Coring and Core Analysis (Porosity Measurement)

Porosity Measurement

Measurement of Porosity

Porosity is a measure of the reservoir storage capacity. It is defined as the void volume (pore volume) of a sample divided by its bulk volume. It enters most equations as a fraction and is reported in core analysis studies as a percent. It varies from less than 10% to greater than 40% in sandstones and from 5% to 25% in limestones and dolomites. Porosity can be greater than 25% in some vuggy or moldic limestones or dolomites. In some diatomaceous earth deposits, porosities approach 65%. These high values are the result of pore space being present between the diatoms as well as the porosity found within the individual diatom skeletal structure.

 

Pores vary in size from microscopic ( Figure 1 ,Thin section of intergranular pore space) to vugs, caverns, or fractures normally introduced by secondary diagenetic processes ( Figure 2 , Thin section of core containing vugs) . A porous rock sample will have a measurable pore volume (PV), a measurable grain volume (GV), and a measurable bulk volume (BV). Two of these three variables must be measured or calculated in order to determine porosity. These three variables may be combined in different ways to furnish porosity. The measurement technique selected depends on the rock type analyzed and the time required to obtain the data. The following equations apply:

Percent porosity = (1)

Percent porosity = (2)

Percent porosity = (3)

Total pore space is defined as all pore space present in a rock sample, whether it exists as an isolated pore sealed by secondary cementation, or whether it is connected to other pores. Effective pore space is defined as the pore volume of interconnected pores. Only the latter contributes to production, but certain down hole logs sense total porosity. While both total and effective porosity exist as theoretical possibilities, practical experience has shown that differences between the two are normally of little concern. Most laboratory techniques sense effective porosity, but total porosity can be determined if the sample is broken down into grain size and a specialized technique employed.

Total and effective porosity have a different meaning in current log analysis and should not be confused with the definition given above. Total porosity is that which is available when bound water is removed from the clays present.

Boyle's Law Technique

The Boyle's law method of measuring porosity is a gas transfer technique that involves the compression of gas into the pores or the expansion of gas from the pores of a clean, dry sample. Either pore volume or grain volume may be determined, depending upon the instrumentation and procedures used. It is an accurate technique when performed properly; it is fairly rapid for the majority of samples encountered, and it yields cores that can be used for further testing. It is essential that the samples be clean and dry, otherwise you will obtain erroneously low porosity values.

BULK VOLUME: The measurement of bulk volume is critical when pore volume is being calculated from the difference between bulk volume and grain volume. A good technique utilizes Archimedes' principle of displacement.

One of two applications of this principle is typically used. The first application requires that the sample be saturated with a liquid and then weighed. The sample is then submerged in the same fluid, and its submerged weight taken. The bulk volume is the difference between the two weights divided by the density of the fluid with which the core is saturated and in which it is immersed. The second application also requires that the sample be saturated with water or other suitable liquid. Water is typically used, because it can be easily vaporized from the core after the test is complete.

After saturation, the sample is immersed in a small vessel of water previously placed on the laboratory scales. For this immersion, the core sample must be suspended and lowered into the water without touching the sides of the vessel. Two weights are taken: that of the vessel and water before the core sample is immersed, and that of the vessel, water, and sample afterwards. The weight difference is equal to the weight of the water displaced by the core sample. Because the density of water is 1.0 g/cm3, this weight difference in grams is numerically equal to the bulk volume of the core sample in cubic centimeters.

Another suitable technique involves immersing the sample in mercury and measuring the volume of mercury displaced, employing a mercury pump calibrated for plug size samples.

Bulk volume can also be determined by calipering the length and diameter of a core sample and then applying appropriate mathematical formulas. Generally, information developed by calipering is not sufficiently accurate to yield valid porosities when grain volume is to be subtracted to yield pore volume. In other cases the bulk volume is determined by a direct measure of the pore volume, and this is summed with a direct measure of the grain volume.

