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  • PPM to lb/MMCF

    I am trying to find a conversion equation for converting parts per million of known gases to pounds per million cubic feet. On one hand, I have found a few sources that convert to pounds per cubic foot, at 6.2428E-05, and would just multiple that times 10^6 to get million cubic feet. BUT, I am having no luck in finding the basis of the 6.2428E-05. What is the molar mass that this factor is based upon, because I need to apply this across multiple known gases with different molecular weights.

    Plus, 100 ppm would convert to 6242.8 lb/MMCF, which, for other reasons, seems entirely wrong.


    Apologies about the writing, English is my first language, which makes this more problematic then if English was a second language.

  • #2
    Originally posted by HK57 View Post
    I am trying to find a conversion equation for converting parts per million of known gases to pounds per million cubic feet. On one hand, I have found a few sources that convert to pounds per cubic foot, at 6.2428E-05, and would just multiple that times 10^6 to get million cubic feet. BUT, I am having no luck in finding the basis of the 6.2428E-05. What is the molar mass that this factor is based upon, because I need to apply this across multiple known gases with different molecular weights.

    Plus, 100 ppm would convert to 6242.8 lb/MMCF, which, for other reasons, seems entirely wrong.


    Apologies about the writing, English is my first language, which makes this more problematic then if English was a second language.
    Ppm ratios of gases are normally given as molar ratios, micromoles of pollutant per mole of gas mixture. You would need to know the molar mass of the pollutant, and the molar volume of the mixture, which would depend on temperature and pressure. Since you are using Customary units, I would assume you would use pound-moles. I would only know how to do this in metric then convert. As a minimum, we need to know the pollutant and it's molecular weight and the temperature and pressure of the mixture, as well as whether it approximates an ideal gas.

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    • #3
      Let's assume standard barometric pressure and temperature. 527.67 Rankine and 29.921 inches of Mercury; 293.15 Kelvin and 760 millimeters of mercury. The three most common molecular weights of the known gases I am dealing with are 64.0188, 46.0055, and 28.0104 g/mol and they can approximate ideal gases for these purposes. Of course I'd like to know the different steps, if I needed to apply Normal pressure and temperature or the temperature and pressure of the conditions.

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      • #4
        Originally posted by HK57 View Post
        Let's assume standard barometric pressure and temperature. 527.67 Rankine and 29.921 inches of Mercury; 293.15 Kelvin and 760 millimeters of mercury. The three most common molecular weights of the known gases I am dealing with are 64.0188, 46.0055, and 28.0104 g/mol and they can approximate ideal gases for these purposes. Of course I'd like to know the different steps, if I needed to apply Normal pressure and temperature or the temperature and pressure of the conditions.
        Standard molar volume is 22.414 dm at 273.15 K, 24.055 dm at 293.15 K (and standard pressure).

        1 ppm = 1 mol (pollutant)/ mol (gas mixture). For your first gas 64.0188 g/mol, we have

        64.0188 g/mol x 1 mol/mol x 1 mol/0.024055 m or 2.661135 mg/m

        1000 ft = 28.3168 m, so it would contain 75.3611 mg or 0.000 166 lb/1000 ft

        So 1 ppm = 0.000 166 lb/1000 ft

        For other pollutants, just substitute the molecular weight in g/mol
        For other temperatures and pressures determine molar volume of ideal gas

        22.414 dm x Tact/Tstd x Pstd/Pact, where Tstd = 273.15 K, Pstd = 101.325 kPa or 760 mm Hg

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        • #5
          Originally posted by JohnS View Post

          Standard molar volume is 22.414 dm at 273.15 K, 24.055 dm at 293.15 K (and standard pressure).

          1 ppm = 1 mol (pollutant)/ mol (gas mixture). For your first gas 64.0188 g/mol, we have

          64.0188 g/mol x 1 mol/mol x 1 mol/0.024055 m or 2.661135 mg/m

          1000 ft = 28.3168 m, so it would contain 75.3611 mg or 0.000 166 lb/1000 ft

          So 1 ppm = 0.000 166 lb/1000 ft

          For other pollutants, just substitute the molecular weight in g/mol
          For other temperatures and pressures determine molar volume of ideal gas

          22.414 dm x Tact/Tstd x Pstd/Pact, where Tstd = 273.15 K, Pstd = 101.325 kPa or 760 mm Hg
          Oops: The above is correct but you wanted per million cubic feet, so 1 ppm = 0.166 lb/MMCF for the 64.0188 g/mol gas

          Also, I have to caution you. Please do not use the above for compliance. Most emission regulations require correction of the exhaust volume to dry exhaust (exclude the water vapor) at a specified residual oxygen level (which determines how much excess air you can run in combustion). The regulations vary by country and type of prime mover (diesel engine, gas turbine, steam plant, etc). You need to consult an engineer familiar with applicable local regulations for compliance.

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          • #6
            I am not very good at "science in Customary" but I will take a cut at it. Just as I can regard a molar ppm as mol/mol, I can regard it as pound-moles per million pound-moles (lb-mol/MMlb-mol). Now I only need to convert the numerator to mass and the denominator to volume (in Customary)

            For the numerator, multiply the ppm level by molecular weight (pounds per pound-mole) to get mass, ppm x 64.0188 lb for the first gas. That is mixed in 1 million pound-moles of gas mixture.

            For the denominator, how big is 1 million pound-moles of ideal gas. The ideal gas equation, PV = nRT, works in any units if you have the gas constant, R, in those units. The Wikipedia article on gas constant gives it in various units. Closest to our purpose is 0.730 240 507 295 273 atmft/(Rlb-mol). Your pressure is 1 atm, so we only need to multiply by temperature to get 385.326 ft/lb-mol. But we have 1 million pound-moles in our denominator, and you want million cubic feet so 385.326 MMCF/MMlb-mol

            We have a simple formula, ppm MW/385.326 lb/MMCF, agreeing with earlier post.

            For other temperatures and pressures recalculate molar volume V/n = RT/P, using above (Customary) value of the gas constant. to replace 385.326.

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            • #7
              I did catch that million cubic feet so had made that correction.
              The 385.3 number is more familiar to me as something we have also made use of.

              I have come to dislike seeing CF, or equivalents in other unit dimensions - I am handed CF but then look over at my calculations for ACF, NCF, SCF, DSCF, WSCF and am left with... okay, where does CF fit into those.

              You give me a better understanding then what I've had before, when it starts clicking together - but I seem to just be a hobbyist about this with no actual background in understanding it.

              Thanks

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