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ETH Zürich
ICBGM 2012Modeling Chemical Reactions Using Bond Graphs
Jürgen Greifeneder and François Cellier / Genua / July 2012
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
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
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
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
=
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
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
ETH Zürich
Modeling Chemical Reactions Using Bond GraphsHow to compute h?
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 8
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
.
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:
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
ETH Zürich
Example: Hydrogen-Bromine-SynthesisReaction Equations and Network
Jürgen Greifeneder, François CellierApril 22, 2023 | Slide 14
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
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
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
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