Porosity and grain size of porous solids

[eneacasucci]

TL;DR Summary

My professor said "the porosity of samples is inversely related to the grain size and decreases linearly as grain size increases"?
I've tried to figure it out considering a 2D case with a square area and in it circular grains of different sizes but the free space (porosity) happens to be the same... (Attached picture).
I'm feeling stupid but I can't understand this concept clearly

 

[berkeman]

Porosity of what material? What is the context of your question?

 

[eneacasucci]

Porosity of what material? What is the context of your question?

Not a specific material, just the general concept of porosity of a solid material composed of grains.

academic.oup.com/jge/article/15/2/613/5078500

 

[berkeman]

That looks to be talking about sandstone. Metals have grains too, but are generally not porous...

 

[eneacasucci]

That looks to be talking about sandstone. Metals have grains too, but are generally not porous...

I'm still not able to figure out why the porosity of samples is inversely related to the grain size and decreases linearly as grain size increases. I've tried to make simple examples to have a feeling but it didn't work...

 

[berkeman]

I'm guessing it has to do with the area of the grains versus the area between the grains. Is most of the water movement in the spaces between the grains?

 

[eneacasucci]

I'm guessing it has to do with the area of the grains versus the area between the grains. Is most of the water movement in the spaces between the grains?

Yes but I've tried to make the calculations in 2d (but it is the same in 3D) as in the picture I've attached but the areas of the free space are the same :(

 

[berkeman]

It looks like it depends on the size of the grains/particles and their arrangement (to make it easier or harder for the water to move through the material):

https://en.wikipedia.org/wiki/Porous_medium

 

[eneacasucci]

It looks like it depends on the size of the grains/particles and their arrangement (to make it easier or harder for the water to move through the material):

https://en.wikipedia.org/wiki/Porous_medium

View attachment 325244

here, however, we are mainly talking about water movement in relation to compaction, not porosity, and there are different grain sizes, we don't see here why the porosity decreases as grain size increases

 

[berkeman]

Hmm, the text you posted says that bulk density increases with grain size, which would seem to lead to the decreased porosity, but I don't see that bulk density increase with grain size geomtrically. Have you found anything else that says this?

 

[berkeman]

I looked a little more at that article you posted, and it looks like it depends on a lot of things. Have you read the whole article and followed some of the links?

Theoretically porosity is independent of median grain size. This ideal situation, which corresponds to a maximum degree of sorting, rarely occurs in nature. Several investigators have presented that well sorted naturally deposited sand grains affect porosity values. Pryor (1973) analyzed several sands and illustrated that porosity decreased with increasing median grain size. Bell (2016) stated that porosity ranges from 44%–49%, 41%–48% and 39%–41% for fine, medium and coarse sands respectively. Al-Homadhi and Hamada (2001) reported that as grain size is increased, porosity decreases slightly. This behavior is seen in the three class of cementation. Ogolo et al (2015) studied the moderately sorted and well sorted sands obtained from three different locations in the Niger Delta and indicated that porosity decreases with increasing grain size. They generally observed that porosity decreased from about 42% to 26% as the sand grain size increased from 45 to 1000 μs. However, in contrast with these findings, Brown (1993) illustrated that, in carbonate rocks, as grain size increases, porosity increases. He noted that this relation of porosity to grain size is usually seen in petrographic studies on detrital rocks. Also, Ulusay et al (1994), working with sandstones, indicated that the relationship between effective porosity and grain size is statistically significant and there is a tendency for porosity to increase with median grain size.

 

[eneacasucci]

I looked a little more at that article you posted, and it looks like it depends on a lot of things. Have you read the whole article and followed some of the links?

