Maximal Flow Unit Network: Superstructure-Based Integration of Batch Scheduling and Sustainable Water Network Design

Sustainable water management has become increasingly important across process industries. In the pharmaceutical and specialty chemical sectors, batch processes play a central role and are significant consumers of water. The water usage in such processes is closely tied to the operational schedules. Therefore, integrating batch process scheduling with a water network design is essential for improving overall water efficiency and sustainability. In this work, a novel superstructure-based representation technique, named maximal flow unit network (m-FUN), is proposed to rigorously represent the intricacies of a batch network optimization problem. The corresponding discrete-time grid-based formulation rigorously accounts for various process and utility constraints, including storage limitations and water reuse requirements, while remaining adaptable to diverse objective functions. The main advantage of the proposed framework is the seamless integration of utility networks with process networks. Furthermore, the proposed m-FUN representation inherently represents the plant topology, which facilitates the easy integration of design decision-making with the batch scheduling model. The proposed method has been tested on four different networks having varying degrees of complexity, with several possible use cases that can occur during batch operations. The results demonstrate that the m-FUN framework effectively captures intricate process details while maintaining a high computational performance, making it a promising modeling technique for batch scheduling and optimization of batch water networks (BWN).