. [49] is the underlying reason for this difference (see Fig. SPM.4). These differences highlight the need for accurate speciation data in order to perform comprehensive optimization of n-butane kinetic parameters. 4.4. n-Dodecane pyrolysis

Fig. 14. Comparison of species mole fractions in n-butane pyrolysis as a function of time, for hot section temperature of 1100 K (experiments (symbols) and predictions (lines)) with models by Wang et al. [35], Pyun et al. [49], and AramcoMech 2.0 [36]. Inflow conditions are XC4 H10 = 0.02, XN2 =0.98 and p=1 atm.

A major focus of the MFTR developed was to quantify the pyrolysis of large hydrocarbon fuels, for a range of temperatures and residence times of interest. As the first step in this effort, the pyrolysis of pre-vaporized n-dodecane was considered because of its importance in many real fuels and the availability of reasonably well validated chemical kinetic models [34,35,50,51]. Unfortunately, replicating the exact experimental inflow and reactor conditions of Banerjee et al. [51] nor jet-stirred reactor conditions of Herbinet et al. [73] were not possible owing to vitiation effects of Ref. [51] and long residence times of Ref. [73]. Alternatively, by measuring the conversion of n-dodecane in present experiments, quantification of species yield as a function of fuel conversion as shown in Fig. 9 may provide a mechanism for future comparison of species yield between different reactors. Figure 16 shows the species yield from n-dodecane pyrolysis as a function of time in the MFTR, for 1100 K and 1 atm (see Fig. SPM.12 for species yield from n-dodecane pyrolysis as a function of temperature for a residence time of 50 ms). In these experiments, a much higher dilution was used in comparison to ethane or n-butane experiments described earlier, i.e. 0.25% n-dodecane in nitrogen. Such high dilution was required for two reasons: (i) to minimize any local temperature departure from the target values due to endothermic pyrolysis of n-dodecane and (ii) to minimize the influence of unquantified large hydrocarbon species on

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Fig. 15. Differences in reaction rates (a) C4 H10 (+M) ⇒ 2C2 H5 (+M) and (b) C4 H10 (+M) ⇒ nC3 H7 +CH3 (+M) for the three models adopted [35,36,49].

the reported C0 –C4 mole fractions. As described in the experimental section, the lighter C0 –C4 species were separated from heavier molecules by sending the sample gas through a dry-ice/ethanol bath at 195 K (see Fig 4). Since the heavier condensed species were not quantified, no mass balance analysis is reported here. However, owing to 99.75% dilution with nitrogen, the mole fractions estimated from GC sample loop analysis is minimally affected. For flow residence times starting from 10 ms, Fig. 16 shows that all the four models considered predict the key pyrolysis species, namely ethylene, methane, and hydrogen, in reasonably good agreement. As discussed in Section 4.1, at 10 ms the analytical criterion for negligible flow stratification is not satisfied, yet the present results show an excellent trend without any need for zero-time shifting. Except for ethane and propene, all the other C0 –C4 species variation vs. time profiles fall in-between model predictions. The four n-dodecane models implemented showed the largest deviation in predicting acetylene, 1,3-butadine, and propyne, almost a factor of five. Since the experimental uncertainties are much narrower than current model predictions, there is a considerable room to tighten the model uncertainties based on the present data. Unlike the analysis of ethane and n-butane data, the analysis of n-dodecane models are complicated by the fact that some models contain non-integer stoichiometric coefficients and unknown uncertainty factors of key reactions. Thus, only limited model analysis has been performed and are reported in supplementary material section. For example to understand the origin of large variations in acetylene during n-dodecane pyrolysis (see Fig. 16), sensitivity analysis of acetylene with respect to the rate parameters are presented in Figs. SPM.5(a–d). From these results, the wide spread of acetylene mole fractions can be attributed to the differences in reactions C2 H4 + CH3 = C2 H3 + CH4 and C2 H2 + H(+M) = C2 H3 (+M). Specifically, the differences observed between Wang et al. [35] vs. Banerjee et al. [51] can be attributed to a factor of two variation of the most sensitive reaction controlling acetylene formation as seen in Fig. 17(a). In contrast, the most sensitive reaction controlling acetylene formation in models by Ranzi et al. [34] and by MzeAhmed et al. [50] is C2 H2 + H(+M) = C2 H3 (+M) and differ by a factor of four (see Fig. 17(b)). The lowest rate assigned for this reaction in the model by Ranzi et al. [34] leads to the prediction of acetylene formation in n-dodecane pyrolysis with close agreement with present data, as seen in Fig. 16. Considering the complexity of n-dodecane pyrolysis pathway, optimization of kinetic parameters from a limited set of speciation data as collected here will remain a great challenge. Fig. 16. Comparison of species mole fractions in n-dodecane pyrolysis as a function of time, for hot section temperature of 1100 K (experiments (symbols) and predictions (lines)) with models by Wang et al. [35], Ranzi et al. [34], Banerjee et al. [51], and Mze-Ahmed et al. [50]. Inflow conditions are XC12 H26 = 0.0025, XN2 =0.9975 and p=1 atm.

