Combustion Flame Speeds and Stability of Associated Natural Gas

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Combustion Flame Speeds and Stability of Associated Natural Gas with High Concentrations of C2-C4 Alkanes Farhan Arafin, and Erica L. Belmont Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b01739 • Publication Date (Web): 16 Oct 2018 Downloaded from http://pubs.acs.org on October 17, 2018

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Combustion Flame Speeds and Stability of Associated Natural Gas with High Concentrations of C2-C4 Alkanes F. Arafin, E. Belmont* University of Wyoming, Mechanical Engineering, 1000 E. University Ave., Laramie, USA 82071 *Corresponding

author, email: [email protected]

ABSTRACT: Associated gas worth of tens of billions of dollars is flared annually during oil and gas production, which leads to resource waste and environmental issues. The combustion characteristics of associated gas mixtures with high concentrations of C2-C4 hydrocarbons, sometimes called high-BTU gases, were examined in this study. Specifically, adiabatic laminar flame speeds and combustion stability, including critical heat loss at extinction, were quantified for a range of associated gas mixtures. The study used a porous plug burner facility for stabilization of premixed, laminar flat flames with measured heat loss from the flames. Standoff distances of associated gas flames were 1 ACS Paragon Plus Environment

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measured using CH* chemiluminescence for validation of the technique by comparison with numerical simulations and analytical modeling, and standoff distance was used to determine stable operating points. Laminar flame speeds of the major component gases (methane, ethane, propane, and butane) and three associated gas mixtures from the Bakken gas field in North Dakota were investigated at lean to mildly rich equivalence ratios (ϕ=0.7-1.1). Numerical simulations were performed using USC II and Aramco 1.3 mechanisms for comparison of numerical and experimental laminar flame speeds of component and associated gas mixtures. Additionally, a flame speed correlation was introduced to model the flame speeds of these quaternary gas mixtures. Finally, a heat loss ratio was defined through comparison of heat loss and burner firing rate, and critical heat loss ratios were identified where these associated gas mixtures become unstable and extinguish. Results are discussed in the context of utilization of associated gas with high concentrations of C2-C4 alkanes.

1. INTRODUCTION Natural gas (NG) is one of the most extensively used sources of energy for heating, cooking, transportation, and electricity generation [1]. However, the composition of natural gas can vary significantly with location and season. A previous study [2] showed that natural gas can vary in composition from 55.8 to 98.1 vol% methane, which is the 2

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major component, with significant variation in other components as well; ethane and propane can vary from 0.5 to 13.3 vol% and 0 to 23.7 vol%, respectively, while other hydrocarbons can be present in trace amounts or more depending upon the source of extraction and type of refining process. Among these mixtures of natural gas constituents, those which have lower concentrations of methane than the pipeline standard are frequently known as associated gas. They are commonly not processed or transported as fuel for a range of reasons including the isolation of wells, insufficient infrastructure to collect the gas, and relatively low value of the gas [3]. Rather, a common practice is to burn off this gas via flaring during oil production when it comes to the surface in places having no infrastructure for its utilization [4]. Estimates by the EIA [5] and the World Bank [4] show that 5 trillion cubic feet of natural gas, which is 4% of total production, was flared worldwide in 2011. Natural gas worth 55 billion USD was flared worldwide and gas worth 2.3 billion USD was flared in the US in 2011. According to Olivier et al. [6], gas flaring during oil production produced approximately 250 million tons of CO2 emissions globally in 2011, yet no value, such as electricity, was gained from this fuel source. Besides greenhouse gas production, variable amounts of air pollutants such as nitrogen oxides, carbon monoxide, volatile organic compounds (VOCs), polycyclic aromatic hydrocarbons (PAHs), and black carbon particles are also emitted to the atmosphere during flaring because of little or no pollution control 3


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[7], causing severe local and regional air pollution. Given this ongoing waste of fuel and source of emissions, it is important to investigate the utilization of associated gas as an alternate fuel source and understand its combustion characteristics. Thus, this study characterizes associated gas mixtures with high levels of C2-C4 alkanes. Utilization of associated gas in natural gas engines is challenging because such engines are sensitive to variations in composition due to the possible occurrence of engine knock. Several studies have been done to investigate the effect of varying fuel composition on engine performance. Chen et al. [8] investigated the effects of methane content in NG on combustion and performance of a liquefied natural gas (LNG) heavy-duty engine. They found that NG with lower methane content has poorer anti-knock performance, which also affects the power and fuel economy. Maximum load at high speed is limited for engines operating on NG with lower methane contents when the compression ratio is increased. Since associated gas mixtures have lower methane content than conventional NG, they are expected to have poorer fuel performance in existing engines. McTaggartCowan et al. [9] also investigated the implications of NG composition on combustion in a heavy-duty engine and on associated pollutant emissions. Their results showed that black carbon particulate matter emissions increased with ethane and propane content. With higher percentages of ethane, propane, and sulfur, combustion of associated gas mixtures can be more polluting than NG combustion. In a computational study, El-Sherif [10] 4


