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Show Heater Recirculation Pattern Analysis and Burner Spacing Optimization Authors: Addison Cruz, Research and Development Engineer/Scientist; Matthew Martin, Honeywell Fellow; Kurt Kraus, P.E. Callidus Technologies, LLC Tulsa, OK USA Email: Addison.Cruz@Honeywell.com Abstract Most heaters are designed with the assumption that, given particular burner spacing, the heater performance is invariant with respect to burner type. However, there have been few published studies to rigorously test this theory. By combining statistical analysis and Computational Fluid Dynamics, appropriate burner spacing with different burner models can be tested virtually to provide general information. Analysis of these results allows for rigorous burner spacing optimization within a given heater for specific burner types. This information can be employed in burner retrofit projects to provide superior results with minimal cost; and within the heater design process, to provide improved performance through optimal burner and heater coupling. Summary The effects of burner spacing on recirculation patterns and negative effects in a firebox were studied and analyzed using Computational Fluid Dynamics, and the results of these incorporated into statistical models to determine key criteria affecting the smooth recirculating flow of infurnace flue gases. Through a rigorous statistical comparison of carefully selected simulation models it was found that different types of burners behave differently in the same arrangement and firebox setting, and that there is value to considering the burner details when assessing the constraints of burner spacing and heat input to a particular furnace. Using a multivariate regression model in the analysis of simulation results, burners can be optimally arranged in heater retrofit applications, and this is particularly useful in cases outside the API standard 165 kw/m3 [b] and suggested standard 285,000 Btu/hr-ft2 [a] heat densities. Simplifying these results can serve as an estimation tool in the design of new heaters to allow for optimal burner spacing and for assessing the possibilities of retrofitting existing furnaces with new burners for maximum heater performance and minimum emissions. This study is based on a simple refinery heater configuration and is it proposed that the procedure can be repeated to cover different applications provide tools to assist the optimization of a wider range of furnace types. 1. The Occurrence of Recirculation 1.1 Recirculation Background Process heaters are used in many different applications in petroleum and petrochemical complexes. Each application uses a unique shape of firebox, and within similar applications the specifics of the firebox can vary significantly. 1 #12;Burners are integral to heater performance, and the heater designer has the option of burner types, spacing, and count. The relatively high-velocity jet issuing forth from a burner throat into the relatively low-velocity of a firebox necessitates a recirculation flow. This recirculation improves efficiency of heat transfer to the process fluid through increased convective heat transfer, and it improves material life by reducing peak temperatures on the tubes. However, this recirculation must be accurately predicted and allowed for to eliminate uncertainty and undesired effects, such as flame impingement on the heater tubes and coalescing flames resulting in a larger-than-desired combustion zone. One consideration in heater design is how to best accommodate the internal flue gas recirculation patterns and spacing burners accordingly. The heater is a large capital expenditure compared to burners. To meet increasingly stringent regulations and to continue to improve performance, often the burners are replaced within the existing firebox because this is the most cost-effective solution. Since the fireboxes were often initially designed to work with older burner technology, undesirable effects due to recirculation patterns can surface with newer burners. This occurs particularly since newer burner technology generally delays combustion to reduce emissions, producing longer flames more susceptible to recirculation currents. To combat this, Computational Fluid Dynamics (CFD) modeling is sometimes used to predict success of retrofitting within the current configuration, or determine changes to be made to suitably shift the recirculation patterns within the firebox. These changes usually consist of different burner spacing or small alterations within the burner, since these are the only viable solutions to modifying recirculation patterns or the flame patterns therein. 