5. Conclusions The microflow tube reactor described here offers a versatile and promising configuration for the analysis of species evolution as

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Fig. 17. Differences in reaction rates (a) C2 H4 + CH3 ⇒ C2 H3 + CH4 and (b) C2 H2 + H(+M) ⇒ C2 H3 (+M), for the four models adopted [34,35,50,51] in n-dodecane pyrolysis.

a function of composition, temperature, and flow residence time. While the use of small diameter laminar flow reactors for such investigations is not new, the present approach provides nearly constant temperature conditions with well defined flow residence times which is critical for kinetic model development efforts. Furthermore, the present low temperature, variable residence time experiments fill a key reaction regime not easily accessible via shock tube experiments. The scaled-down reactor developed, with a small mixing volume that facilitates rapid mixing of hot inert gas stream with the fuel in less than 2.5% of the hot section residence time, has been used to eliminate the need for zero-time shifting for a broad range of fuel molecules and temperature/residence time conditions considered. If it can be generalized for other conditions, especially for higher pressure, this feature can reduce the modeling complexity, for example the need to implement PSR + PFR type modeling efforts, and can be directly used in model optimization efforts with parametric perturbations. Furthermore, the MFTR’s excellent sensitivity to temperature, composition, and residence time variations, together with well defined species uncertainties, ensure that the data collected can be an effective tool in future chemical kinetic pathway and model optimization investigations. While ethane and n-butane pyrolysis have been extensively investigated for the present inflow conditions, it is shown here that the recent models can have up to a factor five variation in predicting some species, but within or close to the kinetic model uncertainty bounds as demonstrated via Monte Carlo simulations. Specifically, it is also shown here that the 2σ uncertainty bounds of present measured species concentrations are much narrower than the kinetic parameter uncertainty bounds, indicating the importance of the present data in reducing the model uncertainties. In comparison to ethane and n-butane pyrolysis, n-dodecane pyrolysis models are not as well developed and show a significant variation in predicting acetylene, 1,3-butadine, and propyne yields. While no Monte Carlo simulations were performed with n-dodecane models as key reaction uncertainty factors were not available, the experimental measurement uncertainties are shown to be much narrower than the range of four models implemented. Acknowledgments This research was sponsored by the AFOSR Basic Research Initiative on Catalytic Fuel Cracking and under the Grant FA9550-121-0496 with Dr. Chiping Li as the technical monitor. Appendix A. Characteristic time scales The definitions of characteristic time scales and nondimensional parameters discussed in the paper are listed in

Table A.1 Definitions of characteristic time scales and non-dimensional parameters and their values for a 4 mm ID flow reactor at 1100 K and at two different flow residence times. Characteristic time

Formula

Values (ms) (for τres =100 ms)

Values (ms) (for τres =10 ms)

τ conv , R τ conv , L τsp−di f f , R τsp−di f f , L τth−di f f , R τ momnt τ chem , R

R/v¯ L/v¯ R2 /D R2 /G R2 /α R2 /ν k−1

0.5 100 27 17,430 19 26 68

0.05 10 27 178 19 26 68

Non-dimensional parameter

Formula

Values (for τres =100 ms)

Values (for τres =10 ms)

Re Pr Sc Pesp−di f f Peth−di f f DaII

τ momnt /τ conv , R τth−di f f , R/τmomnt τsp−di f f , R/τmoment τsp−di f f , R/τconv , R τth−di f f , R/τconv , R τsp−di f f , R/τchem

48 0.74 1.03 50 36 0.4

484 0.74 1.03 500 359 0.4

Note: R – radius of the reactor; L – length of the reactor; v¯ – mean velocity; ν, α , D are momentum, thermal, and species diffusion coefficients; G – axial diffusion with Taylor–Aris dispersion; k – first-order rate constant.

Table A.1. Also listed are the relevant quantitative values corresponding to pyrolysis of ethane at short and at long residence time cases, i.e. 10 and 100 ms, respectively, at 1100 K and 1 atm. These values were used to assess the criteria for negligible radial stratification of temperature and species. In Table A.1, the estimated chemical time scales correspond to those at maximum reaction rate, which is a function of temperature, pressure, and concentration. However, along the reactor, the chemical time scale varies with fuel decomposition (see Fig. A.1). As seen from Fig. A.1, the species dispersion in the axial direction is always negligible, while the radial diffusion of species and temperature is much faster than the chemical time scales. The values listed also imply that for flow residence times below 27 ms, the criterion for negligible stratification τsp−di f f,R /τconv,L < 1.0 is not satisfied and may influence the measured data. On the other hand, Fig. 6 shows that even at high velocities corresponding to 10 ms residence time, the stratification effects are negligible. This is perhaps due to the fact that there is no single diffusion time scale associated with the multi-component system, hence the value of τsp−di f f,R listed above, i.e. based on the diffusivity of ethane in nitrogen (DC2 H6 ,N2 ), must be tempered with the broad range of diffusion and chemical time scales in the reacting flow system.

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Fig. A.1. Characteristic time scales evaluated from axi-symmetric 2D simulation of ethane pyrolysis at 1100 K and 1 atm, (a) for 10 ms and (b) for 100 ms.

Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.combustflame.2016.11.019.

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