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found that an increase of ethane concentration in NG led to an increase in the lean flammability limit and burning velocity. Burcat et al. [11] studied the ignition delay times of C1-C5 alkanes by shock-tube measurements and found that the ignition delay times decrease with increasing number of carbon atoms in the molecule, with the exception of ethane. Therefore, the presence of higher hydrocarbons in natural gas can promote ignition by changing auto-ignition behavior of the fuel. Adiabatic laminar flame speed is a fundamental physical property of a combustible mixture related to its thermal diffusivity, reaction rate, and flame temperature. A substantial number of investigations have been done to determine the laminar flame speeds of the pure components of associated gas, including methane, ethane, propane, and butane [12, 13, 14, 15]. In addition, some studies also focused on the laminar flame speeds of fuel blends for the validation of chemical kinetics mechanisms [16, 17]. In such fuel blends, higher carbon number hydrocarbons increase the volumetric heating value of the fuel. Bourque et al. [17] performed atmospheric and high pressure laminar flame speed experiments with two natural gas blends and captured the basic trends of laminar flame speed with composition and pressure using a detailed chemistry mechanism. An additional important fuel characteristic is stability under heat loss and extinction at a critical level of heat loss. Numerous studies have examined flame stability using flat flame burners, and have identified thermal-diffusive and hydrodynamic instabilities as 5


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contributing to development of cellular flame structures and eventual pulsation or blowoff of a flat flame from a burner surface [18]. Stability is particularly important for the design of efficient and clean combustors, as heat loss can result in local extinction, unburned fuel and high levels of emissions [19]. Yuuki et al. [20] studied the structure of a stoichiometric methane/air flame and asserted that the critical flame temperature for the stability of this flame on a porous plug burner was 1550 K, below which the overall activation energy and standoff distance increased rapidly and the flame became unstable. Eng et al. [21] showed that the flame temperature monotonically changed with fuel flow rate, while the heat loss rate showed non-monotonic behavior, and both directly affected the flame location above a burner surface. In this study, two combustion characteristics have been investigated for the purpose of characterizing associated gas mixtures with high levels of C2-C4 alkanes: laminar flame speed and stability under heat loss. Representative associated gas compositions from the Bakken formation in North Dakota were selected for this study based on their range of low methane numbers, making them challenging fuels for utilization. Results include laminar flame speeds of component gases for validation of the experimental setup and chemical kinetic models, as well as flame speeds for three different associated gas mixtures over a range of equivalence ratios. Flame standoff distances were measured and compared with numerical and analytical results for further technique validation and assessment of 6


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stable operating points. A correlation was developed for the laminar flame speeds of these quaternary associated gas mixtures, and its extensibility to flame speed prediction with variation in pressure was assessed. Finally, the flame stability for each of these mixtures was measured and a critical heat loss ratio was defined where flame extinction occurs as a function of equivalence ratio.

2. METHODS 2.1. Associated gas compositions. The associated gas compositions examined in this study were derived from measured compositions in the Bakken formation, as presented in [22]. Associated gases from the Bakken formation are high in C2+ hydrocarbons, which are often referred to as Natural Gas Liquids (NGL). These gases typically have higher energy contents (50-75 MJ/m3) when compared to residential pipeline gas (approximately 37 MJ/m3) [22]. From the range of gas mixtures, three compositions were selected in order to examine a wide range of methane numbers (MN). MN, defined as the volume percentage of methane blended with hydrogen which matches the engine knock intensity of a target gaseous fuel, is typically 75-95 for natural gas [23]. The MN of Bakken associated gas typically ranges from 41 to 56, indicating a lower resistance to engine knock compared to natural gas, and the three compositions selected for this study cover this range of MN. The four highest concentration component gases 7


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(methane, ethane, propane, and butane) were considered and their concentrations were normalized as presented in Table 1. Lower amounts of pentane, carbon dioxide and N2 were not considered. Component gases and associated gases were assessed over a range of equivalence ratios (ϕ) from 0.7 to 1.1 due to the relevance of this equivalence ratio range to practical combustors.

Table 1. Compositions (normalized) of associated gas from the Bakken gas field examined in this study.

Component Methane Ethane Propane Butane MN LHV (MJ/kg)

Composition (mol %) Gas A Gas B Gas C 62.2 49.0 76.2 21.5 19.1 13.7 12.2 15.2 5.7 4.1 16.7 4.5 50 41 56 48.1 49.0 47.3

2.2. Burner facility. Experiments were conducted using a McKenna burner at local pressure, which is 75 kPa in Laramie, WY, and measured flame speeds were adjusted to 101 kPa via the power law [24], described in detail later, for straightforward comparison to other studies. A schematic of the experimental setup is shown in Fig. 1. The burner was constructed with a bronze porous plug, and a cooling water jacket embedded inside the 8


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porous plug facilitated extraction of heat through the water jacket. The inlet and outlet temperatures of the coolant water were monitored by a pair of K-type thermocouples throughout the experiments, and the flow rate of coolant water was measured. The burner was equipped with a nitrogen (N2) shroud flow to isolate the flame from ambient air. The shroud gas was heated to the coolant outlet temperature in order to minimize conductive heat losses through the burner walls. The flow rate of N2 was varied such that the velocity of the shroud flow was equal to the reactant velocity.

