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.

Deep and Shallow Water Low-Speed Maneuvering Tests: Comparison Between Experimental and Simulation Results

2016 ◽  
Author(s):  
Felipe Ribolla Masetti ◽  
Pedro Cardozo de Mello ◽  
Guilherme F. Rosetti ◽  
Eduardo A. Tannuri
Keyword(s):  
Mathematical Model ◽  
Small Scale ◽  
Shallow Waters ◽  
Hydrodynamic Coefficients ◽  
Low Speed ◽  
Tunnel Model ◽  
Oceanographic Research ◽  
Simulation Results ◽  
The University ◽  
The Mathematical Model

This paper presents small-scale low-speed maneuvering tests with an oceanographic research vessel and the comparison with mathematical model using the real time maneuvering simulator developed by the University of São Paulo (USP). The tests are intended to verify the behavior of the vessel and the mathematical model under transient and low speed tests. The small-scale tests were conducted in deep and shallow waters, with a depth-draft ratio equal to 1.28, in order to verify the simulator ability to represent the vessel maneuverability on both depth conditions. The hydrodynamic coefficients used in the simulator model were obtained by CFD calculations and wind tunnel model tests carried out for this vessel. Standard turning circle and accelerating turn maneuvers were used to compare the experimental and numerical results. A fair agreement was achieved for shallow and deep water. Some differences were observed mainly in the initial phase of the accelerating turn test.

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.

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>

scholarly journals A Mathematical Model of Co-current Imbibition Phenomenon in Inclined Homogeneous Porous Medium

10.29007/jq63 ◽  
2018 ◽  
Author(s):  
Mahendra A. Patel ◽  
Narendrasinh Desai
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Numerical Solutions ◽  
Approximate Analytical Solution ◽  
Spontaneous Imbibition ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Homogeneous Porous Medium ◽  
The Mathematical Model ◽  
Wetting Fluid

Spontaneous imbibition is the process in which the wetting phase is drawn into a porous medium by means of capillary force. Cocurrent and countercurrent spontaneous imbibitions are defined as wetting and non-wetting fluid flow in identical, and opposite directions respectively. The mathematical model is developed for cocurrent imbibition phenomenon in the inclined oil formatted homogeneous porous medium. An approximate analytical solution of the governing equation is derived by homotopy analysis method. The graphical and numerical solutions are discussed.

scholarly journals Milk runs model with overtime: application to cluster supply chain

2015 ◽  
Vol 14 (4) ◽  
pp. 139-147
Author(s):  
Michał Tomczak ◽  
Robert Bucoń
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Outcome Analysis ◽  
Small Scale ◽  
Construction Sites ◽  
Construction Enterprises ◽  
Distribution Centre ◽  
The Mathematical Model ◽  
First Time ◽  
Organizational Principles

Paper identifies obstacles limiting functioning and development of small and medium construction enterprises. It also includes a description of cluster supply chain (CSC) idea as a suggested solution to some of the problems resulting from the small scale of company activities. One of more important issues of every distribution centre, i.e. portions of deliveries smaller than truck capacity for particular consumers, is also discussed. This problem was formulated for the first time in dairy industry, therefore, it was called milk runs. Moreover, the authors of this paper presented the outcome analysis of survey carried out among construction engineers and managers. This study aimed at determining organizational principles for logistic centre working with CSC framework. The mathematical model depicting milk runs deliveries with overtime consideration, done for many construction sites within a distribution centre is presented hereunder. This model may be potentially used to optimize distribution centres working within cluster supply chain framework.

Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium

2020 ◽  
pp. 4-23
Author(s):  
M.V. Alekseev ◽  
N.G. Sudobin ◽  
A.A. Kuleshov ◽  
E.B. Savenkov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Chemical Reactions ◽  
Three Dimensional ◽  
Element Model ◽  
Lumped Element ◽  
The Matrix ◽  
Thermochemical Processes ◽  
Lumped Element Model ◽  
The Mathematical Model

The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration

Influence of a Porous Insert on the Fluid Flow inside the Gasifier Shaft

2016 ◽  
Vol 685 ◽  
pp. 235-239 ◽  
Author(s):  
Pavel V. Openyshev ◽  
Mikhail A. Sheremet
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Fluid Flow ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Turbulent Model ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Porous Insert ◽  
The Mathematical Model

Turbulent fluid flow inside the vertical gasifier shaft having the porous insert has been numerically analyzed. The effect of the porous medium structure on the fluid flow has been studied. The mathematical model has been formulated in dimensional primitive variables using the realizable k-ε turbulent model. The distributions of velocity and skin friction coefficient inside the gasifier shaft have been obtained. The results clearly show an essential effect of the porous medium structure on turbulent fluid flow.

