A Validation of Flare Combustion Efficiency Simulations

Our objective is to predict the combustion efficiency of industrial flares by using Large Eddy Simulations (LES). The practical utility of the results of a computer simulation is proportional to the degree to which the error and uncertainty in the simulation results have been quantified by validation with experimental data. The available combustion efficiency data from flare experiments is both expensive and sparse. The International Flare Consortium has recently released experimental data on tests performed at the CANMET wind tunnel flare facility. For this paper we have used experimental data from the 4 inch flare tests for measured outlet species concentrations to obtain combustion efficiency as a function of crosswind velocity. We have also included data from buoyant helium plumes measured by Sandia National Laboratory in the validation hierarchy. We have used this validation process to demonstrate and advocate a validation procedure that is philosophically influenced by the Scientific Method, made quantitatively rigorous by Bayesian Inference, but made simple and practical through the use of a consistency constraint. The consistency constraint requires all experiments and all simulations to be bounded by their individual experimental uncertainty. This approach draws on prior information to exploit the consistency requirement among the available experimental data sets and the simulations of these sets to quantify the uncertainty in model parameters, boundary conditions and experimental error and simulation outputs. The final result is a predictive capability for flare combustion efficiency where no experimental data are available but where the validation process produces error bars for the predicted combustion efficiency.

A V A L I D A T I O N O F F L A R E C O M B U S T I O N E F F I C I E N C Y S I M U L A T I O N S Anchal Jatale, Philip Smith, Jeremy Thornock, Sean Smith The Institute for Clean & Secure Energy The University of Utah A B S T R A C T Our objective is to predict the combustion efficiency of industrial flares by using Large Eddy Simulations (LES). The practical utility of the results of a computer simulation is proportional to the degree to which the error and uncertainty in the simulation results have been quantified by validation with experimental data. The available combustion efficiency data from flare experiments is both expensive and sparse. The International Flare Consortium has recently released experimental data on tests performed at the CANMET wind tunnel flare facility. For this paper we have used experimental data from the 4 inch flare tests for measured outlet species concentrations to obtain combustion efficiency as a function of crosswind velocity. We have also included data from buoyant helium plumes measured by Sandia National Laboratory in the validation hierarchy. We have used this validation process to demonstrate and advocate a validation procedure that is philosophically influenced by the Scientific Method, made quantitatively rigorous by Bayesian Inference, but made simple and practical through the use of a consistency constraint. The consistency constraint requires all experiments and all simulations to be bounded by their individual experimental uncertainty. This approach draws on prior information to exploit the consistency requirement among the available experimental data sets and the simulations of these sets to quantify the uncertainty in model parameters, boundary conditions and experimental error and simulation outputs. The final result is a predictive capability for flare combustion efficiency where no experimental data are available but where the validation process produces error bars for the predicted combustion efficiency. B A C K G R O U N D Flaring waste streams of combustable material is an important control practice for destroying unwanted hydrocarbons and other combustable material released during hydrocarbon and petrochemical processing operations in an effective and safe manner in the open atmospherei. The need for effective disposal of gases stems to meet the environmental regulations since methane is 20 times more effective in trapping heat in the atmosphere, thus results in potential global warming, compared to the combustion products such as CO2ii. Hence, both government and industrial personnel are concerned with the effect of flaring hydrocarbon on the air quality. Combustion efficiency is a most common measure effectiveness of flaring systems. All studies performed to date have reached the conclusion that the proper operation of such flares produces near complete conversion of the hydrocarbons to combustion products. Thus, the focus of the US EPA in regulating