Questions tagged [porous-media]
Porous media are solid materials that contain interconnected pores allowing fluids to pass through.
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Newton's 1st and 2nd laws and Darcy's law as a force balance
In a derivation of Darcy's law from a macroscopic force balance approach, the authors arrive at the following vector equation for the average forces per unit fluid volume for a fluid at rest:
$$\tag{1}...
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1answer
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Porous media flow equation in terms of fluid compressibility and determination of coefficients?
I'm having trouble understanding an equation and solution method given in literature. The 1D flow equation for "high rate" linear gas flow through a porous medium is given as:
$$\tag{1} p_1-...
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Strains in a homogeneous isotropic linear elastic porous body
I am trying to understand a claim made in many papers (Geertsma, 1957a; Rice, 1976) and textbooks (Jaeger and Cook; Zimmerman) related to mechanics of porous media.
Consider an isotropic linear ...
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Question on the average non-Darcy linear flow through multiple units in series
Assuming Darcian linear flow through multiple units in series, e.g., two or more cores stacked upon each other within a permeameter, one can derive the average (harmonic mean) permeability of the ...
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Fluid dynamics for the sepiolite
I would like to know some about the physics of an interesting material, the sepiolite. I mean the material from the Wikipedia article Sepiolite where are explained the general and identification ...
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1answer
46 views
Origin of terms in the Nernst-Planck equation
We know the Nernst Planck equation is
$$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \...
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Differences between porous and black silicon
Does anybody know what are the differences between porous and black silicon?
Both of them are produced by etching in HF solutions, both have similar porous/skeleton structure.
Maybe black Si is just ...
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17 views
What is the relationship between pressure and concentration in liquids in porous media?
I am working on a model in porous media. In particular, it is about the formation damage due to the precipitation. I assigned Dirichlet boundary condition for the concentration near the well-bore, ...
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“Directional” conductivity in linear flux-potential laws?
Question: Has the notion of "directional conductivity" been defined and used in the study of heat flow and electric current flow?
Context: The table below gives three laws that describe linear flux-...
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1answer
35 views
Reynolds limits on laminar flow between irregular plates (fracture)
I'm trying to understand the limits of laminar flow in a system comprised of two plates of varying width. The idea is to model a naturally fractured system and understand up to when flow and pressure ...
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Dimension reducing of heat equation 2D problem
I have two metal objects of different thickness and conductivity:
1) thicker, but poorly conductive. It's properties: $k_1, H$
2) thin and much better conductive. It's properties: $k_2, h$
...
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1answer
36 views
What are the assumptions for porous media to be considered as continuum?
The poroelastic models like - Biot theory- are built on the continuum approach. But I am not able to understand, how this heterogeneous media can be considered as a continuum.
However, If the porous ...
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What is the meaning of effective density in porous media? Is the density of air inside the pore space not same as density of free air?
I am trying to understand the physical meaning of using effective density in porous media. Is it a fictitious value? Can't I use the density of solid and fluid as it is while modeling porous media?
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Onsager reciprocal relations and Darcy's permeability tensor for anisotropic porous media
The wiki entry on soil tensor permeability states that
The tensor is symmetric by the Onsager reciprocal relations
Bear & Cheng (2010, p122)* state that:
The hydraulic conductivity tensor, $...
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1answer
52 views
Acoustics: Construction of the pressure field with transmitted and reflected plane waves
So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
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Computing the porosity of a core sample from a set of digital images
Are there any references of books and/or papers about methods to compute the porosity of a given core sample (from an oil and gas reservoir) if this core is given as a set of digital images (for ...
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Can the principal values and directions (axes) of a rock's permeability anisotropy be determined on a single cylindrical core sample?
If a rock core (a right-cylinder of rock), as shown at the left of the image below, has bedding planes oriented arbitrarily with respect to the long axis of the core, how does one go about determining ...
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2answers
90 views
Percolation theory: What is the critical amplitude for the “backbone” of a 2-D network?
Disclaimer: I am just learning about percolation theory for the first time, so I am not too familiar with some of the terminology.
Suppose you have a 2-D square lattice with bonds connecting sites. ...
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1answer
266 views
Percolation theory: Is there a clear relationship between “probability of connection” and “effective porosity”?
Disclaimer: I am a geophysicist, not a physicist. Sometimes we speak a slightly different language and use different terms.
Suppose you have an $N$ x $N$, 2-D rectangular lattice with bonds which ...
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1answer
94 views
Can the coefficient of inertial resistivity ($\beta$-factor) be a 2nd rank tensor?
Question: Can the Forchheimer $\beta$-factor be a 2nd rank tensor (like permeability, $k$)?
