Porosity
Think about a sponge or a sand beach
2 mm wide (white – grains, blue – epoxy)
© 2015 James J. Sheng
Several Concepts of Porosity
Conceptual representation of different pores
Pore throat
pore
© 2015 James J. Sheng
volumeBulk
IsolatedDeadendctedInterconne
volumeBulk
VolumePoreTotal
V
V
b
p
volumeBulk
volumeporedeadendconnectedporosityEffective
int
volumeBulk
volumeporeIsolatedporosityeIneffectiv
Definitions
(Total) porosity
Relation among them?© 2015 James J. Sheng
Porosity calculation
•Spherical model: uniform spheres packed in a cubic pattens•Sphere completely enclosed in a cube
r=radiusWhat is the grain volume?
Vsphere=4/3*π*r3= Vm
Bulk volume= volume of a cube:Vb=(2r)3=8r3
Pore volume:Vp= 8r3- 4/3*π*r3
Porosity:Ø=Vp/Vb=(Vb-Vm)/Vb=1- Vm/Vb
Vp=(24-4π)r3/3Ø= (24-4π)/(3*8)Ø= 0.476 or 47.6%
© 2015 James J. Sheng
Why is porosity important?
Porosity is used in calculation of oil:
OOIP = VbɸSoi/Boi
OOIP = Original Oil-in-Place
Higher ɸ more oil
© 2015 James J. Sheng
What factors affect porosity?(Brainstorm)
© 2015 James J. Sheng
Packing of uniform spheres
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Sorting
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Cementation
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Primary and Secondary Porosity
•Primary has to do with initial deposition of sediments•Secondary porosity comes from solution, dolomitization, fractures, vugs, etc.
• SolutionCaCO3+2H = Ca(HCO3)2
•Magnesium ions replacing calcium ions2CaCO3 + Mg++ = CaMg(CO3)2 + Ca++
Dolomite crystals are denser and occupy less space•Compaction can reduce porosity
© 2015 James J. Sheng
Vugs
The vug is larger than many of the surrounding grains of sediment. The width of the view is approximately 2 mm.
© 2015 James J. Sheng
Dual-porosity model
© 2015 James J. Sheng
What is Shale
• Shale is a fine-grained sedimentary rock
• Shales are typically deposited in very slow moving water and are often found in lakes and lagoonal deposits, in river deltas, on floodplains and offshore from beach sands.
• Shale is characterized by breaks along thin laminae or parallel layering
• Usually has extra low permeability
© 2015 James J. Sheng
POROSITY AND PERMEABILITY ANALYSIS ON NANOSCALE FIB-SEM IMAGING OF
SHALE ROCK
Figure 1. A sample shale gas rock. (a). Optical photograph of the whole thin section. (b). Close up of yellow box in (a) with light microscope under plain light. (c). Close up of the yellow box in (b) with SEM
It is clear that porosity cannot be detected by microscope. A further close up on the yellow box is shown in Figure c using SEM, which reveals the pores, organic matter and mineral matrix at nano scale.
Shale porosity: a few %
© 2015 James J. Sheng
Methods of Determination of Porosity
Core plugs•Conventional core analysis•Computerized Tomography (CT)•Special core analysis
Well logging•Density, Neutron, Acoustic, NMR•Covered in a well logging course
Drilled cuttings•Microscopy (thin sections) – based on dye color•Micro-CT - pixel size to 1 µm•Darcylog (IFT product) – based on gas compressibility
© 2015 James J. Sheng
Question:
1. Sit in a boat without an engine.
2. Sit in a airplane by shutting the engine. What will happen?
What the difference?
© 2015 James J. Sheng
Archimedes Principle
water
Wd
Fb
Fb=Vdisplaced*density
Which density?
© 2015 James J. Sheng
Porosity from Core Plugs
Conventional core analysis
We need to determine two of three parameters:•Vb
•Vp
•Vs
b
sb
sp
p
b
p
V
VV
VV
V
V
V
© 2015 James J. Sheng
Determine Vb – bulk volume(1) Caliper, if a sample is a cylindrical,
Vb= (πd2/4)*LBecause there is always some irregularity in cutting core plugs we take several measurements of L and D and average them.(2) Use mercury – Sample directly put in a container of mercury.Vb = displaced mercury (mercury cannot enter sample pores)(3) Archimedes PrincipleCoat the sample with epoxy and then immerse in water. People also use paraffin, silicone and heat shrinkable Teflon.
water
Wd
Wim Fb Fb=Vdisplaced*water density
Vdisplaced = ?
