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# Viscosity of Gases

01/30/2021 11:38 AM

Can anybody help me with a formula to calculate the viscosity of a gas mixture?

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#1

### Re: Viscosity of gases

01/30/2021 12:11 PM

For each gas, sum viscosity x mole fraction x sqrt(Molecular weight) in numerator

For each gas, sum mole fraction x sqrt(Molecular weight) in denominator

The ratio is the viscosity of the mixture.

Here is an example.

https://petrowiki.spe.org/Gas_viscosity#:~:text=%CE%BCga%20%3D%20viscosity%20of%20the,atmospheric%20pressure%20(obtained%20from%20Fig.

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#3

### Re: Viscosity of gases

01/30/2021 12:18 PM

Thank you for the information. The formula is that from Millers Flow Handbook and uses a nomograph. The numbers from said nomograph are rather open to interpretation. I have produced a spreadsheet based on his formula but I think it is 15% error to a known figure.

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#5

### Re: Viscosity of gases

01/31/2021 12:21 PM

It would be interesting to the group to know what your known reference is?

I’m not surprised there might be some error in a relationship undoubtedly empirically derived from a clever combination of measurable material properties, outliers are how we advance our knowledge.

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#6

### Re: Viscosity of gases

02/01/2021 7:08 AM

I hope I have interpreted your question accurately.

The source for my information is Miller's Flow Handbook, where he shows the formula - also kindly submitted by Rixter. Even increasing the size of the nomograph from A5 (as in the book) to A4 still leaves something to be desired.

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#7

### Re: Viscosity of gases

02/02/2021 12:11 AM

I wouldn’t be surprised you would find an error by extending a nomograph. The formula would generally be preferred if you are looking for accuracy.

My question is, what is the particular gas combination that you know is being wrongly reported by the formula? And how do you know what the actual viscosity is, I assume by direct measurement?

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#8

### Re: Viscosity of gases

02/02/2021 5:32 AM

My gases combination is methane 40%, ethane 20%, propane 20%, CO2 5%, hydrogen 5% and nitrogen 10%. Temperature is 26.7°C and pressure is 101 kPa ab.

I believe the viscosity is 0.0102 cP, but my calculation via Miller's nomograph is 0.00823 cP, which is approx. 19% lower than my starting figure. So I wondered whether there was another formula by which I could check those figures. I don't suppose you have a formula - do you?

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#9

### Re: Viscosity of gases

02/02/2021 11:27 AM

No, I only have Richardson’s book, but I haven’t looked at the calculation method. I misunderstood when you said you enlarged the nomograph, I thought you were extrapolating beyond the limits.

Just curious at this point, what leads you to believe the the actual viscosity is different? You have higher than expected pressure losses in a pipe line, for example?

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#10

### Re: Viscosity of gases

02/03/2021 6:20 AM

I achieved the figure of 0.0102 cP via another piece of software and wondered whether I could check if that original figure was correct. So, I tried Miller's method. I could have taken figures from the CRC Handbook, but that is somewhat time consuming, even though the results are more accurate. For the purpose of this investigation I just ignored any possible losses.

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#11

### Re: Viscosity of gases

02/03/2021 12:36 PM

I now understand the reason for your question, sorry, no help here..., but very interesting for our readers. I don’t have CRC tables, and haven’t run across software to do things like that, lately in my career I usually plug formulas into fill in the blanks spreadsheets and hammer out a solution often because I can’t or don’t know how to factor the equations or I’m too lazy.

You should mention the software someplace too, as it could be helpful to others in the future, or may come up as a search term for someone else more knowledgeable or helpful than I.

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#12

### Re: Viscosity of gases

02/03/2021 12:47 PM

The software used is GPSA Gas Prop - read only - compatibility mode.

It was written by Dennis Kirk and produces all the bells and whistles that I have required. If you investigate this site I would appreciate your feedback, or observations from others who might be interested in this fascinating topic!

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#2

### Re: Viscosity of gases

01/30/2021 12:13 PM

"The viscosity of a gas can be thought of as a measure of its resistance to flow and is measured in the CGS unit Poise = dyne sec/cm2. The viscosity of gases near room temperature are in the centiPoise range, so that is a commonly used unit. Gas viscosity is only weakly dependent on pressure near atmospheric pressure."

" The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature."

https://www.engineersedge.com/physics/viscosity_of_air_dynamic_and_kinematic_14483.htm

Numerical estimates for the bulk viscosity of ideal gases

https://aip.scitation.org/doi/10.1063/1.4729611

The question you want to ask yourself right now is, just how far down the rabbit hole do I want to go...?

https://pubs.acs.org/doi/10.1021/ie50475a011

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#4

### Re: Viscosity of gases

01/30/2021 12:22 PM

Thank you for the information. Much to ponder on.

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