In most cases in literature, the quadratic Forchheimer equation is applied only to one-dimensional flow. ...
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1answer
79 views
Integrating the quadratic Forchheimer equation
Starting with the commonly cited Forchheimer equation:
$$\tag{1} -\frac{dp}{ds}=\frac{\mu q}{kA}+\frac{\beta \rho q^2}{A^2}$$
multiplying through by density
$$\tag{2} -\rho \frac{dp}{ds}=\frac{\mu \...
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1answer
240 views
Darcy's law using Hubbert potential vs pseudo-pressure for a gas
How does one show the equivalence (or difference) of Darcy's law written using Hubbert's potential of a real gas to that of Darcy's law written using the concept of pseudo-pressure (aka pseudo-...
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When does a finite size random graph percolate?
Assume we are simulating percolation on a 2d lattice. While the system is of finite size, we say that the critical state appears when a cluster connects two opposing ends of the lattice. The bigger ...
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1answer
455 views
How to implement Hubbert's potential to calculate permeability using Darcy's law?
Question: How does one implement Hubbert's potential to calculate permeability without making assumptions to neglect any aspects of the potential defined by Hubbert?
Question's supplemental material: ...
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Permeability anisotropy of porous media
Imagine if one were to cut a cylindrical plug out of a perfectly homogeneous rock exactly along one of the principal axis of permeability anisotropy, specifically Kmax. Then, imagine inserting only ...
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1answer
267 views
Biot coefficient as function of porosity
Can the Biot poroelasticity coefficient $\alpha$ be approximated as a function solely of porosity $\phi$, and if so then how (and under what conditions)?
I've read (e.g. 2.02-3 here) that it can, ...
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3answers
145 views
Does groundwater flow depend on the geometry of the aquifer?
I consider two cases of a confined aquifer and want to calculate the pressure / hydraulic head in a quasi 1d case. These two cases are shown in my drawing.
I assume homogenious, isotropic darcy flow, ...
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1answer
1k views
Non-Darcy Flow : Forchheimer plotting method
Recalling Darcy's equation for gas flow, assuming ($z\mu_g$) = Constant
$$\tag{1} q_{g,sc}=\frac{kA}{L}\left(\frac{T_{sc}}{Tp_{sc}}\right)\left(\frac{1}{2z\mu_g}\right)(p_1^2-p_2^2)$$
For ...
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1answer
794 views
Darcy Flow in porous material - consider porosity in cross-section area?
According to Darcy's Law, the volumetric flow rate Q of a fluid occuring due to a pressure difference $\Delta p$ over a distance L and through a cross-sectional area A of a porous medium (volume V) ...
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1answer
423 views
Can Smoothed-Particle Hydrodynamics (SPH) be used to simulate porous media flow and deformation?
I am trying to use Smoothed-Particle Hydrodynamics (SPH) to study fluid flow in and around porous media. The aim is to observe how it causes erosion and failure. For this, from my understanding, there ...
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315 views
Are there solid materials with controllable porosity?
In analogy to piezoelectric materials, where the application of an electrical field creates mechanical deformation in the material, I have the following question.
Are there solid materials whose ...
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2answers
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Can facial surgical mask effectively filter particles of smoke pollution?
Singapore is having an episode of its regular hazy season because of smoke from forest fires. Some people have been using surgical masks like the the one shown at the bottom of this post, presumably ...
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351 views
Darcy law yields extreme speed for gas flow throgh packed spheres?
The darcy law is as follows:
$u=-\frac{k}{\mu}\nabla p$.
Assume we have a gas, then $\mu$ is about $10^{-5}$.
$k$ for packed spheres a few mm in diameter is of order $10^{-8}$ $m^2$.
Say the ...
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0answers
168 views
How do I simulate a constant velocity flow in porous media
I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation....
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1answer
220 views
How can one build a multi-scale physics model of fluid flow phenomena?
I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
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2answers
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How thin a filter to filter particles out of salt water to make salt for human consumption?
I have gathered some salt in the Death Valley and for the fun of it I would like to clean it and make it edible. The process I plan to follow is simple:
Dissolve the salt in water.
Boil water for 30 ...
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2answers
493 views
Laws of fluid flow in porous medium
What are the equations that describe the flow of a fluid in a porous medium? Is there a variation of the Navier-Stokes equations?
I would like to model the flow of air through a sponge-like structure....
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3answers
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When water climbs up a piece of paper, where is the energy coming from?
Take a glass of water and piece of toilet paper. If you keep the paper vertical, and touch the surface of the water with the tip of the paper, you can see the water being absorbed and climbing up the ...
