(400c) Integrated Scheduling and Dynamic Optimization of Batch Processes Using State Equipment Networks

Integrated Scheduling and Dynamic Optimization of Batch Processes Using State Equipment Networks

Yisu Nie and Lorenz T. Biegler

Department of Chemical Engineering, Carnegie Mellon University

Traditionally, scheduling and dynamic real-time optimization (DRTO) of a batch process are approached independently. However, an integrated decision-making approach is preferable for the sake of process profitability and flexibility. A foreseeable solution to the problem is to recover the dynamic characteristics of batch operations by directly incorporating dynamic models into scheduling formulations. The objective of this work is to propose an efficient structure based on state equipment network (SEN) that applies to the integration of general batch processes. This approach improves the overall batch process performance by simultaneously optimizing its production schedule and corresponding control profiles of each process unit.

As an alternative to conventional network structures for batch scheduling problems, such as state task network (STN) and resource task network (RTN), SEN addresses batch scheduling from an equipment-oriented perspective, in which complete connectivity of all process units is postulated and these units are described in the form of rigorous models without pre-assigned tasks. By virtue of that, SEN is able to provide a consistent modeling strategy and proper handling of units that operate under different operating modes. To start with, we adopt a unit-specific event-based continuous time representation for the scheduling problem, where time horizon is divided up into a finite number of asynchronous event time slots with regard to each unit. SEN can be efficiently applied to sequence, size and time all possible batch operations within the interest of time.

On the other hand, SEN regards different operating modes, which we also call operating states, as separate dynamic systems connected by exclusive disjunctions. Time-varying dynamic characteristics of batch units can therefore be captured by SEN, using binary variables with an additional temporal dimension. To facilitate DRTO in a batch process, we prefer to use first-principle models for predictions that suit the context of batch processing, employed in the form of differential-algebraic equations (DAE). Finally, SEN also recovers material quality information that has usually been discarded in STN and RTN, to account for time-varying operating strategies.  The overall formulation falls into the category of mixed logical dynamic optimization (MLDO). We elaborate on a procedure to translate MLDOs to mixed integer nonlinear programs (MINLP) coupled with a simultaneous collocation strategy.  An illustrative example is studied, where a multiproduct batch plants are optimized to obtain the best revenue over a fixed time horizon, equipped with single or parallel units in each processing stage. We compare a traditional recipe-based approach, in which all controls are predefined, with an integrated approach. The comparison shows a significant increase of net income in the integrated scheme.