Thank you, yes I read it and that's why when I read "Theoretically porosity is independent of median grain size" I tried to make the 2D drawing to """demonstrate""" it, and actually that's what I got. Maybe in the non-theoretical case we don't have the "maximum degree of sorting" and so that's why things change

 

[jrmichler]

here, however, we are mainly talking about water movement in relation to compaction, not porosity, and there are different grain sizes, we don't see here why the porosity decreases as grain size increases

Theoretically porosity is independent of median grain size

If we are looking at porosity:

1) In soils
AND
2) Where porosity is the fraction of open space between soil particles
AND
3) Using a simplified soil particle model where all of the particles are equal size spheres
but NOT
4) Water flow through the soil
THEN
The porosity is always the same regardless of sphere size. However, in the real world, porosity has a relationship with particle size. This implies that:

1) Larger particles have different average shape than smaller particles, so pack with lower porosity
OR
2) Larger particles have larger percentage of smaller particles, so pack with lower porosity
OR
3) Something else that makes larger particles different from smaller particles

 

[Baluncore]

It has everything to do with the distribution of particle size in the mix, and for a rock, the cement that holds the particles in place.

Low porosity requires, a few big particles, with more medium-size particles that fit in the gaps, with smaller particles in the very many more smaller gaps, and so on, ad infinitum.

 

[jrmichler]

Sand of "uniform" particle size has a wide range of particle sizes. This figure, from Introductory Soil Mechanics and Foundations, 3rd Edition, by Sowers and Sowers shows a typical range of particle sizes for a uniform graded sand:

The particle sizes in uniform graded sand range in size by almost a full order of magnitude. While most of the particles have a small range of sizes, the resulting porosity will differ from a porosity calculated using spheres. And it is easy to believe that the particle size distribution will vary with median particle size, which would explain the data in Posts 3 and 11.

 

[Lord Jestocost]

TL;DR Summary: My professor said "the porosity of samples is inversely related to the grain size and decreases linearly as grain size increases"?
I've tried to figure it out considering a 2D case with a square area and in it circular grains of different sizes but the free space (porosity) happens to be the same... (Attached picture).

Maybe, the following might be of help:

“It was noted above that the ordered cubic packing of identical sphere leads to a porosity that is grain size independent. This is also true for the other ordered packing lattices, but not true for the random arrangement of spheres. In real depositional environments, ordered packings are not formed because they are energetically unstable, and the grains become randomly distributed.
The equilibrium porosity of a porous material composed of a random packing of spherical grains is dependent upon the stability given to the rock by frictional and cohesive forces operating between individual grains. These forces are proportional to the exposed surface area of the grains. The specific surface area (exposed grain surface area per unit solid volume) is inversely proportional to grain size.
This indicates that, when all other factors are equal, a given weight of coarse grains will be stabilized at a lower porosity than the same weight of finer grains……”

Dr. Paul Glover, University of Leeds: https://homepages.see.leeds.ac.uk/~earpwjg/PG_EN/CD%20Contents/GGL-66565%20Petrophysics%20English/Chapter%202.PDF

See also: Oxford Universtiy Press: https://academic.oup.com/jge/article/15/2/613/5078500

 

[hutchphd]

Are we talking about uniformly increasing all grain sizes? Porosity is just the ratio Void volume to total volume $$Porosity= \frac {V_{void}} {V}~=1-\frac {V_{grains}} V $$ So this will not depend upon size, except for surface effects.

 

[eneacasucci]

Maybe, the following might be of help:

“It was noted above that the ordered cubic packing of identical sphere leads to a porosity that is grain size independent. This is also true for the other ordered packing lattices, but not true for the random arrangement of spheres. In real depositional environments, ordered packings are not formed because they are energetically unstable, and the grains become randomly distributed.
The equilibrium porosity of a porous material composed of a random packing of spherical grains is dependent upon the stability given to the rock by frictional and cohesive forces operating between individual grains. These forces are proportional to the exposed surface area of the grains. The specific surface area (exposed grain surface area per unit solid volume) is inversely proportional to grain size.
This indicates that, when all other factors are equal, a given weight of coarse grains will be stabilized at a lower porosity than the same weight of finer grains……”

