png 406 write up 1

HOPE MEYERS

Rock and Fluid Laboratory

Absolute and Effective Porosity

Sieve Analysis

Absolute Permeability

Gas Permeability and Klinkenberg Effect

Energy and Mineral Engineering Department

The Pennsylvania State University

March 4, 2011

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TABLE OF CONTENTS

Effective Summary…………………………………………………………2

Introduction………………………………………………………………4

Results and Discussion……………………………………………………6

Conclusion…………………………...…………………………………..17

Sample Calculations……………………………………………………..18

Nomenclature……………………………………………………………18

References……………………………………………………………….19

1

Executive Summary

In the Absolute and Effective Porosity lab the objective was to illustrate the

concept of porosity and to determine the absolute and effective porosity of porous media.

I also had to estimate error in the porosity calculations from the errors associated to each

parameter measured. There were three parts to this experiment. In part one: The Marble

Experiment, I had to fill a beaker with several marbles, and then fill the beaker to the top

with water in order to measure the porosity. With the measurements of the weight of the

marbles, the size of the marbles, and the volume of water used, the porosity could be

determined. In part two: The Helium Porosimeter, I obtained a core sample and

vacuumed all the air out of the sample, and filled the pore space with helium gas. Using

the measurements of the core sample, as well as initial and final pressures of the gas, I

could determine the porosity. In part three: The Barnes Method, a core sample was used

and all the air from it was removed. After the air was removed, water was introduced to

the sample and the water filled up all the empty pore space. Using the weights of the

unsaturated and saturated core, the weight of the fluid absorbed, and the volume of the

fluid absorbed, I could calculate the effective porosity. In the Sieve Analysis lab the

objective was to conduct a standard grain size analysis test and determine the relative

proportions of different grain sizes. A sieve set was used, and 250 grams of sand was

poured into the sieve. The sieve was then placed in the sieve shaker for 10 to 15 minutes.

Afterwards, the sand was separated and weighed. This process was repeated four times.

This lab helped in seeing different grain sizes, and how they are distributed in sand

samples. In the Absolute Permeability lab the objective was to determine absolute

permeability of an unconsolidated pack using fundamental laboratory equipment and

procedures, and to compare results for different grain size distributions and generalize the

effect of grain size distribution on porosity and permeability. I connected the sample to a

valve which was connected to a beaker of water. I opened the valve to saturate the sample

and then weighed the saturated core. Then I let the water run through the sample and out

the other side in order to measure the flow rate. Using core measurements, viscosity and

density of water, and the flow rate I could calculate the “false” pore volume, calculated

pore volume, calculated bulk volume, and porosity. In the Gas Permeability and

Klinkenberg Effect lab the objective was to determine the apparent permeability of a

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reservoir rock using a gas permeameter, demonstrate and measure the dependence of

permeability to gas at varying pressures, and then predict the “absolute” permeability to

liquid using Klinkenberg’s correction, and exercise the use of the radial form of Darcy’s

flow equation. I used a Ruska Permeameter in order to determine gas permeability of a

core sample. As opposed to the previous labs, gas was used as the measurement fluid in

this lab.

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Introduction

Porosity is the backbone of the first experiment, Absolute and Effective Porosity.

Porosity is defined as, “a measure of the storage capacity [in a rock] that is capable of

holding fluids” (Ahmed, 32). There are two different types of porosity because in rocks

fluids can be stored in two different types of areas. Some areas are interconnected to each

other, while other areas are completely isolated (Ahmed, 32). The absolute porosity is

“the ratio of the total pore space in the rock to that of the bulk volume” (Ahmed, 32).

This means that all of the pore space, interconnected and isolated, is included. Effective

porosity is “the percentage of interconnected pore space with respect to bulk volume”

(Ahmed, 33). Porosity is important because the spaces in the rocks where fluids can

reside are where petroleum engineers can find oil. The porosity of the rock can determine

how easy or how difficult is would be to extract the oil. “The effective porosity is the

value that is used in all reservoir engineering calculations because it represents all the

interconnected pore space that contains the recoverable hydrocarbon fluids” (Ahmed, 33).

