In this module you will learn about

Porosity

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Titlepage
Topic Overview
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

1 General Aspects 2 Idealized Models 3 Measurments

of porosity

Developers References
Titlepage
General aspects
Topic Overview
 One may distinguish between two types of porosity,
1 General Aspects
namely absolute and effective
2 Idealised Models
 Absolute and effective porosity are distinguished by their
3 Measurements
of Porosity
access capabilities to reservoir fluids

Permeable
spaces Void spaces
contributes contributes
to effective to absolute
porosity porosity

Art-micrograph of sandstone with oil

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Titlepage
Genetically the following types of porosity can be distinguished:
Topic Overview

1 General Aspects

2 Idealised Models
 Intergranular porosity
3 Measurements  Fracture porosity
of Porosity
 Micro- porosity
 Vugular porosity
 Intragranular porosity

Rock media having both fracture and intergranular

pores are called double-porous or fracture-porous
media.

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Titlepage
Consolidated
Topic Overview
 From the point of view of pores susceptibility to mechanical
1 General Aspects changes, one should distinguish between consolidated and
2 Idealised Models unconsolidated porous media
– Consolidated porous media pertain to sediments that have been compacted and
3 Measurements
of Porosity cemented to the degree that they become coherent, relatively solid rock
– A typical consequences of consolidation include an increase in density and
acoustic velocity, and a decrease in porosity

Sandstone with quartz cement and secondary

porosity

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Titlepage
Sorting
Topic Overview
 Sorting is the tendency of
1 General Aspects sedimentary rocks to have
2 Idealised Models grains that are similarly
sized--i.e., to have a
3 Measurements
of Porosity narrow range of sizes
 Poorly sorted sediment
displays a wide range of
grain sizes and hence has
decreased porosity
 Well-sorted indicates a
grain size distribution that
is fairly uniform
 Depending on the type of
close-packing of the
grains, porosity can be
substantial.

Photomicrographs of sorting in sandstones

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 Section 2: Idealised Models
Titlepage
Topic Overview

1 General Aspects

2 Idealised Models Parallel cylindrical pores Irregular-packed spheres with

different radii
3 Measurements
of Porosity

Regular orthorhombic-
packed spheres
Regular rhombohedral-
Regular cubic-packed spheres
packed spheres

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Titlepage
Parallel Cylindrical Pores
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

• Estimation of porosity accounting to this model:

Vp r 2  n  m 
    0,785 or 78,5%
Vb 2rn  2rm 4
r- pipe radius
mn - number of cylinders contained in the bulk volum e
Vp - pore volume
Vb - bulk volum e

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Titlepage
Regular Cubic-Packed Spheres
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

• Estimation of porosity accounting to this model:

Vp Vb  Vm 
   1   0,476 or 47,6%
Vb Vb 6
Vp - pore volume
Vb - bulk volum e  ( 2r)3
Vm - matrix vol ume (volume of bulk space occupied by the rock)
14  4
  r 3   8  r 3
83  3

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Titlepage
Regular Orthorhombic-Packed Spheres
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

• Estimation of porosity accounting to this model:

Vp Vb  Vm Vm 4r 3
   1  1 3
 0,395 or 39,5%
Vb Vb Vb 12 3r
Vb - bulk volum e  2r  2r  h  4r 3 sin 60  4 3r 3
4
Vm - matrix vol ume  r 3
3
h - height of the orthorhomb ic - packed spheres

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Titlepage
Regular Rhombohedral-Packed Spheres
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

• Estimation of porosity accounting to this model:

Vp Vb  Vm Vm 4r 3
   1  1 3
 0,26 or 26,0%
Vb Vb Vb 12 2r
Vb - bulk volum e  2r  2r  h  4 2r 3
4
Vm - matrix vol ume  r 3
3
h - height in the tetrahedr on  4r 2  2r 2  2r

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Titlepage
Irregular-Packed Spheres with Different Radii
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

• The figure shows an example of an idealised porous

medium represented by four populations of spheres
(sorted by radii)

• The histogram shows the hypothetical grain-size

distribution.

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Titlepage
Example
Topic Overview
Porous medium blended with three types of sediment fractions:
1 General Aspects – Fine pebble gravel
with porosity (pebble=0,30)
2 Idealised Models – Sand (sand=0,38)
– Fine sand (f.sand=0,33)
3 Measurements
of Porosity

Vp
  f .sand  sand  pebble  0,037 or 3,7%
Vb
Vp f.sand Vf.sand f.sand sandVsand f.sand sandpebbleVpebble
tot.      f.sand sandpebble
Vb Vpebble Vpebble Vpebble

 Vp  f.sand Vf.sand, Vb  Vpebble 

 
 Vf.sand  sandVsand, Vsand  pebbleVpebble

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Titlepage
Measurement of porosity
Core Analysis
Well Logs
Topic Overview

