PETROLEUM ENGINEERING
LABORATORY WORKBOOK
Department of Petroleum Engineering
Curtin University
Semester 2, 2013
0 INTRODUCTIONKnowledge of petrophysical and hydrodynamic properties of reservoir rocks and basic
reservoir fluid properties are of fundamental importance to a petroleum engineer. Lab
analysis conducted on rock and fluid samples and well logging are the two major sources of
information when it comes to reservoir rock and fluid properties. While lab analysis is a
direct way to measure such properties, well logging is generally considered as an indirect
technique to gather information on the reservoir rock and fluid properties. Presented in this
unit (Petroleum Engineering Lab) are some details on a number of simple but effective
methods used to analysis rock and fluid properties and review the nature and quality of the
information that can be obtained from them.
0.1 Rock Samples (Cores)Cores are obtained during the drilling of a well by replacing the drill bit with a diamond
core bit and a core barrel. The core barrel is basically a hollow pipe receiving the continuous
rock cylinder, and the rock is inside the core barrel when brought to surface.
Continuous mechanical coring is a costly procedure due to:
The drill string must be pulled out of the hole to replace the normal bit by core bit and core barrel.
The coring operation itself is slow.
The recovery of rocks drilled is not complete.
A single core is usually not more than 9 m long, so extra trips out of hole are required.
Coring should therefore be detailed programmed, especially in production wells. In an
exploration well the coring cannot always be accurately planned due to lack of accurate
knowledge about the geological setting. Apart from normal coring operation during drilling,
small core-plugs may be taken after drilling the well through sidewall coring. In sidewall
coring a wireline-conveyed core gun is used, where a hollow cylindrical “bullet” is fired in to
the wall of the hole. These plugs are small and may be fractured and therefore usually are
not very valuable for reservoir engineers.
During drilling, the core becomes contaminated with drilling mud filtrate and the
reduction of pressure and temperature while bringing the core to surface results in gas
dissolution and further expansion of fluids. The fluid content of the core observed on the
surface cannot be used as a quantitative measure of saturation of oil, gas and water in the
reservoir. However, if water based mud is used the presence of oil in the core indicates that
the formation is oil bearing.
0.2 Fluid SamplesReservoir fluid samples may be taken either on the surface or underground within the
production interval. The surface fluid sampling can be performed on the wellhead if the
wellhead conditions allow single phase flow within the flow-line. One other more
frequently used surface sampling technique is sample collection from the separator. At the
separator gas and liquid samples are taken independently and then they are recombined
with appropriate ratios under in-situ reservoir conditions to obtained representative fluid
samples.
Underground or bottom-hole samples are taken using specially designed cells which are
lowered inside the production interval of the well and then representative fluid samples
can be taken.
0.3 Laboratory AnalysisWhen the so called whole-core arrives in the laboratory core-plugs are usually drilled
from it every 20-30 cm throughout the reservoir interval. All these plugs are analysed with
respect to porosity, permeability, saturation and lithology. This analysis is usually called
routine core analysis. The results from routine core analysis are used in interpretation and
evaluation of the reservoir. Presented in Table 0-1 is a list of data normally measured
during routine core analysis and example applications of these data.
Table 0-1 Routine core analysis and applications
Special core analysis (SCAL) includes several measurements with the main objective of
obtaining detailed information on the multiphase flow behaviour and reservoir rock-fluid
interactions. SCAL provides information on the distribution of oil, gas, and water in the
reservoir (capillary pressure data), residual oil saturation and multiphase flow
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 1
characteristics (relative permeabilities). Measurements of electrical and acoustic properties
are occasionally included in SCAL. Wettability analysis and lab based enhanced oil recovery
(EOR) investigations are also often part of SCAL. This information is mainly used during the
interpretation of well logs and also in computer based reservoir simulation models. The
special core analysis is normally performed at reservoir in-situ conditions of pressure and
temperature.
Table 0-2 presents a list of various SCAL analyses which are normally performed on
reservoir rock and fluid properties.
Table 0-2 SCAL core analysis and applications
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0.4 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 3
1 POROSITY
1.1 DefinitionsFrom the viewpoint of petroleum engineers, the two most important properties of a
reservoir rock are porosity and permeability. Porosity is a measure of storage capacity of a
reservoir. It is defined as the ratio of the pore volume to bulk volume, and is may be
expressed as either percentage or a fraction. In equation form:
1-1
Two types of porosity may be measured: total or absolute porosity and effective
porosity. Total porosity is the ratio of all the pore spaces in a rock to the bulk volume of the
rock (Equation 1-1).
Effective porosity Фe is the ratio of interconnected void spaces to the bulk volume
(Equation 1-2). Thus, only the effective porosity contains fluids that can be produced from
wells. For granular materials such as sandstone, the effective porosity may approach the
total porosity, however, for shales and for highly cemented or vugular rocks such as some
limestones, large variations may exist between effective and total porosity.
1-2
Porosity may be classified according to its origin as either primary or secondary. Primary
or original porosity is developed during deposition of the sediment. Secondary porosity is
caused by some geologic process subsequent to formation of the deposit. These changes in
the original pore spaces may be created by ground stresses, water movement, or various
types of geological activities after the original sediments were deposited.
Fracturing or formation of solution cavities often will increase the original porosity of the
rock.
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Figure 1-1 Cubic packing (a), rhombohedral (b), cubic packing with two grain sizes
For a uniform rock grain size, porosity is independent of the size of the grains. A
maximum theoretical porosity of 48% is achieved with cubic packing of spherical grains, as
shown in Figure 1-1a. Rhombohedral packing, which is more representative of reservoir
conditions, is shown in Figure 1-1b; the porosity for this packing is 26%. If a second, smaller
size of spherical grains is introduced into cubic packing (Fig. 1c), the porosity decreases
from 48% to 14%. Thus, porosity is dependent on the grain size distribution and the
arrangement of the grains, as well as the amount of cementing materials. Not all grains are
spherical, and grain shape also influences porosity. A typical reservoir sand is illustrated in
Figure 1-1d.
1.2 Effect of Compaction on PorosityCompaction is the process of volume reduction due to an externally applied pressure.
For extreme compaction pressures, all materials show some irreversible change in porosity.
This is due to distortion and crushing of the grain or matrix elements of the materials, and
in some cases, recrystallization. The variation of porosity with change in pressure can be
represented by:
1-3
Where Ф2 and Ф1 are porosities at pressure P2 and P1 respectively, and Cf is formation
compressibility. Formation compressibility is defined as summation of both grain and pore
compressibility. For most petroleum reservoirs, grain compressibility is considered to be
negligible. Formation compressibility can be expressed as:
1-4
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Where dP is change in reservoir pressure. For porous rocks, the compressibility depends
explicitly on porosity.
1.3 Porosity Measurements on Core-PlugsFrom the definition of porosity, it is evident that the porosity of a sample of porous
material can be determined by measuring any two of the three quantities: Bulk volume,
pore volume or grain volume. The porosity of reservoir rock may be determined by:
- Core analysis
- Well logging technique
- Well testing
The question of which source of porosity data is most reliable cannot be answered
without reference to a specific interpretation problem. These techniques can all give
correct porosity values under favourable conditions. The core analysis porosity
determination has the advantage that no assumption needs to be made as to mineral
composition, borehole effects, etc. However, since the volume of the core is less than the
rock volume which is investigated by a logging device, porosity values derived from logs are
frequently more accurate in heterogeneous reservoirs.
In the following sections we will discuss how to estimate pore-, grain-, and bulk-volumes
from core plugs.
1.4 Bulk Volume MeasurementAlthough the bulk volume may be computed from measurements of the dimensions of a
uniformly shaped sample, the usual procedure utilises the observation of the volume of
fluid displaced by the sample. The fluid displaced by a sample can be observed either
volumetrically or gravimetrically. In either procedure it is necessary to prevent the fluid
penetration into the pore space of the rock. This can be accomplished (1) by coating the
sample with paraffin or a similar substance, (2) by saturating the core with the fluid into
which it is to be immersed, or (3) by using mercury.
Gravimetric determinations of bulk volume can be accomplished by observing the loss in
weight of the sample when immersed in a fluid or by change in weight of a pycnometer
with and without the core sample.
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1.5 Pore Volume MeasurementAll the methods measuring pore volume yield effective porosity. The methods are based
on either the extraction of a fluid from the rock or the introduction of a fluid into the pore
spaces of the rock.
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. 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.
For pore volume measurement using Boyle’s law 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.
Helium can be injected into the core through valve 2 as illustrated in Figure 2-2, and
using the following equations the sample's pore space could be measured:
PRVR=Pe(VR+Vp) 1-5
Where:
PR: Reference cell pressure,
Pe: Equilibrium pressure,
VR: Reference cell volume,
Vp: Pore volume
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Figure 1-2: Schematic diagram of helium porosimeter used for measuring pore volume.
