Mathema'cal Model for Op'miza'on of Regenera've Feed Water Systems at Thermoelectric Power Plants.

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1 Mathema'cal Model for Op'miza'on of Regenera've Feed Water Systems at Thermoelectric Power Plants. Jesús M. Blanco Jon Mar/nez

2 Contents 1. INTRODUCTION 2. AIMS AND SCOPE 3. METHODOLOGY 4. OPTIMIZATION PROCEDURE 5. IMPLEMENTATION TO A CASE STUDY 6. SIMPLIFIED CFD MODEL 7. CONCLUSIONS REFERENCES 2/32

3 1. INTRODUCTION STEAM TURBINE STEAM GENERATOR WATER/STEAM REGENERATIVE HEATER CONDENSER 3/32

4 1. INTRODUCTION The decreasing of the energy losses in condenser means : EFFICIENCY Steam Generator Extrac'on 1.. Extrac'on Z Condenser STEAM TURBINE STEAM GENERATOR WATER/STEAM REGENERATIVE HEATER CONDENSER 4/32

5 2. AIMS AND SCOPE The objec've is based in the development of a computer applica'on suitable to calculate the op'mal distribu'on in the regenera've system for thermal power sta'ons. There could be other objec'ves, such as: Calcula'ng thermal proper'es for the whole set of points in the cycle. First approach to a design point in power systems. 5/32

6 3. METHODOLOGY COMPUTED DIAGRAM 6/32

3. METHODOLOGY Steam consump'on (D 0 ) in turbine with regenera've

extrac1ons): Power coefficient for incomplete produc1on: W elec :

$of enthalpy for steam frac'on in the extrac'on r η elec_mec = η gn η mec$

7 3. METHODOLOGY Steam consump'on (D 0 ) in turbine with regenera've extrac'ons: D cond0 : Steam consump1on in turbine (Same process without extrac1ons): Power coefficient for incomplete produc1on: W elec : Electrical Power (kw) H cond : Gap of enthalpy (Real Process) H r : Gap of enthalpy for steam frac'on in the extrac'on r η elec_mec = η gn η mec η mec : Mechanical efficiency in turbine η gn : Electrical generator efficiency 7/32

steam parameters in the heater (inlet and outlet) )

8 3. METHODOLOGY D r : Steam consump1on in extrac1on r HEAT BALANCE IN HEATER f (Water consump1on in heater, steam parameters in the heater (inlet and outlet) ) SURFACE HEATER MIXTURE HEATER Da.r: Water consump1on in heater 8/32

9 3. METHODOLOGY (kg/h) Steam specific consump'on (kg/kw h): 9/32

10 3. METHODOLOGY INTERMEDIATE OVERHEATING Heat consump1on in turbine: Steam specific consump1on in turbine: 10/32

11 3. METHODOLOGY Regenera've Hea'ng Increase steam specific consump'on d Because of the increase in temperature and enthalpy of feed water Decrease of transferred heat/kg steam Increase of power sta'on efficiency Decrease of heat specific consump'on 11/32

12 4. OPTIMIZATION PROCEDURE Absolute performance in turbine group > 2 Alterna've expressions 1st Alterna1ve expression Common expression of cycle efficiency It is not possible to visualize the increase of the efficiency because of the common oscilla'on of the parameters Q 0 and q cond Transferred heat in overhea1ng 12/32

13 i (kj/kg) 4. OPTIMIZATION PROCEDURE Absolute performance in turbine group > 2 Alterna've expressions i 0 P 0 i 1 h 0 2nd Alterna1ve expression P 1 i 2 P 2 P r i r i z- 1 Hcond Ha h 1 q 0 cond : Specific heat consump'on in the steam flow (kj/kg) Upper and lower regenera've extrac'ons: i z P z- 1 i cond P z Enthalpies in upper an lower extrac1on. Pcond i cond.a s (kj/kg K) 13 /32

14 Efficiency calcula'on approach 4. OPTIMIZATION PROCEDURE 14/32

process R > 1 according to ηcond < 1 The regenera've hea'ng causes an increase

15 Efficiency varia'on es'ma'on 4. OPTIMIZATION PROCEDURE It is concluded: Ar: Energy coefficient of regenera've process R > 1 according to ηcond < 1 The regenera've hea'ng causes an increase in the cycle efficiency due to: - Decrease of heat losses in condenser - Energy produccion because of the extracted steam 15/32

steam work process in turbine is invariable: Without intermediate overhea'ng With intermediate

16 4. OPTIMIZATION PROCEDURE Calcula'on aim Deduce q r to τ r ra'o which op'mizes the performance. τ r : Feed water hea1ng in the extrac1on r q r : Transferred heat for the steam in the extrac1on r If steam work process in turbine is invariable: Without intermediate overhea'ng With intermediate overhea'ng Auxiliar factor: τ 0 : Water hea1ng in the steam generator q 0 : Heat in the forma1on and overhea1ng of steam 16/32

condi'onal APPROXIMATION extreme method STATION LINEAR LOS APROX.

