harrison

Viscosity of n-hexadecane, n-octadecane and n-eicosane at pressures up
to 243 MPa and temperatures up to 534 K
Hseen O. Baled a,b,⇑
, Dazun Xing a,b
, Harrison Katz b
, Deepak Tapriyal a,c
, Isaac K. Gamwo a
, Yee Soong a
,
Babatunde A. Bamgbade a,d
, Yue Wu a,d
, Kun Liu d
, Mark A. McHugh a,d
, Robert M. Enick a,b
a
National Energy Technology Laboratory, Office of Research and Development, Department of Energy, Pittsburgh, PA 15236, USA
b
Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
c
URS, NETL Site Support Contractor, Pittsburgh, PA 15236, USA
d
Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
a r t i c l e i n f o
Article history:
Received 7 August 2013
Received in revised form 10 January 2014
Accepted 12 January 2014
Available online 21 January 2014
Keywords:
Hexadecane
Octadecane
Eicosane
High pressure
Rolling-ball viscometer
Viscosity
a b s t r a c t
Viscosity data are reported for n-hexadecane (C16), n-octadecane (C18), and n-eicosane (C20) at pres-
sures between (3 and 243) MPa and temperatures between (304 and 534) K. These extreme conditions
are representative of those encountered in ultra-deep petroleum formations beneath the deepwaters
of the Gulf of Mexico. The measurements are taken with a novel windowed Inconel rolling-ball viscom-
eter designed by our team that is calibrated with n-decane. A comparison of the reported viscosity values
with the available literature data that cover limited pressure and temperature ranges, shows that the
mean absolute percentage deviation, d, ranges between 1.1% and 4.8%. The reported data extend the data-
base of viscosity to the high-temperature, high-pressure region where most gaps occur in the literature
data for n-hexadecane and n-octadecane. To the best of our knowledge, the results for n-eicosane are the
first reported viscosity values at pressures above 2 MPa over the entire temperature range. The viscosity
results are modeled with the free volume theory model in conjunction with density values obtained using
the Peng–Robinson equation of state (EoS) and the PC-SAFT EoS. The d values obtained with this model
range from 2.0% to 3.5%. The data are also correlated by a non-linear surface fit as a simultaneous function
of temperature and pressure that yields d values of 0.40%, 0.43%, and 0.38% for C16, C18, and C20,
respectively.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Viscosity data of pure hydrocarbons and mixtures at different
temperatures and pressures are required in many petroleum
reservoir applications, including the estimation of reserves, the
calculation of flow rates in porous media or wellbores, and the
determination of the mobility ratio of a displacement process.
Despite the significance of viscosity in the petroleum industry,
there is still a lack of experimental viscosity data for many hydro-
carbons, particularly at extreme high-temperature, high-pressure
(HTHP) conditions. For example, ultra-deep petroleum formations
found at depths of approximately 4600 meters or more, can exhibit
pressure and temperature values as high as 241 MPa and 533 K,
respectively. The hydrocarbons produced from these ultra-deep
formations experience significant decreases in temperature and
pressure during production; hence, it is highly desirable to attain
a database of viscosity data that covers the entire temperature
and pressure ranges associated with this process. Reliable and
accurate viscosity models for reservoir simulation can be gener-
ated from this data.
In this study, a windowed, variable-volume, Inconel rolling-ball
viscometer is used to conduct viscosity measurements for n-hexa-
decane, n-octadecane, and n-eicosane at pressures up to $243 MPa
and temperatures up to $534 K. The data thus obtained extend the
pressure and temperature ranges of the available literature
high-pressure data [1–13] for these long-chain, normal alkanes.
The results are described by an empirical 10-parameter surface fit-
ting equation as a function of pressure and temperature. In order to
also provide a modeling tool that is easily adapted to estimating
viscosity of multi-component mixtures in reservoir simulators,
the experimental viscosity data generated in this study are also
modeled with the free volume theory (FVT) [14]. Because FVT pre-
dictions of viscosity require fluid density value as an input, HTHP
density values are determined with the Peng–Robinson (PR) EoS
[15] and the perturbed-chain, statistical associating fluid theory
(PC-SAFT) EoS [16] models.
0021-9614/$ - see front matter Ó 2014 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jct.2014.01.008
⇑ Corresponding author at: Department of Chemical and Petroleum Engineering,
University of Pittsburgh, 1249 Benedum Engineering Hall, 3700 O’Hara Street,
Pittsburgh, PA 15261, USA. Tel.: +1 412 624 9649; fax: +1 412 624 9639.
E-mail address: hob9@pitt.edu (H.O. Baled).
J. Chem. Thermodynamics 72 (2014) 108–116
Contents lists available at ScienceDirect
J. Chem. Thermodynamics
journal homepage: www.elsevier.com/locate/jct

2. Experimental
2.1. Materials
All chemicals were obtained from Sigma–Aldrich and used as
received without further purification. The provenance and
mass fraction purity of the chemicals used in this study are listed
in table 1.
2.2. Rolling-ball viscometer details
A windowed, variable-volume, rolling-ball viscometer was used
for the collection of high-temperature, high-pressure viscosity
data. The high-pressure apparatus is detailed in our previous work
related to the identification of a HTHP Deepwater Viscosity
Standard [17] and only a brief description is provided here. An
expanded view of the viscometer shown in figure 1 is very similar
to the HTHP densimeter used by our group [18]. The cell is
constructed from Inconel 718, has an outside diameter of
7.6200 cm, an inside diameter (ID) of 1.5875 cm in the portion of
the viscometer where the ball rolls, an ID of 1.9050 cm in the
segment that retains the movable piston and a maximum working
volume of 50 cm3
. The spheres of various diameters (e.g.
1.5716 cm ± 0.0005 cm) are also made of Inconel 718 [Industrial
Tectonics Inc.] to minimize the effects of temperature and pressure
on the calibration constant.
A schematic diagram of the entire system is shown in figure 2. A
borescope (Model HawkeyeÒ
Pro Hardy 6.35 mm, Gradient Lens
Corporation) can be positioned against the window at the front
end of the cell to verify that only a single fluid phase is present dur-
ing the experiment, and to confirm that the ball is rolling, rather
than sliding, down the bore of the viscometer. The cell also has
three sets of small opposing sapphire windows arranged a fixed
distance of 3.81 cm apart along the sides of the viscometer. The
ball velocity was determined from the time it takes the ball to roll
past each of the three sets of small opposing sapphire windows, or
the time it takes the ball to roll between two sets of windows. The
O-rings used in conjunction with the windows and piston are com-
posed of Viton or, for higher temperature studies, FF 200 (Parker
Seals Company). The technique used to detect the ball position is
similar to that used by Sawamura and Yamashita [19]. The detec-
tion system is composed of a fiber optic light source (Model LSX
24B, InterTest) and three pairs of glass fiber optic cables (Model
IF23SM900, Banner Engineering Corporation) attached to the small
sapphire windows. The three glass fiber optic sensors (Model
R55FVWQ, Banner Engineering Corporation) were interfaced with
a computer through a LabVIEW program.
A movable piston (3.175 cm long, 1.895 cm diameter) with an
O-ring around its perimeter separates the liquid sample and over-
burden fluid (water). A small pressure gradient of $0.1 MPa is
required to move the piston. The liquid sample was compressed
to the desired operating pressure using a high-pressure generator
(Model 37-5.75-60, High Pressure Equipment Company) that
compresses the overburden fluid. System pressure was measured
on the overburden fluid using a pressure transducer (Model 245,
Viatran Corporation, accurate to ±0.35 MPa). The transducer was
calibrated at pressures to 56 MPa using a Heise pressure gauge
(Heise Corporation, Model CC, (0 to 68.9) MPa, accurate to
±0.07 MPa). Therefore, the transducer is considered accurate to
±0.07 MPa to pressures of 56 MPa and to ±0.35 MPa for pressures
from (56 to 245) MPa. The viscometer cell was jacketed with band
heaters (1000 W, Rama Corporation) and fiberglass insulation
paper. A type-K thermocouple (Omega Corporation) was used to
measure the temperature of the fluid in the view cell. The thermo-
couple was calibrated (293 to 533 K) against a high precision ther-
mometer (Medicus Health, 0.01 °C resolution, accurate to ±0.05 °C).
The temperature of the viscometer was controlled with a precision
temperature controller (Oakton Digi-Sense, 0.1 °C resolution, cali-
brated by InnoCal using methods traceable to NIST standards).
The viscometer was calibrated with n-decane (C10) because of
the relatively large amount of density and viscosity data available
for this normal alkane. The governing equation for determining the
calibration constant, k, of a rolling-ball viscometer is:
k ¼
l Á v
ðqb À qflÞsinh
; ð1Þ
where k has units of (cm4
Á mÀ1
Á sÀ2
), l is viscosity, v is terminal
velocity of the rolling ball, and qb and qfl are ball density and fluid
density, respectively. The viscosity data of n-decane were taken
from NIST Chemistry WebBook [20] which implements a viscosity
correlation proposed by Huber, Laesecke, and Xiang [21]. The esti-
mated uncertainty of this correlation is 2% in the dense liquid to
200 MPa. The correlation was only extrapolated for one data point
out of 18 data points at T = 429 K and two data points out of 15 data
points at T = 534 K. We do not expect the uncertainty to be much
higher than 2% at pressures to 235 MPa. The density data were
obtained from NIST Chemistry WebBook [20] and were compared
against the densities reported by Liu et al. [22] and found to have
TABLE 1
Provenance and purity of the chemicals used in this study.
