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. .
Predicting the Viscosity of Hydrocarbon
Liquid Phases From Their Composition
A, H. Houpeurt, SPE-AIME,ELF-RE
M. B. Thelliez, U. of Paris VI
Introduction
Routine laboratory measurements of viscosities at high
pressure and high temperatureare always expensive and
often inaccurate. When values are needed for many
pressure-temperature combinations, it is obviously de-
sirable to be able to calculate them instead of measuring
them.
A few years ago, the ELF-ERAP group decided to
elaborate on a method for determining, with appropriate
accuracy, the viscosity of hydrocarbon liquid phases.
A procedure for predicting the viscosities of hy-
drocarbon liquid phases from their composition is pro-
posed. It is similar to that used by Standing and Katzs
for determining the density of reservoir oils.
This work is based on 1,092 viscosity measurements
made on 23 mixtures for 479 pressure-temperature
combinations between 30 and 130“C and between 50
and 500 atm.
These measurements were made with a specially de-
signed capillary tube viscosimeter, The analysis of 289
measurements made on n-C4, n-C5, and n-Ca in the
same range of pressures and temperatures showed a
standard deviation of less than 0,0075.
Three conclusions were reached.
1. The kinematic viscosity, v (p,T), of a C4+at pres-
sure
p
and temperature
T
may be calculated from its
composition and the kinematic viscosities, Vf, of its
components atp and T using the equation
fogv
p,T = xxi iog
Vi p, T)
2. The absolute viscosity of different values of C4+at
any pressure and temperature, P p, T , may be calcu-
lated from their “standard” viscosities, W* (at 1 atm
and 2(F’C),using functions ofp and
T
that appear to be
independent of the nature of the Cq+.
3, ‘Theabsolute viscosity, Ph p, T , of a liquid phase
composed of a C4+ and light components (methane,
ethane, propane, carbon dioxide, and nitrogen) depends
only on the viscosity of that C4+at p and T, and on the
amount of each light component in the mixture,
A tentative correlation relating the standard viscosity
of a C4+to its average molecularmass is also presented.
Fig. I allcws the determination of ~c~+ p, T from
P*c~+and also contains the correlation ~*(R).
Fig. 2 is a new presentationof the results of Standing
and Katz, It is used to determine the densities of a C4+
that are needed for calculating its kinematic viscosities.
Fig. 3 presents the netw~rks for correcting the vis-
cosity of a C4+ when it is mixed with known amounts
of propane, ethane, methane, carbon dioxide, and
nitrogen.
The procedure was experimentallychecked using two
mixtures for 16 pressure-temperaturecombinations. An
average relative error of 0.0345 was obsemed, with a
maximum deviation of 0.08, but only a limited number
of k,eavycomponents were investigated.
Review of Ulterature
Refs. 1 through 4 present methods for determining the
viscosity of oils. All are based on compilations of avail-
able data and are very empirical.
When many pressure-temperature combinations are involved in predicting viscosities, it is
‘
desirable to be able to calculate them rather than to have to measure them. Here, a
procedure similar to that used to determine the density of reservoir oils is proposed for
.
predicting the viscosities of hydrocarbon liquid phuses from their composition.
.
FEBRUARY, 1976
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Basic Ideas
.
We tried to find more fundamental relations governing
the viscosities of the mixtures through a systematic (al-
though obviously limited) investigation of mixtures of
paraffins and of oils. We thougnt that the viscosity of
a liquid phase could be determinedby a method similar
to that used by Standing and Katzs for calculating its
density.
In short, a “standard density” was calculated for
the C4+. This figure was corrected successively for
the propane content of the Cs+, for the ethane content
of the C2+, and for the methane content of the Cl+.
The figure thus obtained was corrected for pressure and
temperature.
It was necessaryto ( 1)elaborateon a method for cal-
culating a standard viscosity of a C4+;(2) study the ef-
fect of the presenceof light paraffins (propane, ethane,
and methane}, carbon dioxide, and nitrogen; and (3)
correct the figures for pressure and temperature.
The experimental work showed that the correction for
pressure and temperature must be applied to the stand-
ard viscosity of the C4+and that this corrected figure
had to be revised for the amount of light paraffins and
other compounds present.
Laboratory Measurement.sof Absolute
Viscositks
An adequate viscosimeter was needed to measure the
viscosities in the large range of pressures, temperatures,
and viscosities that had been chosen, ‘l%isapparatus is
described in the Appendix.
