Istanbul Technical University-Petroleum and Natural Gas Engineering

1. PET 321E – Petroleum and Natural Gas Lab. 1 | 1 3
Porosity
Porosity
From the viewpoint of petroleum engineers, one of the most important properties of a reservoir rock is
POROSITY. Porosity is an intensive property describing the fluid storage capacity of a rock. It is defined
as the ratio of pore volume to bulk volume. In other words, it can be described as the fraction of rock
that is occupied by pores. The porosity is conventionally given by the symbol ∅ and is expressed either
as a fraction varying between 0 and 1, or a percentage varying between 0% and 100%. However, the
fractional form is ALWAYS used in calculations.
Porosity is calculated using the relationship given below.
∅ =
𝑉𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
=
𝑉𝑏𝑢𝑙𝑘 − 𝑉𝑔𝑟𝑎𝑖𝑛
𝑉𝑏𝑢𝑙𝑘
where;
𝑉𝑝𝑜𝑟𝑒 : pore volume – the empty space within the rock occupied by fluid (Fig. 1),
𝑉𝑔𝑟𝑎𝑖𝑛 : grain volume – the volume occupied by the solid part of the rock (Fig. 1),
𝑉𝑏𝑢𝑙𝑘 : bulk volume – the total volume of the rock, includes the pore volume and the grain volume
(Fig. 1).
A) Bulk Volume B) Grain Volume C) Pore Volume
Figure 1: Idealized schematic representation of bulk, grain and pore volume of a rock.
Some of the pores in the reservoir rocks can be completely isolated from other pores around them, in
other words, they can be disconnected from the other pores. In this case, there is no fluid flow occurs

2. PET 321E – Petroleum and Natural Gas Lab. 2 | 1 3
Porosity
between disconnected pores with other pores, and therefore, there is no pressure communication in
between them. Since the isolated (disconnected) pores filled with oil, gas and/or water have no effect
on the production of oil and gas, petroleum engineers do not interested in with this type of pores.
Therefore, isolated pores are called as dead pores and the total volume of dead pores as dead pore
volume (Fig. 2).
On the other hand, the pores interconnected to each other contribute to the mass transfer in the rock
pores are called as effective pores and the total volume of effective pores as effective pore volume or
simply pore volume (Fig. 2).
Figure 2: Pore spaces in a rock.
From the viewpoint of petroleum engineers, effective porosity which is the ratio of effective pore
volume to the bulk volume is the most important property of a rock.
A range of differently defined porosities is recognized and used within the petroleum industry.
1. Total (or Absolute) Porosity: defined as the ratio of all pore volume to the bulk volume of rock.
∅ 𝑡 =
𝑉𝑑𝑒𝑎𝑑 𝑝𝑜𝑟𝑒 + 𝑉𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
2. Effective (or Connective) Porosity: defined as the ratio of effective pore volume to the bulk volume
of rock.
∅ 𝑒 =
𝑉𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
Rock Matrix Effective Pores Dead PoresRock Matrix

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Porosity
In most of the reservoir rocks, the dead pore volume has a negligible value compared to the total pore
volume, and effective porosity almost equals the total porosity. Therefore;
∅ 𝑒 ≤ ∅ 𝑡
For granular materials such as sandstone, the effective porosity may approach the total porosity,
however, for shales and highly cemented or vugular rocks such as some limestones, large variations may
exist between effective and total porosity.
3. Primary (or original) Porosity is developed during the deposition of the sediment.
4. Secondary Porosity is caused by some geologic process subsequent to the formation of the deposit.
These changes in the original pore spaces may be created by ground stresses, water movement, or
various other types of geological activities after the original sediments were deposits. Fracturing or
formation of solution cavities often will increase the original porosity of the rock.
Factors that Affect Porosity: The primary porosity is affected by three major microstructural
parameters. These are grain shape, grain size, grain packing, and grain sorting.
1. Grain Shape: Not all the grains are spherical, and grain shape influences the porosity. Fig. 3
shows the relation between the grain shape and the porosity. As it can be seen the porosity for
more angular grains is larger than those that are sub-spherical.
Figure 3: Relation between the grain shape and the porosity.
High
Low
Very
Angular
Angular
Sub-
Angular
Sub-
Rounded Rounded
Well-
Rounded
ROUNDNESS
Porosity
Porosity