Chemical name Molar mass CAS no. Source Mass fraction purity
n-Decane 142.28 124-18-5 Sigma–Aldrich P0.99
n-Hexadecane 226.44 544-76-3 Sigma–Aldrich P0.99
n-Octadecane 254.49 593-45-3 Sigma–Aldrich 0.99
n-Eicosane 282.55 112-95-8 Sigma–Aldrich 0.99
FIGURE 1. Expanded view of the windowed variable-volume rolling-ball viscometer.
H.O. Baled et al. / J. Chem. Thermodynamics 72 (2014) 108–116 109

an estimated uncertainty of 0.3%. The calibration data cover tem-
peratures between (304 and 534) K, pressures between (5 and
235) MPa, and viscosity values between (0.159 and 1.638) mPa Á s.
An Inconel 718 ball with a ball diameter, d, to viscometer diameter,
D, ratio of 0.995 was used for the calibration of the viscometer at
temperatures (304 and 326) K. A larger sphere with a diameter
ratio, r, of 0.998 was used to calibrate the apparatus at temperatures
(429 and 534) K because the smaller ball (r = 0.995) rolls too quickly
to obtain precise data. The tilt angle was set at 10o
for all calibration
isotherms. The calibration results are shown in figures 3 and 4,
which present the calibration constant values, k, as a function of
pressure for each isotherm. The pressure dependence reflects the
decrease in the ball diameter and the simultaneous increase in
the cell internal diameter with increasing pressure. The tempera-
ture dependence reflects the simultaneous increase in the ball
diameter and tube inner diameter. The ball and cell are manufac-
tured from the same Inconel alloy in order to minimize the temper-
ature effects on the calibration constant. Although one can estimate
the magnitude of these small changes in dimensions using the iso-
thermal compressibility and thermal expansivity of Inconel, one
cannot calculate the calibration constant as a function of tempera-
ture and pressure based on the magnitude of these changes. Unlike
the coaxially falling cylinder viscometer, the complex geometry of a
sphere rolling along the bottom of a tilted cylinder makes an ana-
lytic derivation of the calibration constant intractable; the rolling-
ball viscometer must be experimentally calibrated.
The calibration results were linearly correlated with the pres-
sure for all isotherms as shown in equation (2):
k ¼ a
p
MPa

þ b; ð2Þ
where p is the pressure. The slope, a, and intercept, b, values are
listed in table 2 for the four isotherms.
To obtain reliable viscosity results, the flow of fluid around the
ball has to be in laminar region. In order to verify that the flow is
FIGURE 2. Schematic diagram of the rolling-ball viscometer: (1) pressure transducer, (2) Heise pressure gauge, (3) tilt table, (4) temperature controller, (5) pressure regulator,
(6) methane cylinder, (7) glass fiber optic sensors, (8) data acquisition device, (9) computer, (10) water, (11) high-pressure generator, (12) inclinometer, (13) magnet, (14) DC
motor, (15) temperature readout, (16) type-k thermocouple, (17) glass fiber optic cables, (18) borescope, (19) fiber optic light source, (a) cell body, (b) band heaters, (c)
magnetic stir bar, (d) small sapphire window, (e) pin, (f) piston, (g) Inconel ball, (h) sapphire window.
FIGURE 3. Rolling-ball viscometer calibration constant, k, at different pressures, p,
measured with n-decane and Inconel ball (r = 0.995) at T = 303.9 K (s), T = 325.7 K
(h).
FIGURE 4. Rolling-ball viscometer calibration constant, k, at different pressures, p,
measured with n-decane and Inconel ball (r = 0.998) at T = 429.1 K (N), T = 533.9 K
(Ç).
TABLE 2
Parameters, a and b, used in equation (2) to correlate the calibration results obtained
with two diameter ratios, r, for each isotherm, T.
T/K a/cm4
Á mÀ1
Á sÀ2
b/cm4
Á mÀ1
Á sÀ2
r
303.9 3.75992 Á 10À4
0.14276 0.995
325.7 3.88927 Á 10À4
0.14198 0.995
429.1 2.20546 Á 10À4
0.05693 0.998
533.9 2.26869 Á 10À4
0.05845 0.998
110 H.O. Baled et al. / J. Chem. Thermodynamics 72 (2014) 108–116

laminar in each of these experiments, a log–log plot of the resis-
tance factor, f, vs. the Reynolds number, Re, was generated for all
isotherms [23]. The results are shown in figure 5.
f ¼
5p
42
g
ðD þ dÞ
2
v2d
ðqb À qflÞ
qfl
sinh; ð3Þ
Re ¼
v d
2
ðD þ dÞ
qfl
l
; ð4Þ
where g is the gravitational acceleration at Pittsburgh, PA
(9.80269 m Á sÀ2
) [24]. Turbulent flow is typically indicated by a
gradual flattening of the log f vs. log Re data at higher values of Re
of any isotherm [23]. If the data are linear for each isotherm, how-
ever, as shown in figure 5, then the nature of the fluid flow around
the rolling ball is laminar (note that the isotherms do not have to be
coincident).
