free saturation and maximum saturation

jorne · Post by **jorne** » Wed Mar 10, 2010 4:19 am -1100

Dear WUFI team,

I am studying frost damage risk, and i read a document in wufi forum about free saturation and maximum saturation.

I want to know:
what is the diference between free saturation and maximum saturation?
where I can find this properties in wufu?

Regards

Manfred Kehrer · Wed Mar 10, 2010 8:19 pm -1100

free saturation:
amount of water which is absorbed by a material by capillary activity. To be measured if you put a specimen into liquid water.

maximum saturation:
In addition to free saturation, water can additionally absorbed via vapor diffusion and condensation. All pores of the material, which are described by the porosity value, can be filled in that way.
To be measured with heliumpyknometer or mercury intrusion.

Please see also here:
http://www.wufi-forum.com/viewtopic.php?t=301

jorne · Post by **jorne** » Thu Mar 11, 2010 7:59 am -1100

Thanks for your answer. Only other question:

When RH=100%, the situation is of free saturation or maximum saturation??

REGARDS

Thomas · Post by **Thomas** » Thu Mar 11, 2010 8:56 am -1100

jorne wrote:When RH=100%, the situation is of free saturation or maximum saturation??

When you look at a moisture storage function (there is a schematic diagram in the online help: Reference | Material Data | Moisture Storage Function) then free saturation is the water content which is reached when the relative humidity reaches 100%.

In this situation, the material will not absorb any more water voluntarily, even though the pore space is not completely filled with water. Some dead-end pores are filled with air pockets and cannot be filled with water.

Higher water contents are possible under certain circumstances, for example
- slow dissolving of the entrapped air into the water and capillary absorption of water into the newly accessible spaces, or
- filling of the pores by condensation rather than capillary suction. Condensation starts in the small pores; any air pockets are therefore driven out right from the beginning and cannot become trapped at pore ends.

These higher water contents may range from free saturation up to maximum saturation (when the entire pore space is completely filled). At all of these higher water contents, the relative humidity is still 100%.

The reason why the relative humidity does not change is this: there is a mathematical relationship connecting the relative humidity with the capillary tension in the water: in a situation where there is a high tension in the water, this tension causes strong curvature of the water surfaces in the pores; the strongly curved surfaces in turn have a reduced saturation vapor pressure, so they are in equilibrium with relative humidities less than 100%.

On the other hand, in situations where the capillary tension is zero, the surfaces are not curved, and the saturation humidity above these flat surfaces is 100%. This is the situation for all moisture contents at and above free saturation: the material will not take up any more water by capillary action, the tension is therefore zero, the relative humidity above the pore water surfaces is therefore 100%.

Regards,
Thomas

jorne · Post by **jorne** » Thu Mar 11, 2010 10:58 pm -1100

thanks a lot for your good and complete answer.

regards

Jorne

manexi · Post by **manexi** » Thu Jun 30, 2011 11:19 pm -1100

Hello Wufi Team!

Sorry for bringing back such an old topic, but while looking for some different info I found your answer interesting and I have some questions concerning the physics of water transfer.

I always thought that the moisture storage function represented both diffusion (vapour) and capillary (liquid, semiliquid) transfer... and even condensation when w>=wf (RH=100%), yet you seem to declare that it only represents the capillary transfer:

free saturation: amount of water which is absorbed by a material by capillary activity

In addition to free saturation, water can additionally be absorbed via vapour diffusion and condensation

Does this mean that the water content that I read in the WUFI output represents only the capillary water? ...should I then add the vapour mass to this? I don't think so, water content should refer to all the water in the material, but I ask you just incase

btw, what's the difference between the sorption isoterm and the moisture storage function?

Thank you!

Best ragards,
Manexi.

Manfred Kehrer · Sun Jul 03, 2011 2:21 pm -1100

manexi wrote: Does this mean that the water content that I read in the WUFI output represents only the capillary water?

