API 521 Eq (4)

[ginsoakedboy]

Equation (4) of API 521 suggests a calculation of cubic expansion coefficient as:

alpha_v = (rho_2)^2 - (rho_1)^2
-------------------------------
2 x dT x rho_2 x rho_1


However if I do the same calc from first principles, I get:

alpha_v = (rho_2 - rho_1) x 2
--------------------------
dT x (rho_2 + rho_1)


Numerically, these turn out to be really close but, I don't understand why is there a difference in the relations. What am I missing?

 

[ginsoakedboy]

Edit to the last post: The signs in the numerators should be reversed in both relations.

Also, I do not have access to Perry's. Please describe the reasoning behind the difference in these relations.

 

[ginsoakedboy]

Does anyone have an idea what I am on about here?

 

[ginsoakedboy]

Wow, the silence is deafening.

 

[SNORGY]

htlyst:

I have an old edition of API RP 521. (1999).

Forgive me accordingly...but the Equation #4 therein contained has nothing at all to do with a cubic expansion coefficient. I wanted nonetheless to look into this and do the derivation myself so that I could provide a constructive post here.

I regret that, as it is, the only thing I can offer takes the correctness of your post at face value. If one accepts that, and then if I see two equations, one with a term in the form of (a^2 - b^2) and the other with a term in the form of (a + b), I immediately look for some difference or error in the algebra regarding how the "sums and differences of squares" are handled. If you feel one or the other equations is in doubt, my first inclination is to look there.

I am sorry I am unable to be of more help with the information I have at my disposal.

Regards,

SNORGY.

 

[ginsoakedboy]

SNORGY,

Thank you for your response. I have included a screenshot of the latest API 521 as an attachment.

I actually did try deriving Equation 4 and was able to. The only thing I had done differently was to substitute 1/rho = v (sp. vol.) at a different step in the derivation.

I have posted my derivations and results in another forum at:

http://www.cheresources.com/invision/index.php?/topic/8778-equation-4-of-api-521/

(click on thumbnails)

While I can explain what causes difference, I still don't know why is there a difference. Does anyone know?