# Valeri MourzenkoFrench National Centre for Scientific Research | CNRS · Institut Pprime

Valeri Mourzenko

PhD

## About

91

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## Publications

Publications (91)

Reliable predictions from numerical simulations in fire safety applications require knowledge of the combustible materials’ properties in their initial and thermally degraded states. The thermal conductivity of the sheath material of electrical cables, present in massive amounts in industrial plants, is addressed here. An evolutive conceptual model...

The homogenization approach to wave propagation through saturated porous media is extended in order to include the compressibility of the interstitial fluid and the existence of several connected pore components which may or not percolate. The necessary theoretical developments are summarized and the Christoffel equation whose solutions provide the...

Sensitivity to the boundary conditions (BC’s) when determining macroscopic transport coefficients by numerical upscaling in finite domains is a well known methodological issue, explored here with the purpose of: quantifying the influence of the BC’s in relation with the parameters of the system (porosity, characteristic length scale, conductivity c...

The increasing access to 3d digital images of porous media provides an ideal avenue for the determination of their transport properties, by solving the governing equations in their actual microscale geometry and evaluating the tensor coefficient that relates the mean flux and driving gradient. However, the first and puzzling question along the way...

The effective flow and conduction properties of fractures with Gaussian spatial correlations are investigated by solving the microscale governing equations in three-dimensional samples, along the lines initiated by Mourzenko et al. (J Phys II(5):465–482, 1995), Volik et al. (Trasnp Porous Media 27:305–325, 1997) but in greater details, over a wider...

Thermal convection is numerically computed in three-dimensional (3D) fluid saturated isotropically fractured porous media. Fractures are randomly inserted as two-dimensional (2D) convex polygons. Flow is governed by Darcy's 2D and 3D laws in the fractures and in the porous medium, respectively; exchanges take place between these two structures. Res...

The percolation threshold of fracture networks is investigated by extensive direct numerical simulations. The fractures are randomly located and oriented in three-dimensional space. A very wide range of regular, irregular, and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes a...

A three-dimensional numerical tool for the microscale simulation of smoldering in fixed beds of solid fuels is presented. The description is based on the local equations and accounts the local couplings of the transport and reaction mechanisms. The chemical model includes devolatilization and cracking of the kerogen, calcination of the carbonates c...

The mechanical and transport properties of a Bentheim sandstone are studied both experimentally and numerically. Three classical classes of loads are applied to a sample whose permeability is measured. The elasticity and the Stokes equations are discretized on unstructured tetrahedral meshes which precisely follow the deformations of the sample. Nu...

Barometric pumping plays a crucial role in the release of trace gases from fractured porous media to the atmosphere and it requires a rigorous and complete modeling in order to go beyond the approximate schemes available in the literature. Therefore, a coupled set of convection and convection-diffusion equations for a slightly compressible fluid in...

The geometrical properties of the matrix blocks formed by a random fracture network are investigated
numerically, for a wide range of fracture shapes and for fracture densities ranging from the dilute limit to well
above the threshold where the material is entirely partitioned into finite blocks. The main block characteristics are
the density and v...

The intersection between a network of polygonal fractures and a cubic cavity is numerically studied. Several probabilities are defined and particular attention is paid to the probabilities of intersection or not of the percolating cluster with the cavity; they depend on the size of the domain, on the fracture density, and on the relative size of th...

Geophysical Research Abstracts Vol. 15, EGU2013-2543, 2013 Natural fracture fields are almost necessarily heterogeneous with a fracture density varying with space. Two classes of variations are quite frequent. In the first one, the fracture density is decreasing from a given surface; the fracture density is usually (but not always see [1]) an expon...

A single fracture can be represented as a void space between two rough surfaces which touch one another. Transmissivity and conductivity can be determined numerically by solving the Stokes and the Laplace equations between these two rough surfaces. These problems were first solved and published by the same authors between 1995 and 2001 (see the cor...

Field observations from several outcrops in the Eastern High Atlas Mountains, near Amellago (Morocco), are used to determine fracture-network model parameters, such as the aspect ratio of the fractures represented as rectangles whose longer side is horizontal, the volumetric area of fracture surfaces, the fracture mean size and the fracture density...

This book aims to estimate the macroscopic properties of fractures, fracture networks and fractured porous media from easily measurable quantities. Attention is focused on geological media where rocks are necessarily fractured at various scales by the slow but constant motion of continental masses. This book is situated between three disciplines. F...