Determining the Viscosity of a C4
Eyring’s theory, if applied to the viscosity of the
liquids, leads to the approximate expression
h NA
AFW
()
=~exp ~ .
. . . . . . . . . . . . . .
(1)
If the activation energies were actually additive in a
mixture, the following would result from Eq. 1:
logpv=xx,logp~l~~. . . . . . . . . . . . . . . ...0.(2)
Eq, 2 is equivalent to
logvfi=zx*logv*Mf. . . . . . . . . . . . . . . . . ...(3)
Fig.1 —viscosityof heavyliquidphaeasG+.
224 JOURNALOF PETROLEUMTECHNOLOGY
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Since the activation energies are not really additives, it
seemed possible to simplify Eq. 2 to
logp=xx/log ~,
..00..0 ..,,0.0,0,...0(4)
or to simplify Eq, 3 to
logv=zx~logv~,
. . . . . . .
..,,.,,..:..,6(5)
Since these equations were only approximate, it was
necessary to test them exp&imentally.
Eqs. 4 and 5 were tested with two different mixtures
of C,+ for 50 pressure-temperature combinations; the
compositions of the mixtures are given in the first and
last lines of Table 1. The comparison was favorable to
Eq. 5; the average experimental and calculated ‘:alues
were 0,01 and 0.024, respectively, using Eq. 5, and
0.029 and 0.041 using [email protected].
It was concluded that [email protected] couId lead to a conve-
nient calculation of the viscosity of a mixture of liquid
CA+
. “
Practica Use of Eq. 5
[email protected] may be used only if the kinematic viscosities of
the componentsare known in the range of pressures and
temperatures of interest.
As a preliminary part of the research, we collected
data for density and viscosity and selected the best val-
ues. This study showed the need for completing the
network of the viscosities for n-C4, n-C5, n-C6, and
n-C7, which was performed using the appwatus de-
scribed in the Appendix.
These data were published in a handbookGgiving
densities, absolute viscosities, and kinematic viscosities
between 50 and 500 atm and between 3(Yand 130 ‘C
for the first 10paraffins, carbon dioxide, and nitrogen,
When an oil field is discovered, measurements of its
viscosities and densities in the range of interest can be
included with the basic measurements. Consequently, it
was concluded that the published monographs and such
specific measurements allowed calculation of the vis-
cosity of any C4+at any pressure and temperature using
Eq. 5.
Structure and Use of Fig. 1
It seemed worthwhile to investigate the possibility of
avoiding the numerousmeasurementsof the viscosity of
the C,+ covering the range of pressure and temperature
that had been chosen, “
It is well known that C,+ with the same molecular
mass may behave very differently. It is obvious that the
degree of uncertaintyof the calculated values of the vis-
cosity of a C4-I.will reflect that of the viscosity of the
c, +
I twas decided to study first the kind of relations that
could exist between the viscosities of a given C4+ at
different pressuresand temperatures. A standard viscos-.
ity was defined as ~e true viscosity at 1atm and 20 “C,
written as
P (PJn = P* f(P) gw)
. . . . . . . . . . . . . . . . . . . . ( 6 )
In Eq. 6, K* is specific for the given CA+,but~ (p) and
g~) me, resp=tiveiy, functions of the pressure and the
temperature that are valid for any C4+.
Eq. 6 allows calculation of P* if Y (p,n is known.
It was determined that different values of P led to
FEBRUARY, 1976
the same value of A*, and that the value of P* fitted
with the true value of the viscosity in the standard
conditions.
Moreover, when many values of P* were compared
with the average molecular mass of the corresponding
C4+,it was concluded that a pr~tical correlation could
be established bptweenP* and M.
This comelati~n does not include the pure compo-
nents that were not included in Eq. 6, Moreover, if
many different C,+ had been used, it is likely that the
correlation would have been more compiex and that the
possibility of drawing different curves grouping dif-
ferent kinds of C,+ would have been noticed.
The correlation only offers a way to calculate an ap-
proximate value of the viscosity of a CA+when the only
data available on the C,+ are its molecular mass and
specific gravity. Obviously, it is much better to know
the true value of its standard viscosity and to use Fig. 1
after calculating the standard viscosity of the C4+using
Eq. 5.
The different way$of using Fig. 1 follow.
