Lesson 3 Porosity

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


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%


Why is porosity important?

Porosity is used in calculation of oil:

OOIP = VbɸSoi/Boi

OOIP = Original Oil-in-Place

Higher ɸ more oil


What factors affect porosity?(Brainstorm)


Packing of uniform spheres


Sorting


Cementation


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


Vugs

The vug is larger than many of the surrounding grains of sediment. The width of the view is approximately 2 mm.


Dual-porosity model


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


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 %


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


Question:

1. Sit in a boat without an engine.

2. Sit in a airplane by shutting the engine. What will happen?

What the difference?


Archimedes Principle

water

Wd

Fb

Fb=Vdisplaced*density

Which density?


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


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


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


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


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?


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?


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


http://en.wikipedia.org/wiki/File:Boyles_Law_animated.gif

Reference Volume

Sample Holder Volume

Gas

Measurement schematic

Determine Vs – Solid grain volume

Gas Porosimeter


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


Billet

Gas



V1

VR

VB

V2=V1+VR-VB

P3

P4

P3V1 = P4V1 + (P4VR – P4VB) V1 = P2VBP4/(P4P1 – P2P3)

V2 = V1 + VR


P2

Every V is known.

Reference Volume


Core

Gas



V1

VR

Vgr

V3=V1+VR-Vgr

P5

P6

P5V1 = P6V3=P6V1 + (P6VR – P6Vgr)


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.


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)


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


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


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


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


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


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


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


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


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


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

)(

)(

#


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

)(

)(

)(

#



Typical porosity values

Conventional reservoirs: 0.1-0.35

Shale reservoirs: ~5%


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

Lesson 3 Porosity

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Transcript of Lesson 3 Porosity