(659g) Parameter Estimation and Model Discrimination of Batch Solid-Liquid Reactors

Heterogeneous solid-liquid
reactions are of great significance in metallurgical, agrochemical and
pharmaceutical processes. This kind of industrial process is usually conducted
in batch reactors, generating fine chemicals with high profits. Hence,
understanding the mechanism and constructing qualified models are desired to
facilitate process optimization and controller design. Motivated by this, we
explore a model building exercise for a real industrial process that involves
multiple solid-liquid reactions in a series of two batch reactors. Key
activities are to elucidate the kinetic and transport models, estimate model parameters
with limited plant data, and validate the models.

For our target application, the
batch reactor operates sequentially through steps such as preparing, feeding,
reacting, impurity removing, sampling and discharging. In the reacting step,
solid particles react with liquid reactants and generate solid and/or liquid
products. The kinetic mechanism is complicated through coupled mass and heat
transfer and different models have been proposed by previous researchers,
including two particular mechanisms -- solid surface reaction models [1] and
dissolution models [2] with insoluble solid component reactions taking place on
the interface and products sticking on or cracking away from the reaction
surface. On the other hand, if solid components dissolve into the solvent, even
in trace amounts, reactions may occur in liquid phase and the dissolution rate
influences the production rate.

It is well known that model
discrimination is difficult and requires carefully designed experiments.
However, in this case only limited plant data are available to identify the
model and uncertainties in the reaction process, such as solid particle sizes
and shapes, must be resolved. Moreover, simple models with assumptions of
uniform size and ideally nonporous spherical particles cannot fit data well. To
deal with these issues, a generalized model is applied for both surface
reaction and dissolution-controlled mechanisms. The particle morphology is
considered similar to that described in [1] by introducing a shape factor. A
particle size distribution is also implemented. This model requires estimation
of several parameters, including shape factors, activation energies and
diffusion coefficients. To enhance the model estimability, a number of
parameters are lumped in the model.     

Based on the above process
characteristics, a dynamic model is derived with multiple stages. The parameter
estimation is solved in an ‘Errors-in-Variables-Measured’ (EVM) optimization formulation
[3]. Orthogonal collocation on finite elements is applied to discretize the
problem, resulting in a large scale nonlinear programming problem. The problem
is formulated in AMPL and solved by a nonlinear optimization solver IPOPT. The
estimation performance is evaluated by calculating confidence intervals at the
optimal solution. In our case, only reactor temperature profiles and end-point
compositions are measured, with no concentration data available during
reactions. Results show good fitting on process data and small confidence
intervals, which indicates good model parameter selection and estimation. These
results lead us to elucidate the likely mechanistic model for subsequent
optimization studies.

References

[1] TapioSalmi, Henrik Grénman, Johan Wärnå, and Dmitry Yu Murzin. New
modelling approach to liquid–solid reaction kinetics: From ideal particles to
real particles. ChemicalEngineering Research and Design,
91(10):1876–1889, 2013.

[2] Claire L.Forryan, Oleksiy V.Klymenko, ColinM. Brennan, and Richard G.
Compton. Heterogeneous kinetics of the dissolution of an
inorganic salt, potassium carbonate, in an organic solvent, dimethylformamide.
The Journal of Physical Chemistry B, 109(16):8263–8269, 2005.

[3] Victor M.Zavala, and Lorenz T. Biegler. "Large-scale
parameter estimation in low-density polyethylene tubular reactors." Industrial & engineering
chemistry research 45.23
(2006): 7867-7881.