The reason for using helium during the experiment over other gases is that helium has
tiny molecules and combined with its high diffusivity can penetrate even the smallest pores
of the sample easily and quickly. Helium is also non-toxic and non-reactive with the sample,
so it is considered non-damaging to the sample during the measurements.
The second method to measure the samples pore volume is using a saturation technique.
The weight of a dry sample is measured first and then it is immersed in brine solution with a
known salinity value in a container which could be effectively vacuumed. The salinity of the
brine needs to be known as it is required to calculate its density. After every 24 hours the
sample needs to be removed from the vacuum container and weighed. The weight of the
sample would keep increasing until it becomes constant and does not change anymore by
keeping it immersed in brine. The difference between the weight of the dry and the fully
brine-saturated sample is equal to the weight of the water which has gone into the sample
occupying the interconnected pores. Knowing the density of the brine the volume of the
brine present inside the sample can be calculated which would be equal to the sample pore
volume. The porosity measurement using the saturation technique is extremely time-
consuming compared to the helium technique using which could take as short as 5 minutes
to measure a sample’s porosity.
When a rock has a small fraction of void space, it is difficult to measure porosity by the
mentioned methods. In this case, mercury injection is used. The method consists of forcing
mercury under relatively high pressure in the rock pores. A pressure gauge is attached to
the cylinder for reading pressure under which measuring fluid is forced into the pores. The
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volume of mercury entering the core sample is obtained from the device with accuracy up
to 0.01 cm3.
1.6 Grain Volume MeasurementThe grain volume of pore samples is sometimes calculated from sample weight and
knowledge of average density. Formations of varying lithology and, hence, grain density
limit the applicability of this method. Boyle’s law is often employed with helium as the gas
to determine grain volume. The technique is fairly rapid, and is valid on clean and dry
sample.
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. 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. The measurement of
the grain volume of a core sample may also be based on the loss in weight of a saturated
sample plunged in a liquid.
Grain volume may be measured by crushing a dry and clean core sample. The volume of
crushed sample is then determined by (either pycnometer or) immersing in a suitable
liquid.
1.7 Experiments
1.7.1 Effective Porosity Determination by Helium Porosimeter
Method
I. Description
The helium porosimeter uses the principle of gas expansion, as described by Boyle’s law.
A known volume (reference cell volume) of helium gas, at a predetermined pressure, is
isothermally expanded into a sample chamber. After expansion, the resulted equilibrium
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pressure is measured. This pressure depends on the volume of the sample chamber minus
the rock grain volume, and then the porosity can be calculated.
II. Procedure
The core plug should have already been dried out in the oven.
Measure the dimensions of the sample. To do this, measure the diameter of the sample
at five spots along the length of the sample and take an average of all five
measurements. Do the same for sample length.
Using the instrument’s air gun clean the outside of the sample.
Verify that the Helium Porosimeter core-holder is not under pressure. The “Confining
Pressure” gauge should show a negative value. To make sure there is no pressure
applied to the core, perform the “load/unload” command once.
Then, first slightly unscrew and lift the top end plug of the core-holder by pulling back
the locking feature and then while being careful not to drop the sample which may be
already inside core-holder, unscrew and open the bottom end plug and remove the
sample.
Put the new sample inside the core holder and finger tight the bottom part. Then pull
back the locking feature and lower the top part and again finger tight.
Add your core sample data into the apparatus software. This is done by clicking on the
small yellow button on top-left of the main window. Then close the sample data
window and click on “Porosity-Permeability” button on the bottom of the main window
click start. This button is greyed out if there is no sample data added to the software.
Choose your sample from the list which appears and enter the number of confining
pressure tests you want to have. Start with 500 psi then 1000 psi and two
measurements under the final pressure (i.e. 2000 psi). In this window you have the
option of measuring the permeability as well but for this experiment remove the ticks
next to permeability and choose the porosity only.
When the end of measurements is indicated by the software, release and unload the
sample. Follow the procedure explained in steps and .
Repeat these steps for the next samples.
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At the start and very 2-3 measurements one test should be run using a 1.5” standard steel
sample to verify that the apparatus is calibrated. If you find the instrument inaccurate
please talk to one of your lab instructors.
III. Calculations and report
- For each sample, tabulate the porosity data under different confining pressures
and discuss the effect of different confining pressures on the porosity. Do you see
any trend apparent among the data for each sample?
- Calculate the formation compressibility for each individual sample and for each
pressure interval.
1.7.2 Porosity Determination by Liquid Saturating Method
I. Description:
The determination of the effective liquid porosity of a porous plug is the initial part of
the measurement of capillary pressure using porous plate method in core laboratories.
Before the capillary pressure is determined the volume of the saturating liquid (brine or oil)
in the core must be known. Thus, the effective liquid porosity of the core can be calculated
in the beginning of capillary pressure measurement.
II. Procedure
Weigh a dry core plug, Wdry, measure its diameter D, and length L using a calliper.
Prepare 0.5 litres of 20,000 ppm by weight brine using NaCl.
Put the core in the beaker filled with brine and then transfer the beaker into a
desiccator connected to a vacuum pump and run vacuum pump for about 30 minutes.
Weigh the saturated core, Wsat1.
Repeat steps 3 and 4 for the 2nd time, Wsat2.
Repeat steps 3 and 4 for the 3rd time but this time leave the sample under vacuum for
24 hours, Wsat-final.
Remove the sample from the beaker and leave it inside the oven to dry out.
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III. Calculations and Report
- For each weight measurement step calculate the saturated brine weight, Wbrine = Wsat –
Wdry. Any trend apparent among the data? Why?
- Calculate the portion of the pore volume saturated with brine for each weight
measurement step, V= Wsat / ρbrine.
- Calculate effective porosity, φe = Vp/Vb.
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1.8 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory
work book, Department of Petroleum engineering and Applied Geophysics,
Norwegian University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing,
Elsevier, Burlington, Massachusetts.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 13
2 CLEANING AND SATURATION DETERMINATION
2.1 DefinitionsBefore measuring porosity and permeability, the core samples must be cleaned of
residual fluids and thoroughly dried. The cleaning process may also be part of fluid
saturation determination. Fluid saturation is defined as the ratio of the volume of fluid in a
given core sample to the pore volume of the sample.
2-6
2-7
where Vw, Vo, Vg and Vp are water, oil, gas and pore volumes respectively and Sw, So and Sg
are water, oil and gas saturations.
Note that fluid saturation may be reported either as a fraction of total porosity or as a
fraction of effective porosity. Since fluid in pore spaces that are not interconnected cannot
be produced from a well, the saturations are more meaningful if expressed on the basis of
effective porosity. After cleaning a sample, the weight of any water extracted from the
sample is calculated using volume of water by the relationship
2-8
where ρw is water density in g/cm3.
Similarly, the weight of oil removed from the core may be computed as the weight of
removed liquid less weight of water.
2-9
where WL is the total weight of liquids removed from the core sample in grams.
Oil volume may then be calculated as Wo/ρo. Pore volume Vp is determined by a porosity
measurement, and oil and water saturation may be calculated by Equation 2-6. Gas
saturation can be determined using Equation 2-7.
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2.2 Measurement Methods
2.2.1 Direct Injection of Solvent
The solvent is injected into the sample in a continuous process. The sample is held in a
rubber sleeve thus forcing the flow to be uniaxial.
2.2.2 Centrifuge Flushing
A centrifuge which has been fitted with a special head sprays warm solvent onto the
sample. The centrifugal force then moves the solvent through the sample. The used solvent
can be collected and recycled.
2.2.3 Gas Driven Solvent Extraction
The sample is placed in a pressurized atmosphere of solvent containing dissolved gas.
The solvent fills the pores of sample. When the pressure is decreased, the gas comes out of
solution, expands, and drives fluids out of the rock pore space. This process can be
repeated as many times as necessary.
2.2.4 Soxhlet Extraction
A Soxhlet extraction apparatus is the most common method for cleaning sample, and is
routinely used by most laboratories. As shown in Figure 2-2a, toluene is brought to a slow
boil in a lab flask; its vapours move upwards and the core becomes engulfed in the toluene
vapors (at approximately 110 ᵒC). Eventually the water within the core sample in the
thimble will be vaporized. The toluene and water vapours enter the inner chamber of the
condenser; the cold water circulating about the inner chamber condenses both vapours to
immiscible liquids. Recondensed toluene together with liquid water falls from the base of
the condenser onto the core sample in the thimble; the toluene soaks the core sample and
dissolves any oil with which it come into contact. When the liquid level within the Soxhlet
tube reaches the top of the siphon tube arrangement, the liquids within the Soxhlet tube
are automatically emptied by a siphon effect and flow into the boiling flask. The toluene is
then ready to start another cycle.
