Comparison of empirically based calculation methods for pipe flares to computational fluid dynamics

As available computational resources increase and the use of computational fluid dynamics (CFD) becomes more widely accepted wider classes of industrial scale combustion systems are being simulated and optimized using these resources. A largebody of empirically based work has already been assembled to model the behavior of the large-scale turbulent diffusion flames used in flares. The work of Brzustowski and others is the de-facto standard for flare flame behavior calculations. Performing the calculations outlined by Brzustowski still requires significantly less time than performing a simulation of the same conditions using CFD, however the use of CFD may allow extrapolation to conditions not within the data set or calculation methods currently in use. Others have recently used CFD to model flare systems with success, but to our knowledge no direct comparison has been made with previous empirical work. This validation is necessary; the validation typically performed for commercially available CFD codes are taken from well-controlled lab-scale experiments and not industrial scale flows. Additionally, comparison between the results produced by CFD and those of previous published calculation methods will allow one to identify when the relatively fast empirically based methods are adequate and when a more time consuming CFD study should be performed. The predicted radiation and plume trajectory of a simple pipe flare in a cross wind is compared to the empirical data and calculation results from the "API method" of 2007 and the "Brzustowski and Sommer's" method for several different cross winds. Identification of differences in the results, and recommendations for the when it is appropriate to apply each of the calculation methods are made.

Comparison of Empirically Based Calculation Methods for Pipe Flares to Computational Fluid Dynamics Matthew Martin Callidus Technologies, LLC Tulsa, OK USA Email: [e-mail] ABSTRACT As available computational resources increase and the use of computational fluid dynamics (CFD) becomes more widely accepted wider classes of industrial scale combustion systems are being simulated and optimized using these resources. A large body of empirically based work has already been assembled to model the behavior of the large-scale turbulent diffusion flames used in flares. The work of Brzustowski and others is the de-facto standard for flare flame behavior calculations. Performing the calculations outlined by Brzustowski still requires significantly less time than performing a simulation of the same conditions using CFD, however the use of CFD may allow extrapolation to conditions not within the data set or calculation methods currently in use. Others have recently used CFD to model flare systems with success, but to our knowledge no direct comparison has been made with previous empirical work. This validation is necessary; the validation typically performed for commercially available CFD codes are taken from well-controlled lab-scale experiments and not industrial scale flows. Additionally, comparison between the results produced by CFD and those of previous published calculation methods will allow one to identify when the relatively fast empirically based methods are adequate and when a more time consuming CFD study should be performed. The predicted radiation and plume trajectory of a simple pipe flare in a cross wind is compared to the empirical data and calculation results from the "API method" of 2007 and the "Brzustowski and Sommer's" method for several different cross winds. Identification of differences in the results, and recommendations for the when it is appropriate to apply each of the calculation methods are made. Keywords Flare, Pipe Flare, Pressure-Relieving and Depressurizing Systems, Computational Fluid Dynamics 1. INTRODUCTION Industrial flares are used to safely dispose of combustible fluids in the case of required depressurizing for large-scale processes. The depressurizing requirement may be planned, as in the case of periodic maintenance, or may be unplanned as is the case when equipment failure may force a halt to the process. A large volume of fluid must be safely disposed in a relatively short period of time for typical refining, natural gas production and chemical processes. Combustion of such a large volume of fluid over a short period of time produces a large amount of power. The principle heat transfer mechanism for such industrial scale flames to the far field is thermal radiation, and the ability to design systems for the proper disposal of the relief fluids relies on the ability to predict radiation. Empirically based prediction techniques are the current standard method for predicting thermal radiation from industrial flares. Possibly the two most popular techniques are those outlined in the example calculations available in ‘ANSI/API Standard 521' [1]. The relatively easy access to these methods as well as their apparent accuracy within a range