Continuous-Time Models for Scheduling of Parallel Batch Digesters for Pulp Production

The problem of short-term scheduling of batch digesters [1-2] involves development of a mathematical model for finding the optimal sequence of various operations, and their corresponding batch start and end times. The aim is to produce pulp of different qualities in a multi-digester facility comprising multiple production lines. In each production line there are parallel batch digesters along with shared resources (chip filling station, impregnation liquor pump, hot liquor pump, and blow down tank) for meeting the overall pulp demand in a specified time horizon. Unlike conventional batch digesters, displacement batch digesters offer improved energy efficiency through storage and reuse of the hot spent liquor in subsequent batches. Recently, Shaik and Bhat [3] proposed a mixed-integer linear programming (MILP) model for scheduling of displacement batch digesters using discrete-time formulation and State-Task-Network (STN) representation. In their model material balances were modified to include the flow to/from flow transfer tasks, and resource balances were proposed to monitor the utilization of digesters, and extensions to handle shared resources.

In this work, we consider scheduling of both conventional and displacement batch digesters using a resource-task-network (RTN) representation of production recipes, based on unit-specific event based continuous time representation resulting in a MILP problem. The basic framework is adapted from the unit-specific event based models [4-5] dealing with unification of STN/RTN representations and generalization of resource balances. The objective of the scheduling problem is either maximization of production or maximization of total duration of heating and cooking tasks which in turn reduces the overall energy consumption. Illustrative case studies will be presented on both conventional and displacement batch digesters for a digester house comprising of two parallel production lines with four digesters for producing pulp of two different qualities, to demonstrate the proposed modifications and comparison of results with discrete time model [3].

References

[1] Hvala, N.; Strmcnik, S.; Cernetic, J. (1993). Scheduling of batch digesters according to different control targets and servicing limitations, Comp. Chem. Eng., 17, 739-750.

[2] Castro, P.; Matos, H.; Barbosa-Povoa, A.P.F.D. (2002). Dynamic modeling and scheduling of an industrial batch system, Comp. Chem. Eng., 26, 671-686.

[3] Shaik, M.A.; Bhat, S. (2014). Scheduling of displacement batch digesters using discrete time formulation, Chem. Eng. Res. & Des., 92, 318-339.

[4] Shaik, M.A.; Floudas, C.A. (2009). Novel unified modeling approach for short-term scheduling, Ind. Eng. Chem. Res., 48, 2947-2964.

[5] Shaik, M.A.; Vooradi, R. (2013). Unification of STN and RTN based models for short-term scheduling of batch plants with shared resources, Chem. Eng. Sci., 98, 104-124.