PEPSE Modeling of Triple Trains of Turbines Sending Extraction Steam to Triple Trains of Feedwater Heaters

Transcription

1 PEPSE Modeling of Triple Trains of Turbines Sending Extraction Steam to Triple Trains of Feedwater Heaters Gene L. Minner, PhD SCIENTECH, Inc 440 West Broadway Idaho Falls, ID 83402

2 ABSTRACT This paper reports a robust method for modeling turbine cycle arrangements where extractions from three parallel turbine trains cross-tie to supply shell steam to three parallel trains of feedwater heaters. This technique successfully analyzes arrangements where the three feedwater heaters are the same or where they differ from one to the other. In addition one or more of the heaters out of service can be analyzed with the method. These arrangements are encountered in steam turbine cycles that receive main steam from nuclear heat sources. INTRODUCTION This paper was inspired by questions that have been asked by customers using the PEPSE technical support service. In some analysis tasks for nuclear power plants, modelers choose to simulate flow arrangements where three turbine extraction lines combine at a header, with the outflow then splitting to three feedwater heaters. Combinations involving extraction from a single turbine or two turbines are routinely addressed by PEPSE, but modeling extractions from three turbines to three heaters is not routine. In order to model three, creativity in modeling is required. The objective of modeling the triple combination is to calculate the correct amount of extraction steam that flows to each of the three feedwater heaters. Possible simulations include the three feedwater heaters all being the same or different, or possibly out of service. In the simulation method that is presented, all three could be represented in performance mode, where TTD and DCA are explicitly specified, or one or more could be represented in design mode. The descriptions of inputs for PEPSE models are given in Ref 1. EXAMPLE MODEL An example model is used as a vehicle for discussion of this method. The figure below shows a submodel, called UGM02A.MDL, that includes three parallel turbines and three parallel feedwater heaters with the extraction lines cross-tied. Typically this type of arrangement would be repeated several times in a full system model, and the same modeling approach could be used for all such occurrences. For simplicity s sake, this paper deals with the combination shown. 10-1

3 In the schematic above, the cross-tie is represented by the triple-mixer, component 53. The splits to the three heaters are modeled by components 61 and 62. The turbines in this model are LP s represented as Type 8 components, having been excerpted from a full system model. The feedwater heaters are all modeled in the full design mode. Each feedwater heater has a unique need for incoming shell steam flow in order to attain an energy balance. In the simpler, routine application, this need is communicated using the demand reference for the feedwater heater. The analysis task in this complex arrangement is to communicate to the three turbines the needed steam flows for the feedwater heaters. Some assumptions are needed for this model. Assumptions: In order to make this method work, several assumptions were made. 1. Because of the cross-tie, based on pressure drop considerations, it is assumed that the flow rate supplied from the three turbines are all equal, but alternative assumptions could be made and implemented. This is rationalized based on the further assumption that the supply lines from each of the three turbines are similar and that the condition at the turbine s extraction point is the same from one turbine to the other. One alternative method could calculate the flow proportions based upon detailed hydraulic analysis for the extraction lines. 2. The proportion of feedwater flow to each of the feedwater heaters must be measured or assumed. In the example of this paper, it is assumed that the feedwater flows to the three 10-2

4 parallel heaters are equal to each other. Alternative assumptions are possible if sufficient supporting information is available. 3. The drain cascade from higher pressure heaters is represented by source component 20. In this example application, it is assumed that the cascaded flow rates are identical among heaters A, B, and C. In a full system model, no such assumption would be required. Other heaters in the model would have determined the amounts of cascaded flows, and they would not necessarily have been equal. This assumption made here does not diminish the utility of the modeling technique under discussion. IMPLEMENTATION OF DETAILS IN UGM02A.MDL Motivated by ease-of-use, this method relies to the greatest extent possible on standard, existing, frequently used modeling techniques in PEPSE. It has been stated that the extractions from the three turbine components are cross-tied at mixer component 53. Therefore, the thermal condition received by the three heaters is the same. This equalization happens automatically in the model at mixer 53. The flow rates to the individual heaters are furnished by eligible demand suppliers that are referenced as such by the heaters. For the B and C heaters, the demand suppliers are demand splitter components 61 and 62, respectively. There is no obvious eligible demand splitter to supply the A heater. This heater receives steam from the U port of splitter 61. Consequently, the A heater must take the steam that is left over after the B and C heaters have satisfied their demands. The only possible remaining eligible demand supplier is the extraction port of one of the turbines in the model. But which turbine is appropriate for this demand? We could choose any one of the three, but we will choose the A turbine, component 210. Thus, in the input for A heater, component 222, we indicate 210 as the ID of the demand supplier. See Appendix A for the complete input data file. It has been assumed that the three turbines supply equal amounts of extraction flow. This equality is obtained using operations, numbers 101 and 102. Variable WEXTP is used as it sets the extraction flow from the turbine component. Table A-1 of Appendix A contains the model s data file (UGM02A.JOB). This file shows the operations that accomplish the equalization. Because the extraction update algorithm thinks that turbine 210 will make the total flow adjustment needed by heater 222, there is a problem in this setup. The equalization of extraction flows by the operations would cause three times as much flow update as is actually needed. To prevent this excess adjustment, we specify a relaxation factor equal to 1/3 ( ) for the heater 222 demand calculations. Thereby the amount of the demand update is divided among the three turbines. The first variable used in the operations for the equalization is WEXTHL taken from Appendix E of the Volume I PEPSE Manual. This variable has been calculated for turbine 210 in the normal course of computations by the demand updating specified for heater 222. See Tables 1 and 2 for the graphics input forms showing the relaxation factor and an example setup of an operation. 10-3

