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