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Porosity
2. Grain Size: Porosity is independent of grain size. Consider a cube having dimensions of 2rx2rx2r,
and insert a grain having radius of r into the cube (Fig. 4). Porosity can be calculated as follows:
𝑉𝑏𝑢𝑙𝑘 = 2𝑟 × 2𝑟 × 2𝑟 = 8𝑟3
𝑉𝑔𝑟𝑎𝑖𝑛 =
4
3
𝜋𝑟3
∅ =
𝑉𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
=
𝑉𝑏𝑢𝑙𝑘 − 𝑉𝑔𝑟𝑎𝑖𝑛
𝑉𝑏𝑢𝑙𝑘
=
8𝑟3
−
4
3 𝜋𝑟3
8𝑟3
= 0. 476 𝑜𝑟 48%
As it can be seen the grain radius (grain size) do not have an effect on the porosity.
Figure 4: Relation between the grain size and the porosity.
3. Grain Packing: For a uniform grain size, porosity is independent of the size of the grains.
However, the porosity is dependent on the arrangement of the grains, or in other words, it is
dependent on grain packing. A maximum theoretical porosity of 48% is achieved with the cubic
packing of spherical grains (Fig. 5), and the porosity for the rhombic packing is 27%.
Cubic Packing,  = 48% Rhombic Packing,  = 27%
Figure 5: Relation between the grain packing and the porosity.
2 r
2 r
2 r r
Porosity = 48% Porosity = 27 %

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Porosity
4. Grain Sorting: The porosity is dependent on the grain size distribution, or in other words, it is
dependent on grain sorting. If all the grains are of the same size, then sorting is said to be
GOOD, and if the grains of many diverse sizes are mixed together, sorting is said to be POOR
(Fig. 6).
Good Sorting Poor Sorting
Figure 6: Relation between the grain sorting and the porosity.
Porosity decreases as grain sorting become poorer. This is because intergranular pore of a given grain
size may be occupied by ever smaller grains.
Reservoir pore volume is always filled with one or more fluid which means the reservoir rock is
saturated with at least one fluid. As it is shown in Fig. 7, reservoir rock can be saturated with [water],
[water+oil], [water+gas], or [water+oil+gas]. The reservoir pore volume has to be equal to the total fluid
volume which fills the reservoir pores. For example; if the reservoir rock is saturated with water, oil, and
gas, then the following formula can be written.
𝑉𝑝𝑜𝑟𝑒 = 𝑉𝑜𝑖𝑙 + 𝑉𝑔𝑎𝑠 + 𝑉 𝑤𝑎𝑡𝑒𝑟
where,
𝑉𝑝𝑜𝑟𝑒 : effective pore volume,
𝑉𝑜𝑖𝑙 : oil volume in interconnected pores,
𝑉𝑔𝑎𝑠 : gas volume in interconnected pores,
𝑉 𝑤𝑎𝑡𝑒𝑟 : water volume in interconnected pores.
Porosity

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Porosity
The saturations of reservoir rock with respect to these three saturating fluids are symbolized as 𝑆 𝑜 for
oil, 𝑆 𝑔 for gas, and 𝑆 𝑤 for water. The saturation of each phases is the ratio of the saturating fluid volume
to the total pore volume, or in other words;
𝑆 𝑜 =
𝑉𝑜𝑖𝑙
𝑉𝑝𝑜𝑟𝑒
, 𝑆 𝑔 =
𝑉𝑔𝑎𝑠
𝑉𝑝𝑜𝑟𝑒
, 𝑆 𝑤 =
𝑉 𝑤𝑎𝑡𝑒𝑟
𝑉𝑝𝑜𝑟𝑒
where,
𝑆 𝑜 : oil saturation, fractional,
𝑆 𝑔 : gas saturation, fractional,
𝑆 𝑤 : water saturation, fractional.
Regarding the definition of saturation, the arithmetic summation of saturations given above is obtained
that;
𝑆 𝑜 + 𝑆 𝑔 + 𝑆 𝑤 =
𝑉𝑜𝑖𝑙 + 𝑉𝑔𝑎𝑠 + 𝑉 𝑤𝑎𝑡𝑒𝑟
𝑉𝑝𝑜𝑟𝑒
=
𝑉𝑝𝑜𝑟𝑒
𝑉𝑝𝑜𝑟𝑒
= 1
𝑆 𝑜 = 0.80
𝑆 𝑔 = 0.00
𝑆 𝑤 = 0.20
𝑆 𝑜 = 0.50
𝑆 𝑔 = 0.30
𝑆 𝑤 = 0.20
Oil Water Gas
Figure 7: Distribution of fluid saturations in pores.

