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Contract number
Time span of the project

As of 30.01.2020

Number of staff members
scientific publications
Objects of intellectual property
General information

Name of the project: Multi-scale dynamics of flows and unordered porous media

Strategy for Scientific and Technological Development Priority Level: а

Goals and objectives

Research directions: Mechanics and machinery

Project objective: Creating a new direction of scientific research that combines generating new fundamental knowledge in the field of rheology and mechanics of destruction of complex media and development of new digital technologies for intensification of hydrocarbons extraction by hydrofraking; research of cerebral hemodynamics and analysis of strength characteristics of biomaterials.

The practical value of the study

  • An experimental device for research of foam flow in Hele-Shaw cells. We have investigated flow of foam around obstacles with variation of geometric parameters. Our research has showed significant impact of shape on dynamics of foam flow around and we have found correlation between velocity of flow after an obstacle and concentration of liquid in foam.
  • Preliminary experiments have been conducted in which we simultaneously filmed destruction of a material and recorded acoustic emission data during propagation of cracks in synthetic materials (in particular, in plexiglas).
  • New methods have been developed for capsulation of microbubbles of gases and microdrops of fluids (liquid oils): by stabilizing interphase surface, by creating a layer of nanoperticles on interphase surface, by creating conditions for local flow of the polymerization reaction.
  • We have obtained theoretical estimates of the electric field that occurs near the crack during hydraulic fracturing due to leaks of contrast fluid from the crack in the formation under the effect of the initial high pressure in the crack and elastic forces in the rock that makes the crack close after pumping is finished. We have build a mathematical model of hydrofracking in porous elastic media at set parameters: inhomogeneous medium (physical qualities change over space), flat crack, pumping is conducted through a well that crosses the plane of the crack perpendicularly. The main feature of the model is accounting for pressure in pores and full coupling of the stress-strain states of the formation and filtration of the fluid.
  • Our researchers have conducted experimental research of hydrofracking of thin-walled cylinders with an opening. The research has been completed using a device that creates static and pulse oil pressure. The cylinders were made of GF-177 cement material and of a mixture of alumina cement and sand. We have refined a method for producing samples and mastered working with experimental equipment.
  • A technology has been developed to produce samples of disordered media – plates with different configurations of surface defects to study capillary displacement fronts in Hele-Shaw cells.
  • We have processed results of intraoperative monitoring of velocity and pressure in brain vessels gathered in 2017 in 13 neurosurgical operations using the unique Volcano ComboMap/ComboWire measurement and instrumentation complex.
  • A mathematical model has been developed to determine effective electrical conductivity taking into consideration the structure and complexity of electro-composite of the oil-carrying layer type. A computational algorithm has been created that accounts for division of scales.
  • A model of multi-stage fracking has been built to calculate overall inflow of fluid towards a horizontal well in the light mutual impact of hydrofracking cracks, inhomogeneity of qualities of the layer, accounting for finite permeability of cracks and hydraulic resistance of the well.
  • The Laboratory has developed a numerical model of development of cracks during fracking in a porous elastic medium during pumping of liquids with power-law rheology 
  • Our researchers have determined boundary strains in concrete under both homogeneous and inhomogeneous strain states.
  • We have shown that with increase of the height of an obstacle maximum defect of foam longitudinal velocity first grows linearly, than reaches the maximum value at some particular value of the height of the obstacle and then decreases to the value corresponding to the value of the of full complete blocking of the opening in the cell by the obstacle. The existence of the maximum of the effect at a particular height of the obstacle can be explained by the balance between the growth of surface energy and the gross of viscous loss with increase of the height of the obstacle.
  • An embolization agent has been created that has been used in research of the model setting of the microchannel embolization problem.
  • To model the process of embolizationn of arteriovenous malformation we have suggested to use the Buckley–Leverett equation that describes two-phase filtration of blood and embolizate inside the arteriovenous malformation. A criterion of success of embolization of arteriovenous malformation has been proposed. Firstly, success of embolization can be determined by the extent to which the volume of the arteriovenous malformation is filled with embolyzate and, secondly by the extent of overlap of cross-section of the arteriovenous malformation.

Implemented results of research:

  • Results of our research in hydrofracking have been achieved in collaboration with Gazpromneft Research and Development Center LLC. Works in adaptation of the produced models to industrial applications were financed by a commercial agreement.
  • The build hydrofracking models are expected to be included in the Hydrofracking Simulator developed within the Federal Target Program «Development of an industrial hydrofracking simulator» (sponsored by a grant from the Ministry of Science and Higher Education of the Russian Federation).

Education and career development:

  • A lecture course in methodologies and methods of data processing in the field of mechanics of unordered media for employees of the Laboratory has been read by Stéphane Santucci.
  • We have organized training for postgraduates and young researchers at prestigious foreign schools in our domain of studies: 3 people studied in Udine (Italy), one in Graz (Austria), one in Berlin (Germany)

Organizational and structural changes:

To complete works within the Federal Target Program «Development of an industrial hydrofracking simulator» a temporary research team has been created that includes the main contributors to the project. During the development of the project this team can serve as a core of an engineering center for modeling technological processes in hydrocarbon extraction.

Other results:

  • During a comparison of data of intraoperative monitoring and data of 3D numerical modeling it turned out that for the problem of determining a potential place of aneurysm rupture a significant role can be played by the patient-specific blood flow profile set as a boundary condition; while data on strength of cerebral aneurysm can be taken from the literature. For the same problem we have demonstrated advantage of hydroelastic computations over the rigid one for the purpose of usage of such computations for pre-surgery modeling.
  • To research the possibility of the proposed mathematical model we have reviewed flat flow in a channel under the effect of pressure gradient for fluid with cane-like particles. In the initial moment particles are oriented across the flow. It has been determined that for low Reynolds numbers corresponding to the velocity of rotation of particles the model is reduced to a stationary system of equations for velocity of flow microrotations, and time is a parameter. These equations allow to determine orientation of particles and their micro-inertia depending on transverse spatial coordinate and time.


  • Laboratory of Physics of École normale supérieure de Lyon (France), University of Houston (USA), The University of British Columbia (Canada), National medical research center for Circulation Pathology named after. academician E.N. Meshalkin (Russia), Federal Center of Neurosurgery (Russia), International Tomography Center of the Siberian Department of the Russian Academy of Sciences: joint scientific research
  • Moscow Institute of Physics and Technology (Russia), Skolkovo Institute of Science and Technology (Russia), Peter the Great Saint Petersburg Polytechnic University (Russia): works within the consortium created for implementation of the Federal Target Program «Development of an industrial hydrofracking simulator»


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Schwaab M.., Biben Th., Santucci S., Gravouil A., Vanel L.
Interacting cracks obey a multiscale attractive to repulsive transition. Physical Review Letters 120(25): 255501 (2018).
Korobeynikov S.N.
Bases-free expressions for the families of objective strain tensors, their rates, and conjugate stress tensors. Acta Mechanica 229(1): 1061–1098 (2017).
Shelukhin V.V.
Thermodynamics of two-phase granular fluids. Journal of Non-Newtonian Fluid Mechanics 262 (2018).
Korobeynikov S.N., Alyokhin V.V., Babichev A.V.
Simulation of mechanical parameters of graphene using the DREIDING force field. Acta Mechanica 229(11): 1–36 (2018).
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