[tinkpen]

Hoping someone can help me out with how to calculate the average H₂S mole fraction in the inlet gas of a sour natural gas processing plant based on known SO₂ emissions, S produced and inlet gas volume.  I have tried using the equation below (provided in a consultant's report) but end up with mole fractions greater than 1 in some cases or a much higher fraction than seems reasonable for inlet gas that should be composed mostly of methane.  If someone could review the equation and let me know where the error could be, it would be greatly appreciated!  I should mention that I am not an engineer or a chemist by trade (science background though) so if anyone is willing to walk me through how this question should be approached so I can understand the theory behind the equation that would also be great.

Here is the equation:

Y_H2S=(V_STP*(ER_SO2/MW_SO2 + m_S/MW_S)*MW_H2S*g_c)/Q_receipts

where,
Y_H2S = average mole fraction of H₂S in the inlet gas received at a facility (kmol/kmol)
V_STP = volume of one mole of gas at standard conditions of 101.325 kPa and 15^oC (m³/kmole) = 23.6444813 m³/kmole
ER_SO2 = reported emission rate of SO₂ (t/year)
m_S = reported production rate of elemental sulphur (t/y)
MWSO₂ = molecular weight of SO₂ (kg/kmol) = 64.066 kg/kmol
MW_S = atomic weight of elemntal sulphur (kg/kmol) = 32.066 kg/kmol
MW_H2S = molecular weight of H₂S (kg/kmol) = 34.08 kg/kmol
Q_receipts = total field gas receipts (10³m³/y)
g_c = constant of proportionality = 1
       

[Borek]

Can you show example data giving incorrect results? At first sight the logic behind the equations looks OK (but then I have not analyzed it thoroughly).

My first instinct would be to check the units...

[tinkpen]

Sure! 

here are examples using data from three different gas plants:

Gas Plant 1 has SO₂ emissions of 10,000 t/y, with S production of 600,000 t/y and an annual gas volume processed of 5X10⁹m³.  Using the equation above I get a mole fraction for H₂S of 3.04, which is obviously incorrect.

Gas Plant 2 has SO₂ emissions of 5600 t/y, with S production of 55,000 t/y and also has an annual gas processing volume of 5X10⁹m³.  The H2S mole fraction I get using the above equation is 0.2905, which seems very high for a flow composed mostly of methane.

Gas plant 3 has  SO₂ emissions of 200 t/y, with S production of 2500 t/y and also has an annual gas processing volume of 2.15X10⁶m³.  The H2S mole fraction I get using the above equation is 0.3039, which again seems very high.

Any help would be appreciated! 

[Borek]

Y_H2S=(V_STP*(ER_SO2/MW_SO2 + m_S/MW_S)*MW_H2S*g_c)/Q_receipts

Now that I tried to plug in the numbers looks like there is a mistake in the equation - MW_H2S shouldn't be there.

That will make your results 34 times lower.