Post on 27-Mar-2018
Pennsylvania State University
College of Earth and Mineral Science
Department of Petroleum and Natural Gas Engineering
Relative Permeability
PNG 406: Rock and Fluid lab
Group A - Section 2
Group Members:
Faisal Alaamri
Fatimah Alali
Sarah Alamer
Layla Alshammasi
1
Executive Summary
The objective of this lab (lab 6) was to determine the relative permeability of oil and
water in an unconsolidated porous medium. However, since Soltrol is more available and easier
to obtain, we used it instead of oil. It has lower density than water as oil.
First, we set up the apparatus as the previous lab. The lab was split into three groups.
Each group has coarse particles, fine particles, or mixed particles that have been already packed
and prepared for this lab. Our group (group A) has coarse particles.
After setting the apparatus as the previous lab, we began the experiment by inserting
Water into the Soltrol Saturated sample and recording the time and volume in regular time
periods in order to find the flow rate of water and Soltrol. For the Water to go through the
sample, it needed a difference in the pressure. Therefore, we put the beaker in a height of 15
inches above the sample. It is important to note that we had to maintain the pressure constant by
adding Water to the beaker whenever we notice a decrease in the Water volume in the beaker.
After recording the volume of Soltrol that has been forced out from the sample by Water
in a set of time periods, we noticed Water Start coming out of the sample. The difference in
densities between water and Soltrol made it very easy for us to notice when Soltrol is coming.
The Next step was to record the volume of Soltrol in a set of time periods to find its flow
rate so that we can find its effective permeability. Using the absolute permeability we calculated
from lab 3, we were able to calculate the relative permeabilties of water and Soltrol.
Despite the high accuracy we wanted to achieve in this lab, the data we obtained may not
be very accurate. One reason for that is the misreading of the oil and water volumes. Another
reason is failure to maintain exactly one constant pressure (height of Water in the beaker).
Table of Content
2
Title Page
Executive Summary 1
Introduction 3
Result and Discussion 5
Conclusion 7
Sample Calculation 8
Nomenclature 9
References 10
Appendices 11
3
Introduction
Objective:
The purpose of this experiment is to find the relative permeability of oil and water in an
unconsolidated porous medium.
Background information:
Absolute permeability is a rock property that measures the ability of a rock to transmit fluid.
Absolute permeability is determined when the rock is saturated completely with a single-phase,
homogeneous, and non-reactive fluid. However, rocks most likely contain more than one fluid,
and the saturation of the fluid is usually less than 100%. The ability to measure rocks
transmitting fluids in this case in known as effective permeability. Effective permeability is
given by the equation:
kf
= -qfmf
A
dL
dpf
Relative permeability is also an important characteristic, and it is the ratio of the effective
permeability to the absolute permeability. Relative and effective permeability are directly
proportional each other. Relative permeability is given by the equation:
krf
=kf
k
There are several methods to measure effective and relative permeability, and these method are
either “steady state”, or “unsteady state” methods. Steady state methods require balancing fluid
flow, where the outlet flow must equals the inlet flow. On the other hand, the unsteady state
methods consist of flooding a water-saturated sample with oil, while observing water and oil
expelled and change in pressure.
The relative permeability of a sample can be measured by drainage or imbibition
processes. Drainage means decreasing water saturation, in a water-saturated core sample by
flooding oil. Imbibition means flooding the previous flooded-oil sample with water, increasing
water saturation. Drainage and ambition can be calculated by the following equations:
4
pore volume - cumulative water produced
pore volume(%)
i
drainage
iwS
imbibition
Sw
i (%)=pore volume( )-(total water out)+ cumulative oil produced( )
i
pore volume
In addition, capillary pressure is a term defined as the difference in pressure across the
two phases. The relationship between capillary pressure and water saturation under drainage and
ambition is illustrated in the picture below:
Finally, to find the relative permeability, Darcy’s law that is used these processes takes the
forms:
Oil: o oo
o
q Lk
A p
Water: w ww
w
q Lk
A p
5
Result and Discussion
In this experiment, our goal was to determine the relative permeability of oil and water in
an unconsolidated porous medium. In continuation of a previous experiment in which we
determined experimentally, the absolute permeability of three different samples of different
grains sorting going through the same procedures. Our group studied the coarse grains while the
other two groups studied fine grains and mixed grains.
Relative permeability is the ratio of effective permeability over the absolute permeability.
In this case we can determine the absolute permeability having the irreducible water saturation
and the residual oil saturation.
During our experiment, the sample was initially filled to its capacity with oil. Water was
pumped in (imbibition cycle) from a beaker on 15 inches height. And we kept getting oil flowing
out of the sample and volume of produced oil was recorded every 30 seconds until at some point
where water starts coming out, total volume was recorded along with the water volume, which is
the reading at the thin layer between water: the fluid of higher density and oil: the fluid of lower
density after calculating the water saturation (see sample calculations) we plot water saturation
vs. time and we get the following graph:
Imbibition refers to the increasing saturation of the wetting phase, which is water in this
case. During our experiment we were injecting water to a sample fully saturated with soltrol. The
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
wat
er s
atu
rati
on
(%
)
time (s)
Water Saturation Vs. Time in Imbibition Cycle
6
water saturation in the sample kept increasing until it reached 1- Sor . From the graph above, we
can see that the Residual Oil Saturation (Sor) equals to 0.344. However, since we don’t have
enough data to compare the imbibition process to the drainage, we will be missing some
information such as the residual water saturation Swirr. Using this Value of Sor we can predict a
recovery factor of to go up to 66.6%. However, in this percentage of recovery factor, we did not
take into account the residual water saturation because the sample was completely filled with
Soltrol and drainage process was not preformed.