Use of Fig, 1 ‘ “
The correlation w*(R) is presented in the upper left-
hand comer of Fig, 1.
The value ofW*is corrected first for the pressure and
then for the temperature using the two networks irl the
central part’of the figure.
An additional and often useful correlation betweenM
and
p ,
a standard density at 20 ‘C and 1 atm, is given
in the lower right-hand comer of Fig. 1. It is extracted
from Fig, 2.
Use of Fig. 2 and Eq. 5
Two different methods are presented for determining
the absolute viscosity of a CQ+at any pressure and
[email protected] – Densityof liquidphases.
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8/19/2019 Predicting the Viscosity of Hydrocarbon Liquid Phases From Their Composition
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.,
temperature, They offer two different ways for checking
theresults given by Fig. 1 i%I.S,
Iogu = Zxiloglq ,
can be used to calculate the kinematic viscosity of a C4+
from the viscosities of its components, and we can de-
duce the absolute viscosity if we know the density.
@. S can be used both for the standard viscosities
and for the viscosities at any pressure and temperature.
The kinematic viscosities of Cf, Cs. and G at any
pressure and temperature are easily obtained from
previouslypublishedmaterial. The kinematicviscosityof
C,+ could be calculated from the absolute viscosity
if the density were known. The absolute viscosity is
known either through direct measurement, or through
Fig. 1 if the molecular weight of the C,+ is known. The
density of C,+ will be determined through Fig. 2, along
with the density of C4+, which is required to complete
the calculation.
Fig, 2 is a presentationof the results of Standing and
Katz5concerning the densities of the C4+ at any pres-
sure and temperature. The purpose of Fig, 2 is to save
time when applyingthe methodof Standing and Katz to
Eq. 5.
Examples
Caicuiate the viscosity of oil 1, whose composition is
given in Table 2, at 300 atm and 100‘C.
use
of h rt
From the composition, we first calculate
~c,+ = ~
X f ,s
253,7,
Through the comelationP* (B)* ~lg. 1 gives
L*~4+= 12.0
Cp,
Entering thisvaiue into the pressure-correctionnetwork
(going horizontally to the l-atm line, then vertically to
the 300-atm line), we get 19.3 cp.
Entering the temperature-correction network (going
horizontally to the 20 ‘C line, then verticallyto the 100
“C line), we get
PC4+
= 3.65
CF.
Use of Fig. 2 and Eq. 5
Table 3 contains the dataa needed for solving the prob-
lem. P* and V*are the actual values of P and v for the
bodies that are actuaily liquids at 300 atm and 100 ‘C.
.
. .
TI
226
Fig. 3 – Viscosity of
liquid
phasascontainingdisaolvadgases.
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TABLE 1- ~EITlON OF MVE$T’KJATEDmRES AND GENEnALDATAON W WASUFW%NTS
Bodbs (peroentMOW
Number of Numb. ’ of ?om~rature Pressure
Point*
CO* N* C,
Measuro-
Fy
l?:inm~
Ca C~ t% G Ca n+, CB H, H, H, P,?.
memta
—— .— —. .
——
5.0
11.5
46.7
53.3
73.8
%
65.7
9.6 35.2
1,354,0
17.6
20.1
82.4
79.9
10.s
89.6
20.5
10.8
21.5
34.6
30.1 1s.0
20.0 30.1
25.0 15.0 20.0
30.0 10.0 25.1
15.0520.0 30.0
4.3
05.7
10.4
69.6
95.0
5.6 23,9 19.9
4.9 5,0 24,7 10,0 15,1
4.0 3.5 3.8
For Cq, they were extrapolated from the values in the
liquid state.
Calculating P*cq+ instead of deducing it_from the
molecular weight through the correlation F*(M) of Fig.
1: Eq. 5, written for the standard viscosities, is
log V*C,+= x .q Iog V**.
For CT+,the correlationM*(R) of Fig. 1 gives
/L*c,+= 32.5 CF.
For C,+, the correlation p*(~) from Fig, 2 gives
/l*c,+ = 0.s47
gdcc,
and for C4+,
P*c,+ = 0.833
gin/cc.
so,
V*C7+
= 38.3 cSt.
Eq. 5 gives
V*C4+
= 14077‘cSt,
from which we calculate *cq+ = 12.3 cp, a value
that is different by only 0.02 from that given by Fig, 1
when applied directly to C4+.The result of the calcula-
tion is then the same as above,
Calculation
of PG.: Eq, 5, written for ,tie required
pressure and temperature, is
log VC4+ = x -q
log vi.
