Finding permeability using nitrogen

1. i
Phoenicia University
Department Of Engineering
Faculty Of Petroleum Engineering
Reservoir Rock Properties Laboratory
PENG211L
Gas Permeameter
Submitted by:
Bassam El Ghoul
Mohamad Houdroj
Elio Kattoura
Submitted to:
Mr. Jamil Mahfoud
April 24, 2018

2. ii
CONTENTS
CHAPTER 1 INTRODUCTION ............................................................................................................1
1.1Definition……………………………………………………………………………………….1
1.2Objective……………………………………………………………………………………….1
CHAPTER 2 APPARATUS .....................................................................................................................3
CHAPTER 3 OTHER EQUIPMENTS .................................................................................................5
CHAPTER 4 PROCEDURE....................................................................................................................6
CHAPTER 5 CALCULATATION ........................................................................................................7
CHAPTER 6 RESULTS AND DISCUSSION...................................................................................10
CHAPTER 7 ERROR AND RECOMMENDATION.....................................................................12
CHAPTER 8 CONCLUSION................................................................................................................13
CHAPTER 9 REFERENCES ................................................................................................................14

3. iii
LIST OF TABELS
TABLE 5.1 PERMEABILITY RESULTS FOR Q=5.................................................9
TABLE 5.2 PERMEABILITY RESULTS FOR Q=10...............................................9

4. iv
LIST OF FIGURES
FIGURE 2.1 GAS PERMEAMETER .....................................................................3
FIGURE 3.1 INDIANA……………………………………………………………………………………………………….5
FIGURE 3.2 TORREY…………………………………………………………………………………….5
FIGURE 3.3 SILURIAN…………….. ....................................................................5
FIGURE 3.4 CALIPER …………………………………………………………………………………...5
FIGURE 3.5 AIR TANK ………………………………………………………………………………….5
FIGURE 3.6 NITROGEN TANK..........................................................................5
FIGURE 6.1 K VS DELTA P FOR Q=5 ........................................................... 10
FIGURE 6.2 K VS DELTA P FOR Q=10 ......................................................... 10

5. 1
CHAPTER 1 INTRODUCTION
1.1. Definition:
Permeability is the capacity of a porous medium to transmit fluids, in other words, permeability is the
measure of how ease can the fluid flow through a porous medium. Looking at Darcy’s law
formulated in 1856, in the equation EQ (1.1) below, the flow rate is directly proportional to the
permeability, as permeability increases, the flow increases thus production of hydrocarbons increases,
and as the essential aim of oil and gas industry is the production of hydrocarbons, the permeability is
an essential measurement that needs to be taken accurately in order to exactly determine the
production rate in oil and gas wells. EQ (1.1) is the general equation of Darcy’s law for an
incompressible fluid, however gas is compressible, and to account for the compressibility of gases,
Darcy’s law of gases under steady state and isothermal conditions is given as EQ (1.2) below.
Another phenomena that can affect the permeability of the rock is Klinkenberg effect , the gases
exhibit slippage at the grain interface this slippage results a higher flow rate for the gas at a given
pressure differential. To account for klinkenberg effect EQ (1.3) is employed, as the term (1 +
𝑏
𝑝̅
) on
the right side of EQ (1.3) is always equal or greater than 1, thus the apparent permeability to gas Kg
on the left-hand side of the EQ (1.3) is equal or greater of the absolute permeability of the rock. Gas
permeameter is an experiment conducted to determine the permeability to gas Kg in samples from
the oil and gas wells, using Darcy’s law and a computer software. As Darcy’s law is implemented in
this experiment it is limited to steady state flow. A mass flow meter and a relative pressure
transmitter are used to measure the flow of the gas and the pressure drop across the sample and this
lead to an accurate measurement of permeability. These measurements have a significant importance
in the industry to determine the flow rate of an oil and gas well (Mahfoud, 2018).

6. 2
𝑄 = −
𝑘𝐴𝛥𝑃
µ𝛥𝑙
𝐸𝑄(1.1)
𝐾𝑔𝑎𝑠 =
2𝜇𝑍𝑇𝑃𝑏 𝐿𝑄 𝑏
𝐴𝑇𝑏 (𝑃1
2
− 𝑃2
2
)
𝐸𝑄 (1.2)
𝐾𝑔 = 𝐾𝐿 (1 +
𝑏
𝑝̅
) 𝐸𝑄(1.3)
1.2. Objective:
The aim of this experiment is to find the effective permeability of different cores, using the
gas permeameter.

