A general framework and optimization models for the scheduling of continuous chemical processes

Abstract

We present a framework for the formulation and solution of continuous process scheduling problems. We focus on modeling transient operations such as startups, shutdowns, and transitions between steady states. First, we show how the concept of processing tasks can be generalized to represent continuous processes, including their transient operations. Second, we discuss how to systematically calculate the parameters describing material consumption/production and utility consumption during transient operations. Finally, we present new mixed‐integer linear programming formulations for the scheduling of continuous chemical production.

A General Framework and Optimization Models for Integrated Capacity and Production Planning

“…The MILP model formulation is presented using uppercase italic letters for variables, lowercase italic letters for indices, uppercase bold letters for sets, and lowercase italic Greek letters for parameters. The system representation is based on the STN representation and on previous work on scheduling of continuous chemical processes . The representation consists of sets of tasks, i ∈ I , units, j ∈ J , that can process tasks, and a set of materials, k ∈ K , that are consumed or produced by tasks.…”

“…Equation tracks the material balance of all of the materials. true S kn = S k , n − 1 + ∑ i ∈ I k ∑ j ∈ boldJ i ∑ t ∈ T ij ρ italicijkt B italicij , n − t − 1 + ξ k , n − 1 , ∀ k ∈ K , n ∈ N where B ijn is the size of task i that starts processing in unit j at time point n . Parameters ρ ijkt ∈ [−1,1] define the consumption (<0) and production (>0) of material k at time periods t ∈ T ij = {0,1,···,τ ij } relative to time point n when task i starts processing in unit j . Such definition of the consumption/production of a task allows for a flexible modeling of tasks which can produce/consume material throughout their duration rather than only at their beginning/end.…”

“…For continuous processes, both the rate of production and the duration and starting time of the task must be decided . To model continuous tasks, we introduce the concept of subtasks.…”

“…For continuous processes, both the rate of production and the duration and starting time of the task must be decided. 52 To model continuous tasks, we introduce the concept of subtasks. The steady-state phase of a run of a continuous task is represented by steady-state subtasks i ∈ I SS with processing time τ ij = 1.…”

Upcoming Transformations in Integrated Energy/Chemicals Sectors: Some Challenges and Several Opportunities

“…Such local solutions would differ depending on the availability of resources and the local demands; as these local solutions would vary with time, a truly agile industry will be necessary. Perhaps tools such as those developed for the optimization and scheduling of industrial processes − could be helpful in guiding the implementation of this new realization of global industries. With this in mind, in Table some research opportunities which are more local compared to those discussed in Table are presented.…”