Dr. Paul Glover, University of Leeds: https://homepages.see.leeds.ac.uk/~earpwjg/PG_EN/CD%20Contents/GGL-66565%20Petrophysics%20English/Chapter%202.PDF

See also: Oxford Universtiy Press: https://academic.oup.com/jge/article/15/2/613/5078500

Thank you so much (not only you of course but all the ones that answered, I'm really grateful, thank you for your time).
It is much clearer now.
These documents say that in the non-ideal case, with random packing, the frictional and cohesive forces influence porosity, of course <grain size → >surface → > forces.
It is also stated (p.5 second link) that " With an increase in frictional forces acting between individual grains, the grains tend to pack less closely together and thus the porosity increases."
This is the last thing I cannot figure out: >frictional forces⇒ grain pack less closely
why?

 

[jrmichler]

It is also stated (p.5 second link) that " With an increase in frictional forces acting between individual grains, the grains tend to pack less closely together and thus the porosity increases."
This is the last thing I cannot figure out: >frictional forces⇒ grain pack less closely
why?

This is a topic of considerable interest to civil engineers. The same book referenced in Post #15, Introductory Soil Mechanics and Foundations, 3rd Edition, by Sowers and Sowers, has a chapter on the compaction and stabilization of soils. Soils are made of particles. Building foundations, roadbeds, and dams all require solid earth foundations underneath. Solid foundations require minimum porosity. Porosity is reduced by compaction. From that book, Section 5:2 Theory of Compaction: "Densification, or a reduction in the void ratio, occurs in a number of ways: reorientation of the particles; fracture of the grains or the bonds between them, followed by reorientation; and bending or distortion of the particles and their adsorbed layers. .... In a cohesionless soil or crushed rock the densification is primarily attained by reorientation of the grains, ... The reorientation is resisted by the friction between the particles."

Think of this the next time you dig a hole, back fill it, then jump on it to pack it down. Your feet are reorienting the soil particles through the process of compaction by jumping up and down.

As a side note, that book was already on my desk because I am trying to figure out how to convince the other members of the town board that we need to do a better job of compaction after digging stumps out of roads and replacing culverts. Some of our town roads were built over 100 years ago by piling dirt over swamps. Stumps and boulders work their way up from frost action, then get dug out when it comes time to replace the blacktop. Improper compaction causes the new blacktop to break up in a few years.

 

[eneacasucci]

This is a topic of considerable interest to civil engineers. The same book referenced in Post #15, Introductory Soil Mechanics and Foundations, 3rd Edition, by Sowers and Sowers, has a chapter on the compaction and stabilization of soils. Soils are made of particles. Building foundations, roadbeds, and dams all require solid earth foundations underneath. Solid foundations require minimum porosity. Porosity is reduced by compaction. From that book, Section 5:2 Theory of Compaction: "Densification, or a reduction in the void ratio, occurs in a number of ways: reorientation of the particles; fracture of the grains or the bonds between them, followed by reorientation; and bending or distortion of the particles and their adsorbed layers. .... In a cohesionless soil or crushed rock the densification is primarily attained by reorientation of the grains, ... The reorientation is resisted by the friction between the particles."

Think of this the next time you dig a hole, back fill it, then jump on it to pack it down. Your feet are reorienting the soil particles through the process of compaction by jumping up and down.

As a side note, that book was already on my desk because I am trying to figure out how to convince the other members of the town board that we need to do a better job of compaction after digging stumps out of roads and replacing culverts. Some of our town roads were built over 100 years ago by piling dirt over swamps. Stumps and boulders work their way up from frost action, then get dug out when it comes time to replace the blacktop. Improper compaction causes the new blacktop to break up in a few years.

That's very informative!
I think everything has been explained now
<grain size → >surface → > frictional forces → > resistance to reorientation → <packing → >porosity
and vice versa > grain size →...→ < porosity

P.S. I think now I understood the point, I would like to thank you all for your time, knowledge and patience