Figure 1. Schematic of the experimental setup. The premixed reactants were prepared by feeding the component gases and air to a mixing manifold. The flow rates of the component gases and air were controlled using calibrated Teledyne Hastings mass flow controllers. Dried and filtered air was used, and all 9


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the component gases, including methane (CH4), ethane (C2H6), propane (C3H8) and butane (C4H10), had purity equal to or greater than 99.5%.

2.3. Standoff distance. Standoff distance measurements were conducted for all component gases and associated gas mixtures over the range of tested equivalence ratios in order to validate the technique against numerical and analytical model results as well as assess the stability of each operating point. A Canon EOS 7D camera with a 100mm f/2.8 macro lens and a 430±10 nm optical bandpass filter was used to measure the spatial location and intensity of CH* chemiluminescence. First, a scale photo was taken to determine the length per pixel of the photo, which was approximately 10 µm. Then, 10 images were captured of each flame at a given flowrate. An example of a flame image taken with the CH* filter is shown in Fig. 2. The distance from the burner surface to the peak intensity location within the flame gives the standoff distance.

10


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Figure 2. Sample photo of a ϕ = 1.0 associated gas B flame at 35.8 cm/s through the CH* filter. The flatness of a flame was assessed by measuring the standoff distance across the center 10% of the flame. Stable flames had variation in standoff distance across this region of less than 0.1 mm. Unstable flames exhibited variation in standoff distance that exceeded this value.

2.4 Laminar flame speeds. A technique similar to that described in the study of Botha and Spalding [25] was followed to determine the adiabatic laminar flame speeds of unstretched flames. Following the Botha and Spalding technique [25], the flame was established with a reactant flow rate that gave a flat, stabilized flame above the burner surface. When steady state was achieved at a given reactant flow rate, inlet and outlet coolant temperatures were recorded and the flow rate of water through the cooling jacket

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was measured in order to calculate the heat loss per volume of fuel, 𝑄, from the flame using Eqn. 1 𝑄=

𝑚𝑤𝑐𝑝∆𝑇 𝑉𝑓

(1)

where 𝑚𝑤 is the mass flowrate of coolant water, 𝑐𝑝 is the specific heat of water, ∆𝑇 is the temperature difference between inlet and outlet water, and 𝑉𝑓 is the volumetric flowrate of reactants. Reactant flow rates were increased after each measurement within the range of tested flowrates. There was a region of linear variation between the unburned mixture velocity and the heat loss per fuel volume, as seen in [25] and [26]. The adiabatic laminar flame speed was then obtained through linear extrapolation to zero heat loss. An example of the laminar flame speed extrapolation for a C3H8/air mixture at a stoichiometric ratio is shown in Fig. 3.

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Figure 3. Flame speeds of C3H8/air at ϕ = 1.0 over a range of tested flow rates, which produce varying amounts of heat loss to the burner. The non-linearity of the experimental data points relative to the extrapolated line was evaluated using Eqn. 2 % 𝑜𝑓 𝑛𝑜𝑛𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦 =

|𝑆𝐿(𝑒𝑥𝑝) ― 𝑆𝐿(𝑙𝑖𝑛𝑒𝑎𝑟)| × 100 𝑆𝐿(𝑙𝑖𝑛𝑒𝑎𝑟)

(2)

where 𝑆𝐿(𝑒𝑥𝑝) is the experimental flame speed value at a certain reactant flowrate and 𝑆𝐿(𝑙𝑖𝑛𝑒𝑎𝑟) is the flame speed value according to the linear trend line. The investigated reactant flow rate range produced a maximum of approximately 5% in the variation of the linearity. Reactant flow velocities tested in the experiments fell within a range of approximately 20-60% of the adiabatic flame speed. Higher flow velocities introduced cellular flame 13


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structures and eventually led to wrinkling of the flame. Therefore, flames with visible cellular structure or wrinkling were not utilized for laminar flame speed determination. Flames were also not stable at significantly lower flow velocities than this range, where cellular structures and planar pulsations would develop. For lower reactant flow velocities, any flame with more than 2% uncertainty in flame standoff distance from the burner surface was not considered to be sufficiently stable for flame speed measurement.