5 Table 1 Input form to show heater A s relaxation factor 10-4

6 Table 2 Input form to show example equalization operation The input file in Table A-1 gives a comprehensive presentation of the data for several cases. These cases include all three heaters in operation and various combinations of heaters out of service. The analyses for heaters out of service are accomplished by closing the shell steam inlet streams to the respective heaters. The figures of Appendix A also show schematics including computed results for these various combinations of heaters out of service. The heater A out of service case is not included in the figures shown in Appendix A. As modeled in UGM02A.MDL, if heater A is out of service, there is no mechanism to communicate a flow update to the turbine components. This shortcoming could be overcome by modifying the setup of the demands for this case, but this is messy. It would be better to have a model that would handle the heater A out of service combination automatically. Some alternative modeling approach is needed to address this situation. 10-5

7 A MORE VERSATILE MODEL The second example model, UGM02B.MDL, below, overcomes the shortcoming of UGM02A.MDL relative to analyzing heater A out of service. The difference here from the previous model, UGM02A.MDL, is that an additional demand splitter is included now to supply steam to heater A. The B port of splitter 150 supplies shell steam to heater A, component 222. With this arrangement, the input data for the three heaters, then, reference the demand splitters, 61, 62, and 150, as their suppliers of shell steam. This schematic arrangement appears to be unconventional. The U port of splitter 150 feeds a stream to sink component 160. This part does not actually exist in the real system. Because it does not truly exist, our simulation must provide an answer that has zero flow to this sink, and we need to be sure to check for this result in the output. Addition of this connection is a trick that allows heater component 222 to have its own demand splitter. It becomes necessary to communicate the flow update requirement upstream to the turbines, beyond the demand splitters. As with the first example, this is accomplished by using operations. Table B-1 of Appendix B shows the input file (UGM02B.MDL) that includes the operations that provide this result. These are operations 201, 202, 211, 212, 221, 231, 232, and 233. Note that the previous example, UGM02A.MDL, was able to use variable WEXTHL as the "first" variable in the equalization operations because one of the feedwater heaters was 10-6

8 "updating" the extraction flow for turbine 210. This is not the case here; all of the heaters are "updating" demand splitters. Therefore, a slightly different tactic is applied. Operations form the sum of "flow updates" for the three heaters. Next the operations form the sum of the existing extraction flows. The new total extraction flow for the three heaters combined is taken by adding the total existing extraction flow and the total flow update. Once this new combined extraction flow is known, it is divided equally among the three turbine components again using input variable WEXTP for the turbine components. Table B-1 also gives a comprehensive view of the data for 8 cases that include all possible combinations of heaters out of service. The figures of Appendix B show the computed results for all of these cases. Clearly, this form of the model deals successfully with the heater A out of service analysis task, as well as with other combinations. Comparison of the flow results to the feedwater heaters in Appendix A and Appendix B reveal identical matches for comparable cases. ALTERNATIVE METHOD OF MODELING The method of analysis that has been discussed depends mainly on energy-balance considerations. An alternative way to analyze three-on-three arrangements would be to base the flow calculations on precise modeling of hydraulics, with pressure matching at cross-ties. This means that the pressure-drop characteristics of the lines from the turbines to the cross-ties, and the lines from there to the feedwater heaters would be carefully characterized. Alternatively, the relative flows could be calculated as an extension of some measured/known flow condition, based on use of Darcy s formula for the flow-pressure relationship. Greg Boerschig presented the hydraulic balancing method in a paper at the 1987 User s Group Meeting in Charleston, South Carolina, Ref 2. CONCLUSION A method for modeling triple trains of steam turbines that send extraction steam through crossties to triple trains of feedwater heaters has been described, and two example applications have been shown. This method handles symmetric heater arrangements and non-symmetric arrangements. Included in the scenarios that can be addressed is the heater-out-of-service case, as well as combinations of performance mode and design mode heater descriptions. REFERENCES 1. Minner, Gene, et al, PEPSE Manual Volume 1, SCIENTECH, Inc, Boerschig, Greg, Modeling Technique for Atypical Turbine Extraction/Feedwater Heater Demand Mismatch, Performance Software User s Group Meeting Proceedings, June 17-19,1987, Charleston, South Carolina. 10-7