required for engineering design seem to drive their continued popularity. It is noteworthy that these are not the only available calculation techniques; a survey paper that gives many alternative techniques is available in ‘Heat Radiation from Flares' [2]. Computational fluid dynamics (CFD) has become increasingly popular as a design and screening tool as the associated software has become easier to use and the cost of the typically substantial computing resources required has decreased. The primary appeal for the use of CFD in engineering design is that the calculations are at least in a portion based on first principles and is therefore thought to provide the ability to solve a more general class of problems. One often over-looked aspect of CFD modeling is that many of the sub-models required to provide closure to the descriptive equations are empirically based, particularly those related to turbulence. Thermal radiation also proves to be particularly difficult to model; transmission is effectively instantaneous compared to the flow speeds in question, and although any individual thermal radiation model may be based on fundamental principles, many of the fluid properties that determine the incident radiation at a surface are not. In addition to the accuracy of any given calculation technique, the amount of time required to perform the calculation is critical to its usefulness. CFD calculations typically take much longer to 1 perform when compared to the relatively simple empirically derived approaches presented. Distance required from a point source of irradiation is taken from equation 24 of C.2.5 [1], and rearranged to solve for the radiation intensity, as shown in Equation 1 below: 2. PRELIMINARIES AND REVIEW 2.1 Flare and Flow Description The flare to be modeled consists of a derrick-supported stack to be topped with a pipe flare tip of standard design. A tip of standard design is usually comprised of a large diameter pipe with some method of flame retention intended for lower flow rates. At higher flow rates, the flame characteristics near the tip are dominated by the ‘turbulent diffusion' between the large-scale jet of flare gas and the atmosphere, reducing the impact of the flame retention device on characteristics of the flame. The derrick-supported stack and tip are to be 197 ft tall. The tip exit velocity is designed to be approximately 400 ft/s. The gas to be flared is effectively 100% methane. The flow rate of gas to the flare is 102.27 lb/s. The temperature of the flare gas is -148 F. Figure 1 shows a schematic diagram of the flare. 2.2 ‘Clause 6' Calculation Method The equations and data already found in readily available sources are not replicated here; the results are presented in summary form. The calculation method for plume trajectory and radiation taken from ‘Clause 6' of ‘ANSI/API Standard 521' is as follows [1]: 1) Calculate the required flare diameter. 2) Calculate the anticipated flame length. 3) Calculate the flame distortion caused by wind. 4) Calculate the flare stack height. For the purposes of this simulation, the flare tip diameter has already been fixed at 26 inches by using an equivalent inverse of the equation of step 1 as presented in ‘Clause 6'. The anticipated flame length, as calculated from a curve fit of Figure 8 [1] of ‘Clause 6' is 306 ft. Qr = f r × Q flare 4×π × d 2 (1) Where: Qr =Radiation Intensity (Btu/hr-ft2) fr =Fraction of Heat Released as Radiation () Qflare =Heat Release from Flare (Btu/hr) d =Distance from Flame Center (ft) The fraction of heat release as radiation is taken to be 0.10, which is at odds with the nearest corresponding tip diameter value from Table 10 of [1]. This is done because in practice it has been found, but is still highly debated, that the values proposed by the GPSA handbook provide results that are closer to measured values. 2.3 Brzustowski and Sommer's Method from ANSI/API Standard 521 The calculation method of Brzustowski and Sommer's as outlined in ‘ANSI/API Standard 521'is essentially the same as the ‘Clause 6' calculation, but the determination of the flame distortion and the resulting flame center differs. The method also commonly makes use of an atmospheric absorption term, which is used to include the effect of the participation of water vapor in the atmosphere on the radiation intensity from the flare. This term is purposefully left out of these calculations so that the ‘Clause 6' method, the Brzustowski and Sommer's method and the CFD model can be compared on a consistent basis. 