Master Thesis: Density of Oil-related Systems at High Pressures - Experimental measurements of HPHT density

Density of Oil-related Systems at
High Pressures
Experimental measurements of HPHT density
Vasos Vasou
s131031
MASTER THESIS
DEPARTMENT OF CHEMISTRY
Lyngby, Denmark
JULY 2015

Supervisors:
Senior researcher
Wei Yan
Post Doc.
Teresa Regueira Muñiz

Acknowledgment
Upon the completion of my Master of Science’s thesis I would like, first and foremost,
to express the deepest appreciation to my supervisors senior researcher Wei Yan and
Post Doc.Teresa Regueira Muñiz for their continuous advice and guidance throughout
the project.
In addition, a thank you to the administration and the technicians at CERE for their
help and assistance throughout the experimental work of this project.
This work as part of a bigger project is funded by the Danish National Advanced
Technology Foundation (Maersk Oil and DONG E&P are partners), which is gratefully
acknowledged.
Last but not least, a special thank to all my friends and family for their unconditional
support and understanding throughout writing this thesis and my life in general.

ABSTRACT
The need for more energy recourses in combination with the gradual decrease of easily
accessible hydrocarbons has led the industry to exploit deeper reservoirs, which are
associated with higher pressures and temperatures. The correct identification of the
physical properties of the reservoir hydrocarbons, such us density, is a significant
parameter for estimating the amount of recourses in place and forecasting the
production. Therefore in this work the measurement of the density of the binary system
methane - n-decane for four different compositions (xmethane = 0, 0.227, 0.6016, 0.8496)
and under a wide range of pressure (up to 1400 bar) and temperature (up to 190 °C)
was carried out with the use of an Anton Paar DMA-HPM densimeter.
The calibration of the DMA-HPM densimeter was performed for pressures up to 140
MPa (1400 bar) and temperatures up to 190 °C (463.15 K) with a modified Lagourette
equation proposed by Comuñas et al and for the validation of the apparatus, the density
of n-decane was measured and compared with the literature. The results were then
compared with the data from NIST and they were in good agreement with an AAD of
0.08%.
For the mixture with a mole fraction of methane xmethane = 0.227 and after a correlation
with the Tait equition the experimental data had an AAD of 0.17% with the literature.
For the mixture with a mole fraction of methane xmethane = 0.6017 the AAD was
between 0.19% and 0.30% with the literature. The last mixture under study had a mole
fraction of methane xmethane = 0.8496 and gave an expected high AAD around 11%
because it was compared with a mixture with lower methane mole fraction (xmethane =
0.799).
Finally a comparison of two cubic EoS (SRK and PR) with two non-cubic EoS (PC
SAFT and SBWR) was performed. PC SAFT was the one that performed better with
AADs lower than 1.2%. The SRK, on the other hand, showed very high deviations
between 10% and 20%. For the pure n-decane the non-cubic equations performed
much better with lower deviations. For the mixture with methane mole fraction xmethane
= 0.227 the non-cubic equations performed better with AADs around 1%. For the
mixture with methane mole fraction xmethane = 0.6017 PC SAFT had an AAD around
0.6% and both PR and SBWR showed an AAD around 4%. Finally, for the mixture
with methane mole fraction xmethane = 0.8496 PC SAFT and PR showed the lowest
deviations with an AAD of 0.67% and 0.87%, respectively.

Table of Contents
Acknowledgment
.....................................................................................................
2

ABSTRACT
................................................................................................................
3

Table
of
Contents
....................................................................................................
5

List
of
figures
...........................................................................................................
7

List
of
tables
............................................................................................................
9

1
Introduction
.......................................................................................................
1

1.1
HPHT
reservoirs
.......................................................................................................................................
1

1.2
Scope
of
this
thesis
...................................................................................................................................
4

1.3
Literature
review
......................................................................................................................................
4

2
Density
..............................................................................................................
7

2.1
Introduction
................................................................................................................................................
7

2.2
Density
measurement
methods
.........................................................................................................
8

2.2.1
Pycnometertic
densitometers
..........................................................................................................
8

2.2.2
Hydrometers
............................................................................................................................................
9

2.2.3
Refractometer
and
index
of
refraction
densitometers
.......................................................
10

2.2.4
Vibrating
tube
densitometers
.......................................................................................................
11

3
HPHT
Density
Measurements
...........................................................................
13

3.1
U-‐tube
basic
principle
..........................................................................................................................
13

3.2
Calibration
procedure
..........................................................................................................................
16

3.3
Experimental
setup
...............................................................................................................................
19

3.4
Experimental
procedure
.....................................................................................................................
25

3.4.1
Apparatus
cleaning
procedure
.....................................................................................................
25

3.4.2
Mixture
preparation
.........................................................................................................................
26

3.4.3
Performing
a
measurement
...........................................................................................................
27

4
Density
modelling
............................................................................................
29

4.1
Cubic
EoS
....................................................................................................................................................
29

4.2
Non-‐cubic
EoS
..........................................................................................................................................
30

5
Results
and
discussion
.....................................................................................
32

5.1
Densimeter
calibration
and
validation
results
..........................................................................
32

5.2
Mixture
methane
–
n-‐decane
(xmethane
=
0.227)
..........................................................................
38

5.3
Mixture
methane
–
n-‐decane
(xmethane
=
0.6017)
.......................................................................
41

5.4
Mixture
methane
–
n-‐decane
(xmethane
=
0.8496)
.......................................................................
44

5.5
Density
modeling
....................................................................................................................................
48

6
Conclusion
and
future
work
.............................................................................
49

7
Bibliography
.....................................................................................................
51

8

Appendix

………………………………………………………………………………………………………56

List of figures
Figure
1:
HPHT
tiers
classification
from
Baker
Hughes
(BakerHughes,
2005)
__________________________
1

Figure
2:
HPHT
tiers
classification
from
Schlumberger
(Belani
&
Orr,
2008)
___________________________
2

Figure
3:
Technology
Gaps,
2012
(Shadravan
&
Amani,
2012)
___________________________________________
2

Figure
4:
Most
important
challenges
of
HPHT
reservoirs
(Shadravan
&
Amani,
2012)
_________________
3

Figure
5:
Oil
in
Water
_______________________________________________________________________________________
7

Figure
6:
Schematic
of
a
pycnometer
(Eren,
1999)
_______________________________________________________
8

Figure
7:
Schematic
of
a
Hydrometer
(Paar,
2015)
_______________________________________________________
9

Figure
8:
Index
of
refraction
densitometer
(Eren,
1999)
_______________________________________________
10

Figure
9:
(a)
Single
vibrating
tube
densitometer,
(b)
Two-‐tube
vibrating
densitometer
(Eren,
1999)

_____________________________________________________________________________________________________________
11

Figure
10:
U-‐tube
filled
with
water
(Paar,
2015)
_______________________________________________________
13

Figure
11:
U-‐tube
filled
with
air
(Paar,
2015)
___________________________________________________________
13

Figure
12:
U-‐tube
measurement
cell
(Paar,
2015)
______________________________________________________
14

Figure
13:
U-‐tube
setup
of
the
Anton
Paar
DMA-‐HPM
measuring
cell
(Paar,
2015)
__________________
14

Figure
14:
Five
key
points
of
the
Mass
Spring
Model
____________________________________________________
15

Figure
15:
Graph
for
air
and
water
adjustment
(Paar,
2015)
__________________________________________
16

Figure
16:
Anton
Paar
DMA-‐HPM
measuring
cell
(Paar,
2015)
________________________________________
19

Figure
17:
Anton
Paar
DMA-‐HPM
(DTU
laboratory)
____________________________________________________
20

Figure
18:
PolyScience
advanced
programmable
temperature
controller
with Swivel
180™
Rotating

Controller
(DTU
laboratory)
_____________________________________________________________________________
20

Figure
19:
(a)
Anton
Paar
mPDS
5
(Paar,
2015),
(b)
Anton
Paar
mPDS
5
(DTU
laboratory)
________
21

Figure
20:
Snapshot
of
the
recording
window
from
the
Microsoft
Excel®
spreadsheet
provided
by

Anton
Paar
________________________________________________________________________________________________
21

Figure
21:
Snapshot
of
the
data
transfer
section
and
the
stability
slope
section
of
the
recording

window
____________________________________________________________________________________________________
22

Figure
22:
Snapshot
of
the
data
spreadsheet
of
the
Microsoft
Excel®
tool
_____________________________
22

Figure
23:
SIKA
digital
pressure
gauge
Type
P
(DTU
laboratory,
left)
(SIKA,
2015,
right)
___________
23

Figure
24:
Edwards
E2M1.5
two-‐stage
oil
sealed
rotary
vane
pump
and
Edwards
Active
Digital

Controller
(ADC)
gauge
(DTU
laboratory)
______________________________________________________________
23

Figure
25:
Teledyne
Isco
260D
syringe
pump
(DTU
laboratory)
_______________________________________
24

Figure
26:
Experimental
setup
(DTU
laboratory)
_______________________________________________________
24

Figure
27:
Schematic
of
the
experimental
density
measurement
setup
________________________________
25

Figure
28:
Mixture
(top)
and
Nitrogen
cylinder
(bottom)
(DTU
laboratory)
__________________________
26

Figure
29:
Methane
weighing
with
Mettler
Toledo
PR1203
balance
(DTU
laboratory)
______________
27

Figure
30:
Period
of
the
evacuated
densimeter
for
temperatures
from
5°C
to
190°C)
________________
34

Figure
31:
Water
measured
period
for
temperatures
from
5°C
to
190°C
and
pressures
from
1
bar
to

1400
bar
___________________________________________________________________________________________________
34

Figure
32:
Characteristic
parameter
A(T)
for
temperatures
from
5°C
to
190°C
______________________
35

Figure
33:
Ratio
between
parameter
A(T)
and
parameter
B(T,p)
_____________________________________
35

Figure
34:
n-‐decane
measured
period
for
temperatures
from
5°C
to
190°C
and
pressures
from
1
bar

to
1400
bar
________________________________________________________________________________________________
36

Figure
35:
Relative
deviations
between
the
experimental
density
values
of
n-‐decane
and
the
data

from
Lemmon
&
Span
(2006)
as
a
function
of
temperature
____________________________________________
37

Figure
36:
Relative
deviations
between
the
experimental
density
values
of
n-‐decane
and
the
data

from
Lemmon
&
Span
(2006)
as
a
function
of
pressure
_________________________________________________
37

Figure
37:
Surface
ρ(T,p)
for
our
experimental
results
for
the
mixture
methane
–
n-‐decane
(xmethane
=