7. 3
CHAPTER 2 APPARATUS
Permeameter: is an instrument designed to determine the permeability of a gas at steady state, in
other words there is a constant pressure and flow through the sample.
A mass flow meter of range 5-500 cc/min together with 0-100 psi relative pressure transmitter are
used to sense gas flow and pressure drop across the sample and therefore provides an accurate
determination of permeability, when the transmitters have been correctly calibrated.
The instrument can be used with our standard hassle-type core holder for 1 or 1.5 diameter sample (1
to 3 lengths) up to 400 psig confining.
Figure 2.1 Gas Permeameter (Mahfoud J. , 2018)
Core Holder
Flow
rate
indicator
Pore pressure indicatorConfining pressure
valveConfining pressure indicator
Pore pressure valve
Flow rate adjuster

8. 4
1. Core holder: to insert the core to be tested inside it, where air and nitrogen gas will be
pumped in it.
2. Pore pressure indicator: to read the pore pressure recently.
3. Confining pressure valve: if the valve is on the left side then we are venting the chamber to
the atmosphere, however if it is on the right side then we are fixing the core in place.
4. Coning pressure indicator: to read the confining pressure value.
5. Pore pressure valve: upon switching to the right we are enabling the gas to invade the core.
6. Flow rate adjuster: to adjust the value for the gas flow rate inside the chamber.

9. 5
CHAPTER 3 OTHER EQUIPMENTS
1. Core samples: undergo the experiment on them.
2. Caliper: to measure the length and diameter of the core sample.
3. Nitrogen Tank: to supply helium through the chamber.
4. Air tank: to supply helium through the chamber.
5. Excel software: to input data and check the validity of Darcy’s law and it is valid we get the
value of the permeability.
Figure 3.1 Indiana Figure 3.2 Torrey Figure 3.3 Silurian
Figure 3.4 Caliper Figure 3.5 Air Tank Figure 3.6 Nitrogen Tank
(United Rent-All Omaha NE, 2018)

10. 6
CHAPTER 4 PROCEDURE
1- Switch flow valve off.
2- Switch confining valve to vent.
3- Open core chamber and load the core then close chamber tightly.
4- Hands screw the inlet plug to get contact with the sample and hold it in place.
5- Switch confining valve to confine to seal the sleeve around the core.
6- Switch the air and helium tank and adjust them to 99 psi.
7- Switch flow valve into the pore pressure side.
8- Gases will invade the core.
9- Regulate flow rate, turn CW to increase flow and CCW to decrease it.
10- Enter data to the software to get the value of the permeability.
11- Turn flow valve to vent.
12- Open the chamber and remove the core.
13- Roll the core on a piece of tissue to clean it.

11. 7
CHAPTER 5 CALCULATATION
Darcy’s Law is a relation between the flow rate of an incompressible fluid with a constant viscosity
and the permeability of a porous media (Schmidt, 2015). These assumptions can work for many
fluids. However, when it comes to gas, it is highly compressible, so Darcy’s Law equation cannot be
used. The derivation of gas flow rate for a linear horizontal system, Darcy’s equation can be written
as Equation 5.1:
Eq 5.1
Where q is the flow rate at reservoir condition in rcf/d (Thomas W. Engler, 2010).
Usually, we prefer to determine the flow rate in standard condition in scf/d. Where we derive it
from Boyles’s Law for real gas:
(
𝑃𝑉
𝑍𝑇
)
𝑅𝑒𝑠
= (
𝑃𝑉
𝑍𝑇
)
𝑆𝐶
𝐸𝑞 5.2
where:
P = absolute pressure, psia;
V = volume, cu ft,
Z = compressibility factor;
Tres = reservoir temperature, ˚R;
Tsc = temperature at standard conditions, ˚R.
Where It can be written for volumetric flow rate as:
(
𝑃𝑞
𝑍𝑇
)
𝑅𝑒𝑠
= (
𝑃𝑞
𝑍𝑇
)
𝑆𝐶
𝐸𝑞. 5.3
And rearranged to:
𝑞 𝑟𝑒𝑠 = 𝑞 𝑠𝑐
𝑃𝑠𝑐 𝑇𝑟𝑒𝑠 𝑧 𝑟𝑒𝑠
𝑃𝑟𝑒𝑠 𝑇𝑠𝑐 𝑧 𝑠𝑐
𝐸𝑞.5.4
Substituting equation 4 in equation 1 we will have:

