Porosity.ppt

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Porosity
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Developers References
Topic Overview
Titlepage
Topic Overview
2 Idealized Models
1 General Aspects 3 Measurments
of porosity

1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
General aspects
 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
Art-micrograph of sandstone with oil
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Void spaces
contributes
to absolute
porosity
Permeable
spaces
contributes
to effective
porosity

1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Genetically the following types of porosity can be distinguished:
Rock media having both fracture and intergranular
pores are called double-porous or fracture-porous
media.
 Intergranular porosity
 Fracture porosity
 Micro- porosity
 Vugular porosity
 Intragranular porosity
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Consolidated
 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Sorting
 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 2: Idealised Models
Parallel cylindrical pores
Regular cubic-packed spheres
Regular orthorhombic-
packed spheres
Regular rhombohedral-
packed spheres
Irregular-packed spheres with
different radii
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• Estimation of porosity accounting to this model:
78,5%
or
785
,
0
4
2
2
2










rm
rn
m
n
r
V
V
b
p
Parallel Cylindrical Pores
e
bulk volum
-
V
volume
pore
-
V
e
bulk volum
in the
contained
cylinders
of
number
-
n
m
radius
pipe
-
r
b
p

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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
47,6%
or
476
,
0
6
1 







b
m
b
b
p
V
V
V
V
V
Regular Cubic-Packed Spheres
3
3
m
3
b
p
3
4
8
3
4
8
1
rock)
by the
occupied
space
bulk
of
(volume
ume
matrix vol
-
V
2
e
bulk volum
-
V
volume
pore
-
V
r
r
r)
(

 









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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
39,5%
or
395
,
0
3
12
4
1
1 3
3








r
r
V
V
V
V
V
V
V
b
m
b
m
b
b
p 

Regular Orthorhombic-Packed Spheres
 
spheres
packed
-
ic
orthorhomb
the
of
height
-
h
3
4
ume
matrix vol
-
V
3
4
60
sin
4
2
2
e
bulk volum
-
V
3
m
3
3
b
r
r
r
h
r
r








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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
26,0%
or
26
,
0
2
12
4
1
1 3
3








r
r
V
V
V
V
V
V
V
b
m
b
m
b
b
p 

Regular Rhombohedral-Packed Spheres
r
r
r
r
r
h
r
r
2
2
4
on
tetrahedr
in the
height
-
h
3
4
ume
matrix vol
-
V
2
4
2
2
e
bulk volum
-
V
2
2
3
m
3
b









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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• 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.
Irregular-Packed Spheres with Different Radii
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
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)
3,7%
or
037
,
0
. 

 
 pebble
sand
sand
f
Vb
Vp





















pebble
pebble
sand
sand,
sand
f.sand
pebble
b
f.sand,
f.sand
p
pebble
sand
f.sand
pebble
pebble
pebble
sand
f.sand
pebble
sand
sand
f.sand
pebble
f.sand
f.sand
.
V
V
V
V
V
V
V
V
V
V
V
V
V
V













b
p
tot
V
V
Example
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Measurement of porosity
Measurement of Porosity
Uncertainty
Well Logs
Core Analysis
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Full-diameter
Core Analysis Grain-volume
measurements based
on Boyle`s law
Bulk-volume
measurements
Pore-volume
measurements
Fluid-Summation
Method
Core Analysis
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.1: Full-diameter Core Analysis
• 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:
• 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.2: Grain-Volume Measurements Based on
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.
Porosity measurements based on the
Boyle`s law
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Boyle`s Law
• Helium gas is often used due to its following properties:
• 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• Calculation of the grain volume
• Ideal gas law:
• In case of vacuum inside the sample chamber:
• Assuming adiabatic conditions, we obtains:
Boyle`s Law
)
(
2
1 g
s
ref
ref V
V
V
p
V
p 


2
1
2
2
p
V
p
V
p
V
p
V
ref
s
ref
g



nRT
pV 
V
p
V
p 2
1
1 
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.3: Bulk-Volume Measurements
• 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• Example: Uncertainty analysis in measuring the bulk
volume using Archimedes` principle.
• The core is measured in two steps:
– 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:
• Differentiating the equation above gives us:
w
b
m
m
V

1
2 

w
w
b
b
b
b dr
r
V
dm
m
V
dm
m
V
dV








 1
1
2
2












w
w
w
b
d
m
m
dm
m
m
dm
m
m
dV


 1
2
1
1
2
2
1
2
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• If the density measurement as well as the two mass-
measurements above, is considered to be independent
measurements, the relative uncertainty in the bulk volume
is:
• It may also be written as:
• 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%.
2
2
1
2
2
2 






 



















 
w
w
m
m
m
V
V
b
b


2
2
2 






 








 








 
w
w
b
w
b
b
V
m
V
V



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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.4: Pore-Volume 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.
• Helium or one of its substitutes is injected into the core
plug through the end stem.
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.4: Pore-Volume Measurements
• Calculations of the pore volume
• It is important to notice that the Hassler core holder has to
be coupled to a volume of known reference, Vref.
 
 
 
0
2
1
0
2
2
1
2
1
0
p
p
p
where
and
ref
p
ref
p
ref
V
p
p
p
p
p
V
nRT
V
V
p
nRT
V
p
V
p









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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Section 3.5: Fluid-Summation Method
• 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:
• 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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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• The laboratory procedure provides the following
information:
• 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:
g
b
g
g S
V
V
f 


2
2
and
V
W app
b
s 

 1
1
2
1
2
1
2
2
s
s
b
b
app
b
s
W
W
V
V
V
W 


 
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• The formation oil- and water factor are calculated as follow:
• The sum of the fluid-volume factor then gives the porosity value:
o
b
o
o S
V
V
f 


1
1
w
b
w
w S
V
V
f 


1
1
  
 




 g
w
o
g
w
o S
S
S
f
f
f
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
• 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:
 
m
V
V
p 
0
0
 
m
V
V
p 
1
1
0
1
0
0
1
1
p
p
V
p
V
p
Vm



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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Porosity Estimation from Geophysical Well Logs
• Porosity can be estimated from:
– Formation resistivity factor
– Microresistivity log
– Neutron-gamma log
– Density (gamma-gamma) log
– Acoustic (sonic) log
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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Potential Error in Porosity Estimation
• 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
)
,
,
( b
p
m V
V
V
f


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1 General Aspects
2 Idealised Models
3 Measurements
of Porosity
Topic Overview
Titlepage
Potential Error in Porosity Estimation
b
p
V
V


b
b
p
p
V
dV
V
dV
d




2
2







 








 


b
b
p
p
V
V
V
V


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If the porosity is defined as
The equation can be differentiated
The potential error of prosity measurement is then

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

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