In the experiment titled Sieve Analysis, grain size was the main component. A

sieve is defined as “a utensil consisting of a circular frame with a finely meshed or

perforated bottom used to separate the coarser from the finer particles of any loose

material” (OED Online). The sieve was used to separate various grains of a sand sample.

Sieve analysis is important because grain size determines the porosity and permeability of

a rock sample. Permeability is “the degree to which a solid allows the passage through it

of liquid or gas” (OED Online). A larger grain size will have a higher permeability while

a smaller grain size will have a lower permeability.

In the Absolute Permeability lab the permeability of various grain sizes were

tested using water. As stated before in the Sieve Analysis lab, the permeability of a

sample is how well a liquid flows through it. Permeability is important because it

determines how easily a liquid or gas will flow through a rock sample, which is how

petroleum engineers know how easy or hard it will be do extract oil from rock. Rocks

that have larger grain sizes have greater permeability because they have more pore space

between the grains. Rocks that have smaller grain sizes have less permeability because

they have smaller pore spaces between the grains.

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In the Gas Permeability and Klinkenberg Effect lab, the permeability of a core

sample was tested by using gas. Since gas is a compressible substance its volume and

flow rate vary with the pressure that it is measured at. Liquids are not compressible, so

they can be measured more easily as they were in the previous experiment. The

Klinkenberg Effect is the dependence of the permeability of the reservoir rock to gas on

the mean pressure. When a gas behaves more like a liquid, it has permeability close to

that of a liquid but when a gas behaves more like a gas, it can give false readings of

permeability. This is what we call the Klinkenberg Effect.

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Results and Discussion

There were a total of four labs conducted over the course of a four week period,

and each lab built upon the ideas and concepts of the ones before. Overall, the labs

coincided with one another in the realm of porosity and permeability of gases and liquids.

Porosity was found to have an effect on permeability, because the higher the porosity a

substance, the greater the permeability. This is because if there is more pore space in a

material, a liquid or gas can flow through larger pore spaces more easily. Also, when gas

was used to determine permeability, the Klinkenberg Effect was evident as shown by lab

findings.

Absolute and Effective Porosity Lab

In the Absolute and Effective Porosity lab the results were very clear. The first

part was an activity where the porosity was measured by using marbles and water. By

finding the weight of all the marbles, the beaker, and the water, the bulk volume and the

pore volume could be calculated. The following table shows the values calculated for the

weights and volumes needed to determine pore volume by volume and by weight.

Average marble volume 1.73 cc

Weight of empty beaker (W1) 107.3 g

Weight of all marbles and beaker (W2) 373.13 g

Bulk Volume (V1) 489.06 cc

Pore Volume (V2) 116 mL

Number of marbles (Nm) 51

Grain Volume (V3) 88.23 cc

Bulk Volume 204.23

The pore volume was then determined in two different ways in order to calculate the

porosity. In the first way, it was determined volumetrically where the porosity was

calculated by dividing the pore volume by the bulk volume. The second way the pore

volume was determined was by the water’s weight. The following table shows the data

from the experiment used to calculate the different porosities.

Porosity (volume determined 0.57

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volumetrically)

Final weight of water in beaker (W4) 115.93 g

Volume of water in pore space (V4) 115.93 cc

Porosity (volume determined by weight) 0.515

By using different methods to find the pore volume, the porosity changed.

Although both porosities were relatively close in value, if the pore volume is determined

by volume or by weight, the results will differ. These values show that there is high

porosity in a group of marbles. Just by looking at the marbles in the beaker, it was clear

that there was a lot of pore space in between them. Also, only absolute porosity was

measured in this experiment. This part of the experiment was important in order to instill

a basic idea of the topic of porosity. There were multiple errors that may have occurred in

this experiment. Measuring the diameter of the marbles may have been skewed, because

they were very small. With their size, the measurements may have been slightly off. If the

diameter of the marbles was not accurate, then the volume of the marbles may have been

slightly inaccurate as well, which in turn would have affected the grain volume, and the

bulk volume.