12. 8
Eq 5.5
And finally, by integrating equation 5 we can have an empirical equation relating the flow rate at
standard condition and the permeability of a porous media.
𝑞 𝑠𝑐 = 0.003164
𝐴𝑘𝑇𝑆𝐶 ( 𝑝1
2
− 𝑝2
2)
𝑃𝑠𝑐 𝑇𝑧𝐿µ
𝐸𝑞 5.6
where,
qsc {scfd} k {md}
A {ft2} T {˚R}
P {psia} L {ft}
µ{cp}
We can then rearrange equation 6 to find the permeability:
𝑘 =
𝑞 𝑠𝑐 𝑃𝑠𝑐 𝑇 𝑧𝐿µ
0.003164 𝐴 𝑇𝑆𝐶 ( 𝑝1
2 − 𝑝2
2)
𝐸𝑞 5.7
Using equation 5.7 we will calculate for each value of q the permeability for 5 different value of
delta P.
The values below are constant in all calculations of permeability.
Psc= 14.696 psia
T= room temperature = 22˚C = 531.27˚R
Z = 1 at standard conditions.
L is the length of the core = 5 cm = 0.164 ft
µ = 0.017560 cp.
Tsc = 60˚F = 519.67˚R
A is the area = 2 pi r h =2* 3.14*0.041*0.164= 0.0422 ft2
For q1=5 scf/day
and delta p1= 0.5 psi and P2= 1 psi

13. 9
P1=P2+delta p1 = 1+0.5=1.5
𝑘 =
5 ∗ 14.696 ∗ 531.27 ∗ 1 ∗ 0.164 ∗ 0.01756
0.003164 ∗ 0.0422∗ 519.67(1.52 − 12)
= 1296.183 𝑚𝑑
Table 5.1 Permeability Results for q=5
Q (scf/day) Delta p (psi) P1 (psi) P2 (psi) K (md)
5 0.5 1.5 1 1296.183
1 2 1 540.0761
1.5 2.5 1 308.6149
2 3 1 202.5285
2.5 3.5 1 144.0203
For q2=10 scf/day
and delta p1= 0.5 psi and P2= 1 psi
P1=P2+delta p1 = 1+0.5=1.5
𝑘 =
10 ∗ 14.696 ∗ 531.27 ∗ 1 ∗ 0.164 ∗ 0.01756
0.003164∗ 0.0422 ∗ 519.67 ∗ (1.52 − 12)
= 2592.365 𝑚𝑑
Table 5.2 Permeability Results for q=10
Q (scf/day) Delta p (psi) P1 (psi) P2 (psi) K (md)
10 0.5 1.5 1 2592.365
1 2 1 1080.152
1.5 2.5 1 617.2298
2 3 1 405.0571
2.5 3.5 1 288.0406

14. 10
CHAPTER 6 RESULTS AND DISCUSSION
Figure 6.1 K vs Delta P for q=5
Figure 6.2 K vs delta P for q=10
Figure 6.1 and 6.2 represent the permeability versus the difference in pressure at a flow rate of q1=5
scf/day, and q2= 10 scf/day proportionally. The two graphs match the same form, which is an
exponential decrease in permeability while increasing the pressure difference. This relation can be
related to the equation 5.7, where the difference in pressure is inversely proportional to the
permeability. In other hand, figure 6.2 is twice higher than figure 6.1 because the direct relationships
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
K(md)
delta p (psi)
k vs delta p for q=5scf/day
0
500
1000
1500
2000
2500
3000
0 0.5 1 1.5 2 2.5 3
K(md)
delta p (psi)
k vs delta p for q=10scf/day

15. 11
between the permeability and the flow rate, where we used a flow rate of 5 in the first graph and a
flow rate of 10 in the second (Shimamoto & Tanikawa, 2006).
Another thing to discuss is the high value of the permeability for both flow rate, compared to the
permeability conducted using a liquid. This huge difference between the permeability of liquid and
gas is named as Klinkenberg effect. As mentioned in the introduction, this effect is due to no slip
boundary condition of a liquid and not for gas. Where the molecules of liquid are imbibed by the rain
surface, they will cause a decrease the liquid velocity, and form an elliptical velocity profile, which
will decrease the permeability. In the other hand, for gases, like nitrogen in this experiment, the
molecules slip on the grain surface so that it will not cause any retardance to the flow, which will
increase its permeability.