GRAIN VOLUME: Measurement of grain volume is easily completed using a type of Boyle's law apparatus illustrated in Figure 1 (Grain volume determination using Boyle's law porosimeter). A clean, dry sample is placed in a chamber of known volume. This chamber is isolated from the upstream pressure chamber, which is also of known volume. The upstream pressure chamber is charged to a pressure of approximately 100 psi (689 kPa) and then isolated. The connection between the pressure chamber and sample chamber is opened and gas expands into the sample chamber, causing a drop in the original reference pressure. If volumes of the pressure and sample chamber are known, the grain volume may be calculated by using the measured pressures and the equation shown beneath Figure 1.

Precautions are necessary to secure valid data when utilizing this technique. In rocks containing free carbon and clays, air molecules can be adsorbed on the mineral surfaces, and can produce an erroneous measurement of grain volume and porosity. This limitation is overcome by using helium gas in the laboratory apparatus. Helium has an extremely small molecule that rapidly penetrates small pores. It is inert and will not be adsorbed on the rock surfaces as air can be.

Another advantage of this laboratory approach is that grain volume determined during this measurement can be subsequently combined with measured weights on the sample to yield reliable grain density values. Incomplete cleaning and insufficient drying will yield erroneously low grain densities and erroneously high grain volumes.

PORE VOLUME: Pore volume is often determined indirectly by calculating the difference between measured values of bulk volume and grain volume. It can also be measured directly by using Boyle's law equations. In order to do this it is necessary to alter the sample holder from the configuration illustrated in Figure 1. The sample must be placed in a holder that has no void space around the periphery of the core and on the ends. An apparatus suitable for this measurement is referred to as a Hassler holder or a hydrostatic load cell. The hydrostatic load cell is illustrated in Figure 2
(Hydrostatic load cell for direct measurement of pore volume ).

Helium can be injected into the core through the end stems as illustrated, and the equation beneath can be modified to furnish the sample's pore space. Dead volume in the system is measured by substituting a solid metal plug for the core plug. The sample is then inserted. It is essential that the end stems butt closely against the sample faces. If not, a dead volume not measured with the metal plug is created, which will yield an erroneously high pore space. The sample should have flat end surfaces at right angles to the axis of the core. The fact that some samples are less than perfect can be compensated for by placing a thin rubber pad (with a center hole) between the sample face and the metal end stem. The compressible rubber fills the space and allows calculation of valid data.

 

Parameter	Inadequate drying*	Properly dried
Porosity	6.7	7.8(+ 16.4%)
Grain density	2.62	2.64(+ .02 g/cm3)
Permeability	0.03	0.06 (+50%)

*These data were rushed for well completion and used successfully for that purpose. However, this information would not be adequate for estimating reserves.

Table 1. Example of errors in porosity, grain density, and permeability as a result of inadequate core drying

Measurements on cores that are not clean and dry yield values of pore space that are too small. Table 1 presents selected data measured on core samples that were rushed through the analysis without adequate time being allowed for core drying. These data were required within a short time for completion purposes, and, while adequate for that objective, would not be suitable for calculation of reserves-in-place.

Summation-of-Fluids Technique

Porosity determination by summation-of-fluids has been used extensively. The technique measures gas, oil, and water in the pore space of fresh core of known bulk volume. These volumes are summed to yield the pore volume and hence the porosity. This is the most rapid technique known, and, when it is used in suitable rock types with proper oil and water calibrations, it yields valid porosity values. The technique is well suited for routine laboratory work, and it allows porosity and saturations to be determined on the same sample.

The determination of porosity requires measurements on two portions of a core. One portion is approximately 100 g in weight, and is crushed to fragments approximately 1/4 inch (0.6 cm) in diameter. These are placed in a cylindrical metal holder with a cap on one end ( Figure 1 , Schematic of summation-of-fluids retort). Extending from the opposite end of the holder is a long, steel condensing tube, approximately 1/4 inch (0.6 cm) in diameter. Each sample holder contains material from a single sampled depth, and multiple sample holders are placed in a retort and heated simultaneously. Water and oil contained in the pores are vaporized, move down through the stainless steel tube, and are subsequently condensed into calibrated glassware. The volumes of oil and water are read and recorded for future calculations. A schematic of the retort is shown in Figure 1.

