Modeling of magmatic channel formation in thin lithosphere areas

2020 ◽  
Author(s):  
Yuri Perepechko ◽  
Konstantin Sorokin ◽  
Georgiy Vasilyev
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Saturated Porous Medium ◽  
High Stress ◽  
Marked Change ◽  
Porous Matrix ◽  
Small Scale ◽  
Magma Intrusion ◽  
Magma Flow

<p>The aim of the research is to construct a mathematical model of the formation of a fracture system in magma intrusion in the permeable zones of the lithosphere and on this basis to study the formation of magmatic channels in the lithosphere and crust. The lithosphere substrate is modeled by a saturated porous medium in which the processes of small-scale destruction in the mantle magma intrusion lead to the formation of faults and, consequently, to a magmatic channel. Destruction and occurrence of micro-fracture fields can be associated with both magma flow and external seismic effect leading to the rock breaking. The process of small-scale destruction is described within the framework of the dynamics of the elastoplastic fracture-porous medium and causes variations in the rheological properties of the lithosphere substrate. A feature of this process is the destruction substrate in the compression zone represented by a narrow area with a sharply changing concentration of micro-fractures. The micro-fracture accumulation provides the conversion of the broken area into a macro-fissure. The elastoplastic porous matrix in the destruction zone contains both broken and intact substrate, the relative content of which is determined by relaxation of deformations, the speed of which depends on stress and yield stress point according to the power law. The obtained mathematical model provides investigation of currents in fractured-porous media and their effect on the small-scale destruction. Based on the TVD-Runge Kutta method numerical simulation of the compressible fluid infiltration into the fracture-porous permeable channel has shown that stresses in the compression domain can reach stress limits of breaking and result in fracture formation. Change in relaxation time does not result in a marked change in stress fields. The concentration of maximum stresses is observed in the channel center leading to an increase in its fracture porosity. The computational results show the appearance of high stress values in the compression domain in the process of a liquid phase injection, for instance, magma, into a low-permeable fracture-porous layer. The introduction of the destruction criterion will help to associate the occurrence of such regions to the local breaking of the porous matrix. Thus, the proposed micro-fracture generation mechanism can be used to describe the formation of fracture or channels in micro-fracture porous media. Work is done on state assignment of IGM SB RAS with partial support from the Russian Foundation for Basic Research, grants No. 16-29-15131, 19-05-00788.</p>

Linear Stability Analysis of Bioconvection in Porous Media: The Effect of Fouling

2003 ◽  
Author(s):  
A. V. Kuznetsov ◽  
A. A. Avramenko
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Stability Analysis ◽  
Saturated Porous Medium ◽  
Porous Matrix ◽  
Critical Porosity ◽  
Gyrotactic Microorganisms ◽  
Porosity And Permeability ◽  
Fluid Saturated Porous Medium ◽  
The Stability

In this paper, the effect of fouling on the stability of a uniform suspension of gyrotactic motile microorganisms in a fluid saturated porous medium is investigated. Fouling may occur because of the deposition of microorganisms on a porous matrix. This deposition decreases porosity and permeability of the porous medium. Stability analysis carried out in this paper reveals that there is a critical porosity of the porous medium. If the porous medium utilized for this process has a smaller porosity than critical, the uniform suspension of gyrotactic microorganisms is stable and bioconvection does not develop. If the porous medium has lager porosity than critical, the uniform suspension is unstable and bioconvection develops.

Forced Convection in a Channel Filled With Porous Medium, Including the Effects of Flow Inertia, Variable Porosity, and Brinkman Friction

1987 ◽  
Vol 109 (4) ◽  
pp. 880-888 ◽  
Author(s):  
D. Poulikakos ◽  
K. Renken
Keyword(s):  
Porous Medium ◽  
Forced Convection ◽  
Flow Model ◽  
Saturated Porous Medium ◽  
Porous Matrix ◽  
Parallel Plates ◽  
Entry Length ◽  
Variable Porosity ◽  
Flow Inertia ◽  
Temperature And Flow Fields

This paper presents a series of numerical simulations which aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium. In modeling the flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Two channel configurations are investigated: parallel plates and circular pipe. In both cases, the channel wall is maintained at constant temperature. It is found that the general flow model predicts an overall enhancement in heat transfer between the fluid/porous matrix composite and the walls, compared to the predictions of the widely used Darcy flow model. This enhancement is reflected in the increase of the value of the Nusselt number. Important results documenting the dependence of the temperature and flow fields in the channel as well as the dependence of the thermal entry length on the problem parameters are also reported in the course of the study.