1.2 Recirculation Models A driving mechanism behind recirculation in heaters is jet flow. The flow from the burners Figure 1: Jet flow into a closed domain, creating recirculation patterns; blue represents negative yvelocity, while red represents positive y-velocity (image derived from ANSYS Fluent 16.1) 2 #12;expanding at a sharp angle into the firebox creates a flow separation from the firebox wall. A natural recirculation zone necessarily forms between the burner jet and the heater wall (see Figure 1). To prevent negative effects from recirculation patterns in fireboxes, API 560 has general heater guidelines. API 560 section 6.2.5 defines a constant maximum volumetric heat release of 125 kW/m3 for oil-fired heaters and 165 kW/m3 for gas-fired heaters. API 560 section 14.1.9 defines a minimum burner-to-tube centerline clearance based on heat release per burner [b]. While this provides a simple guide for heater design, it is possible with advanced tools to safely allow increased levels of heat input in certain conditions. To predict firebox recirculation patterns, the Thring-Newby and Craya-Curtet equations offer a correlation between burner momentum and firebox recirculation patterns. The Thring-Newby and Craya-Curtet equations each contain a prediction for the maximum recirculation flow rate based on mass and momentum fluxes and fluid density [c]. These general jet equations correlate well with cold flow cases, but they do not account for heat transfer through the walls and tubes, geometry and type of burner, presence of combustion, and elevation of stack. Furthermore, the maximum recirculation flow rate does not directly correlate with the effects of specific burner design. These API guidelines and jet theory equations offer some prediction of heater recirculation patterns for proper heater design but do not make allowance for specific design parameters. Computational Fluid Dynamics offers a much more comprehensive picture of recirculation patterns and their effect on the heat transfer within a heater but at a higher resource cost. Also, a single steady state case can only predict accurate results for the specific conditions under which it was modeled. 2. Approach 2.1 Methodology Burner spacing has a significant role in the formation of recirculation patterns in a firebox and the effects of recirculation patterns. In this study, burner spacing was investigated in different ways to discover the degree of significance and the optimization potential. The first objective of this study was to see how recirculation patterns are affected by burner type and, as a result, if the same burner spacing rules can be used across all types of burners. The second objective was to find rules for burner spacing over a specified test range and to see if these rules can be consistently applied for retrofit applications. The final objective was to extrapolate the results of the second objective to aid in the design of new heaters. To accomplish these goals, Computational Fluid Dynamics was used to provide the specific data required to run statistical models. 2.2 Computational Fluid Dynamics Computational Fluid Dynamics is a useful tool in the prediction of individual heater operating cases. To expose the critical heater design parameters which affect burner performance within a radiant section the design features of the furnace must be altered within the CFD model in a rigorous and specific manner. For a meaningful regression model of the CFD results, only the critical parameters should be included while discarding the rest. A vertical cylindrical-type heater was chosen for this study. The tube diameters were held constant, and the length and diameter of the firebox were varied. A low-emission and raw gas burner were modeled. The burner size, count, spacing, and heat release were varied in a prescribed manner for each simulation. A fuel gas composition of 50 percent methane and 50 percent hydrogen by volume was used for all simulations. While the heater and burner geometries were varied for each simulation, the CFD setup was completely consistent across the different test cases with the same turbulence, 3 #12;The data chosen to extract from the cases was the maximum carbon monoxide concentration on the tubes and at the outlet. Concentration of carbon monoxide on the tubes is a commonly-used standard for measuring flame impingement on firebox tube banks. Maximum gas temperature near the tubes is another acceptable standard for measuring flame impingement on firebox tube banks, but this option was not explored. Regression models were used to interpolate the results within the bounds of the input design variables from the parameterized cases. Additionally, non-dimensionalized results were fit with regression models. 2.3 Statistical Models Statistical modeling can be a powerful tool to analyze data. However, the model can have increased robustness when the critical parameters of the study are set up with statistical modeling in mind, before any data is collected. When the correct statistical models are chosen after data collection, the analysis can produce useful results revealing predictable trends. A 2-sample t-test is a statistical tool that can be used to compare two groups of data. The analysis compares the means of the data points to conclude the likelihood that the difference between the data is only noise. A boxplot is a visual representation of this analysis, and it includes error bars, unusual observations, and the overall mean and median of each data group. A P-Value is the single number associated with the similarity between the data; a high P-Value is indicative of similar data sets, while a low PValue is suggestive that the data is being extracted from two different groups. A multivariate regression analysis is a statistical model that is used to connect and interpolate a set of data. There are many ways to set up and modify a regression model, including choosing the data variables and transforming the data set; iteratively choosing different data variables and adding or changing a transformation can increase the fit of the model to the data. An R2 value is usually associated with a regression model, and this represents the level of confidence for the fit of the regression model to the data. A binary logistic regression model compares the data to a set threshold. If the data and regression model are consistent relative to the threshold (i.e. both over or both under), the regression conforms well to the data; if they are on opposite sides of the threshold, the regression does not match the data. This type of regression represents a simple way to check a full multivariate regression. 