2.5 Numerical simulations. Numerical adiabatic flame speeds were calculated from one-dimensional simulations of freely propagating, premixed flames in a constant pressure, adiabatic system using Cantera [27] with USC II [28] and Aramco 1.3 [29] chemical kinetic models with multicomponent transport properties. All simulations were performed at a reactant temperature of 293 K and 75 kPa pressure. A range of equivalence ratios was selected from ϕ=0.7 to 1.1 in 0.1 increments to compare the results with experimental data. Additional one-dimensional simulations of burner-stabilized premixed flames at constant pressure were conducted using CHEMKIN-PRO [30] and the USC II mechanism for comparison to experiments. A chemical kinetic mechanism for CH* was added to USC II to calculate CH* species profiles [28]. As was defined for experimental standoff distance, the distance from the burner surface to the location of maximum CH* concentration gave the simulated standoff distance value.

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2.6 Analytical model. In addition to the burner-stabilized simulations of standoff distance, an analytical model based on activation energy asymptotics was used to compute the standoff distance as a function of operating conditions [31]. The nondimensional governing equations for flame temperature and standoff distance are 2

𝑓 =

4

( ) [ ( 𝑇𝑓

𝑇𝑎𝑑

exp ― 𝑇𝑎

1 𝑇𝑓

―

1

)]

𝑇𝑎𝑑

𝑥𝑓𝑓 = ―𝑙𝑛[1 ― (𝑇𝑓 ― 𝑇𝑠)]

(3)

(4)

where the nondimensional variables for burning flux, temperature, and standoff distance are defined as

𝑓=

𝑐𝑝𝑇 𝑓 𝑓° , 𝑥= 𝑥 , 𝑇= 𝑓° 𝑞𝑐𝑌𝑢 𝜌𝐷

( )

(5)

and 𝑓 is the burning flux, 𝑓° is the adiabatic burning flux, 𝑇 is the temperature along the distance from burner surface, 𝑇𝑎𝑑 is the adiabatic flame temperature, 𝑇𝑓 is the flame temperature, 𝑥 is the standoff distance, 𝜌 is the density, 𝐷 is the mass diffusion coefficient, 𝑐𝑝 is the specific heat, 𝑞𝑐 is the heat of combustion, and 𝑌𝑢 is the unburned mass fraction. Equations 3 and 4 were used for the analytical calculation of the standoff distance. To obtain dimensional values for the quantities of interest, laminar flame speeds (𝑆𝐿), adiabatic flame temperatures (𝑇𝑎𝑑) and unburned gas density (𝜌𝑢) were obtained from 15


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freely propagating premixed flame simulations in Cantera. Two other parameters, the activation temperature (𝑇𝑎), and the density-diffusivity product (𝜌𝐷), required dimensional values. Both of these parameters were set by calibration to the experimental data using the following procedure, adapted from [32]. First, Eqn. 3 was solved to evaluate 𝑇𝑎 such that 𝑇𝑓 given by the analytical model matched a 𝑇𝑓 that was measured experimentally in the laboratory with an S-type thermocouple for each equivalence ratio and at a flame speed ratio of 𝑓 = 0.4. Radiation correction was done for the S-type thermocouple according to [33]. Using the determined value of 𝑇𝑎 for a particular equivalence ratio, non-dimensional flame temperatures for each flame speed ratio were computed using Eqn. 3. Equations 4 and 5 were then solved to determine the standoff distance for each flame speed ratio at a particular equivalence ratio. Finally, the parameter 𝜌𝐷 was fitted by comparison to experimental standoff distance data.

2.7 Flame speed correlation. A correlation for the laminar flame speeds of the associated gas mixtures examined in this study was proposed following the form originally proposed by Gülder [34] for pure compounds and later extended to ternary natural gas mixtures by Dirrenberger et al. [16]. This correlation is further extended in this study for a quaternary gas mixture 𝑆𝐿 = (1 + 𝛾1𝛼𝜏11)(1 + 𝛾2𝛼𝜏22)(1 + 𝛾3𝛼𝜏33)𝑊ϕ𝜂𝑒 ―𝜉(𝜑 ― 𝜎 ― Ω1𝛼1 ― Ω2𝛼2 ― Ω3𝛼3)

2

(6)

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where 𝑊, 𝜂, 𝜎 and 𝜉 are fitting parameters for methane flame speed as a function of equivalence ratio. The mole fractions of ethane, propane and butane are given by 𝛼𝑖, and 𝛾𝑖, 𝜏𝑖 and Ω𝑖 are fitting parameters which account for the influence of these species on the mixture flame speed. The model parameters 𝑊, 𝜂, 𝜎 and 𝜉 were first fitted using experimentally measured methane flame speeds. Subsequently, optimized values for 𝛾𝑖, 𝜏𝑖 and Ω𝑖 were found using experimentally measured flame speeds for all three associated gas mixtures.

