An Empirical Equation for Flow Through Porous Media

2005 ◽  
Author(s):  
C. A. Ortega Vivas ◽  
S. Barraga´n Gonza´lez ◽  
J. M. Garibay Cisneros
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Pressure Drop ◽  
Empirical Equation ◽  
Experimental Methods ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Flow Through Porous Media ◽  
Flow Through ◽  
Porous Medium Model

This study analyses the macroscopic flow through a two dimensional porous medium model by numerical and experimental methods. The objective of this research is to develop an empirical model by which the pressure drop can be obtained. In order to construct the model, a series of blocks are used as an idealized pressure drop device, so that the pressure drop can be calculated. The range of porosities studied is between 28 and 75 per cent. It is found that the pressure drop is a combination of viscosity and inertial effects, the later being more important as the Reynolds number is increased. The empirical equation obtained in this investigation is compared with the Ergun equation.

An Asymptotic Model of Viscous Flow Limitation in a Highly Collapsed Channel

1998 ◽  
Vol 120 (4) ◽  
pp. 544-546 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
External Pressure ◽  
Asymptotic Model ◽  
Flow Limitation ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Channel One ◽  
Narrow Region ◽  
Flow Through

A viscous flow through a long two-dimensional channel, one wall of which is formed by a finite-length membrane, experiences flow limitation when the channel is highly collapsed over a narrow region under high external pressure. Simple approximate relations between flow rate and pressure drop are obtained for this configuration by the use of matched asymptotic expansions. Weak inertial effects are also considered.

Numerical modelling of nonlinear effects in laminar flow through a porous medium

1988 ◽  
Vol 190 ◽  
pp. 393-407 ◽  
Author(s):  
O. Coulaud ◽  
P. Morel ◽  
J. P. Caltagirone
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Quadratic Term ◽  
Inertial Effects ◽  
Operator Splitting Methods ◽  
Flow Through

This paper deals with the introduction of a nonlinear term into Darcy's equation to describe inertial effects in a porous medium. The method chosen is the numerical resolution of flow equations at a pore scale. The medium is modelled by cylinders of either equal or unequal diameters arranged in a regular pattern with a square or triangular base. For a given flow through this medium the pressure drop is evaluated numerically.The Navier-Stokes equations are discretized by the mixed finite-element method. The numerical solution is based on operator-splitting methods whose purpose is to separate the difficulties due to the nonlinear operator in the equation of motion and the necessity of taking into account the continuity equation. The associated Stokes problems are solved by a mixed formulation proposed by Glowinski & Pironneau.For Reynolds numbers lower than 1, the relationship between the global pressure gradient and the filtration velocity is linear as predicted by Darcy's law. For higher values of the Reynolds number the pressure drop is influenced by inertial effects which can be interpreted by the addition of a quadratic term in Darcy's law.On the one hand this study confirms the presence of a nonlinear term in the motion equation as experimentally predicted by several authors, and on the other hand analyses the fluid behaviour in simple media. In addition to the detailed numerical solutions, an estimation of the hydrodynamical constants in the Forchheimer equation is given in terms of porosity and the geometrical characteristics of the models studied.

The Effect of Inlet and Exit Pressure-Drop on the Determination of Porous Media Permeability and Form Coefficient

2005 ◽  
Author(s):  
Christian Naaktgeboren ◽  
Paul S. Krueger ◽  
Jose´ L. Lage
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Pressure Drop ◽  
Turbulent Pipe Flow ◽  
Flow Adjustment ◽  
Medium Length ◽  
Exit Pressure ◽  
Flow Through

The determination of permeability and form coefficient, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the pressure-drop per unit length caused by the medium. The pressure-drop emerging from flow adjustment effects between the porous medium and the surrounding clear fluid, however, is not related to the porous medium length. Hence, for situations in which the entrance and exit pressure-drops are not negligible, as one would expect for short porous media, the determination of the hydraulic parameters using the HDD equation is hindered. A criterion for determining the relative importance of entrance and exit pressure-drop effects, as compared to core effect, is then of practical and fundamental interest. This aspect is investigated analytically and numerically considering flow through a thin planar restriction placed in a circular pipe. Once the pressure-drop across the restriction is found, the results are then compared to the pressure-drop imposed by an obstructive section having the same dimension as the restriction but finite length, playing the role of the least restrictive porous medium core. This comparison yields a conservative estimate of the porous medium length necessary for neglecting entrance and exit pressure-drop effects. Results show that inlet and exit pressure-drop effects become increasingly important compared to core effects as the porosity decreases and Reynolds number increases for both laminar and turbulent flow regimes. (Correlations based on experimental results available in the literature are employed for turbulent pipe flow). The analysis also shows why the HDD equation breaks down when considering flow through porous media where the entrance and exit pressure-drop effects are not negligible, and how modified permeability and form coefficients become necessary to characterize this type of porous media. Curve-fits accurate to within 2.5% were obtained for the modified permeability and form coefficients of the planar restriction with Reynolds number ranging from 0.01 to 100 and porosity from 0.0625 to 0.909.

