Rev. 0

Document: 9136991-GP0-P07-0010_0 Page 1 of 5 

# Report on Emissions Testing of Pressure Assisted LRGO-HC and Steam Assisted SKEC Burners – Supplement #2

John Zink Shop Order: 9136991 Prepared for 

## The Dow Chemical Company

Purpose: The EPA has performed calculations of exit velocity for the pressure-assisted flare tests.

There is a discrepancy between the JZ calculated values and the EPA values. This discrepancy for the high pressure tests is most likely due to variations in the ratio of specific heat used for the calculations. This supplement has been created to document the exit velocity calculation procedure used by JZ and the parameters used for those calculations. Introduction: The velocities and critical pressures presented in revision 0 of the John Zink report were

calculated using John Zink proprietary software programs. In reviewing the underling formulas imbedded in those programs, it was determined that the ratio of specific heats (gamma) was not adjusted for varying temperature. This supplement will report revised velocity values using temperature adjusted gamma values. Calculation of Critical Pressure: Critical pressure is calculated to determine if a given test point has a burner pressure greater than or less than the critical pressure. If the burner pressure is equal to or greater than the critical pressure, then the velocity of the gas exiting the burner is Mach 1 (the speed of sound).

ܥݎ ݅ ݐ ݅ ܿ ܽ ݈ ܲ ݎ ݁ ݏ ݏݑݎ ݁ = ܤ ܽݎ ݋ ݉ ݁ ݐݎ ݅ ܿ ܲ ݎ ݁ ݏ ݏݑݎ ݁ × ൬ ݇ + 1 2 ൰ ௞ ௞
ି ଵ
Where: k = ratio of specific heats (C P / C V )Rev. 0

Document: 9136991-GP0-P07-0010_0 Page 2 of 5 Example Calculation for Test P1H run 1 Barometric Pressure = 14.38 psia Fuel Temperature = 107°F k = 1.142

ܥݎ ݅ ݐ ݅ ܿ ܽ ݈ ܲ ݎ ݁ ݏ ݏݑݎ ݁ × 14.38= ൬ 1.142 + 1 2 ൰ ଵ
. ଵ ସ ଶ ଵ
. ଵ ସ ଶ
ି ଵ 24.96 = ݌ ݏ ݅ ܽ Critical pressure in gage units = 24.96 psia – 14.38 psia = 10.58 psig Since the burner fuel pressure is 14.5 psig, which is greater than 10.66 psig, the fuel velocity exiting the burner equals the speed of sound.

Calculation of Speed of Sound: If the burner pressure is greater than the critical pressure, the exit velocity equals the speed of sound. Since a normal shock wave forms across the exit when the gas pressure is above the critical pressure, the pressure of the gas at the exit is higher than the barometric pressure. While the gas pressure at the exit can be calculated and the results used to determine a volumetric flow rate, the simplest approach is to calculate the speed of sound for the given conditions. ܵ݌ ݁ ݁ ݀ ݋ ݂ ܵ ݋ ݑ݊ ݀ = ඥ݇ × ܴ × ܶ × ݃ ௖ Where: k = ratio of specific heats (C P / C V )

R = Universal Gas Constant / Molecular Weight (1545.3 / MW) T = Fuel Temperature (°R) g c = 32.2 (lb m – ft) / (lb f – s 2 ) Example Calculation for Test P1H run 1 k = 1.142 T = (460 + 107) = 567°R MW = 42.08 R = 1545.3/42.08 = 36.723 (ft – lb f )/(lb m – °R)

ܵ݌ ݁ ݁ ݀ ݋ ݂ ܵ ݋ ݑ݊ ݀ = ඨ36.723 × 1.142 ݂ ݐ
− ݈ ܾ ௙ ݈ ܾ ௠ − ° ܴ × 567° ܴ × 32.2 ݈ ܾ ௠ − ݂ ݐ ݈ ܾ ௙ − ݏ ଶ 875 = ݂ ݐ

ݏ The fuel exit velocity for test P1H run 1 is 875 ft/sec.Rev. 0

Document: 9136991-GP0-P07-0010_0 Page 3 of 5 Calculation of Volumetric Flow Rate: When the burner pressure is less than the critical pressure, the exit velocity from the tip is less than the speed of sound. In order to determine the exit velocity, the actual volumetric flow rate must be calculated. This is accomplished by determining the number of lb-moles of gas and converting to cubic feet at a standard temperature and pressure. The volumetric flow rate at standard temperature and pressure are adjusted for actual temperature and pressure.