A complete extraction may take several days to several weeks in the case of low API
gravity crude or presence of heavy residual hydrocarbon deposit within the core. Low
permeability rock may also require a long extraction time.
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Figure 2-2 Schematic diagram of Soxhlet (a) and Dean- Stark (b) apparatus
2.2.5 Vacuum Distillation
The oil and water content of cores may be determined by this method. As shown in
Figure 2-3, a sample is placed within a leak-proof vacuum system and heated to a maximum
temperature of 230 ᵒC. Liquids within the sample are vaporized and passed through a
condensing column that is cooled by liquid nitrogen.
Figure 2-3 Vacuum distillation Apparatus
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Core
Trap
2.3 Comparison of Various techniquesThe direct-injection method is effective, but slow. The method of flushing by using
centrifuge is limited to plug-sized samples. The samples also must have sufficient
mechanical strength to withstand the stress imposed by centrifuging. However, the
procedure is fast. The gas driven-extraction method is slow. The disadvantage here is that it
is not suitable for poorly consolidated samples or chalky limestones. The distillation in a
Soxhlet apparatus is slow, but is gentle on the samples. The procedure is simple and very
accurate water content determination can be made. Vacuum distillation is often used for
full diameter cores because the process is relatively rapid. Vacuum distillation is also
frequently used for poorly consolidated cores since the process does not damage the
sample. The oil and water values are measured directly and dependently of each other.
In each of these methods, the number of cycles or amount of solvent which must be
used depends on the nature of the hydrocarbons being removed and the solvent used.
Often, more than one solvent must be used to clean a sample. The solvents selected must
not react with the minerals in the core. The commonly used solvents are:
- Acetone
- Benzene
- Benzen-methol Alcohol
- Carbon-tetrachloride
- Chloroform
- Methylene Dichloride
- Mexane
- Naphtha
- Tetra Chloroethylene
- Toluene
- Trichloro Ethylene
- Xylene
Toluene and benzene are most frequently used to remove oil and methanol and water is
used to remove salt from interstitial or filtrate water. The cleaning procedures used are
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specifically important in special core analysis tests, as the cleaning itself may change
wettabilities.
The core sample is dried for the purpose of removing connate water from the pores, or
to remove solvents used in cleaning the cores. When hydratable minerals are present, the
drying procedure is critical since interstitial water must be removed without mineral
alteration. Drying is commonly performed in a regular oven or a vacuum oven at
temperatures between 50 ᵒC to 105 ᵒC. If problems with clay are expected, drying the
samples at 60 ᵒC and 40 % relative humidity will prevent any damage to the samples.
2.4 Experiments
2.4.1 Saturation Determination, Dean-Stark Distillation Method
I. Description:
The objective of the experiment is to determine the oil, water and gas saturation of a
core sample.
II. Procedure:
Fill 2/3 of the extraction flask with toluene. Also put a small volume of water at bottom of
the trap to increase the water level just reaching the graduated part of the trap so the
volume of any additional fluid entering the trap later can be read.
Take about 30 cm of Teflon tape. Remove the sample from the beaker and quickly weigh it
and tie the Teflon tape around the sample.
Put the wrapped sample inside the flask’s long neck using the long hook provided. Tighten
the ground joint fittings, but do not apply any lubricant for creating tighter joints. Start
circulating cold water in the condenser.
Turn on the heating jacket and adjust the rate of boiling so that the reflux from the
condenser is a few drops of solvent per second.
Continue the extraction for 10-15 hours.
Read the volume of collected water in the graduated tube. Turn off the heater and cooling
water and remove the sample from the apparatus and transfer it into the oven (100 ᵒC) and
set time to 12 hours.
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Once the sample is dry and cooled down obtain the weight of the core.
Calculate the loss in weight WL, of the core sample due to the removal of oil and water.
Measure the density of a separate sample of the oil.
Calculate the oil, water and gas saturations after the pore volume Vp of the sample is
determined.
III. Data and calculations
Sample No.: Porosity:
Where:
Worg: Initial weight of saturated sample
Wdry: Weight of clean and dry sample
IV. Equations
where D and L are diameter and length of the core sample, respectively.
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2.5 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory
work book, Department of Petroleum engineering and Applied Geophysics,
Norwegian University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing,
Elsevier, Burlington, Massachusetts.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 20
3 LIQUID DENSITY
3.1 DefinitionsDensity (ρ) is defined as the mass of the fluid per unit volume. In general, it varies with
pressure and temperature. The dimension of density is kg/m3 in SI or lb/ft3 in the Filed units
system.
Specific gravity (ˠ) of a liquid is defined as the ratio of the density of a liquid to the
density of water both measured at standard conditions. The specific gravity of liquid in the
oil industry is often measured by some form of hydrometer that has its special scale. The
American Petroleum Institute (API) has adopted a hydrometer for oil lighter than water for
which the scale, referred to as the API scale, is:
3-1
0
Note: When reporting the density, the units of mass and volume used at the measured
temperature must be explicitly stated, e.g. grams per millilitre (cm 3) at T(ᵒC). The standard
reference temperature for international trade in petroleum and its products is 15 ᵒC (60 ᵒF),
but other reference temperatures may be used for other special purposes.
3.2 Measurement of DensityThe most commonly used methods for determining density or specific gravity of a liquid
are:
- Westphal balance
- Specific gravity balance (chain-o-matic)
- API hydrometer
- Pycnometer
- Bicapillary pycnometer.
The first two methods are based on the principle of Archimedes: A body immersed in a
liquid is buoyed up by a force equal to the weight of the liquid it displaces. A known volume
of the liquid to be tested is weighted by these methods.
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The API hydrometer is usually used for determining oil gravity in the oil field. When a
hydrometer is placed in oil, it will float with its axis vertical after it has displaced a mass of
oil equal to the mass of hydrometer (Figure 3-4a). The hydrometer can be used at
atmospheric pressure or at any other pressure in a pressure cylinder.
The pycnometer (Figure 3-4b) is an accurately made flask, which can be filled with a
known volume of liquid. The specific gravity of liquid is defined as the ratio of the weight of
a volume of the liquid to the weight of an equal volume of water at the same temperature.
Figure 3-4 Schematic diagram of hydrometer (a), pycnometer (b), and bicapillary pycnometer (c)
3.3 Experiments
3.3.1 Fluid density using the Pycnometer method
I. Description:
This method covers the determination of the density or relative density (specific gravity)
of crude petroleum and of petroleum products handled as liquids with vapour pressure 1.8
bar or less, e.g. stabilized crude oil, stabilized gasoline, naphthane, kerosines, gas oils,
lubricating oils, and non-waxy fuel oils.
II. Procedure
Thoroughly clean the pycnometer and stopper with a cleaning agent, rinse well with
distilled water. Finally rinse with acetone and dry.
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Weigh the clean, dry pycnometer with stopper at room temperature.
Fill the pycnometer with the liquid (e.g. oil, brine) at the same room temperature.
Put on the stopper and be sure there is no gas bubble inside and then dry the exterior
surface of the pycnometer by wiping with a lint-free cloth or paper.
Weigh the filled pycnometer.
Repeat the above steps for all the provided liquids
For each liquid perform the measurements twice and then take and average of the two.
III. Calculation and report
Calculate the liquid density and the average density based on your data.
Calculate the standard deviation (STD) for your measurements.
Calculate the specific gravity.
Error source analysis of the pycnometer method.
Fluid PycnometerMass (gr)
Pycnometer+liquid(gr)
Pycnometer Vol. (cm3)
Density(g/cm3)
Specific Gravity
Standard Deviation
IV. Equations
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3.4 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
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4 VISCOSITY
4.1 DefinitionsViscosity is defined as the internal resistance of fluid to flow. The basic equation of
deformation is given by
4-1
1
where is shear stress, is the shear rate defined as and µ is the viscosity.
The term can be defined as F/A where F is force required to keep the upper plate moving
at constant velocity v in the x-direction and A is area of the plate in contact with the fluid
(Figure 4-5). By fluid viscosity, the force is transmitted through the fluid to the lower plate
in such a way that the x-component of the fluid velocity linearly depends on the distance
from the lower plate.
Figure 4-5 Steady-state velocity profile of a fluid entrained between two flat surfaces
It is assumed that the fluid does not slip at the plate surface. Newtonian fluids, such as
water and gases, have shear-independent viscosity and the shear stress is proportional to
the shear rate (Figure 4-6).
In the oil industry viscosity generally is expressed in centipoise, cp (1 cp =10-3 Pa.s).
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 25
Figure 4-6 Shear stress vs. shear rate for a Newtonian fluid
4.2 Effect of Pressure and Temperature on ViscosityViscosity of fluids varies with pressure and temperature. For most fluids the viscosity is
rather sensitive to changes in temperature, but relatively insensitive to pressure until
relatively high pressures have been attained. The viscosity of liquids usually rises with
pressure at constant temperature. Water is an exception to this rule; its viscosity decreases
with increasing pressure at constant temperature. For most cases of practical interest,
however, the effect of pressure on the viscosity of liquids can be ignored.
