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:

Assoc. Prof. Dr. Orchidea Maria Lecian graduated in Thoeretical Physics at Sapienza University of Rome and ICRA, where sha also defended her PhD Thesis in Relativistic Astrphysics. She was poast-doctoral fellow at IHES, Bures-sur-Yvette, and iat Sapienza Univeristy of Rome. She participated in several intensive-research programs at Centre Emil Borel, Paris, at AEI-MPI Golm, at The Fields Institute for Research in Mathematical Sciences, Toronto, and at UPO in Vercelli.
She has been International Reserarcher and appointed Erasmus Lecturer at Comenius University, Bratislava as SAIA NS'P Fellow. She was Assistant professor at Sapienza Unviersity of Rome, and she was Visiting Professor at Kursk State Unviersity, Russia, with the Programme Education in Russia of the Russian Federtion. She has been Associate Professor at Sapienza University of Rome. She is memeber of diverse research consortia. She was awarded several scientific prizes. She has particpated in several national confrences and international ones. She is author of research papers, conference papers, review papers, invited papers, six books, encyclopedia entries and one book-chapter. She has participated as editor and as reviewer in several international Journals.