ܣ ܥܨܵ = ݉

ሶ × 1 ܯ ܹ × 379.5 3600 × (460 + ܶ) (460 + 60) × 14.696

ܲ Where: ACFS = Actual Cubic Foot per Second

݉ ሶ = mass flow rate (lbm/hr) MW = Molecular Weight T = Fuel temperature (°F) P = Barometric Pressure (psia) 379.5 SCF/lb-mole (standard temperature = 60°F, standard pressure = 14.696 psia) 3600 sec/hr Example Calculation for Test P1L run 1

݉ ሶ = 5241 lbm/hr MW = 42.08 T = 107°F P = 14.29 psia

ܣ ܥܨܵ 5241 = ݈ ܾ ݉

hݎ × 1 42.08 ݈ ܾ

− ݉ ݋ ݈ ݁ ݈ ܾ ݉ × 379.5 ܵ ܥܨ

݈ ܾ

− ݉ ݋ ݈ ݁ × 1

3600 hݎ ݏ ݁ ܿ × (460 + 107) (460 + 60) × 14.696

14.29
ܣ ܥܨܵ 14.723 = ݂ ݐ ଷ

ݏ ݁ ܿRev. 0

Document: 9136991-GP0-P07-0010_0 Page 4 of 5 Calculation of Sub-Sonic Velocity: Once the actual volumetric flow rate is known, the flow rate is divided by the exit area of the flare to obtain a velocity.
ܧݔ ݅ ݐ ܸ ݁ ݈ ݋ ܿ ݅ ݐݕ = ܣ ܥ ܨܵ ܧݔ ݅ ݐ ܣ ݎ ݁ ܽ Example Calculation for Test P1L run 1 Exit Area = 3.65 in2
ܧݔ ݅ ݐ ܸ ݁ ݈ ݋ ܿ ݅ ݐݕ 14.723 = ݂ ݐ ଷ ݏ ݁ ܿ × 1 3.65 ݅ ݊ ଶ × 144

1 ݅ ݊ ଶ ݂ ݐ ଶ 581 = ݂ ݐ

ݏ ݁ ܿ The fuel exit velocity for test P1L run 1 is 581 ft/sec.Rev. 0

Document: 9136991-GP0-P07-0010_0 Page 5 of 5 Table of Results:The following table provides the parameters used and the resulting velocities for the pressureassisted flare tests.

Test ID Barometric

Pressure Mass

Flow Rate Fuel

Temperature Fuel

MW k Critical

Pressure Actual

Exit Velocity psia lbm / hr °F psig ft/ sec P1H run 1 14.38 8576 107 42.08 1.142 10.58 875 P1H run 2 14.29 8201 92 42.08 1.145 10.55 865 P1H run 3 14.35 8146 122 42.08 1.138 10.53 885 Average 875
P1L run 1 14.29 5241 107 42.08 1.142 10.52 581 P1L run 2 14.35 5394 102 42.08 1.143 10.57 590 P1L run 3 14.4 5633 111 42.08 1.141 10.59 624 Average 598
P2H run 1 b 14.29 7965 89 33.36 1.241 11.47 1008 P2H run 2 14.36 7917 98 33.34 1.239 11.42 1016 P2H run 3 14.39 7859 98 33.34 1.239 11.42 1016 Average 1013
P2L run 1b 14.29 4955 82 32.94 1.25 11.46 671 P2L run 2 14.36 4921 92 32.87 1.249 11.51 676 P2L run 3 14.36 4819 93 32.82 1.25 11.52 665 Average 671
P3H run 1 14.3 7584 82 28.61 1.269 11.63 1094 P3H run 2 14.35 7503 84 28.51 1.27 11.68 1098 P3H run 3 14.38 7449 89 28.49 1.268 11.67 1103 Average 1098
P3L run 1b 14.36 4599 66 28.55 1.275 11.73 694 P3L run 2 14.36 4577 82 28.57 1.2 71 11.7 71 1 P3L run 3 14.37 4602 87 28.63 1.267 11.68 719 Average 708