Temperature has different effects on viscosity of liquids and gases. A decrease in
temperature causes the viscosity of a liquid to rise. It is worth noting that the liquid
viscosity increases with increasing molecular weight.
4.3 Methods for Measuring Viscosity
4.3.1 Capillary Type Viscometer
Viscosity of liquids is determined by instruments called viscosimeter or viscometer. One
type of viscometer for liquids is the Ostwald viscometer (Figure 4-7). In this viscometer, the
viscosity is calculated from the comparison of the times required for a given volume of the
tested liquids and of a reference liquid to flow through a given capillary tube under
specified initial head conditions. During the measurement the temperature of the liquid
should be kept constant by immersing the instrument in a temperature-controlled water
bath.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 26
Figure 4-7 Two types of Ostwald viscometers
In this method the Poiseuille’s law for a capillary tube with a laminar flow regime is
used.
4-1
2
where t is time required for a given volume of liquid V with density of ρ and viscosity of
µ to flow through the capillary tube of length l and radius r by means of pressure gradient
∆P.
The driving force ∆P at this instrument is ρgl. Then:
4-1
3
or:
4-1
4
The capillary constant is determined from a liquid with known viscosity.
4.3.2 Falling Ball Viscometer
Another instrument commonly used for determining viscosity of a liquid is the falling (or
rolling) ball viscometer (Figure 4-8), which is based on Stoke’s law for a sphere falling in a
fluid under effect of gravity. A polished steel ball is dropped into a glass tube of a
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 27
somewhat larger diameter containing the liquid, and the time required for the ball to
fall at constant velocity through a specified distance between reference marks is
recorded.
The following equation is used
4-1
5
where: µ= absolute viscosity, cp
t = falling time, sec
ρb = density of the ball, g/cm3
ρf = density of fluid at measuring temperature, g/cm3
K = ball constant.
Figure 4-8 Schematic diagram of the falling ball viscometer
The rolling ball viscometer will give good results as long as the fluid flow in the tube
remains in the laminar range. In some instruments of this type both pressure and
temperature may be controlled.
4.3.3 Rotational Viscometer
Other frequently used viscometers especially for non-Newtonian fluids are the
rotational type consisting of two concentric cylinders, with the annulus containing the
liquid whose viscosity is to be measured (Figure 4-9). Either the outer cylinder or the inner
one is rotated at a constant speed, and the rotational deflection of the cylinder becomes a
measure of the liquid’s viscosity.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 28
Figure 4-9 Schematic diagram of the rotational viscometer
When the distance between the cylinders d, is small, we can define the viscosity
gradient for laminar flow regime as:
4-1
6
where R is radius of the inner cylinder and is angular velocity of the outer cylinder
(rotor) defined by . When the rotor is rotating at a constant angular velocity and the inner cylinder is held motionless, the torque from the torsion spring on the inner
cylinder must be equal but opposite in direction to the torque on the rotor applied from
the motor. The effective area of the applied torque is 2.R.h where h is length of the
cylinder. The viscous drag on the inner cylinder is k.θ.R, where k is the torsion constant of
the spring and θ is angular displacement of the instrument in degrees. Then:
4-1
7
which gives:
4-1
8
where K is the instrument’s constant which is determined by calibration.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 29
Inner cylinder
4.4 Experiments
4.4.1 Liquid Viscosity Measurement using Capillary Type
Viscometer
I. Description
The main objective of the measurement is to determine the kinematic viscosity of
Newtonian liquid petroleum products.
For capillary viscometers the time is measured in seconds for a fixed volume of liquid to
flow under gravity through the capillary at a closely controlled temperature. The kinematic
viscosity is the product of the measured flow time and the calibration constant of the
viscometer. The dynamic viscosity can be obtained by multiplying the measured kinematic
viscosity by the density of the liquid.
II. Definitions
Dynamic viscosity (µ) is the ratio between the applied shear stress and the rate of shear
and is called coefficient of dynamic viscosity µ. This coefficient is thus a measure of the
resistance to flow of the liquid; it is commonly called the viscosity of the liquid.
Kinematic viscosity ( ) is the ratio µ/ρ where ρ is fluid density.
III. Units and dimensions
Where:
cSt = centistokes, cp = centipoise
1cp = 10-3 Pa.s, 1cSt = 10-6 [m2/s]
IV. Procedure
IMPORTANT: make sure you use the right viscometer for the right fluid as directed by
your lab instructor. If not sure about anything ask the lab instructors for advice.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 30
Select a clean, dry calibrated viscometer (Figure 4-10) having a range covering the
estimated viscosity (i.e. a wide capillary for a very viscous liquid and a narrower capillary for
a less viscous liquid).
Charge the viscometer: To fill, turn viscometer upside down. Dip tube (2) into the liquid to
be measured while applying suction to tube (1) until liquid reaches mark (8). After inverting
to normal measuring position, close tube (2) with the rubber stopper before liquid reach
mark (3).
Allow the charged viscometer to remain long enough to reach the room temperature. Read
the calibration constants-directly from the viscometer or its documentations.
Measuring operation: Open tube (1) and measure the time it takes the liquid to rise from
mark (3) to mark (5). Measuring the time for rising from mark (5) to mark (7) allows
viscosity measurement to be repeated to check the first measurement.
If two measurements agree within required error (generally 0.2-0.35%), use the average for
calculating the reported kinematic viscosity.
Figure 4-10 Capillary viscometer apparatus
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 31
4.5 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 32
5 Resistivity
5.1 DefinitionsPorous rocks are comprised of solid grains and void space. The solids, with the exception
of certain clay minerals, are non-conductors. Therefore, the electrical properties of a rock
sample depend on the geometry of the voids and the fluid with which those voids are filled.
The fluids of interest in petroleum reservoirs are oil, gas, and water. Oil and gas do not
conduct electricity. However, water is a conductor when it contains dissolved salts, such as
NaCl, MgCl2, KCl which are normally found in formation reservoir water. Current is
conducted in water by the movement of ions and can therefore be termed electrolytic
conduction.
The resistivity of a porous material is defined by:
5-1
9
where r = resistance, Ω
A = cross-sectional area, m2
L = length, m
and resistivity is expressed in Ohm-meter (Ω.m). However, for a complex material like
rock containing water and oil, the resistivity of the rock depends on the following factors:
- salinity of water
- temperature
- porosity
- pore geometry
- formation stress
- composition of rock.
As mentioned earlier the conductivity of a porous rock is primarily due to the movement
of dissolved ions in the brine that fills the pore of the rock. The conductivity varies with
temperature due to the increased activity of the ions in solution as temperature increases.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 33
Due to the conductivity properties of reservoir formation water, the electrical well-log
technique is an important tool in the determination of water saturation versus depth and
thereby a reliable resource for in situ hydrocarbon evaluation.
The theory of the electrical resistivity log technique generally applied in petroleum
engineering was developed by Archie in 1942, the so called Archie’s equation. This
empirical equation was derived for clean water-wet sandstones over a reasonable range of
water saturation and porosities. In practice, Archie’s equation should be modified according
to the rock properties- such as clay contents, wettability, pore distribution, etc. The
following is a brief presentation of the main electrical properties of reservoir rocks and
related parameters.
Formation Factor: The most fundamental concept considering electrical properties of
rocks is the formation factor F, as defined by Archie:
5-2
0
where
Ro = the resistivity of the rock when saturated 100% with water, Ω.m
Rw = the water resistivity, Ω.m.
The formation factor defines a relationship between the resistivity of the water
saturated rock and the resistivity of the bulk water. Obviously, formation factor depends on
the pore structure of the rock.
Resistivity Index: The second fundamental notion of electrical properties of porous rocks
containing both water and hydrocarbons is the resistivity index I.
5-2
1
where
Rt= the resistivity of the rock when saturated partially with water, Ω.m
Ro = the resistivity of the same rock when saturated with 100% water, Ω.m.
Tortuosity: Wyllie (3) developed a relationship between the formation factor and other
properties of rocks- such as porosity, Ф, and tortuosity, . Tortuosity can be defined as
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 34
(La/L)2, where L is the length of the core and La represents the effective path length
through the pores. Based on simple pore models the following relationship can be derived:
5-2
2
where
F = formation factor
= tortuosity of the rock
Ф = porosity of the rock.
Cementation factor: Archie suggested a slightly different relationship between the
formation factor and porosity by introducing the cementation factor:
5-2
3
where
Ф = porosity of the rock
m = Archie’s cementation factor.
Archie reported that the cementation factor probably ranged from 1.8 to 2.0 for
consolidated sandstones and for clean unconsolidated sands was about 1.3.
