Porosity Measurement of Sandstone Cores by Water Saturation

Reservoir Petrophysics Laboratory ReportPETR 2311Department of Chemical and Biomolecular Engineering

Petroleum Engineering ProgramUniversity of Houston

Title

Porosity Measurement of Sandstone Cores by Water SaturationAuthor(s) and Group Member(s)

Jonathan Delafuente

Kelly Ramirez

Jonathan Nwogu

MohandaAbdallaReviewer(s)

Holley, Thomas

Pitchumani, RamananTeam Number Experiment

Number

Page Count Submission

Attempt

2 1 25 1Date of

Experiment

Date of

Submission

Total Grade

09/20/2011

(Tue)

10/11/2011

(Tue)

Porosity Measurement of Sandstone Cores by Water Saturation

GRADE

Grading Format Content

Figures 5 4Tables 1 5Summary 1 3Conclusions 1 4Background 2 8Material and Methods 2 5Calculation 5 15Results 1 10Discussion 1 10References 1 2Acknowledgements 0 1Division of Labor 0 1Appendices 0 2Observation Notebook 5 5Overall Appeal 0 0Sub TOTAL 25 75COMMENTS:

PETR 2311 (Spring 2011) – Team 00

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EXECUTIVE SUMMARY

The purpose of the Porosity Lab is to be able to determine the

porosity of a core. We determined the porosity of the yellow core

to be 0.160 with an uncertainty of 0.0034, and the porosity of

the gray core to be 0.148 with an uncertainty of 0.0031. By

determining the porosity of this core, we will be able to do so

with almost any material we come across. The experiment will run

at the same temperature with the same type of water.

The yellow and gray sandstone cores were placed in a

container and filled with water until fully saturated.

Measurements were taken of the cores including mass and

dimensions. After placing the cores in the vacuum, measurements

were also taken. There was significant increase in the mass of

the core and increase in the dimensions also. The greatest

difference in mass and dimensions occurred after the cores were

taken out of the vacuum because they were extremely diluted.

Determining the porosity of a given substance helps us

categorize which rocks and minerals are best at storing fluids

such as water and oil. If we come across this type of materialPETR 2311 (Spring 2011) – Team 00

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again in our career, we will be able to draw conclusions as to

whether it will be beneficial to us or not. For example, if the

core we experimented on turns out to be very porous and we come

across the same material during a drilling in our career, we can

conclude that the rock or mineral is beneficial to us because of

its ability to store fluids. This experiment determined that the

porosity of the yellow core was greater than the porosity of the

gray core. This was determined by measuring their initial weight

and dimensions and comparing them to their final, fully saturated

weight and dimensions.

TABLE OF CONTENTS

GRADE..........................................................2

EXECUTIVE SUMMARY..............................................3

CONCLUSIONS....................................................5

BACKGROUND.....................................................7


5


MATERIALS AND METHODS..........................................9

Materials.....................................................9

Methods.......................................................9

Experimental Procedure......................................9

Calculation Procedure......................................13

RESULTS.......................................................15

DISCUSSION....................................................17

REFERENCES....................................................19

NOMENCLATURE..................................................20

DIVISION OF LABOR.............................................21

Mohanda Abdalla..............................................21

Kelly Ramirez................................................21

Jonathan Nwogu...............................................22

Team Leader Jonathan Delafuente..............................23

ACKNOWLEDGMENTS...............................................25


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CONCLUSIONS

1. The purpose of this lab was to determine the porosity of two

cores which were given. In this porosity experiment, two

different cores were measured, one being the grey core and the

other, the yellow core.

2. The values measured were the diameter, length and mass of the

core. First they were measure while the core was dry and they

also measured when the cores were saturated. This measurement

was taken individually and 5 different times to ensure

accuracy.

3. The approximate value in (%) of porosity measured and

calculated by each individuals are as follows:

Yellow Core Grey Core

Mohanda – 15.4% Mohanda – 14.3%

Jon D – 15.7% Jon D – 14.9%

Kelly – 16.85% Kelly – 15.0%PETR 2311 (Spring 2011) – Team 00

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Jonathan – 16.2% Jonathan -14.9%

4. The general reason for discrepancy in the results is because

each individual measured a different core and also the degree

of uncertainty in measuring the different cores varied for

each individual.

