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).

൬ × ݁ݎݑݏݏ݁ݎ݅ܿܲݎݐ݁ ݉݋ݎܽܤ =݁ݎݑݏݏ݁ݎ݈݅ܿܽܲݐ݅ݎܥ

݇+ 1

2

൰

௞

௞ିଵ

Where: k = ratio of specific heats (CP / CV)
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

൬ × 14.38= ݁ݎݑݏݏ݁ݎ݈݅ܿܽܲݐ݅ݎܥ

1.142 + 1

2

൰

ଵ.ଵସଶ

ଵ.ଵସଶିଵ

݅ܽݏ݌ 24.96 =

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.

௖݃ × ܶ × ܴ × ݇ඥ = ݊݀ݑ݋݂ܵ݋ ݁݁݀݌ܵ

Where: k = ratio of specific heats (CP / CV)

R = Universal Gas Constant / Molecular Weight (1545.3 / MW)

T = Fuel Temperature (°R)

gc = 32.2 (lbm – ft) / (lbf – s2)

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 – lbf)/(lbm – °R)

36.723 × 1.142ඨ = ݊݀ݑ݋݂ܵ݋݁݁݀݌ܵ

௙݈ܾ −ݐ݂

݈ܾ௠ − °ܴ

× 567°ܴ × 32.2

ݐ݂ − ௠݈ܾ

875 = ଶݏ − ௙݈ܾ

ݐ݂

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.

×ሶ݉ = ܵܨܥܣ

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

5241 = ܵܨܥܣ

݈ܾ݉

ݎh

×

1

42.08

݈݁݋ ݉ ݈ܾ−

݈ܾ݉

× 379.5

ܨܥܵ

݈݁݋ ݉ ݈ܾ−

×

1

3600

ݎh

݁ܿݏ

×

(460 + 107)

(460 + 60) ×

14.696

14.29

14.723 = ܵܨܥܣ

ݐ݂

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.

= ݕݐܿ݅݋ܸ݈݁ݐ݅ݔܧ

ܵܨܥܣ

݁ܽݎܣݐ݅ݔܧ

Example Calculation for Test P1L run 1

Exit Area = 3.65 in2

14.723 = ݕݐܿ݅݋ܸ݈݁ݐ݅ݔܧ

ݐ݂

ଷ

݁ܿݏ

×

1

3.65 ݅݊ଶ

×

144

1

݅݊

ଶ

581 = ଶݐ݂

ݐ݂

݁ܿ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 1b 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 1.271 11.7 711

P3L run 3 14.37 4602 87 28.63 1.267 11.68 719

Average 708