2.8 Flame stability. In order to quantify the lower limits of stability at low reactant flow velocities, first where significant flame instability is observed and subsequently where a flame cannot be sustained, a heat loss ratio (HLR) was defined as the ratio of the heat loss rate from the flame to the burner versus the heat release rate due to combustion 𝐻𝐿𝑅 =

𝑄𝑙𝑜𝑠𝑠 𝑄𝑟𝑒𝑙𝑒𝑎𝑠𝑒

(7)

with the heat loss rate from the flame, 𝑄𝑙𝑜𝑠𝑠, calculated as 𝑄𝑙𝑜𝑠𝑠 = 𝑚𝑤𝑐𝑝∆𝑡 where 𝑚𝑤 is the mass flowrate of coolant water, 𝑐𝑝 is the specific heat of water, and ∆𝑇 is the temperature difference between inlet and outlet water. The heat release rate from the fuel mixture was calculated as 𝑄𝑟𝑒𝑙𝑒𝑎𝑠𝑒 = 𝑚𝑓𝑢𝑒𝑙𝐿𝐻𝑉, where 𝑚𝑓𝑢𝑒𝑙 is the mass flowrate of the fuel mixture, and 𝐿𝐻𝑉 is the lower heating value of the mixture.

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At each tested flame speed ratio, a flame was defined as unstable if the uncertainty in flame standoff distance at that condition was greater than 2%. While such points were not utilized for flame speed measurement, HLR was assessed at these points in addition to stable operating points in order to determine the critical HLR above which flame extinction occurs at each equivalence ratio.

2.9 Uncertainty Calculation. The measurement of uncertainties was assessed as statistical error using the Student’s t-distribution with two-tailed 95% confidence level. Laminar flame speed measurements were conducted twice, while standoff distance measurements were derived for a sample number of 10 at each flowrate, and uncertainty was calculated based upon these sample sizes. The uncertainty for laminar flame speed measurement is attributed to precision of the mass flow controllers, for which uncertainty of ±1% is attributed to each flow controller, as well as repeatability of measurements. Uncertainty in heat loss measurements is attributed to repeatability of coolant temperature and coolant flowrate. Uncertainty in standoff distance measurement is primarily due to the accuracy of the flow controllers and flame instability.

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3. RESULTS AND DISCUSSIONS 3.1. Standoff distance. Standoff distances for the associated gas mixtures are presented as a function of flame speed ratio, where flame speed ratio is defined as the ratio of inlet velocity of the reactants to the adiabatic laminar flame speed of the mixture (Fig. 4). The trends of the standoff distances were found to be similar for all equivalence ratios of a particular mixture, although the magnitudes of the standoff distances decreased with increasing equivalence ratio. For brevity, the results of only one equivalence ratio (ϕ=0.8) are presented for each of the associated gas mixtures.

Figure 4. Standoff distances of a) associated gas A, b) associated gas B, and c) associated gas C at ϕ=0.8 as a function of flame speed ratio. Experimentally measured values are shown along with the results of numerical simulations performed with USC II and analytical model results. Standoff distance generally decreases as mixture flow velocity, or flame speed ratio, is increased, and a slight increase in standoff distance is observed at the highest tested flame 19


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speed ratios [21]. Ferguson and Keck [35] examined hydrogen, ethylene, and methane flames and observed that standoff distance decreases when the flame temperature increases. Higher mixture flow velocity increases the fuel burning rate and flame temperature through an increased heat release rate, as demonstrated later in this study. Therefore, the decreasing trend of standoff distance with mixture flow velocity found in this work is in accordance with previous investigations of standoff distance. Numerical results match closely with experimental values, thereby validating the experimental technique against numerical model predictions, and any deviations found between numerical and experimental results are regarded to be small (10-4-10-5 m in magnitude). Additionally, analytical results generally agree with the trends and magnitudes of experimental standoff distances and confirm the validity of the captured trend. This is particularly useful because the analytical model utilizes a simplified one-step reaction mechanism and models heat loss to the burner as purely conductive. Thus, the agreement between experimental and analytical results supports the quantification of heat loss from the flame by measured heat loss to the burner surface.

3.2. Laminar flame speeds 3.2.1 Component gases. The experimental setup was utilized to measure the adiabatic flame speeds of the four major components of associated gas mixtures in order to 20


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assess the accuracies of both the experimental technique and the reaction mechanisms for each component gas. These assessments were performed by comparison of experimental results with numerical simulations, and comparison of numerical simulations with other published data. In order to facilitate comparison of the experimental results obtained in this study, which were obtained at the local pressure of approximately 75 kPa in Laramie, WY, measured flame speeds were adjusted to 101 kPa using the power law relation 𝑆𝐿 = 𝛽