Its use requires the knowledgeof PC,+.
From Fig. 1, through the correlationP*(M), we get
~*~V= 32.S
Cp.
The pressure correction gives 53.5 cp, and the tempera-
ture correction leads to
&c,+= 7.4 Cp.
From Fig, 2, through the correlation p* Af , we get
p*c7+= 0.847 gdcc.
FE BRUARY,976
79.6
69,2
78.5
65.5
64.9
49.9
2::
34.95
88.5
44.6
40.9
68.7
3oto130 looto500
23 to 131
100 to 500
71,6 to 132 170 to 516
19to 130.2 103to 516
17,9 to 131,4 51
to
516
31.0
to
129.6 60 to 516
18.7 to 133.5 50 t o 516
19,2 to 132,2 50 to516
15,3 to 129,9 51 to 516
30.6 to 129.2 51 to 516
30.3 to 132.7 51 to516
30.5to 130.2 103to S 6
31.0 to 130.5 103 to 516
30.5 to 133.7 130 to 515
32.7 to 128.3 150to 515
32.7to 126.2 144to 515
33.4 to 123.6 102to 515
33.6 to 126.3 154to 515
33,0 to91.2 102 to 515
34.5 to 127.7 102to 515
.34,5to 130.5 217to 515
35.0 to 130.1 206to 515
35to 130 103 to 515
This becomes 0,865 after pressure correction. After the
temperature correction,
Pc,. = 0.810 gin/cc.
From this figure, we deduce
VC7+ 90.1 Cp,
and from Eq. 5,
Vc,+= 44.7 Cp.
Through the correlation p*(M), Fig, 2 gives
@cd+==0.833 grnicc.
Applying the pressure correction, we get 0.851; after
the temperature correction,
pq+ =
0.797
gmlcc,
The final value of ~cq+is
/.Lc4+ 3.56 Cp.
This value agrees well with the value deduced directly
from Fig. 1 and calculated above (3.65 cp), with the
discrepancy being less than 0.03.
Determining the Viscosity of a Lk@d Phase
Containing Light Paraffks, Carbon
Dioxide, and Nitrogen
Table 1 shows the composition of the different mixtures
investigated to evaluate the effect of light paraffins,
carbon dioxide, and nitrogen on the viscosity of a
liquid-phase.C4+, and to elabort’te on Fig. 3. It also
gives the number of pressure-temp..raturecombinations
for which the viscosity was measwed, the effective
number of measurementsmade (two or i??ree,as a rule,
for each combination), and the range of prmures and
temperaturescovered in each case.
Table 4 gives the molecular weight and the true den-
sity of the three oils (Hl, Hz, and H~) at 20 ‘C and
1 atm that were used as natural heavy components in
the experiment.
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YAWE 2- COWO$lTlON Of OIL 1
Body _n-C4
n-cfi
n.CB
c,+
M,
56.12 ‘ K5 WY7
300. 0
x( 0.10
0.05
0.05
0.60
‘1’ABl. 3- vtSOOSITIESOF wC* n=CMAND tie
(FROM REF. 6)
~
n-C4 n-C6
n.cc
/&*
P
1,650 X 10-6 2,345 X 104 3,125 X 10d
“* &
2,650 x 104
3,750 x 10+
4,740 x 10-6
vSt
2,315 x 10-’
2,660 x 10-’
“3,460x 10-6
The effect of methane was examined for 110 combi-
nations of pressure, temperature, molar fraction, and
CT+.The effect of ethane was investigated in 48 combi-
nations, and that of propane was studied in 71 combina-
tions. The effect of mixtures of methane and ethane was
observed for 39 combinations of pressures, tempera-
tures, and compositions, and the effect of ternary mix-
tures of methane, ethane, and propane was studied for
57 combinations. Finally, the effects of nitrogen content
and carbondioxide were studied for 37 and 35 combina-
tions of the variables, respectively.
From these 839 viscosity measurements, we con-
cluded that the viscosity of a CA+,when mixed with
light components, depends on the components’ molar
fraction only. Figs, 4 through 8 show the experimental
correlation between the viscosity of such mixtures and
the viscosity of the Cq+, respectively, when the light
component is methane, ethane, propane, carbon di-
oxide, or nitrogen, They show that neither the pressure
nor the temperatureacts alone as a significant factor.
