Yuan Jiang a, Eric A. Liese a, Stephen E. Zitney a,b and Debangsu Bhattacharyya b

Transcription

1 Dynamic Modeling of Microtube Recuperators in an Indirect Supercritical Carbon Dioxide Recompression Closed Brayton Power Cycle (+ recent PCHE results) Yuan Jiang a, Eric A. Liese a, Stephen E. Zitney a,b and Debangsu Bhattacharyya b a) National Energy Technology Laboratory, Morganton, WV; b) West Virginia University, Morgantown, WV Solutions for Today Options for Tomorrow The 6th International Symposium Supercritical CO2 Power Cycles March 27-29, 2018, Pittsburgh, Pennsylvania

2 Presentation Overview Introduction Modeling Approach Tools, properties and thermal-hydraulic correlations Steady state optimal design Dynamic modeling Results and Discussion Optimal designs using standard SS316 tubes Time constants and dynamic behaviors Comparison with other types of exchangers Conclusion 2

3 Introduction Background and Motivation Support the DOE 10 MWe pilot plant Supercritical Transformational Electric Power (STEP) by having a dynamic process model that can examine relevant operating scenarios See Symposium papers 16 (Zitney) and 25 (Mahapatra) Using AspenTech software Original system dynamic model used Aspen Library HX model (HeatX) Build custom model for compact heat exchangers Microtube shell-and-tube (MSTE) This paper Printed Circuit Heat Exchanger (PCHE) 3

4 Introduction Microtube shell-and-tube exchanger Microtube shell-and-tube exchanger (MSTE) Similar to shell-and-tube HX but using smaller tubes (~mm) and no baffles in the shell Advanced manufacturing methods all-metal brazing, laser cutting, laser welding, electrical discharge machining wire cutting, diffusion bonding, etc. (Thar Energy, Mezzo Technology) Objectives Develop design and dynamic models for MSTEs used in sco 2 Brayton Cycles with rigorous heat transfer, mass holdup, and pressure drop calculations, which can be simply implemented into system-level models to investigate the cycle dynamics 4

5 Modeling Approach Tools, properties and thermal-hydraulic correlations Software Tools: Aspen Custom Modeler (Equation-oriented) Property model REFPROP (NIST) (Span and Wagner, 1996) Thermal-hydraulic correlations (forced convection in turbulent flow) Heat transfer Nu k = 0.023Re k 0.8 Pr k 0.5 ρ wk ρ k 0.3 Nu k = Τ f k f k Τ8 Re k 1000 Pr k 1Τ2 Τ Pr k Pr 0.11 k Pr wk (Jackson, 2013; Pettersen et al., 2000) (Huai and Koyama, 2007) Pressure drop 1 f cp,k = 2log ε r d hd Re k f cp,k f k f cp,k = T avg k avg T wk 0.1 (Musgrove, 2017) Hydraulic diameter (d i for the tube side; 4 free flow area/wetted perimeter for the shell side) 5

6 Modeling Approach Optimal designs in Aspen Custom Modeler (Jiang, et al.) Assumptions Ideal counter-current flow Fully developed turbulent flow Negligible radial distribution Thermal design (changing properties) Spatial discretization along the axes Cold in ε-ntu method for each sub heat exchanger Mechanical design Pitch: triangular Minimum thickness: ASME, TEMA Industrial standard SS316 tube ε k = Q T N = F c H c,out Tc,out,P H c,out c,in Tc,in,P c,in N NTU k = ln ε k 1 R hc,k ε k 1 Q k R hc,k 1 Hot in mi n( F mh,k C avg ph,k, F mc,k 1 C avg pc,k )(T h,i T c,i 1 ቁ Jiang Y., Liese E., Zitney S., and Bhattacharyya D., Optimal Design of Microtube Recuperators for an Indirect Supercritical Carbon Dioxide Recompression Closed Brayton Cycle, Applied Energy, Volume 216, 15 April 2018, Pages , ISSN , 6

7 Modeling Approach Optimal designs in Aspen Custom Modeler Optimization formulation Decision variables: N t, d to, p t Τd to Objective functions: Case A- min(a o ), Case B- max( A o ΤV HX ), Case C- min(v HX ), Case D- min(m HX ) and Case E- min(τ) Design constraints: Variable Lower limit Upper limit Concerns P (bar) P max Efficiency and Economic N t N t,max Manufacturing and maintenance d so (m) 2.3 Shipping criteria L (m) 8 Shipping criteria LΤd so 3 10 Typical shell-and-tube exchanger p t Τd to Typical shell-and-tube exchanger d to (mm) Typical MSTE 7