5. The value of uncertainty of the porosity calculated by each

individual is as follows:

Yellow Core Grey Core

Mohanda – 0.003119384 Mohanda – 0.004735348

Jon D – 0.0027 Jon D – 0.002

Kelly – 0.00343988 Kelly – 0.00419914

Jonathan – 0.00325 Jonathan – 0.0027

6. Also, the possible sources of errors in this experiment

comprises of error due to parallax, the digital balance not


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being calibrated before measurements were taken, platform

where the cores were weighed on was not stable and also the

core not being completely saturated before it is taken out of

the vacuum oven. These errors definitely had an effect on our

porosity calculations.

7. From the overall data presented, we can conclude that the

yellow core is more porous than the grey core.


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BACKGROUND

Porosity is the most basic property of reservoir rocks

because it determines the ability of a rock to store gas, oil,

water and other fluids. To determine the porosity of a sample

rock, we must first calculate the bulk volume which is our total

volume. Next we must determine the pore volume, which is the

volume where fluid can be stored. The grain volume is solid

material in which fluid cannot be stored. The total porosity can

be determined with the following equation:

Porosityɸ=VVoid

VTotal=VTotal−Vgrain

VTotal [1]

Where porosity has no units and instead is represented as a

percentage or fraction. V(void) is the pore volume, V(grain) is

the grain volume and V(total) is the total volume. We

determined the volume of the core by taking measurements of the

dimensions by using a vernier caliper. We could also find the

volume of the cores by using water displacement. The density of

water is approximately 1g/cm³ and is equal to the mass per unit

volume. Knowing this relationship, the volume of the voids can be


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calculated. If the core is submerged into a known volume of

water, the displacement will show us the new volume.

Experiment

At the beginning of the experiment, the two cores were set

up for us to measure the initial state of the core. The diameter

and length were measured in millimeters/inches and the weight was

measured in grams. After taking the measurements, we filled two

small beakers with water and fully submerged the cores in the

water. The cores were taken to a vacuum chamber after being fully

submerged in the beakers. The vacuum aided the saturation process

by forcing the water into the voids. The vacuum fills the voids

in the core and replaces the empty space with water. After the

vacuum finished, the cores were once again measured and recorded.


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Figure 1: Sketch of Experiment

Equipment used in Experiment

Fisher Scientific ISOTEMP Vacuum Oven: Model 281A, Kocurek

Industries

20 ml Beaker: Uncertainty is 5 mL

Vernier Caliper: MSC Direct catalog no.: 06417216,

Uncertainty is 0.01 mm

Digital Balance: OHAUS Scout Pro Models SP401/SP402.

Uncertainty is .01 g

Digital Balance Vernier Caliper 20ml Beaker

Vacuum Oven


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MATERIALS AND METHODS

Materials

1. Tap Water

2. Bentheimer Sandstone - cream colored

3. Berea Sandstone - light grayish color (A105)

4. Two 20 ml beakers

5. Digital weighing balance, Ohaus Scout™ Pro, SP402,

Ohaus Corporation 19A Chapin Road, P.O. Box 2033, Pine

Brook, NJ 07058

6. Fisher Scientific ISOTEMP Vacuum Oven: Model 281A,

Kocurek Industries

7. Vernier Caliper: MSC Direct catalog no.: 06417216

8. Weighing paper

Methods

Experimental Procedure

1. Gather materials and verify they are working properly.

2. Verify the uncertainties of all measurement devices that

will be used in the lab experiment.


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3. Place the weighing papers on balance and set the balance

zero, and then place one core on top of the weighing paper.

Record this value in grams and repeat this process five

times for accuracy. Each time the core is weighed the scale

with the weighing paper is set to zero.Do the same for the

second core, being sure to label all values with their

correct units and uncertainties.

4. Remove the core from the balance and use the VernierCaliper

measure the lengthand diameter in inches and in millimeters.

Record the measurement and repeat this process five times,

moving the placement of the calipers slightly on the core.

5. Place each core in its own beaker and submerge the core in

water.

6. Place each of the submerged cores in the vacuum and wait a

few minutes until the core is completely saturated with

water.

7. Remove the beakers with the submerged cores from the vacuum.

Take the saturated cores out of the beakers and place them


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on the digital balance with the weighing paper. Record this

mass in grams.

