icbgm 2012 modeling chemical reactions using bond graphs
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ICBGM 2012 Modeling Chemical Reactions Using Bond Graphs. Jürgen Greifeneder and François Cellier / Genua / July 2012. Modeling Chemical Reactions Using Bond Graphs Starting Point. Methodology to model Conduction Convection Evaporation / Condensation Multi-Element Systems - PowerPoint PPT PresentationTRANSCRIPT
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ETH Zürich
ICBGM 2012Modeling Chemical Reactions Using Bond Graphs
Jürgen Greifeneder and François Cellier / Genua / July 2012
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsStarting Point
Methodology to model Conduction Convection Evaporation / Condensation Multi-Element Systems
using true rather than pseudo-bond graphs
Chemical reactions are the final high point to this methodology
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 2
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ETH Zürich
Chemical Reaction
Modeling Chemical Reactions Using Bond GraphsBasics
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 3
A1
A2
B1
B2
heat volume work
T p
AiBj
Unknowns
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to compute reaction rate k and molar flow rate n?
Using Arrhenius’ law:
This requires us to provide the temperature T the molar fractions of each of the components within
the mixture
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 4
Tn
ChR
{c1, c2, …, ck}
hReac
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to compute T and p?
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 5
Each component has its mass, fills an individual volume and holds an individual amount of entropy
This is enough to determine the state of each component {M, S, V}
Temperature and pressure are intrinsic variables, i.e.
This leads to a new capacitive element, called “capacitive field” (CF) compounding three different extrinsic state variables
=
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsEquilibrium Processes
All CF-Elements are connected using HVE-Elements
HVE contains independent equilibrium processes for temperature and pressure
Allowing any exchange speeds for heat resp. volume
T & p of neighboring CFs will equalize over time
T & p of CFs within a mixture will vary only marginal, e.g. in heating or expanding processes
T & p of a mixture can be (as a first order approximation) calculated as weighted average of the components Ts & ps
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 6
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsWhat is h?
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 7
TFm
m
n
g
TFm
h
n
u
M.
M.
Free Gibb‘s Enthalpy per kg
Mass flow
Internal Energy per kg
Molar flow
Free Gibb‘s Enthalpy per mol
Internal Energy per mol
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to compute h?
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 8
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to distribute Sreac ?
Assumption:
heat is transferred over surfaces, i.e. the larger the volume fraction of a component the larger is the probability that this component’s surface is in contact to the heat source (reaction)
Distribute the reaction’s heat production / consumption towards all components linear to their volume fraction.
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 9
.
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to deal with the chemical volume work qReac?
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 10
q21 q2
p*
q2
q31
Dp1q1
0
DqReac p*
To be distributed towards the CF-Elements
p2 Dp2
p*q1p*
q1p1 1 Dp3
q3
q3q3p3
p3
q1Dp1
q2p20
0
0
From
CF-
Ele
men
t
To th
e ch
emic
al re
actio
n ne
twor
k
Boyle-Mariotte
Classical Difference Calculation:
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsEquilibrium and Parallel Reactions
Chemical reactions are reversible, i.e. for each reaction, there exists a reverse reaction, such that R-1 [ R(x) ] = x
The modeling does not care, whether n ≥ 0 or n < 0 Equilibrium reactions can be built using one ChR-
Element In praxis it is easier to use two separate ChR-
Elements, as the determination of n depends on the Educts
The linearity of the network allows to superpose different reactions
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 13
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ETH Zürich
Example: Hydrogen-Bromine-SynthesisReaction Equations and Network
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 14
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ETH ZürichJürgen Greifeneder, François CellierApril 22, 2023 | Slide 16
Collection of reaction enthalpy
Connection to outside
CF-Elements with HVEs
Volume and heat distribution
Thermo-bond to h/n-bond
transformationChemical reaction network Chemical
reactorsState vector
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ETH Zürich
Example: Hydrogen-Bromine-Synthesisisochoric, outside condition: T=800 K, p= 101.3 hPa
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 17
Molar fractions
Temperature
Pressure
Radicals H and Br
HBr
H2 and Br2
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ETH Zürich
Modeling Chemical Reactions Using Bond GraphsSummary
Introduction of new bond variable h
Consistent and complete approach for modeling thermo dynamical phenomena using „true“ bond-graphs
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 18
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ETH Zürich
Modeling Chemical Reactions Using Bond Graphs
Thanks a lot for your attention Mille grazie del attenzione Besten Dank für Ihre Aufmerksamkeit Gracias por su atención Merci beaucoup de votre attention большо́е спаси́бо!
Jürgen Greifeneder, François Cellier