The Preobrazjensky method for porosity determination is Russian Federation standard (regulatory approved) oilfield method for competent clastic rocks. As any other pycnometer method, it measures the open (connected) porosity.

It will not work in unconsolidated and fractured rocks.

The standard procedure is as following:

(1) The core plug left to vacuum-dry in an mildly warm oven (procedure for drying varies from lab to lab).

(2) A length of thin steel wire is attached around the plug. A little loop is made on the wire, allowing to hang the sample at the scales. A little kink is made on the wire above the plug.

(3) The plug surface is brushed gently to remove any loose grains.(4) The plug is suspended from the scales, and the weight Waa* is recorded.(5) The plug is suspended in the glass beaker filled with kerosene (paraffin oil) and set under a

vacuum dome. The vacuum (less than 5 mbar recommended) is pulled for at least 30 minutes, allowing kerosene to penetrate through the pores.

(6) Without removing the plug from the beaker, the loop is attached back to the scales. The wire is lowered to the beaker down to the kink, and the weight Wkk* is recorded.

(7) The beaker is removed, leaving the plug suspended from the scales. As soon as the kerosine film at surface becomes invisible, the weight Wka* is recorded.

(8) The sample is released from the wire loop, and the wire loop is suspended from the scales. This gives the measurement Wwa. Compute Wka = Wka* - Wwa and Waa = Waa* - Wwa.

(9) The wire loop is lowered back into the beaker down to the kink. This gives the measurement Wwk. Compute Wkk = Wkk* - Wwk.

(10) The beaker with kerosene is weighted on separate scales. The volume of kerosene in the beaker and it's weight (the weight of dry beaker is known) produce the kerosene density ρkerosene.

Steps (8), (9) and (10) slow the operations, but make the process more robust. The measurements (8) and (9) make the scales re-zero unnecessary as any systematic zero error is subtracted from itself. The mesurement (10) allows to control the density of kerosene which varies with temperature and uneven kerosene's components evaporation under the vacuum dome.

The acceptable lab shortcuts are as following:● Skip step (10) after every sample. Do it only once before and once after a batch of samples.

This is acceptable as soon as the lab is at constant temperature conditions, the beaker volume is large (1-2 liters) and the batch is not too large (ca 10 measurements, or 2-3 hours).

● Skip kinking the wire and step (9). Compute Wkk = Wkk* - 0.9 Wwa. Because the steel density is approximately 8.0 g/cm3 and kerosene density is 0.8 g/cm3, and the wire is reasonably light comparatively to the weight of the plug, this gives tolerable (very small) stochastic error.

● Weight several meters of wire and then cut it in pieces of the equal length (with precision of few mm). Compute Wwa and skip steps (8) and (9) all together. Assuming the wire diameter is constant (always the case if the wire is obtained from the right source) this will give tolerable stochastic error. The electronic scales with self-zero is a must in order not to make systematic errors.

● 10-12 dry samples are weighted one after another, then put in very large beaker and vacuum-saturated (step 5) all together. Then steps (6) and (7) are performed on each one of them (without making a pause between steps (6) and (7)!). This works fine as soon as the plugs are not disturbed from the beaker.

Shortcuts in the other steps (1) — (7) are not acceptable and will result is systematic errors.

The computation is performes as following. The set of three weightings is obtained as above:● Dry (air-saturated) sample in air: Waa

● Sample, saturated with kerosene, in air: Wka

● Sample, saturated with kerosene, in kerosene: Wkk

Then:

W aa=V⋅1−⋅ma−air (a)

W ka=V⋅1−⋅maV⋅⋅kerosene−V⋅air=V⋅ma−air −V⋅⋅ma−kerosene (b)

W kk=V⋅1−⋅ma−kerosene (c)

Where:φ — porosity, v/vV — plug volume, cm3

ρma — matrix density, g/cm3

ρkerosene — density of kerosene at lab conditions, measured as described above, g/cm3

ρair — density of air at lab conditions, take textbook value of 0.0012 g/cm3

From (a) and (b):

V⋅ma−air=W aa

1−(d)

V⋅ma−kerosene=W kk

1−(e)

Now insert (d) and (e) to (b) and solve for porosity:

W ka⋅1−=W aa−⋅W kk

=W ka−W aa

W ka−W kk(f)

Equations (d) and (e) together allow to eliminate both volume and porosity:

W aa

ma−air=

W kk

ma−kerosene

ma=W aa⋅kerosine−W kk⋅air

W aa−W kk(g)

In some cases, the Russian labs simplified the calculation (g), assuming the density of air to be

negligible. In such case, the density of air in (a)-(c) is replaced with zero, solution (f) does not change, but solution (g) is replaced with:

ma=W aa⋅kerosine

W aa−W kk(h)

Assuming the air density of kerosene at 0.800 and the density of air at 0.0012 g/cm3, the resulting systematic error is positive 0.003 g/cm3 and can be neglected, but with modern computation methods (Excel) there is no reason to substitute the formulas as the number of measurements is the same anyway!