Stability of Bioconvection in Suspensions of Gyrotactic Microorganisms in Porous Media

2002 ◽  
Author(s):  
A. V. Kuznetsov ◽  
A. A. Avramenko
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Saturated Porous Medium ◽  
Critical Value ◽  
Numerical Results ◽  
Velocity Fluctuations ◽  
Gyrotactic Microorganisms ◽  
Upward Direction ◽  
Upward Velocity ◽  
Fluid Saturated Porous Medium

In this paper, a model of bioconvection in a suspension of gyrotactic motile microorganisms in a fluid saturated porous medium is suggested. The microorganisms considered in this paper are heavier than water and gyrotactic behavior results in their swimming towards the regions of most rapid downflow. Because of that, the regions of downflow become denser than the regions of upflow. Buoyancy increases the upward velocity in the regions of upflow and downward velocity in the regions of downflow, thus enhancing the velocity fluctuations. The experiments performed by Kessler (1986) and the numerical results of Kuznetsov and Jiang (2001) indicate that if the permeability of porous medium is sufficiently small it will prevent the development of convection instability. However, for practical purposes, in order to maximize the flux of the cells in the upward direction it is desirable to have the permeability of the porous medium as high as possible. The aim of this paper is to investigate the value of critical permeability. If permeability is smaller than this critical value bioconvection does not occur and microorganisms simply swim in the upward direction.

scholarly journals Transient Fluid Motions in Saturated Porous Media

1957 ◽  
Vol 10 (1) ◽  
pp. 43 ◽  
Author(s):  
JR Philip
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Heat Conduction ◽  
Exact Solutions ◽  
Kinematic Viscosity ◽  
Saturated Porous Medium ◽  
Steady Motion ◽  
Potential Gradient ◽  
Saturated Porous Media ◽  
Approximate Analysis

The transition from rest to steady motion on the sudden application of a potential gradient to the fluid contained in a saturated porous medium is investigated. An approximate analysis gives the result that the time of the effective establishment of the steady motion is proportional to the permeability and inversely proportional to the kinematic viscosity. Two exact solutions (one of them new) for simple cases suggest that the approximate analysis is remarkably accurate. An analogy between this problem and one in heat conduction makes the relevant results in that field immediately applicable here.

scholarly journals Kinetics of filtration consolidation of water-saturated clay soils

2020 ◽  
pp. 86-95 ◽  
Author(s):  
O. V. Ageikina ◽  
V. V. Vorontsov ◽  
R. R. Sufyanov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Experimental Studies ◽  
Saturated Soils ◽  
Consolidation Process ◽  
Filtration Consolidation ◽  
Wide Range ◽  
Water Saturated ◽  
The Mathematical Model

The relevance of the research processes filtration consolidation due to the place of water-saturated soils in various design solutions related to the exploration, production and transportation of hydrocarbons. It should be noted that the diversity of soils led to the emergence of a wide range of mathematical models, obtained on the basis of generalization of experimental data and various assumptions to simplify engineering calculations. The article presents the results of theoretical and experimental studies of the mathematical model of the consolidation process of a water-saturated porous medium. This model is based on simplifying assumptions that are different from those adopted in well-known solutions. A fundamental approach to the formation of the model was developed on the basis of the kinetic representations of chemical reactions used in solving the environmental problems of epoxidation reactions of olefins. We determined the parameters of the mathematical model of the consolidation process of the saturated porous medium of clayey soil and confirmed its adequacy by the research results. In addition, we established the parameters of the field of non-equilibrium filtration, reducing the nonexistent ability of water-saturated soils.

Non-Darcy Mixed Convection With Thermal Dispersion in a Saturated Porous Medium

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
V. V. Sobha ◽  
R. Y. Vasudeva ◽  
K. Ramakrishna ◽  
K. Hema Latha
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Vertical Plate ◽  
Saturated Porous Medium ◽  
Thermal Dispersion ◽  
Convection In Porous Media ◽  
Infinite Vertical Plate

Thermal dispersion due to local flows is significant in heat transfer with forced convection in porous media. The effects of parametrized melting (M), thermal dispersion (D), inertia (F), and mixed convection (Ra/Pe) on the velocity distribution, temperature, and Nusselt number on non-Darcy, mixed convective heat transfer from an infinite vertical plate embedded in a saturated porous medium are examined. It is observed that the Nusselt number decreases with increase in melting parameter and increases with increase in thermal dispersion.

Features of wave propagation in the sand of different saturation

2011 ◽  
Vol 8 (1) ◽  
pp. 25-38
Author(s):  
A.T. Akhmetov ◽  
S.V. Lukin ◽  
D.M. Balapanov ◽  
S.F. Urmancheev ◽  
N.M. Gumerov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Water Saturation ◽  
Weak Shock ◽  
Capillary Forces ◽  
Theoretical Studies ◽  
Longitudinal Waves ◽  
Experimental And Theoretical Studies

There are the results of experimental and theoretical studies on the propagation of weak shock waves in the wet sand at different water saturation. There are mathematical model and numerical analysis of propagation of pressure pulses in porous media, taking into account capillary forces. Non-monotonic dependence of the amplitude of the wave resulting in a wet porous medium vs. the degree of water saturation is installed. The evolution of the fast, slow and filtration waves depends on the saturation of the system with water is analyzed. The influence of capillary forces on the propagation of longitudinal waves is evaluated.

