Transcript Learning module title

In this module you will learn about
Porosity
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Topic Overview
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
1 General Aspects
Developers
2 Idealized Models
References
3 Measurments
of porosity
General aspects
Titlepage
Topic Overview

1 General Aspects
2 Idealised Models
3 Measurements
of Porosity

One may distinguish between two types of porosity,
namely absolute and effective
Absolute and effective porosity are distinguished by their
access capabilities to reservoir fluids
Permeable
spaces
contributes
to effective
porosity
Void spaces
contributes
to absolute
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
3 Measurements
of Porosity





Intergranular porosity
Fracture 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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Consolidated
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
 From the point of view of pores susceptibility to mechanical
changes, one should distinguish between consolidated and
unconsolidated porous media
–
–
Consolidated porous media pertain to sediments that have been compacted and
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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Sorting
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
 Sorting is the tendency of
sedimentary rocks to have
grains that are similarly
sized--i.e., to have a
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
Titlepage
Models
Topic Overview
1 General Aspects
2 Idealised Models
Irregular-packed spheres with
different radii
Parallel cylindrical pores
3 Measurements
of Porosity
Regular orthorhombicpacked spheres
Regular rhombohedralpacked spheres
Regular cubic-packed spheres
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Parallel Cylindrical Pores
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
•
Estimation of porosity accounting to this model:
Vp r 2  n  m 
 
  0,785or 78,5%
Vb 2rn  2rm 4
rmn Vp Vb -
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pipe radius
number of cylinderscontainedin thebulk volume
pore volume
bulk volume
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Regular Cubic-Packed Spheres
Titlepage
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 volume  ( 2r)3
Vm - mat rix vol
ume (volumeof bulk space occupiedby t herock)
14
4

  r 3   8   r 3
83
3

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Regular Orthorhombic-Packed Spheres
Titlepage
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
 0,395or 39,5%
3
Vb
Vb
Vb
12 3r
Vb - bulk volume  2r  2r  h  4r 3 sin 60  4 3r 3
4
Vm - matrix vol
ume  r 3
3
h - height of theorthorhomb
ic - packedspheres
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Regular Rhombohedral-Packed Spheres
Titlepage
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
 0,26 or 26,0%
3
Vb
Vb
Vb
12 2r
Vb - bulk volume  2r  2r  h  4 2r 3
4
Vm - matrix vol
ume  r 3
3
h - height in thetetrahedron  4r 2  2r 2  2r
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Irregular-Packed Spheres with Different Radii
Titlepage
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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Example
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Porous medium blended with three types of sediment fractions:
–
Fine pebble gravel
with porosity (pebble=0,30)
–
Sand (sand=0,38)
–
Fine sand (f.sand=0,33)
Vp

 f .sand  sand  pebble  0,037 or 3,7%
Vb
tot. 
Vp f.sandVf.sand f.sandsandVsand f.sandsandpebbleVpebble



 f.sandsandpebble
Vb
Vpebble
Vpebble
Vpebble
 Vp  f.sandVf.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
1 General Aspects
Full-diameter
Core Analysis
Grain-volume
measurements based
on Boyle`s law
2 Idealised Models
3 Measurements
of Porosity
Fluid-Summation
Method
Bulk-volume
measurements
Pore-volume
measurements
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Section 3.1:
Titlepage
Topic Overview
•
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
•
•
Used to measure the porosity of rocks that are distinctly
heterogeneous. (Ex: carbonates and fissured vugular
rocks)
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:
•
•
•
•
•
•
Full-diameter Core Analysis
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
Titlepage
Topic Overview
Measurements Based on
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
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
•
3 Measurements
of Porosity
Helium gas is often used due to its following properties:
•
•
•
Measurements Based on
Boyle`s Law
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
Titlepage
Topic Overview
1 General Aspects
•
Calculation of the grain volume
pV  nRT
•
Ideal gas law:
•
In case of vacuum inside the sample chamber:
2 Idealised Models
3 Measurements
of Porosity
Measurements Based on
Boyle`s Law
p1V1  p2V
•
Assuming adiabatic conditions, we obtains:
p1Vref  p2 (Vref  Vs Vg )
Vg 
Developers
p2Vref  p2Vs  p1Vref
p2
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Section 3.3: Bulk-Volume
Titlepage
Measurements
Topic Overview
1 General Aspects
2 Idealised Models
•
3 Measurements
of Porosity
•
This technique uses the Archimedes` principle of mass
displacement:
•
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
Titlepage
Measurements
Topic Overview
1 General Aspects
2 Idealised Models
•
3 Measurements
of Porosity
•
Fluids normally used:
•
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
Titlepage
Topic Overview
•
1 General Aspects
2 Idealised Models
•
3 Measurements
of Porosity
Example: Uncertainty analysis in measuring the bulk
volume using Archimedes` principle.
The core is measured in two steps:
–
–
•
•
Measurements
Weighing the sample in a cup of water; m1
(Assuming 100%
water saturation)
Then weighting the sample in air as it is removed from the cup; m2
The bulk volume is:
Vb 
m2  m1
w
Differentiating the equation above gives us:
dVb 
Vb
V
V
dm2  b dm1  b drw
m2
m1
rw
d w 
m2  m1  dm2
dm1
dVb 