These experimental results justify the procedure for
calculating the viscosity of a liquid phase and the design
10
0.+
0.8
OJ*
0.6
0.5
0,4
z
SOJ
a.
0.2
0.1s
‘ i A/r I “’-”
~fllmllll
‘,l
0.2
0,3 0.4 0.S
M 0>
F .4 — Viscosity,p, of methane-oilmixturesas a function
? the “oil”viscosity,&Ii,andof the percentageofmethane.
TABLE 4- PROPERTIESOF 01Lf3
H,,H*,md Ha
oil $
He
F&
CJ%,motpercent
7
CtH1@mot percent
k;
:; 4.7
CA%%,mol percent
17.2
12.3
6.4
CM,* mol peroent
12.2 10?2
7.6
~+, mol parcent 64.4
70.7
78.5
~c7+, gm
143
190
235
M, gm
118 156
203
Density,gin/cc
at 20 “C,1 atm
0.726 0.774
0.812
Note: It Isaatlnutad that~ laknown with an
ccumcy of fived gltein the third
place,
I
of Fig. 3. This procedureis as follows.
The viscosity of the CA+at the required pressure and
temperature is first determined using Fig. 1 (Fig, 2 and
Eq. ”5 offer i-malternative method for checkjng the re-
sults). The figure thus obtained is then corrected suc-
cessively for the propane content of the C3+,,the ethane
content of the C2+and the methane content of the Cl+
using the three networks of Fig. 3.
The correction for the carbon dioxide is made using
the network located in the upper left-handcorner of Fig.
3; this network is quite similar to the three others. The
correction for the nitrogen is made through the correla-
tion presented in the lower right-hand corner of Fig. 3;
the viscosity, P, of the mixture is proportional to the
viscosity of the mixture without nitrogen, ~h, by a fac-
tor depending on the nitrogen content only, as proved .
by Fig. 8.
Fi~. 8 shows that the experimental relation between
P and/& is linear for a given content of nitrogen in the
mixture and that the slope of the strahzht line is not
dependent on this percentage.
,
9%
Smv.
1197,
h (C?)
‘%
5 — VkcOSltY,w of ethane-oilmixturesas a functionof
t e “oil” viscosity,&/Isand of the percentageof ethane.
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Examples
1. Table igivesth ecompositionof a complex mix-
ture containing methane, ethane, propane, butane, pen-
tane, hexane, and a C7+, We calculate the viscosity of
this mixture at 300
atm and 100 ‘C, The steps of the
calculation are as follows.
Calculating ~c,+ (by ~C4+ = Z xtMi),
m,
= 245.
From the correlation in Fig. 1,
p*(R) : /L*c,+= 10 1 Cp.
After pressure correction, this figure becomes 16.2 cp.
After temperature correction,
pQ+ = 3.30 Cp.
Using Fig, 3, for a content of 0.071 of propane,
wc& +
= 2.94
CP.
For a content of 0.096 of ethanc,
PQ?+
= 2,51 Cp.
For a content of 0.375 of methane,
PC,.
= l.llcp.
2. Calculate the viscosity (at 300 atm and 100“C) of
Oil 3, whose composition is given in Table 6. From the
COZ network, entering down with 1.11 cp, and then
going up to the 0.03 line and to the left toward the
scale, we get
Pcoz+
= 0.98 CP.
H=EE w
H=I=kP
0,}
0,1
0,1
p~.”.w)
[email protected] — Viscosity,P, of pro ane-dl mixtureses a function
of the’’oii” viecoaity,wh,an$of the peroentageof propane.
M
I I r
Q7 -
0,4
1
0 4
03
Q2
Q2
0.3 0.40> Q4Q70B 1.0
.5 20
ao 4.05,06s2zoao 10
Fig. 7 “—Viscosity,IA,of carbondioxide-oiimixturesae a
functionof the ‘“oil”viscosity, /i, andof the percentage
of carbondioxide,
1,(
0,1
04
O,J
0.4
0.s
0.4
%
; 0.3
0.2
O.1.s
0.
Oa 0.3
p~ c?
0, o.* 0.7 0.1O.*1.0
F@. 8 – Viscosity,p, of nitrogen-oilmixturesasa function
of the “oii” viscosity,w*,and of the percentageof nitrogen.