9 APPENDIX A Table A-1 Input data file, UGM02A.JOB for first example model PRINT DATE: Friday, April 26, 2002 TIME: 3:03 PM MODEL: UGMO2A.MDL JOB FILE: C:\chkv67\UGM02A.job =C:\CHKV67\UGM02A(SET 1)-BASE, 3 FWH ON 3 LP TURB, X-TIES STREAMS U 62 I U 61 I B 52 I C 56 I U 54 I U 210 I U 310 I U 410 I U 222 S B 322 S B 422 S E 53 IB E 53 IA E 53 IC U 180 I U 60 I U 70 I U 80 I B 222 T U 322 T C 422 T D 130 I D 120 I D 140 I T 90 I T 100 I T 110 I A-1

10 U 30 I B 222 D U 322 D C 422 D U 50 I Intercept Valves to LP Bowl A EXTRACTION LINE PRESSURE DROP B EXTRACTION LINE PRESSURE DROP C EXTRACTION LINE PRESSURE DROP COMPONENTS LP 'A' - 1st Stage LP 'B' - 1st Stage LP 'C' - 1st Stage FWH 4A - MOD FLOW UPDATE TOOLS - reduced relaxation A-2

11 E FWH 4B - MOD FLOW UPDATE TOOLS E FWH 4C - MOD FLOW UPDATE TOOLS E A-3

12 Steam to LP turbine Drain Flow to #4 FWH Feedwater to #4 FWH LP 'A' Intercept Valve LP 'B' Intercept Valve LP 'C' Intercept Valve FWH 4 Extraction Flow Mixer Demand supply to 4B fwh Demand supply to 4C fwh LP Turbine Main Steam Splitter Drain inlet flow split for FWH #4 A-4

13 FW flow split to FWH # SPECIAL FEATURES EQUALIZE B EXTR FLOW TO A EXTR FLOW WEXTHL 222 EQL WEXTP 310 EQUALIZE C EXTR FLOW TO A EXTR FLOW WEXTHL 222 EQL WEXTP "MIXER OUTLET FLOW" WW U GENERATOR # 1 FLAGS AND DATA CYCLE FLAGS END OF BASE DECK / =C..UGM02A(SET 2)-SHUT OFF HEATER B STREAMS SHUT OFF HEATER B CLOSE / =C..UGM02A(SET 3)-SHUT OFF HEATER C A-5

14 REACTIVATE HEATER B OPEN SHUT OFF HEATER C CLOSE / =C..UGM02A(SET 4)-SHUT OFF HEATER B AND C SHUT OFF HEATER B CLOSE. Figure A-1 Results for UGM02A.MDL, all heaters in service A-6

15 Figure A-2 Results for UGM02A.MDL, heater B out of service Figure A-3 Results for UGM02A.MDL, heater C out of service A-7

16 Figure A-4 Results for UGM02A.MDL, heaters B and C out of service A-8

17 APPENDIX B Table B-1 Input data file, UGM02B.JOB for first example model PRINT DATE: Friday, April 26, 2002 TIME: 3:02 PM MODEL: UGMO2B.MDL JOB FILE: C:\chkv67\UGM02B.job =C:\CHKV67\UGM02B(SET 1)-BASE 3 FWH, 3 LP TURB, X-TIES STREAMS U 62 I U 61 I B 52 I C 56 I U 54 I U 210 I U 310 I U 410 I B 322 S B 422 S E 53 IB E 53 IA E 53 IC U 180 I U 60 I U 70 I U 80 I B 222 T U 322 T C 422 T D 130 I D 120 I D 140 I T 90 I T 100 I T 110 I U 30 I B-1

