1. LABORATORY DETERMINATION OF POROSITY
RESERVOIR PETROPHYSICS
LABORATORY DETERMINATION OF POROSITY

2. POROSITY DEFINITION
Porosity: The fraction of the bulk volume of a rock that is porous.
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
 = Porosity, expressed as fraction
Vb = Bulk volume of reservoir rock, ft3
Vm = Matrix volume, ft3
Vp = Pore volume, ft3
Vb = Vm + Vp

3. ROCK MATRIX AND PORE SPACE
Matrix - non pore space; the grains of sandstone, limestone, dolomite, and/or shale
Pore space - filled with fluids: water, oil, and/or gas

4. MEASUREMENT OF POROSITY
Core samples (measure two of: Vb, Vp, or Vm)
Openhole wireline logs
Samples of the rock are obtained from drill cuttings or by coring. The drill cuttings are usually tiny and irregularly shaped, which limits our ability to use them.
See sketches from previous lecture.
Core samples are either obtained using the drilling rig with a special coring bit and barrel (whole core) or using a logging tool (side-wall coring). Whole cores are often 4 to 5 inches in diameter and are usually obtained in 30 or 60-foot segments. They are generally preferred for technical evaluation but they are also more expensive. Side-wall cores can be obtained by making an additional logging run with a special logging device. A geologist usually studies the initial logs and picks intervals where he thinks that he needs a formation sample. Side-wall cores are of less use to the engineer because they are often irregularly shaped and partially damaged (often fractured) from the side-wall coring process.
Open-hole porosity measurement logs (density, neutron, and sonic) are routinely used to estimate formation porosity.

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:
Bulk volume, Vb
Matrix volume, Vm (also called grain volume)
Pore volume, Vp

6. Volume is an extensive property
Fraction of volume consisting of
pores or voids
Fraction of volume consisting
of matrix

7. MATRIX DENSITIES (m) OF TYPICAL PURE COMPONENTS OF RESERVOIR ROCK
These values are important for core and log analysis. Commit them to memory.
Unfortunately, few rocks consist of pure components but exist as a mixture of numerous minerals of varying sizes and compositions. Therefore, one can rarely assume the matrix density and get an accurate estimate of matrix volume.

8. LABORATORY METHODS OF POROSITY DETERMINATION
Bulk volume determinations
Direct calculation
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
Vb = Bulk volume
d = Diameter
L = Length
Most core analyses are conducted on core plugs that are cut from the whole core and are right circular cylinders. Special saws are used to cut the core plugs and their faces, so they are ready for special core analyses.
Irregularly shaped cores require a different measurement.
consistent units, usually cm

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

11. ARCHIMEDES METHOD Wsat - Wdry fluid Vp = Wdry - Wsub Vm = Vb =
 =
Wsat - Wsub
Vb =
Archimedes principle: buoyant force is equal to the weight of the fluid displaced.
Self Study: Review difference between mass and weight.
Self Study: A boat containing a person and a large rock floats in a swimming pool. The level of the water is marked on the side of the pool.
Then, the person throws the rock out of the boat, and it sinks to the bottom of the pool. Does the water level in the pool rise, fall or stay the same?

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. SOLUTION - Example 1 Weight of paraffin coating, Wparaffin =
Weight of dry core sample coated with paraffin - Weight of dry core sample Wparaffin = 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
(V = m/ρ)

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

15. LABORATORY METHODS OF POROSITY DETERMINATION
Matrix (Vm)
Assume rock density based on lithology and measure dry mass
Displacement methods
volumetric
gravimetric (see previous description)
Boyle’s Law:
Ideal Gas Law: R = pV/nT; valid at low pressures and high temperatures (e.g. lab conditions).
R is the Universal Gas Constant. The value and units of R are determined by specification of the units of p,V, n, and T.
For example, R = (psia*ft^3)/(lbmol*deg.R), and
R=8.314 (Pa*m^3)/(mol*K)
Boyle’s Law simply says pV is constant if nT is constant.

16. MATRIX VOLUME FROM MATRIX DENSITY
Known or assumed matrix density

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:
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)
Volumetric - submerge particles into a liquid and observe change in liquid volume.
Archimedes (gravimetric) - measure change in weight of particles submerged in liquid.