229
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CH4
C *H.
C3Hg
n-C4H0
n-CsHlz
n-Cti,4
c,+
TAoLE6. coMPoSll10NoF01L2
Molar
Molar Fraction
Fraction
M or~ of Cl in CI+l
0.3760
16.04
0.3750
000600
30.07 0.0960
0.0400 44;09
0.0710
0,0676
66.12
o.@300
72.16
0.0275 66.17
0.4000 297.00
NA=
Avogadro
number
p = pressure, attq
q = rate of flow of the pump, cc/see
r = radius of the capillary tube, cm
R =
constantof the perfect gases, erg
t = time, seconds
T =
temperature, “K
V= molar volume, cc
x{= molar fraction of component i
TABLE6 COMF02KiOU OF OtL 3
Oii2
0.9500
co*
0.0300
N,
0.0200
After the correction for the nitrogen content by a ratio
of 0.98 corresponding to a content of 0.02, we get
~h
= o Cp.
Check of the Method and Conclusions
Table 1 shows that two mixtures, the first containing
Nz, CI&, CZH6,and the oil H3, and the second conhin-
ing COZ,Ng,CH4, C2H13,nd C3H.S,and the same oil,
were investigated, each for 16 pressure-temperature
combinations, These experimental results were used to
check the method. The average discrepancies between
the calculated and experimental values were 0.024 and
0,045, respectively, with the maximum values being
0.076 and 0.08.
The question arose as to whether the heavy material
acts on the viscosity of the mixture through its own vis-
cosity only. If it does, we can hope that the correction
for the light components is valid for any type of heavy
material, and that only Fig. 1 would need some im-
provements if a more extensive experitpental study
showed that the pressure and temperature correction
chart for the C4+is not accurate enough in some cases
or that the correlation P*(E) would have to account
for a second parameter to cover very different heavy
materials.
If the heavy material does not act through its own
viscosity only, Fig. 3 also would lose its validity. How-
ever, we think that the intermolecular forces between
the heavy materirdsand the light ones are probably not
very dependent on the nature of the former as Iong as
only viscosity is concerned, This is because of the very
large difference in the sizes of the molecules of the light
components and that of the heavy material, which tends
to minimize the differertcesin the intermolecular forces
when the nature of this material is changed, and when
the complexity of the molecules is increased.
Nomenclature I
Au= cross-section of the branch of the U tube
connected to the top of the reception
cell, sq cm
A.= identificationfor the other branchof the U
tube, sq cm
g = gmvity$CmlSCC2.
h = Pkmck’s constant, erg/see
f = length of the capillary tube, cm
M = molecular mass, gm
R = average molecular mass, gm
230
y = location of the meniscus above its starting
point in the branch of the U tube
connected to the top of the reception
cell, cm
z
= identificationfor the meniscus in the other
branch of the U tube, cm
Ap = differencebetween the density of the
mercury and that of the fluid in the
operating conditions, gin/cc
AFp =
free energy of viscosity, erg
e = time constant =
8 PIIW r4 A pg,
Au Az/AM -i- Az, seconds
= absolute viscosity, cp
P* = standard absolute viscosity, cp
Pc,,+= absolute viscosity of a mixture, with the
lighter hydrocarbon being C., cp
PC02
= absolute viscosity of a mixture containing
some C02, cp
~h
= absolute viscosity of a mixture of
hydrocarbons with or without
hetero-elements, cp
v = Vktematicviscosity, stokes
p = density, grn/cc
Acknowhxlgments
We thank the ELF-ERAP Group for permission to pub-
lish this paper. We are deeply indebted to Gondouin,
Dlehl, and Zuravsky, who were in charge of the ex-
perimental work in the laboratories of GEOPETROLE,
and to Neoschil and Verrien (ELF-RE) for many sug-
gestions and contributions.
References
1.
2.
3.
4.
5,
6.
Beal, C.: “’llte Viscasityof Air, Water, NaturalGases, Crude OiI
and Its AssociatedGazes at OMieldTemperaturesandPressures.”
Trans., AIME (1946) 16S, 94-115.
Chew, J. N. and Connaiiy, C. A., Jr.: “A Viscosity Comelation
forGas-SaturatedCrudeOils,”’
Trans.,
AIME(1959)216,23-25.
