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1. RESERVOIR PETROPHYSICS
LABORATORY DETERMINATION
OF POROSITY

2. Porosity: The fraction of the bulk
volume of a rock that is porous.
b
m
b
b
p
V
V
V
V
V
Porosity




POROSITY DEFINITION
• Porosity is a static property – it can be measured
in the absence of flow
• Determining effective porosity requires fluid flow
to determine if pores are interconnected

3. ROCK MATRIX AND PORE SPACE
matrix pore space

4. MEASUREMENT OF POROSITY
1. Core samples (measure two of: Vb, Vp, or Vm)
2. Openhole wireline logs

5. LABORATORY DETERMINATION
OF POROSITY
• Most methods use small samples (core plugs)
• multiple samples must be analyzed to get
statistically representative results
• sampling technique is important
• often all samples are taken from “sweet
spots” skewing analysis
To determine porosity, measure 2 of 3
volumetric parameters:
1. Bulk volume, Vb
2. Matrix volume, Vm (also called grain volume)
3. Pore volume, Vp

6. V
V
V p
m
b


Fraction of volume
consisting of
pores or voids
Fraction of volume consisting
of matrix
Volume is an extensive property

7. MATRIX DENSITIES (m) OF TYPICAL PURE
COMPONENTS OF RESERVOIR ROCK
Lithology Matrix Density
(g/cm
3
)
Sandstone 2.65
Limestone 2.71
Dolomite 2.87

8. LABORATORY METHODS OF
POROSITY DETERMINATION
Bulk volume determinations
1. Direct calculation
2. Fluid displacement methods
• Gravimetric
• Volumetric – mercury pycnometer ( a
precisely calibrated bottle)

9. BULK VOLUME BY DIRECT
MEASUREMENT
• Applicable for regularly shaped cores or
core plugs
• Calculate from core dimensions
• For example; volume of right circular
cylinder
4
L
d
V
2
b



10. LABORATORY METHODS OF
POROSITY DETERMINATION
Bulk volume determinations
1. Direct calculation
2. Fluid displacement methods
• Gravimetric (Archimedes) methods
• Volumetric – in pycnometer

11. ARCHIMEDES METHOD
Wsat Wsub
Wdry
Vp =
Wsat - Wdry
fluid
Vm =
Wdry - Wsub
fluid
 =
Wsat - Wdry
Wsat - Wsub
Vb =
Wsat - Wsub
fluid

12. EXAMPLE 1
Bulk Volume Calculated by
Displacement
A core sample coated with paraffin immersed in a
container of liquid displaced 10.9 cm3 of the liquid. The
weight of the dry core sample was 20.0 g, while the
weight of the dry sample coated with paraffin was 20.9 g.
Assume the density of the solid paraffin is 0.9 g/cm3.
Calculate the bulk volume of the sample.

13. Weight of paraffin coating, Wparaffin =
Weight of dry core sample coated with paraffin - Weight of dry core sample
Wparaffin = 20.9 g = 20.0 g = 0.9 g
Volume of paraffin coating = Weight of paraffin / density of paraffin
Vparaffin = 0.9 g / 0.9 g/cm3 = 1.0 cm3
Bulk volume of core sample = (Bulk volume of core coated with paraffin) –
(volume of paraffin)
Vb = 10.9 cm3 – 1.0 cm3 = 9.9 cm3
SOLUTION - Example 1
(V = m/ρ)

14. LABORATORY METHODS OF
POROSITY DETERMINATION
To determine porosity, measure 2 of 3
basic parameters:
1. Bulk volume
2. Matrix volume
• Assume matrix (grain) density
• Displacement method
• Boyles Law
• Pore volume
(Vm)
(Vb)
(Vp)

15. LABORATORY METHODS OF
POROSITY DETERMINATION
Matrix (Vm)
1. Assume rock density based on lithology and
measure dry mass
• Displacement methods
• volumetric
• gravimetric (see previous description)
• Boyle’s Law:
2
2
1
1 V
p
V
p 

16. MATRIX VOLUME FROM
MATRIX DENSITY
• Known or assumed matrix density
Density
Matrix
Sample
Dry
of
Mass
Vm 

17. APPLICABILITY AND
ACCURACY OF MATRIX
MEASUREMENT TECHNIQUES
• Known or assumed matrix density
– Accurate only if matrix density is known
and not assumed
– Core samples are often mixtures of several
components with varying matrix densities,
so density must be measured

18. LABORATORY METHODS OF
POROSITY DETERMINATION
To determine porosity, measure 2 of 3
basic parameters:
1. Bulk volume
2. Matrix volume
• Assumed matrix (grain) density
• Displacement method
• Boyles Law
3. Pore volume
(Vm)
(Vb)
(Vp)

19. MATRIX VOLUME FROM
DISPLACEMENT METHOD
• Reduce sample to particle size
• Measure matrix volume of particles by
– Volumetric method
– Archimedes method (gravimetric
measurement)

20. EXAMPLE 2
SOLUTION
Calculating the Matrix Volume and
Porosity of a Core Sample Using the
Displacement Method

21. SOLUTION - Example 2
Calculate the Porosity of a Core Sample Using the
Displacement Method and Matrix Volume
The core sample from Example 1 was stripped of the paraffin
coat, crushed to grain size, and immersed in a container with
liquid. The volume of liquid displaced by the grains was 7.7 cm3.
Calculate the matrix volume and the core porosity. Is this
effective porosity or total porosity? (It is total porosity)
Bulk Volume, Vb = 9.9 cm3
Matrix Volume, Vma = 7.7 cm3
b
ma
b
b
p
V
V
V
V
V
Porosity