Saturation Exponent: The well-known Archie’s equation establishes a relationship
between resistivity index and water saturation of rocks as follows:
5-2
4
where
Sw = water saturation
n = saturation exponent, ranging from 1.4 to 2.2 (n = 2.0 if no data is given).
In this equation, Rt and Ro can be obtained from well logging data, saturation exponent n
is experimentally determined in the lab. Therefore, the in situ water saturation can be
calculated using Archie’s equation. Based on the material balance equation for the
formation, i.e. Sw + So + Sg = 1.0, the in-situ hydrocarbon saturations may be calculated.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 35
5.2 Effect of Conductive SolidsThe clay minerals present in a natural rock act as a separate conductor and are
sometimes referred to as “conductive solids”. In reality, the water in the clay and the ions in
the water act as the conducting materials. Figure 5-11 shows variation of formation factor
versus water resistivity for clean and clayey sands. The effect of the clay on the resistivity of
the rock is dependent upon the amount, type and the distribution of the clay in the rock.
Figure 5-11 Apparent formation factor versus water resistivity for clayey and clean sands
The formation factor for clay-free sand is constant. The formation factor for clayey sand,
however, increases with decreasing water resistivity and approaches a constant value at a
water resistivity of about 0.1 Ω.m. The apparent formation factor, Fa, is calculated from the
definition of the formation factor and observed values of Roa and Rw (Fa = Roa/Rw). Wyllie (3)
proposed that the observed effect of clay minerals was similar to having two electrical
circuits in parallel, the conducting clay minerals and the water-filled pores. Thus:
5-2
5
where Roa is the resistivity of a shaly sand when 100% saturated with water of resistivity
Rw. Rc is the resistivity due to the clay minerals. FRw is the resistivity due to the saturating
water, and F is the true formation factor of the rock (the constant value when the rock
contains low-resistivity water).
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 36
Figure 5-12 Water-saturated rock conductivity as a function of water conductivity
Figure 5-13 Formation factor as a function of porosity.
The data presented in Figure 5-12 represent graphically the confirmation of the
relationship expressed in Equation 5-25. The plots are linear and are of the general form:
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 37
5-2
6
where C is the slope of the line and b is the intercept. Comparing Equation 5-25 with
Equation 5-26, it may be noted that C = 1/F and b = 1/Rc. The line for which b = 0 indicates
a clean sand, then:
5-2
7
Equation 5-25 can be rearranged to express the apparent formation factor in terms of Rc
and FRw:
5-28
As . Therefore Fa approaches F as a limit, as Rw becomes
small. This was observed in Figure 5-11.
5.3 Effect of Overburden PressureConfining or overburden pressure may cause a significant increase in resistivity. This
usually occurs in rocks which are not well cemented and in lower porosity rocks. Archie, as
mentioned earlier, reported results of correlating laboratory measurements of formation
factor with porosity in the form of:
5-29
Wyllie (3) investigated the influence of particle size and cementation factor on the
formation factor of a variety of materials. He concluded that the cemented aggregates
exhibit a greater change in formation factor with a change in porosity than the
unconsolidated aggregates. Therefore, the general form of the relation between formation
factor and porosity should be:
5-30
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 38
where m is a constant depending on cementation and a is another constant controlled by
the porosity of the unconsolidated matrix prior to cementation. A comparison of a number
of suggested relationships between porosity and formation factor is presented in Figure 5-
13.
5.4 Resistivity of Partially Water-Saturated RocksWhen oil and gas are present within a porous rock together with a certain amount of
formation water, its resistivity is larger than Ro. That is because there the volume of
conductive water available for the flow of electric current to pass through is less. This
volume is a function of the water saturation Sw. Equation 5-24 indicates that the resistivity
index is a function of water saturation and the pore channels. From the theoretical
development, the following generalization can be drawn:
5-31
where I = Rt/Ro is the resistivity index, C’ is parameter which is a function of tortuosity
and n is the saturation exponent. In Archie’s equation n is 2.0 and in Williams relationship
2.7 (Figure 5-14). All the equations fitted to the experimental data have assumed that both
C’ and n in Equation 5-31 were constants and furthermore C’ = 1.
Figure 5-14 Resistivity index versus water saturation
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 39
The generally accepted formulation which relates water saturations and true resistivity
Rt is that of Archie, which may be rewritten in the following form:
5-32
where a is merely a property of the rock and n is the saturation exponent, which in most
cases is assumed to be 2.0.
5.5 Experiments
5.5.1 Resistivity Measurements of Fluid-Saturated Rocks
I. Description
The objective of this experiment is to measure as many as possible of the main electrical
properties of porous rock like water resistivity, formation factor, tortuosity, cementation
factor, resistivity index and saturation exponent.
II. Procedure
Resistance measurements are performed using a LCR meter. The resistivity of the
sample can then be developed when the size of the sample is known.
III. Calculations and report
A) Calculate water resistivity, Rw:
Using the salinity of the brine provided (30,000 ppm NaCl) calculate the brine resistivity
from the Schlumberger chart booklet. Ask your lab instructor for the booklet.
B) Calculate formation factor, F and cementation factor, m:
Core ID Core D, m Core L, m rx, Ω Ro, Ωm Ф, fraction Cementation factor, m Formation factor, F
C) Calculate resistivity index, I, saturation exponent, n:
Core ID Core D, m Core L, m rx, Ω Rt, Ωm Ro, Ωm Swfraction Resistivity Index, I Saturation exponent, n
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 40
5.6 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
Wyllie M.R.J. and Spangler M.B.: “Application of Electrical Resistivity Measurements to
Problem of Fluid Flow in Porous Media”, Bull. AAPG, Feb. 1952, p. 359.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 41
6 PERMEABILITY
6.1 DefinitionPermeability is a property of the porous medium and it is a measure of capacity of the
medium to transmit fluids. Permeability is a tensor that in general is a function of pressure.
Usually, the pressure dependence is neglected in reservoir calculations, but the variation
with position can be pronounced. Very often the permeability varies by several magnitudes,
and such heterogeneity will of course influence oil recovery.
6.1.1 Darcy’s LawDarcy (1856) performed a series of experiments on the relationship affecting the
downward flow of water through sands. The generalised equation called Darcy’s law may
be written in the form:
6-33
where u is superficial velocity, k is permeability tensor, is fluid viscosity, P is pressure
gradient, is fluid density and g is gravitational vector. Writing flow velocity as the ratio of
volumetric rate to cross-sectional area perpendicular to flow q/A in distance L, Darcy’s law
can be expressed:
6-34
The dimensions of permeability can be established by substituting the units of the other
parameters in the equation. The unit Darcy results from the choice of cgs system units:
The permeability in SI system has dimension of m2.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 42
6.1.2 The Kozeny Equation
Kozeny (1927) made an attempt to systematically quantify the relationship between
porosity and permeability. He made a simplifying assumption that a porous rock could be
considered to consist of a bundle of capillary tubes of equal length. One such tube is shown
in Figure 6-15.
For this situation the Hagen-Poiseuille’s law describes laminar flow, which, for a single
tube, is:
6-35
where
r = tube radius
p = pressure drop across tube = viscosity of the fluid
L = length of tube
q = flow rate
L
rq
p
Figure 6-15 Flow through a Capillary
Comparing Equation 6-35 with Darcy’s law it can be seen that the effective permeability
of a (horizontal) tube is:
6-36
The porosity ( of a bundle of (n) capillaries whose ends occupy a surface area of (A) is
given by:
6-37
so that:
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 43
6-38
From Equation 6-35 the flow rate for n capillaries is:
6-39
which, if compared with Darcy’s law, gives:
6-40
implying that the permeability of a reservoir rock will depend on porosity and the square
of the pore throat size. This shows quite simply that permeability has the dimensions of [L]2.
This approach can be modified to allow for tortuosity, , of the real pore network, such
that the actual length of each capillary is , to give:
6-41
In order to progress further it is useful to introduce the concept of “specific surface”.
The specific surface, , is defined as the interstitial surface area of the pores per unit of bulk
volume.
The internal surface area, S, of n capillary tubes is simply:
6-42
and the bulk volume, Vb, is:
6-43
so that:
6-44
Substituting for n from Equation 6-38 gives:
6-45
and finally substituting for r from this equation into Equation 6-41 gives:
6-46
This is referred to as the Kozeny equation.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 44
In a more general form this equation becomes:
6-47
where ck is the Kozeny constant, which will depend on the geometrical form of the
situation.
For a simple, cubic arrangement of hard spheres, as depicted for touching spheres in
Figure 6-16, it can be shown that:
6-48
where r is the hard sphere radius and csc is the Kozeny constant for the simple cubic
structure.
