1. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 5. mm. systematic modelling What motivates the concept of systematic modelling? The multigate-method used in systematic modelling Introduction to the software MULTIPORT A primer on combustion calculations

2. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Motivation: - The complexity of real systems [Cycle Tempo]

3. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Motivation Real thermodynamic systems are complex. Non-linear equation sets can be tremendously huge making testing and error tracing difficult and time-demanding. Systematic modelling gives overview and ensures that the correct conservation equations are set up.

4. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Methods -Energy and mass balance equations at a multigate approach: Note: Enthalpies must have some referece states! The modelled phenomenon must be stationar. Note neglected terms and assumptions!   )( )1( )( )1( jstream out istream in mm  Continuity                        )( )1( )( )1( )( )1( )( )1( )( )1(, )( )1(, jstream n in mstream out lstream in kstream out mixout istream inmixin WWQQhmhm   energy of onConservati

5. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Standard component models {///////////////////////////////////////////////////} {///////// HE Water-Water /////////} {///////////////////////////////////////////////////} m[!!!]=m[&&&] m[&&&]*(h[&&&]-h[!!!])*1000=Q[&&&] p[!!!]=p[&&&] p[$$$]=p[###] T[!!!]=temperature(water;h=h[!!!]; p=p[!!!]) T[###]=temperature(water;h=h[###]; p=p[###]) Q[&&&]=U[&&&]*A[&&&]*dT[&&&] ddT[&&&]=T[&&&]-T[###] ddT[$$$]=T[!!!]-T[$$$] dT[&&&]=(ddT[&&&]-ddT[$$$])/ln(ddT[&&&]/ddT[$$$]) {///////////////////////////////////////} { Steam turbine } {///////////////////////////////////////} k_d[&&&]=(0,6466*(W[%%]/1e6)^(-0,5)- 0,3616*(W[%%]/1e6)^(-0,25)+1,3026) eta[&&&]=1/(k_d[&&&]*(1-0,151*((W[%%]/1e6)^(-0,25)- 0,34)*(103,4^(0,25)-p[&&&]^(0,25)))) s[&&&]=entropy(steam;p=p[&&&];T=T[&&&]) v[&&&]=volume(steam;p=p[&&&];T=T[&&&]) eta[&&&]=(h[&&&]-h[!!!])/(h[&&&]-h_s[!!!]) m[&&&]=C_t[&&&]*sqrt(((p[&&&]*1e5)^2- (p[!!!]*1e5)^2)/(p[&&&]*1e5*v[&&&])) h_s[!!!]=enthalpy(steam;s=s[&&&];p=p[!!!]) h[!!!]=enthalpy(steam;s=s[!!!];p=p[!!!]) T[!!!]=temperature(steam;s=s[!!!]; p=p[!!!]) x[!!!]=quality(steam; h=h[!!!]; p=p[!!!]) W_aksel[&&&]=W[%%] W_el[&&&]=W[%%]*0,96

6. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example -Basic combined cycle plant

7. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Stationary modelling: A stationary system can always be modeled by setting up an equation set with N eqs. and N unknowns!

8. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Multigate approach: - Setting up the interconnection matrix ±1 ~ Primary flows ±2 ~ Secondary flows ±3 ~ Energy flows

9. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Systematic conservation equations Continuity: Energy: ICM is the interconnection matix, m is the mass flow vector and P is the energy flow vector For energy in flows: P=m·h

10. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen System data: h gas =31 kJ/kg h luft =31 kJ/kg T pinch =10ºC h 8 =3.400 kJ/kg p 18 =40 bar p=1 bar p 13 =0,065 bar h 16 =40 kJ/kg h 17 =105 kJ/kg p 21 =1 bar h 21 =375 kJ/kg h 22 =175 kJ/kg A=4000 m²  pump =80% 22MW 19 w pumpe - Boiler areas are unknown. - Output shaft powers are unknown.

11. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Property matrix:

12. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen The ”closeure” component From the heat exchanger model we also have: => Overdetermined eq. set!

13. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Energy and mass conservation:

14. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Combustion calculations

15. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Dissociation Dissociation expresses the equilibrium of a given reaction. A chemical process never finishes. Therefore unintentional products like CO is Often part of the flue gas. Dissociation can in general be neglected for temperatures below 1600°C.

16. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Adiabatic combustion temp., T ad Numerical determination: Note! Real combustion temperature is always below the adiabatic combustion temperature!

17. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Heating values of a fuel Lower heating value (water on steam form): Heating value for mixtures T=25ºC, p=1 bar SubstanceChemical SignEnthalpy of formation [kJ/kmol] SteamH 2 O (g)-241.941 WaterH 2 O (lq)-285.975 CarbonmonooxideCO-110.576 CarbondioxideCO 2 -393.701 SulphurdioxideSO 2 -297.038 SulphortrioxideSO 3 -395.761 MethaneCH 4 -74.847 EthaneC2H6C2H6 -84.667 PropaneC3H8C3H8 -103.846 n-ButaneC 4 H 10 -124.732 NitrogenoxideNO90.290 NitrogendioxideNO 2 33.095 AmmoniacNH 3 -45.898

18. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen When using MULTIPORT: Use Danish notation (decimal separator is ”,” in generated EES-models)!