Liquid Viscosity

1. Reservoir Fluid Laboratory Course (1st Ed.)

2. 1. Initial definitions
2. Measurement of Density
3. Experiments:
A. Fluid density using the Pycnometer method

3. 1. Introduction (Theory):
2. Types of fluids
3. Viscometers;
A. the falling (or rolling) ball viscometer
B. Capillary Type Viscometer
C. Rotational Viscometers

5. Viscosity as a rheological property
Rheology is the study of
the change in form and flow of matter
in terms of elasticity, viscosity and plasticity.
A clear understanding of the rheological properties of
fluids is vital in many fields of science and engineering.
Viscosity is
the measure of the internal friction of fluid.
This internal friction is caused
when a layer of fluid moves in relation to another layer.
The greater the friction,
the greater the amount of force required
to cause this movement.
This movement is known as shear.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 5

6. Deformation of a liquid under the
action of a tangential force.
To define viscosity
more precisely, let’s
take a look at the
figure.
Two parallel planes of
fluid of equal area “A”
are separated
by a distance dx and are
moving at different
speeds V1, V2.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 6

7. Viscosity definition
The force required to
maintain the difference
in speed is proportional
to the difference in
speed through the
liquid.
μ is known as
the viscosity,
usually in units of
centipoises or Pa.s.
dv/dx (or 𝛾) is
the shear rate.
Describes the shearing
the fluid experiences
when the layers move
with respect of each
other.
Units in reciprocal second,
sec-1.
F/A (or τ) is
the force per unit area
required for the shearing.
This is known as
the shear stress and
it has units of pressure.
Therefore, we can define
viscosity as:
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 7

8. Effect of Pressure on Viscosity
Viscosity of fluids varies with pressure and
temperature.
For most fluids the viscosity is rather sensitive to
changes in temperature, but relatively insensitive to
pressure until rather high pressures have been attained.
The viscosity of liquids usually rises with pressure at constant
temperature.
• Water is an exception to this rule; its viscosity decreases with
increasing pressure at constant temperature.
• For most cases of practical interest, however, the effect of
pressure on the viscosity of liquids can be ignored.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 8

9. Effect of Temperature and Molecular
Weight on Viscosity
Temperature has different effects on viscosity of
liquids and gases.
A decrease in temperature causes the viscosity of a
liquid to rise.
Effect of molecular weight on the viscosity of
liquids is as follows;
the liquid viscosity increases with increasing molecular
weight.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 9

11. Newtonian fluids
A Newtonian fluid is
characterized by having a
constant viscosity at a
given temperature.
This is normally the case
for water and most oils.
A plot of shear rate versus
shear stress would show a
constant slope.
This is the simplest and
easiest fluids to measure
in the lab.
Shear rate versus Shear stress
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 11

12. Non Newtonian fluids
A non-Newtonian fluid is
characterized by not
having a unique value for
viscosity.
That is, the relationship
stress rate/shear rate is
not constant.
The viscosity of these
fluids will depend on the
shear rate applied.
There are several types
of non-Newtonian fluid
behavior that we can
observe in the lab.
The most common are
shown in the figure.
Shear rate versus Shear stress
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 12

13. types of non-Newtonian fluid behavior
Pseudo plastic fluids:
these are fluids like
paints and emulsions,
there is a decrease in
viscosity as the shear rate
increases.
Also known as shear
thinning fluids.
Dilatant fluids:
these are fluids that
increase their viscosity as
the shear rate increases.
Examples are cement
slurries, candy mixtures,
corn starch in water.
Also known as shear
thickening fluids.
Plastic fluids:
These fluids will behave
like solids under static
conditions. They will start
to flow only when certain
amount of pressure is
applied.
Examples are tomato
catsup and silly putty.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 13

14. Viscosity of different material
Below is a table of
viscosity values for some
common materials.
Material Viscosity (cP)
Benzene 0.60
Ethanol 1.06
Water 1 to 5
Mercury 1.55
Pentane 2.24
Blood 10
Anti-Freeze 14
Honey 2,000–3,000
Chocolate Syrup10,000–
25,000
Peanut Butter
150,000–250,000
the application of
(Dilatant materials)
shear thickening fluids
some all-wheel drive
(AWD, 4WD, or 4×4)
systems use a viscous
coupling unit full of
dilatant fluid
Body armor
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 14

16. Instrument selection
Viscosity of liquids is
determined by
instruments called
viscosimeter or viscometer.
Most instruments
designed to measure
viscosity can be classified
in two general categories:
tube type and
rotational type.
The selection of a
particular instrument must
be based on the type of
analysis required and the
characteristics of the fluid
to be tested.
For example,
rotational methods are
generally more appropriate
for non-Newtonian fluids,
while glass capillary
viscometers are
only suitable for Newtonian
fluids.
In this lab,
we will use one instrument
to measure viscosity:
the Ruska Rolling Ball
viscometer.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 16

