Modeling Chemical Reactions in Modelica By Use of Chemo-bonds

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Modeling Chemical Reactions in ModelicaBy Use of
Chemo-bonds
Prof. Dr. François E. Cellier Department of
Computer Science ETH Zurich Switzerland
Dr. Jürgen Greifeneder Corporate Research
Center ABB Germany
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Chemical Reactions and Convective Flows

• Most researchers model chemical reactions using
  (molar) mass flow equations only, not taking into
  account energy flows at all.
• This is possible for isothermal and isobaric
  reactions, but in general doesnt work, because
  the reaction rate constants depend on temperature
  and in the case of gaseous reactions also on
  pressure.
• A better approach to modeling chemical reaction
  systems is by means of bond graphs. This shall
  be demonstrated here.

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Hydrogen-Bromine Reaction I

• Given the following balance reaction
• Its individual step reactions are known and well
  understood

H2 Br2 ? 2HBr
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Hydrogen-Bromine Reaction II

• The mass flow equations can be written as
  follows
• where

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Chemical Energy Flow

• Each mass flow is accompanied by a chemical
  energy flow
• such that

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Hydrogen-Bromine Reaction III

• The step reactions can be interpreted as a bond
  graph

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Hydrogen-Bromine Reaction IV

• Programmed in BondLib

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Hydrogen-Bromine Reaction V

• Simulation results

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Hydrogen-Bromine Reaction VI

• The reaction rate equations can be rewritten in a
  matrix-vector form
• or

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Hydrogen-Bromine Reaction VII

• The energy flow equations can also be written
  down in a matrix-vector form
• or

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The Chemical Reaction Network I

• Thus, the bond graph describing the chemical
  reaction network can be reinterpreted as a
  multiport transformer
• where

nmix N nreac mreac NT mmix
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The Chemical Reaction Bond Graph

• We can now plug everything together

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Hydrogen-Bromine Reaction VIII

• Programmed in MultiBondLib

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Hydrogen-Bromine Reaction IX
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Chemical Reactions and Convective Flows

• The chemical reaction bond graph, as shown until
  now, still doesnt reflect the physics of
  chemical reactions in all their complexity.
• The problem is that a substance that undergoes a
  transformation does not only carry its mass
  along, but also its volume and its heat.
• Hence we should describe each step reactions by
  three parallel bonds, one describing mass flow, a
  second describing volumetric flow, and a third
  describing heat flow.
• Thus, we should really use thermo-bonds.

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Thermo-bonds

• A (red) thermo-bond represents a parallel
  connection of three (black) regular bonds.

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Thermo-bonds and Chemo-bonds

• The (green) chemo-bonds and the (red)
  thermo-bonds are essentially the same thing.
  However, the thermo-bonds have been designed for
  convective flows, and therefore, operate on
  regular mass flows (measured in kg/sec), whereas
  the chemo-bonds were designed for chemical
  reactions, and therefore, operate on molar mass
  flows (measured in mol/sec).

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Hydrogen-Bromine Reaction X

• This version of the chemical reaction network
  contains more information than the original one.
  Yet it is simpler, because the thermal and
  pneumatic ports dont need to be carried
  separately any longer. They are now integrated
  into the chemical reaction network. Each mass
  flow carries its own volumetric and heat flows
  along.

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The Chemical Reaction Network II

• Also the thermo-bond graph describing the
  chemical reaction network together with its
  volumetric and heat flows can be reinterpreted as
  a multiport transformer
• This transformer is now of cardinality 15, as
  there are 5 step reactions, each represented by a
  thermo-bond of cardinality 3.

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Hydrogen-Bromine Reaction XI
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Hydrogen-Bromine Reaction XII
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Efficiency Considerations

• The simulations are so fast that there is very
  little difference between all four of these
  models.

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Conclusions I

• Chemical reactions are quite tricky. To model
  chemical reactions down to their physical and, in
  particular, thermodynamic properties quickly
  leads to models that are rather bulky.
• The bond graph methodology offers us a unified
  framework to deal with this complexity in an
  orderly and organized fashion.
• To this end, we used all three of our bond graph
  libraries BondLib, featuring (black) regular
  bonds, MultiBondLib, featuring (blue) vector
  bonds, and ThermoBondLib, featuring (red) special
  vector bonds for the description of convective
  flows.

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Conclusions II

• To deal with chemical reactions more
  conveniently, we introduced even a fourth bond
  graph library ChemBondLib, featuring (green)
  special vector bonds for the description of
  chemical reaction flow rates.
• The chemo-bonds are identical to the
  thermo-bonds, except that they describe their
  internal mass flows with molar flow rates and
  chemical potentials, rather than with regular
  mass flow rates and Gibbs potentials (the
  specific Gibbs energy).