The Water content is independent of the way the water came into a specific position which means there is no capillary or diffusive water content, just water content. WUFI ónly distinguish diffusive and capillary water in therms of transport not content.

sorption isotherm is a historic name for the part of the moisture storage function determined by weighing specimen in RH controled chambers typical in an RH range up to 93% RH. The other important range between 95% RH and 100% RH is derived by pressure plate measurements. The combined information from sorption and pressure plate measurements is then callED moisture storage funtion.

manexi · Post by **manexi** » Sun Jul 03, 2011 10:50 pm -1100

Thank you very much for your answer, I was kinda having trouble mixing things, but your answer is clear.

Best regards!
Manexi.

P.S. If I wanted to separate liquid from vapour water, should I use the kelvin relation or analyse the liquid and vapour flows over my specimen?

Thomas · Post by **Thomas** » Mon Jul 04, 2011 12:36 am -1100

manexi wrote:Does this mean that the water content that I read in the WUFI output represents only the capillary water? ...should I then add the vapour mass to this?

P.S. If I wanted to separate liquid from vapour water, should I use the kelvin relation or analyse the liquid and vapour flows over my specimen?

We consider the moisture storage function as describing the amount of moisture which is bound to the material. At low humidities, most of the water molecules will be bound by adsorptive forces, at higher humidities most of the water will be held in the pores by capillary forces.

The vapor in the pore air, on the other hand, is not bound to the material and is thus not considered part of its moisture content in the sense above. If you wish to determine the amount of vapor in the pores, you can simply use the inverse of the moisture storage function to look up the relative humidity phi corresponding to the water content w and then compute the water vapor concentration c from the relative humidity:

c = por*phi(w)*psat/(Rd*T)

por: Porosity
phi: relative humidity [-]
psat: saturation vapor pressure at temperature T, [Pa]
Rd: gas constant of water vapor, 461.5 J/(kg K)
T: absolute Temperature, [K]

For example, if you have a Sander sandstone sample with water content w = 19 kg/m³, the inverse moisture storage function tells you that the relative humidity in the pore air is 0.8. If the temperature is, say, 20°C, then the saturation water vapor pressure is 2340 Pa, and the actual vapor pressure in the pores is 0.8*2340 Pa = 1872 Pa.

Converting this to a vapor concentration yields c_air= 1872/461.5/293.15 = 0.0138 kg/m³. This is the vapor concentration per m³ of pore air. Since pores only make up a certain fraction of the total sample volume, this concentration has to be reduced by the porosity to yield the vapor concentration per m³ of sample material:
c_sample = 0.17*0.0138 = 0.0024 kg/m³.

So in this situation one m³ of sandstone contains 19 kg of bound water and 0.0024 kg of water vapor.

Looking at the capillary and the vapor flows will not tell you how much liquid water and how much water vapor is in the sample. As soon as liquid water and water vapor are set into motion, you will also have concurrent evaporation and/or condensation processes, determined by the strengths of the driving potentials and the availability of latent heat.

Regards,
Thomas

manexi · Post by **manexi** » Wed Jul 06, 2011 11:32 pm -1100

Dear Wufi Team,

Thank you both for you detailed answers, it's really helping me in the understanding of water transfer!

Nevertheless, if not for 1 word ("bound"), both your answers seem to be contradictory, and I'm having trouble trying to conciliate both points of view.

On the one hand, I have the water content, taking into account all the water in my specimen

The Water Content is independent of the way the water came into a specific position which means there is no capillary or diffusive water content, just water content

On the other hand I have only the "bound" water taken into account, which leaves the pore air aside

We consider the moisture storage function as describing the amount of moisture which is bound to the material

The vapor in the pore air, on the other hand, is not bound to the material and is thus not considered as part of its moisture content in the sense above

If the vapour is not considered part of the moisture content, then why do we take into account the water vapour partial pressure in order to estimate the moisture content (since this pressure should derive from the gas pressure in the pore)?

dw/dt = -div( D*grad(RH) -d*grad(Pvap) ) + Sources

What I'm trying to say is that the vapour pressure gradient will give me an estimation of where the vapour in the pore air space should go next, but wouldn't it be a useless information (concerning water content) if it wasn't already part of the overall water content? Or in other words: I deduce from the moisture equation that water vapour in the pore air is taken into account while computing the moisture content, thus how can it be part of the transfer phenomenon and still not be part of the resulting moisture content?