17. the falling (or rolling) ball viscometer
An instrument
commonly used for
determining viscosity of
a liquid is
the falling (or rolling)
ball viscometer,
which is based on
Stoke’s law for
a sphere falling
in a fluid
under effect of gravity.
A polished steel ball is
dropped into a glass tube
of a somewhat larger
diameter containing the
liquid, and the time
required for the ball to
fall at constant velocity
through a specified
distance between
reference marks is
recorded.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 17

18. The calculation
The following equation
is used
µ = absolute viscosity, cp
t =falling time, s
ρb = density of the ball,
gm/cm3
ρf = density of fluid at
measuring temperature,
gm/cm3
K = ball constant.
The ball constant K is not
dimensionless, but
involves the mechanical
equivalent of heat.
The rolling ball
viscometer will give good
results as long as
the fluid flow in the tube
remains in
the laminar range.
In some instruments of
this type both pressure
and temperature may be
controlled.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 18

19. Instruments to measure rheological
properties (Ruska falling ball)
Schematic diagram of the falling ball viscometer. Ruska falling ball viscometer
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 19

20. Ruska Apparatus
The Ruska rolling ball
viscometer is used to
determine the viscosity of
bottom hole and surface
samples at elevated
temperatures and pressures, up
to 10,000 psi and 300 °F.
 This instrument operates on the
rolling ball principle, where the
roll time of a ¼ inch diameter
ball is used to obtain viscosity
data.
The viscosity is calculated as
 μ: viscosity
 K: constant
 ρ ball: Density of the ball
 ρ fluid: Density of the fluid
 t: roll back time
The driving force in this
instrument is the difference in
density between the fluid and
the ball.
At a fixed temperature, the
difference in ball and fluid
density will be constant.
The viscosity Will be directly
proportional to the roll back
time.
The constant of the viscometer
must be determined by
previous calibration using a
liquid of known viscosity.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 20

21. Operating Procedure
Choose the correct ball
size.
If the fluid viscosity is
estimated to be between 0
and 5 cP, a 0.252 or 0.248
inch diameter ball should
be used.
Above 25 cP, the 0.234 inch
diameter ball will be
appropriate
Clean the test assembly
with kerosene and vent air
to ensure the chamber is
free of dust.
Place the ball
in the bottom of the
empty measuring barrel.
Evacuate the test
assembly.
This is done by opening
the vacuum pump valve at
the lower end of the unit
and closing the charging
valve.
Charge the test sample
fluid in the viscometer.
The vacuum valve should
be closed while the high
pressure charging valve is
reopened.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 21

22. Operating Procedure (Cont.)
Rock the test assembly to obtain a single phase sample.
 The presence of gas bubbles inside the chamber can prevent the ball
from moving freely and stop the experiment completely.
Set the temperature of the viscosimeter to the desired value.
 Allow 3 hours for the temperature to stabilize.
Bring the ball to the hold position, by rotating the test unit 180
degrees.
Turn on the coil and switch to HOLD. The yellow light must be on
Rotate the assembly to the desired angle (70°, 45°, or 23°),
 this will depend on how viscous the fluid is.
Switch to FALL. The green light must be on.
 The ball is released and the time to travel is displayed.
 When the ball hits the bottom, a sound alarm will be triggered.
Calculate the viscosity by using the equation.
 With the appropriate values for the constant.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 22

24. Ostwald viscometer
One type of viscometer for liquids
is the Ostwald viscometer.
In this viscometer, the viscosity is
deduced from the comparison
of the times required for a given
volume of the tested liquids and of
a reference liquid to flow through
a given capillary tube under
specified initial head conditions.
During the measurement
the temperature of the liquid should
be kept constant by immersing
the instrument in
a temperature-controlled water bath.
Two types of Ostwald viscometers.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 24

25. Calculations for the Ostwald
viscometer
In this method
the Poiseuille’s law for
a capillary tube with
a laminar flow regime is
used
t is time required for
a given volume of liquid
V with density of ρ and
viscosity of μ
to flow through the
capillary tube of length l
and radius r by means of
pressure gradient ΔP.
The driving force P at this
instrument is ρgl. Then
or
The capillary constant is
determined from a liquid
with known viscosity.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 25

