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Computational Fluid Dynamics Modeling of Industrial Flares Operated in Stand-By Mode Kanwar Devesh Singh,† Tanaji Dabade,‡ Hitesh Vaid,† Preeti Gangadharan,† Daniel Chen,*,† Helen H. Lou,† Xianchang Li,‡ Kuyen Li,† and Christopher B. Martin§ †

Dan F. Smith Department of Chemical Engineering, ‡Department of Mechanical Engineering, and §Department of Chemistry and Biochemistry, Lamar University, Beaumont, Texas 77710, United States S Supporting Information *

ABSTRACT: Computational fluid dynamics (CFD) was applied to model industrial flares under low-Btu, low-flow rate conditions (stand-by mode). The modeled tests were conducted at the John Zink R&D facility in Tulsa, OK in September 2010, using propylene/Tulsa Natural Gas/nitrogen as vent gases under open-air conditions. This work focuses on CFD modeling using the EDC (Eddy Dissipation Concept) and PDF (Probability Density Function) models to predict the destruction and removal efficiency (DRE), combustion efficiency (CE), and speciated emissions with a reduced 50-species combustion mechanism. Generally, the EDC model underpredicts DRE/CE while the PDF model overpredicts DRE/CE, when compared with measurements. The sources of discrepancies and the challenges to the flare modeling in the stand-by mode are discussed. In view of the significant differences between the measured and modeled results, further investigations involving a better domain with a refined mesh, a different turbulence model, or a combination of EDC/PDF models are warranted.

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INTRODUCTION Flaring is the most widely used operation in the oil and gas industry to dispose of unwanted gases. It is basically an open-air combustion system that keeps harmful gases such as methane, ethylene, propylene, etc. from entering into the atmosphere by efficiently oxidizing these gases into carbon dioxide and water. However, this seemingly simple process is complicated, since flare performance is affected by a wide range of parameters, most of which never remain constant. The most common among these variables are the fuel to air/steam-assist ratios,1 the heating value of the fuel, the jet velocity, and meteorological conditions.2 As the flare performance decreases, the flares combust less waste gases entering the atmosphere and therefore produce unwanted intermediates3 and radicals (such as HCHO, OH, NO, etc.). DRE (Destruction and Removal Efficiency) and CE (Combustion Efficiency) are the two most commonly used parameters to quantify the flare performance.4 While it is assumed that a flare operating under its designed conditions and in compliance with 40 CFR § 60.185 may achieve 98% DRE or higher,6 a flare operating outside of these parameters may have a DRE lower than 98%.7 Furthermore, DRE may drop below 98% even when the flare operation is in compliance with 40 CFR § 60.18.8 Common industrial practices9 for calculating speciated and total VOC (Volatile Organic Compounds) emissions from flaring activities generally apply a simple mass reduction to the VOC species sent to the flares. In the past, high jet velocity (i.e., high momentum) flares have been studied using both experimental setup10−12 and CFD modeling.13 These high momentum flares only represent conditions such as plant startup, shutdown, or emergency, whereas, on normal days, the industrial flares operate in standby mode. In this work, computational fluid dynamics (CFD) methods are used to simulate the operations at stand-by mode (mainly to handle fugitive emissions and normal plant vent © 2012 American Chemical Society

gases). Specifically, low-Btu, low-flow rate propylene/TNG/ nitrogen flare tests conducted during September 2010 in the John Zink test facility in Tulsa, OK,14 were modeled. In these flare performance tests, plume measurements using both remote sensing and direct extraction were carried out to determine flare efficiencies (DRE and CE) for air-assisted and steam-assisted flares. State-of-the-art field measurement techniques were employed including grab sampling, open-path FTIR13,15−17 remote sensing, and Differential Absorption LIDAR (DIAL).18 Various combinations of fuel BTU and flow rates were performed under open-air conditions. This study uses CFD modeling as a predicting tool for the Tulsa flare performance tests. The CFD modeling is further compared with the flare efficiencies reported in the TCEQ 2010 Flare Study Project Final Report.8 For this purpose, commercial CFD packages such as ANSYS FLUENT 13.0 and CHEMKIN were employed. TCEQ 2010 Flare Study. The main objective of the TCEQ 2010 Flare Study was to quantify the impact of certain factors such as fuel-to-air-assist ratio, fuel-to-steam ratio, LHV (Lower Heating Value) of the fuel, etc. on flare performance parameters like DRE (Destruction and Removal Efficiency) and CE (Combustion Efficiency). Numerous test cases were conducted on industrial-scale flares in open air to observe the effect of the aforementioned factors on flare efficiencies. For this purpose, both air-assisted and steam-assisted flares were used and were Special Issue: Industrial Flares Received: Revised: Accepted: Published: 12611