3. Results 3.1 Burner Differences The purpose of the first section of the CFD study was to prove whether it is possible to model one burner type and extrapolate the recirculation patterns or flame effects to other burner types. The maximum recirculation rate, maximum recirculation elevation, ratio of maximum flame elevation to maximum recirculation elevation, and maximum mole fraction of carbon monoxide on the tubes were extracted from each case for a raw gas burner and low-emission burner and individually compared between the burner types using 2-sample t-tests. The closest correlation between the two burners was in the comparison of the maximum mole fraction of carbon monoxide on the firebox tubes, with a resulting P-Value of 0.050. This means that by looking at Boxplot of CO-Raw Gas, CO-Low Emission 1200 1000 800 Data chemistry, and radiation models and the same boundary conditions used, varying only the flow rates as required. 600 400 200 0 CO-Raw Gas CO-Low Emission Figure 2: Boxplot showing carbon monoxide variance between different burner types 4 #12;the mean performance, with 95.0 percent confidence the results were extracted from different data sets. The corresponding Boxplot confirms this (see Figure 2). Based on these findings, there is a statistically significant difference between the effects of different burner types, demonstrating that the burner type must be accounted for when determining appropriate burner spacing and controlling recirculation currents. This was confirmed by comparing recirculation parameters: maximum recirculation height and maximum recirculation rate; and recirculation effects of flame impingement and flame height. This was also found to be consistent across all investigated heater cases. The raw results and Boxplots for the remaining cases can be found at the end of this paper. 3.2 Retrofit Optimization The purpose of the second section of the CFD study was to discover whether a set of equations can be used to predict optimal burner spacing in a given heater design, and if so with what level of confidence. A model with 16 cases was set up methodically with one additional case, chosen to check against the resulting regression models. These cases used a Callidus low-emission burner. Only a finite range of heater designs were chosen to be modeled, excluding potential designs on both sides of the tested band. Once the cases were set up and run, the maximum mole fraction of carbon monoxide on the tubes and at the outlet was extracted from each case, and the data from each of the 16 different heater designs were analyzed with several regression models in order to extract critical heater design variables and provide equations for optimal burner design within a given heater design. In each regression model, a different set of terms was selected, some with a transformation to the data set. This process generates an optimal correlation of the regression model to the data set and maximizes the interpolative potential. An R2 of 99 percent was obtained for maximum carbon monoxide on the tubes, and an R2 of 95 percent was obtained for maximum carbon monoxide at the outlet (see Figures 3 and 4). When the data from the 16 input cases was compared using a binary logistic regression with a maximum acceptable carbon monoxide on the firebox tubes of 200 PPM, the regression was able to predict all cases successfully. When a binary logistic regression was applied to a maximum acceptable carbon monoxide at the heater outlet of 20 PPM, the regression was able to predict with success 14 of the 16 cases. However, when a binary logistic regression was applied over both thresholds together, 15 of the 16 normal cases and the additional case were successfully predicted. With an adjusted maximum acceptable carbon monoxide on the Maximum Carbon Monoxide on the Tubes 2500 2000 1500 1000 CFD Regression 500 0 Figure 3: Plot showing regression model prediction versus CFD prediction of carbon monoxide on the tubes 5 #12;Maximum Carbon Monoxide at the Outlet 3000 2500 2000 1500 CFD 1000 Regression 500 0 Figure 4: Plot showing regression model prediction versus CFD prediction of carbon monoxide at the outlet tubes of 185 PPM and an adjusted maximum acceptable carbon monoxide at the outlet of 22 PPM, the statistical model could predict success or failure of the burner installation within a given firebox in all cases investigated with CFD, including the additional case. With 97.4 percent confidence, derived from comparing the regression and CFD models with a two-sample ttest, these regression equations are therefore proven to accurately predict optimal burner spacing in retrofit applications for cases that fall in the tested range. 3.3 New Heater Design The third goal of the study was to extrapolate rather than interpolate the data to be useful for heater design. This was accomplished by nondimensionalizing the terms used with success from the earlier regression model. Within the bounded range of the regression model, a second regression model was created with only three non-dimensional terms, one additional term (see Figures 5 and 6). This non-dimensional regression has an R2 of 73 percent for carbon monoxide on the heater tubes and an R2 of 40 percent for carbon monoxide at the outlet. While this may seem outside of the bounds of adequacy, when a binary logistic regression with the same acceptability thresholds of 200 PPM on the firebox tubes and 20 PPM at the heater outlet was used against this non-dimensional regression, the model correctly predicts 12 of the 16 normal cases and the additional case. Using the simple API maximum volumetric heat density of 165 kW/m3 as a comparison with the same binary logistic regression correctly predicts only nine of the 17 cases. Maximum Carbon Monoxide on the Tubes 3000 2500 2000 1500 CFD 1000 Regression 500 0 Figure 5: Plot showing non-dimensional regression model prediction versus CFD prediction of carbon monoxide on the tubes 6 #12;Maximum Carbon Monoxide at the Outlet 3000 2500 2000 1500 CFD 1000 Regression 500 0 Figure 6: Plot showing non-dimensional regression model prediction versus CFD prediction of carbon monoxide at the outlet Using a proposed maximum area heat density of 285,000 Btu/hr-ft2 with the same binary logistic regression correctly predicts 12 of the 17 cases [a]. Using only three terms, this can be an improved rough guide for heater design within the tested bounds. This non-dimensional regression model was tested outside of the bounds with one case on either side of the tested range, and the results from both tests did not match the regression, both failing the binary logistic regression (see Figures 5 and 6). 4. Conclusion When studying or predicting recirculation patterns or effects, different types of burners must be studied independently. Optimal burner spacing can be found in existing applications within the tested range through interpolation. The general design limits of new vertical cylindrical heaters can be estimated for the range investigated, offering an improved alternative over a single heat density number. The results of this Computational Fluid Dynamics study, coupled with careful statistical analysis, can be used to accomplish many goals. By optimizing burner spacing in existing applications, many applications of heaters with extreme heat densities currently outside of the general range of acceptance for low-emission retrofits can be effectively retrofitted with lowemission burners. In the design of new heaters, solutions with extreme heat densities can be exploited successfully, offering a costcompetitive advantage. A technical advantage can be achieved by combining Computational Fluid Dynamics and statistical modeling. There is opportunity for continuing benefit from this line of study, especially with the non-dimensional regression models. There is a potential for more value by successfully creating a regression model that will extrapolate accurately to cover a large range of cases. 5. Future Work Building on the success of the central data range, more work should be done to model the lower and upper data ranges, such that a complete model covering all reasonable retrofit and new vertical cylindrical heater applications can be created. The non-dimensional regression model also should be tested with other heater designs to see if it correlates acceptably. The regression models created are only accurate with Callidus low-emission burners but could be expanded to other burner types. The general implication of this work is that advanced models and statistical analysis can provide for more optimized engineering of heater revamps for increased capacity and reduced NOx emissions. 7 #12;6. References [a]. Dugué, Jacques; Private conversations. [b]. Fired Heaters for General Refinery Service: ISO 13705:2006 (Identical), Petroleum, Petrochemical and Natural Gas Industries: Fired Heaters for General Refinery Service. Washington, D.C.: American Petroleum Institute, 2007. Print. [c]. Rhine, Jeffrey M., and Robert J. Tucker. Modelling of Gas Fired Furnaces and Boilers: And Other Industrial Heating Processes. London: British Gas, 1991. Print. 7. Raw Results Maximum Recirculation Rate Elevation of Maximum Recirculation Rate Ratio of Elevation of Flame Height to Elevation of Maximum Recirculation Rate Maximum Carbon Monoxide on the Tubes 0.005 0.005 0.045 0.05 Table 1: P-Values for Raw Gas versus Low-Emission Burners Boxplot of Elevation-Raw Gas, Elevation-Low Emission 14 8. Extra Plots 12 Boxplot of Recirculation Rate-Raw Gas, Recirculation Rate-Low Emission 10 Data 3.5 3.0 6 4 2.5 2 2.0 0 Elevation-Raw Gas Elevation-Low Emission 1.5 Figure 8: Boxplot showing elevation of maximum recirculation rate variance between different burner types 1.0 Recirculation Rate-Raw Gas Recirculation Rate-Low Emission Boxplot of Ratio-Raw Gas, Ratio-Low Emission Figure 7: Boxplot showing maximum recirculation rate variance between different burner types 16 14 12 10 Data Data 8 8 6 4 2 0 Ratio-Raw Gas Ratio-Low Emission Figure 9: Boxplot showing ratio of elevation of maximum flame height to elevation of maximum recirculation rate variance between different burner types 8 |