A second portion of rock weighing approximately 30 g is obtained by shaping a piece of core to a roughly cylindrical size. The sample is weighed and then placed in a device in which its bulk volume is determined by mercury displacement. The sample is then immersed in mercury and pressure on the mercury is raised to approximately 1000 psi (6895 kPa). At this pressure, mercury enters the sample and compresses the gas, filling the unoccupied pore space. With suitable calculations this furnishes the gas volume as a percent of the bulk volume of the sample.

Knowledge of the bulk volume and weight of the fresh sample into which mercury is injected allows computation of the natural density of the rock. This in turn is used to convert the 100 g to be retorted into an equivalent bulk volume. The oil, water, and gas volumes are each reported as a fraction of the bulk volume of the rock from which they came, and the three are summed to yield the porosity.

This is not a suitable technique for core samples that have been exposed to the atmosphere and in which residual oil and water have evaporated. Fresh cores contain residual oil and water in the finer pore spaces, and any injected mercury only fills the larger spaces occupied by gas. In cores in which all liquids have evaporated, the mercury will not penetrate the smaller gas-filled pores at the 1000 psi (6895 kPa) pressure imposed, and the resulting porosity value will be erroneously low.

OIL VOLUME DETERMINATION: The oil and water contents of a sample are determined by high-temperature retorting at temperatures of up to 1200º F (650 º C). Some oil is lost within the system because of coking and cracking of oil contained within the pore space. This results in an observed oil volume in the condensing glassware that is less than that actually present in the core. A correction is made to increase the observed oil volume prior to the calculation of a summation-of-fluids porosity. This correction is based on calibration curves that had been made previously using oils similar to those from the area from which the core was recovered. In those cases where no oil is available, a standard correction has generally proved adequate. The correction curve is essentially independent of the API gravity, primarily because of the high temperatures induced during the analysis. A typical oil correction curve is shown in Figure 2 (Retort oil correction curve).

 

WATER VOLUME DETERMINATION: During retorting, the recovered water volumes are read at a point that distinguishes pore water from mineral water of crystallization. A plot of water recovered from individual cores as a function of time is shown in Figure 3 (Retort water recovery versus time). These are cumulative-water-recovered curves and most are distinguished by a plateau that represents water held within the pore space by capillary forces. This is the water that is required in the summation-of-fluids analysis. A second plateau representing a greater water volume is termed "total water" in the analysis, and this represents pore water plus any water that has been contributed by adsorbed water or water molecules within clays. Pore water can be easily distinguished from mineral water of crystallization if no clays or other hydratable minerals are present. When clays are present, it is likely that some crystallization water will be included in the summation, and computed porosity and water saturation values will be too high. This error will be proportional to the percentage of clay in the core.

Hensel (1980) documented the idea that data could be improved if the water value were read after subjecting the cores to a temperature of 350ºF (193ºC) for a minimum of 30 minutes. This effectively extends the plateau, and improves the differentiation between capillary-held water and that formed by breakdown of minerals present.

Figure 4 (Summation-of-fluids porosity (water read at 350ºF/177ºC) versus Boyle's law
(helium) porosity) shows the difference in measured porosities between those obtained with Boyle's law procedure and those obtained in retorting when a constant temperature of 350ºF (193ºC) and a plateau technique were used to determine formation water volumes.

 

 

 

POROSITY: Validity of the summation-of-fluids technique can be roughly checked by a balance (Hensel 1980) to yield grain density as illustrated in the following equations:

(1)

(2)

and

Vg = Vb- (Vu + Vo + Vw) (3)

Where:

_w= rock grain density, g/cm3

_o= oil density, g/cm3

_g = water density, g/cm3 (assumed 1.00 for water collected)

W1= weight of crushed rock in retort less weight of contained fluids, g

W2 = weight of crushed rock in retort, g

V_g = grain volume, cm³

V_o = volume of oil collected, cm3 (corrected for vapor losses, coking, etc.)

