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