1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

Measurement of Porosity

Uncertainty

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 Core Analysis
Titlepage
Topic Overview
Full-diameter
1 General Aspects Grain-volume
Core Analysis
2 Idealised Models measurements based
3 Measurements on Boyle`s law
of Porosity

Fluid-Summation
Method
Bulk-volume
measurements

Pore-volume
measurements

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Titlepage
Section 3.1: Full-diameter Core Analysis
Topic Overview
• Used to measure the porosity of rocks that are distinctly
1 General Aspects
heterogeneous. (Ex: carbonates and fissured vugular
2 Idealised Models rocks)
3 Measurements
of Porosity
• The same core-plug is a non-representative elementary
volume for this type of rock.
• In heterogeneous rocks, the local porosity may be highly
variable. It may include:
• micro-porosity
• intergranular porosity
• vugues
• fractures various combinations of these.
• A full-diameter core sample usually has a diameter of 5
inches (12,5 cm) and a length of 10 inches (25 cm)
• Does not differentiate between the actual types of porosity
involved.

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 Section 3.2: Grain-Volume Measurements Based on
Titlepage
Topic Overview
Boyle`s Law
1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

Porosity measurements based on the

Boyle`s law

• Injection and decompression of gas into the pores of a

fluid-free (vacuum), dry core sample.
• Either the pore volume or the grain volume can be
determined, depending upon the instrumentation and
procedures.

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 Section 3.2: Grain-Volume Measurements Based on
Titlepage Boyle`s Law
Topic Overview

1 General Aspects
• Helium gas is often used due to its following properties:
2 Idealised Models

3 Measurements
of Porosity • The small size of helium molecules makes the gas rapidly penetrate
small pores
• Helium is an inert gas that will not be absorbed on the rock surface and
thus yield erroneous results

• Alternatives: N2 and CO2

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 Section 3.2: Grain-Volume Measurements Based on
Titlepage
Boyle`s Law
Topic Overview
• Calculation of the grain volume
1 General Aspects

2 Idealised Models
• Ideal gas law:
pV  nRT
3 Measurements • In case of vacuum inside the sample chamber:
of Porosity

p1V1  p2V
• Assuming adiabatic conditions, we obtains:

p1Vref  p2 (Vref  Vs  Vg )

p2Vref  p2Vs  p1Vref

Vg 
p2

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 Section 3.3: Bulk-Volume Measurements
Titlepage
Topic Overview

1 General Aspects

2 Idealised Models
• This technique uses the Archimedes` principle of mass
3 Measurements displacement:
of Porosity

• The core sample is first saturated with a wetting fluid and then
weighed.

• The sample is then submerged in the same fluid and its submerged
weight is measured.

• The bulk volume is the difference between the two weights

divided by the density of the fluid

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 Section 3.3: Bulk-Volume Measurements
Titlepage
Topic Overview

1 General Aspects
• Fluids normally used:
2 Idealised Models

3 Measurements
of Porosity
• Water which can easily be evaporated afterwards.

• Mercury which normally not enters the pore space in a core sample due
to its non-wetting capability and its large interfacial energy against air.

• A very accurate measurement, with a uncertainty of

0,2%.

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 Section 3.3: Bulk-Volume Measurements
Titlepage
Topic Overview
• Example: Uncertainty analysis in measuring the bulk
1 General Aspects
volume using Archimedes` principle.
2 Idealised Models
• The core is measured in two steps:
3 Measurements – Weighing the sample in a cup of water; m1 (Assuming 100%
of Porosity
water saturation)
– Then weighting the sample in air as it is removed from the cup; m2
• The bulk volume is: m2  m1
Vb 
w
• Differentiating the equation above gives us:

Vb V V
dVb  dm2  b dm1  b drw
m2 m1 rw

m2  m1  dm2 dm1 d w 
dVb     
 w  m2  m1 m2  m1  w 

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 Section 3.3: Bulk-Volume Measurements
Titlepage
Topic Overview
• If the density measurement as well as the two mass-
1 General Aspects
measurements above, is considered to be independent
2 Idealised Models measurements, the relative uncertainty in the bulk volume
3 Measurements is: 2 2 2
of Porosity  Vb   m   w 
   2    
 Vb   m2  m1   w 
• It may also be written as:
2 2
 Vb   m    w 
   2    
 Vb    wVb    w 
• If the uncertainty in determined the water density is
estimated to 0,1% and the weighting accuracy is equal to
0,1g , we find a relative uncertainty in the bulk volume of
approximately 0,5%.

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 Section 3.4: Pore-Volume Measurements
Titlepage
Topic Overview
• A core sample is placed in a rubber sleeve holder that has
1 General Aspects no voids space around.
2 Idealised Models • This is called a Hassler holder, see fig.
3 Measurements
of Porosity

• Helium or one of its substitutes is injected into the core

plug through the end stem.