8 Modeling Approach Dynamic modeling in Aspen Custom Modeler Energy balance Tube side: π N 2 ρ c U c 4 td ti t = G ch c z + h c πn t D ti T t T c Shell side: π D 4 si 2 2 ρ N t D h U h to t = G hh h z + h h πn t D to T t T h + h h πd si T s T h Tube wall: ρ t C pt T t t = k t 2 T t + 4h hd to (T h T t ) z 2 2 4h cd ti T t T c 2 D 2 to D ti D 2 to D ti Shell wall: ρ s C ps T s t = k s Momentum balance ρv t = ρvv z 2 T s + 4h h Dsi (T h T s ) z 2 2 dp dz ± 1 2 D 2 so D si Mass balance ρv 2 ρ fτd hd t + ρv z = 0 8

9 Presentation Overview Introduction Modeling Approach Tools, properties and thermal-hydraulic correlations Steady state optimal design Dynamic modeling Results and Discussion Optimal designs using standard SS316 tubes Time constants and dynamic behaviors Comparison with other types of exchangers Conclusion 9

10 Results and Discussion 10 MWe sco 2 RCBC plant system model Operating conditions of the recuperators Steady state design of 10 MWe cycle Net power = 10 MWe Heat input = 21.3 MWt HTR heat transfer rate = 45.2 MWt LTR heat transfer rate = 14.5 MWt Pressure ratio = 2.64 Bypass flow ~1/3 HT LT HT LT T h,in ( o C) T h,out ( o C) T c,in ( o C) T c,out ( o C) P h,in (bar) P h,out (bar) P c,in (bar) P c,out (bar) F m,h (kg/s) F m,c (kg/s)

11 Results and Discussion ACM Design Model Optimal designs using standard SS316 tubes Standard tube size (Microgroup, 2017) Gauge Size d to (mm) t t (mm) t min (mm) Hypodermic Tube 14 H H Fractional Tube 1/ / / Case A- min(a o ), Case B- max( A o ΤV HX ), Case C- min(v HX ), Case D- min(m HX ) and Case E- min(τ) Baseline optimal designs (N t,max =80k, P max =1.4 bar) HT Recuperator LT Recuperator Cases A, C, D, E B A, C, D, E B Tube size 3/32 14 H 1/16 1/16 N p N t p t Τd to d so (m) t s (cm) L (m) A o (m 2 ) V HX (m 3 ) A o ΤV HX (m) M HX (kg) τ (s)

12 Results and Discussion - ACM Dynamic Model Time constants and dynamic behavior Step change of cold & hot inlet temperature and flowrate HTR tests shown in figure to right Time constant estimates for HTR and LTR shown below HT Recuperator LT Recuperator τ (s) T c,in T h,in G c,in G h,in T c,in T h,in G c,in G h,in T c,out T h,out Tc(0) & Tc(L): cold side inlet and outlet temp Th(L) & Th(0): hot side inlet and outlet temp Gc & Gh: cold and hot side inlet flowrate 12

13 Results and Discussion - ACM Dynamic Model Dynamic response HTR with slow ramps (1 C/min, 10% flowrate/100 min) Tc(0) & Tc(L): cold side inlet and outlet temp Th(L) & Th(0): hot side inlet and outlet temp Gc & Gh: cold and hot side inlet flowrate 13

14 Results and Discussion - ACM Dynamic Model Dynamic response HTR with fast ramps (1 C/sec, 10% flowrate/100 sec) Tc(0) & Tc(L): cold side inlet and outlet temp Th(L) & Th(0): hot side inlet and outlet temp Gc & Gh: cold and hot side inlet flowrate 14

15 Results and Discussions - ACM Design Model Comparison with other types of exchangers CSTEa: ¾ tube CSTEb: ¼ tube P x S: Parallel x Series Conventional shell-and-tube exchanger Microtube shell-and-tube exchanger Printed circuit heat exchanger 15

16 Results and Discussions - ACM Dynamic Model Comparison with other types of exchangers Conventional shell-and-tube exchanger Microtube shell-and-tube exchanger Printed circuit heat exchanger 16

17 Conclusion Steady-state design and dynamic models were developed in Aspen Custom Modeler (ACM) for microtube shell-and-tube exchangers in a 10MWe indirect sco2 RCBC plant. The ACM design model sets up the sizing for the dynamic model. The Aspen Custom dynamic models have been incorporated into the 10 MW model for the HTR and LTR. The microtube shell-and-tube exchangers have relatively fast dynamic behavior because of lower metal mass and higher heat transfer coefficients 17

18 Acknowledgements This project was supported in part by an appointment to the Science Education Programs at National Energy Technology Laboratory (NETL), administrated by ORAU through the U.S. Department of Energy Oak Ridge Institute for Science and Education (ORISE). 18

19 Thank you! Comments/Questions? Disclaimer: This presentation was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 19

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