March July 6, July 9, July 9,

9, 2012 2012 2012 2012

dx.doi.org/10.1021/ie300639f | Ind. Eng. Chem. Res. 2012, 51, 12611−12620

Industrial & Engineering Chemistry Research

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Table 1. Conditions of Air-Assisted Test Cases Actual Vent Gas (VG) Flow Rates

a

case

propylene (lb/h)

TNG (lb/h)

nitrogen (lb/h)

total (lb/h)

LHV (Btu/scf)

air assist flow rate (lb/h)

A1.1 A2.1 A2.3 A2.4 A2.5 A3.1 A3.3 A3.6 A4.3 A5.2 A5.3 A6.1

918.88 355.02 352.14 352.87 354.71 181.23 181.23 181.23 298.74 72.29 71.26 117.80

0 0 0 0 0 18.77 18.37 18.76 30.30 7.69 7.55 11.86

0 0 0 0 0 702.55 700.60 704.18 591.10 274.41 271.37 221.21

918.88 355.02 352.14 352.87 354.71 902.55 900.20 904.17 920.14 354.39 350.18 350.87

2107.71 2125.45 2108.22 2112.57 2123.55 338.67 333.86 337.55 562.91 342.86 341.87 583.73

149173 83818 88791 148799 119580 19387 60121 47494 66471 75139 32876 11403

excess air factor, A/Fa crosswind (mph) 10.96 15.94 17.03 28.48 22.77 6.51 20.23 15.94 13.57 63.07 28.01 5.91

12.72 12.84 10.10 10.00 13.28 10.32 11.09 11.88 10.72 2.15 2.50 15.92

A is the actual amount of air-assist and F is the stoichiometric amount of air.

Table 2. Conditions of Steam-Assisted Test Cases Actual Vent Gas (VG) Flow Rates

a

case

propylene (lb/h)

S1.5 S1.8 S3.7 S4.1 S4.3 S5.2 S5.3 S6.1 S7.3

2337 2338 191 491 485 320 312 826 297

TNG (lb/h)

nitrogen (lb/h)

0.00 0.00 18.90 45.00 45.00 33.80 31.70 79.10 29.90

0 0 716 1800 1802 585 578 1456 1084

Steam Flow Rate total (lb/h)

LHV (Btu/scf)

center (lb/h)

upper (lb/h)

steam/VG flow ratea

crosswind (mph)

2337 2338 926 2335 2332 938 922 2361 1410

2145 2146 346 350 346 595 590 609 353

526 506 0 560 567 454 482 518 516

3794 7044 228 536 1879 1580 783 1003 538

1.85 3.23 0.25 0.47 1.05 2.17 1.37 0.64 0.75

8.00 8.60 7.10 5.60 5.20 10.20 9.30 8.80 7.90

Expressed as an assist ratio.

assisted flare test cases. Tables 1 and 2 summarize the conditions of these cases.

operated at 0.1% and 0.25%, respectively, of the rated capacity.19 Primarily, propylene (C3H6) was used as fuel for both flares. In order to lower the LHV of the fuel, TNG (Tulsa Natural Gas) and N2 were used. Both direct and remote sensing measurements were made during the flare test series to determine flare emissions. Flare Efficiencies. Two types of flare efficiencies were monitored and reported during the flare study: CE and DRE. (1) DRE (Destruction and Removal Efficiency) DRE represents the percent of the fuel* destroyed relative to the amount of fuel actually sent to the flare. Using C3H6 as an example, it can be written as

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METHODOLOGY CFD Fundamentals. Computational Fluid Dynamics basically involves solving sets of transport equations using numerical methods, such as Green Gauss or the Least Squares method.20 The governing transport equations are solved for mass, momentum (turbulence), energy, and chemical species. Direct Numerical Simulation (DNS) for the industrial flares is computationally not feasible, because of the time-dependent governing equations. Large Eddy Simulation (LES) modeling in which large eddies are explicitly computed in a time-dependent simulation using the “filtered” Navier−Stokes equations can be applied for industrial flares, but it is computationally expensive. So, in this study, the more popular Reynolds-Averaged-Navier− Stokes (RANS) equations that govern the transport of the averaged flow quantities with the entire range of the scales of turbulence being modeled was used to model turbulence. The RANS model is widely used for its reduced computational time and wide range of practical applications. The basic governing equations in RANS combustion modeling for describing mass, momentum (turbulence), energy, and chemical species are described below. The continuity equation for the RANS model is given in eq 3:

DRE(C3H6) =

amount of C3H6 fed − amount of C3H6 in flue gas amount of C3H6 fed to the flare

(1)

(2) CE (Combustion Efficiency) CE, on the other hand, takes into consideration the percentage of fuel successfully converted to carbon dioxide, the final oxidation product. It is defined as CE =

amount of fuel converted to CO2 amount of fuel fed to the flare

(2)

Flare Test Cases. Of all the test cases completed during the flare study, 21 cases were successfully simulated using CFD methods. These 21 cases involve 12 air-assisted and 9 steam-