Lohrenz, J., Brsy, B. G., and Clark, C. R.: “Calculating Vis-
cosities of Reservoir Fluids Fmm Their Compositions,” J. Pet.
Td.
Oct.964 1171-1176
rans., AIME, 231.
Little, J. E. and Kennedy, H. T.: “A Correlationof the Viscosity
of Hydrocarbon Systems with Pressure, Temperature, and Com-
tmsition,” Ser. Pet. EnR.J. (June 196S)157-16Z Trans., AfME,
M3.
Standing, M. B. astdKatz, D. L.: “Density of Crude Oiis Satu-
rated With NaturalGases.” Trans., AIME (1942) 146, 159-165.
CR@S-GEOPETROLE “Viscosity and Density of Light Paraf-
fins, Nitrogen and Carbon Dioxyde,” Techt@, cd.; 27 Rue
Wtoux, 75737 Paris. (Fuil-size copies of Figs. 1 through 3 are
now insertedin this book.)
APPENDIX
Fig. 9 shows a schematic of the viscosimeter. The vis-
cosimeter is composedof three vertical, cylindrical cells
and a two-cylinder mercury pump for dkplacing fluids
at a constant volume. The two cells on the right form a
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8/19/2019 Predicting the Viscosity of Hydrocarbon Liquid Phases From Their Composition
9/9
seat
E
/
/
r-
two cylinders mercury pump
Fig 9 — Schematicof the viaoosimeter.
U tube whose bottom is connected to the right sid~ of
the pump; the cell on the left is divided into two rooms
by a seat that holds the capillary tube, One branch of
the U tube is conntictedto the upper room and the see-
ond branchis contteetedto the lower room. The bottom
of that cell is connected to the left side of the pump. As
mercury is displaced from the left side to the right side
of the pump, the cell receives the fluid pushed through
each branchof the U tube. ‘he reception cell and tbe U
tube are immerged in a thermostatic bath.
With the capillary tube in place, the cells are filled
with the liquid under pressure, and convenient amounts
of mercury are Iefl in the reeeption cell and in the U
tube. A bypass enables the operator to equilibrate the
levels of the interfaces in the two branches of the U
tube.
When the thermostaticbath is at the correct tempera-
ture, the pressure is adjusted to its correct value and
measurement is started. When the pump is running at a
constant rate, pushing the mercury into the U tube, the
two interfacesare not rising at first at the same velocity;
the friction in the capillary tube restricts theiflow in the
FEBRUARY,1976
?
~. 10 – Locationof the meniscusvstime in the two
branchesof the U tube for givemvaluesofEland q.
branch that is connected to the top of the reception cell.
The hydrostatic pressure that is thus created will pro-
gressively counterbalance the pressure 10S in the capil-
lary tube, and, after some time, the two meniscusrise at
the same constant velocity (Fig. 10).
Each branch of the U tube holds five electrodes for
recording the displacement of the meniscus. These data
are treated by the least-squares method to get the two
coefficients of the two straight lines corresponding to
the movementof the two meniscus, The commoii slope
of these lines gives the rate of flow through the capil-
lary tube, and the difference betwpen the two constant
terms gives the hydrostatic head pushing the fluid, It is
easy to calculate the viscosity then.
When the preselected values of the radius of the
capillary tube and the rate of flow are convenient, “
the steady flow is obtained before the meniscus touch
the lower electrode in each tube. When the preselected
values are not convenient, the two slopes are different
and the operator is, thus, instantaneous]y informed. It
is nevertheless theoretically possible to calculate the
viscosity from therecordeddata using instantaneous val-
ues of the slope and of the difference of the ordinates,
but such a procedure involves many opportunities of
miscalculation.
With the apparatus working automatically, personal
errors are eliminated and time is saved.
It was experimentally found that the standard devia-
tion was less than 0.0075.
SPT
Original manuscript raoeivadirrStXiety of Petroleum Eng[nwra office July 13,
1974. Paper acwpfed for publication Maii 16,1976. ReMaedmanuecrlpt reoelved
NOW.7, 1975. Paper (SPE S0S7)waa fkat ~reaented at the SPE-AIME 49th Annual
Fall Meeting, held In Houefon, Or%S-9, 1974. @ Oopyrtght197S ArnerioanIrrafi.
tute of Mlnlng, Metallurgical, &mdPatmleum Englneara, hrc.
This paper will be Inoluded In the 1976 Trenaaotlonsvolume.
231
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