(183l) Data-Driven Optimization for Process Intensification Governed By High-Fidelity Models

Process intensification merges processes with different aims to reduce the cost and energy consumption. When the processes are modeled explicitly using algebraic equations, standard local and global solvers can be used for optimization [1]. However, many processes may not have an available algebraic model, or it is insufficient to allow for detailed optimization. We are especially interested in process intensification problems where the process is modeled by high-fidelity models such as those given by set of Nonlinear Algebraic and Partial Differential Equations (NAPDE). One of the approaches studied in the literature involves discretizing the NAPDE model to convert it into a large-scale nonlinear programming problem [2]. However, the level of discretization needs to be moderate to keep the model tractable. An alternate strategy is to use simulation data for optimization. Since the simulations are generally computationally expensive [3-6], it critical that the optima (preferably global) is obtained using few evaluations.

Despite several advancements made in data-driven optimization, many algorithms require that a feasible initial guess is provided. Furthermore, handling hard constraints that leads to simulation failure remains a challenge. In this work, we propose a two-phase algorithm [7] comprising of feasibility and optimization phases. Feasibility phase finds a feasible point if the initial point is infeasible and then moves to the optimization phase that aims to find the optimum point. Both the phases involve iteratively developing surrogate models for each of the black-box objective and constraints and then optimizing the subproblems in a trust-region framework. A novel optimization-based sampling strategy is also proposed that can handle hard constraints.

The two-phase algorithm is applied to optimize two process intensification case studies with governing model given by NAPDE. The performance of the algorithm is compared with NOMAD [8] and COBYLA [9]. The first is a carbon capture case study that utilizes CO₂ from flue gas and natural gas to produce syngas [5]. The resulting optimization problem is a grey-box problem with 10 decision variables, black-box objective function, 7 black-box constraints and 2 hard constraints. For the case of minimizing cost of production of syngas, the two-phase algorithm and COBYLA gives the optimum objective function value as $109.57 and $115.75, respectively. The respective required number of simulations are 681 and 364. On the other hand, NOMAD could not find a feasible point. When the algorithm is applied to maximize CO₂ utilization, the two-phase algorithm, COBYLA and NOMAD yields CO₂ utilization of 99.71%, 99.6% and 97.59%, respectively. The number of evaluations required by the two-phase algorithm, COBYLA and NOMAD are 332, 206 and 1248, respectively. The second case study is the design and synthesis of sorption enhanced steam methane reforming to produce H₂ using natural gas [6]. The resulting optimization problem is a grey-box problem with 10 variables, black-box objective function, 2 black-box constraints and 11 hard constraints. The two-phase algorithm leads to an optimal design of the process that yields 95% pure hydrogen with 10.86% lower cost compared to existing small-scale technologies. The performance of the algorithm will also be compared to other solvers.

References:

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[3] Caballero, J. A. and Grossmann, I. E. An algorithm for the use of surrogate models in modular flowsheet optimization. AIChE Journal, 54(10):2633-2650, 2008.

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[5] Iyer, S. S., Bajaj, I., Balasubramanian, P. and Hasan, M. M. F. Integrated carbon capture and conversion to produce syngas: Novel process design, intensification, and optimization. Industrial & Engineering Chemistry Research, 56(30), 8622-8648, 2017.

[6] Arora, A., Bajaj, I., Iyer, S. S. and Hasan, M. M. F. Optimal synthesis of periodic sorption enhanced reaction processes with application to hydrogen production. Computers and Chemical Engineering, 115, 89-111, 2018.

[7] Bajaj, I., Iyer, S. S. and Hasan, M. M. F. A trust region-based two phase algorithm for constrained black-box and grey-box optimization with infeasible initial point. Computers and Chemical Engineering, 2017, https://doi.org/10.1016/j.compchemeng.2017.12.011.

[8] Abramson, M. A., Audet, C., Couture, G., Dennis Jr, J. E., Le Digabel, S. and Tribes, C. The NOMAD project, 2011.

[9] Powell, M. J. D. A direct search optimization method that models the objective and constraint functions by linear interpolation. In Advances in optimization and numerical analysis, pages 51-67, Springer, 1994.