2.4 Computational Fluid Dynamics Method The software package ‘Fluent' was used to perform the computational fluid dynamic calculations. From the outset, the decision was made not to produce the ‘best' model, but rather what could be considered a typical model, with the following requirements: 1) The computational grid must be of modest to small size. a. The model must be able to be executed using typically available hardware. b. The software licensing cost cannot be prohibitive for evaluating flares - consider the relative cost of the pencil and paper required for the other methods to any software package. c. The model must be able to be solved in a useful amount of time (overnight at most). Figure 1 - Schematic diagram of the derrick-supported stack and flare tip. 2 of combustion equipment, are too narrow and long when compared to reality. Adjustment of the turbulent Schmidt number might remedy this, but has not been fully investigated. Radiation was modeled using both the ‘Discrete Ordinates' (DO) model and the ‘P-1' model. The DO model is applicable over all length scales where as the P-1 model is only applicable over a large optical thickness [3]. However, the DO model is significantly more computationally expensive and has a particular disadvantage for modeling flares, which will be later shown. Fluid properties were defined such that they varied with temperature. No attempt was made to account for dissociation, which might also negatively impact the radiation solution. Figure 2 - Grid Dimensions 2) 3) Special considerations known only to those well versed in the specifics of flare design cannot be included. The general usefulness of the tool must be tested. Optimizations that can be made to the model which may be realistic, but cannot be known or included in the other models should not be included. A computational grid of 199,700 cells was used to represent the flare stack, tip and surrounding atmosphere. The grid was comprised entirely of unstructured hexahedral elements. Details of the derrick were not included, with only a cylinder representing the flare stack. The same grid was used for all cases, whether in still air or with a crosswind. Figure 2 shows the grid dimensions. The fluid was modeled as an incompressible ideal gas. Preferably, the ideal gas law would have been used because the tip velocity exceeds 0.3 Mach, but limitations to the software prevent the use of a velocity inlet to specify the crosswind in conjunction with the ideal gas law for fluid density. An alternative specification for the inlet velocity could possibly be found, but in the spirit of producing a ‘typical' CFD model, the velocity inlet approach was used instead. For sonic flares it is advisable that an alternative approach be found. Turbulence was modeled using the ‘Realizable k-epsilon' (RKε) model. The other standard models can become unrealistic in high strain flows, and the RKε model is reported to be more accurate in predicting the spreading rate of round jets [3]. Chemical reactions were modeled using a two-step Magnussen model, specifically the ‘Eddy-Dissipation' model available in Fluent. The chemical reaction rate is limited by the mixing rate of the fuel and its surroundings, which seems reasonable for a largescale flare [3]. For other combustion equipment modeled by this author, the model is known to over-predict flame temperature in critical regions, particularly because flame will attach where it should not solely because there is enough mixing. Over prediction of flame temperature would have a direct impact on the radiation results. For flares more complex than a pipe flare, this model may be completely inaccurate because mixing may occur at locations other than the diffusion boundary between the flare gas jet and the atmosphere. The ‘Mixture Fraction' model may apply well to flares based on its requirements and assumptions about reaction progress and mixing. It has been the experience of this author that in general the flames produced from this model, for a wide range 3. APPROACH 3.1 Comparison of Various Operating Conditions For the purposes of evaluating the CFD model against the more popular calculation methods, each model will be calculated using 0, 20, and 40 mph crosswinds. A comparison of the results will be made and a discussion of the potential inaccuracy in each model will be included. The velocity ratio required for the graph provided in ‘ANSI/API Standard 521' for the Brzustowski and Sommer's method does not allow for the case where the crosswind velocity is zero. Extrapolation is made to allow for the evaluation of the zero wind velocity case. Flame geometry will be measured and used to calculate the flame centers from the CFD results. Radiation will be measured from the CFD model and compared to the other methods at the centerline of the flare stack along the downwind side at grade. 