∇·(ρv) = 0 12612

(3)



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Table 3. Comparison of EDC and PDF Models EDC (Eddy Dissipation Concept)

PDF (Probability Density Function)

reactions taking place in the flame are governed by the Arrhenius rates incorporates detailed chemical mechanisms molar concentrations are derived from reaction rates, which are calculated using ISAT algorithm any number of inlet streams can be defined computationally very expensive; requires 5−6 days for convergence

where ρ is the density of the fluid and v is the ensembleaveraged velocity vector, which is the sum of the mean (v)̅ and fluctuating velocities (ν′), shown in eq 4:

where Yi is the local mass fraction of each species, Ji̅ the turbulent mass diffusion flux, Ri the net rate of production of species i by chemical reactions, and Si the rate of creation by addition from the dispersed phase and any user-defined sources. This equation is computed when the user-defined function of the reduced mechanism is introduced in the simulation in this study. The Finite Volume Method is used to discretize and solve the governing flow equations. Computational Fluid Dynamics (CFD) Model. All the mentioned simulations were performed using the commercial CFD package ANSYS FLUENT 13.0. The geometry used for the simulation was created and meshed in GAMBIT 2.4.6. All the simulations were performed on a 3D model and only steady-state solutions were obtained. To reduce the computational time, Fluent was run using parallel computing settings. Each case was run on eight local parallel processors. A pressure-based solver with double precision was used for modeling. The turbulence was modeled using the Realizable k−ϵ model.21 Radiation effects were neglected to reduce the computational costs. For the pressure−velocity coupling, the widely used SIMPLE22 algorithm was enabled. Discretization of gradients for constructing values of scalars at the cell faces were computed using the Green-Gauss Cell-based method and the pressure staggering option (PRESTO) was used for pressure discretization. For all other equations, a first-order upwind scheme was used initially, but was later changed to a secondorder upwind scheme. Similarly, the under-relaxation factors were initially set at 0.5 (except for pressure, turbulent viscosity, and body forces, which were kept the same as the default values), and were then gradually brought to their default values with convergence. To describe the chemical state of the flame, CHEMKIN files with detailed reaction mechanism and thermodynamic data were used. Two different types of chemistry-turbulence interaction models were used for simulation. These were the nonpremixed PDF model and the more rigorous, EDC model. The two models are briefly explained below and the comparison can be seen in Table 3. EDC (Eddy Dissipation Concept). The turbulence− chemistry interaction model used in this work is the Eddy Dissipation Concept (EDC) model. The EDC model incorporates detailed chemical mechanisms while modeling reacting turbulent flows. It is the more rigorous of the two mentioned models and, hence, is computationally expensive. The EDC model assumes that the reactions in the flame are occurring in small turbulent structures, called fine scales. The combustion in these fine scales is assumed to be occurring at a constant pressure reactor. The inlet conditions of this reactor are considered to be the current species and temperature in the cell. In general, the reactions taking place in the flame are governed by the Arrhenius rates. These reaction rates are then integrated numerically using ISAT (in situ adaptive tabulation) algorithm. Using the ISAT algorithm for this purpose reduces

(4) v = v ̅ + v′ The ensemble-averaged momentum equation is written as in eq 5:

⎡ ⎛ ⎤ 2 ⎞ ⎜ ⎟ ∇·(ρvv i j) = −∇p + ∇· ⎢μ vi + vj − δij vk − ρvv i j⎥ ⎣ ⎝ ⎦ 3 ⎠

(5)

where p is the local pressure term, μ the viscosity of the fluid, δij the Kronecker delta function, and ρvivj the Reynolds stress term. The Boussinesq hypothesis (eq 6) is a common approach used to relate the Reynolds stresses to mean velocity gradients. ⎛ ∂v ⎛ ∂v ⎞ ∂v ⎞ ⎜ i + j ⎟⎟ − 2 ⎜ρk + μt k ⎟δij −ρvv i j = μt ⎜ ∂xi ⎠ ∂xk ⎠ 3⎝ ⎝ ∂xj

(6)

This hypothesis is used for reducing the computational cost associated with solving the turbulent viscosity (μt). It is used in k−ϵ turbulent modeling, which is followed in this work. In this case, two additional transport equations regarding the turbulence kinetic energy (k) and the turbulence dissipation rate (ϵ) are solved and μt is computed as a function of k and ϵ: The turbulent kinetic energy, k, is defined as 1 k = vv i j (7) 2 For the k−ϵ model, the eddy viscosity is calculated using the Prandtl−Kolmogorov relationship as follows: μt =

ρCμk 2 ϵ

(8)

The other governing equation to be solved is the energy equation (eq 9). The general form of the energy equation is presented below: ∂ (ρE) + ∇·(v (⃗ ρE + p)) ∂t ⎡ ⎤ = ∇·⎢keff ∇T − ∑ hiJi ⃗ + (τeff̅ · v ̅ )⎥ + Sh ⎢⎣ ⎥⎦ j