In the second part of the Absolute and Effective Porosity lab, a core sample was

used and the air was evacuated from the core, and the pore spaces were then filled with

helium gas in order to determine the porosity. The following table lists the values

calculated from the experiment in order to determine porosity.

Volume of reference chamber 33.17 cc

Volume of sample chamber 141.57 cc

Core length 3.1 cm

Core diameter 2.4 cm

Bulk volume (Vbulk) 14.02 cc

Solid sleeve volume (VSolid Sleeve) 3.2 cc

Reference chamber pressure, after

stabilization (pi1)

56.11 psia

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Vacuumed sample chamber initial pressure

(pi2)

0 psia

Final pressure (pf) 11.66 psia

Rock volume (Vrock) 11.92 cc

Porosity 0.1498

In this case, the porosity was very small compared to the porosity of the marbles

in the beaker. This is because the grain size of the core was much smaller than the

marbles, which means there was much less pore space between the grains in the core

sample. Also, because helium was used to determine the porosity, this calculation was

more accurate than the marble experiment because gas has smaller molecules than liquid,

which means the molecules can fit into more pore spaces than liquid could. The

porosimeter gave us information to calculate absolute porosity, not effective porosity.

One source of error that may have occurred was the measurements of the core. If the

measurements were not accurate, then the bulk volume would have been inaccurate. The

initial pressure in the vacuumed sample chamber of the porosimeter was taken to be zero

psia. Considering this porosimeter was very old and took multiple days to start up, the

vacuum may not work as efficiently as it used to. If the initial pressure of the vacuumed

sample chamber was more than one, this would have affected the results of the rock

volume. The valves on the porosimeter needed to be opened and closed often in this

experiment, so if the valves were not completely closed when needed, this could have

affected the pressure values. Because the porosimeter used in the experiment was very

old and outdated, I think a more recent version of a porosimeter could have been useful in

data gathering.

In the third part of the experiment, the Barnes Method was used to find the

effective porosity of the core sample. All of the air from the sample was evacuated, and

then the sample was introduced to water which filled all the pore spaces in the core.

Because water was used as the fluid, this made it easier to calculate the effective porosity

because the density of water is 1 g/cc. The following table contains the values calculated

in order to determine the effective porosity.

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Fluid density 1.00 g/cc

Weight of unsaturated core 33.29 g

Weight of saturated core 36.69 g

Weight of fluid absorbed 3.4 g

Volume of fluid absorbed 3.4 cc

Effective porosity 0.243

The absolute porosity was not found during this part of the experiment. One

source of error could have been when the saturated core was weighed. The excess water

on the core sample was removed as much as possible, but there may still have been some

excess water which would have made a difference in the weight of the saturated core, and

the weight of the fluid absorbed. Also, while letting the water into the vacuumed

chamber, it was very important to let the water in through the stop cock extremely

slowly. While this was done as efficiently as possible, some air could have gone into the

vacuumed chamber which would have caused a difference in the amount of water that

entered the core sample.

Sieve Analysis Lab

In the Sieve Analysis experiment samples of sand was sorted into different

variables of fineness using a sieve. The sand was very fine and was sorted into five

different grain sizes. The sieving process was conducted four times in order to sieve a

total amount of 1000 g of sand. The following table shows how the sand was sorted in

each trial.

Sieve # Sieve

size (in)

1st Trial 2nd Trial 3rd Trial 4th Trial Total

weight

50 0.0117 100 g 87 g 79 g 82 g 348 g

70 0.0083 3 g 1 g 3 g 2 g 9 g

100 0.0059 81 g 82 g 84 g 81 g 328 g

120 0.0049 33 g 51 g 48 g 55 g 187 g

140 0.0041 30 g 23 g 35 g 25 g 113 g

Bottom 3 g 4 g 4 g 4 g 15 g

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Total

Sand

250 g 248 g 253 g 249 g

This particular sample of sand is important to sieve because the grain distribution

can determine the porosity and permeability of a sedimentary rock made by this type of

sand. Although sieving the sand took a lot of time, the way it was completed with a sieve

shaker was the most effective way to properly sort the sand particles. One source of error

in this experiment was that most of the sieves had left over sand particles stuck in the

holes that could not be brushed out. This could have added some weight to the final

numbers if the sand fell out into the samples. Also, when weighing the sand some of the

sand particles did not come out of the holes of the sieve by brushing them, and some of

the sand did not fall exactly on the paper towel used to weigh the sand, which means

small portions of sand may not have been measured.

