(541b) Incremental Identification of Reaction and Mass-Transfer Rates In Gas-Liquid Reaction Systems Using Tendency Modeling

The
identification of reliable reaction and mass-transfer rates is important for
building first-principles models of gas-liquid reaction systems. The
identification of these rates involves the determination of a model structure
(reaction stoichiometry, rate expressions for the reactions and mass transfers)
and of the corresponding parameters. The identification of these rate expressions
from measured concentrations is a challenging task because of the direct
coupling between the reactions and the transfer of reactants and products
between the two phases.

The identification task can be performed
globally in one step by choosing the model structure and estimating the model
parameters via the comparison of model predictions and measured data. The
approach is termed simultaneous
identification since all reactions and mass transfers are identified
simultaneously. The procedure needs to be repeated for all candidate model
structures. Hence, the simultaneous identification can be computationally
costly when several candidate rate expressions are available for each reaction
and mass transfer. Furthermore, since the global model is fitted so as to
reduce the least-squares error, structural mismatch in one rate expression of
the model will typically result in errors in all the parameters.  Finally, it is often difficult to come
up with suitable initial parameter values, which may lead to convergence
problems.

An incremental
identification approach has recently been proposed, which decomposes the
identification task into the following two steps [1, 2]: (i) computation of the
extents of reaction and mass transfer from measured concentrations without
knowledge of the reaction and mass-transfer rates, and (ii) for each rate
individually, identification of the rate expression and its parameters from the
computed extents.  The fact that
each reaction and mass-transfer rate is treated individually in the incremental
approach helps reduce considerably the number of model candidates, thereby
reducing the computational effort. Although the proposed incremental approach
provides an efficient framework for the identification of gas-liquid reaction
systems, a systematic way of selecting the appropriate rate expressions from
several candidate expressions is needed in Step (ii).

Recently, the so-called generalized tendency modeling (GTeMoC) method has been proposed to select appropriate
rate expressions from a large number of rate expression candidates [3, 4]. In the
GTeMoC methodology, a stepwise linear regression is
used as a tool to select
appropriate rate expressions. Moreover, the statistical metrics are developed
to discriminate rate expression candidates and avoid collinearity in rate parameters.
However, the effect of mass transfer rates is not treated explicitly in the GTeMoC method, and lumped rate expressions containing
the effect of reactions and mass transfers are identified.

This work combines the incremental approach and
the GTeMoC methodology so that the reaction and mass-transfer rates can be identified
individually. Hence, the resulting incremental approach proceeds in three
steps: (i) computation of the extents of reaction and mass transfer from measured
concentrations without knowledge of the reaction and mass-transfer rates, (ii)
computation of the reaction and mass-transfer rates through differentiation of
the corresponding computed extents, and (iii) for each rate individually,
identification of the rate expression and its parameters using the GTeMoC
method. The proposed incremental identification approach combines the strengths
of the incremental approach (can handle each reaction and each mass transfer
individually) and the GTeMoC method (can efficiently select the rate expression
from several candidate expressions). The approach will be illustrated via the
simulation of the chlorination of butanoic acid.

References

[1] N. Bhatt,
M. Amrhein, and D. Bonvin. Extents of Reaction, Mass Transfer and
Flow for Gas-Liquid Reaction Systems. Industrial
& Engineering Chemistry Research, 49(17): 7704-7717, 2010.

[2]
N. Bhatt, M. Amrhein, and D. Bonvin. Incremental Identification
of Kinetic and Transport Phenomena Using the Concept of Extents. Submitted to Industrial & Engineering Chemistry
Research, 2011.

[3] F. Makrydaki
and C. Georgakis.  Iterative
Estimation of Kinetic Structures of Complex Reaction Systems. To be submitted, 2011.

[4] F. A. Makrydaki.
Optimization of Batch Reactions using Data-Driven and Knowledge-Driven Models -
The Case of Asymmetric Catalytic Hydrogenation. PhD Thesis, Tufts
University, Medford, MA, USA, 2010.