LES simulations of sour gas flares in Western Canada

In this paper we describe the development of a numerical simulation tool for a sour gas flare of the type typically found in Alberta. The purpose of the model is to provide a way to guide safer sour gas flare operating conditions for varying environmental and operating conditions. The numerical simulation tool (ARCHES) uses a Large Eddy Simulation (LES) model coupled with chemistry and radiation models to provide a high-fidelity (time and space) description of the flow field. Time integrals of the combustion efficiency were obtained to provide mean combustion efficiencies. Due to the expense of running each LES flare calculation, the boundary conditions for the simulations were chosen using a Box-Behnkin experimental design philosophy. The response surface generated from the Box-Behnkin design then served as a surrogate model for the LES calculation and provided insight into the interaction of H2S content, wind speed, and fuel velocity as they related to efficiency of the formation of CO2 and the destruction of H2S. The simulation results show that the local Damkohler number (reaction rate/mixing rate) changes dramatically for flares that have the same momentum flux ratio (momentum flux of flare gas / momentum flux of the crosswind). The results also show that; 1) When strain rates are high in the flow field, local quenching is possibly causing a decrease in combustion efficiency; 2) Buoyancy dominated flares produce low puffing frequency type motions, have low strain rates, and also show low efficiency. The response surface has a maximum efficiency contained within the current design space, which suggests a region of better operating conditions to maximize combustion efficiency depending on the local wind speed. In addition to presenting the results, we will discuss methods for improving the reliability of the calculations by quantifying the uncertainty with the LES model.

L E S S im u la tio n s o f S o u r G a s F la r e s in W e s te r n C a n a d a Jerem y T hornock and P hil Smith* T he In s titu te for C lean & Secure E nergy U niversity of U tah , USA A llan C ham bers T he A lb erta R esearch Council E dm onton, A lberta, C an ad a Ju n e 1, 2009 Abstract In this paper we describe the development of a numerical simulation tool for a sour gas flare of the type typically found in Alberta. The purpose of the model is to provide a way to guide safer sour gas flare operating conditions for varying environmental and operating conditions. The numerical simulation tool (ARCHES) uses a Large Eddy Simulation (LES) model coupled with chemistry and radiation models to provide a high-fidelity (time and space) description of the flow field. Time integrals of the combustion efficiency were obtained to provide mean combustion efficiencies. Due to the expense of running each LES flare calculation, the boundary conditions for the simulations were chosen using a Box-Behnkin experimental design philosophy. The response surface generated from the Box-Behnkin design then served as a surrogate model for the LES calculation and provided insight into the interaction of H2S content, wind speed, and fuel velocity as they related to efficiency of the formation of CO2 and the destruction of H2S. The simulation results show that the local Damkohler number (reaction rate/mixing rate) changes dramatically for flares that have the same momentum flux ratio (momentum flux of flare gas / momentum flux of the crosswind). The results also show that; 1) When strain rates are high in the flow field, local quenching is possibly causing a decrease in combustion efficiency; 2) Buoyancy dominated flares produce low puffing frequency type motions, have low strain rates, and also show low efficiency. The response surface has a maximum efficiency contained within the current design space, which suggests a region of better operating conditions to maximize combustion efficiency depending on the local wind speed. In addition to presenting the results, we will discuss methods for improving the reliability of the calculations by quantifying the uncertainty with the LES model. In tro d u c tio n Hydrogen sulfide (H2S) is a common component of gas streams flared in Western Canada. Large Eddy Sim­ ulations (LES) have been used to study the impact of H2S on carbon and sulfur combustion efficiency. This work was sponsored by the Canadian Association of Petroleum Producers and performed in a partnership between the Alberta Research Council Inc. (Allan Chambers) and the Institute for Clean and Secure Energy at the University of Utah (Philip Smith and Jeremy Thornock). B a c k g ro u n d Hydrogen sulfide (H2S) is a common component of gas streams flared in Western Canada. Sour gas is flared during well testing as a means to dispose of sour solution gas and to provide safe release of sour gas