Viscosity measurements are conducted in the single-phase
liquid region. Therefore the equilibrium pressure at solid–liquid
equilibrium SLE was determined at several temperatures. SLE data
was obtained using a phase behavior cell of identical design to the
viscometer, but without tilting capability, ball insert, or side win-
dows. Initially the temperature and pressure was adjusted until
the hydrocarbon liquid phase in the cell was clear. The pressure
was then isothermally increased and held constant for approxi-
mately 10 min. If the liquid remained clear, the pressure was
increased until it becomes opaque and solid crystals were
observed. The pressure was then decreased to obtain a clear liquid
phase. This process was repeated until the interval between a clear
phase and one where the solution became slightly opaque and con-
tained solid crystals was less than 0.34 MPa. This procedure was
then repeated at a new temperature to determine the new solidifi-
cation pressure.
3. Experimental results and discussions
The density values of n-hexadecane, n-octadecane, and n-eicosane
required to determine the viscosity with equation (1) were
obtained with equation (5), a modified Tait equation [25]:
q À q0
q
¼ Clog10
p þ B
p0 þ B
; ð5Þ
where q is density, q0 is density at p0 = 0.1 MPa, p is pressure, and B
and C are fitted parameters. The parameters q0, B, and C were deter-
mined in previous work of our research team by fitting equation (5)
to high-temperature, high-pressure density data reported by Wu
et al. [26]. The parameter values for each isotherm for the three
compounds are listed in table 3.
The SLE results for the three n-alkanes are provided in table 4.
These results are in very good agreement with literature SLE
data for h-hexadecane [27–30], n-octadecane [29,30] and n-eico-
sane [31,32]. The SLE temperature–pressure data from these refer-
ences, along with the data in table 4, were correlated with a second
order polynomial:
T ¼ A0 þ A1p þ A2p2
: ð6Þ
The optimized parameters for equation (6) are provided in table 5.
The pressure at which crystallization occurs based on the SLE
temperature–pressure correlations (equation (6) and table 5) is
provided in tables 6–8.
The viscosity results for n-hexadecane, n-octadecane, and
n-eicosane are listed in tables 6–8 at temperatures to 534 K and
pressures to 243 MPa, respectively. The combined expanded
uncertainty Uc was obtained by multiplying the combined stan-
dard uncertainty uc by a coverage factor k where uc was calculated
by the law of propagation of uncertainty [33]. The standard uncer-
tainties, u, are u(T) = 0.30 K, u(P) = 0.07 MPa below (56 and
0.35) MPa from (56 to 243) MPa, u(t) = 0.001 s, u(h) = 0.01°. The
estimated accumulated experimental uncertainty, Uc, in the
reported viscosity data calculated by applying the law of error
propagation to equation (1), is Uc(l) = 2.5% l (for 304 and 326 K
isotherms), and Uc(l) = 3.0% l (for (429 and 534) K isotherms), at
a confidence level of approximately 95% (coverage factor, k = 2).
The verification of the flow around the rolling sphere is shown
in figure 6 for n-hexadecane as an example. The linear relationship
of the resistance factor, f, with the Reynolds number, Re, for
each isotherm is indicative of laminar flow. Similar behavior was
observed for all viscosity isotherms of n-octadecane and n-
eicosane.
FIGURE 5. Log–log plot of the resistance factor, f, vs. the Reynolds number, Re, for
the rolling-ball viscometer. A linear correlation for each isotherm, as shown in the
figure, is indicative of laminar flow; 303.9 K (s), 325.7 K (h), 429.1 K (N), 533.9 K
(Ç).
TABLE 3
Tait equation parameters, q0, C, and B obtained for each density isotherm, T.
Compound T/K q0/kg Á mÀ3
C B/MPa
n-Hexadecane
303.9 765.9 0.210 103.61
325.7 750.9 0.210 91.21
429.1 677.3 0.210 45.27
533.7 597.9 0.210 20.37
n-Octadecane
325.6 760.9 0.202 93.76
429.0 687.3 0.202 44.12
533.9 615.4 0.202 26.08
n-Eicosane
325.8 766.5 0.206 95.28
429.3 697.4 0.206 52.78
533.8 617.5 0.206 20.80
TABLE 4
SLE temperature, T, and pressure, p, values for n-hexadecane, n-octadecane, and n-
eicosane.a
n-Hexadecane n-Octadecane n-Eicosane
p/MPa T/K p/MPa T/K p/MPa T/K
54.3 303.6 59.9 315.2 21.6 315.6
106.3 314.5 102.8 324.6 61.5 325.3
158.9 325.0 151.0 334.8 105.5 334.8
210.6 333.9 205.4 344.7 153.8 344.6
267.7 344.4 256.4 354.2 218.8 355.9
263.8 364.3
a
Standard uncertainties, u, are u(T) = 0.3 K, u(p) = 0.07 MPa for p 56 MPa, and
u(p) = 0.35 MPa for p 56 MPa.