flares has been to define proper operational procedures, assuming that if version: Monday, August 27, 2012 i Charles, E. Baukal Jr.,The John Zink Combustion Hand Book, CRC Press, p. 589- 634, 2001. ii U.S. Environmental Protection Agency, Greenhouse Gases and Global Warming Potential Values , http://www.epa.gov. operated properly, the combustion efficiency would be near 100%. This proper operation has been defined in USEPA's 40CFR60.18 "General Control Device Requirements."iii, iv However, defining proper operating procedures to ensure high combustion efficiency for the wide range of conditions that exist for actual flare operations is surely not only difficult (maybe impossible) but unwisev. Since the regulatory goal is to achieve the highest possible combustion efficiency, it would seem wise to encourage creative technical solutions by promoting changes in both design and operations to achieve ever increasing combustion efficiency under an ever widening range of operating conditions. T H E R O L E O F S I M U L A T I O N Flare research over the past decade has increasingly illustrated that there is likely no one simple operational parameter (or even a few parameters) that will characterize the combustion behavior of flare flames.vi Simple correlations are unobtainable because of the complexity of the nonlinear mixing, reaction, and heat transfer present in operating flare flames. This complexity motivates the need to accurately measure combustion efficiency from operating flares so that the effect of different designs and operations can be quantified. However, this same complexity, makes such measurements difficult. To date there is no technology that has been been validated at providing quantitative combustion efficiency measurements from operating, open-air, flare flames. Flare emission measurement have various problems like: effect of high temperatures and radiant heat on test equipment, the meandering and irregular nature of flare flames due to external winds and intrinsic turbulence, the undefined dilution of flare emission plume with ambient air, lack of suitable sampling locations due to flare and/or flame heights. Thus it is difficult to measure combustion efficiency as one need to know simultaneously the composition and velocity to obtain a mass flux surrounding the reacting flare and as measurable combustion reactants or products gets diluted in the surrounding atmosphere. Most of the experimental studies on measuring carbon efficiency, flame shape and size are only limited to laboratory scale flares.vii,viii,ix ,x However, the wide variety of fuel composition, fuel velocities, ambient wind conditions and the size of the flare equipment make experimental studies not feasible for designing industrial flare equipment. Advances in computational combustion aid to tackle this problem cost- effectively using numerical simulations Computing the efficiency accurately through traditional computational fluid dynamics (CFD) simulation tools that are based on Reynolds-Averaged Navier-Stokes (RANS) approaches codes is difficult. The large-scale mixing due to vortical coherent structures in V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 2 of 9 iii 51 Federal Register (FR) 2701, Jan. 21, 1986, as amended at 63 FR 24444, May 4, 1998; 65 FR 61752, Oct. 17, 2000; 73 FR 78209, Dec. 22, 2008 iv made available online by the National Archives and Records Administration at http://ecfr.gpoaccess.gov/ v For a further discussion of current EPA regulations see http://home.earthlink.net/~jim.seebold/id20.html . vi The American Flame Research Committee (AFRC) of the International Flame Foundation (IFRF) has carried on a focused series of flare research forums. The papers from these forums are available online at http://www.afrc.net/index.jsp?page=1;&l2nid=6; vii Johnson, M. R., and Kostiuk, L. W., Efficiencies of Low-Momentum Jet Diffusion Flames in Crosswinds, Combustion and Flame, Vol. 123, pp.189-200, 2000. viii Bourguignon, E., Johnson, M. R., and Kostiuk, L. W., The Use of Closed-Loop Wind Tunnel for Measuring the Combustion Efficiency of Flames in a Cross Flow, Combustion and Flame, Vol. 119, pp.319-334, 1999. ix Johnson, M. R., and Kostuik, L. W., A Parametric Model for the Efficiency of a Flare in Crosswind, Proceedings of the Combustion Institute, Vol. 29, pp. 1943- 1950, 2002. x Majeski, A. J., Wilson, D. J., and Kostuik, L. W., Size and Trajectory of a Flare in a Cross Flow, Combustion Canada 1999, Calgary Alberta, May 1999. these flames is not readily reduced to steady-state CFD calculations with RANS. Also, by time-averaging the equations, unsteady information such as instantaneous mixing and flame shape cannot be captured. Industrial flares operate under turbulent flow conditions, which