02 Porosity
Transcript of 02 Porosity
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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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