(586b) Optimal Integration of Process Design and Dynamic Transitions for Catalytic Distillation Columns: A Discrete-Steepest Descent Framework

Catalytic Distillation (CD) is a typical Process Intensification (PI) application that combines both separation and heterogeneous reaction into a single unit. This process has gained attention given that optimal design and dynamic optimization strategies requires the implementation of efficient Mixed-Integer Nonlinear Programming (MINLP) optimization strategies. Recent studies has shown that it is possible to use CD to produce multiple products [1]–[4]. In particular, transition policies and steady-state process designs have been successfully optimized as independent tasks for multigrade reactive distillation units; however, the simultaneous integration of both tasks have not been considered. Usually, the design of the equipment and the optimization of dynamic transitions are performed sequentially; however, there is no guarantee that a given design can comply with the desired restrictions during operation, e.g., hydrodynamic or product specification constraints. An approach to simultaneously optimize the design and the dynamic transitions of a multigrade CD unit is critical to avoid suboptimal or dynamically infeasible designs at the conceptual design stage.

The Discrete-Steepest Descent Algorithm (D-SDA) is a recent optimization framework that has been applied to the design and synthesis of CD columns with rigorous equilibrium and non-equilibrium models [5], [6]. The D-SDA handles these problems by fixing discrete variables, solving the resulting Nonlinear Programming (NLP) subproblems, and comparing the solution obtained within a neighborhood of the discrete variables at each iteration. If there is no better solution to the NLP subproblems within the neighborhood, then the algorithm stops; otherwise, the algorithm takes the steepest-descent direction to continue the search by performing another iteration. The D-SDA incorporates a reformulation step that allows to decrease the combinatorial difficulties of the problem associated with the presence of discrete design variables, e.g., number of stages and the location of feeds and catalytic stages. In addition, this algorithm applies a rigorous re-initialization strategy at each iteration to handle model nonlinearities, e.g., non-ideal vapor and liquid mixtures, reaction kinetic models, pressure drop calculations and hydrodynamic constraints. The D-SDA has proven to be a useful tool to solve PI problems involving optimal process synthesis and design at steady-state. Nevertheless, this framework is not yet suitable to deal with problems involving process dynamics. This method relies on a partial discrete enumeration based on neighborhoods exploration; accounting for process dynamics may lead to prohibitive computational times since each NLP subproblem becomes a dynamic optimization problem. Also, these subproblems would require custom and near feasible initializations to converge due to the model nonlinearities. Still, no other determinist MINLP solver has shown better performance than the D-SDA when solving CD steady-state design problems [5], [6]. This is because the D-SDA was formulated as a specialized algorithm that takes advantage of the distinctive properties that emerge in CD distillation superstructures, e.g., the presence of binary variables that represent the location of catalytic stages, reflux stream, boil-up stream and feed streams; the presence of binary-binary and binary-continuous products, and the absence of phases at not existing trays that lead to zero flows. Thus, the D-SDA is a promising framework to handle CD superstructures that consider the transient operation of this process.

The aim of this work is to present the optimal integration of process design and dynamic transitions of a multigrade CD process using a new version of the D-SDA algorithm. The problem incorporates dynamic and steady-state operation requirements into a single large-scale Mixed-Integer Dynamic Optimization (MIDO) problem. The objective is to minimize investment and production costs, intensify production throughput and optimize the dynamic operation of a multigrade CD system. An improved version of the D-SDA that returns attractive solutions in reasonable computational times is used to tackle this challenging problem. The new D-SDA algorithm solves the integrated MIDO problem as a multi-scenario problem, where each scenario corresponds to one of the dynamic transitions involved in the process. Moreover, the new D-SDA incorporates a refined initialization strategy and an iterative procedure. At the initialization step, a feasible initialization is found using the conventional D-SDA applied to a steady-state version of the multi-scenario model. This results in an initial CD design that can accommodate multiple grades of a product. Iterations over discrete design variables is performed next. An iteration comprises the solution of the dynamic NLP subproblem for the discrete point being evaluated, and a collection of candidate neighbors that may improve the objective function. The key feature that differentiates the proposed iterative procedure from the conventional D-SDA’s methodology is the implementation of a new systematic procedure that eliminates feasible neighbors for which the overall objective function is not expected to improve, i.e., neighbors are discarded without the need to solve their corresponding dynamic NLP subproblems. For the remaining neighbors, the dynamic NLP subproblems are solved and used to search for an optimal solution using the steepest descent direction method. The improvements made in the new D-SDA framework avoid the solution of multiple NLP dynamic optimization subproblems thus making the original MINLP problem computationally tractable. Another advantage of incorporating this solution procedure is the refinement of the D-SDA’s re-initialization strategy, by using steady-state solutions to progressively generate educated initializations for dynamic NLP subproblems. As a result, the new D-SDA approach overcomes the limitations of the conventional D-SDA when applied to simultaneous process design and dynamic transition problems involving MIDO formulations.

The improved D-SDA framework was applied to the optimal design and optimal dynamic transitions of a multigrade CD unit, with Ethyl Tert-Butyl Ether (ETBE) as the desired product. ETBE columns are typically designed to produce nearly pure ETBE; nevertheless, previous studies have shown the potential benefits of producing ETBE at lower compositions in terms of cost reduction and efficiency [7], [8]. On the other hand, having ethanol impurities in ETBE is not always admissible, e.g., when the aim is to produce non-ethanol gasoline [9], [10]. Therefore, it is necessary to investigate the optimal design of a multigrade CD unit and verify the economic and dynamic viability of this novel operating mode for ETBE production. The results show that the new D-SDA is suitable to generate a design and a dynamic operation scheme for a CD column that produces ETBE at 63%, 83% and 95% molar composition. Also, it was found that the revised D-SDA methodology allows to obtain a design that is different and more affordable than that obtained with a sequential design and dynamic transition strategy. Moreover, savings in computational time were recorded; this is because the assumptions made allowed us to decrease the number of neighbors to be verified at each iteration, which resulted in a decrease on the number of dynamic optimization subproblems that need to be solved. Overall, the application of the new D-SDA framework allowed us to find attractive solutions to the rigorous ETBE case study in acceptable computational times. Future work includes testing this strategy with more challenging case studies in the field of PI; account for products’ due dates, production demands and optimal sequencing constraints in the formulation, and investigate the performance of the new D-SDA framework under closed-loop operation.

References

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