V_w = volume of water collected, cm³

Vs = volume of unoccupied pore space, corrected based on retort sample weight, cm3

V_b = bulk volume of sample used to determine unoccupied pore space, corrected based on retort sample weight, cm³

Further verification is supplied by comparison of the summation porosities with a porosity value calculated via a Boyle's law procedure on adjacent plugs. This comparison requires that the plug used for Boyle's law be properly dried. Excessive drying will dehydrate clays and yield an erroneously high helium porosity that may agree with the erroneous summation data. When troublesome clays are encountered, combination analysis techniques using (1) oil and gas volumes developed from summation-of-fluids and (2) porosity from helium injection on a properly prepared core together will yield water saturation by difference calculations. Table 1, below, which presents data generated on a shaly, dirty sandstone, illustrates the error in porosity that is possible if rocks are improperly analyzed. The example quoted is an actual field case, but the magnitude of porosity differences shown here is unusually high. These rocks contained up to 30% montmorillonite, an amount not normally observed.

Combination Analysis*

Saturations, % Pore Space
Porosity	Oil	Water	Gas
34.0	45.8	33.8	20.4
36.4	47.3	30.2	22.5
28.2	53.5	27.7	18.8
34.9	51.0	28.7	20.3
37.9	60.2	25.3	14.5

Summation of Fluids Analysis**

Saturations, % Pore Space
(1)	(2)	(3)	(4)
Porosity	Oil	Water	Gas
43.4	34.2	48.4	17.4
44.1	39.2	42.4	18.4
35.8	42.3	43.1	14.6
40.3	44.2	38.2	17.6
47.9	47.7	40.9	11.4

* Correct technique.

** Technique was unsuitable for this rock which contained hydratable clays.

(1) Helium porosity on properly cleaned and humidity dried core at 145ºF and 45% humidity.

(2) Oil volume from summation of fluids divided by helium pore volume.

(3) Helium porosity (1) minus summation of fluids gas and oil as a % bulk volume.

(4) Gas volume from summation of fluids mercury injection divided by helium pore volume.

Table 1. A comparison of the results of combination analysis and summation-of-fluids analysis on cores containing hydratable clay.

Analysis of fractured shales containing gas or oil poses special problems. The retort temperature reached in the summation-of fluids analysis is sufficiently high to break down kerogen-like materials whose presence is indicated by dark oil recovery in the retort tube. If cores are selected from a known dry gas or condensate zone, the contribution of the kerogen material may be easily determined. If the matrix and/or fractures contain a dark oil, temperature control and a combination analysis with another technique is required, so that only the live oil is removed and no contribution of the kerogen is included. Oil from the kerogen material would not be recovered under normal producing practices, and inclusion of this material in the calculations will yield an erroneously high porosity in the laboratory analysis.

When a conventional core is analyzed, it is important that attention be paid to securing adjacent portions of rock to use for gas and liquid saturation determinations. Heterogeneous cores can have widely varying pore geometry in the adjacent pieces and, hence, yield erroneous porosity values. Plug samples are normally not used for heterogeneous rock, but, when necessary, this sampling problem can often be overcome with careful attention to sample selection.

Differential flushing of the core may create still another problem. If the sample used for gas measurement is taken from the inner portion of the core and the samples for liquid saturations are taken from a more highly flushed outer portion, the calculated porosity will be higher than the true value. Again, this can normally be overcome with proper sample selection procedures, but should be recognized as a potential source of error.

SIDEWALL CORE ANALYSIS: Most percussion sidewall cores are analyzed using the summation -of-fluids technique. Mercury is first injected into the core sample to yield gas space. The same sample is then retorted to yield oil and water saturations, using procedures previously described.

Resaturation Technique

The resaturation technique requires that the samples be clean and dry prior to measurement. A dry weight of the core is taken and the sample is then evacuated and pressure saturated with either water or a light hydrocarbon. The difference between the saturated and dry weights yields the grams of fluid in the pore space. Dividing this value by the density of the saturating fluid yields the pore volume. The procedure is slow and fairly difficult and requires that fluids used to saturate the rock wet, but do not react with, the rock surfaces. Incomplete resaturation will cause erroneously low porosity values. The advantages of this method include the possibility of using the samples for further testing, although the core must be recleaned if oil is used to saturate the rock. When done properly, the technique is accurate; however, the results are sensitive to preparation. The samples must be clean and dry prior to the initial weighing, otherwise an erroneously low porosity will be measured.

