We propose a systematic control strategy for optimal operation of plants containing integrated process units in the event of unit shutdowns or failures. This entails manipulating the degrees-of-freedom available during and after a shutdown in such a way that production is restored in a cost-optimal fashion while meeting all safety and operational constraints. In this work, we investigate the problem of coordinating various buffer tanks and recycle streams during the period of transition to minimize production losses. The problem is cast in a dynamic optimization framework.

In a typical chemical plant, process units are shut down from time to time either for maintenance or due to equipment failure. From an operations perspective, unit shutdowns can be classified as either critical or non-critical, with the former being those that lead to the shutdown of the entire plant and the latter, those that do not. Under non-critical shutdown scenarios, it is frequently possible for an operator to pursue certain courses of action that will permit the unaffected units to continue operating to some degree. Possible courses of action include reconfiguring the process pathways, re-routing material streams, slowing down production, making use of buffer capacities and so on. The aim of our control scheme is to prescribe a set of optimal control inputs for controlling the process transitions during the shutdown and restoration periods.

The case studies in our work are based on a simulation of a Kraft pulp mill where a process unit is shut down and taken off-line for a period of time, and is subsequently restored. Based on an estimate of the downtime, our proposed control system then computes and implements a set of optimal control trajectories that accommodates the shutdown. While the objective in this work is to minimize production losses over a pre-specified time horizon, the strategy is generic in that resource consumption during the transition could be included and alternative objectives accommodated.

This work extends a prior study [1] by considering in addition two key issues – inclusion of feedback mechanisms to counter uncertainty, and the development of a software-based modeling tool . The downtime estimate is a crucial parameter for performing the control calculations. This estimate will usually be based on past operational experience or on direct information about the prognosis of the shutdown. In practice, this estimate will not correspond exactly to the actual downtime; thus we consider re-optimization based on revised downtime estimates. The remainder of the trajectory is re-optimized from the current state of the system, and the controller performs what is essentially a mid-course correction. This feedback approach has considerable advantages over a multi-scenario optimization approach for dealing with uncertainty in the estimated downtime, in that the resulting control trajectories are less conservative. The performance of this re-optimization scheme is studied in this work under various failure scenarios.

Uncertainty also exists due to model imperfections and unmeasured disturbances. We therefore account for this uncertainty by considering the trajectory optimization problem within a nonlinear predictive control framework. The type of operation under consideration (response to partial shutdown conditions) is inherently unsteady in nature, and the control horizon as measured from the onset of the failure is fixed. Among the distinctive features of the controller are: a shrinking prediction horizon, an economics-driven objective function and the use of a nonlinear differential-algebraic equation-based model. The controller is also "event-aware" in the sense that explicitly known future events such as shutdowns and startups can be specified and accommodated within the prediction algorithm. This form of process event anticipation is distinct from traditional feedforward control in which disturbances are detected solely through plant measurements. Case studies demonstrating the performance of the overall feedback strategy are presented.

In the course of this work, we developed a specialized software-based modeling tool that simplifies the tasks of representing, discretizing, and solving dynamic optimization problems. The main component of this tool is a Domain-Specific Language (DSL) with a minimalist syntax called MLDO (Modeling Language for Dynamic Optimization). The DSL is tailored to the representation of constructs specific to the dynamic optimization problem domain. Models written in MLDO are used as a precursors for generating intermediate AMPL-based models (discretized using an Implicit Runge-Kutta method), which are subsequently solved using a large-scale nonlinear optimizer, IPOPT [2].

References

1. Swartz, Christopher L. E., Balthazaar, Anthony K. S. Dynamic optimization of an integrated multi-unit system under failure conditions, Paper 441c, AIChE Annual Meeting, Cincinnati, Ohio, November 2005.

2. A. Wächter and L. T. Biegler, On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp. 25-57, 2006