Figure 6-16 Simple Cubic Structure
Attempts have been made to use the Kozeny equation for more complex geometries, for
example fractured systems. Permeability in fractured reservoirs is dominated by the small
amount of high conductivity pore space provided by the fracture. These complex structures
need to be simplified dramatically in order to make some progress in describing them
systematically. The idealised system is shown in Figure 6-17, where a is the block dimension
and w is the fracture width.
In this model the bulk volume will be of the order of a3 and the surface area exposed to
flow will be of the order of a2, hence the specific surface will scale as a-1. If it is assumed
that the matrix is impermeable then the fracture porosity of the model will be (a2w/a3 =)
w/a.
Substituting these values into the Kozeny equation gives:
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 45
6-49
a
w
Figure 6-17 Simplified Fracture Model
Obviously this is a gross simplification and assumes not only that the simple approach of
Kozeny applies but also that a representative average of a and w can be determined.
6.1.3 Klinkenberg Effect
Klinkenberg has reported variations in permeability determined by using gases as the
flowing fluid compared to those obtained when using non-reactive liquids. These variations
were considered to be due to slippage, a phenomenon well known with respect to gas flow
in capillary tubes. The phenomenon of gas slippage occurs when the diameter of the
capillary openings approach the mean free path of the gas. The mean free path of a gas is a
function of molecular size and the kinetic energy of the gas. Therefore, permeability of gas
depends on factors, which influence the mean free path, such as temperature, pressure and
the molecular size of the gas.
Figure 6-18 is a plot of the permeability of a porous medium as determined at various
mean pressures using three different gases. Note that for each gas a straight line is
obtained for the observed permeability as a function of the reciprocal of the mean pressure
of the test.
All the lines when extrapolated to infinite mean pressure (1/Pm=0) intercept the
permeability axis at a common point. This point is designated K L, or the equivalent liquid
permeability.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 46
Figure 6-18 Variation in gas permeability with mean pressure and type of gas
Klinkenberg has related apparent permeability ka measured for gas for an average
pressure Pm to the true permeability KL by:
6-50
Where b is a constant depending upon the average free movement of the molecule at
Pm:
6-51
Where r is channel radius and C’ 1.
6.2 Measurement of PermeabilityPermeability is measured by passing a fluid of known viscosity through a core sample of
measured dimensions and then measuring flow rate and pressure drop. Various techniques
are used for permeability measurements of cores, depending on sample dimensions and
shape, degree of consolidation, type of fluid used, ranges of confining and fluid pressure
applied, and range of permeability of the core. Two types of instruments are usually used in
the laboratory:
Unsteady-state permeameter
Steady-state permeameter
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 47
Permeability tests are performed on samples, which have been cleaned and dried, and a
gas (usually air) is used for flowing fluid in the test. This is because:
a. When required, steady state is obtained rapidly,
b. Dry air will not alter the minerals in the rock, and
c. 100% fluid saturation is easily obtained.
Measurement accuracy declines at two extremes of high and low permeability values
and is within 0.5% of true value otherwise.
6.2.1 Steady-state Permeameter
This equipment is designed for plug or whole core permeability measurements. This
experiment may be used for single or multiphase, compressible fluid or liquid
measurements and can also be used under reservoir pressure and temperature.
Figure 6-19 shows a diagram of a steady-state head permeameter. Air is usually used as
gas flow. Upstream and downstream pressures are measured by manometers on both sides
of the core and air flow is measured by means of a calibrated outlet. Air permeability can
then be calculated using Equation 6-52 which is another version of Darcy’s equation
applicable to gas flow. In this equation the gas flow is measured at atmospheric conditions,
thus Patm = 1 atm.
6-52
Hassler core holder may be used with this instrument. The Hassler system is an
improvement of the rubber plug system whose tightness is limited at certain pressures.
The core is placed in a flexible rubber tube (Fig. 3). The Hassler cell has these
advantages:
a. Excellent tightness.
b. Can be used for samples of different sizes.
c. Much higher pressure or _P can be used.
d. Can be used for measuring relative permeability.
Darcy’s equation may be used for determining permeability of liquids.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 48
Figure 6-19 Schematic diagram of permeameter
Figure 6-20 Hassler type core holder
6.2.2 Unsteady-state Permeameter
Pulse decay technique, or transient pulse method, is an unsteady-state permeability
measurement method which can give accurate results in very short period of time. In this
technique, a small pore pressure pulse (normally using a gas e.g. helium, nitrogen) is
applied to one end of a confined sample, and the pressure vs. time behaviour is observed as
the pore fluid moves through the sample from the sample’s upstream reservoir to a 2nd
reservoir located downstream of the sample. When a pressure pulse ΔP0 is applied, the
differential pressure ΔP(t) decays exponentially as a function of time, t:
ΔP = f(V1, V2, t, ΔP0, µ, L, A,) 6-53
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 49
bottom end plug and remove the sample.
Put the rock sample inside the core holder and finger tight the bottom part. Then lower the
top part and after engaging the locking feature again finger tight.
Click on the yellow button on top left hand side of the software main window and add your
core sample data into the apparatus’s sample database and then click close. Please note
that all sample dimensions have to be in centimetres.
Click on “Porosity-Permeability Measurement Button” located on bottom left hand side of
the software’s main window to start the test.
Choose your sample from the list that appears and choose 3 as the number of confining
pressure tests you want to do the measurements for. Then, input three pressures of 500
psi, 1000 psi and 2000 psi. In this window you have the option of measuring the
permeability as well as porosity. In this experiment our aim is to measure the permeability
of the sample but, as can be seen in Equation 6-53, the instrument requires a measure of
sample’s porosity values in order to calculate the permeability using the pules decay
technique. Therefore for each pressure tick both porosity and permeability to be measured
as part of the test.
When the end of measurements is indicated by the software, release and unload the
sample.
Repeat these steps for the next samples
At the start and very 4-5 measurements one test should be run using 1.5” standard
samples to verify that the apparatus is calibrated.
III. Calculations and report
Report the results of the permeability measurements for all the samples tested.
Make a plot of the pressure pulse decay vs. time. And discuss the apparent
trend in the data.
Describe the change in permeability vs. confining pressure.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 50
6.4 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 51
7 CAPILLARY PRESSURE
7.1 DefinitionsCapillary pressure is the force that causes a fluid to rise up a fine tube when one end of
the tube is immersed in a wetting fluid. Evaluating the capillary pressure of reservoir rocks
is important because capillarity controls the static distribution of fluids in the reservoir prior
to production and the distribution of the remaining hydrocarbons after primary production.
Figure 7-21 Capillary Pressure
Consider a capillary tube immersed in a water-gas system, as shown in Figure 7-21. The
capillary force is shown acting along the surface of the water, which forms the contact
angle,, with the wall of the tube. The force is proportional to the energy required to
maintain the interface between the water and oil. This is called interfacial tension, , for a
liquid-liquid interface, or surface tension for a liquid-gas interface, and has the units of
force per unit length. is also sometimes referred to as the specific free energy of the
interface.
The length over which this force is applied in a capillary tube is the circumference of a
circle of radius r. Thus the total capillary force is 2r and the vertical component of the
force is 2rcos. When this is expressed as a pressure, by dividing the total force by the
cross-sectional area, r, the following expression for the capillary pressure, Pc, is obtained.
Petroleum Engineering laboratoryPetroleum Engineering Department, Curtin University 52
7-54
This expression for the pressure difference across the surface of contact of two
immiscible fluids in a spherical capillary is a special form of Laplaces’s equation, Equation 7-
55, which considers a more general geometry.
7-55
In this equation rc1 and rc2 refer to the principal radii of curvature of the interface and
is sometimes referred to as the specific free energy of the interface, more commonly the
surface tension.
For the case of a capillary tube, rc1 and rc2 are equal, and by simple geometrical
considerations they are related to the radius of the capillary as follows:
7-56
Substituting this relationship into Equation 7-55 leads to Equation 7-54.
Equation 7-54 states that for a given wetting and non-wetting phase the capillary
pressure will depend inversely on the capillary radius. This is shown in Figure 7-22 where
the narrower the tube the higher the rise of the wetting phase.
As may be supposed from Figure 7-22, capillary pressure can also be calculated from the
height, h, the fluid rises above the free water level. The hydrostatic pressure equivalent of
the unbalanced column of fluid is equal to the capillary pressure. Based on the knowledge
that the pressure gradient for a column of pure water (density 62.43 lbs/ft3) is 0.434 psi/ft
and that the pressure gradient for a column of fluid of specific gravity, , is 0.434, it
follows that:
7-57
where is the difference in specific gravities between the wetting and non-wetting
phases. The situation is as depicted in Figure 7-23 where the wetting phase is taken to be
water and the non-wetting phase to be oil.