involve wide ranges of length and time scales. The biggest of these scales can be on the order of diameter of the flare tip and the smallest is determined by the viscosity. In general, it is a non-premixed combustion system where the reaction rates are limited by mixing rates. Detailed chemical mechanisms of combustion reactions involve several thousand elementary reactions steps among hundreds of species with a wide range of time scales. These chemical reactions are exothermic, resulting in both convective and radiative heat transfer.xi All of these processes are highly coupled. For example, turbulence enhances mixing and thus chemical reactions. Chemical reaction changes the temperature through the amount of heat generated, and this changes the density and thus the intensity of mixing via turbulence. Resolving all the length and time scales in practical turbulent combustion applications is not possible even on supercomputers for these reasons. Instead, important features of the flame can be captured by resolving large length and time scales responsible for controlling the dynamics, with models for more homogenous smaller scales. This type of numerical scheme is given by Large Eddy Simulation (LES). If one is to rely on simulations to obtain combustion efficiency from flares, we are are left with the nagging question of the accuracy of the simulation. Only a formal method of validating the simulation by comparison with measured data can produce the confidence for extrapolation to operating flares. This validation must include the uncertainty in the measurements and in the simulations to be of practical value to any end user. This paper describes an approach to validation with uncertainty quantification of combustion efficiency from experimental flare data by bringing together the latest available flare data with LES computer simulation technologies and with the most recent advances in the science of validation and uncertainty quantification. E X P E R I M E N T S The data for this analysis comes from the newly released data from the International Flare Consortium where measurements were made in the flare testing facility (FTF) operated by CANMET consisting of a wind tunnel with a high capacity fan feeding through flow straighteners into the working section. The fan is capable of delivering airflow of 23.6 m3/s (50,000 cfm) at 1.5 kPa. The volumetric airflow is measured using a differential pressure flow meter. The working section is 1.2 m wide and 8.2 m long, with ceiling height 1.8 m. This produces a range of crosswind speed up to 45 km/h. The flare pipe is situated near the front of the working section. Flare pipes are 1′′ Nom., 2′′ Nom., and 4′′ Nom., carbon steel, usually 1.0 m long.xii This configuration allows full development of the flare flame, without impingement on the walls, ceiling, or floor of the working section. More complicated flare tips can be used, for example having a windshield over the pipe opening. Windows provide visual access to the flare flame. The facility is illustrated schematically in Figure 1. V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 3 of 9 xi P R. Desam, P. J. Smith, S. G. Borodai and S. Kumar, Computing Flare Dynamics Using Large Eddy Simulations, Combustion and Reaction Simulations (CRSIM) Research Group University of Utah, Salt Lake City, 2003 xii P.E.G. Gogolek , A.C.S. Hayden, Performance of Flare Flames in a Crosswind With Nitrogen Dilution, Journal of Canadian Petroleum Technology, August 2004, Volume 43, No. 8. Figure 1: Schematic of Flare Testing Facility. The set of experiments used in this paper were performed with a 4 inch diameter pipe of 40 inches (1.016 m). The composition of gas used for flaring is (vol %): CH4-95.33 %, C2H6-2.1%, C3H8-0.13%, C4H10-0.02%, N2-1.8%, CO2-0.62%. The fuel flow is coming in with flow rate of 20 Kg/h. The stack gases are sampled using a 0.46 m long sintered metal tube placed at the centerline of the stack. The sampled gases are passed to a bank of analyzers, including O2 (paramagnetic), CO and CO2 (IRD), CH4, and NMHC (FID). Figure 2 shows the data collected for this set of experiments, with respect to different crosswind velocities. Because of the extremely high dilution by the crosswind, the ambient air composition was measured as well. The airflow in the working section has been designed to have very low turbulence intensity. Grids are used to produce a turbulent wind in the working section. The grids are steel slats, with width and spacing to produce the desired turbulence intensity and integral length scale. The conversion efficiency of a flare flame was defined as the mass flow rate of carbon as CO2 in the stack gas, less the CO2 in the inlet air, divided by the flowrate of carbon