Absolute Permeability Lab

In the Absolute Permeability experiment the absolute permeability of three

different particle sizes was found using various laboratory equipments. For each grain

size, there was a core filled with that specific grain size that had been vacuumed in order

to evacuate all the air. Each core was measured in order to find the volume of the core.

The bulk volume was the volume of the core holder, which was the same value for all

groups because the core holders were all the same size. The following table shows the

values calculated for the core filled with fine grains.


Core cross sectional area 6.61 cm2

Core length 64.14 cm

Unsaturated core and tubing weight 2022.1 g

Saturated core and tubing weight 2206.1 g

Viscosity of saturation fluid 1.0020 cp

Density of saturation fluid 1.00 g/cc

“False” pore volume 184 cc

Calculated pore volume 73.93 cc

Calculated bulk volume 423.7 cc

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Porosity 17.5 %

Sand volume 350 mL

Flow rate was also measured for each grain type, and the following chart shows the flow

rate data for the fine grain sample.

Trial Flow rate (mL/min) Height of beaker (in)

1 7.8 19.25

2 6.8 17.5

3 6.0 15.5

4 5.6 14.0

5 4.4 11.25

The following table shows the data found for the coarse grain sample.



Core length 64.14 cm





“False” pore volume 144.1 cc



Porosity 18 %

Sand volume 350 mL

The following table shows the flow rates of the coarse grains.

Trial Flow rate (mL/min) Height (in)

1 12 19

2 11 17.9

3 9 15.6

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4 6.5 12.5

5 4.5 7.5

The following table shows the values measured and calculated for the mixed grains core

sample.



Core length 64.1 cm





“False” pore volume 139.9 cc



Porosity 23 %

Sand Volume 326.7 mL

This table shows the flow rates calculated for mixed grains.

Trial Flow rate (mL/min) Height (in)

1 8.8 19.15

2 8.5 16.5

3 7.2 13.5

4 6.6 12

5 4.6 7.9

From this data, it is easy to see that the porosity of the samples increased as the

sample grain size increased. This means that the smaller the grain size, the less pore

space there is available for fluid to be contained, and the larger the grain size, the more

pore space there is. An interesting point to note in the data collection is that the flow rate

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of the fine grains was significantly slower than the flow rates of the coarse and mixed

grains. The flow rate was slower because the grains were smaller, which makes it harder

for water to flow through such small spaces. Since the flow rate was slow, this means that

the core sample was less permeable than the other samples. For the coarse grains, the

flow rate was much faster than the fine and mixed grains at the greater heights, but then

the flow rates became about the same as the mixed grains at the lesser heights. The coarse

grain sample had minimal flow rates at the greater heights, which is unusual considering

the porosity was so much greater than the coarse and fine grain samples. I have included

a graph for the flow rates for each of the grain sizes, in order to easily visualize the

concept.

4 4.5 5 5.5 6 6.5 7 7.5 80

102030

Height vs Flow Rate (Fine Grains)

Series2

Flow Rate (mL/min)

Hei

ght (

in)

4 5 6 7 8 9 10 11 12 1302468

101214161820

Height vs Flow Rate (Coarse Grains)

Series2

Flow Rate (mL/min)

Heig

ht (i

n)

4 5 6 7 8 9 1005

10152025

Height vs Flow Rate (Mixed Grains)

Series2

Flow Rate (mL/min)

Heig

ht (i

n)

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With the increase in height of the beaker to the core sample, there was greater

pressure, and when the height was closer to the core sample there was less pressure.

