02 porosity

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Shell Nigeria Graduate Training Programme Petrophysics

Martey, A.O Univation2.1

2 POROSITY

In hydrocarbon reservoirs, the pore volume is available for storage of oil, gas, and

water. The porosity or a rock is a measure of the amount of internal space that is

capable of holding these fluids. Total porosity is defined as the, ratio of the volume

of all the pores to the bulk volume of a material, regardless of whether or not all of

the pores are interconnected. Quantitatively, the porosity istheratio of "the volume

of the void space to the total volume of void space plus rock matrix. Porosity is

normally expressed as a fraction or percentage of bulk volume.

Porosity is

( )

b

mab

b

mab

b

p

V

WV

V

VV

V

V

/=

==

Vp = pore volume

Vb = bulk volume

Vma = volume of matrix minerals

W = total weight of matrix minerals

?ma = matrix minerals density (weight per unit of minerals volume)

Effective porosity is defined as the ratio of interconnected pore volume to the bulk

volume of a material.

The pore space available in a given rock depends on: the shape of the grains, the

uniformity of the grains, the way in which they are arranged or packed, and the

amount of cementing material between them. For instance, a "rock" made of

cubically packed uniform spheres, without any cementing material would have a

porosity of 48 per cent. The porosity is entirely independent of the size of the

spheres.


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A rock made of spheres is unknown, but the generalisation can be made that the

more uniform the grains, the larger will be the porosity. For instance, if an actual rock

is composed of grains with a wide range of grain sizes, then there will be a chance

that the smaller grains will fill the interstices between the larger ones.

Ordinary loose sand has a porosity of about 30%, but this drops to about 15% in

sandstones, according to the degree of compaction and the amount of cementing

material.

Porosity of sandstones is controlled primarily by textural properties. These are

1. Grain size

2. Sorting

3. Shape (sphericity)

4. Roundness (angularity)

5. Packing

Of these, sorting and packing are of major importance, grain size, shape and

roundness of relatively minor importance.

Porosity in limestones is much more variable in magnitude than it is in sandstones.

In some (reef-type) formations it is very high, in a few cases exceeding 50 per cent.

However, in general the porosity of carbonate rocks is lower than it is in sandstones.

Dolomites have normally good porosities.

Identical spheres: A loose sand (uncemented, unconsolidated) can be represented

by a particular packing of identical spheres. The porosity of such a packing can be

calculated from its geometry. The calculation of porosity for a cubic packing is shownin Fig. 2.1 (48%). This packing is of course very unstable. Yet, porosities of 40 to 45

per cent exist in unconsolidated sand formations (e.g. Venezuela).


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Fig. 2. 1

It is of interest to note that the porosity is independent of the size of the spheres.

The tightest packing of identical spheres is rombohedral, with a porosity of 26%.

Fig. 2.2


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Porosity is a dimensionless ratio with a value between 0 and 1.0. It should be noted

that it is often quoted, as a percentage (e.g. 26%) but must be entered in equations

and calculations as a decimal fraction (e.g. 0.26).

Grain size distribution: Identical spherical grains do not occur in nature, where

ranges of grain need to be considered, and where the smaller grains tend to occupy

the pore space between the larger ones. Porosity is therefore dependent on the type

of packing and the grain size distribution (that is sorting).

Wentworth designed a classification system defining grain sizes for siliclastics (Table

2.1), and Archie for carbonates (Table 2.2).


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Table 2.1: Siliclastics Table 2.1: Carbonates

Crystal or grain size

Category Median grain size in

Microns

Symbol Range in Microns

Gravel Large

Very Coarse Medium

Coarse Fine

Medium Vefy fine

Fine Extremely fine

400

200

100

50

Very fine Pore size

Silt

2000

1000

500

250

125

62

Symbol Range in

microns

B 2000

1 Micron = 10-3 mm.

Matrix texture:I = Compact

II = Chalky

III = Sucrose

The grain size distribution of a sand or sandstone sample is determined by means of

employing a vertical stack of sieves, the mesh size decreasing from the top

downwards (Fig. 2.3).


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The crushed sample is weighed and placed onto the upper sieve. Vibration of this

sieve stack causes the grains to be rapidly distributed over the sieves. The

cumulative percentage weight on each sieve is plotted against the mesh size (D) and

a distribution curve is obtained (Fig. 2.4).

Fig. 2.3. Assembly of sieve trays (finest screens at the bottom) for analysis of the

grain-size distribution of sediments.


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The degree of sorting, expressed by the Trask coefficient (So), is defined by the

equation:

So

= (D25

/ D75

)1/2

in which

D25 = grain diameter at 25% of sample weight (larger grains)

D75 = grain diameter at 75% of sample weight

Table 2.3 indicates the six sorting categories according to Trask.