into the flame in the fuel. Figure 2: Experimental Data with respect to the crosswind: (From top left to bottom right) Efficiency, CO2 concentration, CH4 concentration, O2 concentration. The simulations were modeled for this facility. The domain is of the same dimensions as the original facility. Fuel is coming out of the 1 m long and 4inch wide pipe with flow rate of 20 Kg/h at 300K. The air comes in at 287 K and contains 350-400 PPM of CO2, V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 4 of 9 similar to current concentration in the atmosphere. This CO2 is taken into consideration while computing the combustion efficiency. The domain was meshed using a trimmer meshing scheme with approximately 10.5 million cells. In order to keep the problem size realistic for such huge domain, regions with mostly steady flow have coarser mesh. These regions changes with change in crosswind velocities. The trimmer meshing model utilizes a template mesh constructed from hexahedral cells from which it cuts or trims the core mesh based on the starting input surface. The template mesh contains refinement in areas of curvature and close proximity based upon the surface cell sizes, as well as fixed cell sizes based on the boundary surface. Growth parameters can be used to control the transitioning of the mesh cell sizes from small to big both at the surface and far field. A maximum and/or minimum cell size can be supplied as well to control the upper and lower cell size bounds. The resulting mesh is composed predominantly of hexahedral cells with trimmed cells next to the surface. Trimmed cells are polyhedral cells but can usually be recognized as hexahedral cells with one or more corners and/or edges cut off. T H E V A L I D A T I O N We have performed quantitative validation through the use of a consistency constraint. We draw on prior information and exploit a consistency requirement among the available experimental data sets and the simulations of these sets to quantify the uncertainty in model parameters, scenario parameters, experimental observations and simulation outputs to produce predictivity.xiii The consistency constraint that measures and produces the posterior uncertainty that is consistent with all experiments and all simulations is similar to the constraints used in data collaboration approachxiv,xv ,xvi : Where e denotes a physical experiment and ye a property of interest that is measured in the experiment. Major difference between Data Collaboration (DC) and our consistency test is that DC is a deterministic method which involves domain-decomposition iteration around two main steps: a surrogate modeling step which converts the validation and prediction models into algebraic models; and an optimization step to solve the constrained optimization problems. Whereas the consistency test here uses randomness (Monte Carlo method) to solve similar equations. This is good for small dimensions and DC was specifically created for higher dimension problem. The consistency test used here begins with specifying the range of active variables and sampling of experimental data to get uncertainties present in them. This is done with the help of mean and standard deviation with a user specified confidence range. Now a 87 !ℵ = min !!!"#$%&'!!"!!"#$%&'(#%$: !! ≥ !! ≥ !!!, !"#!! = 1,…. . , ! 1 − ! !! ≥ !! ! − !! ≥ !! 1 − ! , !"#!!"#ℎ!! ∈ ℵ !!!!!!!!!!!!!!!!!!!!!!!!(36) Where E denotes a physical experiment and Ye a property of interest that is measured in the experiment. The value of Ye is designated ye, and the experimentally measured value is de. The deviation of the measured value from ye has lower and upper bounds: !! ≤ !! − !! ≤ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(37) A dataset unit Ue(de; ue; le; Me) is associated with experiment E and consists of the measured value, the reported uncertainty in the measurement (upper bound and lower bound), and a mathematical model, respectively. A dataset is a collection of dataset units D {(de; ue; le;Me)}. The set of all indices e is ℵ .The model Me is defined as the functional relation between the model parameters and the prediction for Ye. And Me (xe) is denoted as ym. At the end of this step one gets a measure of how well the experimental data matches the simulations data, i.e how consistent the model is. V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 5 of 9 xiii P. Smith, S. Smith, J. Thornock, A. Jatale, D. Nguyen and B. Schroeder, "A Validation Methodology for Quantifying Uncertainty in High Performance Computer Based Simulations with Sparse Experimental Data", ASME Verification and Validation Symposium, May 2-4, 2012. xiv R. Feeley, P. Seiler, A. Packard, and M. Frenklach. Consistency of a reaction dataset. J. Phys. Chem. A, 