(80g) Bayesian Optimization Approach to Operation Recipe Optimization of Semi-Continuous Process

Semi-Continuous process is similar to semi-batch process in that reactants are added repeatedly during the operation. However, the main difference is that the product is removed repeatedly in the semi-continuous process, unlike the semi-batch process where the product is removed only once at the end of reaction. The optimization variables for the operation recipe of semi-continuous process include the amount of reactant and the time points to replenish. In the case of the process of which the amount and state of reactant in the reactor is not measurable, the recipe optimization problem is a kind of hyperparameter optimization. Since the time points to replenish are not predictable, the process operates according to the specified operation recipe set before beginning the operation. The optimization also involves dynamic simulation of the semi-continuous process, which requires a long simulation time to ensure that operational constraints are satisfied during the operation.

Not only a long dynamic simulation time is required, but the sequence of replenishing the reactant requires many iteration steps to converge the non-linear solver since the mass and energy change stiffly. In addition, it also takes much time to simulate all the combination of the optimization variables. In this study, a Bayesian Optimization Algorithm [1], which is one of the machine learning algorithms for hyperparameter optimization, is utilized to reduce the number of dynamic simulation runs for recipe optimization. First, a base-case suboptimal recipe is employed to sequentially replenish the reactant at the time when the reactant is depleted. And then new operation recipes are suggested to minimize the amount of reactant used and to maximize the period of replenishment.

The process presented in this study is a pilot-scale carbonation process that captures 40 tons of carbon dioxide per day using 20wt% aqueous solution of calcium hydroxide with a gas flow containing 16 vol% carbon dioxide and consists of two reactors. The carbon dioxide is dissolved in water slurry mixed with a calcium hydroxide, which results in precipitation of calcium carbonate. In each reactor, the reactant and product have a replacement cycle, and gaseous carbon dioxide passes continuously. This dynamic model was constructed using Aspen Custom Modeler (ACM) V10 owing to the limited availability of the physical properties of the involved species. Reaction kinetic parameters were estimated using the data from real operations as well as the literature [2-5].

For the operation recipe optimization, the six hyperparameters such as maximum and minimum liquid level are selected and the range is determined. This set of hyperparameters is optimized by solving the bayesian optimization algorithm that is carried out by linking MATLAB to ACM. First, the next set of hyperparameters is decided by optimizing the acquisition function using the sampling data from the simulation. Then, after the ACM dynamic model has been simulated with the set of hyperparameters, the results are sent to the algorithm to find the next set of hyperparameters. As a result, two new operation recipes are suggested and the optimal sets of hyperparameters for each case are obtained.

[1] Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical bayesian optimization of machine learning algorithms. In Advances in neural information processing systems (pp. 2951-2959).
[2] Cents, A. H. G., D. W. F. Brilman and G. F. Versteeg (2005). "Absorption in carbonate/bicarbonate solutions: The Danckwerts-criterion revisited." Chemical Engineering Science 60(21): 5830-5835.
[3] Weisenberger, S. and A. Schumpe (1996). "Estimation of gas solubilities in salt solutions at temperatures from 273 K to 363 K." AIChE Journal 42(1): 298-300.
[4] Johannsen, K. and S. Rademacher (1999). "Modelling the Kinetics of Calcium Hydroxide Dissolution in Water." Acta hydrochimica et hydrobiologica 27(2): 72-78.
[5] Velts, O., M. Uibu, J. Kallas and R. Kuusik (2011). "Waste oil shale ash as a novel source of calcium for precipitated calcium carbonate: Carbonation mechanism, modeling, and product characterization." Journal of Hazardous Materials 195: 139-146.