(541c) Optimization of Chlorobenzene Process with High-Fidelity Reactor Models Under Trust Region Strategies

This work demonstrates the optimization of the industrial scale chlorobenzene process, which continuously produces multiple products and includes a multiphase reaction with bubble column reactors (BCRs). The trust region filter (TRF) method is applied to carry out the optimization of large chlorobenzene process with high-fidelity BCR models. The TRF method uses surrogate models that substitute the high-fidelity models that lead to a large and intractable optimization problem.

The chlorobenzene process continuously produces six products, benzene, mono-chlorobenzene, para- and ortho- dichlorobenzene, trichlorobenzene, and hydrochloric acid. Those products are widely used in different fields such as engineering plastics and agrochemicals. In the current volatile market, the manufacturers concern the production balance for their business feasibility and operability for customer demand. From the view of process optimization, the process starts with two multiphase reactors where chlorination reaction occurs. After the reactors, several separations such as distillation and absorption follow to separate each product and treat unreacted chlorine gas. The multiphase reactors play a key role in controlling the production balance. The usage of the high-fidelity BCR models is imperative to obtain realistic optimization results for decision makers.

In this work, we use a BCR with an external loop for the multiphase reaction. The high-fidelity BCR model consists of axial dispersion equations, mechanical energy balance equations, and empirical flow dynamics parameters to consider the influence of fluid dynamics. The system of equations becomes differential algebraic equations (DAEs). The DAEs are discretized with orthogonal collocation finite element method and solved with NLP solver, CONOPT 4. This model is implemented in Pyomo with PyomoDAE. The resulting number of variables and equations is around 30,000, respectively. The size of the high-fidelity model is considerably large. Hence, we use the TRF method to obtain the optimal solution of the target problem with the high-fidelity models to avoid direct implementation of the high-fidelity models in the process model.

The TRF method constructs the trust region subproblem (TRSP) where the high-fidelity model is substituted with a surrogate model and variables are restricted within a trust region radius. Then, the TRSP is iteratively solved by updating the surrogate model. This approach is developed by Eason et al. [1] for derivative free optimization that includes black box models which are expensive in computation. In addition, the approach guarantees the convergence to the target problem with high-fidelity models. In our work, we use a first order correction (FOC) model as the surrogate model. The FOC model applies zeroth and first order correction on a basis function with the derivative of the high-fidelity model. The basis function can be any function. For instance, a reduced order model [2], ideal models such as CSTR and PFR models, polynomial functions, and even data of a high-fidelity model at the initial or previous iteration can be used. The process optimization problem with the TRF algorithm is also implemented in Pyomo and solved with CONOPT 4.

From the convergence results, we compared surrogate models with different basis functions. CSTR models with exact kinetic parameters as a basis function converge to an optimal solution with the fewest iterations and function evaluations of high-fidelity models. The reason why the basis function of the CSTR model is efficient is that CSTR models are low-fidelity models but a reasonable approximation of the high-fidelity models. For example, CSTR models always satisfy the reaction kinetics, mass and energy balances. This property provides good initial values and keeps the values of the surrogate models close to the high-fidelity models. In addition, the optimization result is compared with the solution with low-fidelity CSTR models and shows significant differences in operating conditions. The major difference is that the solution with low-fidelity CSTR models underestimates the chlorine consumption and also overestimates hydrochloric acid production by 20%, respectively. Furthermore, CSTR models are commonly used in the early stage of process development. With our approach, high-fidelity models also can be developed at the same time and be available in later stages of process development. Moreover, during the process development stage, we usually need to evolve from CSTR models to high-fidelity models for process optimization. In such situations, the TRF approach allows us to transition from low- to high-fidelity models directly, using only function calls from high-fidelity models with no additional implementation work.

In conclusion, the optimization with the FOC surrogate model based on CSTR models successfully provides an optimal solution with high-fidelity models under trust region strategies. The CSTR based surrogate model are also more efficient than surrogate models with other basis functions. In addition, the TRF approach allows us to solve an optimization problem with high-fidelity models without additional implementation of large high-fidelity models. Notably, the optimization with CSTR based surrogate models provides a smooth transition from low- to high-fidelity models in process development. Finally, the optimization with high-fidelity models makes the manufacturers’ decision making more realistic, as we observe significant differences in chlorine consumption between low- and high-fidelity models.

References

[1] J.P. Eason, L.T. Biegler, Advanced trust region optimization strategies for glass box/black box models, AIChE J. 2018;64(11):3934-3943.

[2] A. Agarwal, L.T. Biegler, A trust-region framework for constrained optimization using reduced order modeling, Optim. Eng. 2013;14(1):3-35.