Vb
© 2015 James J. Sheng
Determine Vp – pore volume
Use weight of dry sample (Wd) and weight of sample saturated with water (Wsat)
Difference: Saturated core has water
Gained weight: Wsat-Wd= pore volume*density of liquid
Wd Wsat
Unsaturated Saturated
© 2015 James J. Sheng
Determine Vs – Solid grain volume
Use the Archimedes PrincipleThis time the sample is not coated. Water will enter pores. What is the displaced volume?
water
Wd
Wim Fb
Fb=Vdisplaced*water density
Vdisplaced = ?
Vs
© 2015 James J. Sheng
Example calculation #1
1”
4”
If the weight in the air is 110 g, andthe weight in the water is 73 g,what is the porosity of this plug?
© 2015 James J. Sheng
Example calculation #2
1”
4”
1. What is the bulk volume, Vb?2. What is the weight in the air?3. If coated with epoxy or paraffin and
Immersed in water, what is the weight?4. If no coating, how much is the weight?5. If no coating, how much is the buoyancy?6. If saturated with water, what is the bulk density?
© 2015 James J. Sheng
http://en.wikipedia.org/wiki/File:Boyles_Law_animated.gif
Review of Boyle’s law
p1V1 = p2V2
•T maintained the same•Closed system•Ideal gas
© 2015 James J. Sheng
© 2015 James J. Sheng
© 2015 James J. Sheng
Reference Volume
Sample Holder Volume
Gas
Measurement schematic
Determine Vs – Solid grain volume
Gas Porosimeter
© 2015 James J. Sheng
V1VR
V2=V1+VR
P1P2
P1V1 = P2V2 =P2V1 + P2VR VR = (P1V1 – P2V1)/P2
P2: Off P2 TEST Valve (open)P1 Lock in to off
P2
Reference Volume
Sample Holder Volume
Billet
Gas
Measurement schematic
© 2015 James J. Sheng
V1
VR
VB
V2=V1+VR-VB
P3
P4
P3V1 = P4V1 + (P4VR – P4VB) V1 = P2VBP4/(P4P1 – P2P3)
V2 = V1 + VR
P2: Off P2 TEST Valve (open)P1 Lock in to off
P2
Every V is known.
Reference Volume
Sample Holder Volume
Core
Gas
Measurement schematic
© 2015 James J. Sheng
V1
VR
Vgr
V3=V1+VR-Vgr
P5
P6
P5V1 = P6V3=P6V1 + (P6VR – P6Vgr)
P2: Off P2 TEST Valve (open)P1 Lock in to off
P2
Vgr=VR+V1-V1P5/P6
Vp=Vb-Vgr
φ = Vp/Vb
Why using Helium or Nitrogen?•Small molecules to enter small pores•Inertness to avoid reaction and adsorption on grains•Ideal gas equation can be used.
© 2015 James J. Sheng
X-ray Computed Tomography (CT) - ɸ measurementComputed Tomography (imaging)Computerized TomographyCT scanInitially used in medical societyWe use it to measure porosity
Imaging principle (pages 22-23):X-ray are adsorbed;Different parts have different adsorption;Detector will record x-ray strength, resulting in an image.
Images are characterized by CT number;CT numbers represent radiodensity (attenuation coefficient)
© 2015 James J. Sheng
1000)(
water
waterxHUunitHounsfield
CT numbers:
μwater and μair are the linear attenuation coefficients of water and air, respectively.