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Figure 7-22 Capillary Rise in a Series of Tubes
Figure 7-23 Capillary Pressure and Sub-surface Fluid Pressure Gradients
The term in Equation 7-57 is the difference in the specific gravities of the two fluids
(water and air for the situation depicted in Figure 7-21; water and oil for an oil reservoir). If
Equation 7-54 is equated to Equation 7-57 then:
7-58
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Hence, the height of the capillary rise is proportional to the interfacial tension and the
cosine of the wetting angle, and inversely proportional to the radius of the capillary and the
difference in the specific gravities of the wetting and non-wetting phase.
7.2 Drainage and Imbibition During an immiscible displacement procedure, depending on the wettability of the
reservoir rock and wether the wetting phase is displacing or being displaced the
displacement may be classified as either imbibition or drainage. By definition, imbibition is
the dynamic process by which the wetting phase is increasing e.g. displacement of oil by
water in a water-wet reservoir. Conversely drainage is the process by which the wetting
phase saturation is decreasing e.g. displacement of oil by water in an oil-wet reservoir.
It has been determined experimentally that the contact angle is larger when the wetting
phase is advancing over the rock face than when retreating, and this difference is described
as the hysteresis of the contact angle. This concept is important when measuring capillary
pressure and relative permeability. A hydrocarbon reservoir is initially formed under the
drainage process and the imbibition process takes over during production.
7.3 Converting Laboratory Data to Field DataFrom Equation 7-54 it follows that the capillary pressure measured in any given porous
system using a particular pair of fluids is related to that obtained with another pair of fluids
by the ratio “ cos ”. The same principle applies when relating the capillary pressure data
measured under a set of pressure and temperature (P-T) to that measured under a
different set of conditions. This can be shown quite simply by applying Equation 7-54 to
both systems.
where subscript 1 and 2 refer to fluid pair number 1 and 2 or P-T conditions number 1
and 2. Rearranging the above two equations in terms of r and then setting the equal gives:
7-59
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The values of interfacial tension, , and contact angle, , are known for a range of pairs
of fluids under different conditions, and typical values are given in Table 7-3.
Wetting
Phase
Non-wetting
Phase
Conditions Contact
Angle
(Degrees)
Interfacial
Tension
(dynes/cm)
Brine Oil Reservoir 30 30
Brine Oil Laboratory 30 48
Brine Gas Reservoir 0 (50)
Brine Gas Laboratory 0 72
Oil Gas Reservoir 0 4
Gas Mercury Laboratory 140 480
Table 7-3 Typical values for contact angle and IFT for different fluid pairs under different conditions
The relevance of being able to convert from one pair of fluids to another or from one set
of P-T conditions to another is that controlled experiments in the laboratory can be
performed using a simpler fluid or P-T conditions arrangement than actually exists in the
reservoir. It is then a very straightforward matter to convert the laboratory results to
reservoir conditions.
7.4 Capillary Pressure Measurement
7.4.1 Centrifugal Method
In the centrifugal method a sample that has been saturated with the wetting fluid is
placed in a container of the non-wetting fluid. The container is then rotated and the
centrifugal force produces a pressure gradient throughout the sample, directed outward
from the axis of rotation. It is normally the case that the wetting fluid is denser than the
non-wetting fluid so that a higher pressure is developed in the fluid within the sample. The
excess pressure in the wetting fluid is the capillary pressure, and it is this pressure that
causes the wetting fluid to be expelled out of the end of the sample furthest from the axis
of rotation. At the same time non-wetting fluid enters at the nearest end.
At a constant rate of rotation an equilibrium saturation distribution will develop
according to the relationship between capillary pressure and saturation, and it is this
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relationship that needs to be determined. The established equilibrium saturation can be
calculated by measuring the amount of wetting fluid that flows out of the sample. The
prevailing capillary pressure can be determined from the geometry of the centrifuge, the
density difference between the fluids and the angular velocity.
By making such measurements at a series of angular velocities the nature of the capillary
pressure / saturation relationship can be determined.
7.4.2 Displacement Method
The displacement method of determining capillary pressure attempts to model a non-
wetting phase displacing a wetting phase, as would be the case when oil first migrated into
the reservoir. Mercury and air are frequently used as the pseudo-reservoir fluids and the
displacement is proceeds by increasing mercury pressure, in a series of discrete steps, in a
dried and cleaned core plug already saturated with air. The increase in pressure forces the
strongly non-wetting mercury into the core increasing the mercury saturation and this
increase may be determined by measuring the volume of the injected mercury.
Figure 7-24 presents a highly stylised picture of the various steps in the process when a
dry, air-filled core sample is immersed in a bath of mercury and the system is gradually
pressurised. In this situation mercury is the non-wetting fluid and so it will be the largest
rock capillary that will be flooded first. (Although it may seem strange, air is the wetting
phase in this situation and what is depicted in Figure 7-24 is, in fact, a drainage process.)
Figure 7-24 shows an ideal curve for a system with three distinct pore throat sizes. Other
“idealised” situations are of course possible and some of these are shown in Figure 7-25.
The bimodal case is just another example of that already presented in Figure 7-24. A
well-sorted porous core sample is one in which there is essentially only one pore throat
radius to consider. Once this has been breached the entire sample, apart from the small
volume taken up by any compressed air trapped in the pores, will become filled with
mercury. At the other extreme, when the core comprises a continuous range of pore throat
sizes to be overcome, the core will only fill gradually as the pressure is increased.
Obviously a range of outcomes is possible between the extremes of a “well-sorted” and
“unsorted” core sample, and one such case, described as “poorly sorted”, has been
indicated.
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One obvious conclusion from the above discussion would be that it is possible to relate
the gradual flooding of the sample to the pore throat radius and a typical relationship is
shown in Figure 7-26. Therefore, the generated capillary pressure curve for a given porous
medium can be used to extract the pore network and pore size distribution of the porous
medium.
Figure 7-24 Mercury Injection Capillary Pressure Experiment
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Figure 7-25 Idealised Mercury Injection Curve Shapes
Figure 7-26 Calculation of Pore Size Distribution from Mercury Injection
In the left picture presented in Figure 7-26 as can be seen, despite a noticeable increase
in the mercury injection pressure there is not much increase in the mercury saturation in
the porous medium up point “A” on the curve. The pressure at this point is referred to as
the displacement pressure, threshold capillary pressure or capillary entry pressure which in
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A
0100
essence is the minimum pressure required so that mercury would enter the largest
available pore-throat in the pore network of the porous medium under investigation.
It should be noted that mercury is considered a more dangerous material to work with
than perhaps it was in the past, and for this reason many laboratories now use the
centrifuge method for capillary pressure measurement.
7.4.3 Porous Plate Method (restored state)
Water saturated samples for air-water or oil-water tests and oil saturated cores for air-
oil tests are placed on a semi-permeable diaphragm, and a portion of the contained liquid is
displaced with the appropriate fluid of air or oil. A schematic diagram of an apparatus for
performing such tests is seen in Figure 7-27. It consists of a cell for imposing pressure, a
semi-permeable diaphragm, C, manometer for recording pressure, M, and a measuring
burette for measuring produced volumes.
Figure 7-27 The porous plate method assembly
During measurement, the pressure is increased in steps and final equilibrium produced
volumes of the wetting phase are recorded for each step.
The porous plate method is slow and one full curve may take up to 40 days or more to
obtain. However, equipment needed for this method is simple and inexpensive and the
work needed is limited to some volume reading or sample weighing during the process.
Several samples may be run in one chamber. Then the samples have to be removed in
order to weigh them separately between each pressure increase. Preferably, one sample
should be run in an assembly of one-sample cells. Then it is not necessary to decrease
pressure between each reading.
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This method is regarded as the standard method against which all other methods are
compared. Routinely only the drainage curve is measured, but with appropriate
modifications the imbibition curve may be determined in the same manner. The weakness,
as with all the other methods, is the transformation of data to reservoir conditions.
7.5 HysteresisA set of consecutive drainage and imbibition capillary pressure curves are schematically
shown in Figure 7-28, from which it can be seen that different results are obtained
depending on which fluid is displacing which. This phenomenon is referred to as capillary
hysteresis.
Figure 7-28 Capillary Hysteresis
Saturation history dependence of multiphase flow or the hysteresis effect i.e.
irreversibility or path dependence, is evident whenever the porous medium undergoes a
cyclic flooding process. In other words, the multiphase flow through porous medium
depends on the saturation history and saturation path. Therefore multiphase flow
characteristics of a fluid-rock system e.g. capillary pressure, relative permeability, etc,
during an imbibition process are different from those of a consecutive drainage process and
vice versa. From a pore-scale processes point of view hysteresis has at least two main
sources:
Contact angle hysteresis: the advancing contact angle which is measured at the
immiscible interface when the wetting phase displaces the non-wetting phase
i.e. imbibition, is larger than the receding contact angle which is measured at
immiscible interface when the non-wetting phase displaces the wetting phase
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i.e. drainage. These two angles are different due to chemical heterogeneities
and/or surface roughness and tortuosity of the pores and pore throats.