The resaturation method is commonly used as a quality control check in special core analysis tests, as many measurements require resaturation of core samples. Comparison of the resaturation-measured porosity with an originally measured Boyle's law value for the same sample pinpoints problem areas when the two do not agree.

 

 

Precision of Measurement

The Boyle's law, summation-of-fluids and resaturation techniques for porosity measurement have been accepted as yielding values accurate within ± 0.5 porosity points when the limits imposed on each method are properly observed.

In some cases — where the summation-of-fluids data have been found to yield high porosity values because of the presence of clays, and yet where information is required with rapid turnaround for completion or decision purposes — both summation and Boyle's law data have been determined. The summation-of-fluids data furnish rapid information for the completion decision. The plugs to be used for permeability measurements are cleaned, dried, and subsequently used for a Boyle's law porosity value comparison. This yields more accurate data for application in reservoir engineering calculations.

Overburden Pressure Effects

Rocks analyzed at surface conditions have usually been relieved of downhole confining pressures. Well-cemented, elastic rocks do not undergo any major change in volume when their environment is changed from reservoir to surface conditions. For this reason porosity is normally determined with minimal or no confining pressure. Unconsolidated and poorly consolidated rock, however, often expands when released from its natural confining stresses. Porosity should be measured on samples of this type under a confining pressure approximately equivalent to reservoir conditions.

A hydrostatic load cell used for simulating downhole stresses is shown in Figure 1 (Hydrostatic load cell for direct measurement of pore volume). The loading imposed on the core sample is referred to as hydrostatic pressure, or hydraulic loading, because pressures are equal in all directions. A schematic of reservoir loading on a core sample and the concept of net overburden pressure is shown in Figure 2 (Reservoir versus laboratory overburden pressure loading). The laboratory overburden pressure test simulates the net overburden pressure, which is the difference between the overburden pressure caused by the weight of sediments and the reservoir pressure. In the illustration presented, reservoir pressure is estimated to be the pressure related to a normal hydrostatic gradient and is approximately equal to 0.5 psi/ft (11.3 kPa/m) times the depth. When the actual reservoir pressure is known, it should be substituted in this equation,

Reservoir loading is thought to be essentially uniaxial, whereas the loading on the core sample in the laboratory is essentially equal in all directions. In well-indurated rocks this is observed in the laboratory to cause a reduction in pore volume believed to exceed that actually seen in the reservoir. Data presented by Swanson and Thomas (1980) indicate that in unconsolidated cores the application of hydrostatic loading adequately approximates reservoir loading. This conclusion was reached after long-term tests on carefully handled unconsolidated cores.

Figure 3 (Porosity reduction with net overburden pressure) illustrates the reduction in porosity observed for samples of varied levels of cementation. These curves exhibit typical shapes, in that the greatest rate of porosity reduction is typically seen at lower net overburden pressures. Pore space reduction with overburden is minimal in the well-cemented core and assumes more importance as one moves from friable to unconsolidated formations. This type of information is easily obtained in the laboratory.

A reduction in porosity with an increase in overburden pressure has also been observed in high porosity chalk formations. A reduction in pore space would be associated with a reduction in permeability and, hence, reduced formation productivity. Excessive deformation in chalks should supply reservoir energy to displace oil, but could also lead to casing collapse or related reservoir problems.

Exercise 1.

Given the following true values for a core sample:

BV = 12.45 cm3

GV = 9.89 cm3

Dry weight = 26.21 g

Calculate the porosity and specific gravity of the rock.

If, however, the value of bulk volume had been erroneously measured as 12.39 cm3 and the grain volume erroneously measured as 9.83, calculate the error in porosity and grain density that would obtain.

Estimate the errors on both an absolute and a percent basis.

Solution 1:

= 20.6%

GD = dry weight/grain volume

= 26.21/9.89

= 2.65 g/cm3

Erroneous BV = 12.39 cm3 (0.06 cm3 error low)

= 20.2% (error is 0.4 porosity points)

GD = = 2.65 g/cm3 (no error)

Erroneous GV = 9.83 (0.06 cm3 error low)

= 21.0% (error is 0.4 porosity points)

= 2.67 g/cm3 (0.02 g/cm3 error)

Exercise 2.

