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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