Moreover, if the vapour in the pore air space is not taken into account, wouldn't that mean that it has "no weight"? (considering that "weight" is the real measure given to us while constructing the moisture storage curve of a material... at least for RH<93%)

Sorry for all this questions, but it's really gotten me thinking

I hope my questions are not totally "messy".

Cheers.
Manexi

Thomas · Post by **Thomas** » Thu Jul 21, 2011 3:12 am -1100

Hi Manexi,

let me discuss two different aspects, a theoretical one and a practical one.

The theoretical aspect:

When considering moisture transport in porous materials, you should not think of vapor and 'bound' water as two separate entities which are subject to strictly separate transport mechanisms (vapor diffusion and capillary transport).

Because water content and relative humidity are connected via the moisture storage function, there is - for any given temperature T - a unique and strict relationship between the water content w and the vapor pressure p in the pores:

p = phi(w)*psat(T).

Now imagine there is some vapor pressure gradient which causes some vapor to flow out of the grid element under consideration. This outflow would reduce the vapor pressure p, but because the above formula must not be violated, some bound water must evaporate in order to keep p constant. In other words, the vapor transport is ultimately working on w instead of p (p is only _very_ slightly changed by the fact that w has suffered a very small fractional decrease). So what has changed in the end was the amount of bound water w, while the amount of vapor has remained almost unaffected, and you might as well consider only the bound water w which can be transported via two different transport mechanisms. If w is exposed to a capillary pressure gradient, some of it will start to flow; if w is exposed to a vapor pressure gradient, some of it will start to diffuse away while temporarily in the vapor state (which is just a phase the water is going through, if you pardon the pun).

WUFI takes the abstraction even one step further and works with the relative humidity phi, not the water content w. Both the vapor pressure and the water content can be expressed in terms of phi:

p = phi*psat(T)
w = w(phi), the inverse of the moisture storage function

Phi is not a conserved quantity (it can be created and destroyed on the spot), but it can be transported, and the change of phi in a grid element is

dphi/dt = dphi/dw * div( D_phi*grad(phi) + delta_p*grad(phi*psat) )

So if there is a gradient in the quantity phi, some phi is transported as specified by the transport coefficient D_phi, and if there is a gradient in the quantity phi*psat, some phi is transported as specified by the transport coefficient delta_p.
No water vapor or bound water appear as separate entities in these formulas. If needed, they are computed as secondary quantities from the resulting phi.

The practical aspect:

When I'm saying that the vapor in the pores is not considered part of the moisture content I'm referring to the fact that no attempt is made in the measurements of water contents to include the vapor if the water content is determined by weighing the specimen. Because of the buoyancy action of the ambient air, the weighing only registers those parts of the sample whose density is higher than that of the air. If one wished to include the vapor in the pores, it would have to be added as a correction to the result of the weighing. But since the water content is usually of the order of a few kilograms per m³ and the vapor content is a few grams per m³, this correction would be much smaller than the uncertainty of the weighing itself. So there would be no point in applying such an insignificant correction, independent of one's opinion whether the vapor should be included or not.

Other measurement methods like NMR or neutron scattering may automatically include the vapor in the measurement. In this case there's no point in subtracting it if one doesn't wish to include it. The contribution of the vapor is just too small to be of any relevance in the measurement result.

So, as far as measurements of the moisture storage function are concerned, the question whether to include the vapor or not is simply moot in view of the measurement uncertainties.

Regards,
Thomas

manexi · Post by **manexi** » Mon Jul 25, 2011 2:27 am -1100

Hello Thomas,

Thank you for your detailed answer. I was really having trouble getting to understand how all different phenomena worked together.

To think it was all only a "phase" of the transfer phenomena... w goes into "unbound vapour" both w and p are transfered to the next grid and then the extra vapor "bounds back" into w.... and so on and so on.

You're right about the experimental influence of pore air itself, nevertheless, at some point, water vapour is diffusing from one pore to the other throught the air pore, that's why I was having trouble "not taking into account the pore air", but it's ok now

Thank you very much, it has gotten much clearer now.

Best regards,
Manexi