20. EXAMPLE 2 SOLUTION Calculating the Matrix Volume and Porosity of a Core Sample Using the Displacement Method
Bulk Volume, Vb = 9.9 cm3
Matrix Volume, Vma = 7.7 cm3
Porosity,
It is total porosity.

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
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? =
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:
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
p1 = Pressure at initial conditions, psia
p2 = Pressure at final conditions, psia
V1 = Initial volume
V2 = Final volume
Consistent units

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. GAS EXPANSION METHOD TO CALCULATE Vma
Initial conditions P1
Core V1
With V1 known, record p1
p1 = pressure at initial conditions
V1 = Volume of cell 1
Place cleaned, dried core sample in cell 2
Evacuate cell 2
Open valve
Valve
closed
Evacuate
Cell 2
Cell 1

26. GAS EXPANSION METHOD TO CALCULATE Vma
Final conditions P1 P2
Core
With V1 known, record p1
p1 = pressure at initial conditions
V1 = Volume of cell 1
Place cleaned, dried core sample in cell 2
Evacuate cell 2
Open valve
Valve
open
Cell 1
Cell 2

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
This method assumes that the core becomes saturated with the gas. Incomplete saturation would lead to an overestimate of the matrix volume.

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:
Bulk volume
Matrix volume
Pore volume
(Vb)
(Vm)
(Vp)

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

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,
Vp = Pore volume, cm3
Wsa = Weight of core saturated with fluid, g
wdry = Weight of dry core, g
f = Density of saturated fluid, gm/cm
Method follows Archimedes Principle: A body wholly or partly immersed in a fluid is buoyed up with a force equal to the weight of the fluid displaced by the body.

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 = g
Weight of sample saturated with water, Wsat = g
Density of water (f ) = 1.0 g/cm3
Weight of saturated sample submerged in water, Wsub = g
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 = g
Weight of sample saturated with water, Wsat = g
Density of water, f = 1.0 g/cm3
Weight of saturated sample immersed in water, Wsat,I = g

33. EXAMPLE 3 Solution Archimedes Method of Calculating Porosity a Core Sample
Vp =
Wsat – Wdry = f
448.6 – g
1.0 g/cm3
= 21.3 cm3
Vb =
Wsat – Wsub =
448.6 – g
= cm3
It is effective 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)
This method is more difficult to apply to core samples that require a jacket or rubber sleeve such as an unconsolidated sandstone. The jacket creates experimental problems, reducing its accuracy.
This method cannot be used for determining porosity under confining stress, whereas the gas expansion (Boyle’s law) method can be conducted at multiple values of confining stress.

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

36. PORE VOLUME FROM GAS EXPANSION METHOD
Initial conditions P1 V1
Core
The core plug is placed in a Hassler sleeve, making the volume of Cell 2 equal to the bulk volume.
This method is a continuation of the measurement of the matrix volume and uses Boyle’s law. The experiment is set up differently to measure pore volume.
Boyle’s law:
Initial cell conditions: measure V1 in Cell 1
Put core in Hassler sleeve, evacuate
Valve
closed
Cell 1
Cell 2

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

38. PORE VOLUME FROM GAS EXPANSION METHOD
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
The gas expansion method (Boyle’s law method) is probably the preferred method for measurement of core porosity, except for samples that are not perfect right cylinders or ones with large surface vugs or chips. The method is preferable for poorly consolidated samples that require a rubber sleeve or jacket.
One advantage of the method is that it is accurate and reasonably fast. Another important feature is that the measurement can be made at confining pressures approximating reservoir stress conditions.

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

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
Cores from the reservoir allow direct measurements of important reservoir properties. It is important to gather cores from a representative part of the reservoir, as reservoir properties vary horizontally and vertically. If a reservoir is known to be highly heterogeneous, many core samples will be required to describe the reservoir accurately.

41. SOME KEY FORMULAS

42. CROSS BEDDING, CARRIZO SANDSTONE
Tabular crossbedding in Carrizo Sandstone. Note diagenetic effects near boundaries of co-sets and along some laminae.
Where should porosity be measured?