(9)

where keff is the effective conductivity, Ji⃗ the diffusion flux of species i, hi the enthalpy of species i, and τe̅ ff the effective stress tensor. The last and most important governing transport equation to be solved for industrial flare modeling is the species transport equation: ∂ (ρYi ) + ∇·(ρ v ̅ Yi ) = −∇·Ji + R i + Si ∂t

reactions are governed by a conserved scalar quantity known as mixture fraction not so rigorous molar concentrations are derived from the predicted mixture fraction fields only two inlet streams are allowed, i.e., fuel and oxidizer requires less time for convergence; only 2−3 days

(10) 12613



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the computational time for solving the detailed reaction kinetics. In the EDC model, the chemistry was updated after each iteration. To reduce computational time, the ISAT algorithm was enabled. Most of the integration parameters were kept same as the default value, except the “Maximum Storage”, which was changed to 8000 MBs. It should be noted that all of the cases run using the EDC approach were completed in two stages. Initially, “cold f low” was simulated, meaning that combustion chemistry was disabled during this period. Once a converged cold f low was obtained, the region near the flare stack was patched with a temperature of 1800 K. The idea of patching with higher temperature is similar to providing the fuel with a source of ignition. The EDC chemistry modeling was then enabled and then the combustion of the fuel starts, which further raises the plume temperature. Probability Density Function (PDF)/Mixture Fraction/ Flamelet Model. Although the PDF/Flamelet model is the simpler of the two models, it is not as rigorous in calculating species concentrations. Equations for individual species are not solved separately. Instead, this model assumes that “under a certain set of simplifying assumptions, the instantaneous thermochemical state of the f luid is related to a conserved scalar quantity known as the mixture f raction, f.”23 Hence, molar concentrations of various species are derived from the predicted mixture fraction fields. A preprocessed Probability Density Function (PDF) table takes care of the turbulence chemistry interaction. Reaction Mechanism for C1−C3 Combustion. Reaction mechanisms play a vital role while simulating turbulent combustion operations like flaring. The objective of these reaction mechanisms is to perform detailed kinetic modeling under a wide range of conditions. The reaction conditions may vary upon an extensive range of equivalence ratios, temperatures, and pressures. Under valid conditions, the mechanism must be able to solve the complex combustion chemistry and predict the molar concentration of the species involved. These predicted concentration profiles or values should be within the specified uncertainty of the mechanism. For this work, a reduced reaction mechanism developed by Lou et al.24 was used. The reaction mechanism was generated by combining two widely used combustion mechanisms: GRI 3.025 and USC.26 Descriptions of the two mechanisms are given below. GRI 3.0 Mechanism. The GRI Mech 3.0 was generated by the Gas Research Institute and was optimized for the combustion of natural gas. The mechanism has 325 reactions and 53 species, including various NOx species, and can predict NO and NO2 formation very well during the combustion process. The mechanism performs well for an extensive range of combustion conditions, which has been evaluated using standard mechanism tests. USC Mechanism. The University of Southern California (USC) mechanism consists of 75 species and 469 reactions and is a comprehensive kinetic model for representing ethylene and acetylene combustion. It has been evaluated for predicting combustion properties of both C2 and C3 fuels. The drawback of this mechanism is the absence of NOx chemistry in the mechanism. However, these two mechanisms are not satisfactory for the combustion of propylene required for this study because of the following reasons:

(1) The GRI-3.0 mechanism with 53 species was developed and optimized for the combustion of methane, not propylene. (2) A USC mechanism containing 75 species was optimized for ethylene combustion reactions, but the absence of NOx-producing species in the mechanism does not reflect the reality for flaring in air. Thus, the two mechanisms were combined and then reduced to a 50-species mechanism (LU 1.0). The reduced mechanism agrees very well with experimental data of standard tests such as ignition delay,27 laminar flame speed,28 and adiabatic flame temperature.29 The average absolute percent error (the average of absolute value of percent errors) between experimental data and the LU 1.0 mechanism was found to be 4.73% (see Table 4). Figures 1 and 2 indicate a very good agreement between experimental and predicted values for ignition delay (propylene) and adiabatic flame temperature (ethylene), respectively.30 Table 4. Percent Error of Standard Tests (Reduced Mechanism Versus Experimental) Average Absolute % Error indicators laminar flame speed methane propylene adiabatic flame temperature methane ethylene ignition delay methane ethylene propylene average

LU reduced mechanism vs experimental 3.76 6.30 8.42 2.07 2.09 5.15 5.32 4.73

Figure 1. Ignition delay versus temperature for propylene−air mixture.