𝑆𝐿,𝑜(𝑃 𝑃𝑜) [24]. The subscript 𝑜 denotes the reference flame speed and pressure, which in this case are the measured flame speeds at 75 kPa. The exponent, 𝛽, was calculated for each component gas using the USC II mechanism and Cantera, and values of -0.287, 0.206, -0.237 and -0.219 were obtained for CH4, C2H6, C3H8 and C4H10, respectively. These adjusted flame speeds are presented along with the measured and numerically derived flame speeds in Fig. 5. Figure 5a shows the measured, adjusted and simulated laminar flame speeds of CH4/air over a range of equivalence ratios. It can be seen that the maximum laminar flame speed obtained from experiments at 75 kPa was 39.1 cm/s at ϕ=1.0, above and below which lower flame speeds were measured. Experimental and numerically simulated flame speeds are in good agreement, with USC II results showing slightly higher deviation from the experiments than Aramco 1.3. In previous work, Park et al. [36] measured laminar flame speeds of CH4/air flames with a counterflow burner at STP. They modeled the 21


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experiments using USC II and showed that the kinetic model predicts the experimental data for flame speeds closely, where the average deviation between model and experiment was 3.8%. In similar way, Metcalfe et al. [29] modeled flame speeds of CH4/air at STP using the Aramco 1.3 mechanism and showed that the predicted results match fairly closely with the experimental data from Vagelopoulos et al. [37], having an average deviation of 4.9%. In comparison, average differences of 4% and 2% between experimental and numerical results were observed in this study for USC II and Aramco 1.3, respectively. The differences observed in this study are therefore comparable to those observed in other studies. Figure 5b shows the measured, adjusted and simulated laminar flame speeds of C2H6/air over a range of equivalence ratios. Similar trends are observed between experimental and numerical laminar flame speeds, with flame speeds increasing with increase in equivalence ratio and the highest flame speed of 41.9 cm/s measured at the highest tested equivalence ratio of 1.1. However, simulation results for C2H6/air mixture in this study show some higher values than experimental measurements. Experimental results match closely with Aramco 1.3 for lean mixtures, but deviations increase near stoichiometry and in the mildly rich mixture. Metcalfe et al. [29] observed a similar trend with Aramco 1.3 for C2H6/air. They compared numerical flame speeds of C2H6/air at STP with experimental values from [38] and found that deviation slightly increases near stoichiometry. To 22


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investigate the high deviation observed when using USC II, further simulations were performed for C2H6/air mixtures at STP with this mechanism, and the values were compared with the available experimental values from [38]. It was found that USC II consistently overpredicts the laminar flame speed for C2H6/air. Thus, the observed discrepancy between experimental and numerical values is consistent with previous results.

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Figure 5. Experimental and simulated adiabatic laminar flame speeds for (a) methane/air, (b) ethane/air, (c) propane/air, (d) butane/air at 293 K and 75 kPa pressure, as well as experimentally measured flame speeds adjusted to 101 kPa. A comparison of experimental, adjusted and numerical laminar flame speeds of C3H8/air mixtures over a range of equivalence ratios is shown in Fig. 5c, and the numerical and experimental results are found to be in excellent agreement. Lowry et al. [38] summarized experimental laminar flame speeds of C3H8/air at STP from previous works, where it was seen that the flame speed data from previously published results are quite scattered depending on the experimental methods used. USC II and Aramco 1.3 were utilized for C3H8/air mixture simulations at STP and the results were compared with the summarized results in [38]. It was found that, among the experimental works, simulation results match closely with Vagelopoulos and Egolfopoulos [15] and Law and Kwon [39].

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Finally, Fig. 5d shows experimental, adjusted and numerical laminar flame speeds of C4H10/air mixtures over a range of equivalence ratios. The highest experimental flame speed was measured to be 39.5 cm/s at ϕ=1.1, and flame speed decreased with decrease in equivalence ratio. Simulation results are found to be significantly higher than the experimental values, with deviation ranging from 4% to 21% for USC II and 1% to 10% for Aramco 1.3. These findings are in agreement with a summary of experimental C4H10/air flame speeds and comparison with numerical simulations presented by Wu et al. [40], which shows overprediction of both mechanisms over the range of tested equivalence ratios in this study. To investigate this discrepancy, simulations for C4H10/air mixtures at STP were conducted with these mechanisms, and comparison with Bosschaart and de Goey [13] revealed that the overprediction observed in the current study is consistent with other studies that have utilized these mechanisms; while the overprediction in this comparison was lower for Aramco 1.3 at 3% to 14%, it was high for USC II, ranging between 3-20%, which is consistent with the results found in the present work. While it is evident that the numerical results are sensitive to the utilized chemical kinetic mechanism, the comparison plots in Fig. 5 show reasonably good agreement between experimentally measured and numerically simulated component gas flame speeds, and observed deviations are consistent with observations from other studies. 25


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Therefore, the experimental setup used in this work was considered validated and was expected to produce accurate laminar flame speed measurements for the associated gas mixtures.