The viscosity data listed in tables 6–8 were correlated by a non-
linear surface fit as a simultaneous function of temperature and
pressure given by equation (7):
ln
l
MPa Á s

¼
a0 þ a1
T
K
À Á
þ b1
p
MPa
À Á
þ b2
p
MPa
À Á2
þ c1
T
K
À Á p
MPa
À Á
1 þ a2
T
K
À Á
þ b3
p
MPa
À Á
þ a3
T
K
À Á2
þ b4
p
MPa
À Á2
þ c2
T
K
À Á p
MPa
À Á :
ð7Þ
The dimensionless coefficients in equation (7) are given in table 9.
All digits should be used to get an accurate reproduction of the vis-
cosity data. In table 9, d refers to the mean absolute percentage
deviation between experimental data obtained in this study, li,exp,
and calculated values with the surface fitting correlation, equation
(7), li,cal, for n data points, equation (8):
d ¼
1
n
Xn
i¼1
li;cal À li;exp
li;exp

Á 100: ð8Þ
The maximum deviation, k, is also listed in table 9. For all three
studied hydrocarbons, it is less than the estimated, expanded uncer-
tainty (k = 2), 2.5–3.0%, of the experimental data.
Figures 7–9 show the comparison of the experimental viscosity
vs. calculated viscosity with equation (7). The experimental data
are accurately reproduced by the surface correlation. The reported
TABLE 5
Optimized parameters A0, A1 and A2 for the second order polynomial correlating the
temperature, T, and the pressure, p, values for SLE of the normal alkanes. d refers to
the mean absolute percentage deviation, d ¼ 1
n
Pn
i¼1j
Ti;cor ÀTi;exp
Ti;exp
j Á 100, where Ti,exp and
Ti,cor are the crystallization temperatures from experiment and from correlation.
Hydrocarbon n-Hexadecane n-Octadecane n-Eicosane
A0/K 291.81 301.44 310.62
A1/K MPaÀ1
0.2241 0.2385 0.2446
A2 Á 104
/K Á MPaÀ2
À1.0605 À1.2935 À1.6068
d 0.06 0.04 0.08
TABLE 6
Experimental viscosity data, l, at different temperatures, T, and pressures, p, for n-
hexadecane obtained in this study.a
T/K 303.9l/
mPa Á sp/MPa
325.7l/
mPa Á sp/MPa
429.1l/mPa Á s 533.7p/MPal/
mPa Á sp/MPa
3.3 2.826 8.1 1.943 12.8 0.582 14.1 0.272
7.3 2.959 8.3 1.956 12.8 0.586 14.3 0.276
12.9 3.184 21.5 2.263 22.2 0.649 29.9 0.341
19.0 3.454 35.6 2.675 22.7 0.650 30.1 0.342
26.8 3.793 49.3 3.067 35.8 0.742 50.4 0.430
33.6 4.107 63.6 3.550 70.5 1.010 50.5 0.433
Solid
(55.4 MPa)
77.5 4.056 91.6 1.181 77.1 0.534
91.8 4.625 118.8 1.405 104.6 0.642
104.1 5.179 140.3 1.594 125.0 0.721
119.2 5.865 167.8 1.847 152.8 0.829
122.7 6.070 188.0 2.046 188.4 0.983
Solid
(163.9 MPa)
222.9 2.459 210.0 1.077
226.6 1.154
a
Standard uncertainties, u, are u(T) = 0.3 K, u(p) = 0.07 MPa for p 56 MPa,
u(p) = 0.35 MPa for p 56 MPa, and the combined expanded uncertainty Uc is
Uc(l) = 2.5% l (for 304 and 326 K isotherms), and Uc(l) = 3.0% l (for 429 and 534 K
isotherms) at a confidence level of approximately 95% (k = 2).
