# Measurement of Porosity

Objective

The objective for this experiment was to measure the effectual porosity of core samples using a Digital Helium Porosimeter.

Theoretical Background

Porosity is the ability of a solid material such as a rock to allow water to pass through it. The porosity fraction is the result obtained after dividing the pore volume with the bulk volume of the rock. The equation below depicts the calculation of the porosity fraction.

Porosity fraction (𝜙) = (pore volume / bulk volume)

The pore volume is the total space that make up the gaps within the rock while the bulk rock volume is the entire space the rock occupies. The rock volume is often obtained using the displacement method that involves the measurement of the volume of water displaced by the rock or by callipering where an instrument is used to measure this volume. Another factor that is considered is the grain volume which regards the volume that the actual grains occupy. Thus, the pore volume is calculated by the difference of the bulk volume and the grain volume of the core sample. Therefore, the equation for calculating the porosity fraction of the sample is as shown below.

𝜙 = [(bulk volume – grain volume) / (bulk volume)]

This experiment utilized the gas expansion for the Digital Helium Porosimeter. This apparatus was made up of a reference and sample compartment that were connected using valves to the source of the ideal gas used by the instrument. The figure below represents a schematic diagram of the Digital Helium Porosimeter.

Figure 1: A schematic of the digital helium porosimeter using a gas chamber.

In this figure, the sample chamber (V2) is linked to the reference chamber (V1) which is subsequently connected to the pressure regulator. The main approach towards the calculation of the porosity fraction involved the charging of the reference chamber while introducing a low-pressure gas that would create a semi-ideal gas. After this method, the reference chamber is disconnected from the source of the gas but once the volume is recorded. The source can then be opened to create a new value for the pressure whereby according to Boyle’s Law as the volume of the gas expands, the pressure decreases. The volume of the line (Vl) and the volume of the cup (Vc) can then be determined based on the measurements on the disks that are placed on the instrument. These measurements are used to calculate the grain volume and the eventual porosity fraction of the same sample. The equation below depicts how this calculation can be achieved.

{[1- (P1/P2)]Vl + Vc – ∑Vd = Vg}

Where Vl is the line volume, Vc is the cup volume, Vd is the total disk volume, and Vg is the grain volume for the sample. P1 and P2 are the pressures of the gases that are induced into the system of the apparatus in the experiment. Once the grain volume is determined, the value for the porosity fraction can be calculated using the equation below.

𝜙 = [ 1 – (Vg/Vb)]

Where Vg is the volume of the grains in the sample and Vb is the bulk volume of the rock sample.

Procedure

The main apparatus in the device consisted of 3 chambers. These sections were the reference chamber, the sample chamber and the source chamber. The calibration on the source ensured that the pressure of the gas released was at 100 psi. The disks used for the experiment were then placed and the source was turned on to charge the reference chamber. Each disk was aligned next to the digital recorder and after every disk’s volume was recorded they were sealed off. The pressure source was then switched off then started again to measure the second pressure (P2). This disparity in the measurement was calculated using linear regression analysis. Eventually, these figures were used to calculate the grain volume that was used in the calculation for the porosity fraction.

Results and Calculations

The values of the volumes that were obtained from the measurements on the 5 sample disks are presented in the table below.

Disk Number    Volume in cc

1    1.59864

2    4.80933

3    6.41134

4    9.63592

5    16.09359

Table 1: The volumes of the disks recorded in the experiment.

The disks were randomly placed into different groups where their initial volumes were totalled. These disks were then divided into 4 groups where the sum total of the volumes were combined. The table below represents these findings.

Group    P1    P2    Disks    Total Volume    {1-[P1/P2]}

1    91.8

91,9    31.7

24.4    2,3,4,5

3,4,5    36.95

32.14    -1.90

-2.77

2    92.1

92.1    18.8

13.9    4,5

5    25.73

16.09    -3.90

-5.63

3    91.9

92    35.3

24.5    1,2,3,4,5

1,2,4,5    38.55

32.14    -1.60

-2.76

4    91.8

91.8    15.9

22.7    2,3,4

2,4,5    20.86

30.54    -2.77

-3.04

Table 2: The results of the disk samples.

Using the results from the previous experiment and the results from the current experiment, the calculation of the porosity of the core samples can be determined from the figures on table with this equation {[1- (P1/P2)]Vl + Vc – ∑Vd = Vg}. The volume of the cup was found to be 47.457 and the volume of the line was 5.5903.

The calculations for these values follow the equations that were earlier indicated in this report. These equations when applying the values obtained helped to generate the values of the porosity fraction for the samples that were used in the experiment. The porosity value for the first sample was 0.1533 while for the other sample it was 0.1806.

Questions

Q There were disparities from the first experiment and the second one. The value of the porosity fraction from the first experiment was slightly lower than the value obtained from this experiment. This difference is likely to be caused by errors made in the experiment such as the improper calibration of the device. Nevertheless, both experiments showed a similar result in terms of the porosity of the samples since both figures had values that were close to each other. The initial experiment gave porosity values of 0.148 and 0.174 for the 2 samples while the next experiment gave 0.136 and 0.165 for the same two samples.

Q Formation compressibility tends to affect the porosity of rocks. This condition is created by the pressure build up from the extra weight that lies on the existing rock. The issue of compressibility tends to reduce the volume of the existing pores in the rocks implying that the same rock lacks the air spaces which can support life in the same rocks. This natural phenomenon is mathematically associated with porosity since the increase of pressure directly affects the available space in the rocks. The increased pressure often reduces the air spaces that were in the rocks. Hence, these factors tend to have a linear relationship mathematically.

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