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-. -
A Viscosity-Temperature Correlation at Atmospheric
Pressure for
W. B . BRADEN
MEMBER AIME
ABSTRACT
lhis paper presents a suitable method for predicting
.qas-jrce oil iiscositim at tenzprra?nres np to 500F know-
ing only the API gravity of the oil at 60F and the vis-
cosity oj the oil measured at any relatively low tentpera-
rlwe. The API gravity und the one viscosity value are
IIsed
as
parameters to deter tnittethe il p of a straight
line on the ASTM s andard viscosity -tetnperatare churt.
Then. I nowing the dope of the line and one point on
the
line, tltc~v iscosities at higher temperatures can be de-
Iwl]irzed. TIze line slope correlations were developed at
100 und 210F since viscosity data are jreq[{ently n~erts-
tired lit these tetnperat[wes. A procedare is given for
predicting line slopes frot~l }neasmetnents at other tenl-
perat[tres. A notno~ral]r is jwni.rhed for solving the re-
lationship.
The correlation has been evaltlated at tem,veratares up
ro 500F for oils varying in gravity from 10 to 33 API.
The corre:ltion is applicable only to Newtottian ,fluicis.
Cotnpurison at 500F o.f trne viscosities attd tilose pre-
dic ed from ~wlnes at IOOF shows an average deviation
of .?.o per cen[ nlaxinlut}~ [ieviation of 15.Oper cent)-
Preclictions from the valnes at 21OF jor the same oils
.sitow atI avera,qe deviation of 1.5 per cent wa.rimr m
tielialion of 3.4 percent).
INTRODUCTION
Correlations have been developed by Beal and by
Chew and Connally: for predicting viscosities
of
gas-
saturated oils at reservoir conditions. Each of these corre-
lations requires a knowledge of the solution gas-oil ratio
and the viscosity of the gas-free oil at the reservoir tern-
perature. For temperatures below 350F, measurements of
the gas-free oil viscosities can bc made easily using conl-
mercial[y available equipment, In thermal recovery pro-
cesses, however, reservoir temperatures well in excess of
350F are encountered. Viscosity measurements at such
conditions are more ditllcult and time consuming and re-
quire modification of existing equipment or the construc-
tion of new equipment. Measurements are further com-
plicated by the difficulty of handling higi+y viscous oils
associated with thermal recovery processes. Therefore,
it is desirable to have a correlation which allows accurate
prediction of viscosities at high temperatures.
A commonly used technique for predicting viscosities
Ori gi na l m anu scr ip t r ece iv ed i n S oci et y of P e tr ol eum Engi nee rs of fi ce
J u ly 8, 1966. R ev is ed m nnus cr il>t r eceiv ed S eD t, 30, 1966. P a ver S P E
1580 WRSpr es en t ed a t S P E . II st An nu a l F all M eet in g h eld in D .n lja s.
Tex ., O ct . Z-5, 1966. OCoI ]y ,
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?
.
higher temperatures were not available; therefore, no at-
tempt was made to explain these deviations.
All values used in constructing or evaluating the cor-
relation were taken from the straight lines in Fig. 1
and will be referred to as true viscosities as distin-
guished from measured viscosities, Slopes of the lines
were determined using the true viscosities at 100 and
210F with the following equation (the straight-line equa-
tion for the ASTM standard viscosity-temperature charts):
This can be written in the two-point form of the equation
with the elimination of B as follows:
T, + 460
[1
log (s/, + a,) = =4=
log (P, + u,),
2
(2)
where v =
kinematic viscosity, centistokes
CY
=
a
parameter having a value of about 0.6
above 1.5 centistokes; the value varies in
a compIex manner with viscosity below 1.5
loglog(v +a)+Alog(T+460)=B . . (1)
cent istokes
(n
WI
100
x
75
0
t - -
50
~
t-
30
z
w
0
20
.
15
z ,n
100,0
20,0
I 0 ,0
5,0
2,0
I ,0
5
3
2
I
t
o
s
v
F
a
z
w
z
;
I
I
60 100 I 20 140 160 180 200 240 280 320
360 400 440
TEMPERATURE~lEGREES FAHRENHEIT
l,e-CALIFORIAIA CRUDE
2. A- COLOMBIANCRUDE
3. cI - UI DCOHTI HENTRESI OUUH
4. v- CALI FORNI ACRUDE
5. ~- M OCONTI NENTCYLI NDERTOCK
6. 0- M DCONTI NENTEAYYMOTOROI L
?.