TABLE 7
octadecane obtained in this study.a
T/K 325.6 l/mPa Á s p/MPa 428.9 l/mPa Á s p/MPa 533.9 l/mPa Á s
p/MPa
9.8 2.598 6.8 0.685 9.2 0.303
16.4 2.778 21.9 0.831 9.5 0.305
29.6 3.247 42.1 1.023 15.2 0.336
37.2 3.568 63.4 1.232 22.5 0.380
51.0 4.157 84.3 1.446 44.6 0.497
60.5 4.578 104.9 1.649 64.0 0.579
69.0 4.980 125.5 1.878 85.7 0.686
70.8 5.095 147.8 2.125 105.9 0.784
Solid (107.5 MPa) 168.0 2.392 126.6 0.880
188.6 2.650 147.6 0.975
209.6 2.928 147.6 0.985
230.0 3.207 167.7 1.077
243.1 3.396 188.6 1.201
209.1 1.313
229.3 1.411
242.9 1.491
a
u(p) = 0.35 MPa for p 56 M Uc is Uc(l) = 2.5% l (for 326 K isotherm), and
Uc(l) = 3.0% l (for 429 and 534 K isotherms) at a confidence level of approximately
95% (k = 2).
TABLE 8
eicosane obtained in this study.a
T/K 325.8 l/mPa Á s p/MPa 429.3 l/mPa Á s p/MPa 533.8
p/MPa l/mPa Á s
6.7 3.184 5.5 0.837 6.2 0.346
6.7 3.193 7.4 0.858 22.9 0.425
14.4 3.511 21.8 1.029 43.3 0.541
14.4 3.528 41.8 1.262 43.5 0.541
21.3 3.828 63.0 1.498 63.2 0.647
22.3 3.908 63.0 1.523 84.3 0.750
28.7 4.250 83.0 1.777 104.4 0.861
35.5 4.642 103.7 2.043 125.0 0.977
Solid (64.8 MPa) 125.0 2.351 146.1 1.097
144.5 2.631 165.9 1.199
144.7 2.638 187.3 1.341
167.9 2.988 208.2 1.444
187.9 3.321 228.8 1.556
208.9 3.685
228.6 4.040
243.1 4.327
a
u(p) = 0.35 MPa for p 56 MPa, and the combined expanded uncertainty Uc is
Uc(l) = 2.5% l (for 326 K isotherm), and Uc(l) = 3.0% l (for 429 and 534 K iso-
therms) at a confidence level of approximately 95% (k = 2).
FIGURE 6. Log–log plot of the resistance factor, f, vs. the Reynolds number, Re, for
the rolling-ball viscometer with n-hexadecane. A linear correlation for each
isotherm such as those shown in this figure is indicative of laminar flow; 303.9 K
(s), 325.7 K (h), 429.1 (N), 533.7 K (Ç).

data in this study extend the database of viscosity of these three
long-chain alkanes to the high-temperature, high-pressure region
where most gaps occur in the literature data.
3.1. Comparison with literature data
The surface fit correlation, equation (7), with the parameters
presented in table 9, was used to interpolate the viscosity for
n-hexadecane, n-octadecane, and n-eicosane at the same condi-
tions of temperature and pressure found in the literature. The
interpolated data were then compared with viscosity values found
in the selected references. d and k values of the predictions as com-
pared to the experimental data are listed in table 10. In most cases,
the deviations are close to those obtained for the present data. The
largest deviations were found for the reference Gouel [3], where a
RUSKA viscometer was used. This rolling-ball viscometer does not
allow the operator to verify if the sphere is rolling or sliding.
Furthermore, there is no indication in this reference that the vis-
cometer was calibrated as a function of temperature and pressure.
RUSKA viscometer was calibrated with fluids of known viscosity
TABLE 9
Coefficients used in equation (7) to predict the viscosity of n-hexadecane, n-
octadecane, and n-eicosane, along with the mean absolute percentage deviation, d,
and the maximum deviation, k.
Coefficient n-Hexadecane n-Octadecane n-Eicosane
a0 À5.03775 Á 100
À3.70109 Á 101
À2.49078 Á 104
a1 1.38900 Á 10À2
9.62500 Á 10À2
6.14157 Á 101
b1 À3.87000 Á 10À2
À4.44920 Á 10À1
À1.63854 Á 102
b2 À4.92035 Á 10À5
À6.79490 Á 10À4
À8.57781 Á 10À2
c1 6.71288 Á 10À5
8.47059 Á 10À4
2.13683 Á 10À1
a2 À7.71000 Á 10À3
À3.06700 Á 10À2
À1.63583 Á 101
b3 5.57884 Á 10À6
1.75785 Á 10À5
6.74750 Á 10À3
a3 9.66000 Á 10À3
8.91600 Á 10À2
1.64049 Á 101
b4 2.79815 Á 10À6
À8.17123 Á 10À5
1.21345 Á 10À2
c2 À5.37642 Á 10À5
À5.10840 Á 10À4
À1.28045 Á 10À1
d 0.40 0.43 0.38
k 1.29 1.67 1.86
FIGURE 7. Experimental viscosity, l, of n-hexadecane vs. viscosity determined with
surface fitting correlation, equation (7), at different pressures, p. Lines represent
viscosity results obtained with the surface fitting, symbols represent experimental
data obtained with the rolling-ball viscometer; 303.9 K (s), 325.7 K (h), 429.1 (N),
533.7 K (Ç).
FIGURE 8. Experimental viscosity, l, of n-octadecane vs. viscosity determined with
data obtained with the rolling-ball viscometer; 325.6 K (h), 428.9 (N), 533.9 K (Ç).
