Analysis, Modelling and Simulation of Energy Systems, SEE-T9

1
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
Motivation
Cycle Tempo
- The complexity of real systems
3
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
Methods
-Energy and mass balance equations at a multigate
approach
Continuity
)
(
)
(
j
stream
i
stream
å
å

m
m


out
in
)
1
(
)
1
(
stream
stream
energy

of

on
Conservati
ö
æ
ö
æ
)
(
)
(
)
(
)
(
)
(
)
(
j
stream
n
stream
m
stream
l
stream
k
stream
i
stream
å
å
å
å
å
å

ç

ç


-

-


-

W
W
Q
Q
h
m
h
m



ç

ç
,
,
in
out
in
out
out
mix
out
in
mix
in

ç

ç
ø
è
ø
è
)
1
(
)
1
(
)
1
(
)
1
(
)
1
(
)
1
(
stream
stream
stream
stream
stream
stream

• Note
• Enthalpies must have some referece states!
• The modelled phenomenon must be stationar.
• Note neglected terms and assumptions!

5
Standard component models
///////////////////////////////////////
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)))) sentropy(st
eamppTT) vvolume(steampp
TT) eta(h-h!!!)/(h-h_s!
!!) mC_tsqrt(((p1e5)2-(p!!!
1e5)2)/(p1e5v)) h_s!!!enthalpy(ste
amsspp!!!) h!!!enthalpy(steamss!!
!pp!!!) T!!!temperature(steamss!!!
pp!!!) x!!!quality(steam hh!!!
pp!!!) W_akselW W_elW0,9
6
/////////////////////////////////////////////////
// ///////// HE Water-Water
///////// //////////////////////////////////////
///////////// m!!!m m(h-h!!!
)1000Q p!!!p pp
T!!!temperature(waterhh!!!
pp!!!) Ttemperature(waterhh
pp) QUAdT
ddTT-T ddTT!!!-T
dT(ddT-ddT)/ln(ddT/ddT)
6
Example
-Basic combined cycle plant
7
Stationary modelling
A stationary system can always be modeled by
setting up an equation set with N eqs. and N
unknowns!
8
Multigate approach
- Setting up the interconnection matrix
1 Primary flows 2 Secondary flows 3
Energy flows
9
Systematic conservation equations
Continuity
Energy
For energy in flows Pmh
ICM is the interconnection matix, m is the mass
flow vector and P is the energy flow vector
10
System data
p21 1 bar h21375 kJ/kg
22MW
h22175 kJ/kg
Tpinch10ºC
p1 bar
hluft31 kJ/kg
hgas31 kJ/kg
A4000 m²
h83.400 kJ/kg
p1840 bar
wpumpe
19
?pump80
p130,065 bar

• Boiler areas are unknown.
• Output shaft powers are unknown.

h1640 kJ/kg
h17105 kJ/kg
11
Property matrix
12
The closeure component
From the heat exchanger model we also have
gt Overdetermined eq. set!
13
Energy and mass conservation
14
Combustion calculations
15
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 1600C.

16
Adiabatic combustion temp., Tad
Numerical determination
Note! Real combustion temperature is always below
the adiabatic combustion temperature!
17
Heating values of a fuel
Lower heating value (water on steam form)
Heating value for mixtures
T25ºC, p1 bar
18
When using MULTIPORT
Use Danish notation (decimal separator is , in
generated EES-models)!