Mathematical modeling of co-current spontaneous imbibition in heterogeneous porous medium

2019 ◽  
Vol 76 ◽  
pp. 81-97 ◽  
Author(s):  
Tufan Ghosh ◽  
G.P. Raja Sekhar ◽  
Debasis Deb
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Spontaneous Imbibition ◽  
Heterogeneous Porous Medium

Mathematical Modeling of Chemotactic Bacterial Transport through a Two-Dimensional Heterogeneous Porous Medium

2006 ◽  
Vol 10 (1-2) ◽  
pp. 13-23 ◽  
Author(s):  
Mira Stone Olson ◽  
Roseanne M. Ford ◽  
James A. Smith ◽  
Erik J. Fernandez
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Bacterial Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

Spontaneous Displacement of Resident Fluid in Heterogeneous Porous Medium

2018 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Flow Behavior ◽  
Spontaneous Imbibition ◽  
Flow Properties ◽  
Heterogeneous Porous Medium ◽  
Lab On Chip ◽  
One Dimensional ◽  
Diffusive Dynamics ◽  
Fluid Properties ◽  
Homogeneous Porous Medium

Surface tension driven flow in which one fluid displaces another is of importance in microfluidic devices for diagnostics, lab on chip devices and flow in oil reservoirs. Spontaneous impregnation of a preferentially wetting phase displacing an existing non-wetting phase in a homogeneous porous medium is known to follow diffusive dynamics. However, in a heterogeneous porous medium the hydrodynamic interaction between the narrow and the wide pores significantly alters the impregnation behavior. Previous studies have shown that the imbibing fluid interface leads in the narrow pores contrary to the predictions from the diffusive dynamics of homogeneous porous medium. This is due to the higher suction pressure in the narrow pores which draw fluid from the wide pores. The effect of fluid properties and relative flow properties of the pores with respect to other pores on the non-wetting fluid displacement in the heterogeneous porous medium is still unknown. In the current work, we develop a quasi one-dimensional, lubrication approximation model, which predicts the spontaneous imbibition in a heterogeneous porous medium. We explore all the possible relative fluid properties and flow properties of the layers in the heterogeneous porous medium and show that our model is able to predict the flow behavior in all the cases. We also present the results of the spontaneous imbibition experiments, which agree with our model. The experiments show that the two phase interface progresses faster in the narrow pores as predicted by the one-dimensional model. The result is important for predicting and controlling the flow behavior in a heterogeneous porous medium.

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2007 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Linear Model ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Dimensional Parameter ◽  
Pressure Flow ◽  
Darcy Model ◽  
Linear Effects ◽  
Modified Reynolds Equation

The mathematical modeling of aerostatic porous bearings, represented by the Reynolds equation, depends on the assumptions for the flow in the porous medium. One proposes a modified Reynolds equation based on the quadratic Forchheimer assumption, which can be used for both linear and quadratic conditions. Numerical results are compared to those obtained with the linear Darcy model. It is shown that, the non-dimensional parameter Φ, related to non-linear effects, strongly affects the bearing dynamic characteristics, but for values of Φ > 10, the results tend to those obtained with the linear model.

scholarly journals Multidimensional computational models of gas combustion in heterogeneous porous medium

2021 ◽  
Vol 2099 (1) ◽  
pp. 012010
Author(s):  
Yu Laevsky ◽  
T Nosova
Keyword(s):  
Porous Medium ◽  
Parabolic Equations ◽  
Computational Models ◽  
Front Propagation ◽  
Original Model ◽  
Gas Mixture ◽  
Heterogeneous Porous Medium ◽  
Gas Combustion ◽  
Piecewise Constant ◽  
System Of Parabolic Equations

Abstract The processes of filtration gas combustion in heterogeneous porous medium is studying. The presence of two opposite modes of front propagation made it possible to stabilize the combustion front in a composite porous medium with piecewise constant porosity. A feature of this study is the presentation of the original model not in the traditional form of a system of parabolic equations, but in the form of integral conservation laws in terms of the temperature of the porous medium, the total gas enthalpy, and the mass of gas mixture, and the fluxes corresponding to these functions.

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