FIGURE 9. Experimental viscosity, l, of n-eicosane vs. viscosity determined with
data obtained with the rolling-ball viscometer; 325.8 K (h), 429.3 (N), 533.8 K (Ç).
TABLE 10
Mean absolute percentage deviation, d, and maximum deviation, k, obtained with the
surface fit for selected literature data with different temperature, T, and pressure, p,
ranges for n-hexadecane, n-octadecane, and n-eicosane.
Authors T/K p/MPa k d
n-Hexadecane
Kleinschmidt et al. [1] 293–478 0.1–1041 6.8 2.6
Rastorguev et al. [2] 336–532 0.1–49 11.0 2.9
Gouel [3] 300–392 0.1–40 21.4 13.4
Dymond et al. [4] 298–373 0.1–425 4.0 1.6
Ducoulombier et al. [5] 313–373 0.1–100 4.9 1.5
Matthews et al. [6] 313–564 1.4–3.5 8.3 3.7
Tanaka et al. [7] 298–348 0.1–151 3.4 1.1
Rajagopal et al. [8] 318–413 6.9–62 5.8 2.4
Ciotta [9] 298–473 1–103 5.6 2.1
n-Octadecane
Hogenboom et al. [10] 333–408 0.1–360 12.5 4.4
Caudwell et al. [11] 323–473 0.1–92 4.9 2.9
n-Eicosane
Gross and Zimmerman [12] 313–573 0.1 6.2 3.6
Rodden et al. [13] 375–534 1.4 7.2 4.8

and density; however, the authors did not provide the conditions
of the calibration.
4. Viscosity modeling results
Although the viscosity results are well correlated by the surface
fitting model, this model cannot be applied to the changing, multi-
component hydrocarbon mixtures encountered during petroleum
reservoir simulation. Therefore a model capable of being easily
extended to mixtures as well as modeling pure components was
also considered.
The fluid viscosity, l, can be expressed as a sum of two terms
given in equation (9):
l ¼ l0 þ Dl; ð9Þ
where l0 is the viscosity of the fluid in the dilute gas limit, and the
Dl term dominates in the dense state. The dilute gas term l0 is
derived from the kinetic gas theory at very low pressures [34,35].
Many models have been proposed to describe the second term Dl
ranging from highly theoretical to simple empirical correlations.
One of the most successful models is the free volume theory model
(FVT). In this viscosity model, the second term in equation (9), Dl,
is given as an exponential function in the free volume defined as the
empty space between molecules. Allal et al. [14] expressed the vis-
cosity in the dense state in the form:
Dl ¼
qL aq þ pM
q

ffiffiffiffiffiffiffiffiffiffiffiffiffi
3RTM
p exp B
aq þ pM
q
RT
!3=2
2
4
3
5; ð10Þ
where M is the molar mass, q is the density, T is the temperature,
R = 8.3145 J Á molÀ1
Á KÀ1
, and p is the pressure. The three pure-
component parameters L, a, and B were determined by fitting
equation (9) to experimental viscosity data. As stated by Allal
et al. [14] the terms pM/q and aq are linked to the energy necessary
to form vacant vacuums required for the diffusion of the molecules,
and the barrier energy that a molecule must cross to diffuse,
respectively.
The free volume theory was used to model the viscosity data
presented in this study, in conjunction with a density model that
is suitable for pure components or mixtures, such as the Peng–Rob-
inson (PR) EoS [15] and the perturbed-chain, statistical associating
fluid theory (PC-SAFT) EoS [16].
4.1. Free volume theory model coupled with the Peng–Robinson
equation of state
The Peng–Robinson equation of state, PR EoS, is described in
detail elsewhere [15]. The physical properties needed for the PR
EoS predictions were obtained from [20,36].
The free volume theory model parameters associated with the
PR EoS, maximum deviations, k, from the experimental values,
and mean absolute percentage deviation, d, values are presented
in table 11.
4.2. Free volume theory model coupled with the PC-SAFT equation of
state
The perturbed chain-SAFT (PC-SAFT) equation of state is one of
the most successful modifications of the statistical associating fluid
TABLE 11
FVT-model parameters L, a, and B along with the mean absolute percentage deviation,
d, and the maximum deviation, k, for the predictions with the FVT-model in
conjunction with the Peng–Robinson equation of state.
