Here are the two files, which I had mentioned before.

hello

In general, I think (depending on my experience) that porosity measurements is not accurate . so, the same samples of the same weight may be give different values of porosity using the same technique. But we can optimize our test or fix so many factors that can affect the value of porosity such as weight of sample (as you mentioned above), presence of  impurities, the form of material or samples (Rigid or powder), temperature, personal error, instrumental error, amount of moisture in the samples, roughness of the surface for solid rigid samples, exposed total surface area...ect. if you have the same problem you can take results from the more accurate technique. 

Wild guess: You are forcing a liquid into pores within a material. It is possible that there is a region that is relatively closed off. It is also possible that the fluid just happened find a path of least resistance and didn't fill all the gaps. Of course if this were the case, then you should expect a higher than expected variance in the replicates. It would also be important to always test samples of the same size. The chance that you create an air pocket is proportional to the size of the sample.

I would think that all of this was corrected for in some way. Maybe placing samples in vacuum? That is my wild guess.

Timothy's wild guess is right. You must check the wettability of water on allumina. Ifb water does't wet allumina you have problems.... Try to use some alcohol

I agree it could be a wetting problem. I usually perform density measurements, that are easier than open porosity extimation, but in any case I don't use water: I use m-xylene (be aware of hazards), that has a higher wettability.

Thank you for comments. Unfortunately, I still can't understand why the apparent porosity determined by hydrostatic weighing is ca. 2 times higher than that measured by mercury intrusion. Would the porosity determined by hydrostatic weighing be so high if water didn't  wet alumina? Maybe we use inappropriate settings of mercury intrusion porosimeter? Hg surface tension was set on 480.00 erg/cm² and Hg contact angle was set on 140.00o. As far as I have seen in scientific literature HW and MIP gave quite similar results of porosity.

There is limitation for porosity measurement by mercury intrusion porosimeter. Some small pores cannot be detected. At the same time, hydrostatic weighing method may give excessive weight gain due to the possible surface absorption of water molecules. It is hard to say which method is accurate. People usually compare the porosity of different samples with the same method.

I think you should try argon or nitrogen adsorption and/or small angle X-ray and/or Neutron scattering to compare the results obtained by mercury intrusion porosimetry

Mercury intrusion porosimetry is depends on shape of pores. As an example, if your material has bottle-neck type pores  result will be like all pores has size of neck and there are no bigger one. In some cases it can show there are no pores at all if bottle-neck is too small, but if you use Low T nitrogen/argon adsorption technique it will show that pores are exist.

Hello. A possible explanation for the huge diffrence you observed between the measured porosity is due to the pore size: MIP is not adapted to determine pore size over 100-200 microns (or close to this value), so you underestimated the porosity of your sample (because Hg flows directly into the pores without any pressure). If you have SEM images of your samples you can have an idea of the fraction of pores below and above this threshold. And I suppose the fraction of pores above 100-200 microns is significant.

My advice is to measure the MIP relationship between the pressure and apparent porosity. It seems to me you will find some interesting things for yourself concerning your MIP system...

My advice is to measure the MIP relationship between the pressure and apparent porosity. It seems to me you will find some interesting things for yourself concerning your MIP system...

My advice is to measure the MIP relationship between the pressure and apparent porosity. It seems to me you will find some interesting things for yourself concerning your MIP system...

My advice is to measure the MIP relationship between the pressure and apparent porosity. It seems to me you will find some interesting things for yourself concerning your MIP system...

It is true that porosity values can be difficult to determine accurately. In order to calculate porosity, any two of the following three values must be known/measured:

bulk volume (or density), true volume (or density), pore volume.

True density, that is the density of the solid phase) can be taken reasonably well from the literature, or from gas pycnometry if closed porosity is suspected.

Pore volume can be determined directly by imbibition of a wetting liquid (water or some organic) and determining the gain in mass.  The density of the fluid has to be known at the temperature of the test. Air entrapment is the usual problem, and so is best done inside a chamber that can be evacuated. Beware any liquid draining from the pores when it is removed for weighing. Using a none wetting liquid, i.e. mercury, requires pressure to force the mercury into the pores.  Modern mercury intrusion porosimeters working from very low initial pressures (i.e. subambient, less than 0.3 psia) can fill pore volumes from ~950 microns down to ~3.2nm (at 60,000 psi).

Very large pores ( >1mm) will be problematical for both wetting and non-wetting techniques.

Bulk volume of the sample is often the most difficult to determine accurately. If the piece is a regular geometric shape, gross dimensions can be used. But even a "cubic inch" is subject to quite large volumetric errors depending on how its measured.  A mere 1mm error in just one dimension (assuming perfect 25.4mm for the other two sides) gives a volume of 15.742cm3 versus a perfect 16.3871 cm3!! (4%). If the mercury porosimeter is used to determine the bulk volume one must be sure not to refill the sample cell (penetrometer) after the filling step. It is important to use the lowest filling pressure possible.

All of these issues are compounded by any heterogeneity of the sample. The porosity of the larger volume of sample may not be reproduced in a much smaller piece.

If you have bulk volume (or density) and pore volume, calculate the true density of the solid.  This is a "sanity check".  the computed value should be reasonable - close to what one would expect for the sample. If it is not, then one can doubt either the bulk volume or the pore volume determination.  So in this particular case, I would start with the literature (or gas pycnometric measured) true density, calculate bulk volume from the measured pore volume, and see if there is better agreement between the two methods now!  If so, this suggests that the bulk volumes are most likely the source of the disagreement.

I hope that helps.

As long as the measurement is performed correctly, the difference should be very small.

For one, Mercury porosimetry measures pore sizes between about 300 micrometer and 3.5 nanometer.

So, if you have pores outside of that range, they will not be recorded as porosity.

However, looking at the calculated density will tell you if you excluded pore on either end of the distribution.

Another factor could be compressibility. during mercury porosimetry pressures up to 60000psi (4000atm.) are applied and as such, your sample could be compressed (less likely with alumina, but possible with polymers).

I will add a file describing the technique later.

Here are the two files, which I had mentioned before.

Hello,

I don't know if this is relevant to your practical case, but the sampling method may introduce a bias in the actual pore composition.

In your case, can you have as many 1mm-pores in the 1g sample for MIP as in the average material? Intuitively, one could expect such large pores be under-represented in small samples.

Did you manage to check the representativity of the samples? (is the variance high amongst your MIP measurements for different samples of the same material?)

With Small Angle Neutron Scattering the closed porosity also can be senn

Thank you all for valuable comments. At first I'll try the suggestions of Mr. Martin A Thomas.

It would be interesting to get the porosity by the Archimedes method, through its submersion in water ...

If you are using a mercury porosimeter, perhaps the contact angle may need adjusting.  I generally use 140°