7. PET 321E – Petroleum and Natural Gas Lab. 7 | 1 3
Porosity
Porosity Determination: From the definition of porosity, it is evident that the porosity of a sample of
porous material can be determined by only two out of the three volumes namely bulk volume, grain
volume and pore volume are required to calculate porosity.
APPARATUS used in the Experiment:
• Desiccator
• Vacuum pump
• Saturating liquid
• Saturating liquid vessel
• Thermometers
• Electronic balance
• Vernier caliper
METHODS used for the Experiment:
Of the many methods used to determine porosity, only Saturation Method which is common method is
performed in our laboratory. This method uses the principle based on introducing a liquid of known
density into the pores of the core sample. The weight of the dry sample and the weight of the saturated
sample are determined. The pore volume is determined by dividing the difference in weight between
the saturated sample and the dry sample by the liquid density.
Section A: Preparation of Core Sample
1. Take a core sample is flushed and desiccated over a suitable dehydrating material.
2. Record the identity of the core sample that its properties are not known in the raw data sheet.
3. By using vernier caliper, measure the length and diameter of the core sample and repeat your
measurements six times. Record the length and diameter measurements in the raw data sheet.
4. Weigh dry core sample using a balance and record your measurement in the raw data sheet as
dry weight, 𝑚 𝑑𝑟𝑦.

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Porosity
Section B: Saturating the Core Sample
1. Place the glass beads into the bottom of the desiccator (Fig. 8).
2. Place the core sample on to the glass beads in the vertical direction.
3. Place the rubber stopper, having a tubing which providing connection between top and bottom
of desiccator into the mouth of the desiccator.
4. Close and seal the desiccator and evacuate the core sample by opening the vacuum pump for at
least 15 min.
5. To start the saturation procedure, open the liquid valve located on the tubing which provides
the saturating liquid flow from the top of the tubing to the bottom of the desiccator.
6. Close the liquid valve, when the saturating liquid level reached at least 1 cm above the core
sample.
7. Open the vacuum pump and keep the core sample on saturation at least 1 hour.
8. After saturation, allow the air to flow slowly into the system.
9. When the pressure inside the desiccator is reached to the atmospheric pressure, remove the
rubber stopper placed into the mouth of the desiccator.
10. Remove the core sample from the desiccator.
Figure 8: Liquid saturation apparatus (schematic diagram).
..
Desiccator
Core Sample
Glass Beads
Pressure
Gauge
Rubber Stopper
Liquid Valve
Saturating
Fluid
Vacuum Pump

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Porosity
11. Remove the excess drops from the core sample by wiping it with a filter paper, which is
saturated with saturating liquid.
12. Weigh the saturated core sample as quickly as possible to avoid the evaporation of saturating
liquid from the sample.
13. Record your measurement in the raw data sheet as saturated weight, 𝑚 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑.
14. Calculate the weight of the saturating liquid by subtracting the dry weight from the saturated
weight of the core sample.
15. Calculate the pore volume of the core sample by using the weight and density of the saturating
liquid.
16. Write your findings in the raw data sheet.
CALCULATIONS and RESULTS:
Section A: Preparation of Core Sample
1. Calculate the cross-sectional area and bulk volume of the core sample by using each of your core
sample dimension measurements, and write your findings in the raw data sheet.
NOTE:
Cross-sectional Area : 𝐴 = 𝜋
𝐷2
4
, 𝑐𝑚2
Bulk Volume : 𝑉𝑏𝑢𝑙𝑘 = 𝐴 × 𝐿, 𝑐𝑚3
where;
𝐷 : diameter of the core sample, cm
𝐿 : length of the core sample, cm