Although pressure measurements were not taken during this experiment, it is evident that

with an increase in pressure, there is an increase in flow rate. Ultimately, a sample with

larger grains would have higher porosity and greater permeability because of the more

spaces in between the grains that allows fluids to flow more easily.

Because of the difference in flow rate, there may have been some errors in the

experiment. When measuring the flow rate, the volume of the water in the beaker needed

to remain fairly constant in order to be accurate. If the volume was not constant and was

not being filled as the water was running through the sample, this may have cause

discrepancies in the flow rate. The height from the water level to the core sample during

the flow rate estimation was difficult to measure accurately because the apparatus used

was abstract and hard to measure with the measuring tape. The measurements for this

were eyeballed. Also human error caused the “false” and calculated pore volume to have

discrepancies. The “false” pore volumes should have been less than the calculated pore

volume because the “false” pore volume is the weight of the water added to the core, and

the calculated pore volume is the calculated volume of the tube and the volume of the

sand that was added to fill the core tube. Although, the sand that was added to the core

tube was not densely packed, which could also be why the “false” pore volume was more

than calculated pore volume. One way to improve the data was to make the saturation of

the core sample more effective. When the water was connected to the core sample with a

long tube, there were often large bubbles that got in the way of the water flowing into the

vacuumed core. It took a long time for the water to go through the sample and at a point

the water completely stopped flowing and a vacuum had to be used to suck the water

through the rest of the sample in order to saturate it.

Gas Permeability and Klinkenberg Effect Lab

In the Gas Permeability and Klinkenberg Effect lab the apparent permeability and

“absolute” permeability of a sample was found using gas. Using the Ruska Permeameter

and a core sample the permeability of the sample could be found. Measuring all of the

core sample’s measurements, and watching the dials on the Ruska Permeameter, the

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permeability could be found. The following data table shows the measurements used to

obtain the permeability of the core.

Trial Tube Size Tube height (cm) Pressure (atm)

1 Large 2.3 1.39

2 Medium 8.6 1.33

3 Small 3.8 1.29


Core length 3.2 cm

Barometric pressure 1.00 atm

Temperature 23 degrees C

Average (Large) tube height 2.3 cm

qdown at average tube height 9.75 cc/sec

μair at 23 degrees C 0.0176 cp

Core area 9.08 cm2

Permeability of core A 0.157 mD

The gas that was used in the Ruska Permeameter to determine the permeability of

the core was nitrogen. Using formulas that were provided, the permeability was found.

Because gas was used in this experiment to determine permeability, the

Klinkenberg Effect needed to be tested in order to see how it affects the outcome of

permeability. The radial flow experiment showed the Klinkenberg Effect. The following

data sheet includes all of the data found when using the Radial Permeameter.

Inside core diameter 3.015 cm

Outside core diameter 6.025 cm

Core height 5.012 cm

Barometric pressure 0.95 atm

Temperature 28 degrees C

Ln(rout/rin) 0.692

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Pressure Upstream Pressure differential

Trial Vg (ft3,

L)

t(sec) qdown

(cc/sec)

mV psi mV psi

1 3 5 600 1.7 6.613 0.6 1.608

2 3 6 500 2.7 10.503 0.6 1.608

3 3 7 428.57 3.7 14.393 0.6 1.608

4 3 8 375 4.7 18.283 0.6 1.608

When the data above is calculated into permeability, the Klinkenberg Effect is evident

when graphed in relation to the inverse of the mean pressure of the system.

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.40

0.10.20.30.40.50.60.70.8

Klinkenberg Effect

Series2Linear (Series2)

1/pmean (atm-1)

kg(D

arcy

)

This graph on the Klinkenberg Effect shows that as a gas behaves more like a liquid, it

tends to have a permeability of liquid quality. So, if the gas is at high pressure, the

permeability is more accurate. If the gas is at low pressure and behaves more like a gas, it

can skew the values when measuring permeability.

