1. 1 Operation of heat pump cycles Jørgen Bauck Jensen & Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Technology The Gas Technology Center, NTNU-SINTEF / Norwegian Research Council

2. 2 Overview Simple cycles Complex cycles Design vs. operation Model MATLAB Example Conclusion and further work

3. 3 Simple cycles Examples: –Heat pumps –Air-conditions –Refrigerators Control objective1 –Temperature Manipulated input:1 (2) –Compressor on-off/speed –(Valve opening) Remaining DOF’s for optimization0 (1) Operating point given for fixed valve –How does the operating point change with disturbances? Valve opening possible input –How can this improve operation?

4. 4 Complex cycles Examples –Liquefied Natural Gas (LNG) plants –Air separation processes Control objective: 1 –Temperature Manipulated inputs:4 –Compressor speed –Valve openings –Composition Remaining DOF’s for optimization: 3 What is optimal operation!? –Not easy to determine Pre-cooler for the mixed fluid cascade process (MFC)

5. 5 Design vs. operation Snøhvit-project in northern Norway –MFC process for cooling natural gas –Preliminary studies gives potential savings in the order of some percent compared to “optimal” design Design: Objective function includes both investment and operational costs Operation: Objective function depends only upon operational costs Therefore (in some cases) : Optimal operation ≠ optimal design, also at design conditions!!

6. 6 Modeling (dynamic) The model is a set of differential and algebraic equations (DAE) Differential equations –Balance for mass, energy and volume Algebraic equations –Thermodynamic state and property relations –Equilibrium relations –Mass and energy transfer –Control volume balances –Controllers and control elements Purpose of model –Optimization –Control structure analysis –Dynamic simulations Demands for model –Fast –Accurate –Robust Problems –Dynamic two-phase heat exchangers –Solver

7. 7 MATLAB ODE set (ode15s) –Algebraic relations solved internally slows down the ode solver DAE set (ode15s) –Good initial values needed because of algebraic equations DAE set (ode15i) –Not tested –Fully implicit solver in MATLAB 7 –Also a function for initialization Simulink (ode15s) –Nice interface where it is easy to add: Control Visualization –Tools for analysis –In theory easy to arrange states –Not possible to solve set of DAE (?)

8. 8 CO 2 Heat pump - Design Design conditions –22 °C inside –-5 °C outside –Minimum ΔT of 10 °C –10 kW heat supply @ above specifications Design –UA (cooler) = 590 W/K –UA (vaporizer) = 660W/K –Cv (valve) = 1,66∙10 -6 m 2 –Cv (cooler) = 1,79∙10 -5 m 2

9. 9 CO 2 Heat pump – Model Compressor –Adiabatic –70% efficiency Cooler –One-phase heat exchanger –6 control volumes –Valve equation gives flow between control volumes –Heat exchange to air in room at constant temperature Valve –One-phase valve equation –Isenthalpic Vaporizer –Two-phase heat exchanger –One control volume –Equilibrium between the two phases –Heat exchange to outside air at constant temperature Unit# diff. eq.# alg. eq. Compressor-5 Cooler3*62*6 Valve-2 Vaporizer37 Total2126

10. 10 CO 2 Heat pump - Control Constant valve opening: Case A Control objective –Room temperature Manipulated inputs –Compressor work –Valve opening Disturbances –Air temperature (main disturbance) –Set point for room temperature –UA for the room (i.e.. opening a window) Constraints –Valve opening –Compressor work –Pressures

11. 11 CO 2 Heat pump - Control Control objective –Room temperature Manipulated inputs –Compressor work –Valve opening Disturbances –Air temperature (main disturbance) –Set point for room temperature –UA for the room (i.e.. opening a window) Constraints –Valve opening –Compressor work –Pressures Constant high pressure: Case B

12. 12 CO 2 Heat pump – Result Optimal starting point: Constant valve opening gives a maximum loss of 1% within ±10 degrees off design point Easy to implement Constant high pressure gives larger loss Possible to find a variable that gives zero loss Fixed valve opening is a good self optimizing control variable!

13. 13 CO 2 Heat pump - Operation Optimal operating point –23 bar LP (subcritical) –90 bar HP (supercritical) –0,9 mol/s circulation –3,35 kW compressor –COP = 2,99 Inaccurate UA values moves optimum –Designed for 50% –Optimal at 34% –Optimal pressure ratio sensitive to temperature out of heat exchangers –Verified with HYSYS model Constant room temperature Optimal operating point

14. 14 CO 2 Heat pump – Result Larger losses than from optimal starting point Disturbance in one direction improves performance Constant valve opening is still the best strategy in average Non-optimal starting point: Point 2 Choice of self optimizing control variable does not depend on starting in optimal point!

15. 15 Conclusion & further work Simple cycles –Constant valve is a good self optimizing control variable Choice of self optimizing control variable is not dependent on starting in optimal point Optimization in operation –Mostly thermodynamic studies are reported –Important because design and operation are different in some cases Look into industrial complex cycles where small improvements are important

16. 16 References The Gas Technology Center, NTNU-SINTEF Norwegian Research Council 1.http://www.statoil.com/STATOILCOM/snohvit/svg02699.nsf?OpenDatabase&lang=en 2.S. Skogestad, I. J. Halvorsen and J. C. Morud, Self-optimizing control: The basic idea and Taylor series analysis, AIChE Annual Meeting, Miami Beach, 16-20 Nov. 1998, Paper 229c Acknowledgements