Fig. 2.4


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Table 2.3

Category Trask coefficient

Extremely well

Very well

Well

Moderately

Poor

Very poor

1.00

1.10

1.20

1.40

2.00

2.70

5.70

Actual porosity values: These may be as high as 45% in loose sands, and as low

as 1 % instill prolific fractured carbonates.

A common range ofporosities in sandstones and carbonates is as follows:

recant sands (loose) 35 - 45%

sandstones 20 - 35%

tight sandstones 15 - 20%

limestones (Middle East) 5 - 20%

dolomites (Middle East) 10 -30%

chalk (North Sea) 5 -40%


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Some non-productive rocks also have high porosities. Shales, clays, and extremely

fine-grained chalks fall into this category. They may have porosities 40% and higher.

In general, a field appraisal classification of reservoir porosity is:

5 10% poor

10 20% good

> 20% very good

Porosity determination

Buoyancy technique - Effective porosity

Porosity is determined routinely on core samples as shown opposite in Fig. 2.5. Bulk

volume, Vb , is determined by immersing in mercury. Because of the low atmospheric

pressure, mercury does not invade the pore spaces, so the displacement of mercury

(measured by Archimedes Principle of bouyancy) is equal to the bulk volume of the

rock.

Grain volume, Vg, is determined by immersion in chlorothene which, through wetting

the grain surface, invades all pore spaces connected to the surface of the sample.

Hence the volume of chlorothene displaced is equal to Vg. The reduction in weight isthe buoyancy, which is the product of the matrix volume (plus unconnected pore

volume) and the density of the saturating fluid.

Vg=( ) ( ) ( )

densityechlorothen

weightscaffoldCweightscaffoldsampleDweightsampleAchlochloair

_

_,_,_, ++

From these two measurements, plus dry sample weight in air, porosity and grain

density are calculated thus:

b

mb

V

VV =

Matrix density ?m =mVvolumematrix

airinWeight

__

__


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Gas expansion method (Boyles Law Porosimeter)- Effective

porosity

An alternative for measuring grain volume is the Boyle's law method where Helium is

used to invade the pore space (Fig. 2.6). The dry sample is inserted in the sample

chamber and both chambers are evacuated. The two valves isolating the expansion

chamber are then closed, and an initial pressure P1 is applied to the sample

chamber. Then the valve on the left ofthe sample chamber is closed, and the valve

between the sample chamber and the expansion chamber is opened. The pressure

between two chambers is allowed to equalise to pressure P2.

Fig. 2.5

Fig. 2.6


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Knowing Vb (again obtained by mercury immersion), Vs and Ve, the porosity can be

calculated from the formula shown below.

For ideal gases at constant temperature

P1V1 = P2 V2

Vs =volume of empty sample chamber

Ve = volume of expansion chamber

P1 [Vs - (Vb -Vp)] = P2 [Vs -(Vb -Vp) + Ve]

P1Vs - P1Vb + P1Vp = P2Vs - P2Vb + P2Vp+P2Ve

( ) ( )

( )b

seb

b

p

VPP

VPPVPVPP

V

V

21

21221

+==

Clearly only connected porosity is measured. If there is non-connected porosity, it

will not be invaded by Chlorothene or Helium, and will be included in the grain

volume with a consequent reduction in apparent grain density.

Additionally Mercury may invade large vugs or fractures or even pore space in very

coarse grained rock with a reduction in apparent bulk volume. This leads to a

decrease in calculated porosity.

Finally the porosity is that of a 'dry' sample dependent on the drying process

particularly important in shaly sands.

Pycnometer Method - Total Porosity

The weight, W of the cleaned and dried core sample is obtained by weighing the

sample in air. The Bulk Volume Vb is measured by immersion of the sample in

mercury.

A representative portion of the sample is then crushed to individual grain size. The

crushed sample is weighed and its volume determined in a pycnometer by

displacement of a non-wetting fluid.


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The grain density ?g, will be the weight of the crushed sample divided by its volume.

The grain volume, or matrix volume, of the original sample Vg, is calculated by

dividing its weight by the grain density.

The Total porosity is then equal to the bulk volume minus the grain volume divided

by the bulk volume.

= (Vb Vg) IVb or = [Vb - (W / ?g)] IVb

This measurement gives the best results, but the disadvantage of this method is that

the sample is destroyed in the process and no other measurements, such as

permeability, can be taken on the sample afterwards.


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IN UNCONSOLIDATED SANDS THE PORE SIZE IS ABOUT

1/3 OF THE GRAIN SIZE. IN COMPACTED SANDS THE

PORE SIZE IS ABOUT 1/10 OF THE GRAIN SIZE.

DECREASE IN PORE DIAMETER IS THE RESULT OFCOMPACTION / DEPTH OF BURIAL


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Martey A O Univation2.22

02 porosity

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