8. Dispose of the water and clean the area.

Materials Used in Experiment


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A B C D E F

G

A. Cores: Berea Sandstone (top) and Bentheimer Sandstone

(bottom)

B. Beakers

C. Weighing paper

D. Tap water

E. Vacuum Oven

F. Digital Balance

G. Vernier Caliper


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Graphic Display of Experimental Procedure

1 2 3

4 5 6

Repeat steps 1-3

End of Experiment

7 8 9


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Calculation Procedure

1. The calculation of porosity using the measurements which was

recorded from the lab experiment.

a. First we must calculate the total volume of the

sandstone. The sandstone is in the general shape of a

cylinder. Use the length and diameter previously

measured in the formula of the volume of a cylinder.

Equation 1a.

b. We must calculate the void volume by finding the

difference in the masses of the dry cores and the water

saturated cores. Dividing this number by the density of

water will get the volume of the voids. Equation 1b.

c. Using the calculated void volume and total volume, the

porosity can be calculated. Equation 1c.

2. Error analysis


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a. The uncertainties of all measurements must be taken

into consideration.

b. Void volume uncertainty is found by equation 2a

c. Total volume uncertainty is found by equation 2b.

d. Overall Porosity uncertainty is found by equation 2c.

Vt=Πd2L4

(PI*(24.94mm)^2*25.36mm) / 4 = 12388.88mm^3

(1

a)

Vv=Ms−Mdρw

(27.18g-25.23g) / (.001g/mm^3) = 1950.00 mm^3

(1

b)

Φ=VvVt

1950.00 mm^3/ 12388.88 mm^3 = .157

(1

c)

δVv=δMs+δMd

ρw(2


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(.011g +.01g) /(.001g/mm^3)= 20.1 mm^3 a)

δVt=|∂V∂d

|δd+|∂V∂L

|δL

((PI*(24.94mm)* (25.36mm))/2)*.0547mm +

((PI*(24.94mm)^2)/4)*.0547mm

= 82.15 mm^3

δΦ=(|δVvVvbest

|+|δVt

Vtbest|)Φbest

[[(20.1 mm^3)/ (1950.00 mm^3)] / [(82.15

mm^3)/(12388.88mm^3)]]*.157

=.0027

(2

b)

(2

c)


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RESULTS

Yellow Core

Mohanda Jon D KellyJonathan

Vv (mm) 1922 1950 2106 2342

Vt (mm)12498.52

103 12388.812498.52

114450.

7

Porosity0.153778

195 0.1570.168499

94 0.162

The above tables represent the Total and Void volumes along with

the porosities of the each core for all team members.


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Grey Core


Vv (mm) 1770 1840 1860 1876

Vt (mm)12370.241

14 12330.712370.24

1112579.

8

Porosity0.1430853

27 0.1490.150360

85 0.149


Grey Core


Uncertainty Vv(mm)

76.13994393 31.458

76.1399439 43.32

Uncertainty Vt(mm)

47.68288736 20

40.4959014 50

Uncertainty Porosity

0.004735348 0.002

0.00419914 0.0027


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Yellow Core


Uncertainty Vv(mm)

81.65012918 82.15

81.6501292 66.7

Uncertainty Vt(mm)

26.43167673 20.954

29.2353841 40.12

Uncertainty Porosity

0.003119384 0.0027

0.00343988

0.00325


The above tables represent the calculated error analysis of the

Volumes and porosity of each team member’s cores.

DISCUSSION

1. Effective Porosity

The calculations shown in the attached excel sheet uses our

team’s combined to show the effective porosity of the cores.

The effective porosity is taken to be the “dead end pores that

may be filled with water or oil” (Tiab 91). In this case, the

pores of our cores were filled with water. We calculated the

effective porosity by finding the grain volume, which was

subtracted by the total volume and then finally divided

entirely by the total volume. The resulting porosities also

contain uncertainties which were calculated for eachPETR 2311 (Spring 2011) – Team 00

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individual data. These uncertainties were found by each

individual piece of equipment used in the lab. For ease of

calculation units were converted, such as the diameters of the

core from inches to centimeters. The errors given for each

piece of equipment is one such that cannot be avoided. On the

other hand, errors including those of air bubbles in the cores

or uneven saturation were negligible.

2. Absolute Porosity

Absolute porosity is calculated by taking the void volume

divided by total volume of the core. The calculation of

absolute porosity is unnecessary in this experiment. The cores

which we experimented on could have a considerable absolute

porosity but if the pore channels are not connected within the

core, they lose fluid conductivity since the fluid has no way

of being reached. In a real life scenario, if oil is occupying

an unconnected void space, it is of little interest to the

engineer who seeks oil. Effective porosity is the value used

in all petroleum engineering calculations which is why

absolute porosity is an unnecessary calculation.