17 Without intermediate overhea'ng 4. OPTIMIZATION PROCEDURE The mean func'on of the heat distribu'on in performance expression is αcond. Calcula'on Method First Condi1ons: THERMAL POWER Lagrange s LINEAR condi'onal APPROXIMATION extreme method STATION LINEAR LOS APROX. between the BARRIOS factors qr y Cádiz τj (Spain) Lagrange s extreme func'on: Coefficient: Courtesy: Centrales Termoleléctricas by V.Ya.Rizhkin (λ: Indeterminate propor1onal factor) 17/32

18 Without intermediate overhea'ng 4. OPTIMIZATION PROCEDURE Equa'ons: It is deduced: /32

19 4. OPTIMIZATION PROCEDURE Without intermediate overhea'ng LAGRANGE S EXTREME FUNCTION Increase of ra1o 19/32

20 4. OPTIMIZATION PROCEDURE WITH INTERMEDIATE OVERHEATING i: The last extrac1on before the overhea1ng 20/32

21 With intermediate overhea'ng 4. OPTIMIZATION PROCEDURE Addi'onal condi'ons (j) : f(number of intermediate overhea'ngs) Condi1on of design: 1 intermediate overhea1ng 21/32

22 With intermediate overhea'ng 4. OPTIMIZATION PROCEDURE Condi1on of design: 1 intermediate overhea1ng Separa'on of procedure Without intermediate overhea1ng in 2 phases: BEFORE and AFTER overhea'ng Geometrical progression factors: m 1 y m 2 Itera've Process 1. Defini'on m 1 Available parameters 2. Random Boundary value condi'on for m 2 [1,01-1,04] (τ i ) 22/32

23 5. IMPLEMENTATION TO A CASE STUDY MENU Jesús M Blanco Jon Marxnez 23/32

24 5. IMPLEMENTATION TO A CASE STUDY OPTION: NEW DESIGN DATA ENTRY FORMS 24/32

thermal cycle (DESIGN POINTS) The applica'on calculates the

25 5. IMPLEMENTATION TO A CASE STUDY OPTION: RESULTS The applica'on shows the different thermodynamic states for the thermal cycle (DESIGN POINTS) The applica'on calculates the best distribu'on for the regenera've system (OPTIMIZATION) 25/32

26 5. IMPLEMENTATION TO A CASE STUDY OPTION: MODIFY ACTUAL DESIGN COMPARATIVE STUDY THERMAL POWER STATION LOS BARRIOS Cádiz (Spain) CYCLE WITH 5 AND 7 REGENERATIVE HEATERS 26/32

27 5. IMPLEMENTATION TO A CASE STUDY OPTION: RESULTS/REGENERATIVE SYSTEM COMPARATIVE STUDY 7 HEATERS 5 HEATERS 5 HEATERS 7 HEATERS 27/32

28 5. IMPLEMENTATION TO A CASE STUDY OPTION: MODIFY ACTUAL DESIGN COMPARATIVE STUDY Points: Thermodynamic 7 HEATERS states 5 HEATERS 51,026 % 50,034 % 28/32

Simmetry T = 524 K Operation 75%: Inlet T r = 608 K T exit =

29 6. SIMPLIFIED CFD MODEL SURFACE HEATER (Temperature field estimation) Design condition: T r = 610 K T exit = 597 K Simmetry T = 524 K Operation 75%: Inlet T r = 608 K T exit = 595 K T = 524 K Outlet Simmetry Operation 50%: T r = 602 K T exit = 591 K 29/32

30 7. CONCLUSIONS Regenerative systems drive to a substantial increase in cycle efficiency for thermal power plants, compared to conventional schemes. Optimal ratio between the feed water heating (τ r ) and the heat transferred for the steam (q r ) in the different extractions has revealed as the key issue. An iterative process has been carefully addressed, allowing an easy way to optimize the number of extractions, using a linear approach but also manufacturer data when available. A particular case study has been implemented, showing that its use can be fully generalized to most of the nowadays powerplants. 30/32

31 REFERENCES V. Ya. Rizhkin, Centrales termoeléctricas, Ed. Mir, (1979). P. K. Nagg, Power Plant Engineering, Ed. McGraw-Hill, ISBN: (2008). J. M. Blanco, F. Peña, L. Martin, I. Loroño, Chapter 5: Progress in natural gas, burning technologies, general considerations and other fuel alternatives mostly used for firing up thermal power plants, Natural Gas Research Progress, NOVA Science Publishers, I.S.B.N: , pp (2008). C. Sánchez, Tecnología de las centrales térmicas convencionales, Ed. UNED, ISBN: , (2010). J. M. Blanco, L. Vazquez, F. Peña, Investigation on a new methodology for thermal power plant assessment through live diagnosis monitoring of selected process parameters; application to a case Study, Energy, 42, , (2012). J. M. Blanco, L. Vazquez, F. Peña, D. Díaz, New investigation on diagnosing steam production systems from multivariate time series applied to thermal power plants, Applied Energy, 101, , (2013). 31/32

32 QUESTIONS?

Feedwater Heaters (FWH)

Feedwater Heaters (FWH) A practical Regeneration process in steam power plants is accomplished by extracting or bleeding, steam from the turbine at various points. This steam, which could have produced