108:9573-9583, 2004. xv R. Feeley, M. Frenklach, M. Onsum, T. Russi, A. Arkin, and A. Packard. Model discrimination using data collaboration. J.Phys. Chem. A, 110:6803-6813, 2006. xvi M. Frenklach, A. Packard, P. Seiler, and R. Feeley. Collaborative data processing in developing predictive models of complex reaction systems. International Journal of Chemical Kinetics, 36(1):57-66, 2004. feasible region for active variables is obtained between the provided ranges using Monte Carlo sampling. Once sampling is done the model is evaluated at each of the sample points and for each of the experiments or scenarios. This is followed by performing consistency analysis by subjecting the results to the constraints. This step gives a value which tells us how good the evaluated value matches the experimental value. For a point to be called consistent it should satisfy the inequalities for each of the experiments. The wind tunnel flare system was simulated under the different operating conditions shown in Figure 2. These simulations were run on 480-600 processors. The simulations were run for sufficient computational time to allow flow to develop completely. The mass flow weighted time average values of the desired quantities were collected at the measurement location for 4000 realizations. The time step used for simulations was 5E-4 sec. Figure 3 compares flame structures and efficiencies for low (3m/s), high(12m/s) and medium(5m/s) cross wind velocity. The color bar was modified to show the progress of the combustion efficiency (progress variable) from 0.99 to 1 for better differentiation. All the areas with efficiency values less than 0.99 are in grey. Also pure air was assigned an efficiency of 1. Higher crosswind velocities give less time for air/ fuel mixing. This leads to more unburnt fuel and low combustion efficiencies. Also the phenomenon of fuel slip can be seen on the downwind side of the flare stack for low cross wind velocities. Fuel slip or fuel stripping refers to the breaking of the unburned fuel away from the main flame structure and then being transported as unburned fuel pockets. Figure 4 shows the temperature distribution for the same cases to indicate where the combustion process has been completed. The wind tunnel flare system has a common active design variable (crosswind velocity), thus uncertainties in 2 directions were considered. After analyzing the experimental data the crosswind velocities were divided in 6 different groups or clubs resulting in 6 dataset V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 6 of 9 Figure 3: Progress variable (combustion efficiency) at a plane in the domain for crosswind velocities of (from top to bottom): 3m/s, 5m/s, 12m/s. units. Each club was interpreted as containing experimental replicates. Since each data set unit contains sparse data, a Student T test results in a confidence interval of 1.5 times the variance of the data for a 90% confidence interval. The consistency test was performed for the CO2, O2 and CH4 concentrations. The combustion efficiency is a derived quantity from these species concentration and was thus not used in this consistency constraint but produced as an output. A Monte Carlo approach was used to apply the consistency constraint across the uncertainty range of all of the active uncertain variables over 500,000 random points. Figures 5-8 show the priors and posteriors for the variables of interest. In these plots red denotes the experimental data and the box signifies the uncertainty region in them. The green box shows the subspace that is consistent with all measurements and all simulations. This analysis has 6 different crosswind clubs for 3 different desired variables (Concentration of CO2, CH4 and O2) total of 18 dataset units. Each of the 500000 simulation points were tested for consistency for all 18 dataset units. Simulation results are consistent with all 6 clubs simultaneously for CO2 and O2 concentration, shown by the overlapping of prior and posteriors regions in figures 5 & 6. For the CH4 concentration simulations results are consistent for only 5 of 6 clubs. Crosswind club 1 from 3.373 m/ s to 3.932 m/s shows a lower CH4 concentration for model (Figure 7). The derived combustion efficiencies are consistent with the experimental data except in the low crosswind club. A consistency over 17 dataset units was achieved. Figure 4: Temperature profile at a plane in the domain for crosswind velocities of (from top to bottom): 3m/s, 5m/s, 12m/s. V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 7 of 9 Figure 5: Priors and posteriors for CO2 concentration as a function of crosswind velocity. Figure 6: Priors and posteriors for O2 concentration as a function of crosswind velocity. Figure 7: Priors and posteriors for CH4 concentration as a function of crosswind velocity. 