Unfortunately, we can’t take advantage of a pressure drop vs. water saturation plot in this
experiment since the gauge pressure wasn’t working. And we assumed that pressure was
constant during the whole lab. Otherwise we would at least have an insight regarding the effect
of increase and decrease in pressure on both the drainage and imbibition processes. However, we
could still theoretically calculate the relative permeabilities of soltrol and water using one point
data.
The average flow rate of oil was 0.144 CC/s and the pressure was 0.0368 atm. Using
Darcy's Law to find the permeability of oil, ko was found to equal 104.9±0.1 Darcy.
The major source of error in this specific lab was misreading of the data since we had the
coarse grains whom result in high permeability that there was not enough time to precisely read
the measurements, besides, our placement for the beaker in a higher place allowed the flow of
both water and soltrol inside the tunnel to go even faster. Another source of error that we
assumed that there was no pressure change at all since pressure readings were not taken into
account in this experiment. Either ways, due to the quick transmit of fluids we would not be able
to benefit from the inaccurate pressure readings. Other sources of error would include human
error in reading measurements.
To go further in improvement to this lab should take into account accurate pressure
readings, more accurate human readings by developing simple ways for instance using a colored
water, as well as collecting more data, meaning more time intervals but not longer.
7
Conclusion
The relative permeability of a core sample is defined as the ratio of the effective
permeability to the absolute permeability. Absolute permeability is a characteristic of the sample
when only one phase fluid goes through it; however, effective permeability is the ability of one
fluid in a multi-fluid system to flow through the sample. Therefore, relative permeability could
be found by comparing the fluid flow in a one-phase and two-phase system. In this lab, the
imbibition processes was used to determine the relative permeability.
Observing the graph of the saturation of water with time, we can see that the water
saturation has been increasing in the sample until it reached a point where water start flowing out
from the sample. Thus, we found the residual oil saturation, which is the saturation of oil that
remains in the swept zone of a waterflood, to be 0.344.
In addition to that, observing the flow rate of oil coming out from the sample allowed us
to calculate the effective permeability of the oil with the presence of water . Using Darcy's law,
the oil permeability was found to be 104.9 Darcy. Comparing this result with the absolute
permeability obtained in lab 3, the relative permeability, which is obtained by dividing the
effective over the absolute permeability was found to be
A possible sources of error include human error in the reading of measurements, as well
as the possibility of miss-reading oil for water, and vice versa. The high permeability of the
coarse grained sample and the high pressure difference made the flow faster thus harder for us to
accurately read the flow volume. Another possible source of error is the failure to maintain
exactly one constant pressure by maintaining the height of Water in the beaker.
8
Sample Calculations
To calculate the relative permeability, we first need the flow rate
P= =
= 0.0368 atm
o oo
o
q dLk
A dp
oro
kk
k
Error: 0.00
9
NOMENCLATURE
General variables:
L- length [cm]
V- volume [cc]
P- pressure [atm]
t- time [seconds]
q- production rate [cc/s]
k- permeability [Darcy]
kr- relative permeability [Darcy]
A- area [cm^2]
S- saturation [%]
µ- density [cp]
sub o- indicates oil, in this case soltrol
sub w- indicates water
10
REFERENCES
1) Experiment 6: Png 406 Lab manual
2) Dandekar, Abhijit. Petroleum Reservoir Rock and Fluid Properties. 2nd ed. Boca Raton,
Florida: CRC Press, 2013. 19. Print.
11
APPENDICES
12
L= 38.1 cm
P = 0.0368 atm
Time
interval
(sec)
Cum
time
(sec)
Cum
Voil
(cc)
Cum
Vwater
(cc)
Cum
Vo+w
(cc)
Produced
Vo (cc)
Produced
Vw (cc)
Sw
imb
0 0 0 0 0 0 0 0
30 30 5 0 5 5 0 3.380663
30 60 7.5 0 7.5 2.5 0 5.070994
30 90 11 0 11 3.5 0 7.437458
30 120 14 0 14 3 0 9.465855
30 150 16 0 16 2 0 10.81812
30 180 21 0 21 5 0 14.19878
30 210 27 0 27 6 0 18.25558
30 240 32 0 32 5 0 21.63624
30 270 38 0 38 6 0 25.69304
30 300 43 0 43 5 0 29.0737
30 330 49 0 49 6 0 33.13049
30 360 55 0 55 6 0 37.18729
30 390 63 0 63 8 0 42.59635
30 420 67 0 67 4 0 45.30088
30 450 72 0 72 5 0 48.68154
30 480 78 0 78 6 0 52.73834
30 510 83 1 84 5 1 56.119
30 540 84 4 88 1 3 56.79513
30 570 91 6 97 7 2 61.52806
30 600 94.5 9.5 104 3.5 3.5 63.89452
30 630 97 12 109 2.5 2.5 65.58485