Geometry for Flares. Since the main objective of this research was to simulate test cases completed during the Tulsa Flare Study, the dimensions of both air-assisted and steamassisted flares were kept similar to the actual flares used during the tests. The detailed geometry configurations are discussed below. Air-Assisted Flare. To keep the geometry simple, a rectangular domain was built in GAMBIT. The length, width, and height of the geometry were kept as 30 m, 10 m, and 30 m, respectively. The flare was located at 5 m from the left side and 12614



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circular area acted as a source for the air assist. The crosswind flows from left to right side of the domain. The largest velocity and species concentration gradients were located in regions near the stack. To increase the accuracy of the reacting flow profile, the mesh density near the stack was kept higher relative to other zones in the domain. The grid had 840 000 cells and was successfully checked for skewness. Steam-Assisted Flare. The CFD domain for steamassisted flare cases was kept similar to the air-based domain. Few changes were made in the stack configuration. The stack height was reduced to 5 m, which also reduced the height of the domain to 20 m. The full domain can be seen in Figure 5. Major changes were made in the fuel inlet configuration. To replicate the original steam-assisted flare, 20 steam nozzles (acting as sources for “Upper Steam”) were added around the stack. All the nozzles are angled at 45° and point toward the stack. Center steam and fuel are provided from the stack top surface. The steam nozzles and the various inlet surfaces can be seen in Figure 6. Fluent Post Processing. To compare the simulation results with experiments, data were obtained during the postprocessing part of the simulation procedure. Since CE and DRE values were to be compared, the mass flow rates of various species entering and exiting the domain were required. For this purpose, the surface integral of the speciated flow rate (over respective surfaces) provided the flow rates of the fuel and pilot. Moreover, the final combustion products were taken as the surface integral over all the pressure outlet surfaces. The flow rates of fuel and CO2 at these surfaces were then used in eqs 1 and 2 to calculate DRE and CE for each case.

Figure 2. Adiabatic flame temperature versus equivalence ratio for ethylene−air mixture.

at the center of the width. The CFD domain for the air-assisted cases is shown in Figure 3. This configuration provided enough time for the flame chemistry to be completed inside the domain.

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RESULTS The simulation results of air-assisted and steam-assisted flare cases are discussed below. Comparison of Predicted and Measured DRE/CE Values. Tables 5 and 6 compare the DRE and CE values predicted by the CFD simulations with analytical results generated from field sampling during the TCEQ 2010 Flare Study Project at the John Zink facility in Tulsa, OK. Also, the normalized emission rates and carbon distribution among the combustion products (only air-assisted test cases) are shown in Table 7. CE/DRE as a Function of Air-Assist Flow Rate. Figures 7 and 8 show the DRE/CE values as a function of air-assist flow rate for the air-assisted test cases. Although the modeled DRE values seem to follow the same trend, the predicted DREs are ∼12% lower, compared to those measured using the EDC model. CE/DRE as a Function of the Lower Heating Value (LHV). Similar to the previous plots of efficiencies versus the air assist flow rate, the variation of DRE/CE with LHV also seems to follow the trend closely, but the difference in predicted and measured values remains at ∼12%. The plots are shown for the air-assisted test cases in Figures 9 and 10. Steam-Assisted Cases. Figures 11−14 show the same plots when the steam-assisted test cases were run.

Figure 3. CFD domain for air-assisted cases.

The height of the flare stack was kept as 10 m, and the diameter was kept as 1.05 m. To avoid complex geometry and, hence, an unnecessarily large number of cells, the fuel jet opening was modified. A simpler ring-shaped geometry was built, as shown in Figure 4. The original areas of the pilot, fuel jet, and air assist were kept the same by changing the diameters. The pilot stream was given from the centermost surface, and the fuel was sent into the domain from the ring. The rest of the

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DISCUSSION

The uncertainties in the results include those given by the CFD mechanisms, the CFD models, and the 2010 Tulsa Flare tests. Basically, the mechanism uncertainty factor depends on residence, temperature, fuel composition, species, etc. For

Figure 4. Side view of an air-assisted stack, showing the three inlet surfaces. 12615



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Figure 5. Computational fluid dynamics (CFD) domain for steam-assisted cases.

Figure 6. Side view of a steam-assisted stack, showing the three inlet surfaces.

Table 5. Comparison of Predicted and Measured DRE and CE Values of Air-Assisted Cases Destruction and Removal Efficiency, DRE (%)

Combustion Efficiency, CE (%)

Simulation test point

flow rate (lb/h)

LHV (Btu/scf)

EDC

A1.1 A2.1 A2.3 A2.4 A2.5 A3.1 A3.3 A3.6 A4.3 A5.2 A5.3 A6.1

149 173 83 818 88 791 148 799 119 580 19 387 60 121 47 494 66 472 75 140 32 876 11 404