- GULF COASTCRUOE
8. o- NORTH LOUI SI ANAHEAVYCRUDE
LEGEND
9. 9API )
9. Q-
10. 9 API )10, -
14. 5API ) l l i u-
13. 4API )
12. A-
22, 9:API ) 13. 0-
23. 5,API ) 14. Q-
15. 1API )
15. v-
18. 3API )
HI DCONTI NENTEDOI L
SOUTHTEXAS CRUDE
6ULF COASTCRUDE
M DCONTI NENTI GHTPARAFFI NOI L
\
0
\
>
b
\
\
\
b
~
L
\
\
o
480
520
24. O API )
IT. 8 API )
20. 5 API )
26, 7 API )
PENNSYLVANI AACUUMDI STI LLATE 32. 7API )
WYOM N6CRUDE
21. 4API )
NI DCONTI NENTRESSEDDI STI LLATE29. 2API )
I . IVJSCOSITYs TEMPERATUREATA.
I.lllft
] Oi nsAl .OF
PETI{ OI.KINIEcIIxu I.oI;\
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A = negative slope of the line
T = temperature, F
B = ordinate intercept
log = logarithm to the base 10.
The correlation was then developed by plotting the
viscosities at 100 and 210F vs API gravities at 60F. Lines
of constant A (negative line slope) were drawn to fit
the pIottaf points. The results (Figs. 2 and 3) allow
determination of line slope for any oil knowing only the
viscosity at 100 or 21OF since viscosity data are usuafly
available at these temperatures. A procedure is given in
the next section for predicting viscosities from measure-
ments at other temperatures, In Fig. 4, a nomogram is
provided which takes into account the variation of a, and
it should be used when viscosities below 1.5 centistokes
are encountered.
USE OF THE CORRELATION
To predict a viscosity knowing the viscosity value at
either 100 or 21oF, the following procedure is used:
(1) find A from Figs. 2 or 3; and (2) use the nomo-
gram in Fig. 4 to find the viscosity.
To predict a viscosity when a viscosity other than
100 or 21OF is known, the following procedure can be
used: (1) on the nomogram, use A=4.O and find the
viscosity at either 100 or 21OF, whichever is closer; (2)
from Figs. 2 or 3 make a second approximation to A;
(3) repeat Steps 1 and 2 using the new A until the
value of A becomes constant; and (4) use the nomo-
gram to find the viscosity.
105
I I
I
v-.)
I
I
,., I
t
.
I,
40
GRAVITY, API
I , 2DETERMINATIONOF
A
AT 100II.
Nft VEMfl ER 1966
TASLE 1EVALUATION OF THE CORRELATION
For The Nine More VISCOUS 011s
(Samples 1 l h ro. gh 9]
Temperaturer c. m whi ch predlcli.an
WO
made, F
I 00,0 100.0
Tnmperatweotwhi ch v is co si ty
was predlded, F
210.0
500.0
Moxlmum devi ation from trcm val ue at predicted
t em pe ra tu re, p er ce nt 8.8 6.0
A ve ra ge d ev lc tf io n from true value otprad cted
temper .at we, p er c ent
3.1
3.0
For The Six less Viscous 011s
(Samples 10 Ihm.gh 15]
Tamp er ot vre f rom w hi ch p r.adi cf i en
WES
made, F
100.0
100.0
Temp erat ure at w hi ch v isc wi ty
wcs predi cted, F
210.0 300.0
M.axl mum d ev iat io n f rom f rue VOIUW at p redi ct ed
t em per at ur e, p er ce nt
5.4
4
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*-
u
T
,n7 SAMPLE PROBLEM
A
M
q 600
.-
,06
t
GIVZN. VISCOSITY :100 CSTK AT 1000F
1
4,3
GRAVITY
e
,~OAp,
,05
TO FIND: VISCOSITY AT 500e F
I
1
ROCEDURE:
104
I. FINO FROM FIGURE 2 ,A=4.00
/1
4,2
2. CONNECT A~4.00 TO T:IOQ
3. CONNECT THE INTERSECTION
(Q3
WITH M TO v :100
4. MARK THE INTERSECTION WITH
4.1
to
I
5.?ONNECT A:4.00 TO T=500
g
6, CONNECT
THE INTERSECTION
II
//
o
Ioz --
WITH M TO THE MARK ON B
+
7.;:;tAD TO u AND READ L06
/ ,
g
----
redictionof the ShrinkuJw of (lwde Oils, LJrilL
Prod. Pr,/c., API (1942) 137.
e limited to 500F.
149N
JOIJR~AJ, oJr PET~OJ F:IJM rrECJJXOJ OGY