The advantage of the Preobrazjensky method is that there is no need to determine the exact plug volume and that the porosity equation (f) does not require the knowledge of air and kerosene densities. The disadvantage is in relative difficulty in determining the kerosene-saturated weight in air Wka and that the matrix density is a function of kerosene density — which in turn rapidly changes with temperature. Another big disadvantage is that your hands and clothes will smell of kerosene whatever you do (Reference: Jerome K. Jerome, «Three Men in a Boat»). Liquids other than kerosene are sometimes used, including distilled water, but they do not produce the same accuracy as kerosene, because either of difficulty penetrating into the pores or too fast / too slow speed of evaporating from the plug's surface.

Being performed correctly, the method guarantees the absolute accuracy of 0.002 PU and 0.005 g/cm3

(for any reasonable core samples).

From the formulas above it is evident that if Wka contains a systematic error, the result of formula (f) will be systematically wrong. Unfortunately, the step (7) in the procedure is quite tricky to perform. After lifting the sample brom the beaker, the kerosene starts evaporating. If too little time is allowed, the thin film of kerosene is left on the sample's surface, making it marginally heavier. If too much time is allowed, some pores will be free of kerosene, resulting in too low weight. Thus, one must catch the exact moment than the film outside the sample has already evaporated but the kerosene in the surface pores has not started evaporating yet. The technician observes the sample's surface and takes the measurement as soon as the kerosene film on surface «becomes invisible». The term «becomes invisible», naturally, varies from technician to technician and from lab to lab. For the typical core plug size: 24 mm in diameter, 70 mm in length, the surface area is 62 cm2. Considering 0.1 mm kerosene film is barely visible for some people, the mass of kerosene left at surface can be as high as 0.5 g (compare with 30 g core plug weight). This results in systematic positive porosity error of up to 1.3-2.0 PU (the error is higher for low-porosity plugs), but no additional error in matrix density determination, as formulas (g) or (h) do not depend on Wka . The smaller the plug volume, the bigger the porosity error («square-cube» law at work). It is recommended that the same technician performs the steps (6) and (7), preferably at the same lightning conditions at all times.

Another source of systematic errors is the sample vacuum-drying istep (1). Naturally, the porosity measurement depends on drying procedures and varies from lab to lab. The effects of drying include: incomplete drying, resulting in systematically lower porosity and lower matrix density, and clay alteration. The latter effect is outside the scope of this paper.

The unacceptable lab shortcuts are as following:● Performing step (4) ahead of step (2), e.g. weighting the dried samples and only then attaching

the wires. The effect varies depending on the rock type, and for very competent rocks could be negligible. For less consolidated rocks this usually results in systematic under-estimation of both porosity and matrix density.

● Any shortcuts in step (5), such as: not using vacuum dome, pulling insufficient vacuum, not allowing sufficient time for kerosene to penetrate sample, etc. will inevitably result in incomplete kerosene penetration and large stochastic errors. The effect is usually more pronounced in rocks with small pores.

● Ignoring the effect of the steel wire and taking: Waa = Waa*, Wka = Wka*, Wkk = Wkk*. With the electronic self-zero scales available, this results in systematic matrix density error of positive 0.002-0.003 g/cm3 (typically 0.10 g for 40 cm length of 0.2 mm steel wire, compared to ca 30 g typical sample weight). If the scales are of older type — does not have the self-zero capability, an unpredicted large stochastic error in matrix density will result! The smaller the plug volume, the bigger the error. Fortunately enough, this shortcut has little to no effect on the porosity equation (f) as nearly the same offset weight is added and subtracted above and below the division line.

● Saturating the samples (step 5) in one beaker, but performing the measurement (step 6) in another beaker. The properties of kerosene vary in time and with temperature, so this will result is perhaps very large (up to plus or minus 0.5PU and 0.03 g/cm3) stochastic errors on porosity and matrix density.

● Separating steps (6) and (7) in time, for reasons discussed above.● Ignoring density measurements on kerosene and taking textbook values will result is very varge

(up to plus or minus 0.06 g/cm3) systematic errors on matrix density, but does not affect porosity. The error is independent of the plug volume. Sometimes this last error is tolerated, presuming that the core porosity is the primary (very important to client) measurement and the matrix density is a secondary (far less important) measurement. In such cases, the resulting matrix density should be clearly marked: «reference only, assuming density of kerosene at xxx g/cm3».