CT numbers (Hounsfield unit):Pure water: 0Air: -1000
© 2015 James J. Sheng
CTN vs. bulk density
Calibration with known media (fluids and rocks)
Density (ρ)
CTN
CTN vs. bulk density
y
x
y=ax+bρ=a(CTN)+b
© 2015 James J. Sheng
Calculation of porosity (CT)For an oil saturated rock, Total mass of an oil-saturated rock (o,m) = Total mass of oil (o) + Total mass of matrix (m)Vo,m*ρo,m = Vo*ρo + Vm*ρm
ρo,m = (Vo/Vo,m)*ρo + (Vm/Vo,m)*ρm
ρo,m = ɸ*ρo + (1-ɸ)*ρm
a(CTN)o,m +b= ɸ*[a(CTN)o +b)+ (1-ɸ)*[a(CTN)m +b]a(CTN)o,m +b= ɸ*a(CTN)o +ɸb+ (1-ɸ)*a(CTN)m +b(1-ɸ)a(CTN)o,m = ɸ*a(CTN)o + (1-ɸ)*a(CTN)m
CTNo,m = ɸ*CTNo + (1-ɸ)*CTNm
For air-saturated rock,CTNa,m = ɸ*CTNa + (1-ɸ)*CTNm
ɸ=(CTNo,m- CTNa,m )/(CTNo-CTNa )
If using a water-saturated rock,ɸ=(CTNw,m- CTNa,m )/(CTNw-CTNa ) © 2015 James J. Sheng
Porosity measurement
Core plugs
Special core analysisCorrected pressure effect by applying confining pressure
© 2015 James J. Sheng
Methods of Determination of Porosity
Core plugs•Conventional core analysis•Computerized Tomography (CT)•Special core analysis
Well logs•Density, Neutron, Acoustic, NMR•Covered in a well logging course
Drilled cuttings•Microscopy (thin sections) – based on dye color•Micro-CT - pixel size to 1 µm•Darcylog (IFT product) – based on gas compressibility
© 2015 James J. Sheng
Estimate porosity from density measurement (DPHI)
ρb = ɸ ρf + (1 − ɸ)ρm
ɸ = (ρb - ρm )/(ρf - ρm )
Densities (g/cm3):Sandstone: 2.65Limestone: 2.71Dolomite: 2.87
Water: 1.0Oil: 0.6-1.0Gas: < 0.4
© 2015 James J. Sheng
Averaging of Porosity
Principle:
Total pore volume = sum of the pore volume of each subdivision
Total porosity = sum of the porosity of each subdivision
pip VV
© 2015 James J. Sheng
Plug
0.3
0.1
0.2
Average porosity for this well in this layer:
Well #1
1ft
1ft
1ft
Averaging of porosityLa
yer
1
2.03
1.02.03.0
2.03
)1(1.0)1(2.0)1(3.0
nhn
h
h
h
)hA(hA
hAVVV
)Ah(VV
VV
i
i
iisameh
i
ii
iii
ibaveragebp
iiibipi
pip
i
© 2015 James J. Sheng
Plug
0.3
0.1
0.2
Average porosity for this well:
Well #1
1ft
0.5ft
1ft
Averaging of porosity
2.03
1.02.03.0
22.05.2
)5.0(1.0)1(2.0)1(3.0
h
h
i
ii
average
La
yer
1
© 2015 James J. Sheng
Shale Layer
Layer 1
Layer 2
Layer 3
h1
h2
h3
n
h
h
h
h
hAhA
hAVVV
AhVV
VV
i
i
iisamethebecannoth
i
ii
iii
ibaveragebp
iiibipi
pip
i
)(
)(
Well #1-real situation
Average porosity near one well
© 2015 James J. Sheng
A1
A2
A3
Well #1
Well #3
Well #2
Average porosity for one layer in a field
i
ii
iiiii
iibp
iiiibipi
pip
A
A
hAhA
hAVV
hAVV
iwellneararearepresentsi
VV
)(
)(
#
© 2015 James J. Sheng
V1
V2
V3
Well #1
Well #3
Well #2
Average porosity for a whole field
field
ii
ii
iii
iiiii
iibp
iiiibipi
pip
V
V
hA
hA
hAhA
hAVV
hAVV
iwellnearVOLUMErepresentsi
VV
)(
)(
)(
#
© 2015 James J. Sheng
© 2015 James J. Sheng
Typical porosity values
Conventional reservoirs: 0.1-0.35
Shale reservoirs: ~5%
© 2015 James J. Sheng
Study guide – Porosity
• Remember definitions of different porosities and understand their meaning
• Know the pores and pore throats and their difference
• Know the primary and secondary porosities and their difference
• Can list several factors which affect porosity
• Know how to calculate porosity
• Know how to determine porosity in lab and their principles
• Able to calculate average porosity
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