RESERVOIR PETROPHYSICS

LABORATORY DETERMINATIONOF POROSITY

Porosity: The fraction of the bulk volume of a rock that is porous.

b

mb

b

p

VVV

VV

Porosity −===φ

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

ROCK MATRIX AND PORE SPACE

matrix pore space

MEASUREMENT OF POROSITY

1. Core samples (measure two of: Vb, Vp, or Vm)

2. Openhole wireline logs

LABORATORY DETERMINATIONOF 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 3volumetric parameters:

1. Bulk volume, Vb2. Matrix volume, Vm (also called grain volume)3. Pore volume, Vp

VVV pmb +=

Fraction of volume consisting of pores or voids

Fraction of volume consistingof matrix

Volume is an extensive property

MATRIX DENSITIES (ρm) OF TYPICAL PURE COMPONENTS OF RESERVOIR ROCK

Lithology Matrix Density (g/cm3)

Sandstone 2.65 Limestone 2.71 Dolomite 2.87

LABORATORY METHODS OFPOROSITY DETERMINATION

Bulk volume determinations

1. Direct calculation

2. Fluid displacement methods

• Gravimetric

• Volumetric – mercury pycnometer ( a precisely calibrated bottle)

BULK VOLUME BY DIRECT MEASUREMENT

• Applicable for regularly shaped cores or core plugs

• Calculate from core dimensions

• For example; volume of right circular cylinder

4LdV

2

bπ

=

LABORATORY METHODS OFPOROSITY DETERMINATION

Bulk volume determinations

1. Direct calculation

2. Fluid displacement methods

• Gravimetric (Archimedes) methods

• Volumetric – in pycnometer

ARCHIMEDES METHODWsat WsubWdry

Vp =Wsat - Wdry

ρfluid

Vm =Wdry - Wsub

ρfluid

φ =Wsat - Wdry

Wsat - Wsub

Vb =Wsat - Wsub

ρfluid

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.

Weight of paraffin coating, Wparaffin =

Weight of dry core sample coated with paraffin - Weight of dry core sampleWparaffin = 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)

LABORATORY METHODS OF POROSITY DETERMINATION

To determine porosity, measure 2 of 3basic parameters:

1. Bulk volume

2. Matrix volume• Assume matrix (grain) density• Displacement method• Boyles Law

• Pore volume

(Vm)

(Vb)

(Vp)

LABORATORY METHODS OFPOROSITY DETERMINATION

Matrix (Vm)1. Assume rock density based on lithology and

measure dry mass

• Displacement methods• volumetric • gravimetric (see previous description)

• Boyle’s Law:

2211 VpVp =

MATRIX VOLUME FROM MATRIX DENSITY

• Known or assumed matrix density

DensityMatrixSampleDryofMassVm =

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

LABORATORY METHODS OF POROSITY DETERMINATION

To determine porosity, measure 2 of 3basic parameters:

1. Bulk volume

2. Matrix volume• Assumed matrix (grain) density• Displacement method• Boyles Law

3. Pore volume

(Vm)

(Vb)

(Vp)

MATRIX VOLUME FROM DISPLACEMENT METHOD

• Reduce sample to particle size• Measure matrix volume of particles by

– Volumetric method– Archimedes method (gravimetric

measurement)

EXAMPLE 2SOLUTION

Calculating the Matrix Volume and Porosity of a Core Sample Using the

Displacement Method

SOLUTION - Example 2Calculate 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

mab

b

p

VVV

VV

Porosity −==φ= = 9.9 cm3 – 7.7 cm3

9.9 cm3= 0.22

LABORATORY METHODS OF POROSITY DETERMINATION

To determine porosity, measure 2 of 3basic parameters:

1. Bulk volume

2. Matrix volume• Assumed matrix (grain) density• Displacement method• Boyles Law (Gas Expansion)

3. Pore volume

(Vm)

(Vb)

(Vp)

MATRIX VOLUME FROM GAS EXPANSION METHOD

• Involves compression of gas into pores

• Uses Boyle’s law

2211 VpVp =

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

ValveclosedCell 1

EvacuateCell 2

GAS EXPANSION METHOD TO CALCULATE Vma

Initial conditions

V1

P1

Core

Valveopen

Final conditionsP2

Core

Cell 1

GAS EXPANSION METHOD TO CALCULATE Vma

Cell 2

P1

GAS EXPANSION METHOD TO CALCULATE Vma

• Vf = Volume of Cell 1 + Volume ofCell 2 - Matrix Volume of Core

• Vt = Volume of Cell 1 + Volume ofCell 2

• Vm = Vt - Vf

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

LABORATORY METHODS OF POROSITY DETERMINATION

To determine porosity, measure 2 of 3basic parameters:

1. Bulk volume2. Matrix volume3. Pore volume

(Vm)(Vb)

(Vp)

LABORATORY METHODS OF POROSITY DETERMINATION

Pore volume determination (Effective)

1. Gravimetric (Archimedes)Wsat - Wdry

ρfluid

2. Boyle’s Law:• (Gas expansion)

Vp =

2211 VpVp =

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

drysatp

WWV

ρ−

=

EXAMPLE 3Archimedes 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 (ρf ) = 1.0 g/cm3

Weight of saturated sample submerged in water, Wsub = 269.6 g

EXAMPLE 3Solution

Archimedes Method of CalculatingPorosity a Core Sample

Vp = Wsat – Wdry =

ρf

448.6 – 427.3 g1.0 g/cm3 = 21.3 cm3

Vb = Wsat – Wsub =

ρf

448.6 – 269.6 g1.0 g/cm3

= 179.0 cm3

b

p

VV

Porosity ==φ 0.1221.3 cm3

=179.0 cm3

=

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)

LABORATORY METHODS OF POROSITY DETERMINATION

Pore volume determination (Effective)

1. Gravimetric (Archimedes)Wsat - Wdry

ρfluid

2. Boyle’s Law:• (Gas expansion)

Vp =

2211 VpVp =

Core

PORE VOLUME FROM GASEXPANSION METHOD

V1

ValveclosedCell 1 Cell 2

P1Initial conditions

Final conditions

Valveopen

Core

PORE VOLUME FROM GASEXPANSION METHOD

Cell 1 Cell 2

P1P2

• Very accurate for both high-quality (high φ) and low-quality (low φ) core samples

• Should use low-molecular-weight inert gases (e.g., helium)

• Measures effective (connected) pore volume

PORE VOLUME FROM GAS EXPANSION METHOD

SUMMARY

1. Bulk volume2. Matrix volume3. Pore volume

To determine porosity, measure 2 of 3basic parameters:

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

b

mab

b

p

VVV

VV

φPorosity −===

))((

))(1(

)(

VmVVVVVVV

bm

bp

pmb

ρ

φ

φ

=

−=

=

+=

SOME KEY FORMULAS

CROSS BEDDING, CARRIZO SANDSTONE