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3. Assumptions used in experimentation and calculation

During the experiment, the scale we used to measure the mass

of our cores was not personally calibrated by our team but we

assume it was accurate. The uncertainty of the scale was also

taken in our calculations. Another assumption made is that the

vacuum used in the lab is 100% effective and that all the

connected voids in the core were fully saturated. Also, when

using density in our calculations, we used 1g/cm³ even though

density changes slightly at different temperatures. We find

that the difference in density is very small at different

temperatures; therefore we round it off to 1g/cm³. To conduct

further study on cores we could use different ways of

calculating the porosity. The method we used in this

experiment is known as imbibition. The core was saturated

under a vacuum, the weight was taken and the dry weight is

subtracted from that amount. Then we use the density of water

to divide that amount and get our porosity. Another method

mentioned by Professor Pitchumani is the gas expansion method

in which the core would enclosed in a container of known


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volume and pressure which is connected to another container of

know volume and pressure. When the valve of the two containers

is opened, the gas passes through the second container until

there is uniform pressure. The ideal gas law would then be

used to calculate the volume of the pores. This method was not

used because such materials were not available.


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REFERENCES

DjebbarTaib, and Erle C. Donaldson. Petrophysics: theory and practice of

measuring reservoir rock and fluid transport properties. Gulf Professional

Publishing, 2004: Chapter 3.

Amyx, J. W., Bass, D. M., Jr., and whiting, R. L. Petroleum Reservoir

Engineering. McGraw-Hill Book Co., New York, NY, 1960: Chapter 2.

Anderson, G. Coring and Core Analysis Handbook.PennWell Books, Tulsa,

OK, 1975: Chapter 2.

Pitchumani, Ramanan. Error Analysis lecture 2b; Petrophysics course

notes.


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NOMENCLATURE

Greek Symbols

ρw Density of water

g/m^3

ϕ Total Porosity no

units

Alphabetical Variables

Vt Total Volume m^3

Vv Void Volume m^3

d Diameter

m

L Length m


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Ms Saturated mass g

Md Dry mass g


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DIVISION OF LABOR

MohandaAbdalla:

1. Experimental work

Recorded all measurements for Length and Diameter of

each core.

Weighed each core on the balance for the dry mass.

Soaked the cores in water and placed in vacuum.

Weighed the saturated cores for the saturated mass.

2. Calculation and analysis

Used the measurements of length and diameter along with

the masses to find the total volume and void volume of

each core.

Used the divide the volumes to get an overall porosity

for each core.

Calculated the error analysis of each step to find the

uncertainty of the porosity we found.

3. Report writing

Wrote the executive summary

Scanned all lab papers to put in the final reportsPETR 2311 (Spring 2011) – Team 00

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4. Literature Search

Read the section on porosity in the course textbook.

Kelly Ramirez:



each core.







each core.


for each core.



3. Report writing

Wrote the background and discussion.


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Provided the drawings of the graphic display of

experimental procedure.

Helped organize and revise the overall final draft of

the report.



Jonathan Nwogu:



each core.







each core.


for each core.


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3. Report writing

Helped with the discussion of the results.

Organized the reference and put into APA format.

Acknowledged the professor and TA.



Team Leader

Jonathan Delafuente:



each core.






34




each core.


for each core.



Provide the excel sheet with formulas for easy access

to final calculations.

7. Report writing

Wrote the materials and methods with the schematic

drawing that team member Kelly provided.

Provided all formulas used in the calculation process.

Wrote the Nomenclature of each symbol use in the lab

calculations.

Provide tables for the result section of the lab.

Organized the final product of the lab report.




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ACKNOWLEDGMENTS

RamananPitchumani:Professor Pitchumani was in the lab from

beginning to end. The entire lab experiment was explained step by

step and what was needed to be done. Prior to the porosity lab

experiment Professor Pitchumani thoroughly defined porosity and

why it is important to petroleum engineers.

Guoyuan He: He was responsible for operating the vacuum oven,

making sure the student’s cores were completed saturated. Our

group had individual questions regarding the schematic of the

experiment and he answered them completely.


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Porosity Measurement of Sandstone Cores by Water Saturation

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