Generally, the excavation process of a gallery generates fractures in its immediate vicinity. The corresponding zone which is called the excavated damaged zone (EDZ), has a larger permeability than the intact surrounding medium. Therefore, some of its properties are of crucial importance for applications such as the storage of nuclear wastes. Field...

Reactive flow through geological formations occurs in many situations due to human intervention or during natural processes. For instance, chemical dissolution and precipitation play a major role in diagenesis or in the formation of karsts. The quantitative description of the injection of a reacting fluid from a well into a fractured porous medium...

The main purpose of this review paper is to summarize some recent studies of fracture networks. Progress has been made possible thanks to a very versatile numerical technique based on a three-dimensional discrete description of the fracture networks. Any network geometry, any boundary condition, and any distribution of the fractures can be addresse...

Reactive flow through geological formations occurs in many situations due to human intervention or during natural processes. For instance, chemical dissolution and precipitation play a major role in diagenesis or in the formation of karsts. The quantitative description of the injection of a reacting fluid from a well into a fractured porous medium...

The asymptotic behaviors of the permeability of isotropic fracture networks at small and large densities are characterized, and a general heuristic formula is obtained which complies with the limiting behaviors and accurately predicts the permeability of these networks over the whole density range. Theses developments are based on extensive numeric...

A general three-dimensional numerical model for single phase, slightly compressible flow through fractured porous media is described. It is based on a discrete fracture representation. Three sets of applications are presented. In the first one, pressure drawdown well tests in closed oil reservoirs are simulated for complex model situations where th...

Since only intersections with lines or planes are usually available to quantify the properties of real fracture networks, a stereological analysis of these intersections is a crucial issue. This article-the second of a series-is devoted to the derivation of the direct relations between the properties and the observable quantities. First, this deriv...

This paper deals with the reconstruction of a fracture network observed in an underground gallery of a tunnel buried in clay stones in Switzerland, below Mont Terri. The trace maps of the Gallery 04 and of the EZ-G niche of this site have first been digitized and used in various ways to characterize the data. The traces have been divided into two g...

Glossary
Definition of the Subject
Introduction
Fracture Networks
Percolation of Fracture Networks
Determination of the Dimensionless Density from Experimental Data
Role of the Dimensionless Density in Other Geometrical Properties and Permeability
Future Directions
Bibliography

The quantitative description of the injection of a reacting fluid from a well into a fractured porous medium is a subject of high interest for CO2 sequestration. Ideally, one wishes to analyze the damages caused by the fluid to the well itself and to its immediate surroundings. In order to attain this goal, one has to solve a coupled system of equa...

Description of the material
Ground oil shale semicoke was prepared in a laboratory retorting furnace under inert atmosphere. A laboratory combustion cell was then used to operate the combustion of the semicoke added with more or less sand and/or carbonates. This enabled to vary independently the amount of CaCO3 and the amount of fixed carbon in the...

A Bentheim sandstone sample is analyzed, based on two CT-scan images of a 27 mm3 block containing 5003 or 10003 voxels of size 6μm or 3 μm, respectively. In a first step, the properties of the real material have been investigated in details. Geometric parameters such as the porosity e, the volumetric surface area S and the statistical properties of...

This contribution surveys the methods used in order to determine the acoustic properties of porous
media which may be either dry or saturated with one or two compressible fluids. Generally speaking,
the effective acoustic properties are determined by an homogeneization technique which derives the
macroscopic behaviour from the solution of local equ...

Conductive/radiative heat transfer in porous media is addressed by direct numerical simulations on the microscale. The objective is to quantify the relative importance of the radiative contribution in reactive flow (fixed bed solid fuel combustion), and to model it in a form suitable for a macroscopic description.

Combustion in porous media is addressed by means of direct, detailed numerical simulations on the microscale. More specifically, fixed bed combustion of solid particles is considered, with application to the burning of oil shales. The transport processes (convection, diffusion, conduction) and the chemical reactions are explicitely described on the...

Three dimensional samples of three different foams are obtained by microtomography. The macroscopic conductivity and permeability of these foams are calculated by three different numerical techniques based on either a finite volume discretization or Lattice Boltzmann algorithm. Permeability is also measured and an excellent agreement is obtained be...

Objective: Metallic foams single phase transport properties, such as permeability or thermal conductivity, are usually determined experimentally, whereas numerical approaches have been recently developed. They focus on the resolution of local partial differential equations on the pore scale, which requires the foam structure determination at this l...