16. 12
CHAPTER 7 ERROR AND RECOMMENDATION
Table 5.1 and 5.2 illustrates the permeability values for the three tested cores. We found that the
permeability values of the samples are bit high. Thus certain factors are affecting our results.
Starting by the first error, according to Klinkenberg the permeability for a core sample using liquid is
not the same when using gas as a fluid. Knowing that permeability is a rock property that doesn’t
depend on the fluid used to test it. But what happens at low pressure as in the laboratory the
permeability of a core sample using gas as fluid is higher than using liquid as a fluid. This is due to
the motion of the gas molecules. At low pressure the gas molecules are in a constant motion and the
molecules have negligible collision against the walls. This action will diminish the friction loss at the
walls which eases the flow of the gas through the chamber and core sample. Therefore the
permeability of the core sample will be increased. In contrast, with liquids where they face an
attraction with the walls. And in such action decreasing the value of the permeability. Moreover,
Darcy’s law is applicable when there is laminar flow, uncompressible fluid which opposite to gas
that has turbulent flow as well as it is compressible. Finally, the cores may have certain fractures, and
as fractures are presented our permeability get higher.
For the human errors, we were not getting the exact value of the flow rate as we are adjusting the
flow rate value. Add to that measuring the dimensions of the core must be précised since our
measurements affects directly permeability as we are measuring the area.
Basically, we must get rid of such errors as much as we can by adjusting the flow rate of the gas in
accurate way so we can get an exact value for the flow rate. Count for the errors that are presented in
the gas permeameter software so we can get more précised answer. Measure the dimensions of the
core in a precise way.

17. 13
CHAPTER 8 CONCLUSION
Permeability is the ability of a rock to transmit fluids through a porous media. This permeability is
usually determined in the laboratory, by injecting a fluid in a sample and measuring its flow rate and
pressure difference. In this experiment, we used a Nitrogen to determine the permeability of the core.
This experiment is easy, and effective, where after loading the core and seal it, we start to change the
flow rate and finding the permeability using the software.
We calculated the permeability of the three cores using different values of difference in pressure for
two flow rates.
This experiment also has disadvantages, where the limitations due to Darcy’s law are not applicable
in our situation, what is why, we need a correction factor in order to get the exact numbers of
permeability. Furthermore, Klinkenberg effect shows that the usage of gas in finding permeability, is
more practical and can give us a closer look to the real permeability in the formation.
This experiment Is subjected to a lot of error form different source, human and mechanical, and
electrical, where we can increase the efficient of the experiment by avoiding them, and following the
recommendations.

18. 14
CHAPTER 9 REFERENCES
(2018). Retrieved from United Rent-All Omaha NE: http://www.unitedrent-all-
omaha.com/product/helium-tank-rental/
Mahfoud, J. (2018). Retrieved from ELEARNINGFORCE:
https://lms.pu.edu.lb/sites/12017SPRING6022/Documents/Forms/AllItems.aspx
Mahfoud, J. (2018). Gas Permeameter. Retrieved from Lms:
https://lms.pu.edu.lb/sites/12017SPRING6022/Documents/Forms/AllItems.aspx
Quarries, C. (N.d). Retrieved from https://www.bereasandstonecores.com/
Schmidt, B. E. (2015, January 12). Compressible Flow Through Porous Media with Application to.
California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA.
Caltech Hypersonics Group. Retrieved from
http://shepherd.caltech.edu/T5/publications/PorousMediaReport.pdf
Shimamoto , W., & Tanikawa, W. (2006). Klinkenberg effect for gas permeability and its
comparison to water permeability for porous sedimentary rocks. Retrieved from
Hydrology and Earth System Sciences Discussions: https://www.hydrol-earth-syst-sci-
discuss.net/hessd-2006-0075/hessd-3-1315-2006.pdf