petrophysics and reservoir properties laboratory

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


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.


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.


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


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.


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


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


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


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.


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.


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.


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.


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.


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.


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


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


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.


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.


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.


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.


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.


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


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).


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.


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


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.


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.


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.


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


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.


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


(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.


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).


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:


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


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


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.


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







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.


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.


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:


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.


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:


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.


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


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.


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


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.


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.


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.


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.


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


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


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


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.


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


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


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.


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


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.


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


Pa

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


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.


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


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


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


8.5 References Coretest Systems. 2010. “TPI-219 Teaching Helium Porosimeter Manual”.

Micromertics website: www.micromeritics.com


http://www.micromeritics.com/

petrophysics and reservoir properties laboratory

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