96 Figure 14: Priors and posteriors for CO2 concentration in all the 6 clubs The disagreement of CH4 concentration for low crosswind club can be either a model issue or the experiment collection issue. Since the model was able to generate results consistent with experimental data of CO2 and O2 concentration for this low crosswind case, more chances are that couple of experiments in this dataset units can have error in reporting. Experimental data suggests that as Crosswind velocity decreases efficiencies increases. Theoretically, increase in efficiency signifies more burned fuel and higher convention to CO2. Though data presented shows increase in CO2 concentration it does not shows the decrease in CH4. This requires sitting with the experimentalists and understanding about things which may have caused the error or get informed about any process which was not mentioned with the provided results. Figure 18 shows the consistency space for each of the 6 crosswind clubs. It also gives the range of alpha for which results are consistent. From the analysis the alpha range for which results are consistent with the experiments came to be 6.85-8.5. This range of model parameter can be used as prior information for future validation studies. The color bar in these plots signifies the consistency measure for the points. Blue being the most consistent and red being at the edge of consistency. 97 Figure 15: Priors and posteriors for O2 concentration in all the 6 clubs Figure 16: Priors and posteriors for CH4 concentration in all the 6 clubs 97 Figure 15: Priors and posteriors for O2 concentration in all the 6 clubs Figure 16: Priors and posteriors for CH4 concentration in all the 6 clubs V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 8 of 9 Figure 8: Priors and posteriors for combustion efficiency as a function of crosswind velocity. The inconsistency of CH4 concentration for the low crosswind club can be either a modeling or experimental issue. The model and the experiment are consistent at this crosswind velocity for CO2 and O2 concentrations. Both the experimental data and the simulation results show combustion efficiency increasing as the crosswind velocity decreases. The increase in efficiency signifies more burned fuel and higher convention to CO2. While the experimental data shows an increase in CO2 concentration it does not shows the corresponding decrease in CH4. that is shown by the model. More information is needed about the circumstances of the data collection for CH4 at this low crosswind condition. C O N C L U S I O N S : LES simulations have been coupled with the International Flare Consortium windtunnel experimental observations through a formal validation/uncertainty quantification methodology. This coupling has identified consistency between each and every experiment with each other and with LES simulation results. This analysis not only lends confidence to the simulation capabilities but narrows the experimental uncertainty in the measurements. Measurements alone have not been able to produce combustion efficiency from operating, open-air, flare flames. The recent TCEQ tests at John Zink are currently being analyzed in an attempt to produce such measurements, but there are many nagging questions because of the difficulty of simultaneously measuring the composition and velocity to obtain a mass flux surrounding the reacting flare. As the instrumentation becomes more sophisticated the measurement itself needs to incorporate sophisticated models to convert the measured variable to the desired combustion efficiency. LES can provide the sophistication needed to produce combustion efficiency. This formal validation procedure allows for the simulation to be tightly coupled with data from measurable variables to produce the associated combustion efficiency with error bars. The resulting information can be extrapolated to real operating systems through the validated LES tool. The V/UQ procedures produces a surrogate model that is like simple analytic solutions: ie, easy to manipulate, easy to do the inverse problem. For example measurable variables, such as CO2, O2 or CH4 concentrations can be easily obtained at various locations in or around the flare then through the V/UQ process described in this paper, these measurements can be inverted to obtain the associated combustion efficiency with the associated uncertainty without having to revert to additional large-scale LES computations. Figure 16: Priors and posteriors for CH4 concentration in all the 6 clubs Figure 17: Priors and posteriors for combustion efficiency in all the 6 clubs V a l i d a t i o n o f F l a r e C o m b u s t i o n E f f i c i e n c y page 9 of 9