# What is Relative permeability: Definition and 15 Discussions

In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability. It can be viewed as an adaptation of Darcy's law to multiphase flow.
For two-phase flow in porous media given steady-state conditions, we can write

q

i

=

k

i

μ

i

P

i

for

i
=
1
,
2

where

q

i

{\displaystyle q_{i}}
is the flux,

P

i

{\displaystyle \nabla P_{i}}
is the pressure drop,

μ

i

{\displaystyle \mu _{i}}
is the viscosity. The subscript

i

{\displaystyle i}
indicates that the parameters are for phase

i

{\displaystyle i}
.

k

i

{\displaystyle k_{i}}
is here the phase permeability (i.e., the effective permeability of phase

i

{\displaystyle i}
), as observed through the equation above.
Relative permeability,

k

r
i

{\displaystyle k_{\mathit {ri}}}
, for phase

i

{\displaystyle i}
is then defined from

k

i

=

k

r
i

k

{\displaystyle k_{i}=k_{\mathit {ri}}k}
, as

k

r
i

=

k

i

/

k

{\displaystyle k_{\mathit {ri}}=k_{i}/k}
where

k

{\displaystyle k}
is the permeability of the porous medium in single-phase flow, i.e., the absolute permeability. Relative permeability must be between zero and one.
In applications, relative permeability is often represented as a function of water saturation; however, owing to capillary hysteresis one often resorts to a function or curve measured under drainage and another measured under imbibition.
Under this approach, the flow of each phase is inhibited by the presence of the other phases. Thus the sum of relative permeabilities over all phases is less than 1. However, apparent relative permeabilities larger than 1 have been obtained since the Darcean approach disregards the viscous coupling effects derived from momentum transfer between the phases (see assumptions below). This coupling could enhance the flow instead of inhibit it. This has been observed in heavy oil petroleum reservoirs when the gas phase flows as bubbles or patches (disconnected).

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1. ### Ampere's Law for a toroid (finding relative permeability of iron)

Why is this equation: B(D - d)/mu + Bd = mu0 N I true? B = magnetic field in the hole of the toroid D = Average diameter of the toroid d = Diameter of hole of toroid mu = relative permeability of iron, or whatever the toroid is made of mu0 = 4pi x 10^-7 N = Number of turns on the toroid I =...
2. ### What is the Relative Permeability of Iron in a Solenoid?

So the equation is L=μoμrN^2A/l I am wanting to make μr the subject and I think this is how i do it? μr = L*l/μoN^2A However when I type in this equation i am expecting to get about 200 for the relative permeability of iron. However, i am getting like 9x10-3 which is nowhere near 200. For...
3. ### Theoretical ξr of a molecule from the absolute configuration

I am wondering if anybody knows how to calculate the theoretical relative permittivity of a molecule (1) using the theoretical configuration and values that are easily accessible (2). I am also wondering what the technique would be. In my pharmaceutical reaction class and also O-chem 2 we have...
4. ### Why we use relative permeability

Why we use relative permeability if we have absolute permeability in electromagnetism?
5. ### Interpret current density in plasma as material property?

Homework Statement An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by n^2 = 1 - \frac{\omega_P^2}{\omega^2}, where the plasma frequency \omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)...
6. ### Dynamic Relative magnetic permeability

I want to know that are there any materials or methods by which their relative magnetic permeability (μr) be instantaneously,continuously & periodically varied. Kindly provide the reference document/video for the description if possible.
7. ### Calculate the required relative permeability of magnetic mat

Homework Statement Consider the core of dimensions given in example 5-1. A coil requires an inductance of 23.6μH, a maximum current of 4A is allowed, and flux density is not to exceed 1.3T. Calculate the required relative permeability, μr, of the magnetic material that should be used. (HINT...
8. ### Magnetic coercivity and relative permeability

So when looking at a hysteresis loop, the x-axis is the magnitude of H-field, and the y-axis is the magnitude of B-field. H is in units of electricity and B is in units of magnetic flux density. My question relates to how coercivity is determined if the material being magnetized has a...
9. ### Magnetic susceptibility and relative permeability

Homework Statement find the derivation of χm=μr-1 where Xm is the magnetic susceptibility and μ is the relative permeability. Homework Equations M=Xm.H M is the magnetization,H is the magnetic field μr=μ/μo where μo is the permeability of a vacuum, The Attempt at a Solution I...
10. ### Magnetic Susceptibility VS. Relative Permeability

What is the difference between the two and what are the applications of them in a magnetic material?
11. ### Relative Permitttivity & Relative Permeability Dependency

Hi Everyone, I want to know that is there anyway to relate the relative permittivity (εr) & relative permeability (μr) ?... I am having relative permittivity of an material & i want to find out its relative permeability ... Like if εr = 2.2, then μr = ?... Please reply ...
12. ### Changing/Controling relative permeability

Hey everyone, I've been looking at metamaterials, and it's quite an overwhelming subtopic to be introduced to. Most of the stuff I'm finding has to do with negative permeabilities. I'm wondering how exactly we control what relative permeability a material has and how fine that control is, not...
13. ### Confusing on permeability and relative permeability

In some textbook of fundamental electromagnetism, the relation between magnetic field \vec{B} and so called magnetizing field \vec{H} is \vec{B} = \mu_0\vec{H} But later on, they introduce a so called relative permeability \mu_r = \frac{\mu}{\mu_0} I might be wrong but my...
14. ### H of a toroidal coil with relative permeability

Consider a toroidal coil of rectangular section of N turns, for every one of which circulates a stream I. The inner radius of the coil is a and b is the exterior and the height is h. The core of this coil is a material inhomogeneous in such a way that their magnetic permeability just depends on...
15. ### Relative Permeability of Lead: Can I Assume Value of 1?

Simply, all I want to know is the value of the relative permeability of lead?? Can I assume this value to 1??