In part 2 of “Temperature Correction Factors for LPG and NGL” we talked about table 23E, which is used to convert a relative density at observed temperature to a relative density at 60 deg Fahrenheit.
In part 3 we will discuss the use of table 54E, which is used to obtain the CTL (temperature correction faction) from a density at 15 deg Celsius at observed temperature.
This article is the third in a series of six and attempts to explain the practical use of these tables, and table 54E in particular.
Okay, let’s get started!
The implementation methods for all standards are explained in detail in the API MPMS publication 11.2.4 and all formulas required to do the calculations are supplied. It is however not that easy to translate the explanations into for example an excel spreadsheet without a thorough study of the implementation methods. The first two articles explained how to implement table 24E and table 23E, and an example spreadsheet was attached to both articles that shows how to actually use the formulas. In the same way that table 23E relies on table 24E, table 54E explained in this article, relies on both table 23E and 24E.
Table 54E: Calculating Temperature Correction Factor (CTL) based on density at 15 deg C and observed temperature in deg C.
In all the implementation methods the calculations are performed using reference fluids that are close in density on either side of the input density. These reference fluids have a number of defined parameters that represent the equations for their corresponding states (i.e. whether they are in liquid or solid state, saturated or not etc). Utilizing these reference fluids and their given critical temperatures, the temperature correction factor can be calculated from the densities of the reference fluids, after they have been scaled to the observed reduced temperature (reduced by the critical temperature of the input fluid).
As described in part 2, the table with all data for the reference fluids is again necessary. The required data is given on page 13 of chapter 11.2.4, at the end of section 220.127.116.11.
NOTE: for all calculations double precision is required and figures are rounded to 12 decimals. It is important to follow this convention otherwise results will be different from those as calculated by API.
Input: (example figures and calculated results in blue letters)
- Density at 15 deg C (Ύx) (352.59)
- Observed temperature in °C (Tf) (-45.02)
Step 54/1: Round the density to the nearest 0.1 and round the observed temperature to the nearest 0.05 °C:
- Ύx = 352.6, Tf = -45.0
Step 54/2: Convert the rounded observed temperature to units of °Fahrenheit: Tx = (Tf * 1.8) + 32
Tx = -49.0
Step 54/3: Check if Tx and Ύx fall within the required boundaries:
- Temperature: -50.8 <= Tx <= 199.4 °F
- Density: 350.0 <= Ύx <= 688.0
If either one of the values is not within the boundaries the CTL cannot be calculated.
Step 54/4: Convert the 15°C density to relative density, relative to the density of water at 60°F:
ΎTB = Ύ15 / 999.016
ΎTB = 0.352947300143
Step 54/5: Use the procedure described in part 2 (regarding table 23E) to compute a relative density at 60°F from the known relative density at 15°C. Enter the procedure at step 23/4 so as to avoid additional rounding of the input values. Input values are the density at base temperature ΎTB and the base temperature of 15°C entered in our example as 59°F). The output of table 23E is also not rounded.
Ύ60 = 0.350947981103
Step 54/6: The thus calculated density must be greater than or equal to 0.34995 and less than 0.68805.
Step 54/7: Use table 24E to calculate the CTL from 60°F to the observed temperature Tx. Avoid rounding the input values, so enter the procedure at step 24/4. Also do not round off the output value for the CTL:
CTL1 = 1.374246650551
Step 54/8: Use table 24E to calculate the CTL from 60°F to the new base temperature 15°C. Avoid rounding the input values, so enter the procedure at step 24/4. Also do not round off the output value for the CTL:
CTL2 = 1.005696910034
Step 54/9: Compute the desired CTL to reduce volume from the observed temperature Tx to the base temperature of 15°C. The calculation is done by computing the ratio of CTL1 / CTL2
CTL = 1.36646203924852
Step 54/10: Check to ensure that only a positive value for CTL is used. If the resulting CTL is less than or equal to zero, set an error flag and quit the procedure.
Step 54/11: Round off the resulting CTL to the nearest 0.00001
CTL = 1.36646
Well, this brings us to the end of the procedure. Attached to this post is an excel spreadsheet that has been compiled using the here described procedure. The spreadsheet makes use of macros for table 24E and 23E. The spreadsheet is protected without a password.
Please feel free to download and use the spreadsheet for your own purposes. If you want to use it in your own products then please include a reference to this website (mooringmarineconsultancy.wordpress.com) for it.