EricLemmon
commented
4 years ago Calculation of heating values in U.S. customary units and understanding what exactly is shown in GPA-2145 is substantially more difficult than those in SI for multiple reasons, including:
- Some of the properties in the first section (U.S. units) of GPA-2145 are only there for historical reasons. Others are not always clear about their meaning, such as “Fuel as Ideal Gas (Btu/gal)”.
- Some values are based on a pressure of 14.73 psia and others on 14.696 psia. One has to be careful to read the appendix to understand which is used.
- U.S. customary units are often rounded to different significant figures depending on the source reporting the factors.
- 60 F is NOT equal to 15 C, but rather 15.555555… C (15 C is exactly equal to 59 F). A user's comparisons between the U.S. section and the SI section will show slight differences, where these differences could be due to either the Btu to J conversion value, the change from 14.73 psia to 1 atm (14.696 psia), or the enthalpy difference between 59 F and 60 F.
- Contracts for buying/selling natural gas often use standard conditions of 60 F and 14.73 psia, but some of the volumetric heating values in the table use a pressure base of 14.696 psia.
- There are multiple definitions for some properties, such as:
- Conversion values between Btu and J are quite numerous, mostly based on different temperature ranges where the energy difference was measured. The natural gas industry uses the “steam” value, often called IT, but the default Refprop conversion value is the Thermochemical value, although in retrospect it would have perhaps been better to use the IT value. The following shows some values that have been used (taken from https://physics.nist.gov/cuu/pdf/sp811.pdf):
| Btu Units | SI Units | Conversion value |
|---|---|---|
| British thermal unit(IT) (BtuIT) | joule (J) | 1055.056 |
| British thermal unit(th) (Btuth) | joule (J) | 1054.350 |
| British thermal unit (mean) (Btu) | joule (J) | 1055.87 |
| British thermal unit (39 ºF) (Btu) | joule (J) | 1059.67 |
| British thermal unit (59 ºF) (Btu) | joule (J) | 1054.80 |
| British thermal unit (60 ºF) (Btu) | joule (J) | 1054.68 |
Some useful links with additional details: https://en.wikipedia.org/wiki/British_thermal_unit https://github.com/usnistgov/REFPROP-issues/issues/17
- For reference, below are additional details on the two values used in Refprop.
| Conversion | Corresponding Btu variant |
|---|---|
| 1 cal(th) = 4.184 J | 1 Btu(th) = 1054.35026448889 J |
| 1 cal(IT) = 4.1868 J | 1 Btu(IT) = 1055.05585262000 J |
- There are two definitions for the gallon, the one used throughout the U.S. and the Imperial gallon. Fortunately, the Imperial gallon is about 1.2 times larger than the U.S. gallon, so errors are easier to spot.
All properties in Refprop and thus GPA 2145 are based on equations of state that use the SI unit system. Values in GPA-2145 were converted to the U.S. system with the use of exact conversion values, and thus the loss of digits is not an issue. The following exact conversion values form the basis for all others (these lines were taken directly from the code):
CtoK = 273.15 FtoR = 459.67 RtoK = 5/9 ATMtoMPa = 0.101325 KGFtoN = 9.80665 INtoM = 0.0254 LBMtoKG = 0.45359237
These are then used to obtain all other conversion values:
BTUtoKJ=CALtoJ LBMtoKG RtoK LBFtoN=LBMtoKG KGFtoN IN3toM3=INtoM3 FT3toM3=FTtoM3 GALLONtoM3=IN3toM3 231 PSIAtoMPA=LBMtoKG / INtoM / INtoM KGFtoN / 1000000 FTLBFtoJ = FTtoM LBFtoN
The Gas Processors Association (GPA) has a document numbered GPA-2145 (from 2016) that reports thermodynamic properties for most fluids of interest to this community. The first half of the document reports the values in U.S. customary units (formally known as English units) and the second half reports the values in SI units. The tables in the first half of the document have a few entries that might be difficult to understand and how they were calculated. To help explain these, it is easier to start with the values in the SI section and then return to the first section (see the next post in this issue).
GPA-2145 was developed with the use of the most accurate equations of state available at the time it was published. These equations are available in the Refprop program of NIST, and the calculations were done through the Excel spreadsheet that comes with the program, and which was designed to directly link to the Refprop DLL to obtain the properties requested. For fluids not available in this program, a link was established with the TDE program from a group in our division called TRC (Thermodynamic Research Center). The TDE program contains a vast amount of experimental data taken from the literature and gives estimates of properties based on these data. When an equation of state is available, their calculations are based on that equation (through the Refprop DLL link).
I've pasted a picture from Refprop for hexane at 15 C and 0.101325 MPa below, along with a snapshot of the values from GPA 2145. Aside from the last digit, the numbers between the program and 2145 are nearly the same. Under the Options/Properties menu and then under the Special tab is an option for the ideal gas density. That is also included in the table below. If you multiply the heating values by the ideal gas density, you will then get the last two items in the GPA table.