4. RESULTS 4.1 Flame Center Calculation Flame center determination for the various empirical methods appears to be based largely of visual observation of the geometrical center of the flame. The same method will be applied to the CFD model. The geometrical center of the flame is not necessarily the center of radiation. The flame is most likely far more luminous in some regions when compared to others and the actual temperature of the flame will vary along the flame length. The fluid composition surrounding the flame front changes along the length of the flame, due to back mixing of combustion products, which in turn alters the local absorption coefficient and the resulting thermal irradiation. Although flame geometry is generally of great interest for any CFD model involving combustion, there is no universally accepted ‘flame' criterion; there is no ‘flame' function provided by the CFD software in order to visualize the results. Much of the difficulty in flame visualization arises from the use of chemistry models that do not include radical species which are often short lived within the flame-front and so are more reliable indicators of flame; one could consider the use of the electrical ‘flame-rod' detector common in process heater pilots to see the utility of radical detection. Other methods employed are the use of various concentrations of CO (a partial product that is often available 3 from the simulation), temperature, oxygen, or mean mixture fraction. The author has found that a threshold surface of reaction rate seems to produce the most realistic results when compared to visible flame, but there is a dearth of empirical data with which to validate this approach. The use of stoichiometric mixture fraction to represent the flame surface seems to be a common practice. Mixture fraction is calculated from the CFD results in the following manner, as used in [4] (but not as a flame surface) and elsewhere: z = z st = sY f sY − Y o + Y o0 0 f 0 o Y 0 f sY + Yo0 +Y 0 o = 0.055 Comparison of Predicted Flame Geometry for Various Models Horizontal Distance Vertical Distance to to Flame Center Flame Center From Model Wind Speed (MPH) From Stack (ft) Stack (ft) 'Clause 6' 0 0 153 'Clause 6' 20 114 76 'Clause 6' 40 128 57 B&S* 0 0 388 B&S 20 58 69 B&S 40 65 45 CFD 0 0 166 CFD 20 59 51 CFD 40 67 32 *Extrapolating Curve Fit (2) Table 1 - Flame center predictions 4.2 Radiation Calculations Using WSGGMDomain Based Absorption Coefficients (3) Where: s=stoichiometric mass fraction, Yf=mass fraction of fuel Yo=mass fraction of oxidizer, Y0f=initial mass fraction of fuel Y00=initial mass fraction of oxidizer, z=mixture fraction, zst=stoichiometric mixture fraction The estimated flame length from the CFD model by mixture fraction is 197 ft, which does not correspond well with the API predicted flame length of 306 ft. Past experience is that other models have had better correspondence with the API predicted flame length than has been achieved in this case. Possible reasons for the relatively poor correspondence include the use of incompressible gas coupled with the relatively high exit velocity or shortcomings in the mixing assumptions of the chemistry model. The under-prediction of visible flame geometry by stoichiometric mixture fraction has been recurrent for the author when investigating a large variety of combustion equipment. Using an iso-surface of 2000 PPM CO (dry) results in much closer agreement with the API predicted flame length. This isosurface has proven to be a good approximation of visible flames across a wide variety of combustion equipment, although adjustment may be required depending on the fuel and other variables. The CFD model predicts a 313-331 ft long flame, depending on the other model parameters. Radiant intensity data was exported from the CFD model at grade along the centerline of the flare stack. Data is only compared along the downwind, highest radiation, side of the stack. One should note that the ‘Incident Radiation' or ‘Surface Incident Radiation' that is available as a field variable from the CFD software is not the radiation intensity that is of interest. Manipulation of the field variables is required to obtain the proper value for post-processing. For the Discrete Ordinates radiation model the number of ‘rays' that are emanated from each cell center in the CFD model is a user selectable parameter. The default number of rays is 8, which is known to be inadequate for flare radiation calculations. Increasing the ray count to 18 results in radiation plots similar to those of Figure 3, which is also inadequate for properly evaluating the radiation map around the flare. Increasing the ray count to 64 results in a plot that appears to be adequate, but this is also dependant on the grid that is used. Increasing the ray count of the DO model increases the time to find a solution as well as the memory requirements, making a very high ray count unattractive. The participating properties of the fluids in the system have a direct impact on the predicted thermal radiation. The absorption coefficient of the participating gases, primarily CO2 and H2O, is dependant on the mean beam length though the participating gases from the point of radiation to the receiver. Table 1 shows the results for flame center location from the various models. Both the Brzustowski and Sommer's and the CFD model compare favorably for the horizontal distance from the flame center to the stack. The vertical distance of the flame center from the top of the flare stack is closer in agreement for all three methods. The figures used to derive the flame centers are given at the end of this paper. Figure 3 - Radiation map at grade (Btu/hr-ft2). A low ray count used with the DO model provides inadequate results to evaluate flare irradiation. 