Real gas pseudo-pressure calculation

[pet_spec]

Hey guys,

I am trying to verify the pseudo-pressures shown in the image below:

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I tried to calculate pseudo-pressure by direct integration of the :

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Can you please the method for exact pseudo-pressure calculation?

Thanks.

[vinomarky]

It looks to be correct. Perhaps the problem is that you are doing the integration too coarsely?

If you fit a 5th order polynomial to viscosity, and 3rd order to Z as functions of P, then calculate the respective values at single psi increments and sum appropriately I get values that are pretty close - if you did the same via mathematical integration of the polynomials you'd probably get bang on.

Even if you use the data as given, you'd get in the ballpark

[pet_spec]

It looks to be correct. Perhaps the problem is that you are doing the integration too coarsely?

If you fit a 5th order polynomial to viscosity, and 3rd order to Z as functions of P, then calculate the respective values at single psi increments and sum appropriately I get values that are pretty close - if you did the same via mathematical integration of the polynomials you'd probably get bang on.

Even if you use the data as given, you'd get in the ballpark

Can you please show your method on paper and attach its scanned version? How do you make polynomial fitting?

Thanks

[vinomarky]

You are going to have to learn how to be a bit more of a problem solver. This is not difficult stuff here - you'd expect technical assistants to need everything spelled out, engineers need to be able to think through problems.

Learn how to use Excel - become an Excel guru, the skills will hold you in good stead through your career

If you simply take those values from the table and plot then vs pressure in Excel, then ADD TRENDLINE - select polynomial of sufficient order to represent the shape, then ask it to annotate with the equation. Format the annotation to scientific with 3 decimals and read off the values. If you were doing this on many columns of data you could do some googling and see how to do polynomial fitting with array formula.
Using just the coarse data in the table, the math is trivially simple;

P ----------- m(p)
400 ----------- 2*400/(0.01286*0.937) * (400-0) = 26.5 E6
800 ----------- 2*800/(0.01390*0.882) * (800-400) + 26.5E6 = 78.7E6

Obviously, there are some significant errors using 400psi steps, but since we usually use m(p) in terms of differences between two relatively narrow pressure points, the absolute error is less important than the relative error between two points.

If you use polynomial approximations and do the above math on single psi steps (or less), or even better, direct integrate the ugly polynomials then you should get far better agreement.

[pet_spec]

You are going to have to learn how to be a bit more of a problem solver. This is not difficult stuff here - you'd expect technical assistants to need everything spelled out, engineers need to be able to think through problems.

Learn how to use Excel - become an Excel guru, the skills will hold you in good stead through your career

If you simply take those values from the table and plot then vs pressure in Excel, then ADD TRENDLINE - select polynomial of sufficient order to represent the shape, then ask it to annotate with the equation. Format the annotation to scientific with 3 decimals and read off the values. If you were doing this on many columns of data you could do some googling and see how to do polynomial fitting with array formula.
Using just the coarse data in the table, the math is trivially simple;

P ----------- m(p)
400 ----------- 2*400/(0.01286*0.937) * (400-0) = 26.5 E6
800 ----------- 2*800/(0.01390*0.882) * (800-400) + 26.5E6 = 78.7E6

Obviously, there are some significant errors using 400psi steps, but since we usually use m(p) in terms of differences between two relatively narrow pressure points, the absolute error is less important than the relative error between two points.

If you use polynomial approximations and do the above math on single psi steps (or less), or even better, direct integrate the ugly polynomials then you should get far better agreement.

Thanks a lot . That was really helpful.