2108 2125 2108 2113 2124 339 334 338 563 343 342 584

78.65 84.14 87.42 81.82 82.95

76.11

Simulation PDF

measured

EDC 59.98 63.97 77.18 72.42 52.54

100.00 100.00 100.00 100.00 100.00 100.00 100.00

98.06 97.15 96.19 92.26 95.09 99.56 88.13 91.73 93.77 69.18 82.32 99.71

66.91

PDF

measured

100.00 100.00 100.00 100.00 100.00 100.00 100.00

96.72 95.54 94.02 87.64 91.84 99.08 84.68 88.88 91.50 62.48 78.44 99.32

deviation ranges from 0.1% to 8.3% for DRE and from 0.1% to 9.2% for CE, as given in the TCEQ 2010 Flare Study Final Report. The reported repeatability, as represented by the standard deviations of test results, is deemed as measurement precision. For measurement uncertainty, the accuracy for CO, CO2, C3H6 given by the vendors (e.g., ARI) in the 2010 Comprehensive Flare Study QAPP is adopted in Table 8. Generally, the EDC model used for the air-assisted cases underpredicts DRE by 6%−19%, with an average of 12%. The same model underpredicts CE by 12%−39%, with an average of

major species, generally, these mechanisms can reflect laboratory data within ±10% for CO, within ±15% for NO, etc., which are generally accepted in the combustion chemistry community (see Table 8). Using a fairly typical flare mole fraction data (CO2, 0.06; CO, 0.01; CH4, 0.03; C3H6, 0.03), the CFD prediction and Tulsa flare test uncertainties for DRE and CE were estimated (see Table 9).18,19,31 Using the combined uncertainties, the expected discrepancies between the predicted and measured DRE and CE values are ±25% and ±39%, respectively. Note that the percent standard 12616



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Table 6. Comparison of Predicted and Measured DRE and CE Values of Steam-Assisted Test Cases Destruction and Removal Efficiency, DRE (%) test point S1.5 S1.8 S3.7 S4.1 S4.3 S5.2 S5.3 S6.1 S7.3 a

a

Combustion Efficiency, CE (%)

flow rate (lb/h)

LHV (Btu/scf)

simulation − PDF model

measured

simulation − PDF model

measured

4320 7550 228 1096 2447 2035 1264 1521 1054

2145 2146 346 350 346 595 590 609 353

100.00 100.00 100.00 100.00 100.00 100.00 99.97 99.98 99.99

99.90 97.80 99.50 96.40 27.30 38.10 89.20 99.50 71.30

99.90 100.00 100.00 100.00 100.00 100.00 93.05 95.85 99.62

99.90 95.70 99.20 95.00 21.60 32.20 86.60 99.20 71.30

The EDC model predicts DRE = 99.63% and CE = 97.38% for S1.5.

Table 7. Normalized Emission Rates and Carbon Distribution of Air-Assisted Cases Normalized Emission Rates (kg/kg C3H6 in) species CO THC CH2O C2H4 HOx

A1.1 2.86 2.72 1.72 1.08 8.41

× × × × ×

10−1 10−1 10−2 10−2 10−3

A2.1 1.90 2.78 1.21 1.27 8.07

× × × × ×

10−1 10−1 10−2 10−2 10−3

A2.3

A2.4

1.25 × 10−1 1.71 × 10−1 7.16 × 10−3 1.18 × 10−2 4.97 × 10−3 Carbon Distribution (%)

1.29 2.15 4.06 1.17 4.71

× × × × ×

10−1 10−1 10−3 10−2 10−3

A2.5 4.03 2.93 1.99 1.77 1.48

× × × × ×

10−1 10−1 10−2 10−2 10−2

A5.3 1.29 2.71 1.03 6.62 7.18

× × × × ×

10−1 10−1 10−2 10−3 10−3

species

A1.1

A2.1

A2.3

A2.4

A2.5

A5.3

CO2 CO2 THC CO

59.98 59.98 25.74 14.28

63.97 63.97 26.55 9.48

77.18 77.18 16.58 6.24

72.42 72.42 21.11 6.47

52.54 52.54 27.31 20.15

66.91 66.91 26.48 6.61

Figure 7. Destruction and removal efficiency (DRE), as a function of the air-assisted flow rate (measured vs CFD, air-assisted cases).

Figure 9. DRE, as a function of the lower heating value (LHV) (measured vs CFD, air-assisted cases).

Figure 8. Combustion efficiency (CE), as a function of the air-assisted flow rate (measured vs CFD, air-assisted cases).

Figure 10. CE, as a function of the lower heating value (LHV) (measured vs CFD, air-assisted cases). 12617



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Figure 11. DRE, as a function of the steam-assisted flow rate (measured vs CFD, steam-assisted cases).

Figure 14. CE, as a function of LHV (measured vs CFD, steamassisted cases).

Table 8. Uncertainties in Species Prediction and Measurement

Figure 12. CE, as a function of the steam-assisted flow rate (measured vs CFD, steam-assisted cases).

species

mechanism uncertainty (%)

prediction uncertainty (%) (mechanism + CFD)

AQRP measurement uncertainty (%)

CO2 CO CH4 C3H6 H2O H2 OH NO O2

4 10 0.005a 10 4 10 10 15 0.004a

6.00 15.00 0.0075a 15.00 6.00 15.00 15.00 25.00 0.006a

10 10 10 10 15 15 15 5 2

a

Note: CH4 and O2 prediction uncertainties are given in terms of mole fraction.