3.2.2 Associated gases. Figure 6 summarizes the experimentally measured and numerically simulated flame speeds for the three associated gas compositions examined in this study, as defined in Table 1. Experimental values measured at 75 kPa are presented, along with those values adjusted to 101 kPa using the power law relation [24], as was done for the component gases. The exponent of the power law, 𝛽, was calculated using the USC II mechanism and Cantera to be -0.237, -0.235 and -0.242 for gas compositions A, B and C, respectively. Notably, 𝛽 is not highly sensitive to associated gas composition over the range of compositions examined in this study, and a single, average 𝛽 of -0.238 could be used with less than 0.1 cm/s change in adjusted flame speeds. The associated gas-specific values of 𝛽 were used to generate the adjusted flame speeds shown in Fig. 6, however. Figure 6a summarizes flame speeds for associated gas composition A. The peak adiabatic laminar flame speed value at 75 kPa was found to be 40.7 cm/s at ϕ=1.1, and the average flame speed uncertainty for this gas mixture was 1.5 cm/s. Comparison of the simulated and experimental flame speed values shows good agreement between experimental and Aramco 1.3 results. The comparison with USC II results shows fairly good agreement near stoichiometry and for the mildly rich mixture. However, deviation increases for the leaner mixtures with the highest deviation of 10.9% observed at ϕ=0.7. 26


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Figure 6b summarizes flame speeds for associated gas B, which has the lowest methane concentration among the three compositions studied in this work. Similar to other results, laminar flame speeds for this composition increase as equivalence ratio is increased from lean to near stoichiometry and the highest adiabatic laminar flame speed is found to be 40.1 cm/s at ϕ=1.1. The average uncertainty in laminar flame speed for associated gas B is 1.5 cm/s. Laminar flame speeds are overpredicted by both Aramco 1.3 and USC II. Deviation ranges from 3.3% to 5.0% for Aramco 1.3, while it ranges from 3.5% to 13.8% for USC II. Both mechanisms overpredicted flame speeds for C4H10/air, and the higher percentage of C4H10 in this mixture might be the source of the flame speed overprediction. Figure 6c summarizes flame speeds for associated gas C, which has the highest CH4 concentration among the three investigated associated gas compositions. The highest laminar flame speed is 41.2 cm/s at ϕ=1.1, which is in good agreement with the simulation values. The deviation between experimental and numerical results at lower equivalence ratios may be due to a more limited flow rate range from which flame speeds were extrapolated due to flame instability, or due to non-additive effects of fuel mixtures not captured by the mechanisms. As seen for the other associated gas mixtures, better agreement between experimental data and simulation results was achieved with Aramco 1.3 as compared to USC II.

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Figure 6. Comparison of experimental and numerical laminar flame speeds for a) associated gas A, b) associated gas B and c) associated gas C at 293 K and 75 kPa pressure, as well as experimentally measured flame speeds adjusted to 101 kPa. 28


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Notably, the laminar flame speed values of the various investigated associated gas mixtures are similar across the range of tested compositions. The highest laminar flame speed results for all of these mixtures are found to be at ϕ=1.1 and the values are within a range of 40-42 cm/s, while the lowest flame speeds for all mixtures were measured at ϕ=0.7 to be in the range of 20-22 cm/s. These results suggest that this wide range of associated gas mixtures could be utilized nearly interchangeably in a combustor based upon flame speed alone, although other combustion characteristics are also of significant importance. Additionally, the results indicate that Aramco 1.3 does reasonably well at predicting flame speeds for all three associated gas mixtures, with an average discrepancy of 3.5% between experimental and numerical values. Thus, Aramco 1.3 is a viable mechanism for simulation of associated gas mixtures over a wide range of MN. Table 2 gives the fitted parameters for the proposed flame speed correlation given by Eqn. 6. The extensibility of the model, including the fitted parameters, for flame speed evaluation with variation in pressure was evaluated by applying this model not only to the experimental data obtained at 75 kPa but also to the adjusted data at 101 kPa. Two sets of parameters were derived for methane: one for 75 kPa using experimentally measured methane flame speeds at 75 kPa, and a second for 101 kPa using experimentally measured methane flame speeds adjusted to 101 kPa via the power law. A single set of the remaining parameters was applied at both pressures. All parameters compare favorably with those 29


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suggested by Dirrenberger et al. and others for binary mixtures of CH4 with C2H4 and C3H8 [16]. The fitting coefficients for CH4 with C4H10 are likewise reasonable when compared with those for CH4 with C2H4 and C3H8.

Table 2. Parameter values for associated gas flame speed correlation. Parameter

CH4

CH4

Parameter

CH4 -C2H4

CH4 -C3H8

CH4 -C4H10

(75 kPa)

(101 kPa)

𝑊 (cm/s)

39.91

36.69

𝛾𝑖

0.130

0.177

0.109

𝜂

-0.535

-0.524

𝜏𝑖

0.811

1.130

2.157

𝜎

1.077

1.079

Ω𝑖

-0.018

-0.042

0.126

𝜉

6.244

6.075

Figure 7 shows the results of the flame speed correlation compared with experimentally measured flame speeds for each of the associated gas mixtures at 75 kPa and 101 kPa. Good agreement is observed between the values, with an average discrepancy of less than 3% between the flame speeds predicted by the correlation and the experimentally measured values at both pressures. Thus, the correlation is shown to be viable for predicting flame speeds of quaternary associated gas mixtures over a wide range of 30


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Energy & Fuels

compositions. Furthermore, the results suggest that the correlation can be applied over a range of pressures without the need to refit parameters 𝛾𝑖, 𝜏𝑖 and Ω𝑖.