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 Section 3.4: Pore-Volume Measurements
Titlepage
Topic Overview
• Calculations of the pore volume
1 General Aspects

2 Idealised Models

3 Measurements
p0V p  p1Vref  nRT
p2 V p  Vref   nRT
of Porosity

and

Vp
 p1  p2 V
p2  p0 ref

where p1  p2  p0 
• It is important to notice that the Hassler core holder has to
be coupled to a volume of known reference, Vref.

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 Section 3.5: Fluid-Summation Method
Titlepage
Topic Overview
• Technique is to measure the volume of gas, oil and water
1 General Aspects
present in the pore space of a fresh or preserved core of
2 Idealised Models known bulk volume.
3 Measurements
of Porosity
• The core sample is divided into two parts:
• One part (ca. 100 g) is crushed and placed in a fluid-extraction resort.
Vaporised water and oil move down and are collected in a calibrated
glassware, where their volumes are measured.
• Second part of the rock sample (ca. 30 g) is weighed and then placed in
a pycnometer, filled with mercury. The bulk volume is determined,
measuring the volume of the displaced mercury.
• Then the pressure of the mercury, PHg , is raised to 70 bar.
At this pressure mercury are filling the pore space
originally occupied with gas. Gas volume can then be
calculated

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 Section 3.5: Fluid-Summation Method
Titlepage
Topic Overview
• The laboratory procedure provides the following
1 General Aspects
information:
2 Idealised Models • First sub sample gives the rock`s weight, WS1 , and the volumes of oil,
3 Measurements Vo1 , and water, VW1 , are recorded.
of Porosity

• Second sub sample gives the volume of gas, Vg2 , and the rock`s bulk
volume, Vb2.

• Fraction of the gas-bulk volume:

Also: Vg 2
fg   S g
•

Vb 2

Ws1
Ws1  Vb1   appand Ws 2  Vb 2   app  Vb1  Vb 2
Ws 2

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 Section 3.5: Fluid-Summation Method
Titlepage
Topic Overview • The formation oil- and water factor are calculated as follow:
1 General Aspects

2 Idealised Models

V Vw1
3 Measurements
of Porosity f o  o1  S o fw   S w
Vb1 Vb1
• The sum of the fluid-volume factor then gives the porosity value:

f o  f w  f g   S o  S w  S g   

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 Section 3.5: Fluid-Summation Method
Titlepage
Topic Overview
• Example: Use of pycnometer in matrix volume calculation.
1 General Aspects
• In order to define the matrix volume, Vm , of a core sample,
2 Idealised Models
the following measuring steps are carried out:
3 Measurements 1. The pycnometer cell is fully saturated with mercury.
of Porosity
2. The pycnometer piston is withdrawn and a gas (air) volume of V0 is
measured.
3. The core sample is placed in the cell, and the cell volume is sealed. The
equilibrium condition inside the cell is written:
4. Mercury is injected into the cell and a new gas volume, V1 , and
pressure, is measured.
5. New equilibrium is reached and we write:
• Finally; the matrix volume is found as follows:
p0 V0  Vm 

p1 V1  Vm 

p1V1  p0V0
Vm 
p1  p0
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Titlepage
Porosity Estimation from Geophysical Well Logs
Topic Overview

1 General Aspects

2 Idealised Models
• Porosity can be estimated from:
3 Measurements
of Porosity
– Formation resistivity factor
– Microresistivity log
– Neutron-gamma log
– Density (gamma-gamma) log
– Acoustic (sonic) log

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Titlepage
Potential Error in Porosity Estimation
Topic Overview
• Experimental data
1 General Aspects
– Involve a degree of uncertainty related to the possible
2 Idealised Models
measurement errors
3 Measurements
of Porosity
– The measurement of porosity is normally a function of Vp, Vm
and/or Vb

  f (Vm ,V p ,Vb )

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Titlepage
Potential Error in Porosity Estimation
Topic Overview If the porosity is defined as
1 General Aspects
Vp
2 Idealised Models

3 Measurements

of Porosity Vb
The equation can be differentiated

d dVp dVb
 
 Vp Vb
The potential error of prosity measurement is then

2
 V p   Vb 
2

    
 
  V p   Vb 

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Titlepage
FAQ
Topic Overview  Add Q&A
1 General Aspects

2 Idealised Models

3 Measurements
of Porosity

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Titlepage
References
Topic Overview Figures taken with permission from the authors of
1 General Aspects Reservoarteknikk1: A.B. Zolotukhin and J.-R. Ursin
2 Idealised Models
Figures also taken with permission from Ola Ketil Siqveland
3 Measurements
of Porosity

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