4 Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model 1000 900 Radiation Intensity (Btu/hr-ft2) 800 700 600 CFD Results - 20 MPH Wind 500 Clause 6 Method - 20 MPH Wind 400 B&S Method - 20 MPH Wind 300 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) Figure 4 - Radiation intensity (Btu/hr-ft2) at grade along the downwind side of the flare using WSGGMDomain Based Absorption Coefficients. The CFD software provides several methods for determining the absorption coefficient. One method is the 'Weighted Sum of Grey Gases - Domain Based' calculation. The CFD software will automatically calculate a mean beam length for the geometry under consideration, which will in turn be used to calculate the absorption coefficient of the participating gases. The Brzustowski and Sommer's calculation method performs a similar calculation by providing a correction factor ‘τ', which is used to correct for atmospheric participation. It may therefore seem reasonable that the beam length from the atmospheric domain used in the CFD model be included in the absorption coefficient calculations, although in this case there is no water vapour in the atmosphere to participate in the radiation calculations. However, one must consider that the size of the domain for the atmosphere surrounding the flare is essentially arbitrary apart from flow considerations, and the domain dimensions directly affect the mean beam length. For closed domains such as process heaters, the calculation technique seems to work well and reasonable answers result. However, for open domains such as are used for flares, it is less clear how to define the proper volume of absorbing gases. Figure 4 shows the results evaluated at 20 MPH. There is very poor agreement between the CFD model and the empirical results. Results for the other wind speeds are included at the end of this paper. The P1 radiation model appears to give better results for the zerowind case, but still significantly under-predicts the radiation intensity for the other cases. From the CFD software documentation: "In problems with localized sources of heat, the P-1 model may over-predict the [ir]radiative fluxes. The DO model is probably the best suited for computing radiation for this case, although the DTRM, with a sufficiently large number of rays, is also acceptable" [3]. The known over-prediction of this model is the most likely cause for the coincidental agreement in the zero-wind case; the flare flame most likely qualifies as a local source. 4.3 Radiation Calculations Using Corrected Absorption Coefficients Given the clear failure of WSGGM-Domain Based absorption coefficients to predict irradiative flux that is in line with the empirically derived calculations, other methods must be employed. The CFD software provides a WSGGM-Cell Based method, which calculates the mean beam length based on a characteristic cell size from the CFD model. The software documentation warns that the solution will be grid dependant, and this has been found to be true in practice [3]. The choice of cell based absorption coefficients has rarely given reasonable results. The software user can choose alternate methods for absorption coefficient calculation of their own device, and this has been done in this case. A modified mean beam length is calculated and used as opposed to the default methods employed by the software. Figure 5 shows the results for a 20 MPH crosswind using the modified absorption coefficients. The agreement seems good 5 Figure 5 - Radiation intensity (Btu/hr-ft2) at grade along the downwind side of the flare using modified absorption coefficients. particularly in the far field. The empirical calculation methods are generally more useful in the far field [1 - page 89], and the agreement with the CFD model is better in this range as well. The results for the other wind speeds are included at the end of this document. It is important to note that the modified absorption coefficient method used is not merely a scalar multiplier used to adjust the radiation results. In this case the modification increased the radiation levels over those predicted by default in the software. In other cases, the modification has reduced the predicted irradiative output. 5. ITEMS OF INTEREST 5.1 Modeling of Large Domains The mass contained in the flow issuing forth from a flare tip into a large domain that is typically of interest for radiation modeling is small compared to the mass held in the atmospheric domain. This makes the use of standard measures of convergence for CFD models, particularly scaled residuals, very difficult. The CFD practitioner is encouraged to review the scaling procedure used and determine its adequacy for problems of this nature. Strong buoyant forces dominate the flow at distances greater than several orifice diameters from the flare tip for low wind speed cases. This can make convergence very difficult compared to those with higher wind speeds. Careful selection of the pressurevelocity coupling scheme and the use of very conservative underrelaxation factors may aid convergence. 5.2 Improvements to the CFD Model Two improvements to the CFD model readily present themselves, but were purposefully not made. The first of these is to include a more realistic inlet velocity profile for the wind based on empirical correlations available in literature, as opposed to the constant velocity profile used. This can be accomplished with relatively little effort through the use of ‘User Defined Functions' (UDF's) linked into the CFD solution routine. A second improvement could be to include a sink term in the energy equation to reduce the ambient temperature as the elevation increases. Both of these effects are regularly included in non-CFD plume modeling. Soot models are available within the CFD code; their effectiveness has not been fully evaluated by this author, but preliminary work suggests the effect is of second order compared to the gray gas calculations. 6. CONCLUSIONS 6.1 Comparison of Methods The CFD simulation and the Brzustowski and Sommer's calculation method compare very favorably for determination of flame center. The ‘Clause 6' method compares reasonably well for the vertical deflection of the flame center with the other two methods, but the horizontal deflection is generally much greater for comparable wind speeds. The prediction of flame center in the CFD model is relatively immune to the choice of radiation model. 6 Using domain based absorption coefficient calculations, the radiation results for the CFD model did not compare well with the other calculation methods. Despite the large discrepancy in flame center prediction, the ‘Clause 6' method and the Brzustowski and Sommer's method compared very favorably. This is due to the distance of the flame center to the point of measurement; if the stack were shorter the results would not be as similar. 6.2 Recommendations for the Use of Empirically Based Methods The speed with which the empirically based methods can be calculated makes them very attractive in most cases. The greatest shortcoming for most of the available methods is the recurrent use of a ‘fraction of heat radiated', which is experimentally determined and varies both with flare design and firing conditions beyond a change in flow rate or gas composition. The empirically based methods presented here do not address any either difference in flare design or more complex firing issues. It is therefore recommended that these methods be used when there are no flow obstructions nearby the flare to alter the assumed effect of the wind, and when the flare can be considered to be a properly functioning standard pipe flare. Use of these methods for more complex flare tip designs is not recommended unless specific information for the fraction of heat radiated is available from the manufacturer. The methods might still be used even without manufacturer's data to provide a worstcase bound assuming a suitably high irradiative fraction is used. Due to the relatively large amount of time and resources required to perform CFD modeling, the empirically based methods are recommended for flares of simple design in simple flow environments. the fraction of heat radiated from the ‘Clause 6' and Brzustowski and Sommer's methods was selected to be 0.10; the absorption coefficient calculation method functions independently of any ‘target' irradiative fraction and still produced very similar results. CFD modeling is still a useful tool for evaluating more complex flare tip designs particularly if the sub-models, such as oxidation chemistry, are properly applied. Additionally, for situations where nearby structures could potentially affect the air flow to the flare, flow modeling may be the only potential method to determine the effect on the flare flame. CFD is also recommended if the thermal radiation in the near-field of the flare is particularly critical. The CFD results predicted higher thermal radiation levels near the flare stack than the empirical methods while maintaining accuracy in the far field. This suggests that CFD modeling may overcome the shortcomings of the single point methods suggested in the ‘ANSI/API Standard 521' [1 -page 89]. 6.4 Concluding Remarks There are obvious improvements that can be made to the CFD model used in order to improve the accuracy, the first of which is to increase the cell count of the model. However, the intent of this modeling was to examine what reasonable CFD model requirements could produce rather than assuming that all users have access to a large compute cluster and unlimited software licenses. It appears that through proper selection of the CFD models and careful operation of the software, very reasonable agreement with the empirical work of others can be achieved. Furthermore, the single point methods presented in ‘ANSI/API Standard 521' are still very useful, far more economical, reasonably accurate, and substantially faster than computational fluid dynamics if the flow field around the flare is not highly complex. 