constitutive relations
DESCRIPTION
Constitutive Relations. What are constitutive relations?. Relate conserved extensive quantities to intensive variables Help define physico-chemical quantities (e.g. enthalpies, densities, viscosities ,…) Define transfer rates (mass, energy, …) Other relations to “constitute” the model. - PowerPoint PPT PresentationTRANSCRIPT
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Constitutive Relations
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
What are constitutive relations?
Relate conserved extensive quantities to intensive variables
Help define physico-chemical quantities (e.g. enthalpies, densities, viscosities ,…)
Define transfer rates (mass, energy, …) Other relations to “constitute” the model
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
How do constitutive relations arise ?
qJt
Related to the terms in the conservation equations for mass, energy and momentum
• Constraints on the system (control relations)
• Convective flow terms (process streams)
• Molecular flow streams (fluxes)• Internal processes
• Defining intensive variables in terms of extensive quantities and other physico-chemical properties
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Balance volumes, flows and system processes
Hot oil in
Hot oil out
EM ,1S
EM ,2S
Hot oil in
Hot oil out
EM ,1S
EM ,2S
E3S
Hot o il in
Hot o il out
Cold feed in
Heated liqu id out
EM ,1S
EM ,2S
Q hQ rloss
Q hloss
Hot o il in
Hot o il out
Cold feed in
Heated liqu id out
EM ,1S
EM ,2S
E3S
Q rloss Q h
Q hloss
Q r
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Classes of Relations
ConstitutiveEquations
Property definitions
Balance volumerelations
Reaction rates
Equipment andcontrol constraints
Transfer relations
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
1. Transfer Relations
General form
Particular forms
mass transfer
heat transfer
)()(),(),( rprprprate
GGGCCKj *
TUAqCV
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
2. Reaction rates
Reaction rate
General reaction expression
dt
dn
Vr i
i
1
RT
E
A
BAAA
ekk
CCfkr
0
,...,
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
3. Thermodynamic relations
Property relations (density, viscosity, …)
Equilibrium relations Raoult’s law Relative volatility, K-value Activity coefficient
),,(iLxTPf
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Thermodynamic properties
Enthalpy
linear
nonlinear
T
T pR RdTTcThTh )()()(
VAPp
p
TcTh
TcTh
)(
)(
T
T p
p
dTTcThTh
TaTaac
0)()()(
...
0
2
210
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Thermodynamic properties
Equations of state
ideal gas
cubic EoS
– SRK– Peng Robinson– NRTL
nRTPV
),( TVfP
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
4. Balance volume relations
Relations between phases
LGVVV
VG
VL
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
5. Equipment and Control
Sensors
)(
)(~
)(~)(
TT
dt
dT
TTMc
AU
dt
dT
TTAUdt
TMcd
dt
dU
f
f
p
f
p
TT f
Fluid
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
6. Control Elements
Transmitters (4-20mA, 20-100kPa)
gain theisG
zero theis
signalinput theis
)(
0
0min
z
I
GzIOO
p
ppp
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Controllers
Traditional (P, PI, PID)
dt
dKdt
KKBO
dtK
KBO
KBOSKBO
DC
I
C
CC
I
C
CC
CPPCC
)(
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Actuators on valves
factor damping andconstant time,
gainactuator
1)-(0movement stem
22
2
2
a
a
G
S
IGSdt
dS
dt
Sd
x
Pdiaphragm area, A
stem velocity, v
stem packing
plug and seat
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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
PROCESS MODELLING AND MODEL ANALYSIS
Valves
Static valves
Control valves characteristics
PCFV
PScCFV
)(
root square )(
percentage equal )(
linear )(1
SSc
aSc
SScS