In this module you will learn about Porosity Press the button to start

In this module you will learn about

Porosity

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1 General Aspects2 Idealised Models

3 Measurements of Porosity

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Topic Overview

TitlepageTopic Overview

2 Idealized Models

1 General Aspects 3 Measurments of porosity



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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



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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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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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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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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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Titlepage

• 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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Titlepage

47,6%or 476,06

1

b

mb

b

p

V

VV

V

V

Regular Cubic-Packed Spheres


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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Titlepage

39,5%or 395,0312

411

3

3

r

r

V

V

V

VV

V

V

b

m

b

mb

b

p


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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Titlepage

26,0%or 26,0212

411

3

3

r

r

V

V

V

VV

V

V

b

m

b

mb

b

p


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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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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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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Topic Overview

TitlepageMeasurement of porosity

Measurement of Porosity

Uncertainty

Well Logs Core Analysis

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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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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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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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Titlepage


• 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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Titlepage

• Calculation of the grain volume• Ideal gas law:

• In case of vacuum inside the sample chamber:

• Assuming adiabatic conditions, we obtains:


)(21 gsrefref VVVpVp

2

122

p

VpVpVpV refsrefg

nRTpV

VpVp 211

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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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• 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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• 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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• 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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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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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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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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• 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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• 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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• 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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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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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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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



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TitlepageFAQ

Add Q&A

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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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In this module you will learn about Porosity Press the button to start