Analysis of Linear Encroachment in Two-Immiscible Fluid Systems in a Porous Medium

1994 ◽  
Vol 116 (1) ◽  
pp. 135-139 ◽  
Author(s):  
Vijayaraghavan Srinivasan ◽  
Kambiz Vafai
Keyword(s):  
Porous Medium ◽  
Theoretical Study ◽  
Saturated Porous Medium ◽  
Immiscible Fluids ◽  
The Other ◽  
Immiscible Fluid ◽  
Fluid System ◽  
Inertia Effects ◽  
Fluid Systems ◽  
First Time

The flow of two immiscible fluids in a porous medium was analyzed accounting for boundary and inertia effects. This problem was first solved by Muskat using Darcy’s equation for fluid flow in a saturated porous medium. In the present analysis the boundary and inertia effects have been included to predict the movement of the interfacial front that is formed as one fluid displaces the other. In the present work a theoretical study that accounts for the boundary and inertia effects in predicting the movement of the interface for linear encroachment in two immiscible fluid system in a porous material is presented for the first time. The results of the present study when compared with the Muskat’s model show that consideration of the boundary and inertia effects becomes important for low values of mobility ratio (ε<1.0) and higher values of permeability (K>1.0 × 1.0−10 m2).

On the Linear Encroachment in Two-Immiscible Fluid Systems in a Porous Medium

2003 ◽  
Vol 125 (4) ◽  
pp. 738-739 ◽  
Author(s):  
Kambiz Vafai ◽  
Bader Alazmi
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Experimental Studies ◽  
Accurate Solution ◽  
Immiscible Fluid ◽  
Inertia Effects ◽  
General Behavior ◽  
Fluid Systems

A careful review to the previous study of Srinivasan and Vafai on the linear encroachment in two-immiscible fluid systems in a porous medium reveals some typos in their analytical solution. In the present study, an accurate analytical solution, which accounts for boundary and inertia effects, is obtained to predict the movement of the interfacial front and corrections to previous results are provided wherever necessary. Despite the similarity in the general behavior of the present accurate solution and the previous one, the existence of an accurate analytical solution is essential for future numerical and experimental studies.

scholarly journals Numerical calculation of unstable immiscible fluid displacement in a two-dimensional porous medium or Hele-Shaw cell

1985 ◽  
Vol 26 (4) ◽  
pp. 452-469 ◽  
Author(s):  
M. R. Davidson
Keyword(s):  
Porous Medium ◽  
Numerical Procedure ◽  
Immiscible Fluids ◽  
Boundary Integral ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Time Step ◽  
Fluid Displacement ◽  
Numerical Errors ◽  
Hele Shaw Cell

AbstractA numerical procedure for calculating the evolution of a periodic interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell is described. The motion of the interface is determined in a stepwise manner with its new velocity at exach time step being derived as a numerical solution of a boundary integral equation. Attention is focused on the case of unstable displacement charaterised physically by the “fingering” of the interface and computationally by the growth of numerical errors regardless of the numerical method employed. Here the growth of such error is reduced and the usable part of the calculation extended to finite amplitudes. Numerical results are compared with an exact “finger” solution and the calculated behaviour of an initial sinusoidal displacement, as a function of interfacial tension, initial amplitude and wavelength, is discussed.

Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space

1983 ◽  
Vol 105 (1) ◽  
pp. 124-129 ◽  
Author(s):  
A. Bejan ◽  
R. Anderson
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Open Space ◽  
Saturated Porous Medium ◽  
Temperature Fields ◽  
Interface Temperature ◽  
Fluid Systems ◽  
Two Fluid ◽  
Fluid Reservoir

This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK1/2) / (k′Ra1/4), where k, k′, RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.

Using Dissipative Particle Dynamics to Model Binary Immiscible Fluids

1997 ◽  
Vol 08 (04) ◽  
pp. 909-918 ◽  
Author(s):  
Keir E. Novik ◽  
Peter V. Coveney
Keyword(s):  
Phase Separation ◽  
Dissipative Particle Dynamics ◽  
Particle Dynamics ◽  
Immiscible Fluids ◽  
Promising Method ◽  
Domain Growth ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Fluid Systems

We investigate the domain growth and phase separation of two-dimensional binary immiscible fluid systems using dissipative particle dynamics. Our results are compared with similar simulations using other techniques, and we conclude that dissipative particle dynamics is a promising method for simulating these systems.

scholarly journals Two-phase MHD Flow through Porous Medium with Heat Transfer in a Horizontal Channel

2020 ◽  
pp. 79-90
Author(s):  
Devendra Kumar ◽  
B. Satyanarayana ◽  
Rajesh Kumar ◽  
Bholey Singh ◽  
R. K. Shrivastava
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Differential Equations ◽  
Velocity Profile ◽  
Parallel Plate ◽  
Immiscible Fluids ◽  
Immiscible Fluid ◽  
Flow Through ◽  
Plate Channel

The present study deals with two layered MHD immiscible fluid flow through porous medium in presence of heat transfer through parallel plate channel. The fluids are incompressible, and flow is fully developed. The fluids are of different viscosities and thermal conductivities so flowing without mixing each other. Two different phases are accounted for study and are electrically conducting. Temperature of the walls of parallel plate channel is constant. Rheological properties of the immiscible fluids are constant in nature. The flow is governed by coupled partial differential equations which are converted to ordinary differential equations and exact solutions are obtained. The velocity profile and temperature distribution are evaluated and solved numerically for different heights and viscosity ratios for the two immiscible fluids. The effect of magnetic field parameter M and porosity parameter K is discussed for velocity profile and temperature distribution. Combined effects of porous medium and magnetic fields are accelerating the flow which, can be helpful in draining oil from oil wells.

Analytical Approach on Nonlinear Vibration and Wave Response of Saturated Porous Media Subjected to Multiple Excitations

2009 ◽  
Author(s):  
Liming Dai ◽  
Guoqing Wang
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Approach ◽  
Wave Motion ◽  
Numerical Approach ◽  
Immiscible Fluids ◽  
The Other ◽  
Energy Sources ◽  
Saturated Porous Media ◽  
System Parameters

This research investigates the wave motions of a porous medium saturated by multiple immiscible fluids in porous media subjected to multiple external excitations, via an analytical and numerical approach. The findings of this research contribute to the comprehension of fluids and solid interactions in porous media excited by multiple energy sources. With the approach developed, the vibrations of any desired point and wave motion at desired domain can be quantitatively determined in terms of amplitude and frequency of the vibrating points and therefore the wave propagation in the domain. The relationships among the relative displacements, porosity of the porous medium, saturations of the fluids and the other system parameters are also studied quantitatively.

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