IAPWS-IF97

Jurisdiction of 1073.15 oK Temperature

During our verification work of ES_StableIF97 for numerical consistency with "ASME International Steam Table for Industrial Use" based on the IAPWS-IF97 published in the year of 2000, we found that there is inconsistency in the steam properties at 1073.5 oK temperature, i.e. 800 oC.

For example, the specific volume at 0.30 Mpa and 800 oC is presented as 1.6501 m3/kg in ASME Steam Table, while that of ES_StableIF97 is presented as 1.6500 m3/kg if the calculated value is rounded to five(5) significant digits as in ASME Steam Table.

This inconsistency between ASME Steam Table and ES_StableIF97 is caused by the jurisdiction of 1073.15 oK(= 800 oC) temperature.   1073.15 oK temperature is the boundary temperature between Region 2 and Region 5 of IAPWS-IF97.   

ENGSoft found that this is caused by the fact that ASME Steam Table uses Region 5 equations for 1073.15 oK temperature, while ES_StableIF97 uses Region 2 equations.

The following is the comparison table showing the difference between the use of Region 2 and 5 equations for 0.30 Mpa and 1073.15 oK(= 800 oC).

Description

ASME Steam Table

ES_StableIF97

by Region 2 Equation

ES_StableIF97

by Region 5 Equation

Pressure

MPa

0.30

0.30

0.30

Temperature

oC

800

800

800

Sp. Vol presented (*)

m3/kg

1.6501

1.6500

1.6501

Sp. Vol calculated

m3/kg

?

1.650 048 739 515 96

1.650 054 733 283 02

(*) : Rounded to five(5) significant digits.

 

Interpretation of IAPWS-IF97

The Section 2 of IAPWS-IF97 "Structure of the Formulation" describes the following.

< Quote >

"The IAPWS Industrial Formulation 1997 consists of a set of equations for different regions which cover the following range of validity.

273.15 K < T < 1073.15 K

p < 100 MPa

1073.15 K < T < 2273.15 K

p < 50 MPa

< Unquote >

The second range described above is for Region 5, while the first range is for other remaining regions including Region 2.   In this description the equal sign is put in for Region 2 and it implies that 1073.15 K temperature is a part of Region 2, not Region 5.

 

The Section 6 of IAPWS-IF97 "Equations for Region 2" describes the following.

< Quote >

"Equation (15) covers region 2 of IAPWS-IF97 defined by the following range of temperature and pressure, see Fig. 1:

273.15 K < T < 623.15 K

0 < p < ps(T)Eq.(30)

623.15 K < T < 863.15 K

0 < p < ps(T)Eq.(5)

863.15 K < T < 1073.15 K

0 < p < 100 MPa

< Unquote >

In this description the equal sign is put in for 1073.15 K temperature and it says that 1073.15 K temperature is a part of Region 2.

 

The Section 9 of IAPWS-IF97 "Basic Equations for Region 5" describes the following.

< Quote >

"Equation (32) covers region 5 of IAPWS-IF97 defined by the following temperature and pressure range:

1073.15 K < T < 2273.15 K

0 < p < 50 MPa

< Unquote >

In this description the equal sign is put in also for 1073.15 K temperature and it says that 1073.15 K temperature is a part of Region 5.

 

ENGSoft questioned this subject to IAPWS and received the answer that the 1073.15 oK temperature is governed by Region 2 equations.

Therefore, 1073.15 oK temperature is calculated by Region 2 equations in ES_StableIF97 instead of Region 5 equation.


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