Figure 7. Comparison of experimental (Expt) and correlation (Corr) laminar flame speeds for a) associated gas A, b) associated gas B and c) associated gas C at 75 kPa and 101 kPa.

3.3 Flame stability. Considering the importance of flame stability in achievement of clean and efficient combustion, particularly when flame quenching and extinction occur 31


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at extreme instability, the relationship between flame stability and heat loss was further examined, first through quantification of heat loss to the burner over a range of flame speed ratios. Figure 8 shows the experimentally measured heat loss to the burner as well as the rate of heat release, calculated from fuel flow rate and heating value, for associated gas A at ϕ=0.8 over a range of flame speed ratios. Heat release rate is observed to increase with flame speed ratio, as expected, which leads to an increase in flame temperature, but heat loss rate exhibits a non-monotonic trend in which heat loss rate peaks near a flame speed ratio of 0.3.

Figure 8. Heat release rate, flame temperature and heat loss rate as functions of flame speed ratio for associated gas A at ϕ=0.8.

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The results in Fig. 8 demonstrate that the magnitude of heat loss rate alone is insufficient for the prediction of flame instability and extinction. Therefore, flame stability of associated gases was further investigated by quantification of a heat loss ratio (HLR) from the ratio of heat release rate and heat loss rate. HLR was calculated for the three associated gas mixtures at all tested equivalence ratios over a wide range of flame speed ratios. The results are presented in Figs. 9a, 9b and 9c for associated gases A, B and C, respectively. Operating points are distinguished as stable (filled markers) or unstable (open markers) based upon uncertainty in standoff distance, where the instability manifests as development of cellular flame structures and planar pulsations. Results show that HLR increases as the flame speed ratio decreases, which is supported by previous numerical studies of flat flame instability due to thermal-diffusive effects [41]. Values at the lowest flame speed ratios for each equivalence ratio are observed to deviate from a monotonic trend for all associated gas mixtures due to the flame being highly unstable and close to extinguishment as these points; therefore, the measurement of HLR has large uncertainty at these points. The ranges of HLR over which stable flames are obtained and unstable flames exist are widened as equivalence ratio is increased. Specifically, stoichiometric and mildly rich flames remain stable with higher HLR at lower flame speed ratios relative to leaner flames which become unstable and extinguish at significantly lower HLR and higher flame speed 33


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ratios. This phenomenon can be understood in the context of flame temperature; richer flames within this range of equivalence ratios have higher flame temperatures and can sustain greater specific heat loss per unit of fuel or heat release before becoming unstable. The trends observed in this research are in good qualitative agreement with studies that predict instability when flame temperatures below approximately 1550 K are reached due to heat loss, regardless of equivalence ratio [20]. This study characterizes this stability limit as a function of equivalence ratio for increased resolution of this phenomenon and resolves two HLR limits for loss of stability and extinction. These critical HLR points are useful for combustor design, as excessive HLR will lead first to unstable combustion, with low efficiency, unburned fuel and high levels of pollutants, and subsequently extinction where combustion is not sustained.

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Figure 9. Heat loss ratio (HLR) over a range of flame speed ratios for a) associated gas A, b) associated gas B, and c) associated gas C.

4. CONCLUSIONS A porous plug flat flame burner facility was employed in this study to measure laminar flame speeds of associated gas mixtures with high levels of C2-C4 alkanes. Validation of the experimental setup and the measurement technique was performed with satisfactory 35


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comparison to numerical data for component gas flame speeds and numerical and analytical model results for standoff distances. Then, adiabatic laminar flame speeds for three associated gas mixtures from the Bakken formation over a range of equivalence ratios from 0.7 to 1.1 were measured. Comparison of experimental and numerical results suggested satisfactory performance of the Aramco 1.3 mechanism for simulating a wide range of associated gas compositions. Additionally, a correlation was proposed for quaternary associated gas mixtures which performed well in modeling of associated gas flame speeds over a range of pressures. The associated gas mixtures were further explored in terms of flame stability for a wide range of equivalence ratios. Heat loss ratios were calculated for a range of flame speed ratios and the limits where flames become unstable and extinguish were determined. Results showed that leaner flames have lower heat loss ratio stability limits as compared to equivalence ratios nearer stoichiometry, and these limits were quantified.

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Combustion Flame Speeds and Stability of Associated Natural Gas

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