One possible source of error for this experiment could be the efficiency of the

Ruska Permeameter. The one that my group used had a pressure gauge that was off, so

we had to compensate our values for the incorrect readings that it would give us. Also,

our lab group did not have a chance to conduct the Radial Permeameter portion of the

experiment, and only the values from another experiment were available. I think being

able to conduct the entire lab would have made the experience worthwhile. Not being

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able to visualize what happened during the experiment made it difficult to interpret what

was really going on.

Conclusion

All of these experiments were conducted in order to give a greater understanding

of porosity, permeability, and how the two can be tested and relate to one another. The

experiments progressed in an effective manner, starting very simply with the subject of

porosity. Porosity, as shown by the first lab, increases with the size of the grains because

there are more spaces in between the grains for water or gas to flow. The second lab also

dealt with porosity, because the larger grains that were sieved would have had a greater

porosity than the smallest grains that were sieved. Also, the sand that we sieved in that

experiment was used to create the core samples for the third experiment. In the third

experiment, permeability and porosity came together to show that the greater the

porosity, the greater the permeability. The fine grains had slower flow rates, which mean

the permeability was less than the permeability of the coarse and mixed grains. Finally,

the permeability was tested using gas. Because gas is highly compressible, it sometimes

gives false readings of permeability, which we tested for using the Radial Permeameter.

The Klinkenberg Effect was proven correct, and by using the Ruska Permeameter the

permeability of a core sample using Nitrogen gas was found.

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Sample Calculations

1. Φ = V2/V1 = 116 mL/204.23 mL = 0.57

2. Vrock = Vreference chamber (p1i-pf) / (p2

i-pf) + Vsample chamber – Vsolid sleeve

Vrock = 33.17cc (56.11psia – 11.66psia) / (0psia – 11.66psia) + 141.57cc –

3.2cc

Vrock = 11.92 cc

3. Φ = 1 – Vrock / Vbulk = 1 – 11.92cc / 14.02cc = 0.1498

4. Φeffective = Vi / Vbulk = 3.4cc / 14.02cc = 0.243

5. pdownqdown = pupqup 1.14atm(qdown) = 1.39atm(8cc/s) qdown=9.75cc/sec

6. kg = [2μLqdownpdown] / [A(pup2 – pdown

2)] = [2(0.0176cp)(2.3cm)(9.75cc/sec)

(1.14atm)] / [9.08cm2(1.392 – 1.142)]

kg = 0.157mD

7. qmean = [qdownpdown] / pmean = [600cc/sec(1.302atm)] / 1.351atm = 578 cc/sec

8. kg = [qdownpdownμln(ro / ri)] / [πh(pup2 – pdown

2)]

= [600cc/sec(1.302atm)(0.0176cp)ln(6.025cm/3.015cm)] / [π(5.012cm)(1.42 –

1.3022)] kg = 2.28 Darcies

Nomenclature

1. Φ—Absolute porosity V2—Pore volume (mL) V1—Bulk volume (mL)

2. Vrock—Rock volume (cc) Vreference chamber—Reference chamber volume (cc)

p1i –Pressure in reference chamber after stabilization (psia)

p2i –Initial pressure in vacuumed sample chamber (psia)

Vsample chamber –Volume of sample chamber (cc)

Vsolid sleeve –Volume of solid sleeve (cc)

3. Vbulk = Bulk Volume (cc)

4. Φeffective = Effective porosity Vi—Interconnected pore volume

5. pdown—downstream pressure (atm) pup—upstream pressure (atm)

qdown—downstream flow rate qup—upstream flow rate

6. kg –apparent permeability (Darcy) μ—viscosity (cp)

L—tube height (cm) A –core area (cm2)

7. qmean—mean flow rate (cc/sec) pmean—mean pressure (atm)

8. ro—outside core diameter (cm) ri—inside core diameter (cm) h—core height(cm)

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9. References

Ahmed, Tarek. Working Guide to Reservoir Rock Properties and Fluid Flow. Burlington:

Elsevier Science & Technology, 2009. Print.

OED Online. November 2010. Oxford University Press. 28 February 2011

<http://www.oed.com/view/Entry/179420?rskey=u1NU7h&result=1&isAdvanced

=false>.

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png 406 write up 1

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