 w  m2  m1 m2  m1  w 
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Section 3.3: Bulk-Volume
Titlepage
Topic Overview
Measurements
•
If the density measurement as well as the two massmeasurements above, is considered to be independent
measurements, the relative uncertainty in the bulk volume
is:
2
2
2
 Vb 
 m   w 

  2
  

 m2  m1   w 
 Vb 
•
It may also be written as:
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
2
 Vb   m    w 

  2
  

 Vb    wVb    w 
•
2
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
Titlepage
Topic Overview
•
1 General Aspects
2 Idealised Models
•
Measurements
A core sample is placed in a rubber sleeve holder that has
no voids space around.
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
Titlepage
Topic Overview
•
Measurements
Calculations of the pore volume
1 General Aspects
2 Idealised Models
p0V p  p1Vref  nRT
3 Measurements
of Porosity
p2 V p  Vref   nRT
and
V p
 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
Titlepage
Topic Overview
•
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
•
Technique is to measure the volume of gas, oil and water
present in the pore space of a fresh or preserved core of
known bulk volume.
The core sample is divided into two parts:
•
•
•
Method
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
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
•
Method
The laboratory procedure provides the following
information:
•
3 Measurements
of Porosity
•
First sub sample gives the rock`s weight, WS1 , and the volumes of oil,
Vo1 , and water, VW1 , are recorded.
Second sub sample gives the volume of gas, Vg2 , and the rock`s bulk
volume, Vb2.
•
Fraction of the gas-bulk volume:
•
Also:
fg 
Vg 2
Vb 2
Ws1  Vb1  app and Ws 2  Vb 2   app  Vb1  Vb 2
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 S g
Ws1
Ws 2
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Section 3.5: Fluid-Summation
Titlepage
Topic Overview
•
Method
The formation oil- and water factor are calculated as follow:
1 General Aspects
2 Idealised Models
V
f o  o1  S o
Vb1
3 Measurements
of Porosity
•
Vw1
fw 
 S w
Vb1
The sum of the fluid-volume factor then gives the porosity value:
f o  f w  f g   So  Sw  S g   
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Section 3.5: Fluid-Summation
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
•
•
3 Measurements
of Porosity
Method
Example: Use of pycnometer in matrix volume calculation.
In order to define the matrix volume, Vm , of a core sample,
the following measuring steps are carried out:
1. The pycnometer cell is fully saturated with mercury.
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 
Vm 
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p1V1  p0V0
p1  p0
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Porosity Estimation from Geophysical Well Logs
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
• Porosity can be estimated from:
–
–
–
–
–
Formation resistivity factor
Microresistivity log
Neutron-gamma log
Density (gamma-gamma) log
Acoustic (sonic) log
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Potential Error in Porosity Estimation
Titlepage
Topic Overview
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
• Experimental data
– Involve a degree of uncertainty related to the possible
measurement errors
– The measurement of porosity is normally a function of Vp, Vm
and/or Vb
  f (Vm ,Vp ,Vb )
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Titlepage
Topic Overview
Potential Error in Porosity Estimation
If the porosity is defined as
1 General Aspects

2 Idealised Models
3 Measurements
of Porosity
Vp
Vb
The equation can be differentiated
d
dV p dVb



Vp
Vb
The potential error of prosity measurement is then
2
 V p   Vb 
  

 


 V p   Vb 

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FAQ
Titlepage
Topic Overview

Add Q&A
1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
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References
Titlepage
Topic Overview
1 General Aspects
Figures taken with permission from the authors of
Reservoarteknikk1: A.B. Zolotukhin and J.-R. Ursin
2 Idealised Models
3 Measurements
of Porosity
Figures also taken with permission from Ola Ketil Siqveland
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