Robust resource targeting in continuous and batch process

Piyush Kumar Kumawat,Nitin Dutt Chaturvedi

doi:10.1007/s10098-021-02118-8

Piyush Kumar Kumawat, Nitin Dutt Chaturvedi

Open Access

https://doi.org/10.1007/s10098-021-02118-8

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Abstract

Water is considered a significant resource in process industries. It is essential for planners to target and optimize the use of water as an external resource for industrial operations. Such optimization problems account for uncertainties related to internal resources and must be handled to provide solutions for real plants of industrial relevance. In this paper, these parametric uncertainties are addressed, while targeting resources for continuous and flexible schedule batch process. The proposed robust counterpart formulations include resource minimization constraints for continuous and batch processes to satisfy the demand. Three different robust optimization methodologies are adapted and extended to handle parametric uncertainties associated with internal resources. Assuming bounded and known uncertainty, the resultant formulations are then implemented to literature examples, and the results are compared with the deterministic formulation. The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for the defined problem because it preserves the linearity and provides a mechanism to control the degree of conservatism, guaranteeing feasibility. The proposed formulations are also explained using illustrative examples estimating the additional 4.04% and 11% requirement of resource in continuous and batch process, respectively, to handle uncertainty with a known risk. This model will assist the planner to decide the resource requirement under uncertain conditions and do the necessary preparation accordingly, and thus, it immunes the process against uncertainties to satisfy demands.Graphic abstract

Highlights

Water is one of the essential commodities in process industries and can be conserved via modifying process behaviour, optimization, proper scheduling in order to decrease overall water usage and improving internal reuse (Klemeš 2013)
The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for the defined problem because it preserves the linearity and provides a mechanism to control the degree of conservatism, guaranteeing feasibility
A budget parameter is introduced to control the conservatism of the solution. This formulation is capable to control those parameters that are allowed to get their worst-case value and to tradeoff with an upper bound of probability violation (Thiele 2007). Implementation of this methodology is evident in aspects of process systems engineering, Li and Ierapetritou (2008), presented the robust counterpart mixed-integer linear programming (MILP) formulation to target uncertainties while scheduling production in a batch process

Summary

Graphical Abstract

Sets Nsr Nsk s ε S ssr ε Ssr ssk ε Ssk iεIkεK number of sources number of sinks any state source state (Ssr ⊂ S) sink state (Ssk ⊂ S) unit event point. Flow available from source related to ‘ssr’ nominal value of flow available from source related to ‘ssr’ variation amplitude from F̅sr(ssr) csr (ssr ) c̅sr(ssr ) ĉsr (ssr ) Fsk (ssk ) csk (ssk ) Ωfc, Ωcc. Гcc contaminant concentration of source related to ‘ssr’ nominal value of contaminant concentration of source related to ‘ssr’ variation amplitude from c̅sr(ssr) flow demand related to sink ‘ssk’ concentration demand related to sink ‘ssk additional parameters associated with RO 2 for continuous process formulation budget parameter associated with RO 3 for continuous process formulation. Tsr,s(ssr, i, k) time at which source related to state ‘ssr’ starts in unit ‘i’ at event point ‘k’. Tsr,e(ssr, i, k) time at which source related to state ‘ssr’ ends in unit ‘i’ at event point ‘k’. Гcb formulation budget parameter associated with RO 3 for batch process formulation

Introduction

Problem Statement and Optimization Model

Batch Process

Illustrative Example 1

Findings

Conclusion