Table 9. Uncertainty Estimates for Prediction and Measurementa uncertainty Destruction and Removal Efficiency (DRE) Combustion Efficiency (CE) a

prediction (%)

measurement (%)

±15.00

±10.00

±19.00

±20.00

Using data taken from refs 18, 19, 24, 25, and 29.

systems with relatively fast chemistry. The model thus fails to capture deep nonequilibrium effects such as ignition, extinction, and slow chemistry (like NOx/radical formation).23 This approach is appropriate only at high temperatures (2100− 2400 K) and, hence, is not suitable for the low heating value (LHV) and high air-/steam-assisted flare cases where the modeled temperatures are in the range of 1600−1950 K. On the other hand, the EDC approach underpredicts the DRE/CE values. This chemistry−turbulence interaction approach is highly rigorous and capable of closely simulating real flames. However, circumstances in implementing this model can affect the final results. The main potential cause appears to be the very low fuel flow rates coupled with high assistance from the air/steam used during the flare study made the convergence of the EDC model slow or even impossible. Furthermore, the LHV values were kept very low in most of the test cases, which made the flame unsustainable in many EDC modeling cases. Even though the EDC model underpredicts the experimental results (in all cases except steam case S 1.5) in low LHV/low jet velocity flares in this study, the same EDC model

Figure 13. DRE, as a function of LHV (measured vs CFD, steamassisted cases).

25%. On the other hand, using the PDF model, the mean deviations of the predicted DRE and CE values from the measured values are 16% and 18%, respectively (see the Supporting Information). It is observed that the PDF model almost universally overpredicts the CE and DRE values, compared to the measured values (except in Case S 6.1, where PDF underpredicts CE by 3%). The reason for the overprediction can be traced from the underlying assumption of the PDF model used during the simulation. The Steady Laminar Flamelet approach, which is a submodel of the PDF model, was used to incorporate the chemical kinetic effects into the flame. However, this steady laminar flamelet approach is suitable for modeling combustion 12618



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has been used numerous times for flare modeling that routinely gives >98% combustion efficiencies for high LHV/high jet velocity flares.32 The large simulation domain with a relatively small active combustion zone leads to a large number of cells (>2 million) that contribute to the slow convergence and relatively large carbon balance errors (sometimes as large as 10% and need to be further normalized). This situation can be improved in future studies by replacing the current domain with a cylindrical domain, which is more congruent with the cylindrical stack at the center and, hence, is capable of a refined and structured mesh. The grab sampling method used in the Tulsa flare tests may also lead to discrepancies between the measurements and the model predictions. During the TCEQ 2010 Flare Study, local sampling was conducted for direct extraction using a collector (suction tube) at various locations under variable wind conditions. The DRE and CE were calculated based on concentration ratios as shown in eqs 1118 and 12: DRE (%) =

(C3H6)in − (C3H6)plume (C3H6)in

Article

CONCLUSION Compared to the 2010 Tulsa flare test cases, the EDC model underpredicts the destruction and removal efficiency (DRE) of air-assisted cases by 6%−19%, with an average of 12%. It underpredicts the combustion efficiency (CE) by 12%−39%, with an average of 25%. Comparing the EDC results with measured results, both DRE and CE are within the uncertainty limits (±25% and ±39%, respectively). The potential causes for the large discrepancies may be the low flow rates, low heating values, high air/steam assists, large number of simulation cells coupled with complex chemistry/transport phenomena, and the difference between local sampling and the full surface integration (CFD post-processing). The Probability Density Function (PDF) model is not suitable for modeling low-flow-rate low-heating-value flares, because the underlying assumption of infinitely fast combustion, while valid for high temperatures (>2100 K), is not appropriate at the modeled temperature range (1600−1950 K). Contrary to the EDC model, the PDF model overpredicts the DRE value by 0.1%−72%, with an average of 16%. It overpredicts the CE value by 0%−78%, with an average of 18%. As a result, the PDF model predicts little or no intermediate species and radicals such as formaldehyde, OH, NO, etc. However, it does appear that measured DREs/CEs from the TCEQ 2010 Flare Study fall somewhere between the EDC and PDF model predictions under low-jet-velocity, lowBTU conditions. In view of the significant differences between the TCEQ 2010 Flare Study measurements and the present CFD model results, further investigations are warranted. Future studies involving a cylindrical domain with a more-efficient, structured mesh must be explored. Next, the Large Eddy Simulation turbulence model, which is a transient formulation method, has the potential to give better results, although it is computationally very intensive. Third, combining the two models, PDF and EDC for simulating a low jet and low LHV flare is a viable option. An initial flame developed by the PDF model can be put into more rigorous chemistry-turbulence interaction using the EDC model.