0.227)
______________________________________________________________________________________________________
39

Figure
38:
Surface
ρ(T,p)
for
the
results
from
Audonnet
&
Pádua
(2004)
for
the
mixture
methane
–
n-‐
decane
(xmethane
=
0.227)
__________________________________________________________________________________
39

Figure
39:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
–
n-‐
decane
(xmethane
=
0.227)
and
the
data
from
Audonnet
&
Paduá
(2004)
(xmethane
=
0.227)
as
a
function

of
temperature
____________________________________________________________________________________________
40

Figure
40:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
–
n-‐
decane
(xmethane
=
0.227)
and
the
data
from
Audonnet
&
Paduá
(2004)
(xmethane
=
0.227)
as
a
function

of
pressure
_________________________________________________________________________________________________
40

Figure
41:
Surface
ρ(T,p)
for
our
experimental
results
for
the
mixture
methane
–
n-‐decane
(xmethane
=

0.6017)
____________________________________________________________________________________________________
42

Figure
42:
Surface
ρ(T,p)
for
the
results
from
Audonnet
&
Pádua
(2004)
for
the
mixture
methane
–
n-‐
decane
(xmethane
=
0.601)
__________________________________________________________________________________
42

Figure
43:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
-‐
n-‐
decane
(xmethane
=
0.6017)
and
the
data
from
Audonnet
&
Paduá
(2004)
(xmethane
=
0.601)
and
Canet
et

al.
(2002)
(xmethane
=
0.6)
as
a
function
of
temperature
__________________________________________________
43

Figure
44:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
-‐
n-‐
decane
(xmethane
=
0.6017)
and
the
data
from
Audonnet
&
Paduá
(2004)
(xmethane
=
0.601)
and
Canet
et

al.
(2002)
(xmethane
=
0.6)
as
a
function
of
pressure
______________________________________________________
44

Figure
45:
Surface
ρ(T,p)
for
our
experimental
results
for
the
mixture
methane
–
n-‐decane
(xmethane
=

0.8496)
____________________________________________________________________________________________________
45

Figure
46:
Surface
ρ(T,p)
for
the
results
from
Audonnet
&
Pádua
(2004)
for
the
mixture
methane
–
n-‐
decane
(xmethane
=
0.799)
__________________________________________________________________________________
45

Figure
47:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
-‐
n-‐
decane
(xmethane
=
0.8496)
and
the
data
from
Audonnet
&
Paduá
(2004)

(xmethane
=
0.799)
as
a

function
of
temperature
__________________________________________________________________________________
46

Figure
48:
Relative
deviations
between
the
experimental
density
values
of
the
mixture
methane
-‐
n-‐
decane
(xmethane
=
0.8496)
and
the
data
from
Audonnet
&
Paduá
(2004)
(xmethane
=
0.799)
as
a
function

of
pressure
_________________________________________________________________________________________________
47

Figure
49:
Density
as
a
function
of
pressure
for
all
compositions
at
5
°C
and
190
°C
_________________
47

Figure
50:
AAD
of
the
comparison
between
the
experimental
densities
and
those
calculated
with
the

EOS
for
the
whole
temperature
and
pressure
range
____________________________________________________
48

List of tables
Table
1:
HPHT
applications
categories
____________________________________________________________________
1

Table
2:
Experimental
uncertainty
of
density
(Segovia
et
al.,
2009)
___________________________________
19

Table
3:
Mixture
compositions
___________________________________________________________________________
26

Table
4:
Mixture
composition,
pressure
and
temperature
range
_______________________________________
28

Table
5:
Pressure
steps
___________________________________________________________________________________
28

Table
6:
Temperature
steps
______________________________________________________________________________
28

Table
7:
Tc,
Pc,
ω
and
Zc
for
methane
and
n-‐decane
_____________________________________________________
30

Table
8:
Interaction
parameters
for
the
methane
–
n-‐decane
binary
mixture
(Wei
et
al.,
2015)
_____
30

Table
9:
Values
for
ρw,
τw,
ρd,
τv
___________________________________________________________________________
32

Table
10:
Experimental
density
values
(kg/m3)
of
n-‐decane
___________________________________________
36

Table
11:
Experimental
density
values
(kg/m3)
of
the
mixture
methane
-‐
n-‐decane
(xmethane
=
0.227)
38

Table
12:
Parameters
obtained
in
the
Tait
equation
with
the
results
from
Audonnet
&
Pádua
(2004)

(xmethane
=
0.227)
and
our
experimental
results
(xmethane
=
0.227)
_______________________________________
39

Table
13:
Experimental
density
values
(kg/m3)
of
the
mixture
methane
-‐
n-‐decane
(xmethane
=
0.6017)

_____________________________________________________________________________________________________________
41

Table
14:
Parameters
obtained
in
the
Tait
equation
with
the
results
from
Audonnet
&
Pádua
(2004)

(xmethane
=
0.601),
our
experimental
results
(xmethane
=
0.6017)
and
those
from
Canet
et
al.
(2002)

(xmethane
=
0.6)
_____________________________________________________________________________________________
41

Table
15:
Experimental
density
values
(kg/m3)
of
the
mixture
methane
-‐
n-‐decane
(xmethane
=
0.8496)

_____________________________________________________________________________________________________________
44

Table
16:
Parameters
obtained
in
the
Tait
equation
with
the
results
from
Audonnet
&
Pádua
(2004)

(xmethane
=
0.799)
and
our
experimental
results
(xmethane
=
0.8496)
_____________________________________
46

Table
17:
AAD
and
MAD
of
the
comparison
between
the
experimental
densities
and
those
calculated

with
the
EOS
for
the
whole
temperature
and
pressure
range
__________________________________________
48

Table
18:
Technical
specifications
of
the
External
Measuring
Cell
DMA-‐HPM
(Paar,
2015)
__________
56

Table
19:
Technical
specifications
of
the
PolyScience
advanced
programmable
temperature

controller
with Swivel
180™
Rotating
Controller
(PolyScience,
2015)
_________________________________
57

Table
20:
Technical
specifications
of
the
evaluation
unit
mPDS
5
(Paar,
2015)
_______________________
57

Table
21:
Technical
specifications
of
the
SIKA
digital
pressure
gauge
Type
P
(SIKA,
2015)
(SIKA,

2015)
______________________________________________________________________________________________________
58

Table
22:
Technical
specifications
of
the
Edwards
E2M1.5
two-‐stage
oil
sealed
rotary
vane
pump

(Edwards,
2015)
__________________________________________________________________________________________
59

Table
23:
Technical
specifications
of
the
Edwards
Active
Digital
Controller
(ADC)
gauge
(Edwards,

2015)
______________________________________________________________________________________________________
60

Table
24:
Technical
specifications
of
the
Teledyne
Isco
260D
Syringe
Pump
(Isco,
2013)
____________
61

Table
25:
Chemical
and
physical
properties
of
Ethanol
(VWR,
2015)
__________________________________
62

Table
26:
Chemical
and
physical
properties
of
Toluene
(SIGMA-‐ALDRICH,
2014)
____________________
62

Table
27:
Chemical
and
physical
properties
of
n-‐decane
(SIGMA-‐ALDRICH,
2014)
___________________
63

Table
28:
Chemical
and
physical
properties
of
methane
(AGA,
2015)
_________________________________
63

1
1 Introduction
1.1 HPHT
reservoirs

In a constantly growing world due to the increase of global population and the
technological advancement of new emerging technologies energy demand is,
subsequently, rising. The need for more energy recourses in combination with the
gradual decrease of easily accessible hydrocarbons has drawn the attention of the
industrial world into the exploration of less accessible, deeper and more
technologically challenging formations. This pursuit for more hydrocarbons has led the
industry to exploit deeper reservoirs, which are associated with higher pressures and
temperatures. Several studies have defined reservoirs as High Pressure High
Temperature (HPHT) when they are associated with pressures exceeding 700 bar
(10000 psi) and temperatures over 150 °C (300 °F) (Cullen, 1993; Guilory, 2005; Ling
et al., 2009; Primio & Neumann, 2007). Even though, HPHT drilling is not rigorously
pursuit during times of decreased oil price due to high cost, there are a lot of HPHT
fields around the world mainly in the Gulf of Mexico, Middle East, South Asia, Africa
and the North Sea (Bland et al., 2006).
A tier structure categorizing the various HPHT applications is widely accepted in the
industry (Table 1). This way the details and the limitations of available technology in
each category are specified. (Thompson et al., 2012; Shadravan & Amani, 2012).
Table 1: HPHT applications categories
Tier category Pressure - bar (psi) Temperature - °C (°F)
Tier 1 (HPHT) 700 (10000) < p < 1400 (20000) 150 (300) < T < 205 (400)
Tier 2 (ultra HPHT) 1400 (20000) < p < 2100 (30000) 205 (400) < T < 260 (500)
Tier 3(extreme HPHT) p > 2100 (30000) T > 260 (500)
An example of how the industry defines the tiers for HPHT applications can be seen in
Figure 1 and Figure 2 from Baker Hughes and Schlumberger, respectively.
Figure 1: HPHT tiers classification from Baker Hughes (BakerHughes, 2005)

2
Figure 2: HPHT tiers classification from Schlumberger (Belani & Orr, 2008)
On April 2010 methane gas under high pressure from the Macondo HPHT well in the
Gulf of Mexico was shot up from the well into the platform where it expanded and
ignited leading to a devastating explosion (Garg & Gokavarapu, 2012). This shocking
accident alerted the industry and brought the risk and challenges of drilling in deep,
unconventional formations into perspective (Shadravan & Amani, 2012). The industry
is constantly improving the technologies required for drilling and producing in such
harsh formations but the gap between the available technology and the demands for
production from HPHT fields still remains. In the 2012 HPHT well summit in London,
the technological gaps were identified as depicted in Figure 3.
Figure 3: Technology Gaps, 2012 (Shadravan & Amani, 2012)

3
In general, the initial challenge when it comes to the decision-making process
regarding HPHT reservoirs is the high cost. The Rate of Penetration (ROP) in HPHT
wells is 10% slower than normal drilling conditions and in combination with the
increased depth of the reservoir, the average drilling time for HPHT wells can be up to
30% longer (Proehl & Sabins, 2006). The slower drilling increases the rental time of
the rig and the drilling equipment, which essentially skyrockets the overall cost.
The most important challenges that contribute to the increased cost of HPHT wells can
be seen in Figure 4.
Figure 4: Most important challenges of HPHT reservoirs (Shadravan & Amani, 2012)
During the design of the well, the stability of the borehole can be especially
complicated because of the thermal effect on the fracture gradient. Increasing
temperatures can induce high tensile or compressive stresses on the formation. In
addition, the high temperature can affect the density of the drilling mud and the well
cementing operations with altering the chemical and physical behaviour of the cement
(Radwan & Karimi, 2011). Materials under high temperatures expand, leading to a
more general well growth that can result to an elevation of the whole structure during
production. One more problem the industry faces is the effect of the extreme
temperature to the downhole equipment. Most of the tools in the market are rated to
150 °C so when the temperature exceed that the tools won’t be applicable. Also, the
equipment’s failure rate when operates above 140 °C is much higher than in cooler
environments (Gjonnes & Myhre, 2005). Finally another important challenge is the
lack of experienced personnel, which can be an even greater problem during decision-
making processes and safety measures especially regarding the handling of the drilling
fluids in high temperatures.

4
1.2 Scope
of
this
thesis

As already mentioned, the development of HPHT reservoirs can be a particularly
challenging and risky endeavour but if done successfully can also be highly rewarding.
A successful operation in the oil industry is one with positive revenue and to achieve
that in a highly cost and demanding HPHT reservoir the technical risks must be
reduced. In order to accomplish that, a better understanding of the behaviour of the
hydrocarbon reservoir fluids is crucial. The correct identification of the physical
properties of the reservoir hydrocarbons is a significant parameter for estimating the
amount of recourses in place and forecasting the production. Under this work the
property that is studied is density. The experimental data for density in high pressures
and temperatures are insufficient, so further experimentation under extreme conditions
is needed. As mentioned before, most of the tools in the market are not designed to
withstand such extreme conditions making the gathering of data extremely difficult.
For the industry to be able to predict with accuracy the physical properties of
hydrocarbon related systems under HPHT conditions, the development of predictive
models is required.
Under this thesis the five major tasks presented below are considered:
• Literature review of the existing relevant data on density of alkane binary
mixtures under high pressures and temperatures.
• Calibration of the densimeter for pressures up to 140 MPa (1400 bar) and
temperatures up to 190 °C (463.15 K).
• Validation of the apparatus through the use of n-decane.
• Measurement of the density of the binary system methane - n-decane for three
different compositions and under a wide range of pressure and temperature.
• A comparison of two cubic Equations of State (EoS) (Soave–Redlich–Kwong
and Peng–Robinson) with two non-cubic EoS (Perturbed Chain Statistical
Associating Fluid Theory and Benedict–Webb–Rubin).
1.3 Literature
review

Canet et al. (2002) used an Anton Paar DMA 60 densimeter to measure the density of
the binary mixture methane – n-decane over the temperatures from 20 °C to 100 °C
with a 20 °C step. They covered the whole composition range of the binary mixture by
measuring the density for compositions with methane mole fraction equal to: xmethane =
0.3124, 0.4867, 0.6, 0.7566, 0.9575. The pressure range under experimentation was
between 200 bar and 650 bar and then the results were extrapolated up to 1400 bar.
The experimental densities were then, compared with those generated by the Lee &
Kesler (1975) equation with an absolute average deviation of 3.3% with the mixing
rules proposed by Spencer & Danner (1972) and 7.3% with the mixing rules proposed
by Joffe (1947).

5
Audonnet & Pádua (2004) also measured the density of the methane – n-decane binary
mixture in a temperature range from 30 °C to 120 °C and for pressures up to 750 bar.
They covered the whole composition range of the binary mixture by measuring the
density for compositions with methane mole fraction equal to: xmethane = 0, 0.227,
0.410, 0.601, 0.799. The obtained results were then correlated using the Tait equation
(Dymond & Malhotra, 1988) and compared with literature. For the composition xmethane
= 0.601 the experimental results were compared with Canet et al. (2002) and found to
have a standard deviation of 0.17% and with De Sant’ Ana (2000) and found to have a
standard deviation of 0.3%.
Another work, from Amorim et al (2007), used a densimeter provided by Anton Paar.
The densimeter DMA 512 P was used in a temperature range of 45 °C to 140 °C and
for pressures between 68.95 bar and 620.53 bar. The calibration fluids were toluene,
cyclohexane and n- heptane and the density of the binary mixture of n-hexadecane –
cyclohexane was measured with an experimental error of 0.5 kg.m-3
. The deviation of
the density measurements with the literature was 0.75 kg.m-3
. All data were correlated
successfully with a modified EoS from Peng & Robinson (1976).
Gil et al. (2007) discussed the measurement of the density for the binary mixture CO2 –
ethane for pressures between 100 bar and 200 bar with a pressure step of 5 bar. The
Anton Paar DMA 512 P that was used was calibrated from 5 °C to 45 °C and for
pressures up to 200 bar with mili-Q water as the reference fluid. The densities of the
mixture were calculated with the use of the cubical EoS suggested from Peng &
Robinson (1976) and Patel & Teja (1982) and after comparison between the
experimental values and the calculated values the root-mean-square deviation was
3.67% for Peng-Robinson and 4.33% for Patel-Teja. The mean standard deviation of
density was 0.09%.
Many authors used the Anton Paar densimeters to measure densities of pure
compounds. The Anton Paar DMA-HPM densimeter was used from Comuñas et al.
(2008) to measure the density of diethyl adipate over the temperatures from 20 °C to
130 °C and pressures up to 1400 bar. To calculate density a modified equation from
Lagourette et al. (1992) was used and the uncertainty was 0.05%. For the validation of
the densimeter the results for the densities of 1-butanol and toluene were compared
with the literature and the average absolute deviation was lower than 0.08%.
Caudwell et al. (2004) used a vibrating-wire instrument for the measurement of the
density of n-dodecane and n-octadecane for temperatures between 25 °C to 200 °C and
pressures up to 2000 bar. For the calibration procedure measurements of vacuum, air
and toluene at 25 °C were taken. After comparison with the experimental data from
Harris et al. (1997) and Kashiwagi et al. (1982) the uncertainty was 0.2%.
Segovia et al. (2009) also used the DMA-HPM densimeter from Anton Paar, which
was calibrated in the temperature region between 10 °C and 125 °C and for pressures

6
up to 700 bar. The Lagourette et al (1992) equation as modified by Comuñas et al
(2008) was used and vacuum, water and n-decane were the calibration fluids. The
density of toluene and n-decane were then measured and the absolute average
deviation with Cibulka & Hnedkovsky (1996) was 0.03% and 0.07%, respectively.
After literature review and research the fact that the industry lacks experimental data
for high-pressures over 700 bar was confirmed. More experimental data are necessary
to enhance the knowledge around the density of alkane binary mixtures over extreme
pressure and temperature conditions.

7
2 Density
2.1 Introduction

Viana et al. (2002) identifies density as a fundamental parameter that contributes to the
characterization of the product. Density is defined as the exact mass of a solid, gas or
liquid that is occupying a specific volume and the SI unit is kilogram per cubic meter
(kg/m3
). The most common symbol for density is the Greek letter ρ and it can be
mathematically defined as:
ρ =
!
!
[1]
where m is the mass and V is the volume.
The effects of density can be observed on both solids and fluids. An example can be
seen in Figure 5. Oil and water don’t mix and oil swim on top creating a two layer
liquid. The water has higher density and less buoyancy than the oil, so it will sink
while the oil with the lesser density swims on top.
Figure 5: Oil in Water
The effects of density on gases is less visible but equally important. For example the
fact that helium has lesser density that the atmospheric air it might not be easy to grasp
but it can become very obvious when a Helium balloon is let go and rises up into the
sky. Another effect of density can be seen when even the slightest change in the
density of the air directly influence the weather.
Pressure and temperature are two important parameters that affect density. An increase
on pressure will cause an increase on density whereas, on the other hand, for most
materials the temperature affects density inversely proportional. In petrochemistry the
density of oil is very important because with precise measurements a material
characterization and quality control of oil products can be achieved.

8
2.2 Density
measurement
methods

In general, the measurement of fluids densities is a much more complex science than
the measurement of the density of solids. Density measurements on fluids are divided
into two forms, static and dynamic. Sydenham (1999) defines the static characteristics
of the instrumentation as the performance criteria for the measurement of quantities
that remain constant, or vary only quite slowly while dynamic characteristics are the
set of criteria defined for the instrument, which are changing rapidly with time. Static
density measurements are well developed and usually more precise and with greater
resolution than dynamic measurements. Commonly, dynamic-type measurements are
used for real-time experiments where the properties of the fluids are not constant.
Static density measurements, on the other hand, are employed in laboratory conditions
(Eren, 1999).
A quick review of the basic available density measurement methods and a comparison
between them regarding precision, speed, cost and applications is presented. These
methods include:
• Pycnometric densitometers
• Hydrometers
• Refractometer and index of refraction densitometers
• Vibrating tube densitometers
2.2.1 Pycnometertic
densitometers

Pycnometers are static devices with a container of fixed volume and a capillary bore.
They are commonly used in the chemical and pharmaceutical industry and in research
facilities or universities (Paar, 2015). A schematic of a pycnometer can be seen in
Figure 6.
Figure 6: Schematic of a pycnometer (Eren, 1999)
The first step to measure the density of a liquid is to find out the mass of the empty
pycnometer by weighing it. Then, to determine the volume, a liquid with well-known
density, such as distilled water, is used. The rise of the capillary will give the volume.
The pycnometer is then weighed again to get the mass of the water by subtracting it
with the mass of the empty pycnometer. This procedure is repeated with the liquid of
the unknown density to determine its mass (measured weight minus weight of empty

9
pycnometer) and its volume with the capillary bore. Finally, with equation (2) the
density of the unknown liquid is calculated.
ρunknown =
!!"#"$%"
!!!!
. 𝜌!!! [2]
Pycnometers are usually made of glass or sometimes metal when the density of the
fluid is measured under extremely high pressure. To assure the accuracy of the
measurement pycnometers have to be nonmagnetic, because even the slightest ambient
magnetic effect can alter the calculation of the density (Eren, 1999).
The most important advantage of the pycnometer is precision. If they used correctly
they can provide accurate results. Also, pycnometers can be used to measure both the
density and the specific gravity of fluids. Pycnometers, though, have a number of
disadvantages like the fact that the precision of the measurement depends on the
operator and only a skilled operator can achieve an accurate measurement. The overall
apparatus for the determination of the density with a pycnometer can be very
expensive if an extremely precise measurement is needed. The high cost arises from
the requirement of a very precise weighing scale and the need for controlled laboratory
conditions. In addition, is a slow and time-consuming method (Eren, 1999).
2.2.2 Hydrometers

Hydrometer (Figure 7) is one of the oldest density measuring techniques and is also the
most commonly used in the beverage and the chemical industry to ensure good quality
control (Paar, 2015).
Figure 7: Schematic of a Hydrometer (Paar, 2015)
The hydrometer consists of a main floating glass body, with a cylindrical stem with a
scale and a bulb filled with metal weight. The measurement procedure is very simple
since it only involves the immersion of the hydrometer in the sample and the reading
of the density directly from the scale. The deeper the hydrometer sinks the less dense
Scale
Fluid
vessel
Weight
bulb

10
the sample is. The principle used for determining the density with the hydrometer is
buoyancy.
Hydrometers have both advantages and disadvantages. The main advantages are the
low cost and the simplicity and speed of the procedure. Because hydrometers are so
commonly used their specifications are traceable to international standards. On the
other hand their reliability is debatable because it is easy for the scale to be misread. In
addition, a temperature correction and a large sample volume (up to a 100 mL) are
required. Finally, hydrometers are made of glass, which makes them extremely fragile
(Eren, 1999).
2.2.3 Refractometer
and
index
of
refraction
densitometers

Refractometers can measure what is commonly known as index of refraction (n). The
refraction index is the dimensionless number of the comparison between the speed of
light in a vacuum and the velocity of light through a medium, which basically
describes how much of the light, is refracted when entering a sample.
n =
!
!
[3]
where c is the speed of light in vacuum and u is the velocity of light in a medium.
The index of refraction densitometer, as can be seen in Figure 8, consists of a
transparent cell that the liquid or gas flows through, a laser or light beam and a sensor.
As the laser beam passes through the cell and the sample is refracted with an angle.
That angle of refraction depends on the shape, size and thickness of the container and
on the density of the sample. Since, the container’s characteristics are constant and
well known the only unknown variable is the density of the sample. An accurate
measurement of the position of the beam and the refraction angle can relate to the
sample’s density (Eren, 1999).
Figure 8: Index of refraction densitometer (Eren, 1999)

11
Refractometers can find applications in industry such as the control of adulteration of
liquids (oils, wines, gasoline) and in the chemical industry.
2.2.4 Vibrating
tube
densitometers

The effectiveness of vibrating densitometers is based on the principle that every fluid
has a unique natural frequency. This resonance frequency (f) depends on the stiffness
of the body and the combined mass of the body and the fluid and is described with
equation (4) (Tropea et al., 2007):
f =
!
!!
!
!!(!.!)
[4]
where K is the elasticity constant of the body, m is the mass of the body containing the
fluid, ρ is the fluid density and V is the volume of the body.
The frequency is also related to oscillation period (τ) as:
τ =
!
!
[5]
There are two types of vibrating tube densitometers, the single tube and the two tube
vibrating densitometer as can be seen in Figure 9. The single tube has pressure losses
and some obstruction on the natural flow. The two-tube densitometer is designed in a
way that the two tubes are vibrating in an antiphase, which provides higher accuracy
(Eren, 1999).
Figure 9: (a) Single vibrating tube densitometer, (b) Two-tube vibrating densitometer (Eren, 1999)
The vibrating tube densitometer can be applied on research and on huge variation of
applications in the industry such as quality control or R&D investigations (Paar, 2015).
The most important advantage of the vibrating tube densitometer is that in the right
instrument setup can provide very high accuracy and repeatability. Some other
advantages are the high measurement speed (a few minutes) and the very little sample
(a) (b)

12
volume that is needed (1 mL). The only limiting factor is the possible dynamic
influence of viscosity on the results.
In general, the vibrating tube densitometer method is the most advanced, precised and
fast method for measuring the density of fluids. The experimental apparatus that was
used for the determination of the density for this report uses the oscillating U-tube
method, which is an advanced vibrating tube method. More details about the
oscillating U-tube method are provided in HPHT Density Measurements.

13
3 HPHT Density Measurements
3.1 U-‐tube
basic
principle

The Anton Paar DMA-HPM measuring cell measures the density of fluids based on the
oscillating U-tube method introduced by Dr. Hans Stabinger in the 1960s. The overall
idea of the oscillating U-tube method is based on the principle that every fluid has it’s
own characteristic frequency and that frequency is directly related to the sample’s
density. A hollow U-shaped tube is filled with the sample fluid then, the tube is
subjected to an electromagnetic force and is excited into periodic oscillation (Furtado
et al., 2009). Then, the frequency as a function of time is recorded and a sin-wave of a
certain period and amplitude is created as can be seen in Figure 10 and Figure 11.
Figure 10: U-tube filled with water (Paar, 2015)
Figure 11: U-tube filled with air (Paar, 2015)

14
The classic way the U-tube oscillator operates is by a magneto-electrical system as can
be seen in Figure 12. Alternating voltage is sent through the electric coil on the tube,
which creates an alternating magnetic field. The magnet on the tube reacts to the
alternating current and as a result an excitation is generated. The frequency of the
magnet’s oscillation that is caused is measured with an amplifier.
Figure 12: U-tube measurement cell (Paar, 2015)
The constant search for faster, more precise and more accurate measurements and the
technological advancements of the 21st
century lead to a constant redevelopment and
improvement of the U-tube. One of the most advanced U-tube setups in the market is
the one in the Anton Paar DMA-HPM measuring cell, which was used for the series of
experiments for this report. The tube is made of Hatelloy C-276, which is a nickel-
based super alloy widely used in the industry because of its high corrosion resistance
and high temperature strength (Ahmad et al., 2005). The U-tube is kept oscillating
continuously at a characteristic frequency because of an electronic excitation generated
from a piezoelement. Two optical pick-ups record the oscillation and an extra tube acts
as a reference oscillator and speeds up the measurement. The U-tube setup of the
Anton Paar DMA-HPM measuring cell can be seen in Figure 13.
Figure 13: U-tube setup of the Anton Paar DMA-HPM measuring cell (Paar, 2015)
The physical background of this principle is based on the Mass Spring Model (MSM),
which is a vertical system that consists of a spring attached on an unwavering point on

15
the upper end and has an attached mass on the lower end (Figure 14). When the mass is
pulled down and let go, the MSM oscillates and the period of the oscillation can be
described with equation (6).
Figure 14: Five key points of the Mass Spring Model
τ = 2π .
!!(! .!)
!
[6]
where m is the mass of the sphere, ρ is the density, V is the volume of the sphere and K
is the spring constant.
Solving equation (6) for density:
ρ = τ2
.
!
! . !!!
−
!
!
[7]
Hans Stabinger (1994) studied the relation between the period of oscillation and the
density and found a way to implement the MSM mechanically. To achieve this,
Stabinger introduced two adjustment constants namely A and B described from
equations (8) and (9), respectively.
A =
!
! . !!!
[8]
B =
!
!
[9]

16
Replacing the two adjustment constants in equation (7):
ρ = A . τ2
- B [10]
Now to relate these equations to the oscillation U-tube method the two adjustment
constants are different for each instrument so the unique A and B constants need to be
calculated and stored into every oscillator. In order to achieve that two different
samples of a precisely known density should be used. Typically, double distilled
freshly degased water at 20 °C and dry and clean air are used. The water must be very
well distilled before inserted in the tube to avoid gas bubbles; otherwise the lack of
quality in the adjustment process can give incorrect density values (Paar, 2015).
Figure 15 illustrates the graph of the formula for the air and water adjustment as a
function of density and square period. Because the density of the water and the air are
known the adjustment constants A and B can be calculated as they define a straight line
in the graph. Now, for the calculation of the density for a sample that is inserted in the
tube the instrument measures the period of oscillation and then applies that value to the
adjustment line and converts it to the corresponding density.
Figure 15: Graph for air and water adjustment (Paar, 2015)
3.2 Calibration
procedure

The vibrating tube densitometer is calibrated through the oscillation period
measurement of two fluids with well-known densities. As mentioned before Hans
Stabinger (1994) studied the relation between the period of oscillation and the density
and introduced equation (10), which can be also written, for the two reference fluids,
as:
𝜌!(T,p) = A(T,p) . 𝜏!
!
(T,p) - B(T,p) [11]

17
𝜌!(T,p) = A(T,p) . 𝜏!
!
(T,p) - B(T,p) [12]
where 𝜌! and 𝜌! are the known densities of fluids 1 and 2 and τ1 and τ2 are the
measured oscillation periods of the two fluids at each temperature and pressure.
Solving the system of the above two equations, parameters A(T) and B(T,p) are
derived:
𝐴(𝑇, 𝑝) =
𝜌! 𝑇, 𝑝 − 𝜌!(𝑇, 𝑝)
𝜏!
!
𝑇, 𝑝 − 𝜏!
!
(𝑇, 𝑝)
[13]
𝐵(𝑇, 𝑝) = 𝐴(𝑇, 𝑝) . 𝜏!
!
(𝑇, 𝑝) − 𝜌!(T,p) [14]
Lagourette et al. (1992), proposed a calibration method that is based on the hypothesis
that parameter A(T) is only temperature dependent, while parameter B(T,p) is both
temperature and pressure dependent. If water was used as the first reference fluid and
instead of a second reference fluid the tube was used under vacuum and by taking into
account that the density of vacuum is zero then:
𝜌!(T,p) = A(T,p) . 𝜏!
!
(T,p) - B(T,p) [15]
0 = 𝐴(𝑇). 𝜏!
!
(𝑇, 0) − 𝐵(𝑇, 0) [16]
where the subscript w refers to water and the subscript v refers to vacuum. Parameter
B(T,p) can then be obtained:
𝐵(𝑇, 𝑝) = 𝐴(𝑇). 𝜏!
!
(𝑇, 𝑝) − 𝜌!(T,p) [17]
Lagourette et al. (1992) proposed that B(T,0) ≈ B(T,0.1MPa) therefore equation (17)
can be written as:
𝜌!(T,0.1MPa) = A(T) . 𝜏!
!
(T,p) - 𝜌!(T,p) [18]
Parameter A(T) is then, described as:
𝐴(𝑇) =
𝜌! 𝑇, 0.1𝑀𝑃𝑎
𝜏!
! 𝑇, 0.1𝑀𝑃𝑎 − 𝜏!
!(𝑇, 0)
[19]
Finally, Lagourette et al. (1992) described the density of any fluid with the following
equation:
𝜌 𝑇, 𝑝 = 𝜌! 𝑇, 𝑝 + 𝜌! 𝑇, 0.1𝑀𝑃𝑎
𝜏!
𝑇, 𝑝 − 𝜏!
!
𝑇, 𝑝
𝜏!
! 𝑇, 0.1𝑀𝑃𝑎 − 𝜏!
! 𝑇, 0
[20]

18
where τ is the oscillation period of the measured fluid.
For this work, the calibration method is summarised below:
• Equations (15) to (20) were used for the densimeter calibration at pressures
between 0.1 MPa and 140 MPa and temperatures between 5 °C and 75 °C. The
density of water was taken from NIST (National Institute of Standards and
Technology) that uses the equation of state from Wagner and Pruss (2002) and
the period of water and vacuum were measured.
The limitations, on the temperature range, of the above equation are due to the fact that
water over 100 °C is at a vapour state.
• For the extension of the calibration to temperatures up to 190 °C and for
atmospheric pressure, equations (21) to (23) that were suggested from
Comuñas et al. (2008) were used:
𝐴(𝑇) =
𝜌! 𝑇, 0.1𝑀𝑃𝑎
𝜏!
!
𝑇, 0.1𝑀𝑃𝑎 − 𝜏!
!(𝑇, 0)
[21]
𝐵(𝑇, 0.1𝑀𝑃𝑎) = 𝐴(𝑇). 𝜏!
!
(𝑇, 0.1𝑀𝑃𝑎) − 𝜌!(T,0.1MPa) [22]
ρ T,0.1MPa = ρd T,0.1MPa . 1+
τ2 T,0.1MPa -‐τd
2
T,0.1MPa
τd
2 T,0.1MPa -‐τv
2 T
[23]
where τd is the measured oscillation period of n-dodecane and ρd is the density
of n-dodecane.
• For the temperatures 100 °C and 150 °C and pressures higher than 0.1 MPa and
for the temperature 190 °C and pressures higher than 1 MPa equations (17),
(21) and (24) were used:
ρ T,p = ρw T,p + ρd T,0.1MPa .
τ2 T,p -‐τw
2 T,p
τd
2 T,0.1MPa -‐τv
2 T
[24]
For this equation the density of water was taken from NIST that uses the
equation of state from Wagner and Pruss (2002), the density of n-dodecane was
taken from NIST that uses the equation of state from Lemmon & Huber (2004)
and the oscillation periods of water and vacuum were measured. The oscillation
period of n-dodecane was measured in a previous work (Chasomeris et al.,
2015).

19
• Finally, for the temperature of 190 °C and the pressure of 1 MPa the following
equation was used:
ρ T,p = ρd T,p + ρd T,0.1MPa .
τ2 T,p -‐τd
2 T,p
τd
2 T,0.1MPa -‐τv
2 T
[25]
Segovia et al. (2009) suggested the following experimental uncertainties for the
density, which are adopted for this work:
Table 2: Experimental uncertainty of density (Segovia et al., 2009)
Temperature (°C) T <100 T =100 & T=150 T =190 100 < T <190
Pressure (bar) 1 < p < 140 p=1 p=1 & p=10 10< p
Uncertainty (kg/m3
) 0.7 5 5 3
The relative deviation, the absolute deviation and the absolute average deviation
(AAD) were calculated with equations (26) to (28).
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 % =
𝜌!"# − 𝜌!"#
𝜌!"#
. 100 [26]
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 % =
𝜌!"# − 𝜌!"#
𝜌!"#
. 100 [27]
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 % =
1
𝑛
𝜌!"# − 𝜌!"#
𝜌!"#
. 100
!
!!!
[28]
where 𝜌!"# is the experimental density (kg/m3
), 𝜌!"# is the density from literature
(kg/m3
) and n is the number of measurements.
3.3 Experimental
setup

For the determination of the density for this report the External Measuring Cell DMA-
HPM (Density Measuring Apparatus) from Anton Paar was used.
Figure 16: Anton Paar DMA-HPM measuring cell (Paar, 2015)

20
The DMA-HPM can provide reliable density measurements for a sample at extreme
conditions with high pressures up to 1400 bar and at a wide range of temperatures
extending from -10 °C up to 200 °C.
Figure 17: Anton Paar DMA-HPM (DTU laboratory)
The DMA-HPM is commonly used in reservoir studies because of its high accuracy,
which can be up to 0.0001 g/cm3
(Paar, 2015). An extended version of the
specifications of the DMA-HPM can be found in Table 18 in Appendix A: Technical
Specifications.
For the temperature regulation of the DMA-HPM measuring cell a circulating bath
thermostat provided by PolyScience was used. In particular, the PolyScience advanced
programmable temperature controller with Swivel 180™ Rotating Controller that was
used for the experiments can be seen in Figure 18.
Figure 18: PolyScience advanced programmable temperature controller with Swivel 180™ Rotating Controller
(DTU laboratory)
With a temperature range from -20 °C to 200 °C and temperature stability and
precision of 0.01 °C the PolyScience advanced programmable temperature controller
was ideal for regulating the apparatus temperature through the whole range required
for this set of experiments. An extended version of the specifications of the
PolyScience advanced programmable temperature controller can be found in Table 19
in Appendix A: Technical Specifications. The temperature of the densimeter was
measured with a PT100 platinum thermometer.

21
In order to get the density measurements the DMA-HPM is connected to the evaluation
unit mPDS 5 from Anton Paar (Figure 19). The mPDS 5 continuously records the
density of the sample and converts the raw values from the sensors into application
specific results. The mPDS can display a number of parameters such as the oscillation
period, the temperature and the pressure of the sample in the measuring cell. An
extended version of the specifications of the mPDS 5 can be found in Table 20 in
Appendix A: Technical Specifications.
Figure 19: (a) Anton Paar mPDS 5 (Paar, 2015), (b) Anton Paar mPDS 5 (DTU laboratory)
The user has access to the recorded measurements from a Microsoft Excel®
spreadsheet installed on a computer which, is connected to the mPDS 5. The
spreadsheet that is provided by Anton Paar and records all the measurements can be
seen in Figure 20.
Figure 20: Snapshot of the recording window from the Microsoft Excel®
spreadsheet provided by Anton Paar
The most important features to understand from the recording window are the date
transfer section and the stability slope section (Figure 21). The data window box under
the data transfer section corresponds to the number of measured points in one cycle
that are used to calculate the average deviation values for the pressure, the temperature
and the period of oscillation. The stability slope section allows the user to define the
maximum deviations above which the average deviation of the measured values for the
(a) (b)

22
pressure, the temperature and the period of oscillation should not exceed. The
recording window continuously records measurements and only stops when the
average deviations of all three parameters for two consecutive cycles don’t exceed the
maximum deviations defined by the user.
Figure 21: Snapshot of the data transfer section and the stability slope section of the recording window
Finally, when the stability slope criteria are met and the recording process ends, the
user can access the recorded values from the data spreadsheet of the Microsoft Excel®
tool (Figure 22). On this particular spreadsheet the recorded average values for
temperature (°C), period of oscillation (/µs) and pressure (bar) can be found.
Figure 22: Snapshot of the data spreadsheet of the Microsoft Excel®
tool
During the experimental procedure the user had to manually change the pressure of the
mixture. The pressure is measured through a digital pressure gauge. The SIKA digital
pressure gauge Type P (Figure 23) can read high pressures up to 1500 bar, fast and
with high accuracy. The temperature effect on the pressure measurements is lower than
±0.002%. More detailed specifications can be found in Table 21 in Appendix A:
Technical Specifications. The fluid piston cylinder can be seen along with the overall
experimental setup in Figure 26.

23
Figure 23: SIKA digital pressure gauge Type P (DTU laboratory, left) (SIKA, 2015, right)
For the calibration of the equipment and the calculation of the mixture’s density the
oscillation period under vacuum needed to be measured. Also, for cleaning purposes
the whole system needed to be under vacuum. To achieve vacuum in the experimental
system the Edwards E2M1.5 two-stage oil sealed rotary vane pump was used and the
Edwards Active Digital Controller (ADC) gauge was used to display the pressure, in
order to verify that the system was indeed under vacuum. Both Edwards’ products can
be seen in Figure 24 and their specifications can be found in Table 22 and Table 23 in
Figure 24: Edwards E2M1.5 two-stage oil sealed rotary vane pump and Edwards Active Digital Controller (ADC)
gauge (DTU laboratory)
In addition, two 260D syringe pumps from Teledyne Isco were used to ensure constant
pressure and constant flow during the mixture insertion process. The Teledyne Isco
260D syringe pump (Figure 25) is designed specifically for refilling under high

24
pressure (Isco, 2013). More detailed specifications can be found in Table 24 in
Figure 25: Teledyne Isco 260D syringe pump (DTU laboratory)
For the effective blend of the mixture a steel cylinder of variable volume was used
(Figure 28). To achieve better homogeneity for the mixture the cylinder contains a
steel ball as an agitator and a piston separating the mixture and the hydraulic water.
The overall experimental setup can be seen on the two photos taken at the DTU
laboratory during the experiments period in Figure 26.
Figure 26: Experimental setup (DTU laboratory)

25
A detailed schematic of the density measurement setup with all the components used
for the experiments is depicted in Figure 27.
Figure 27: Schematic of the experimental density measurement setup
3.4 Experimental
procedure

3.4.1 Apparatus
cleaning
procedure

The cleaning of the equipment between the experiments is essential for the quality of
the measurement. After the sample is removed some residues and contaminants might
reside in the apparatus. It is very important that they are removed by rinsing before the
new sample is inserted. The cleaning procedure was repeated every time after the
measurements of each sample were finished.
Cleaning of the densitometer and the fluid piston cylinder:
The sample already inserted in the densitometer was removed from the outlet valve. To
make sure the entire sample was out of the system the fluid piston cylinder was moved
back and forth several times. Then, for the cleaning of the densitometer, two rinsing
fluids were used. The first fluid that was used was toluene. Toluene is an aromatic
hydrocarbon and a strong organic solvent, which makes it ideal for cleaning petroleum
mixtures. After the equipment was rinsed with toluene several times, ethanol was
inserted in the system. The use of ethanol as the second rinsing fluid was chosen
because ethanol is a volatile fluid that can clean toluene. The fact that it is volatile is
Inlet
valve
Outlet
valve

26
important because after rinsing several times the ethanol was evaporated without
leaving any residue. Before putting the system under vacuum, pressurized air was
inflated to confirm the removal of any last residue. Finally, the system was put under
vacuum for an hour in 75 °C to dry out and then left under vacuum over night at
ambient temperature.
Cleaning of the mixture cylinder and peripheral lab equipment:
The sample already in place was carefully ejected from the cylinder in a fume hood.
Toluene and ethanol were used as rinsing fluids like before. All the parts of the
cylinder were rinsed thoroughly several times with the cleaning fluids, then dried out
with pressurized air and eventually put under vacuum.
Figure 28: Mixture (top) and Nitrogen cylinder (bottom) (DTU laboratory)
All the peripheral equipment used during the experimental procedure was cleaned
thoroughly with both cleaning agents and then dried out under pressurized air. Such
equipment included: Beakers, funnel, pipet, Erlenmeyer flask and burette.
3.4.2 Mixture
preparation

The first step for the mixture preparation is the calculation of the quantities of each
component to achieve the desired composition. The details for each mixture
composition can be seen in Table 3.
Table 3: Mixture compositions
Methane
mole fraction
n-decane
mole fraction
Methane
mass (g)
n-decane
mass (g)
n-decane
volume (mL)
Mixture molar
mass (g/mol)
0.2270 0.7730 3.376 101.862 140.2 113.631
0.6017 0.3983 13.392 78.613 108.2 66.325
0.8496 0.1504 35.597 55.799 76.8 35.028

27
The density of n-decane used for the calculations was ρdec = 726.55 kg/m3
at Tambient =
24.97 °C (Lemmon & Span, 2006).
The first fluid to be transferred in the evacuated cylinder was n-decane. For the
transfer, a 50 mL burette with readability ± 0.01 mL was connected to the cylinder and
carefully the desirable volume of n-decane was transferred. Methane is a gas and the
transfer was more complicated. Initially, the methane was transferred from the gas
pressurized-bottle into the gas cylinder in Figure 29. Safety goggles were used because
of the danger of methane leaking during the transfer. Then, the gas cylinder was placed
on Mettler Toledo PR1203 balance (readability 0.001g) and was connected to the
mixture cylinder. The methane mass transferred in the mixture cylinder was read from
the balance.
Figure 29: Methane weighing with Mettler Toledo PR1203 balance (DTU laboratory)
During the insertion of the mixture from the cylinder to the evacuated densimeter
attention was paid on potential pressure drop. To maintain constant pressure and
constant flow during the insertion of the sample two Isco pumps were used. As can be
seen in Figure 27, the first pump was connected to the mixture cylinder that led to the
inlet valve and the second was connected to the nitrogen cylinder that led to the outlet
valve. Finally, to ensure the homogeneity throughout the whole system the mixture
was purged five times before closing the inlet and outlet valves and begin the
experiments. All the chemical and physical properties of the fluids that were used can
be found in Appendix B: Fluids properties.
3.4.3 Performing
a
measurement

Under this thesis the density of the binary system methane - n-decane is measured for
different compositions and under a wide range of pressure and temperature. The
mixture compositions under study and the pressure and temperature range for each
mixture can be seen in Table 4. The decision of the starting pressure point for each

28
fluid was made based on the two-phase region because for the oscillating U-tube to
function the mixture has to be in a single liquid phase.
Table 4: Mixture composition, pressure and temperature range
Methane mole
fraction
Pressure range
(bar)
Temperature range
(°C)
0 1 - 1400 5 - 190
0.227 100 - 1400 5 - 190
0.6017 400 - 1400 5 - 190
0.8496 400 - 1400 5 - 190
In order to cover the whole range of pressure and temperature specific steps were
chosen. The temperature steps and the pressure steps can be found in Table 5 and
Table 6, respectively.
Table 5: Pressure steps
Pressure steps
(bar)
100
200
400
600
800
1000
1200
1400
Table 6: Temperature steps
Temperature steps
(°C)
5
25
50
75
100
150
190
Firstly, the desirable temperature was set on the PolyScience advanced programmable
temperature controller from the user. After the temperature was stabilized, the first
pressure step was manually reached. Once the pressure was stabilized the user could
initiate the measurement from the Microsoft Excel®
spreadsheet provided by Anton

29
Paar. On the Microsoft Excel®
spreadsheet the values for the data transfer and the
slope stability were added by the user for all the experiments as can be seen in Figure
21. After the recording process ended, the user could access the recorded values from
the data spreadsheet of the Microsoft Excel®
tool (Figure 22). Finally, the pressure was
increased and after all the pressure steps were measured the same procedure was
repeated for the remaining temperatures.
4 Density modelling
Nowadays the most accepted and implemented models for PVT modelling of reservoir
fluids are the cubic EoS such us the Soave–Redlich–Kwong (SRK) (Soave, 1972) EoS
and the Peng–Robinson (PR) (Peng & Robinson, 1976) EoS. On the other hand
though, recently developed non-cubic EoS such us the Perturbed Chain Statistical
Associating Fluid Theory (PC-SAFT) (Gross & Sadowski, 2001) EoS and the Soave
modified Benedict–Webb–Rubin (Soave-BWR) (Soave, 1999) EoS could potentially
replace this classical cubic equations (Wei et al., 2015). For the purpose of this work a
comparative study of the aforementioned cubic and non-cubic equations will be
attempted regarding the measured densities for the pure n-decane and the binary
mixture of methane - n-decane for the different compositions.
4.1 Cubic
EoS

The non-cubic EoS under study are the SRK (Soave, 1972) EoS and the PR (Peng &
Robinson, 1976) EoS.
The SRK EoS gives, in general, very accurate results for density for an empirical
equation (Wei et al., 2015). The initial RK equation introduced by Redlich & Kwong
(1949) is:
p =
!"
!!!
−
!
!(!!!) !
[29]
The modified SRK EoS that is under examination in this work and introduced by
Soave (1972) reads as:
p =
!"
!!!
−
!(!,!)
!(!!!)
[30]
where p is the absolute pressure, R is the universal gas constant (=8.3144621
J/mol*K), T is the absolute temperature, v is the specific volume, ω is the acentric
factor, α(Τ) is the modified parameter for SRK and α and b are the parameters from
original Redlich-Kwong.

30
The parameters α and b are estimated based on the acentric factor, the critical
temperature (Tc) and critical pressure (pc) of the mixture. The critical properties of the
fluids studied in this work can be seen in Table 7:
Table 7: Tc, Pc, ω and Zc for methane and n-decane
Component Tc (K) pc (bar) ω Zc
methane 190.56 45.99 0.0115 0.2897
n-decane 617.70 21.10 0.4923 0.2518
The PR EoS introduced by Peng & Robinson (1976) reads:
p =
!"
!!!
−
!(!,!)
! !!! !!(!!!)
[31]
4.2 Non-‐cubic
EoS

Gross & Sadowski (2001), modified the initial SAFT EoS introduced by Chapman et
al. (1990) and the main difference between the original SAFT and the modified PC-
SAFT according to Wei et al. (2015) is that the modified version of the equation uses
the mixture of hard-sphere chains as the reference system and then introduces the
dispersive attractions achieving this way to be more accurate when modeling
asymmetric and highly non-ideal systems. PC-SAFT EoS requires only three
parameters that are not directly associated with the component and those are the chain
length m, the segment diameter s and the segment energy ε.
The Soave-BWR was introduced by Soave (1999) and has the following form:
Z =
!
!"#
= 1 + 𝐵𝜌 + 𝐷𝜌!
+ 𝛦𝜌!
1 + 𝐹𝜌!
𝑒𝑥𝑝 (−𝐹𝜌!
) [32]
where Z is the compressibility factor, p is the absolute pressure, R is the universal gas
constant (=8.3144621 J/mol*K), T is the absolute temperature, ρ is the density and A,
B, D, E, and F are the five model parameters.
The critical parameters needed for the Soave-BWR regarding the binary mixture of
methane – n-decane can be seen in Table 7. Finally, Table 8 presents the interaction
parameters for the binary mixture of methane – n-decane:
Table 8: Interaction parameters for the methane – n-decane binary mixture (Wei et al., 2015)
EoS kij
SRK 0.0411
PR 0.0422
PC-SAFT 0.0167
SBWR -0.0366

31
After a comprehensive research and study Wei et al. (2015) concluded that both the
non-cubic EoS are much better than the cubic ones regarding the density calculation
for the light and heavy components of a reservoir fluid.
For further reading about the four EoS under study the reader is referred to see the
article from Wei et al. (2015)

32
5 Results and discussion
5.1 Densimeter
calibration
and
validation
results

For the calibration of the densimeter the oscilation periods of the tube when filled with
water and under vaccum were measured. In addition, the density of water was taken
from NIST that uses the EoS from Wagner and Pruss (2002) and the density of n-
dodecane was taken from NIST that uses the EoS from Lemmon & Huber (2004). All
the values mentioned above can be seen in Table 9. The oscillation period of n-
dodecane was measured in a previous work (Chasomeris et al., 2015).
Table 9: Values for ρw, τw, ρd, τv
Temperature
(°C)
Pressure
(bar)
ρw
(kg/m3
)
τw
(µs)
ρd
(kg/m3
)
τv
(µs)
5 1 999.97 2665.303 759.94 2586.522
5 10 1000.40 2665.346 760.38 2586.522
5 50 1002.40 2665.517 762.94 2586.522
5 100 1004.80 2665.732 766.13 2586.522
5 200 1009.50 2666.161 771.89 2586.522
5 400 1018.70 2666.996 777.36 2586.522
5 600 1027.60 2667.796 782.45 2586.522
5 800 1036.00 2668.631 787.04 2586.522
5 1000 1044.10 2669.385 791.73 2586.522
5 1200 1051.90 2670.103 745.67 2586.522
5 1400 1059.30 2670.791 746.55 2586.522
25 1 997.05 2672.023 749.40 2593.217
25 10 997.45 2672.061 752.63 2593.217
25 50 999.25 2672.222 759.22 2593.217
25 100 1001.50 2672.421 764.97 2593.217
25 200 1005.80 2672.820 770.45 2593.217
25 400 1014.30 2673.600 775.62 2593.217
25 600 1022.50 2674.347 780.52 2593.217
25 800 1030.30 2675.148 727.70 2593.217
25 1000 1037.90 2675.874 728.72 2593.217
25 1200 1045.20 2676.565 732.00 2593.217
25 1400 1052.20 2677.238 735.92 2593.217
50 1 988.03 2680.148 743.19 2601.720
50 10 988.43 2680.170 749.84 2601.720
50 50 990.16 2680.331 755.88 2601.720
50 100 992.31 2680.526 761.56 2601.720
50 200 996.53 2680.915 766.91 2601.720
50 400 1004.70 2681.676 709.00 2601.720

33
50 600 1012.60 2682.406 710.07 2601.720
50 800 1020.10 2683.209 713.88 2601.720
50 1000 1027.40 2683.920 718.36 2601.720
50 1200 1034.50 2684.600 726.66 2601.720
50 1400 1041.30 2685.261 734.10 2601.720
75 1 974.84 2688.125 740.82 2610.395
75 10 975.24 2688.158 747.11 2610.395
75 50 977.01 2688.322 753.03 2610.395
75 100 979.19 2688.522 759.94 2610.395
75 200 983.48 2688.915 760.38 2610.395
75 400 991.76 2689.687 762.94 2610.395
75 600 999.69 2690.425 766.13 2610.395
75 800 1007.30 2691.192 771.89 2610.395
75 1000 1014.60 2691.902 777.36 2610.395
75 1200 1021.70 2692.585 782.45 2610.395
75 1400 1028.50 2693.253 787.04 2610.395
100 1 - - 690.00 2619.218
100 10 958.77 2696.000 692.01 2619.218
100 50 960.63 2696.168 696.05 2619.218
100 100 962.93 2696.380 701.17 2619.218
100 200 967.44 2696.792 710.54 2619.218
100 400 976.10 2697.593 718.82 2619.218
100 600 984.34 2698.358 726.40 2619.218
100 800 992.22 2699.196 733.23 2619.218
100 1000 999.76 2699.919 739.69 2619.218
100 1200 1007.00 2700.623 651.13 2619.218
100 1400 1014.00 2701.313 652.88 2619.218
150 1 - - 659.07 2637.323
150 10 917.31 2711.462 665.99 2637.323
150 50 919.56 2711.665 678.15 2637.323
150 100 922.32 2711.919 688.58 2637.323
150 200 927.69 2712.408 697.71 2637.323
150 400 937.86 2713.336 705.93 2637.323
150 600 947.38 2714.209 713.50 2637.323
150 800 956.35 2715.156 617.73 2637.323
150 1000 964.85 2715.955 619.74 2637.323
150 1200 972.93 2716.727 628.01 2637.323
150 1400 980.64 2717.485 636.98 2637.323
190 1 - - 651.93 2652.243
190 10 - - 664.25 2652.243
190 50 878.72 2723.847 674.89 2652.243
190 100 882.16 2724.157 684.26 2652.243

34
190 200 888.77 2724.749 692.78 2652.243
190 400 901.04 2725.860 690.00 2652.243
190 600 912.29 2726.885 692.01 2652.243
190 800 922.70 2727.923 696.05 2652.243
190 1000 932.44 2728.833 701.17 2652.243
190 1200 941.59 2729.706 710.54 2652.243
190 1400 950.24 2730.542 718.82 2652.243
The relation between the oscillation period of the tube under vacuum and the
temperature can be observed in Figure 30. The oscillation period is increasing with the
increase of temperature.
Figure 30: Period of the evacuated densimeter for temperatures from 5°C to 190°C)
The water oscillation period was measured for temperatures from 5°C to 190°C and
pressures from 1 bar to 1400 bar and can be seen in Figure 31. It can be observed that
for each temperature the oscillation period is increasing with the increase of pressure.
Figure 31: Water measured period for temperatures from 5°C to 190°C and pressures from 1 bar to 1400 bar
2580

2590

2600

2610

2620

2630

2640

2650

2660

0
20
40
60
80
100
120
140
160
180
200

Period
(μs)

Temperature
(°C)

2655

2665

2675

2685

2695

2705

2715

2725

2735

0
200
400
600
800
1000
1200
1400
1600

Period
(μs)

Pressure
(bar)

5
°C

25
°C

50
°C

75
°C

100
°C

150
°C

190
°C

35
The characteristic parameter A(T), on the other hand, is decreasing with the increase of
temperature. The relation between the characteristic parameter A(T) and the
temperature can be seen in Figure 32.
Figure 32: Characteristic parameter A(T) for temperatures from 5°C to 190°C
The ratio of parameter A(T) with parameter B(T,p) was also calculated and can be seen
in Figure 33. It can be observed that for each temperature the ratio is slightly
decreasing with the increase of pressure.
Figure 33: Ratio between parameter A(T) and parameter B(T,p)
2,26

2,28

2,30

2,32

2,34

2,36

2,38

2,40

2,42

2,44

0
20
40
60
80
100
120
140
160
180
200

A
(T)
(10^9kg
s-‐1
m-‐3)

Temperature
(°C)

1,41

1,42

1,43

1,44

1,45

1,46

1,47

1,48

1,49

1,5

0
200
400
600
800
1000
1200
1400

A(T)/B(T,p)(105s-‐2)

Pressure
(bar)

5°C

25°C

50°C

75°C

100°C

150°C

190°C

36
Various authors, including Lugo et al. (2001) and Segovia et al. (2009), have presented
their results in similar way and the trends observed in Figure 32 and Figure 33 are in
agreement with both authors.
The oscillation period of n-decane was also measured and as can be seen in Figure 34
it is increasing with the increase of pressure and temperature.
Figure 34: n-decane measured period for temperatures from 5°C to 190°C and pressures from 1 bar to 1400 bar
For the validation of the densimeter the density of n-decane was calculated with
equations (20), (23), (24) and (25) and the results can be seen in Table 10.
Table 10: Experimental density values (kg/m3
) of n-decane
Pressure
(bar)
Temperature (°C)
5 25 50 75 100 150 190
1 741.52
726.79
707.99
688.13
668.01
626.02
-‐

10 742.10
727.33
708.71
689.15
669.50
627.77
591.07

50 745.01
730.49
712.32
693.41
674.51
634.86
600.80

100 748.34
734.20
716.60
698.41
680.29
642.76
611.37

200 754.34
741.00
724.39
707.38
690.52
656.34
628.47

400 765.38
753.18
737.94
722.52
707.62
677.72
653.92

600 775.29
763.90
749.70
735.33
721.71
694.57
673.11

800 783.41
772.30
758.80
745.85
732.59
707.19
687.87

1000 791.32
780.67
767.67
755.69
743.15
719.41
701.26

1200 798.88
788.45
776.14
764.58
752.68
730.14
712.93

1400 806.00
795.67
783.80
772.72
761.15
739.68
723.30

2640

2650

2660

2670

2680

2690

2700

2710

2720

0
200
400
600
800
1000
1200
1400
1600

Period
(μs)

Pressure
(bar)

5
°C
25
°C
50
°C
75
°C
100
°C
150
°C
190
°C

37
The results were then compared with the data from NIST, where an EoS proposed by
Lemmon and Span (2006) was used and they were in good agreement with an AAD of
0.08%. The relative deviations as a function of temperature and pressure can be seen in
Figure 35 and Figure 36, respectively.
Figure 35: Relative deviations between the experimental density values of n-decane and the data from Lemmon &
Span (2006) as a function of temperature
Figure 36: Relative deviations between the experimental density values of n-decane and the data from Lemmon &
Span (2006) as a function of pressure
-‐0,25

-‐0,2

-‐0,15

-‐0,1

-‐0,05

0

0,05

0,1

0,15

0,2

0
20
40
60
80
100
120
140
160
180
200

Relative
deviation
(%)

Temperature
(°C)

Lemmon
&
Span
(2006)

-‐0,25

-‐0,2

-‐0,15

-‐0,1

-‐0,05

0

0,05

0,1

0,15

0,2

0
200
400
600
800
1000
1200
1400
1600

Relative
deviation
(%)

Pressure
(bar)

Lemmon
&
Span
(2006)

38
5.2 Mixture
methane
–
n-‐decane
(xmethane
=
0.227)

After considering the two-phase region of this mixture the starting point for the
experimental measurements was set to 100 bar. The measured densities for the mixture
can be seen in Table 11.
) of the mixture methane - n-decane (xmethane = 0.227)
Pressure
(bar)
Temperature (°C)
5 25 50 75 100 150 190
100 719.65
704.51
685.50
665.36
645.32
602.72
565.48

200 726.66
712.33
694.89
676.13
657.89
620.21
588.86

400 739.10
726.16
710.05
693.79
677.79
645.84
620.23

600 749.90
737.96
723.07
708.12
693.58
665.10
642.60

800 758.69
747.16
733.05
719.85
705.82
679.31
659.24

1000 767.22
756.35
742.76
730.37
717.49
692.67
674.08

1200 775.28
764.63
751.76
739.93
727.59
704.21
686.78

1400 782.73
772.09
759.81
748.59
736.76
714.39
698.00

The experimental results were then compared with the results obtained from Audonnet
& Pádua (2004). Because their work was measuring the density of the mixture under a
different pressure and temperature region a correlation with the use of the Tait
equation (Dymond & Malhotra, 1988) was performed.
The Tait equation:
ρ(T,p) =
!!(!,!!)
!!!!"
! ! !!
! ! !!!(!)
[33]
where:
𝐵 𝑇 = 𝑎 + 𝑏𝑇 𝐾 𝑐𝑇!
(𝐾) [34]
𝜌!(𝑇, 𝑝!) = 𝑎! + 𝑏! 𝑇(𝐾) [35]
and p0 is the reference pressure equal to 100 bar (10 MPa).
The standard deviation (σ) of the fit and the parameters obtained in the Tait equation
for the correlation for both our experimental results and those from Audonnet & Pádua
(2004) can be seen in Table 12. The surface ρ(T,p) as a function of pressure and
temperature for our results and those from Audonnet & Pádua (2004) can be seen in
Figure 37 and Figure 38, respectively.

39
Table 12: Parameters obtained in the Tait equation with the results from Audonnet & Pádua (2004) (xmethane = 0.227)
and our experimental results (xmethane = 0.227)
Audonnet & Pádua (2004) Experimental results from this work
Parameter Value Parameter Value
a (MPa) 226.4559 a (MPa) 662.7
b (MPa/K) -0.6141 b (MPa/K) -2.507
c (MPa/K2
) 0.000277 c (MPa/K2
) 0.002468
a1 (g/cm3
) 0.94161 a1 (g/cm3
) 0.9529
b1 (g/cm3
K) -0.000792 b1 (g/cm3
K) -0.000812
C (-) 0.088353 C (-) 0.115981
σ (g/cm3
) 0.0004 σ (g/cm3
) 0.0049
Figure 37: Surface ρ(T,p) for our experimental results for the mixture methane – n-decane (xmethane = 0.227)
Figure 38: Surface ρ(T,p) for the results from Audonnet & Pádua (2004) for the mixture methane – n-decane
(xmethane = 0.227)

40
The comparison of the experimental results with the results obtained from Audonnet &
Pádua (2004) was possible for the temperatures of 50 °C, 75 °C and 100 °C and the
pressures between 100 bar and 600 bar. The relative deviations as a function of
temperature and pressure can be seen in Figure 39 and Figure 40, respectively. The
experimental results are in good agreement with those from Audonnet & Pádua (2004)
with an AAD of 0.17%.
Figure 39: Relative deviations between the experimental density values of the mixture methane – n-decane (xmethane
= 0.227) and the data from Audonnet & Paduá (2004) (xmethane = 0.227) as a function of temperature
Figure 40: Relative deviations between the experimental density values of the mixture methane – n-decane (xmethane
= 0.227) and the data from Audonnet & Paduá (2004) (xmethane = 0.227) as a function of pressure
-‐0,2

-‐0,1

0,0

0,1

0,2

0,3

0,4

0
20
40
60
80
100
120

Relative
deviation
(%)

Temperature
(°C)

Audonnet
&

-‐0,2

-‐0,1

0,0

0,1

0,2

0,3

0,4

0
100
200
300
400
500
600
700

Relative
deviation
(%)

Pressure
(bar)

Audonnet
&
Padua
(2004)

41
5.3 Mixture
methane
–
n-‐decane
(xmethane
=
0.6017)

Pressure
(bar)
Temperature (°C)
5 25 50 75 100 150 190
400 653.14
635.15
616.25
596.81
582.46
539.57
510.36

600 667.75
651.73
634.75
617.86
605.90
568.99
544.38

800 678.97
666.25
648.77
633.80
622.46
589.47
568.15

1000 689.76
675.81
661.15
647.59
637.24
606.82
587.47

1200 699.17
685.79
672.41
659.54
649.91
621.59
603.54

1400 707.55
695.16
683.31
669.86
660.88
634.60
617.76

The Tait equation was used again to correlate the results with those from Audonnet &
Pádua (2004) and Canet et al. (2002). The standard deviation (σ) of the fit and the
parameters obtained in the Tait equation for the correlation for both our experimental
results and those from Audonnet & Pádua (2004) and Canet et al. (2002) can be seen in
Table 14.
Table 14: Parameters obtained in the Tait equation with the results from Audonnet & Pádua (2004) (xmethane =
0.601), our experimental results (xmethane = 0.6017) and those from Canet et al. (2002) (xmethane = 0.6)
Audonnet & Pádua
(2004)
Experimental results
from this work
Canet et al.
(2002)
Parameter Value Parameter Value Parameter Value
a (MPa) 226.4559 a (MPa) 112.8 a (MPa) 123.4
b (MPa/K) -0.6141 b (MPa/K) -0.5697 b (MPa/K) -0.1635
c (MPa/K2
) 0.000277 c (MPa/K2
) 0.0005512 c (MPa/K2
) -0.0004013
a1 (g/cm3
) 0.94161 a1 (g/cm3
) 0.8645 a1 (g/cm3
) 0.870269
b1 (g/cm3
K) -0.000792 b1 (g/cm3
K) -0.000848 b1 (g/cm3
K) 0.000824
C (-) 0.088353 C (-) 0.07272 C (-) 0.1066
σ (g/cm3
) 0.003 σ (g/cm3
) 0.0058 σ (g/cm3
) 0.0007
The surface ρ(T,p) as a function of pressure and temperature for our results and those
from Audonnet & Pádua (2004) can be seen in Figure 41 and Figure 42, respectively.

42
(xmethane = 0.601)

43
The comparison of the experimental results with the results obtained by Audonnet &
pressures 400 bar and 600 bar. The experimental results have an AAD of 0.30% with
those obtained from Audonnet & Pádua (2004).
The comparison of the experimental results with the results obtained from Canet et al.
(2002) was possible for the temperatures of 25 °C, 50 °C, 75 °C and 100 °C and the
pressures between 400 bar and 1400 bar. It is important to mention that Canet et al.
(2002) only measured experimental densities up to 600 bar. The measurements from
600 bar to 1400 bar were extrapolated and therefore they are not experimental. The
AAD with the values obtained from Canet et al. (2002) is 0.19%.
The relative deviations as a function of temperature and pressure can be seen in Figure
43 and Figure 44, respectively.
Figure 43: Relative deviations between the experimental density values of the mixture methane - n-decane (xmethane =
0.6017) and the data from Audonnet & Paduá (2004) (xmethane = 0.601) and Canet et al. (2002) (xmethane = 0.6) as a
function of temperature
-‐0,4

-‐0,2

0,0

0,2

0,4

0,6

0,8

1,0

0
20
40
60
80
100

Relative
deviation
(%)

Temperature
(°C)

Audonnet
&
Padua
(2004)
Canet
et
al.
(2002)

44
0.6017) and the data from Audonnet & Paduá (2004) (xmethane = 0.601) and Canet et al. (2002) (xmethane = 0.6) as a
function of pressure
5.4 Mixture
methane
–
n-‐decane
(xmethane
=
0.8496)

Pressure
(bar)
Temperature (°C)
5 25 50 75 100 150 190
400 494.66
472.29
450.75
426.98
405.39
364.81
334.45

600 521.06
505.01
485.38
465.12
449.22
412.75
390.26

800 539.24
524.48
507.40
490.46
476.43
444.28
425.01

1000 553.96
541.21
525.24
509.94
497.59
468.78
451.16

1200 566.76
553.90
540.18
526.00
514.30
488.41
470.83

1400 577.99
565.54
552.81
539.67
527.66
503.89
486.86

The Tait equation was used again to correlate the results with those from Audonnet &
Pádua (2004). The standard deviation (σ) of the fit and the parameters obtained in the
Tait equation for the correlation for both our experimental results and those from
Audonnet & Pádua (2004) can be seen in Table 16. The surface ρ(T,p) as a function of
pressure and temperature for our results and those from Audonnet & Pádua (2004) can
be seen in Figure 45 and Figure 46, respectively.
-‐0,4

-‐0,2

0,0

0,2

0,4

0,6

0,8

1,0

0
200
400
600
800
1000
1200
1400

Relative
deviation
(%)

Pressure
(bar)

Audonnet
&
Padua
(2004)
Canet
et
al.
(2002)

45
(xmethane = 0.799)

46
Table 16: Parameters obtained in the Tait equation with the results from Audonnet & Pádua (2004) (xmethane = 0.799)
and our experimental results (xmethane = 0.8496)
Audonnet & Pádua (2004) Experimental results from this work
Parameter Value Parameter Value
a (MPa) 59.35 a (MPa) 45.02
b (MPa/K) -0.04397 b (MPa/K) -0.3238
c (MPa/K2
) -0.0002849 c (MPa/K2
) 0.0003153
a1 (g/cm3
) 0.861934 a1 (g/cm3
) 0.7293
b1 (g/cm3
K) -0.00082 b1 (g/cm3
K) -0.000912
C (-) 0.0937 C (-) 0.09733
σ (g/cm3
) 0.0004 σ (g/cm3
) 0.0068
It should be mentioned here that our mixture with methane mole fraction xmethane =
0.8496 has significantly more methane than the mixture prepared from Audonnet &
Pádua (2004), which has a methane mole fraction xmethane = 0.799.
The comparison of the experimental results with the results obtained from Audonnet &
pressures of 400 bar and 600 bar. The relative deviations as a function of temperature
and pressure can be seen in Figure 47 and Figure 48, respectively. The experimental
results have an AAD of 11.11% with those obtained from Audonnet & Pádua (2004).
The high negative deviations are due to the fact that our mixture has significantly
lower methane than the mixture prepared from Audonnet & Pádua (2004), which
results in lower density values.
0.8496) and the data from Audonnet & Paduá (2004) (xmethane = 0.799) as a function of temperature
-‐14

-‐12

-‐10

-‐8

-‐6

-‐4

-‐2

0

0
20
40
60
80
100
120

Relative
deviation
(%)

Temperature
(°C)

Audonnet
&
Padua
(2004)

47
0.8496) and the data from Audonnet & Paduá (2004) (xmethane = 0.799) as a function of pressure
The density, for all compositions at 5 °C and 190 °C, as a function of pressure can be
seen in Figure 49. Three parameters that have an effect on density are the methane
mole fraction in the mixture, the pressure and the temperature. The effect of those three
parameters on the density can be observed in Figure 49. The density is increasing with
the increase of pressure and decreasing with the increase of temperature. Finally, the
increased amount of methane in the mixture decreases the density.
Figure 49: Density as a function of pressure for all compositions at 5 °C and 190 °C
-‐14

-‐12

-‐10

-‐8

-‐6

-‐4

-‐2

0

0
100
200
300
400
500
600
700

Relative
deviation
(%)

Pressure
(bar)

Audonnet
&
Padua
(2004)

300

400

500

600

700

800

300
500
700
900
1100
1300

Density
(kg/m3)

Pressure
(bar)

n-‐decane
at
5
°C
Xmethane=0.227
at
5
°C
Xmethane=0.6017
at
5
°C
Xmethane=0.8496
at
5
°C

n-‐decane
at
190
°C
Xmethane=0.227
at
190
°C
Xmethane=0.6017
at
190
°C
Xmethane=0.8496
at
190
°C

48
5.5 Density
modeling

As mentioned before a comparison of two cubic (SRK & PR) and two non-cubic (PC-
SAFT & Soave-BWR) EoS was performed. As far as the pure n-decane is concerned
the two non-cubic EOS performed better than the cubic ones. SRK showed the highest
AAD with 19.36% and PC SAFT the lowest with 1.12%.
For the binary mixture the best-performed equation for all methane fractions was PC
SAFT and the worst-performed was SRK. SBWR performed well with the mixture
with the lowest methane mole fraction, while PR performed better with the mixture
with the highest methane mole fraction.
The AAD of the comparison between the experimental densities and those calculated
with the EOS for the whole temperature and pressure range can be seen in Table 17
and Figure 50.
Table 17: AAD and MAD of the comparison between the experimental densities and those calculated with the EOS
for the whole temperature and pressure range
Fluid
SRK PR PC SAFT SBWR
AAD
(%)
MAD
(%)
AAD
(%)
MAD
(%)
AAD
(%)
MAD
(%)
AAD
(%)
MAD
(%)
n-decane 19.4 24.7 6.80 12.1 1.12 2.82 0.69 2.70
xmethane=0.227 18.6 23.4 6.41 10.9 1.03 2.44 1.07 2.51
xmethane=0.6017 15.8 19.1 4.11 7.15 0.65 1.50 4.09 6.31
xmethane=0.8496 9.92 12.6 0.87 4.41 0.67 4.10 5.46 7.45
* MAD: Maximum Absolute Deviation
Figure 50: AAD of the comparison between the experimental densities and those calculated with the EOS for the
whole temperature and pressure range
0

5

10

15

20

25

SRK
PR
PC
SAFT
SBWR

Xmethane
=
0.227
Xmethane
=
0.6017
Xmethane
=
0.8496
Decane

Master Thesis: Density of Oil-related Systems at High Pressures - Experimental measurements of HPHT density

Master Thesis: Density of Oil-related Systems at High Pressures - Experimental measurements of HPHT density

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