26. Description of the Liquid Viscosity
Measurement using Capillary Type
The main objective of
the Liquid Viscosity
Measurement is
to determine the kinematic
viscosity of Newtonian
liquid petroleum products.
For capillary viscometers
the time is measured in
seconds
for a fixed volume of liquid
to flow under gravity
through the capillary at a
closely controlled
temperature.
The kinematic viscosity is
the product of
the measured flow time
and the calibration constant
of the viscometer.
=(Const.*t)
The dynamic viscosity can
be obtained by
multiplying
the measured kinematic
viscosity
by the density of the liquid.
=Kinematic viscosity* ρ
=(Const.*t)*ρ
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 26

27. Definitions, Unit and dimensions:
Dynamic viscosity (μ)
is the ratio between the applied shear stress and
the rate of shear and is called coefficient of dynamic viscosity μ.
This coefficient is thus
a measure of the resistance to flow of the liquid;
it is commonly called the viscosity of the liquid.
Kinematic viscosity (υ)
is the ratio μ/ρ where ρ is fluid density.

Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 27

28. The experiment procedures:
Select a clean, dry calibrated
viscometer having a range
covering the estimated viscosity
(i.e. a wide capillary for a very viscous
liquid and a narrower capillary for a less
viscous liquid).
The flow time should not be less than
200 seconds.
Charge the viscometer:
To fill, turn viscometer upside down.
Dip tube (2) into the liquid to be
measured while applying suction to
tube (1) until liquid reaches mark (8).
After inverting to normal measuring
position,
close tube (1)
before liquid reach mark (3).
Viscometer apparatus
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 28

29. The experiment procedures: (Cont.)
Allow the charged viscometer
to remain long enough to reach the room temperature.
Read the calibration constants-directly from the viscometer.
Measuring operation:
Open tube (1) and measure
the time it takes the liquid to rise from mark (3) to mark (5).
Measuring the time for rising from mark (5) to mark (7)
allows viscosity measurement to be repeated
to check the first measurement.
If two measurements agree within required error
(generally 0.2-0.35%),
use the average for calculating the reported kinematic
viscosity.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 29

30. The experiment Calculations:
Calculate the kinematic
viscosity υ from the
measured flow time t and
the instrument constant by
means of the following
equation:
υ = kinematic viscosity, cSt
C = calibration constant,
cSt/s
t = flow time, s
θ = Hagenbach correction
factor,
when t < 400 seconds, it
should be corrected
according to the manual.
t > 400 seconds, θ = 0.
Calculate the viscosity μ
from the calculated
kinematic viscosity υ and
the density ρ by means of
the following equation:
 μ = dynamic viscosity, cp
ρ avr = average density in
g/cm3 at the same
temperature used for
measuring the flow time t.
υ = kinematic, cSt.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 30

31. The experiment report:
Report test results for both
the kinematic and
dynamic viscosity.
Calculate the average dynamic viscosity.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 31

33. the rotational viscosimeter
Other often used viscometers
especially for non-Newtonian
fluids are the rotational type
consisting of two concentric
cylinders, with the annulus
containing the liquid whose
viscosity is to be measured.
Either the outer cylinder or the
inner one is rotated at a constant
speed, and the rotational
deflection of the cylinder
becomes a measure of the
liquid’s viscosity.
Schematic diagram of the rotational viscometer
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 33

34. Calculations for the rotational
viscosimeter
When the distance between
the cylinders d, is small, we
can define the viscosity
gradient for laminar flow
regime as
R is radius of the inner
cylinder (bob) and ω is angular
velocity of the outer cylinder
(rotor) defined by ω = 2π n.
When the rotor is rotating at a
constant angular velocity ω
and the bob is held
motionless, the torque from
the torsion spring on the bob
must be equal but opposite in
direction to the torque on the
rotor from the motor.
The effective area of the
applied torque is 2 π.R.h
 h is length of the cylinder.
The viscous drag on the bob is
k.θ.R,
 k is the torsion constant of the
spring and θ is angular
displacement of the
instrument in degrees.
which gives
 K is the instrument’s constant
which is determined by
calibration.
Summer 14 H. AlamiNia Reservoir Fluid Laboratory Course (1st Ed.) 34

35. 1. (KSU) M. Kinawy. “Reservoir engineering
laboratory manual" Petroleum and Natural
Gas Engineering Department, King Saud
University, Riyadh (2009).
2. “Dilatant.” Wikipedia, the free encyclopedia 1
July 2014. Wikipedia. Web. 5 Aug. 2014.
3. (ABT) Torsæter, O., and M. Abtahi.
"Experimental reservoir engineering
laboratory work book." Department of
Petroleum Engineering and Applied
Geophysics, Norwegian University of Science
and Technology (NTNU), Trondheim (2003).
Chapter 4