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Porosity
2. Determine the pore volume by using the following equation:
𝑉𝑝𝑜𝑟𝑒 =
𝑚 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 − 𝑚 𝑑𝑟𝑦
𝜌𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑛𝑔 𝑙𝑖𝑞𝑢𝑖𝑑
, 𝑐𝑚3
NOTE: Density of the saturating liquid, 𝜌𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑛𝑔 𝑙𝑖𝑞𝑢𝑖𝑑, will be provided by Lab. Coordinator.
3. Determine the measured porosity by using the following equation:
∅ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 =
𝑉𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
× 100
4. Determine the pseudo porosity regarding the bulk volume and the matrix density of the core
sample by using the following equation:
𝑉𝑔𝑟𝑎𝑖𝑛 =
𝑚 𝑔𝑟𝑎𝑖𝑛
𝜌 𝑔𝑟𝑎𝑖𝑛
=
𝑚 𝑑𝑟𝑦
𝜌 𝑔𝑟𝑎𝑖𝑛
, 𝑐𝑚3
∅ 𝑝𝑠𝑒𝑢𝑑𝑜 =
𝑉𝑝𝑜𝑟𝑒
𝑉𝑏𝑢𝑙𝑘
=
𝑉𝑏𝑢𝑙𝑘 − 𝑉𝑔𝑟𝑎𝑖𝑛
𝑉𝑏𝑢𝑙𝑘
= 1 −
𝑚 𝑑𝑟𝑦
𝑉𝑏𝑢𝑙𝑘 𝜌 𝑔𝑟𝑎𝑖𝑛
NOTE: Matrix density of the core sample, 𝜌 𝑔𝑟𝑎𝑖𝑛, will be provided by Lab. Coordinator.
5. Calculate the average bulk volume of the core sample by taking the arithmetic average of the
diameter and length measurements. Write your findings in the raw data sheet.
Section B: Error Analysis
1. Calculate the error percentage in the pseudo porosity by using the measured porosity
calculated pseudo porosity in the following formula:
𝐸∅ =
∅ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − ∅ 𝑝𝑠𝑒𝑢𝑑𝑜
∅ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑
× 100
2. Briefly discuss the error percentage in the pseudo porosity obtained above.

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Porosity
Section C: Approximation to Permeability
The ability of the porous medium to allow the fluid(s) to transmit through its pores is called as
permeability. Although it is natural to assume that permeability depends on porosity, it is not
simple to determine a relationship between porosity and permeability. Generally, there is no
specific correlation between the permeability and porosity. However, according to some earth
scientists, the relationship between porosity and permeability can be approximated if the
average grain size is known. In other words; It is required a detailed knowledge of grain size
distribution to have an idea about the permeability of a rock. One of the most well-known
models linking porosity and permeability is known as the Kozeny-Carman Equation which is
given below.
𝑘 = 3.631 × 109
𝐷𝑔𝑟𝑎𝑖𝑛
2
× ∅3
(1 − ∅2)
where,
𝑘 : permeability, mD
∅ : porosity, fraction
𝐷𝑔𝑟𝑎𝑖𝑛 : average diameter of the grains, inches

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Porosity
Name, Surname : .....................................................................
Faculty ID Number : .....................................................................
Group : .....................................................................
Date : .....................................................................
RAW DATA SHEET
Porosity
Ambient Temperature, °C (°F) : --------------------- Ambient Pressure, mmHg : ----------------------
Core sample identity :
# Diameter, cm
Cross-Sectional
Area, cm2
Length,
cm
Bulk
Volume,
cm3
Pseudo
Porosity, %
Error in
Porosity, %
1
2
3
4
5
6
Ave.
Min. Bulk Volume , cm3
Max. Bulk Volume , cm3
Average Bulk Volume , cm3
Min. Pseudo Porosity , %
Max. Pseudo Porosity , %
Dry Weight ,g
Saturated Weight ,g
Porosity , %
Lab. Coordinator Name, Surname:
Date:
Signature:

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Porosity
Ambient Temperature, °C (°F) : --------------------- Ambient Pressure, mmHg : ----------------------
Core sample identity :
# Diameter, cm
Cross-Sectional
Area, cm2
Length,
cm
Bulk
Volume,
cm3
Pseudo
Porosity, %
Error in
Porosity, %
1
2
3
4
5
6
Ave.
Min. Bulk Volume , cm3
Max. Bulk Volume , cm3
Average Bulk Volume , cm3
Min. Pseudo Porosity , %
Max. Pseudo Porosity , %
Dry Weight ,g
Saturated Weight ,g
Porosity , %
Lab. Coordinator Name, Surname:
Date:
Signature: