The speaker: Professor Anvarbek Meirmanov (National Research University "Higher School of Economics", Moscow, Russia)

Title of the talk: “Mathematical models of oil reservoir.”

Time: Thursday, 25 of March 2021, 15:00 - 16:00.

Abstract. This report is devoted to mathematical models of displacement of oil by some suspension in rocks during oil production. Mathematical models of the oil reservoir are very important from both theoretical and practical points of view. So far, one of the most popular such models is the Backley-Leverett model [1]. Probably, the next known model could be the Muskat problem [2]. Each of these models is a phenomenological mathematical model. That is, it describes the physical process at the macroscopic level, where the characteristic size of the domain under consideration is several meters. We discuss existing phenomenological models of oil reservoir and suggest new exact mathematical models based on ideas R. Barridge and J. Keller [3] and E. Sanchez-Palencia [4] (mathematical modelling) and G. Nguetseng [5] (homogenization). Finally, we illustrate our results with some numerical implementations for one-porosity geometries and compare obtained results for different mathematical models.

  1. S.E. Buckley and M.C. Leverett, 1942, Mechanism of fluid displacements in sands, Transactions of the AIME, v.146, pp. 107-116.
  2. M. Muskat, Two fluid systems in porous media. The encroachment of water into an oil sand, Physics, 5, 1934.
  3. R. Barridge and J. Keller, Poroelasticity equations derived from microstructure, J. Acoust. Soc. Am., V. 70, issue 4, 1981.
  4. E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Phys., 127, Springer-Verlag, Berlin–New York, 1980.
  5. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., V. 20, issue 3, 1989, 608 - 623.

ZOOM link:
https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09

ZOOM Id: 836 7313 8944
Passcode: 808818

We are pleased to inform you that the information on previous talks is available on the seminar web page https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid see Past Talks section.

Organizing Committee: Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo and Konstantin Pileckas.
This seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers.