in this module you will learn about porosity press the button to start
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In this module you will learn about
Porosity
Press the button to start
1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
References
Topic Overview
TitlepageTopic Overview
2 Idealized Models
1 General Aspects 3 Measurments of porosity
1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
References
Topic Overview
TitlepageGeneral 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 spacescontributesto absoluteporosity
Permeablespacescontributesto effectiveporosity
1 General Aspects2 Idealised Models
3 Measurements of Porosity
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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-porousmedia.
Intergranular porosity Fracture porosity Micro- porosity Vugular porosity Intragranular porosity
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageConsolidated
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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSorting
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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 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 Aspects2 Idealised Models
3 Measurements of Porosity
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• Estimation of porosity accounting to this model:
78,5%or 785,0422
2
rmrn
mnr
V
V
b
p
Parallel Cylindrical Pores
ebulk volum -V
volumepore -V
ebulk volum in the contained cylinders ofnumber -nm
radius pipe -r
b
p
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
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Topic Overview
Titlepage
47,6%or 476,06
1
b
mb
b
p
V
VV
V
V
Regular Cubic-Packed Spheres
• Estimation of porosity accounting to this model:
33
m
3b
p
3
48
3
4
8
1
rock) by the occupied spacebulk of (volume umematrix vol-V
2ebulk volum-V
volumepore-V
rr
r)(
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
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Topic Overview
Titlepage
39,5%or 395,0312
411
3
3
r
r
V
V
V
VV
V
V
b
m
b
mb
b
p
• Estimation of porosity accounting to this model:
Regular Orthorhombic-Packed Spheres
spheres packed-icorthorhomb theofheight -h3
4 umematrix vol-V
3460sin422ebulk volum -V
3m
33 b
r
rrhrr
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
Titlepage
26,0%or 26,0212
411
3
3
r
r
V
V
V
VV
V
V
b
m
b
mb
b
p
• Estimation of porosity accounting to this model:
Regular Rhombohedral-Packed Spheres
rrr
r
rhrr
224on tetrahedrin theheight -h
3
4 umematrix vol-V
2422ebulk volum -V
22
3m
3b
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
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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 Aspects2 Idealised Models
3 Measurements of Porosity
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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. pebblesandsandfVb
Vp
pebblepebblesand sand,sandf.sand
pebbleb f.sand,f.sandp
pebblesandf.sandpebble
pebblepebblesandf.sand
pebble
sandsandf.sand
pebble
f.sandf.sand.
VVVV
VVVV
V
V
V
V
V
V
b
ptot
V
V
Example
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageMeasurement of porosity
Measurement of Porosity
Uncertainty
Well Logs Core Analysis
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 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 Aspects2 Idealised Models
3 Measurements of Porosity
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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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
Titlepage
Section 3.2: Grain-Volume Measurements Based on 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 Aspects2 Idealised Models
3 Measurements of Porosity
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Titlepage
• Calculation of the grain volume• Ideal gas law:
• In case of vacuum inside the sample chamber:
• Assuming adiabatic conditions, we obtains:
Section 3.2: Grain-Volume Measurements Based on Boyle`s Law
)(21 gsrefref VVVpVp
2
122
p
VpVpVpV refsrefg
nRTpV
VpVp 211
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 3.3: Bulk-Volume Measurements
• 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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 3.3: Bulk-Volume Measurements
• 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:
wb
mmV
12
ww
bbbb dr
r
Vdm
m
Vdm
m
VdV
11
22
w
w
wb
d
mm
dm
mm
dmmmdV
12
1
12
212
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 3.3: Bulk-Volume Measurements
• 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%.
22
12
2
2
w
w
mm
m
V
V
b
b
22
2
w
w
bwb
b
V
m
V
V
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
Developers
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Topic Overview
TitlepageSection 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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 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.
021
02
21
2
10
pppwhere
and
refp
refp
refVpppp
pV
nRTVVp
nRTVpVp
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 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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TitlepageSection 3.5: Fluid-Summation Method
• 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
gg SV
Vf
2
2
andVW appbs 112
12122
s
sbbappbs W
WVVVW
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 3.5: Fluid-Summation Method
• The formation oil- and water factor are calculated as follow:
• The sum of the fluid-volume factor then gives the porosity value:
ob
oo SV
Vf
1
1w
b
ww SV
Vf
1
1
gwogwo SSSfff
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageSection 3.5: Fluid-Summation 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:
mVVp 00
mVVp 11
01
0011
pp
VpVpVm
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepagePorosity 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 Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepagePotential 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
),,( bpm VVVf
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepagePotential Error in Porosity Estimation
b
p
V
V
b
b
p
p
V
dV
V
dVd
22
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 Aspects2 Idealised Models
3 Measurements of Porosity
Developers
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Topic Overview
TitlepageFAQ
Add Q&A
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1 General Aspects2 Idealised Models
3 Measurements of Porosity
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Topic Overview
TitlepageReferences
Figures taken with permission from the authors ofReservoarteknikk1: A.B. Zolotukhin and J.-R. Ursin
Figures also taken with permission from Ola Ketil Siqveland
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