Compound L/Å a/m5
Á molÀ1
Á sÀ2
B k d
n-Hexadecane 0.4195 344.869 3.5018 Á 10À3
11.42 2.97
n-Octadecane 0.4411 474.969 2.5198 Á 10À3
13.58 3.54
n-Eicosane 0.4041 547.543 2.2153 Á 10À3
8.89 2.65
TABLE 12
PC-SAFT parameters, m, r, and e from Gross and Sadowski [16].
Compound m r/Å e/K
n-Hexadecane 6.6485 3.9552 254.70
n-Octadecane 7.3271 3.9668 256.20
n-Eicosane 7.9849 3.9869 257.75
TABLE 13
FVT-model parameters L, a, and B along with the mean absolute percentage deviation,
d, and the maximum deviation, k, for the predictions with the FVT-model in
conjunction with the PC-SAFT equation of state.
Compound L/Å a/m5
Á molÀ1
Á sÀ2
B k d
n-Hexadecane 0.4677 329.287 2.5410 Á 10À3
9.26 2.54
n-Octadecane 0.5057 402.459 1.8483 Á 10À3
10.92 2.82
n-Eicosane 0.4603 461.281 1.6484 Á 10À3
5.22 2.24
FIGURE 10. Relative deviations of the calculated viscosity from experimental data
for n-hexadecane. FVT-model PR EoS, open markers; FVT-model PC-SAFT EoS,
filled markers; 303.9 K (d), 325.7 K (j), 429.1 (N), 533.7 K (Ç).
for n-octadecane. FVT-model PR EoS, open markers; FVT-model PC-SAFT EoS,
filled markers; 325.6 K (j), 428.9 (N), 533.9 K (Ç).

theory (SAFT) equation of state [37,38]. It is derived and described
in detail by Gross and Sadowski [16]. For non-associating fluids like
normal alkanes, the PC-SAFT EoS can be given in terms of the com-
pressibility factor, Z, as the sum of the ideal gas contribution
(Zid
= 1), the hard-chain contribution (hc), and the dispersion term
(disp), which accounts for dispersive attractions between the
chains,
Z ¼ Zid
þ Zhc
þ Zdisp
: ð11Þ
In PC-SAFT EoS, each pure non-polar, non-associating compound is
characterized by three parameters, the number of segments per
chain (m), the segment diameter (r), and the segment energy
parameter (e = e/kB) [39]. These three PC-SAFT parameters required
to calculate the density for n-hexadecane, n-octadecane, and
n-eicosane, were taken from Gross and Sadowski [16] and listed
in table 12.
The mean absolute percentage deviations, d, as well as the
maximum deviations, k, of the FVT model when coupled with the
PC-SAFT EoS from experimental values are presented in table 13.
Figures 10–12 show the relative deviations between the experi-
mental data collected in this study with the predictions obtained
with free volume theory model in combination with the PR EoS
and PC-SAFT EoS. The viscosity predictions obtained with the free
volume theory model in conjunction with the PC-SAFT EoS are
slightly better than those calculated in combination with the PR
EoS. This can be attributed to the fact that the PC-SAFT EoS yields
more accurate density predictions than the PR EoS does [26].
Viscosity data from selected references were compared with the
viscosity predictions obtained with the free volume theory (FVT)
using L, a, and B parameters presented in tables 11 and 13. In most
cases, the performance of the free volume theory (FVT) coupled
with the PC-SAFT is superior to the performance of the combina-
tion with the PR EoS, table 14.
5. Conclusions
In this study, a windowed, variable-volume, rolling-ball viscom-
eter calibrated with n-decane, has been used to measure the
viscosity for n-hexadecane, n-octadecane, and n-eicosane at tem-
peratures to 534 K and pressures to 243 MPa, extending the cur-
rent database for these long-chain hydrocarbons. The viscosity
data presented in this work were correlated with an empirical
10-parameter surface fitting function, which yields a mean abso-
lute percentage deviation, d, of less than 0.5%. The viscosity data
correlated with the surface fitting were compared with selected lit-
erature data at the same temperature and pressure conditions and
the mean absolute percentage deviations, d, are in most cases with-
in experimental uncertainty of 3%. The viscosity data measured in
this study were modeled with the free volume theory model in
conjunction with density data obtained with the Peng-Robinson
(PR) EoS and the perturbed-chain, statistical associating fluid
theory (PC-SAFT) EoS. The performance of the free volume model
coupled with the PC-SAFT is slightly better than the performance
of the combination with the PR EoS.
Acknowledgments
This technical effort was performed in support of the National
Energy Technology Laboratory’s Office of Research and Develop-
ment support of the Strategic Center for Natural Gas and Oil under
RES contract DE-FE0004000.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.jct.2014.01.008.
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