(284g) Parameter Estimation and Process Optimization of Heterogeneous Batch Reactors Under Uncertainty

Heterogeneous
solid-liquid batch reactors are widely applied to produce fine chemicals in
metallurgical, agrochemical and pharmaceutical processes. Compared with
fundamental homogenous reactions, solid-liquid reactions are usually coupled
with mass transfer, such as liquid phase diffusion and solid particle
dissolution. However, a detailed reaction mechanism is typically inaccessible
in a real industrial plant due to limited prior knowledge and difficulty of
measurements. Understanding reaction mechanisms and constructing acceptable
models based on obtainable information are desired to facilitate process
optimization and control. In this study, we first introduce a model
identification and parameter estimation procedure and implement it on our batch
reactors with limited real plant/experimental data. Optimal control is then
implemented on the estimated model to reduce total batch time while satisfying
operation constraints and final concentration requirements.

Two particular
mechanisms -- solid surface reaction models and dissolution controlled models
are considered in the targeted solid-liquid reactions. A uniform kinetic model
is developed with a model indicating factor to differentiate mechanisms.
Particle morphology is considered similar to that described in [1] by
introducing a shape factor. In addition, several other parameters are also
included, such as activation energies, diffusion coefficients and heat transfer
coefficients. A detailed procedure for parameter estimation [2] and model
identification [3] is implemented, including pre-selection of estimable
parameter subset, simultaneous estimation by using measured data, estimation
quality evaluation, model simplification and model discrimination. In our case,
only reactor temperature profiles and highly limited concentrations are
measured. Small confidence intervals and good data fitting are obtained by the
identified model.

The
motivation behind the model identification effort is to develop an optimal
control solution to minimize batch time and increase process capacity. The end
of batch is defined by satisfying final conversion requirements. Feeding of
liquid reactive components and reactor/jacket inlet temperatures are treated as
decision variables. Optimal control is obtained by solving the optimality
conditions of the Hamiltonian together with the corresponding adjoint system. A dynamic model is derived with multiple
stages describing different batch operation steps. Orthogonal collocation on
finite elements is applied to discretize the problem, resulting in a large
scale nonlinear programming problem formulated and solved in AMPL/IPOPT.
Finally, to address potential parametric uncertainties, disturbances and model
mismatch, a robust optimization strategy is applied by adding back-off terms to
ensure that constraints are satisfied in the worst-case scenario.

References

[1] Salmi, Tapio,
Henrik Grénman, Johan Wärnå,
and Dmitry Yu Murzin. "New modelling approach to liquid–solid
reaction kinetics: From ideal particles to real particles." Chemical Engineering Research and
Design 91.10 (2013):
1876-1889.

[2] Lin, Weijie, Lorenz T. Biegler, and Annette M. Jacobson. "Modeling
and optimization of a seeded suspension polymerization process." Chemical Engineering Science 65.15 (2010): 4350-4362.

[3] Stewart, W. E., Y. Shon, and G. E. P. Box. "Discrimination
and goodness of fit of multiresponse mechanistic
models." AIChE journal 44.6 (1998): 1404-1412.

[4]
Diehl, Moritz, Hans Georg Bock, and Ekaterina Kostina.
"An approximation technique for robust nonlinear
optimization." Mathematical
Programming 107.1 (2006):
213-230.