Spiky particles are constructed by superposing spheres and oblate ellipsoids. The resulting star particles (but nonconvex) are randomly packed by a sequential algorithm. The geometry, the conductivity, and the permeability of the resulting packings are systematically studied. Overall correlations are proposed to approximate these properties when th...

A 3d microscale numerical tool for the simulation of smoldering in fixed beds of solid fuels is presented. The description is based on the local equations and fully preserves the coupling of the transport and reaction mechanisms. A set of simulations demonstrates the ability of the model to handle a variety of situations, with non trivial chemical...

Among hydrogeological processes, free convection in faults has been cited as a possible cause of gold mineralization along major fault zones. Here, we investigate the effects of free convection to determine whether it can cause giant orogenic gold deposits and their regular spatial distribution along major fault ⁄ shear zones. The approach comprise...

Networks composed by heterogeneous fractures whose local permeability is a binary correlated random field are generated. The percolation and permeability properties of a single heterogeneous fracture are strongly influenced by finite size effects when the correlation length is of the order of the fracture size. For fracture networks, a mean-field a...

Our objective is to determine the macroscopic acoustical properties of porous media (either dry or saturated by an interstitial fluid) and to relate them to the mechanical and hydromechanical characteristics of the medium and its components. Wave propagation in a dry elastic material is governed by the elastodynamic equation. For a dry medium, the...

This paper summarizes several systematic studies of fracture networks when the fractures have either a size
distribution, or anisotropic orientations, or non uniform properties or spatial distribution. The numerical approach is based on a 3d discrete description of the fracture network. Any network geometry and any distribution of the fracture prop...

Smoldering in porous media is a very complex situation that happens in situations where a reactive part of the porous material is oxidized using heat content without flaming. A three-dimensional numerical tool for the simulation of smoldering in fixed beds of solid fuels is presented in this paper. The description is based on the microscale equatio...

The homogenization procedure is applied to the problem of wave propagation in the biphasic mode in porous media saturated with a Newtonian fluid. The local problems corresponding to the solid and fluid phases have been solved separately for complex three-dimensional media. The effective rigidity tensor, some effective coefficients, the dynamic perm...

Loose packings of spheres with bidisperse or log-normal distributions are generated by random sequential deposition. Porosity, conductivity, and permeability are determined. The porosities correspond to loose packings, but they follow the usual trends for bidisperse packings. The conductivity and permeability follow power laws as functions of the p...

Our major purpose is to obtain precise numerical simulations on dispersion and reaction in these media in order to analyze the short time and long time behaviours of solute, and to compare the results with the predictions of various theories. Three major steps are needed for the numerical solutions. First, an unstructured tetrahedral mesh of the fr...

The permeability of geological formations which contain fractures with a power-law size distribution is addressed numerically by solving the coupled Darcy equations in the fractures and in the surrounding porous medium. Two reduced parameters are introduced which allow for a unified description over a very wide range of the fracture characteristics...

A numerical model is presented which describes the evolution of a system containing a large number of deformable spherical grains based on Newton's second law. Starting from an initial state with fixed positions, velocities and grain characteristics, the system evolution is simulated by successive steps. The acceleration of each grain results from...

Les propriétés acoustiques de milieux poreux sont étudiées dans le cadre général de la théorie de l'homogénéisation, en supposant que l'échelle caractéristique des pores est petite devant la longueur d'onde, en appliquant les développements successifs du formalisme de Botin et Auriault (1993). Pour les milieux secs, on détermine la célérité d'une o...

There are two basic problems to be addressed. The first one is to solve precisely the partial differential equations which govern the phenomena which occur in these media and which are of interest in a large number of applications. The second one is to define a methodology in order to be able to estimate the macroscopic properties of real media by...

A three-dimensional numerical tool for the simulation of smoldering in fixed beds of solid fuels is presented in this paper. The description is based on the microscale equations, in a detailed discretized image of the porous medium. Simplifying assumptions are used, but the local coupling of the transport and reaction mechanisms is fully preserved....

This paper presents a numerical model and a set of results on the deformation of fractured porous media, on their effective mechanical moduli, and on the influence of the deformation on the flow properties. The model is three-dimensional, incorporates randomly located discrete fractures, and accounts for their non linear rheology.