Natural Convection Experiments in a Stratified Liquid-Saturated Porous Medium

1986 ◽  
Vol 108 (3) ◽  
pp. 660-666 ◽  
Author(s):  
D. C. Reda
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
High Permeability ◽  
Transfer Rates ◽  
Variable Porosity ◽  
Radial Extent

Natural convection heat transfer from a constant-flux cylinder, immersed vertically through a stratified (two-layer) liquid-saturated porous medium, was investigated experimentally. Measured radial temperature profiles and heat transfer rates agreed well with numerical predictions based on the work of Hickox and Gartling. The 1:6 permeability-ratio interface existing between the two layers was found to effectively trap buoyancy-driven fluid motion within the high-permeability region, beneath the interface. Within this high-permeability region, Nusselt number versus Rayleigh number data were found to correlate with previously measured results, obtained for the same basic geometry, but with a fully permeable upper-surface hydrodynamic boundary condition. In both cases, the vertical and radial extent of the region under study were large compared to the radius of the heat source. Combined results indicate that, for a given Rayleigh number in the Darcy-flow regime, heat transfer rates from cylinders immersed vertically in uniform liquid-saturated porous media of large vertical and radial extent potentially approach limiting values. Variable-porosity effects which occur in unconsolidated porous media adjacent to solid boundaries were investigated numerically for cases where the particle-to-heater diameter ratio was small (≈ 10−2). Results showed variable-porosity effects to have a negligible influence on the thermal field adjacent to such boundaries under conditions of Darcy flow.

scholarly journals Oscillatory motion of an electrically conducting viscoelastic fluid over a stretching sheet in a saturated porous medium with suction/blowing

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
K. Rajagopal ◽  
P. H. Veena ◽  
V. K. Pravin
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Porous Media ◽  
Skin Friction ◽  
Viscoelastic Fluid ◽  
Stretching Sheet ◽  
Saturated Porous Medium ◽  
Oscillatory Motion ◽  
Power Series Method ◽  
Viscoelastic Parameter

The effect of an oscillatory motion of a viscoelastic fluid over an infinite stretching sheet through porous media in the presence of magnetic field with applied suction has been studied. The surface absorbs the fluid in a porous medium in the presence of magnetic field and the velocity oscillates depending on the stretching rate(b). Analytical expressions for the velocity and the coefficient of skin friction have been studied, first by the perturbation method and then by power series method. The effect of viscoelastic parameterk1, porous parameterk2, magnetic parameter Mn, and the vertical distancexin the presence of suction/blowing on the velocity and the flow characteristics are discussed. The velocity of the viscoelastic fluid is found to decrease in the presence of magnetic field and porous media, as compared to the study of viscous fluid. It is also found that the effect of unsteadiness in the wall velocity and skin friction are found to be appreciable in the presence of suction/blowing parameter.

scholarly journals The mathematical model of gas flowing in porous medium based on the homogenization method

2021 ◽  
Vol 252 ◽  
pp. 02046
Author(s):  
Wei Xiong
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Flow Field ◽  
Homogenization Method ◽  
Darcy Law ◽  
Small Scale ◽  
Matrix System ◽  
Fluid Equation ◽  
Coal Matrix ◽  
The Mathematical Model

Considered the characteristics of porous medium in the coal seam and goaf, in order to reflect the accurately influence of various porous media against the gas flow, the mathematical model of discrete multi-scale network and macroscopic flow, CFCM (Coal-Fracture-Cavity-Model), was presented. The porous medium is classified into coal matrix, fracture and hole systems based on the size, and the coal matrix system includes micro fractures and micro-porous. The coal matrix system and fracture system can be regarded as diffusion and percolation areas; hole system can be regarded as a free-flowing area. The computation model of flow field in micro-scale, small-scale and large-scale are obtained according the Fick’s diffusion law, Darcy’s permeability law and Forchheimer generalized Darcy law respectively, the homogenization method is used to analyse the mathematical model by scale upgrading and the equivalent Darcy’s fluid equation of porous medium is got to describe the characteristics of the medium in the flow field accurately. An example calculated shows that the coal matrix and fracture systems are the most influential factors of the flow field in goaf and the two systems above would prevent the diffusion of airflow. The study validates the correctness of the classification method and the model of flow equation.

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