Filtration of anomalous thermoviscous liquid in layered non-uniform formation

2006 ◽  
Vol 4 ◽  
pp. 251-257
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Flow Rate ◽  
Pressure Difference ◽  
Viscosity Coefficient ◽  
Filtration Flow ◽  
Nonmonotonic Dependence ◽  
Flow Features ◽  
Numerical Research ◽  
The Mathematical Model

The mathematical model is developed and the numerical research of a filtration flow features of liquid with model nonmonotonic dependence of viscosity on temperature is conducted. Existence of the ”viscous barrier“ defining character of a filtration flow of anomalous thermoviscous liquid in the porous medium is established. Characteristic pictures of the steady distribution of viscosity and temperature in layered non-uniform formation are constructed. It is established that formation flow rate depends on a maximum of viscosity coefficient and pressure difference essentially.

Modeling and Simulation of Thermostatic Mixing Valve

2013 ◽  
Vol 365-366 ◽  
pp. 370-374
Author(s):  
Hai Chu Chen ◽  
Fang Yi Wu ◽  
Ping Zhang ◽  
Gen Liang Xiong ◽  
Yin Fa Zhu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Flow Field ◽  
Modeling And Simulation ◽  
Adaptive Controller ◽  
Theoretical Research ◽  
New Type ◽  
Fluent Software ◽  
Simulation Results ◽  
The Mathematical Model

It researched a new type of intelligent thermostatic mixing valve which could keep the temperature and flux of the valve outlet water constant through the adaptive controller. It firstly established the mathematical model about angle - flux and angle - temperature of the valve. And then it based on thekεturbulence model and applied Fluent software to numerical simulation of the valve about the flow field. Finally, it compared the simulation results with the calculated value. The results show that they are basically consistent, prove the correctness of the theoretical research, and can be used to improve designing of the thermostatic valve.

A Theoretical Study of the Phase Angle for the β Type Pulse-Steam Stirling Expander

2014 ◽  
Vol 597 ◽  
pp. 425-430
Author(s):  
Guang Jer Lai ◽  
C.K. Lin ◽  
Yoshiyuki Kobayashi ◽  
Masahiro Matsuo ◽  
Min Chie Chiu
Keyword(s):  
Mathematical Model ◽  
Output Power ◽  
Phase Angle ◽  
Small Scale ◽  
Steam Boiler ◽  
Isothermal Process ◽  
Characteristic Analysis ◽  
Flow Energy ◽  
Cogeneration System ◽  
The Mathematical Model

This paper introduces a small steam expander linked to a moderate/small industrial steam boiler to form a small scale cogeneration system for the purpose of energy conservation and carbon-emission reduction. Here, a traditional regulator will be replaced by the steam expander. In order to effectively extract the high pressure steam’s unused energy (flow energy) from the boiler, the steam will be induced into an expanding process. Here, a Pulse-Steam Stirling Expander (PSSE), which is different from a normal steam expander, is proposed in the study. In order to decrease the steam condensation and increase the overall output power, the PSSE expander adopts an isothermal process instead of the traditional isentropic process. The PSSE cycle, which is composed of an isothermal process and an isovolumetric process, is similar to the Stirling cycle. Therefore, considering the influence of the valve’s opening/closing within the PSSE cycle and adopting the Stirling engine’s Schmidt theory, the mathematical model of the PSSE cycle has been established. The characteristic analysis of the PSSE expander has been assessed based on the mathematical model. Moreover, a prototype of the PSSE expander has been constructed and tested. According to theoretical analysis and experimental data, the output power for the PSSE expander is closely related to the phase angle between the displacer and the piston. Consequently, the mathematical model of the PSSE expander proposed in this study can be applied to design the practical PSSE expander in industry.

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