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 Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Krzysztof M. Graczyk ◽  
Maciej Matyka
Keyword(s):  
Neural Networks ◽  
Porous Medium ◽  
Porous Media ◽  
Deep Learning ◽  
Lattice Boltzmann ◽  
Good Accuracy ◽  
Two Dimensional ◽  
Empirical Estimate ◽  
Flow Through ◽  
Boltzmann Method

AbstractConvolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

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.

Computational study on drilling mud flow through wellbore annulus by Giesekus viscoelastic model

2020 ◽  
pp. 095440892094380
Author(s):  
Mohammad Amir Hasani ◽  
Mahmood Norouzi ◽  
Morsal Momeni Larimi ◽  
Reza Rooki
Keyword(s):  
Reynolds Number ◽  
Friction Coefficient ◽  
Pressure Drop ◽  
Elastic Property ◽  
Taylor Number ◽  
Drilling Fluids ◽  
Drilling Mud ◽  
Axial Pressure ◽  
Flow Through ◽  
Mud Flow

Cuttings transport from wellbore annulus to the surface via drilling fluids is one of the most important problems in gas and oil industries. In the present paper, the effects of viscoelastic property of drilling fluids on flow through wellbore annulus are studied numerically by use of computational fluid dynamics simulation in OpenFOAM software. This problem is simulated as the flow between two coaxial annulus cylinders and the inner cylinder is rotating through its axes. Here, the Giesekus model is used as the nonlinear constitutive equation. This model brings the nonlinear viscosity, normal stress differences, extensional viscosity and elastic property. The numerical solution is obtained using the second order finite volume method by considering PISO algorithm for pressure correction. The effect of elasticity, Reynolds number, Taylor number and mobility factor on the velocity and stress fields, pressure drop, and important coefficient of drilling mud flow is studied in detail. The results predicted that increasing elastic property of drilling mud lead to an initial sharp drop in the axial pressure gradient as well as Darcy-Weisbach friction coefficient. Increasing the Reynolds number at constant Taylor number, resulted an enhancing in the axial pressure drop of the fluid but Darcy-Weisbach [Formula: see text] friction coefficient mainly reduced.

Lateral-Flow Effect on Endwall Heat Transfer and Pressure Drop in a Pin-Fin Trapezoidal Duct of Various Pin Shapes

2000 ◽  
Vol 123 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Chau-Ching Lu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Lateral Flow ◽  
Transfer Enhancement ◽  
Pin Fin ◽  
Flow Reynolds Number ◽  
Outlet Flow ◽  
Flow Through

The effects of lateral-flow ejection 0<ε<1.0, pin shapes (square, diamond, and circular), and flow Reynolds number (6000<Re<40,000) on the endwall heat transfer and pressure drop for turbulent flow through a pin-fin trapezoidal duct are studied experimentally. A staggered pin array of five rows and five columns is inserted in the trapezoidal duct, with the same spacings between the pins in the streamwise and spanwise directions: Sx/d=Sy/d=2.5. Three different-shaped pins of length from 2.5<l/d<4.6 span the distance between two endwalls of the trapezoidal duct. Results reveal that the pin-fin trapezoidal duct with lateral-flow rate of ε=0.3-0.4 has a local minimum endwall-averaged Nusselt number and Euler number for all pin shapes investigated. The trapezoidal duct of lateral outlet flow only (ε=1.0) has the highest endwall heat transfer and pressure drop. Moreover, the square pin results in a better heat transfer enhancement than the diamond pin, and subsequently than the circular pin. Finally, taking account of the lateral-flow rate and the flow Reynolds number, the work develops correlations of the endwall-averaged heat transfer with three different pin shapes.

Effects of the Divergence Angle on the Onset of Asymmetric Flow Through a Planar Diffuser

2009 ◽  
Author(s):  
Majid Nabavi ◽  
Luc Mongeau
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Turbulent Flow Regime ◽  
Flow Through ◽  
Gradual Expansion

In this study, two-dimensional laminar incompressible and turbulent compressible flow through the planar diffuser (gradual expansion) for different divergence half angles of the diffuser (θ), and different Reynolds numbers (Re) was numerically studied. The effects of θ on the critical Reynolds number at which the onset of asymmetric flow is observed, were investigated. In the laminar flow regime, it was observed that for every values of θ, there is a critical Re beyond which the flow is asymmetric. However, in the turbulent flow regime, for θ ≥ 20°, even at low Reynolds number the flow is asymmetric. Only for θ ≤ 10°, symmetric flow was observed below a critical Re.

Prediction of Pressure Drop for Incompressible Flow Through Screens

1993 ◽  
Vol 115 (2) ◽  
pp. 239-242 ◽  
Author(s):  
E. Brundrett
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Incompressible Flow ◽  
Pressure Loss ◽  
Effective Porosity ◽  
Local Damage ◽  
Number Range ◽  
Flow Through ◽  
Careful Specification ◽  
Cosine Law

A new pressure loss correlation predicts flow through screens for the wire Reynolds number range of 10−4 to 104 using the conventional orthogonal porosity and a function of wire Reynolds number. The correlation is extended by the conventional cosine law to include flow that is not perpendicular to the screen. The importance of careful specification of wire diameter for accurate predictions of porosity is examined. The effective porosity is influenced by the shape of the woven wires, by any local damage, and by screen tension.

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