× 100 (11)

Here, (C3H6)in rerpesents the mass flow rate of C3H6 in the vent gas entering the flare and (C3H6)plume represents the mass flow rate of C3H6 found in the flare plume after combustion has ceased. CE (%) = CO2 (plume) × 100 CO2 (plume) + CO(plume) + ∑ hydrocarbons(plume) (12)

Here, CO2(plume) is the volume concentration of carbon dioxide in the plume (ppmv), CO(plume) the volume concentration of carbon monoxide in the plume (ppmv), and ∑hydrocarbons(plume) the volume concentration of all the unburned hydrocarbons in the plume multiplied by the number of carbons in the hydrocarbon (ppmv). The measurements were carried out at certain carefully selected locations away from the plume (e.g., collector inlet temperature 105−150 °C) and some variations of eqs 11 and 12 (e.g., propylene to carbon monoxide and methane to carbon monoxide ratios) were also used.18 In contrast, the CFD-predicted DRE and CE values were calculated from eqs 1 and 2, based on emission mass flow rates, using rigorous surface integration. Future study based on CFD simulation to explore the differences between local sampling at various selected locations and the full pressure outlet surfaces integration are thus warranted. In future studies, a few modifications can be explored for simulating low BTU and low flow rate flares: (1) Cylindrical geometries/domains with more efficient, structured meshes can be used. (2) Large Eddy Simulation turbulence model, a transient formulation method, may give better results, although it is computationally more intensive. (3) A sustainable flame can be initiated using the PDF model. Once converged, the same case can be restarted using the EDC model, which will refine the flame profile using the more-detailed approach.

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ASSOCIATED CONTENT

* Supporting Information S

For boundary conditions and model parameters used during the CFD simulation, refer to the supporting document. This information is available free of charge via the Internet at http:// pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 409-880-8786. Fax: 409-880-2197. E-mail: daniel.chen@ lamar.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The preparation of this report is based on work supported by the State of Texas through the Air Quality Research Program administered by The University of Texas at Austin by means of a Grant from the Texas Commission on Environmental Quality (TCEQ). The authors also gratefully acknowledge the financial support from TCEQ Supplemental Environmental Program 12619



Article

(20) Ferziger, J. H.; Peric, M. Computational Methods for Fluid Dynamics, 3rd ed.; Springer: Berlin, 2002. (21) FLUENT 6.2, User’s Guide; Fluent, Inc., 2005. (22) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; McGraw−Hill: New York, 1980. (23) FLUENT 6.2, Theory Guide; Fluent, Inc., 2005. (24) Lou, H. H.; Martin, C. B.; Chen, D.; Li, K.; Li, X.; Vaid, H.; Kumar, A. T. Singh, K. D.; Bean, D. P. A Reduced Reaction Mechanism for the Simulation in Ethylene Flare Combustion. Clean Technol. Environ. Policy 2012, 14 (2), 229−239 (DOI: 10.1007/ s10098-011-0394-9). (25) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.; Lissianski, V. V.; Qin, Z. GRI-Mech 3.0. Available via the Internet at http://www.me.berkeley.edu/gri_mech/. (26) Davis, S. G.; Law, C. K.; Wang, H. Reaction Mechanism of C3 Fuel Combustion. Available via the Internet at http://ignis.usc.edu/ Mechanisms/C3/c3.html. (27) Qin., Z; Yang., H; Gardiner, C. Measurement and modeling of shock-tube ignition delay for propene. Combust. Flame 2001, 124, 246−254. (28) Davis, S. G.; Law, C. K. Determination of and Fuel Structure Effects on Laminar Flame Speeds of C1 to C8 Hydrocarbons. Combust. Sci. Technol. 1998, 140 (1), 427−449. (29) Law, C. K.; Makino, A.; Lu, T. F. On the Off-Stoichiometric Peaking of Adiabatic Flame Temperature. Presented at The 4th Joint Meeting of the U.S. Sections of the Combustion Institute, Paper No. 1844, Drexel University, Philadelphia, PA, March 2005. (30) Lou, H. H.; Chen, D.; Martin, C. B.; Li, X.; Li, K.; Vaid, H.; Kumar, A. T. Singh, K. D. Validation of a Reduced Combustion Mechanism for Light Hydrocarbons. Clean Technol. Environ. Policy 2011, DOI: 10.1007/s10098-011-0441-6. (31) Quality Assurance Project Plan, Air Quality Research Program (AQRP) Project No. 10-022, Lamar University, Beaumont, TX, February 12, 2011. (32) Flare Speciation and Air Quality Modeling, Quarterly Report, TCEQ SEP Agreement No. 2009-009, June 30, 2012.

(SEP Agreement No. 2009-009) and the Texas Air Research Center (TARC Grant No. 079LUB0096A).

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