LAPSE:2026.0460
Published Article

LAPSE:2026.0460
Structural Constraints with the P-graph Framework: Application to an Ammonia Synthesis Process
June 12, 2026
Abstract
An optimized flowsheet can be generated by numerous approaches. Process optimization via superstructure is one of the methods used to provide solutions that consider the interactions between different decision layers. A process simulator-based optimization is considered in this work, as it offers a reliable and rigorous modeling environment. It is then coupled with a P-graph-based framework to reduce the tedious mathematical writing of the logical constraints to guarantee the structural coherence of a sequence of unit operations.The developed framework consists of three algorithms. The first algorithm transforms the superstructure flowsheet into a P-graph. The second algorithm gets process sub-structures from the superstructure by searching for active units corresponding to a set of decisions made, for example, by an optimizer. The third one checks structural feasibility by verifying that the resulting structure satisfies the five axioms of the original P-graph framework and two additional connectivity tests proposed in this work.The proposed methodology is then applied to an ammonia synthesis process. The results obtained in this work enable a reduction in structural logical constraints while achieving outcomes equivalent to those of a previous study, proving the methodology's efficacy.
An optimized flowsheet can be generated by numerous approaches. Process optimization via superstructure is one of the methods used to provide solutions that consider the interactions between different decision layers. A process simulator-based optimization is considered in this work, as it offers a reliable and rigorous modeling environment. It is then coupled with a P-graph-based framework to reduce the tedious mathematical writing of the logical constraints to guarantee the structural coherence of a sequence of unit operations.The developed framework consists of three algorithms. The first algorithm transforms the superstructure flowsheet into a P-graph. The second algorithm gets process sub-structures from the superstructure by searching for active units corresponding to a set of decisions made, for example, by an optimizer. The third one checks structural feasibility by verifying that the resulting structure satisfies the five axioms of the original P-graph framework and two additional connectivity tests proposed in this work.The proposed methodology is then applied to an ammonia synthesis process. The results obtained in this work enable a reduction in structural logical constraints while achieving outcomes equivalent to those of a previous study, proving the methodology's efficacy.
Record ID
Keywords
MINLP problem, P-graph framework, Process simulator-based optimization, process synthesis, superstructure
Subject
Suggested Citation
Hillaby D, Martinez AP, Portha J, Falk L. Structural Constraints with the P-graph Framework: Application to an Ammonia Synthesis Process. Systems and Control Transactions 5:2058-2065 (2026) https://doi.org/10.69997/sct.126160
Author Affiliations
Hillaby D: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France [ORCID]
Martinez AP: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France [ORCID]
Portha J: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France [ORCID]
Falk L: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France
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Martinez AP: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France [ORCID]
Portha J: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France [ORCID]
Falk L: Université de Lorraine, CNRS, LRGP, Nancy, F-54000, France
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Journal Name
Systems and Control Transactions
Volume
5
First Page
2058
Last Page
2065
Year
2026
Publication Date
2026-06-12
Version Comments
Original Submission
Other Meta
PII: 2058-2065-234-SCT-5-2026, Publication Type: Journal Article
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LAPSE:2026.0460
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https://doi.org/10.69997/sct.126160
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Jun 12, 2026
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References Cited
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