MSc Drilling & Well Engineering Formation Evaluation

POROSITY The porosity of a rock is a measure of the volume of the spaces between the grains, crystals, or particles. Quantitatively, the porosity, Ø, is the ratio of the volume of the void space to the total bulk volume of the rock (void space plus rock matrix), and can be expressed as: Vp Vb - Vma Vb - ( W/ρma ) Ø = = = Vb Vb Vb

where: Vp = pore volume Vb = bulk volume Vma = volume of matrix minerals W = total weight of matrix minerals ρma = density of matrix minerals (weight per unit volume) Packing. 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 the porosity for a sand with a cubic packing is shown in Figure 1. This packing is very unstable, but porosities of 40 to 45 % are known to exist in unconsolidated sands.

Vb = L3

F N

I

n = number of spheres (L/d)3 Vma = n . (π d3/6)

L3 - (L/d)3 . (π d3/6) Ø =

L3 L3 - L3 . (π d3/6 d3) Ø = L3 Ø = 1 - (π/6) = 0.4764

ig. 1 : Porosity of cubic-packed spheres.

ote that the porosity is independent of the size of the spheres.

ssued Oct 2003 Porosity Theo Grupping

MSc Drilling & Well Engineering Formation Evaluation

The porosity, Ø, is a dimensionless ratio, with a value between 0 and 1. It is often quoted as a percentage (e.g. 26 %), but must be entered in all equations and formulae as a fraction. (decimal form e.g. 0.26). Identical spheres can be packed in 6 different ways as shown in Figure 2. The porosity varies from 47.64 %, for the cubic packing, to 25.95 % for rhombohedral and triclinic packing arrangements.

Type: Cubic Hexagonal Rhombohedral Orthorhombic Tetragonal Triclinic Por.: 47.6 % 39.5 % 26.0 % 39.5 % 30.2 % 26.0 %

Fig. 2 : The six possible geometric arrangements of identical spheres. Grain Size Distribution. Identical spherical grains are rarely encountered in nature, where ranges of grain sizes need to be considered. The smaller grains tend to occupy the pore spaces between the larger grains. Porosity is, therefore, dependent on the type of packing and on the grain size distribution. A classification system, defining grain sizes for Table 2 - Carbonates siliclastics is given in Table 1, and for carbonate rocks in Table 2. Crystal or Grain Size

Table 1 – Siliclastics Symbol Microns

Category Median Grain L Size in Microns 400 M

Gravel 200 2000 F

Very Coarse 100 1000 VF

Coarse 50 500 EF

Medium 250 Pore Size

Fine 125 Symbol Microns

Very Fine 62 B < 100

Silt C 100 - 2000 D > 2000

Matrix Texture

Issued Oct 2003 Porosity Theo Grupping

MSc Drilling & Well Engineering Formation Evaluation

1 micron = 10-3 mm I = compact

II = chalky III = sucrosic

The grain size distribution of a sand or sandstone sample is determined by means of a vertical stack of sieves with the mesh size decreasing from the top downwards. The crushed sandstone sample is weighed and placed upon the upper sieve. Vibration of the 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) of the sieves, resulting in a distribution curve as shown in Figure 3.

100

% weight 75 50 25 0 D25 D75 D

Fig. 3 : Grain size distribution. The degree of sorting, expressed by the Trask coefficient (So), is defined by the equation:

So = √ D25/D75

where: D25 = grain diameter at 25 % of sample weight (larger grains). D75 = grain diameter at 75 % of sample weight. The porosity of a sandstone decreases with decreased sorting, i.e. an increased sorting coefficient. The six sorting categories, according to Trask, are indicated in Table 3.

Sorting Trask Coeff. 1.00

Extremely Well 1.10

Very Well 1.20

Well 1.40

Moderately 2.00

Poorly

Table 3

Issued Oct 2003 Porosity Theo Grupping

MSc Drilling & Well Engineering Formation Evaluation

Very Poorly 2.70

5.70 Actual Porosity Values. The porosity may be as high as 45 % in loose sands, and as low as 1 % in still prolific fractured carbonates. A common range of porosities in sandstones and carbonates is as follows:

recent sands (loose) 35 - 45 % sandstones 15 - 35 %

tight sandstones 10 - 15 % limestones 5 - 20 % dolomites 10 - 30 %

chalk 5 - 40 % Some non-productive rocks also have high porosities. Shales, clays and extremely fine-grained chalks may have porosities of 40 % or higher. Porosity Determination. 1. Buoyancy Technique (Effective por.)

Fig. 4 : Matrix minerals volume from

hydrostatic weighing method. (sample weight)air + (sample + crVma = density

Issued Oct 2003 Poros

The matrix volume is determined by hydrostatic weighing, as shown in Figure 4. The cleaned and dried core sample is weighed in air and then saturated with a wetting liquid, such as toluene or chlorothene. The sample is then immersed in the same wetting liquid and weighed again.

The reduction in weight is the buoyancy, which is the product of the matrix volume (plus the unconnected pores), and the density of the saturating liquid. The bulk volume of the sample is measured by immersion in mercury, which is a non-wetting liquid, and does not enter the pores of the core sample at atmospheric pressure.

The porosity is then: Vb - Vma Ø = Vb where: Vb = bulk volume Vma = matrix volume

adle weight)toluene + (cradle weight)toluene

of toluene

ity Theo Grupping

Issued Oct 2003 Porosity

MSc Drilling & Well Engineering Formation Evaluation

Theo Grupping

weight in air The matrix density, ρma, is routinely obtained at the same time: ρma = matrix volume 2. Gas Expansion Method (Effective Porosity). This method is based on Boyle’s Law. A cleaned and dried rock sample is inserted into the sample chamber as illustrated in Figure 5. The sample chamber and expansion chamber are both evacuated. The two valves isolating the expansion chamber are then closed. An initial pressure, P1, is applied to the sample chamber. The valve to the left side of the sample chamber is then closed, and the valve between the sample chamber and the expansion chamber is opened. The pressure between the two chambers is then allowed to equalise and is measured, P2.

Fig. 5 : Boyle’s law porosimeter. Knowing the bulk volume, Vb, which is obtained with the mercury immersion method, the volume of the sample chamber, Vs, and the volume of the expansion chamber, Ve, the porosity can be calculated. For ideal gases at constant temperature: P1V1 = P2V2 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 Vp ( P1 - P2 ) Vb + P2Ve - ( P1 - P2 ) Vs Ø = = Vb ( P1 - P2 ) Vb