On the application of model reduction techniques for dynamic optimization of chemical plants operation
Systematic methods and tools for managing the complexity
Tools Integration - CAPE Methods & Tools (T4-10P)
Keywords: model reduction, dynamic optimization, phenol hydrogenation
In today’s competitive environment, high economical performance of chemical plants is achieved not only by cost-effective steady state integrated design, but also by continuously responding to market conditions through dynamic operation. In the first case, developing plantwide control structures to achieve stable operation is of paramount importance. In the second case, economical optimality is achieved by dynamic optimization techniques.
Both design of plantwide control structure and dynamic optimization requires models of the chemical plant. The quality of these models is crucial for achieving the objective: the models must represent the plant behavior with sufficient accuracy but the complexity must be limited because both applications require repeated solution during a limited time.
Model-order reduction and model simplification might offer a solution. Several linear and nonlinear techniques have been developed and their application to different case studies reported, showing that a significant reduction of the number of equations can be achieved. However, the benefit is sometimes partial, because the problem structure is destroyed and there is little or no decrease of the solution time.
In this contribution, we investigate the application of model reduction techniques in the context of dynamic optimization. More specifically, we focus on the derivation and use of reduced-order models for the design and implementation of optimal dynamic operation in large-scale chemical plants. A case study is considered: cyclohexanone – cyclohexanol by phenol hydrogenation as a dynamic optimization problem. We demonstrate the advantage of considering the inherent structure that exists in a chemical plant. This structure arises from existence of units or groups of units that are connected by material and energy streams, and mirrors the decentralization of the control problem. The recommended procedure is to apply model reduction to individual units of the plant, and then to couple these reduced-order models. This procedure is flexible as the reduction accuracy can vary from unit to unit, is able to retain the nonlinearity of the original plant, and preserves the significance of model variables. Moreover, the sparsity of the reduced-order model has a beneficial effect on the solution time.
In contrast, applying the reduction techniques to the overall model of the plant does not work, because numerical difficulties when dealing with large unstable systems. Even after stabilizing the plant (after decomposition and analysis of individual units) and model reduction, no decrease of solution time is observed. Additionally, the reduced order model contains variables that no longer represent physical quantities from the real plant and the nonlinearity of the real plant is not captured, even when nonlinear techniques are applied.
Presented Thursday 20, 13:30 to 14:40, in session Tools Integration - CAPE Methods & Tools (T4-10P).