This paper examines the various regimes that may prevail in a smouldering process in a combustible
porous medium, and their consequences from a physical point of view and for the formulation of
a macroscopic description. A set of governing parameters are first identified, by use of a dimensional
analysis. Then, their influence is illustrated by dir...

A three-dimensional, microscale numerical model for the simulation of smouldering in fixed beds of
solid fuels is presented. It solves the local governing equations, and therefore explicitly accounts for
the coupling of the transport and reaction mechanisms on the microscopic scale. This article describes
the conceptual and numerical apparatus and...

The influence of various parameters such as the domain size, the exponent of the power law, the smallest radius, and the fracture shape on the percolation threshold of fracture networks has been numerically studied. For large domains, the adequate percolation parameter is the dimensionless fracture density normalized by the product of the third mom...

The percolation and permeability of fracture networks is investigated numerically by using a three dimensional model of plane
polygons randomly located and oriented in space with sizes following a power law distribution. The influence of the range
and exponent of the size distribution, of the fracture shapes and of the exponent of the individual fr...

Fractures and fracture networks determine the permeability of many
natural rocks, and their behavior has generated interest in various
fields [Sahimi, 1995; Adler and Thovert, 1999; Berkowitz, 2002]. This
interest has simultaneously a fundamental and an applied character,
since many applications are crucial for industries such as petroleum and
wast...

Fracture network permeability is investigated numerically by using a three-dimensional model of plane polygons uniformly distributed in space with sizes following a power-law distribution. Each network is triangulated via an advancing front technique, and the flow equations are solved in order to obtain detailed pressure and velocity fields. The ma...

In most geological instances, 2-D or 3-D fracture distributions are not available from field data. We show here that when data relative to fractures are collected along a line such as a road or a well, estimations can be given to the major geometrical properties of the corresponding fracture networks, such as the volumetric density of fractures, th...

Two-phase flow in fractured porous media is investigated by means of a direct and complete numerical solution of the generalized Darcy equations in a three-dimensional discrete fracture description. The numerical model applies to arbitrary fracture network geometry, and to arbitrary distributions of permeabilities in the porous matrix and in the fr...

Flow in fractured porous media was first investigated by Barenblatt and Zheltov [1960] and Barenblatt et al. [1960] by means of the double-porosity model. A direct, exact, and complete numerical solution of the flow in such media is given in this paper for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. T...

[1] A general three-dimensional numerical model for single-phase, slightly compressible flow through fractured porous media is introduced. It is based on a discrete fracture representation. Applications to the simulation of pressure drawdown well tests are presented, for complex situations where the well intercepts a random fracture network with va...

A numerical study of three-dimensional solute transportat fracture intersections by using a particle tracking technique is presented.Two models of orthogonal fracture intersection are considered, namely, twoparallel-walled channels and two rough-walled Gaussian fractures. The fluidvelocity is calculated by solving the three-dimensional Stokes equat...

The permeability of self-affine fractures with various roughness exponents H is investigated by direct three-dimensional numerical simulations. A scaling behavior with an exponent H is exhibited in the self-affine scale range. Permeability can be related to the fractional open area and to the percolation probability by simple models.

Flow in fractured porous media is investigated by a direct, exact and complete numerical solution of the flow equations for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. For single phase flow, the macroscopic permeability of the network has been systematically computed; the main parameters are the fract...

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field.
The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation
threshold for the three-dimensional media is a decreasing function of the variance and correla...

Flow in fractured porous media was first investigated by Barenblatt and Zheltov (1960) and Barenblatt et al. (1960) by means of the double porosity model. A direct and complete solution of the flow in such media is given in this paper. Some preliminary results are presented and discussed; they show the importance of the percolation threshold of the...

The percolation and conductivity of self-affine fractures are investigated over the whole range of their mean aperture and roughness exponent H, by direct three-dimensional numerical simulations. A scaling behavior is exhibited for the conductivity of tight fractures in the self-affine scale range, with exponent H. All the data can be summarized by...

We consider a model of patterning of one-dimensional foam–bubble chain confined in a bamboolike capillary. The discrete model of such a foam describes a distribution of foam films—lamellae that, like “bridges,” span a capillary. This model is a kind of Ulam map, which admits many metastable distributions of lamellae in a bamboolike capillary as gov...

One of the simplest aspects of coupling between mechanics and hydromechanics of fractures is addressed by the numerical resolution of the mechanical and hydrodynamic equations in three dimensions at the local level. A mean field approximation is derived that may include nonlinear effects because of the variations of the contact surface. Three types...