Application of the Michaelis-Menten formalism to hydrocracking-related reactions and analysis of the features of the reactors

Title : Application of the Michaelis-Menten formalism to hydrocracking-related reactions and analysis of the features of the reactors

Abstract:

I establish a comprehensive theoretical foundation for the catalytic hydrocracking of heavy residues, focusing on vacuum residues derived from both coal and petroleum resources. The strategic upgrading of these complex heavy oils centers on crucial industrial chemical objectives, including significantly decreasing fluid viscosity, lowering product boiling points, achieving effective demetallisation, leveling out structural impurities, and increasing the overall hydrogen-to-carbon ratio. Building upon previous historical instances of metallic-catalyst hydrocracking systems, this research models these intricate multi-phase reaction networks utilizing a rigorous mathematical framework grounded entirely in the properties of Markov chains.

Differing substantially from traditional modeling methodologies established in earlier literature, this research introduces the Galerkin representation for the transition probability matrix. This specific matrix is constructed directly from the fundamental matrix governing the physical refining process itself. This mathematical formulation provides an exceptional advantage for accurately describing the continuous time-dependent evolution of both the structural eigenvalues and the system Mean First Passage Times. The chosen probability matrix representation is explicitly independent of and inequivalent to previous historical frameworks. By altering how the time evolution of the individual vector states is mathematically expressed, this formulation yields vastly superior stability. For instance, applying this specialized Galerkin framework to the benchmark Alberty Case II system analytically proves that non-physical numerical oscillations are completely eliminated.

The overall structure of the paper begins with an initial interrogations from  MacDonald hydrocracking formulations before expanding into a detailed methodological exposition. This includes the exact mathematical normalization of reaction rates, the specific derivation of eigenvalues, and numerical applications for calculating state time evolution. Furthermore, explicit analytical expressions are spelled out to detail how the transition matrices map the changing chemical states. Finally, I outline critical prospective future studies made possible by this new analytical framework, thus I provide with new insights about advanced industrial petroleum refinery chemical engineering optimization methodlogies.

Biography:

Prof. Orchidea Maria Lecian graduated in Theoretical Physics at Sapienza University of Rome and ICRA- International Center for Relativistic Astrophysics in 2005 and completed her International Relativistic Astrophysics Phd at Sapienza University and ICRA. She was post-doctoral Fellow at IHES (Bures-sur-Yvette, France), AEI-MPI (Potsdam-Golm, Germany) and Sapienza University of Rome. She has taken part in intensive research programmes at AEI-MPI (Potsdam-Golm, Germany) and The Fields Institute for Research in Mathematical Sciences (Toronto, Canada). She has been researcher for  SAIA- NS'P (The National Scholarship Programme of the Slovak Republic- National Stipendium Program) as Research grantee and appointed Erasmus Lecturer at Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Theoretical Physics and Physics Education- KTFDF.

She has been Assistant Professor at Sapienza University of Rome and is Professor at Sapienza University of Rome. She is wasVisiting Professor at Kursk State University, Chair of Algebra, Geometry and Didactics of Mathematics Theory within the Programme Education in Russia for Foreign Nationals of the Ministry of Science and Higher Education of the Russian Federation in 2022-2023. She has contributed in national conferences and international conferences. She is member of several Research Consortia. She is author of research papers, conference papers, review papers, invited papers and two books. She is reviewer and editorial-board member of several Journals.