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From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems
Aseguramiento Tecnol Pemex Explorac & Prod, Mexico.
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling Phys & Cognit Sci)ORCID iD: 0000-0002-9857-0938
Univ Nacl Autonoma Mexico, Mexico.
2018 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2118, article id 20170225Article in journal (Refereed) Published
Abstract [en]

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals Dfrom the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski- Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).

Place, publisher, year, edition, pages
The Royal Society Publishing , 2018. Vol. 376, no 2118, article id 20170225
Keywords [en]
decision-making and risk analysis, geology, Hilbert's sixth problem, quantum versus classical Bayesian inference, heterogeneity, open quantum systems
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-76464DOI: 10.1098/rsta.2017.0225ISI: 000427878700004PubMedID: 29555799Scopus ID: 2-s2.0-85045560953OAI: oai:DiVA.org:lnu-76464DiVA, id: diva2:1232075
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2019-08-29Bibliographically approved

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