during emergency situations. The impact of H2S on flare combustion efficiency and overall flare emissions Corresponding author: Address: The Institute for Secure and Clean Energy, INSCC 388, University of Utah, 155 South 1452 East, Salt Lake City, UT, 84112, USA; phone: [phone]; fax: [phone]; e-mail:[e-mail] 1 Figure 1: Comparison of LES and RANS simulations to images taken of actual flares at the ARC research facility. Image reproduced in part from [2] is relatively unknown. Only limited experimental measurements have been reported for flaring of gases containing H2S , partly due to the hazard and high cost of these type of experiments [1]. The objective of the project was to develop a numerical simulation tool for a sour gas flare of the type typically used in Alberta, Canada. This flare simulation tool would incorporate hydrocarbon and sulfur reaction chemistry in order to predict flare performance for a range of flare operating conditions. The predictions of flame properties and reaction products would be used to help define safe operating conditions for sour gas flares. Fires and flares have been particularly difficult to simulate with traditional computational fluid dynamics (CFD) that are based on Reynolds-Averaged Navier-Stokes (RANS) approaches. The large-scale mixing due to vortical coherent structures in these flames are not readily reduced to steady-state CFD calculations with RANS. Figure 1 is a comparison of numerically predicted flame shapes and positions with photographs of flares produced in a wind tunnel at the University of Alberta, Edmonton [2]. The volume rendered simulations were produced with an LES-based model from the University of Utah while the 2D simulations were produced with a RANS model by D. Castineira and T. Edgar at the University of Texas-Austin. As can be seen, the LES model simulations closely match the shape and position of the wind tunnel flare for the full range of conditions. The turbulent structure of the flame was also predicted with the LES model. This comparison of the LES flare model simulation results with the wind tunnel flare experimental results builds confidence that that the LES model can be used to accurately capture the performance of a dynamic flare flame. 2 A R C H E S S im u la tio n T o o l Development of a numerical model and the application of the model to a range of flaring conditions were performed by staff at the Center for Simulations of Accidental Fires and Explosions (CSAFE) at the Univer­ sity of Utah. The numerical flare model used a Large Eddy Simulation (LES) method and an incorporated flamelet reaction model to predict hydrocarbon combustion and sulfur compound reactions. Models for turbulent chemistry interaction were also included. Simulations were relatively expensive, requiring 12-36 hours on 180-250 processors (2160-9000 computing hours). Development of a reliable and accurate numerical model requires a rigorous program of software devel­ opment combined with accuracy checking of predictions against experimental data and observations. Initial model simulations were run based on a range of flare conditions from wind tunnel flare tests that were performed previously at the University of Alberta. The wind tunnel test results were for a 2.54 cm (1 in.) diameter flare fueled with sweet natural gas. The LES based model accurately predicted the flame shape and position and also captured the turbulent nature of the flare. The University of Utah LES model included a reaction model to simulation combustion of hydrocarbons. During this project, a reaction model for sulphur species was added to the LES model. E x p e r im e n ta l D e s ig n A mixture of flaring conditions was developed for the numerical simulations in order to cover the full range of conditions recommended by industry. In an effort to reduce the total computing time required to complete the project, the following variables were held constant in the simulations: • flare tip diameter at 25.4 cm (10 in.) • hydrocarbons, CO2, N2 relative compositions in the fuel as the test well flare fuel gas composition • atmospheric conditions of 1 atm and 20°C To maximize the information on the effect of these three variables from the set of numerical simulations, a Box-Behnken response surface design was used with the remaining three variables: • wind velocity from 0 to 15 m/s • flare tip exit velocity from 1 to 15 m/s • H2 S mole fraction from 0 to 30% Table 1 lists the conditions that were simulated with the numerical model. Thirteen simulations were required in this test matrix. R e s u lts a n d D is c u s s io n Images from two of the 13 simulations performed are shown in Figure 2. The complete suite of images and videos of simulated sour gas flares can be seen online at www.flaresimulations.org/arc. Two key metrics were calculated as part of the LES simulations: 1) carbon efficiency - the sum of the carbon leaving the domain as CO2 over the sum of the carbon entering the domain as fuel and 2) sulfur efficiency - the sum of the sulfur leaving the domain as SO2 over the sum of the sulfur entering the domain as H2S. The calculated time-average carbon (nC) and sulfur (nS) efficiencies are tabulated in Table 2. The mean efficiencies n are computed using an integrated time average in an interval where the flare was determined to be at quasi-steady state. The sulfur conversion efficiency was predicted to be higher than the carbon efficiency in all cases for these simulations. However, the chemical kinetic model for sulfur conversion has higher uncertainty associated with it. 3 Simulation 1 2 3 4 5 6 7 8 9 10 11 12 13 Wind Velocity (m/s) 15 15 0 0 15 15 0 0 7.5 7.5 7.5 7.5 7.5 Fuel Velocity (m/s) 15 1 15 1 8 8 8 8 15 15 1 1 8 H2S content (mol%) 15 15 15 15 30 0 30 0 30 0 30 0 15 Table 1: The Box-Behnken experimental design used to relate wind speed, flare tip exit velocity, and H2S concentration to reaction products and flare characteristics. Figure 2: (L) 3D Rendering of CO2 Mass Fraction calculation from Simulation 1 (Wind Speed - 15 m/s; Fuel Velocity 15 m/s; 15% H2S). (R) 3D rendering of Temperature calculation from Simulation 4 (Wind Speed 0 m/s; Fuel Velocity 1 m/s; 15% H2S). 4 Simulation 1 2 3 4 5 6 7 8 9 10 11 12 13 1c 0.93 0.98 0.94 0.98 1.00 0.98 0.98 0.96 0.94 0.96 0.99 0.99 0.97 Vs 0.97 0.98 0.99 1.00 1.00 1.00 0.99 0.99 1.00 Momentum Flux Ratio (R) 0.72 0.003 to to 0.22 0.18 to to 3.1 2.6 0.014 0.011 0.81 Table 2: Time-averaged carbon and sulfur efficiencies calculated from LES simulations. The Box-Behnken experimental design made it possible to test the significance of the main effects of each of the variables (wind velocity, fuel velocity, and H2S content) on the carbon efficiency and their interactions. Initial analysis revealed that the most significant effect was the interaction between wind velocity and fuel velocity. Sulfur content was found to have a negligible effect on the carbon efficiency. This was confirmed by analysis of the response surfaces shown in Figure 4. Sulfur content was subsequently removed as an independent variable and the design re-analyzed. Inspection of the significance revealed that the most significant effect was wind speed, followed by the interaction of wind velocity and fuel velocity and then fuel velocity itself. These findings highlight a complex interaction between the fluxes of the fuel and wind in the vicinity of the flare stack. This interaction is represented numerically in Equations 1 and 2 below where r\c is the average carbon efficiency, f)s is the average sulfur efficiency, vw is the the wind velocity (m/s), vfuei is the fuel velocity (m/s), and ys is the mole fraction of H2S in the fuel. = 0.967 + 0.00358vw + 0.00337vfuel - 0.000089vwvfuel - 0.000333v^uel (1) ns = 0.991 + 0.0011vw + 0.0037vfuel - 0.000017vwvfuel - 0.00005vW (2) This and previous work [5] by our group has shown that the momentum flux ratio (R = pv|et/pvwind) is not a sufficient dimensionless scaling parameter to characterize either flare shape or combustion efficiency. While R is useful for providing some characterization of the mixing for momentum dominated jets in cross­ flow, it is insufficient for characterizing buoyancy-driven jets such as those seen in flares under low jet-velocity and low-wind conditions, and does not sufficiently characterize the local mixing and reaction phenomena that govern combustion efficiency in flares under the wide range of cross-wind conditions seen in Alberta. The complexity of combustion efficiency in these conditions is seen by the variability in the efficiency as a function of R when juxtaposed with the data collected by Seebold et. al. [4] in Figure 3. The local Damkohler number (Da = reaction rate / mixing rate) changes dramatically for flares that can have the same momentum flux ratio R. LES resolves these variations for the range of scales visually in Figure 1. The LES simulation relies on combustion modeling for scales smaller than those shown with Da >> 1. The simulation results shown on these web pages indicate that incomplete combustion occurs under two regimes: 1. When strain rates are high as seen under high wind and/or high jet-velocities. Under these conditions the local flame quenching occurs and products of incomplete combustion (PICs) escape. 