 =
9.9 cm3 – 7.7 cm3
9.9 cm3
= 0.22

22. LABORATORY METHODS OF
POROSITY DETERMINATION
To determine porosity, measure 2 of 3
basic parameters:
1. Bulk volume
2. Matrix volume
• Assumed matrix (grain) density
• Displacement method
• Boyles Law (Gas Expansion)
3. Pore volume
(Vm)
(Vb)
(Vp)

23. MATRIX VOLUME FROM
GAS EXPANSION METHOD
• Involves compression of gas into pores
• Uses Boyle’s law
2
2
1
1 V
p
V
p 

24. GAS EXPANSION METHOD
TO CALCULATE Vma
• Initial conditions, with volumes of 2
cells known
• Place core in second cell, evacuate
gas (air) from second cell
• Open valve

25. Valve
closed
Cell 1
Evacuate
Cell 2
GAS EXPANSION METHOD TO
CALCULATE Vma
Initial conditions
V1
P1
Core

26. Valve
open
Final conditions
P2
Core
Cell 1
GAS EXPANSION METHOD TO
CALCULATE Vma
Cell 2
P1

27. GAS EXPANSION METHOD TO
CALCULATE Vma
• Vf = Volume of Cell 1 + Volume of
Cell 2 - Matrix Volume of Core
• Vt = Volume of Cell 1 + Volume of
Cell 2
• Vm = Vt - Vf

28. APPLICABILITY AND
ACCURACY OF MATRIX
MEASUREMENT TECHNIQUES
• Displacement method - Very accurate when
core sample is crushed without destroying
individual matrix grains
• Gas expansion method - Very accurate,
especially for samples with low porosities
Neither method requires a prior knowledge of
core properties

29. LABORATORY METHODS OF
POROSITY DETERMINATION
To determine porosity, measure 2 of 3
basic parameters:
1. Bulk volume
2. Matrix volume
3. Pore volume
(Vm)
(Vb)
(Vp)

30. LABORATORY METHODS OF
POROSITY DETERMINATION
Pore volume determination (Effective)
1. Gravimetric (Archimedes)
Wsat - Wdry
fluid
2. Boyle’s Law:
• (Gas expansion)
Vp =
2
2
1
1 V
p
V
p 

31. PORE VOLUME FROM
SATURATION METHOD
• Measures the difference between the
weight of a core sample saturated with
a single fluid and the dry weight of the
core
• Pore volume,
f
dry
sat
p
W
W
V




32. EXAMPLE 3
Archimedes Method of Calculating
Porosity a Core Sample
Using the gravimetric method with the following data,
calculate the pore and bulk volumes and the porosity. Is
this porosity total or effective?
Dry weight of sample, Wdry = 427.3 g
Weight of sample saturated with water, Wsat = 448.6 g
Density of water (f ) = 1.0 g/cm3
Weight of saturated sample submerged in water, Wsub =
269.6 g

33. EXAMPLE 3
Solution
Archimedes Method of Calculating
Porosity a Core Sample
Vp =
Wsat – Wdry =
f
448.6 – 427.3 g
1.0 g/cm3
= 21.3 cm3
Vb =
Wsat – Wsub =
f
448.6 – 269.6 g
1.0 g/cm3
= 179.0 cm3
b
p
V
V
Porosity 
 0.12
21.3 cm3
=
179.0 cm3
=

34. Applicability and Accuracy of
Pore Volume Measurement
Techniques
• Saturation (Archimedes) method
– Accurate in better quality rocks if effective
pore spaces can be completely saturated
– In poorer quality rocks, difficult to completely
saturate sample
– Saturating fluid may react with minerals in
the core (e.g., swelling clays)

35. LABORATORY METHODS OF
POROSITY DETERMINATION
Pore volume determination (Effective)
1. Gravimetric (Archimedes)
Wsat - Wdry
fluid
2. Boyle’s Law:
• (Gas expansion)
Vp =
2
2
1
1 V
p
V
p 

36. Core
PORE VOLUME FROM GAS
EXPANSION METHOD
V1
Valve
closed
Cell 1 Cell 2
P1
Initial conditions

37. Final conditions
Valve
open
Core
PORE VOLUME FROM GAS
EXPANSION METHOD
Cell 1 Cell 2
P1
P2

38. • Very accurate for both high-quality (high
) and low-quality (low ) core samples
• Should use low-molecular-weight inert
gases (e.g., helium)
• Measures effective (connected) pore
volume
PORE VOLUME FROM GAS
EXPANSION METHOD

39. SUMMARY
1. Bulk volume
2. Matrix volume
3. Pore volume
To determine porosity, measure 2 of 3
basic parameters:

40. CORES
• Allow direct measurement of reservoir
properties
• Used to correlate indirect measurements,
such as wireline/LWD logs
• Used to test compatibility of injection fluids
• Used to predict borehole stability
• Used to estimate probability of formation
failure and sand production

41. b
ma
b
b
p
V
V
V
V
V
φ
Porosity




)
)(
(
)
)(
1
(
)
(
V
m
V
V
V
V
V
V
V
b
m
b
p
p
m
b









SOME KEY FORMULAS

42. CROSS BEDDING, CARRIZO
SANDSTONE