Mathematical model and numerical algorithm for studying suspension filtration in a porous medium considering the processes of colmatation and suffusion

2018 ◽

Vol 769 ◽

pp. 329-335

Author(s):

Andrey Petrov ◽

Leonid A. Igumnov

Keyword(s):

Mathematical Model ◽

Porous Medium ◽

Boundary Element Method ◽

Boundary Element ◽

Three Dimensional ◽

Element Solution ◽

Harmonic Force ◽

Porosity And Permeability ◽

Beam Thickness ◽

Element Method

The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.

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Numerical Simulation of a New Porous Medium Burner with Two Sections and Double Decks

Processes ◽

10.3390/pr6100185 ◽

2018 ◽

Vol 6 (10) ◽

pp. 185 ◽

Cited By ~ 2

Author(s):

Zhenzhen Jia ◽

Qing Ye ◽

Haizhen Wang ◽

He Li ◽

Shiliang Shi

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Porous Medium ◽

Industrial Development ◽

High Efficiency ◽

Methane Combustion ◽

Combustion Mechanism ◽

Gas Mixture ◽

Temperature And Pressure ◽

Save Energy

Porous medium burners are characterized by high efficiency and good stability. In this study, a new burner was proposed based on the combustion mechanism of the methane-air mixture in the porous medium and the preheating effect. The new burner is a two-section and double-deck porous medium with gas inlets at both ends. A mathematical model for the gas mixture combustion in the porous medium was established. The combustion performance of the burner was simulated under different equivalence ratios and inlet velocities of premixed gas. The methane combustion degree, as well as the temperature and pressure distribution, was estimated. In addition, the concentrations of emissions of NOx for different equivalence ratios were investigated. The results show that the new burner can not only realize sufficient combustion but also save energy. Furthermore, the emission concentration of NOx is very low. This study provides new insights into the industrial development and application of porous medium combustion devices.

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Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Symmetry ◽

10.3390/sym12050696 ◽

2020 ◽

Vol 12 (5) ◽

pp. 696

Author(s):

Bekzodjon Fayziev ◽

Gafurjan Ibragimov ◽

Bakhtiyor Khuzhayorov ◽

Idham Arif Alias

Keyword(s):

Porous Medium ◽

Porous Media ◽

Chemical Engineering ◽

Numerical Study ◽

Kinetic Equations ◽

Sufficient Conditions ◽

Computational Mathematics ◽

Deposition Kinetics ◽

Dynamic Factors ◽

Suspension Filtration

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

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The effect of hydrodynamic dispersion on reactive flows in porous media

European Journal of Applied Mathematics ◽

10.1017/s0956792501004600 ◽

2001 ◽

Vol 12 (5) ◽

pp. 557-569 ◽

Cited By ~ 6

Author(s):

J. CHADAM ◽

P. ORTOLEVA ◽

Y. QIN ◽

R. STAMICAR

Keyword(s):

Mathematical Model ◽

Porous Medium ◽

Critical Value ◽

Reactive Flow ◽

Hydrodynamic Dispersion ◽

Reaction Interface ◽

Shape Stability ◽

Linearized Problem ◽

New Feature ◽

Moving Free Boundary

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

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