6.3 Recommendations for the Use of Computational Fluid Dynamics 7. REFERENCES The results from the CFD modeling presented here show that although there is a widespread appeal for the potential generality of CFD solutions, the result is highly dependant on the modeling method selected. It is shown that reproducing the characteristic flame shape through CFD may be relatively straightforward, but that calculating a reasonable radiation map may be considerably more difficult. [2] Guigard, S., Kinzierski, W., Harper, N. Heat Radiation from Flares. Publication Number T/537 prepared for Science and Technology Branch Environmental Sciences Division Alberta Environment , May 2000 Use of the default absorption coefficient calculation techniques for the modeling of industrial scale flares is not adequate; the CFD practitioner must modify the method to achieve reasonable results. The modification may seem equivalent to using an empirically based ‘fraction radiated' value as is used with the single-point methods. However, the CFD calculation has no ‘knowledge' that [1] Pressure-relieving and Depressuring Systems. API Standard 521, Fifth Edition, January 2007 [3] Documentation for Fluent 6.3. www.fluentusers.com , as of September 2007 [4] Sommerer, Y., Galley, D., Poinsot, T., Ducruix, S., Lacas, F., Veynante, D. Large Eddy Simulation and Experimental Study of Flashback and Blow-Off in a Lean Partially Premixed Swirled Burner. Available through Elsevier Science, September 2004 7 8. Figures Used To Calculate Flame Centers 0 MPH Wind - Y-coordinate plotted against a 2000 PPM CO (Dry) surface used to the flame height (ft). 197 feet is the flare tip exit plane. Z-direction in the CFD model is the Y direction in the API calculations. 20 MPH Wind - X-coordinate plotted against a 2000 PPM CO (Dry) surface used to determine horizontal deflection of the flame (ft). Zero is the flare centerline. 20 MPH Wind - Y-coordinate plotted against a 2000 PPM CO (Dry) surface used to determine vertical deflection of the flame (ft). 197 feet is the flare tip exit plane. Z-direction in the CFD model is the Y direction in the API calculations. 8 40 MPH Wind - X-coordinate plotted against a 2000 PPM CO (Dry) surface used to determine horizontal deflection of the flame (ft). Zero is the flare centerline. 40 MPH Wind - Y-coordinate plotted against a 2000 PPM CO (Dry) surface used to determine vertical deflection of the flame (ft). 197 feet is the flare tip exit plane. Z-direction in the CFD model is the Y direction in the API calculations. 9 9. WSGGM Domain Based Absorption Coefficients, Discrete Ordinates Radiation Model Results Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model 600 Radiation Intensity (Btu/hr-ft2) 500 400 CFD Results - 0 MPH Wind 300 Clause 6 Method - 0 MPH Wind B&S Method - 0 MPH Wind 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model 1000 900 Radiation Intensity (Btu/hr-ft2) 800 700 600 CFD Results - 20 MPH Wind 500 Clause 6 Method - 20 MPH Wind 400 B&S Method - 20 MPH Wind 300 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 10 Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model 1200 Radiation Intensity (Btu/hr-ft2) 1000 800 CFD Results - 40 MPH Wind 600 Clause 6 Method - 40 MPH Wind B&S Method - 40 MPH Wind 400 200 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 11 10. WSGGM Domain Based Absorption Coefficients, P1 Radiation Model Results Radiation at Grade - Comparison of Single Point Methods and the P1 Radiation Model 600 Radiation Intensity (Btu/hr-ft2) 500 400 CFD Results - 0 MPH Wind 300 Clause 6 Method - 0 MPH Wind B&S Method - 20 MPH Wind 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) Radiation at Grade - Comparison of Single Point Methods and the P1 Radiation Model 1000 900 Radiation Intensity (Btu/hr-ft2) 800 700 600 CFD Results - 20 MPH Wind 500 Clause 6 Method - 20 MPH Wind 400 B&S Method - 20 MPH Wind 300 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 12 Radiation at Grade - Comparison of Single Point Methods and the P1 Radiation Model 1200 Radiation Intensity (Btu/hr-ft2) 1000 800 CFD Results - 40 MPH Wind 600 Clause 6 Method - 40 MPH Wind B&S Method - 40 MPH Wind 400 200 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 13 11. WSGGM Domain Based Absorption Coefficients, Discrete Ordinates Radiation Model Results with Modified Absorption Coefficient Calculation Technique Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model, Modified Calculation Method 600 Radiation Intensity (Btu/hr-ft2) 500 400 CFD Results - 0 MPH Wind 300 Clause 6 Method - 0 MPH Wind B&S Method - 0 MPH Wind 200 100 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model, Modified Calculation Method 1200 Radiation Intensity (Btu/hr-ft2) 1000 800 CFD Results - 20 MPH Wind 600 Clause 6 Method - 20 MPH Wind B&S Method - 20 MPH Wind 400 200 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 14 Radiation at Grade - Comparison of Single Point Methods and the DO Radiation Model, Modified Calculation Method 1400 Radiation Intensity (Btu/hr-ft2) 1200 1000 800 CFD Results - 40 MPH Wind Clause 6 Method - 40 MPH Wind 600 B&S Method - 40 MPH Wind 400 200 0 0 200 400 600 800 1000 1200 Distance from Flare Stack (ft) 15