1. www.inl.gov Accuracy Based Generation of Thermodynamic Properties for Light Water in RELAP5-3D 2010 IRUG Meeting Cliff Davis

2. 2 Outline Introduction Thermodynamic properties Region definitions Modification of generating program Results Conclusions

3. Introduction “Exact” properties for working fluids are generated by an equation of state and contained in ‘tpf’ files RELAP5-3D obtains fluid properties for its internal calculations by interpolating between the exact properties in the ‘tpf’ files The accuracy of the properties depends on the number of temperature and pressure points contained in the ‘.i’ files used to generate the ‘tpf’ files and the interpolation algorithms used by the code Historically, the ‘.i’ files have been based on engineering judgment A new, more rigorous approach, referred to as accuracy based property generation, was taken to revise the ‘.i’ file for light water (h2o) The basic approach was to specify the level of accuracy desired and let the generating program determine the required pressure/ temperature mesh 3

4. The accuracy based process required several steps For convenience, the thermodynamic grid was divided into 14 regions so that different levels of accuracy could be allowed in each region The results of the exact solution and the interpolation were then compared at the midpoint of each box in the thermodynamic grid for six basic and five derived properties in each region The maximum errors in each pressure column and temperature row of the thermodynamic grid were compared to an acceptable error – If the maximum errors were too large, more points were placed in the stgh2o.i file, which resulted in a smaller box – The process continued until a converged solution was obtained Calculated results using the original and revised steam tables were compared – Installation problems – New cases that tested code performance in representative or limiting boxes 4

5. The accuracy of the interpolations for various thermodynamic properties was determined for: Six basic properties – v, U, β, κ, C P, and S Five derived properties – 5

6. The thermodynamic grid was divided into 14 regions 6 Regions 1 and 2 were considered to be most important for analysis of light water reactors and were required to have high levels of accuracy Some modifications were made in Regions 3 and 4 Modifications were not made in other regions

7. The generating program was modified to calculate exact and interpolated properties at box midpoints 7 Exact and interpolated values were compared for the midpoint of each box Average and maximum errors were determined for each property in each region

8. The pressure/temperature grid was adjusted to obtain a desired level of accuracy The normalized error, E, at the midpoint of each box was calculated as The ratio, R, of the normalized was compared to a desired error, ε If R was < 2.0, the existing box was judged to be adequate and no changes were made to the box size for the next iteration If R was > 2.0, the area of the box was reduced by a factor of 2.0 for the next iteration The process was continued until convergence was obtained 8

9. 9 Normalized errors in Region 1 with the original steam tables The average errors were relatively small for v, U, and S The average errors for the properties based on derivatives were larger, but were similar to each other The maximum errors were generally an order of magnitude larger than the average errors

10. 10 Normalized errors in Region 2 with the original steam tables The average and maximum errors for the vapor are much higher than those for liquid The maximum errors were large enough to cause inaccurate code calculations

11. 11 The normalized errors in specific volume generally increased with pressure The largest errors generally occur in the vapor near the saturation line The original grid uses very large intervals above 800 K

12. 12 The locations of large errors in specific volume are shown below The normalized error was considered to be large if E > 0.002 Relatively large errors were concentrated in the vapor region near the saturation line The errors were especially large near the critical point and along the pseudo-critical line

13. Revised steam tables were created The normalized error used for convergence testing was based on β, the coefficient of thermal expansion The desired error, ε, was set to 0.005 The revised steam tables contained 144 temperatures and 126 pressures versus 113 temperatures and 98 pressures in the original steam tables The revised steam tables used a finer temperature mesh between 530 and 640 K and between 800 and 1073.15 K The revised steam tables used a generally finer pressure mesh between 4.0 and 21.5 MPa No changes were made to other portions of the thermodynamic grid because the original steam tables were judged to be adequate or the regions were judged to be relatively un-important for analyses of reactors cooled by light water 13

14. 14 The revised steam tables significantly reduced the errors in Region 1 Open symbols were generated with the original tables, while the solid symbols were generated with the revised tables The average of the average errors was reduced by 30% The average of the maximum errors was reduced by 70%

15. 15 The revised steam tables also significantly reduced the errors in Region 2 The average of the average errors was reduced by 60% The average of the maximum errors was reduced by more than 80%

16. 16 The number of boxes with large errors were significantly reduced with the revised tables The normalized error in specific volume was considered to be large if E > 0.002 The average error was only 0.00232 for the 8 boxes in Region 2 that did not meet the error criterion

17. The code response during simple fill problems was investigated A two-volume model, with a time-dependent volume, time-dependent junction, and single volume, was used The pressure and temperature of the single volume remained in the original box throughout the calculation The measures of performance were normalized mass error and rates of pressure and temperature increase The normalized mass errors were significant for the worst boxes in Regions 1 through 4 with the original steam tables – For example, the mass error was more than 40% of the injected mass for the worst box in Region 2 The normalized mass errors for the worst boxes in Regions 1 through 4 were reduced by more than an order of magnitude with the revised steam tables 17

18. Property errors can also affect other parameters 18 These results are for the worst box in Region 2 The average pressurization rate was 14% higher with the revised steam tables The original steam tables might cause an underestimation of peak pressures during high- pressure operational transients that cause flow into the pressurizer

19. The normal installation problems were calculated with the revised steam tables The effects of the steam tables on both mass error and CPU time were generally small There were no clear trends – The mass error decreased in 12 installation problems, increased in 10, and remained constant in 1 – The CPU time decreased in 7 of the installation problems, increased in 14, and remained constant in 2 19

20. 20 Conclusions The original thermodynamic grid is sufficiently detailed to provide acceptably accurate interpolations for most of Regions 1 and 2 There are portions of Regions 1 and 2 where the original thermodynamic grid is not adequate – The largest errors occur in the vapor near the saturation line and are particularly large just above the normal PWR operating pressure of 15 MPa – The original steam tables were judged to be inadequate for vapor temperatures between 800 and 1073.15 K The revised steam tables significantly reduced the relatively large errors that were observed in Regions 1 and 2 However, the revised steam tables did not provide a consistent reduction in mass error for the installation problems Therefore, the revised steam tables will provide significantly improved results for a few cases, but will probably not have a large impact on most problems