Given the following data for a core analysis, calculate the porosity and the saturations of oil, gas, and water.

Gas volume sample

1. Bulk volume: 15.34 cm³
   
2. Weight: 31.86 g
   
3. Gas vol: 1.56 cm³
   
4. Computed natural density = weight/BV = _______ g/cm³
   

Retort Sample

5. Weight: 125 g = W2

6. Bulk volume = Sample weight/natural density = Vb = ______cm³

7. Recovered oil 2.1 cm³

8. Corrected oil: 2.5 cm³ = Vo

9. Initial water: 8.3 cm³ = Vw

10. Final water: 9.2 cm³

11. Fluid densities:  = 0.85 g/cm³

=1.0 g/cm³

Solution 2:

Gas volume sample

1. Bulk volume: 15.34 cm³

2. Weight: 31.86 g

3. Gas vol: 1.56 cm³

4. Computed natural density = weight/BV = 2.08 g/cm³

Retort sample

5. Weight: 125 g = W2

6. Bulk volume = Sample weight/natural density = Vb = 60.1 cm³

7. Recovered oil 2.1 cm³

8. Corrected oil: 2.5 cm³ = Vo

9. Initial water: 8.3 cm³ = Vw

10. Final water: 9.2 cm³

11. Fluid densities:  = 0.85 g/cm³

=1.0 g/cm³

Porosity and saturations

O_B W_B G_B

12. Oil % BV + Water % BV + Gas % BV = Porosity fraction

(8) ÷ (6) + (9) ÷ (6) + (3) ÷ (1)

0.042 + 0.138 + 0.102 = 0.282

13. Porosity percent = porosity fraction x 100 = 28.2

14. Oil saturation % pore space = [(8) + (12) (6)] 100 = 14.8%

15. Water saturation % pore space = [(9) + (12) (6)] 100 = 49.0%

16. Gas saturation = 100 - 14.8 - 49.0 = 36.2%

Exercise 3.

Using the following data, calculate the grain density of the retort sample.

= grain density = grain weight/grain volume

Compare calculated grain density with expected grain density based on the lithologic description of the core and then decide—

Does the data appear to be accurate?

Why?

Gas volume sample

1. Bulk volume: 15.34 cm³

2. Weight: 31.86 g

3. Gas vol: 1.56 cm³

4. Computed natural density = weight/BV = 2.08 g/cm³

Retort sample

5. Weight: 125 g = W2

6. Bulk volume = Sample weight/natural density = Vb = 60.1 cm³

7. Recovered oil 2.1 cm³

8. Corrected oil: 2.5 cm³ = Vo

9. Initial water: 8.3 cm³ = Vw

10. Final water: 9.2 cm³

11. Fluid densities:  = 0.85 g/cm³

=1.0 g/cm³

Porosity and saturations

O_B W_B G_B

12. Oil % BV + Water % BV + Gas % BV = Porosity fraction

(8) ÷ (6) + (9) ÷ (6) + (3) ÷ (1)

0.042 + 0.138 + 0.102 = 0.282

13. Porosity percent = porosity fraction x 100 = 28.2

14. Oil saturation % pore space = [(8) + (12) (6)] 100 = 14.8%

15. Water saturation % pore space = [(9) + (12) (6)] 100 = 49.0%

16. Gas saturation = 100 - 14.8 - 49.0 = 36.2%

Solution 3:

= = grain density

W1 = W2 - [(Vo ) + (Vw)]
= 125 - [(2.5 0.85) + (8.3 1.0)]
= 114.58

Vg = Vb - [Vu + Vo + Vw]

Vu = (Vb) (GB)

Vg = Vb - [(Vb) (GB) Vo + Vw]
= 60.1 - [(60.1) (0.102) + 2.5 + 8.3]
= 43.17

Calculated grain density = = 2.65 g/cm3

Do the data appear to be accurate? Yes

Why? The calculated grain density is that of sandstone. It should be representative of the Jubilee sandstone.