18 B 222 D U 322 D C 422 D U 50 I U 150 I U 160 I B 222 S Intercept Valves to LP Bowl B EXTRACTION LINE PRESSURE DROP C EXTRACTION LINE PRESSURE DRIP A EXTRACTION LINE PRESSURE DROP COMPONENTS LP 'A' - 1st Stage LP 'B' - 1st Stage LP 'C' - 1st Stage FWH 4A B-2

19 E FWH 4B E FWH 4C E B-3

20 RECEIVER OF EXCESS EXTRACTION STEAM Steam to LP turbine Drain Flow to #4 FWH Feedwater to #4 FWH LP 'A' Intercept Valve LP 'B' Intercept Valve LP 'C' Intercept Valve FWH 4 Extraction Flow Mixer Demand supply to 4B fwh Demand supply to 4C fwh B-4

21 Demand supply to 4A fwh LP Turbine Main Steam Splitter Drain inlet flow split for FWH # FW flow split to FWH # SPECIAL FEATURES ADD FWH#4 FLOW UPDATES WWDUSE 222 ADD WWDUSE 322 OPVB 201 CONT'D OPVB 201 ADD WWDUSE 422 OPVB 201 ADD FWH#4 OLD VALUES OF FLOWS WW 232 ADD WW 332 OPVB 211 CONT'D OPVB 211 ADD WW 432 OPVB 211 CALC NEW TOTAL EXTR FLOW OPVB 201 ADD OPVB 211 OPVB 221 EQUALIZE EXTR FLOWS FOR A, B, C TURBINES OPVB 221 EQL WEXTP CONT'D OPVB 221 EQL WEXTP CONT'D OPVB 221 EQL WEXTP B-5

22 GENERATOR # 1 FLAGS AND DATA CYCLE FLAGS END OF BASE DECK / =C..UGM02B(SET 2)-SHUT OFF FWH#4A STREAMS A EXTRACTION LINE CLOSURE - SHUT OFF FWH 4A CLOSE / =C..UGM02B(SET 3)-SHUT OFF FWH#4B STREAMS B EXTRACTION LINE CLOSURE - SHUT OFF FWH 4B CLOSE A EXTRACTION LINE REOPEN - FWH#4A REACTIVATION OPEN / =C..UGM02B(SET 4)-SHUT OFF FWH#4C STREAMS B-6

23 B EXTRACTION LINE REOPEN - FWH#4B REACTIVATION OPEN C EXTRACTION LINE CLOSURE - SHUT OFF FWH#4C CLOSE / =C..UGM02B(SET 5)-SHUT OFF FWH#4A AND 4B STREAMS B EXTRACTION LINE CLOSURE - SHUT OFF FWH 4B CLOSE C EXTRACTION LINE - REACTIVATE FWH#4C OPEN A EXTRACTION LINE CLOSURE - SHUT OFF FWH 4A CLOSE / =C..UGM02B(SET 6)-SHUT OFF FWH$4A AND 4C STREAMS B EXTRACTION LINE - REACTIVATE FWH 4B OPEN C EXTRACTION LINE CLOSURE - FWH#4C CLOSE B-7

24 / =C..UGM02B(SET 7)-SHUT OFF FWH#4B AND C STREAMS B EXTRACTION LINE CLOSURE - SHUT OFF FWH 4B CLOSE A EXTRACTION LINE REOPEN - FWH#4A REACTIVATION OPEN / =C..UGM02B(SET 8)-SHUT OFF FWH#4A, B, AND C STREAMS SHUT OFF EXTRACTIONS CLOSE B EXTRACTION LINE CLOSURE - SHUT OFF FWH 4B CLOSE C EXTRACTION LINE CLOSURE - SHUT OFF FWH#4C CLOSE A EXTRACTION LINE CLOSURE - SHUT OFF FWH 4A CLOSE. B-8

25 Figure B-1 Results for UGM02B.MDL, all heaters in service Figure B-2 Results for UGM02B.MDL, heater A out of service B-9

26 Figure B-3 Results for UGM02B.MDL, heater B out of service Figure B-4 Results for UGM02B.MDL, heater C out of service B-10

27 Figure B-5 Results for UGM02B.MDL, heaters A and B out of service Figure B-6 Results for UGM02B.MDL, heaters A and C out of service B-11

28 Figure B-7 Results for UGM02B.MDL, heaters B and C out of service Figure B-8 Results for UGM02B.MDL, heaters A, B, and C out of service B-12