5 1.00 c 0) u <£ 0 .9 0 LU c o § 0 .8 5 -O E 0.75 10-3 10} 101 10° 10' 10* 10J 104 10s 10' oo < p V V (p V *)« « Figure 3: Comparison of calculated combustion efficiencies nc at different momentum flux ratios with data collected by Seebold et al. [4] 2. When buoyancy dominates the flare plume so that slow mixing produces lower puffing frequencies characteristic of fires where regions of extinction, soot break-through and thus incomplete combustion occur periodically in these puffs. These trends are depicted visually in Figure 4 by contour plots relating wind and fuel velocity to the carbon and sulfur efficiency. Thus, the highest combustion efficiencies occur when the mixing rates of the fuel and the air are sufficiently high to produce complete combustion but not so high as to produce local extinction. The labelled lines are lines of constant momentum flux ratio R. As can be seen, there is no correlation between R and or . This confirms the previous conclusion that the momentum flux ratio is not an appropriate scaling parameter. F u tu re W o rk This sensitivity study has used massively-parallel Large Eddy Simulations (LES) to examine the sensitivity of combustion and sulfur conversion efficiency from one sour gas flare to the effects of wind speed, fuel feed rate and sulfur loading. While the results are insightful, this computational tool is new. It is now important to perform quantifiable validation and uncertainty quantification studies in order to understand the accuracy of the simulations and thus understand what conclusions can be drawn from the set of computations performed in this study. Formal validation and uncertainty quantification is a topic of research that has been studied at the University of Utah for several years. The methods that have been most useful are summarized in a brief report Verification, Validation, and Uncertainty Quantification that can be found online 1. The key features of such a study are based on the concept that by formally quantifying the consistency between a set of experiments and a simulation tool it is possible to quantify the uncertainty in four types of parameters: 1) model parameters, 2) experimental parameters, 3) numerical parameters, and 4) boundary condition parameters. The quantified error or uncertainty in these parameters that are consistent with all experiments 1http://www.inscc.utah.edu/~u0610834/Validation_and_Verification/Home.html 6 Carbon Efficiency Sulfur Efficiency Wind Velocity (m/s) Wind Velocity (m/s) Figure 4: Contour plots showing the effect of wind and fuel velocity on the carbon efficiency nC and sulfur efficiency and all simulation results are then propagated to the output functions (like combustion and sulfur conversion efficiency) so that the accuracy of the simulation can be numerically quantified. This type of validation and uncertainty quantification requires good experimental measurements. Not much experimental data is available for a formal analysis. However some DIAL measurements have been made by the Alberta Research Council. The DIAL method was used to measure the mass flux of methane, C2+ hydrocarbons and sulphur dioxide in the emission plume from a 10 inch diameter flare firing natural gas containing 11% hydrogen sulphide [1]. For this flare, the correlation over-predicts efficiencies, particularly the conversion of H2S to SO2. DIAL measurements were also completed on a 3.5 inch diameter flare firing sweet natural gas. For this flare the DIAL measured combustion efficiency was 98%, similar to the 98% efficiency predicted by the correlation for the same wind speed and fuel exit velocity. Another source of full scale flare tests that reported information on sour flares was Pohl and Solberg [3]. In these studies of 4 and 6 inch diameter flares with no cross wind, only 80% of the H2S was accounted for as SO2 in the flare emissions even though over 98% of the H2S was destroyed in the flare. Also, some laboratory wind tunnel data for flares without H2S have been reported by the University of Alberta, and some data have been recently collected by CANMET. Currently, The University of Utah and John Zink Corporation are engaged in a joint project to develop an LES flare simulation package that includes validation and uncertainty quantification. John Zink is collecting data from their flare test pad for this validation activity. The next step in this study is to leverage the work occurring at CANMET and John Zink to perform a formal validation and uncertainty quantification study of the combustion efficiency of sour gas flares. R e fe re n c e s [1] A. Chambers. Well test flare plume monitoring phase II: DIAL testing in alberta, 2003. [2] M. R. Johnson and L. W. Kostiuk. Efficiencies of Low-Momentum jet diffusion flames in cross winds. Combustion and Flame, 123:189-200, 2000. [3] J. H. Pohl and N. R. Solberg. Evaluation of the efficiency of industrial flares: H2S gas mixtures and pilot assisted flares. Technical Report EPA/600/2-86-080, U.S. E.P.A., December 1986. 7 [4] J.G. Seebold, B.C. Davis, P.E.G. Gogolek, L.W. Kostiuk, J.H. Pohl, R.E. Schartz, N.R. Soelberg, M. Strosher, and P.M. Walsh. Reaction efficiency of industrial flares - the perspective of the past. Vancouver, B.C., 2003. [5] C. Thurston and P. Smith. LES analysis of sour gas flares under variable wind conditions. Hawaii, 2007. 8