Trapping of the non-wetting phase: during an imbibition process due to various
trapping mechanisms part of the non-wetting phase becomes disconnected in
the form of blobs and ganglia. The disconnected non-wetting phase becomes
immobile and trapped within the pores. Due to the presence of this immobile
phase, a subsequent drainage process results in different multiphase flow
behaviour in comparison to the equivalent imbibition process.
7.6 Experiments
7.6.1 Capillary Pressure Measurement using Porous Plate Method
I. Description:
The porous plate method is the most accurate measurement of capillary pressure in
homogeneous and heterogeneous cores. Several plugs can be measured at a time. The
limitation is that the capillary discontinuity may distort the results.
II. Procedure:
1 Weigh the brine saturated core and take note of the core ID.
2 Remove the cell’s lid by loosening its bolts. Then put the saturated core on top of the
porous plate in the cell.
3 Close the cells lid and tighten the bolts to make sure there will be no leaks. Then adjust
the pressure regulator to an output pressure of 3 psi.
4 After 1 week, isolate the air supply to the cell and after releasing the pressure inside
the cell take out the core from the cell.
5 Weigh the core and calculate the water saturation corresponding to the capillary
pressure step.
6 Repeat steps 2-4 every week for pressures of 10, 25, 50 and 80.
III. Calculations and report:
Calculate and fill the data table below.
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Plot capillary pressure curve (Sw-Pc) and pore size distribution
Core No.: , D: cm, L: cm, Wsat: gr, Porosity: %
Date Step No. Pc(i), psi Wwet(i), gr Sw(i), fraction r(i), µm ΔW(i)/Wwater
0
1
2
3
4
5
where
Pc(i) = capillary pressure of the ith step, psi
Wwet(i) = core weight of ith step, gr
Sw(i) = (Wwet(i)-Wdry)/Wwater, ith water saturation of Pc(i)
Wwater = Wsat-Wdry, gr
r(i) = 2σg-w /Pc(i), radius corresponding to Pc(i)(in Pascals), microns(µm)
σg-w = 72.0 dynes/cm, interfacial tension of gas-water
Pc(i) = pressure reading, dynes/cm2
ΔW(i)/Wwater = (Wwet(i-1)-Wwet(i))/Wwater, fraction of the capillaries of r(i) in total pore volume
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Pa
7.7 References Torsæter, O. and Abtahi, M., 2003. Experimental reservoir engineering laboratory work
book, Department of Petroleum engineering and Applied Geophysics, Norwegian
University of Science and Technology
Tiab, D. and Donaldson, E.C., 2004. Petrophysics. Gulf Professional Publishing, Elsevier,
Burlington, Massachusetts.
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8 Grain Density:
8.1 IntroductionGrain volume is usually used for measuring pore volume or porosity of the rock samples
in reservoir evaluation. Besides that knowing grain volume can be helpful in identifying
grain density of the rock sample. However grain volume data itself is not in the interest of
reservoir engineers or geologists in determining reservoir characteristics.
Grain density is calculated by dividing the sample dry weight (in grams) by the grain
volume. It can be utilized in determination of the rock type. Major rock types such as
sandstone, limestone, and dolomite fall into specific grain density range (Table 1).
Table 1: Grain density of the different lithologies.
Lithology Grain Density(cc/gr)
Sandstone 2.65Limestone 2.71
Dolomite 2.85-2.87
Anhydrite 2.96
Coal 1.5
Gypsum 2.35
Sometimes grain density can be utilized to determine if unexpected minerals or other
components exist in the rock fabric. As well as measured grain density could be used for log
interpretation. For example for determining the porosity using the density log it is required
to know about the matrix density or grain density. It is worth mentioning that even small
error (0.01 gr/cc) in matrix density measurement can be translated into an error of 0.5% in
the calculated porosity from density log. Therefore accurate determination of grain density
is very important for the followings petrophysical evaluation in the reservoir.
8.2 Grain Density MeasurementFor calculating grain density it is required to know about grain volume. Boyle’s law is
often employed with helium gas to determine the grain volume. This technique has been
explained completely in experiment number 1 (Porosity) therefore it is not explained here.
For measuring the grain volume of core plug samples helium porosimeter with ususal core
holder could be used but for measuring the grain volume of the crushed samples or
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irregularly shaped rock samples gas pycnometer (Figure 1) can be used. Similarly it uses the
Boyle’s law technique to measure the grain volume of the crushed samples by observing
the change in pressure of helium as it expands into the sample cell.
Figure 1: Gas pycnometer for grain density measurement of crushed samples
(From Micromeritics™)
8.3 Description of Manual Helium PorosimeterThe manual helium porosimeter (TPI-219) (Figure 2) uses the Boyle’s law for measuring
the grain volume of the rock sample. Similar to other instruments which work with this
technique it has two cells: reference cell and sample cell (which is called grain cell). Grain
cell is used for measuring grain volume of core samples of 1.5 inch in diameter. It has 5
different calibrated billets which are used for reducing the dead volume of the grain cell
when the sample is loaded into the grain cell. Grain volume measurements can be made
with TPI-219 at pressures up to 95 psi.
Figure 2: Manual helium porosimeter accompanied with grain cell and calibration
billets.
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8.4 Experiment procedure
I. Measuring System Reference Volume
The reference volume of the porosimeter is a critical value. Accuracy is essential for the
reference volume measurement. Before each use of manual Helium porosimeter, the
system reference volume should be measured. For measuring the reference volume fill the
grain cell with all calibration billets and do the following steps:
1 Read the digital pressure recorder on the front panel when there is not any gas in the
system as the zero pressure in table 2. You should use this value to correct the later
recorded values for the pressures (Pcorrected=Precorded-Zero pressure).
2 Open the SUPPLY GAS valve and pressurize the reference section of the porosimeter.
Close the SUPPLY GAS valve and monitor the pressure for 10 seconds. The pressure
should equilibrate to a point that the last digit fluctuates very slowly. Record the digital
pressure data under Preference in table 2.
3 Open the TO CORE valve. Allow the pressure to equilibrate in the grain cell. When the
pressure comes to equilibrium record the digital pressure data under Pgrain.
4 Open the VENT valve and allow the pressure to deplete.
Now remove billet A from the system and repeat the steps 2 to 4 and record the
appropriate data under “after removing billet” section in the table 2. Repeat this procedure
for other billets as well and record the pressure data.
Now by having all the required data it is possible to calculate the reference volume
based on the recorded values in table 2 using the following formula:
Where:
VREF: System Reference Volume, cm3
VBillets Removed: Volume of the removed billets, cm3
PRef. Full: Reference cell pressure when all billets is in grain cell, psi
PGC Full: Grain cell pressure with all billets is in grain cell, psi
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PRef.Rem.: Reference pressure for measurement with a billet removed, psi
PGC Rem: Grain cell pressure when the billet (or billets) removed, psi
You should re-calculate the reference volume each time that you remove one billet from
the grain cell and finally take an arithmetic average to report the reference volume of the
system and use this value for grain volume measurement.
II. Measuring Grain Volume
5 Weigh the provided dried core sample,
6 Set the sample on the table top. Create a stack of billets next to the sample that is
equal in height or slightly taller than the sample height. You should mix and match the
billets such that you create a stack as close as possible to the height of the sample.
Excess height creates excess dead volume in the chamber, which can increase the
uncertainty of the measurement.
7 After creating a stack equal to or slightly taller than the sample, place the others
(remaining) billets inside the grain cell.
8 Carefully place your sample on top of the billets in the cup and prepare to measure the
sample grain volume.
9 Open the SUPPLY GAS valve and pressurize the reference section of the porosimeter.
Record the digital pressure data under Pref. Sample in table 3.
10 Open the TO CORE valve. Allow the pressure to equilibrate in the grain cell. When the
pressure comes to equilibrium record the digital pressure data under PGC Sample.
Now by having required parameters from tables 2 and 3, it is possible to calculate grain
volume of the sample using the following formula:
Where:
VGrain: Grain Volume, cm3
VBillets Removed: Volume of removed billets, cm3
PRef. Full: Reference Pressure when grain cell is full of billets, psi
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PGC Full: Grain cell pressure when grain cell is full of billets, psi
VRef.: Reference volume of system, cm3
PRef. Sample: Reference cell pressure when sample is inside grain cell, psi
PGC Sample: Grain cell pressure when sample is inside grain cell, psi
III. Report
You should report the following parameters in your report:
Reference volume of the system
Grain volume for the provided samples
Grain density for the provided samples
Determining the rock type of the rock sample
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8.5 References Coretest Systems. 2010. “TPI-219 Teaching Helium Porosimeter Manual”.
Micromertics website: www.micromeritics.com
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