(697g) Optimal Scheduling of Converter Aisle Operation in a Nickel Smelting Plant

The Converter Aisle of a Nickel Smelting plant represents a significant challenge in terms of achieving efficient planning and scheduling. The scheduling is complicated by several factors including hybrid dynamics due to the interaction of discrete logical decisions and operational restrictions. The complexity of this multivariable system greatly complicates the derivation of a schedule by means of inspection, thus necessitating a systematic methodology by which optimal scheduling can be achieved.          

The process configuration includes one or more furnaces which transfer ladles of furnace matte via cranes to several converters which follow a standard batch recipe. Furnaces are characterized by a continuous inlet flow of Dry Solid Charge (DSC) with a discrete drawing of the Flash Furnace Matte (FFM), referred to as tapping. The standard batch recipe on the converters includes iteratively charging the converters with FFM, followed by high purity oxygen blows that reject iron, sulfur, and impurities, thereby purifying the FFM and producing Bessemer Matte (BM). Byproducts resulting from the oxygen blows include SO₂ and a layer of liquid impurities referred to as Converter Slag (CS). Oxygen blows must be followed by a removal of the CS to avoid re-contamination of the BM by means of a Converter Skim [1]. The blow, skim, and charge operations must be performed several times to ensure that the BM will meet the purity tolerances, whereas the number of FFM ladles added to each converter determine the cast size and thus the production level.

The objective of this work is to design a centralized optimization-based scheduling algorithm that will maximize production by coordinating multiple furnaces and several converters operating in parallel by making FFM allocation decisions to satisfy matte demand based on converter cycle progression. Matte allocation decisions are subject to restrictions such as shared crane usage, furnace capacity constraints, and a range of operating furnace flow rates. The scheduling optimization must account for the semi-continuous furnace operation due to the continuous inlet flow and discrete removal. Converters are characterized by both batch and cyclical operation where casting times must be offset so as to account for the limited casting availability. Furthermore, converter blowing must be sequenced and timed to achieve compliance with SO₂ emission tolerances which limit the number of converters operating in parallel. This work builds on an initial simplified model [2], and contributes toward the development of a real-time decision support tool to optimize production and systematically handle constraints.

Continuous-time formulations have been successful in solving industrial problems [3],[4]. As such, the scheduling optimization is formulated as a continuous-time mixed integer linear program (MILP). The formulation is modeled in AMPL and is solved using CPLEX 12.5. A series of symmetry-breaking and tightening constraints are developed and employed to improve the computation efficiency of the optimization to facilitate the use of this technology in real-time applications. A reactive scheduling mechanism is included to allow rescheduling for when process disturbances impact the operating schedule. A methodology for reducing radical scheduling changes due to the optimization during reactive scheduling is presented using a tiered optimization approach that progressively increases the degrees of freedom available as required, in order to achieve a feasible production schedule.

The optimization formulation will be presented, and its performance demonstrated through case studies simulating real plant operating conditions.  Challenges encountered will be identified, and strategies for addressing them discussed. 

[1] Warner. A. E. M., Liu. J., Javor. F., Lawson. R., Shellshear. W., Hoang. T., and Falcioni. R. (2005). Developments in Pierce-Smith Converting at Inco's Copper Cliff Smelter During the Last 35 Years. pp. 27-43, San Francisco, California.

[2] Ewaschuk. C. M., Swartz. C. L. E., and Zhang. Y. (2013). Optimal Converter Aisle Scheduling in a Nickel Smelting Plant. In Proceedings of the IFAC MMM, pp. 202-207, San Diego, California.

[3] Floudas. C.A. and Lin. X. (2004). Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Computers & Chemical Engineering, 28, pp. 4341-4359.

[4] Harjunkoski. I., Maravelias. C. T., Bongers. P., Castro. P. M., Engell. S., Grossmann. I.E., Hooker. J., Méndez. C., Sand. G., Wassick. J. (2014). Scope for industrial applications of production scheduling models and solution methods. Computers & Chemical Engineering, Volume 62, pp. 161-193.