This article discusses the implementation methods for ASTM Petroleum table 54 C as per API MPMS Chapter 11.1 version 2004/2007.
In my previous post we talked about the implementation method used to calculate the CTPL (correction for temperature and pressure on a liquid) using table 54, for products, crude oil and lubrication oils.
I briefly mentioned table 54C, but since the implementation method for table 54C differs slightly from its counterparts for table A, B and D and the article was already lengthy enough, I thought it a good idea to cover table C separately.
Recapitulating from the previous post we saw that for table 54 the following inputs are required:
- commodity group A, B or D (if a pre-calculated thermal expansion coefficient α60 is not given)
- α60 (if commodity group A, B or D is not given)
- observed temperature and base temperature °C
- density at 15 °C (if we need not only CTL but also CPL)
- alternate pressure
The implementation then returns as output:
– the combined correction factor for temperature and pressure (CTPL)
- the scaled compressibility factor (Fp)
In other words, for table 54C we use as input α60, observed temperature, density 15 °C, alternate pressure and base temperature (which is 15 °C).
With the above information the CTL can very quickly be calculated if that is all what is required. The iteration process that was described in the previous post is used to establish the density at 60 °F corresponding to the input density 15 °C, but for calculating only the CTL if α60 is given we do not need this.
If both CTL and CPL are required then the entire process as described in the previous post must be completed, the difference being that instead of calculating α60 using K0, K1 and K2 based on the commodity group, we simply use the value given.
The CTL then follows from the formula as given previously:
CTL = exp(-α * tDiff * [1 + 0.8 * α * (tDiff + 0.01374979547)])
This means also that if we do need the compressibility factor as well, we need to supply a density 15 °C, and instead of calculating α60 during the iteration process, we use the α60 as supplied initially, and go through the iteration process as described.
Let us take an example from the protocol for producing table 54C as described in APIMPMS 126.96.36.199:
α60 = 0.0009005 /°F (= 0.000500222 /°C)
observed temperature = 35.25 °C
tau = observed temperature T(Celsius) / 630: 35.25/630 = 0.055952380952381
delta = (a1+(a2+(a3+(a4+(a5+(a6+(a7+a8*tau)tau)tau)tau)tau)tau)tau)tau: -0.008961120743
with the factors a1…a8 given as:
a1 = -0.148759
a2 = -0.267408
a3 = 1.080760
a4 = 1.269056
a5 = -4.089591
a6 = -1.871251
a7 = 7.438081
a8 = -3.536296
The resulting IPTS68 temperature T68 is then:
T68,C = T90 – delta : 35.25 - (-0.008961120743) = 35.258961120743
T68,F = T68 * 1.8 + 32:
T68,F = 35.258961120743* 1.8 + 32 = 95.466130017337
tDiff = T68,F – 60.0068749:
tDiff = 95.466130017337 - 60.0068749 = 35.459255117337
Using tDiff and α60, we can now calculate a CTL:
CTL = exp(-α * tDiff * [1 + 0.8 * α * (tDiff + 0.013749795470)]):
CTL (observed temperature) = 0.982171549176
Now correct to base temperature:
tau = base temperature T(Celsius) / 630: 15/630 = 0.0238095238095238
delta = (a1+(a2+(a3+(a4+(a5+(a6+(a7+a8*tau)tau)tau)tau)tau)tau)tau)tau: -0.00367850903840073
T68,C = T90 – delta : 15 - (-0.00367850903840073) = 15.003678509038
T68,F = 15.003678509038 * 1.8 + 32 = 59.006621316269
tDiff = T68,F – 60.0068749:
tDiff = 59.006621316269 – 60.0068749 = -1.000253583731
Using tDiff and α, we can now calculate the CTL corrected for the base temperature 15 °C:
final CTL = CTL (observed temperature) / (exp(-α * tDiff * [1 + 0.8 * α * (tDiff + 0.01374979547)]))
final CTL = 0.982171549176 / (exp(-α * tDiff * [1 + 0.8 * α * (tDiff + 0.01374979547)]))
final CTL = 0.981680247250
final CTL (rounded) = 0.98168
This corresponds with the value as per sample tables produced by API.
That brings us to the end of this blog post! If you would like to know a bit more about the ‘Special Applications’, else where in this blog is an article called “The use of ASTM table 6/24/54/60 C with special applications”, that explains a bit more about practical calculations using the thermal expansion coefficient α.
As always, we value your comments and ideas so please leave a message at the end of this blog, or email us if you have questions, queries or criticism!
Finally, the calculations shown here can be verified using Oilcalcs for iPhone /Oilcalcs HD for iPad which can be downloaded here:
Oilcalcs for iPhone
Oilcalcs HD for iPad
Alternatively Oil Calculator Pro is also perfectly suited for this and is available for download in the Google Play Store:
Oil Calculator Pro