Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

Stochastic homogenization and macroscopic modelling of composites and flow through porous media

2002 ◽  
pp. 337-378 ◽  
Author(s):  
Jozef Telega ◽  
Wlodzimierz Bielski
Keyword(s):  
Porous Medium ◽  
Random Distribution ◽  
Flow Through Porous Media ◽  
Macroscopic Models ◽  
Linear Elastic ◽  
Multi Scale ◽  
Convergence Method ◽  
Flow Through ◽  
The Mean ◽  
Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

scholarly journals Lattice Boltzmann Model for Gas Flow through Tight Porous Media with Multiple Mechanisms

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 133 ◽  
Author(s):  
Junjie Ren ◽  
Qiao Zheng ◽  
Ping Guo ◽  
Chunlan Zhao
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Stress Sensitivity ◽  
Lattice Boltzmann Model ◽  
Flow Through Porous Media ◽  
Gas Slippage ◽  
Flow Through ◽  
Boltzmann Model

In the development of tight gas reservoirs, gas flow through porous media usually takes place deep underground with multiple mechanisms, including gas slippage and stress sensitivity of permeability and porosity. However, little work has been done to simultaneously incorporate these mechanisms in the lattice Boltzmann model for simulating gas flow through porous media. This paper presents a lattice Boltzmann model for gas flow through porous media with a consideration of these effects. The apparent permeability and porosity are calculated based on the intrinsic permeability, intrinsic porosity, permeability modulus, porosity sensitivity exponent, and pressure. Gas flow in a two-dimensional channel filled with a homogeneous porous medium is simulated to validate the present model. Simulation results reveal that gas slippage can enhance the flow rate in tight porous media, while stress sensitivity of permeability and porosity reduces the flow rate. The simulation results of gas flow in a porous medium with different mineral components show that the gas slippage and stress sensitivity of permeability and porosity not only affect the global velocity magnitude, but also have an effect on the flow field. In addition, gas flow in a porous medium with fractures is also investigated. It is found that the fractures along the pressure-gradient direction significantly enhance the total flow rate, while the fractures perpendicular to the pressure-gradient direction have little effect on the global permeability of the porous medium. For the porous medium without fractures, the gas-slippage effect is a major influence factor on the global permeability, especially under low pressure; for the porous medium with fractures, the stress-sensitivity effect plays a more important role in gas flow.

Cessation of Darcy regime in gas flow through porous media using LBM: Comparison of pressure gradient approaches

2017 ◽  
Vol 45 ◽  
pp. 693-705 ◽  
Author(s):  
Aliakbar Kakouei ◽  
Ali Vatani ◽  
MohammadReza Rasaei ◽  
Behnam Sedaee Sola ◽  
Hamed Moqtaderi
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Gas Flow ◽  
Flow Through Porous Media ◽  
Flow Through

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Effects of Fluid Inertia and Compressibility on the Performance of Valves and Flow Meters Operating under Unsteady Conditions

1966 ◽  
Vol 8 (1) ◽  
pp. 52-61 ◽  
Author(s):  
D. McCloy
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Flow Measurement ◽  
Fluid Inertia ◽  
Mean Flow ◽  
Flow Meters ◽  
Orifice Area ◽  
Flow Through ◽  
The Mean ◽  
Compressibility Effects

Incompressible flow theory is used in the investigation of the effects of fluid inertia on unsteady flow through valves and flow meters. Two types of oscillatory disturbance are considered, one being due to valve oscillation at constant pressure drop and the other to pressure pulsation at constant orifice area. With the former type of disturbance it is shown that the mean flow rate decreases with frequency of oscillation. When the pressure drop pulsates the mean flow rate increases with frequency. These phenomena are shown to be of importance in hydraulic servomechanisms and in dynamic flow measurement. Compressibility effects are considered and it is shown that cavitation can occur at the valve during oscillation.

Langevin Dynamics Study of the Mean Flow Rate-Energy Stochastic Fluid Intrusion Process in Porous Media

2019 ◽  
Vol 12 (6) ◽  
pp. 398
Author(s):  
Yassine Hariti ◽  
Ahmed Hader ◽  
Layla Amallah ◽  
Imad Achik ◽  
Yahia Boughaleb
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Langevin Dynamics ◽  
Mean Flow ◽  
The Mean ◽  
Stochastic Fluid

scholarly journals An Explicit Algorithm for the Simulation of Fluid Flow through Porous Media

2018 ◽  
Vol 173 ◽  
pp. 06012 ◽  
Author(s):  
Marina Trapeznikova ◽  
Natalia Churbanova ◽  
Anastasiya Lyupa
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
System Of Equations ◽  
Heat Sources ◽  
Flow Through Porous Media ◽  
Multicomponent Fluid ◽  
Medium Flow ◽  
Flow Through ◽  
Porous Medium Flow

The work deals with the development of an original mathematical model of porous medium flow constructed by analogy with the quasigasdynamic system of equations and allowing implementation via explicit numerical methods. The model is generalized to the case of multiphase multicomponent fluid and takes into account possible heat sources. The proposed approach is verified by a number of test predictions.

scholarly journals A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Maria Laura Martins-Costa ◽  
Daniel Cunha da Silva ◽  
Michele Cunha da Silva ◽  
Rogério Martins Saldanha da Gama
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Constitutive Relation ◽  
Porous Matrix ◽  
Flow Through Porous Media ◽  
First Derivative ◽  
Fluid Fraction ◽  
Flow Through ◽  
Matrix Resistance ◽  
Increasing Function

The present work proposes an adequate constitutive relation to treat the process of filling with a fluid porous medium. This relation assures the problem to remain hyperbolic when the porous medium is saturated by the fluid. When the fluid fraction reaches porosity, the proposed constitutive relation increases the porous matrix resistance to more fluid inlet due to an important feature: it is a continuous and differentiable function with first derivative being also an increasing function. This allows assuring that the fluid fraction may exceed the porosity only by a very small value, making the constitutive relation realistic. Some examples compare this new constitutive relation with previous ones, highlighting its advantages.

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