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Rheological characteristics of Saudi crude oil emulsions
Journal of Petroleum Scwnce and Engmeenng, 6 ( 1991 ) 149-160
149
Elsevier Science Publishers B.V., Amsterdam
Rheological characteristics of Saudi crude oil emulsions A.E. Omar, S.M. Desouky and B. Karama Kzng Saud Umverstty Collegeof Engmeermg, P 0 Box 800, Rtyadh 11421, Saudt Arabta (Received February 20, 1990; accepted after revision November 20, 1990)
ABSTRACT Omar, A.E, Desouky, S.M. and Karama, B., 1991 Rheologlcal characteristics of Saudl crude oll emulsions J_ Pet Set. Eng., 6 149-160 Rheologtcal charactensttcs of Saudl crude oli emulsions were measured with a Brookfield wscometer at temperatures of 10 °, 20 °, 30 ° and 40°C. The Saudl field crude oils used m the present study were: heavy, medium, light and extrahght. The emulsion consntuents were crude od, brine, emulsifier (Triton X- 100) and dilute hydrochloric acid. The measured data were first classxfied into two groups for Newtonian and non-Newtonian fluids. The results showed that the non-Newtoman emulsions exhibit pseudoplast~c behavior and their rheolog~cal characteristics can be described by the power-law model. Then, the effect of dispersed phase (oil) concentration and temperature on the rheologlcal behavior of the emulsions were thoroughly investigated using statistical analysis (t-test)_
Introduction The study of the rheological characteristics of crude oil emulsions has received attention in petroleum research laboratories during the past twenty years. The development of new methods of secondary recovery and the potential application of crude oil transportation through pipelines as stable emulsions have leaded to a number of research works dealing with emulsions (Gogarty, 1967; Simon and Poynter, 1968; Marsden and Raghavan, 1973 ). There are two types of crude oil emulsions: oilin-water ( o / w ) and water-in-oil ( w / o ) . The latter is the form of the most produced crude oils of the world and is usually more viscous than either of its constituents. Carny et al. ( 1975 ), Alvarado and Marsden (1979), Flock and Steinborn (1982) and Wyslouzil and Kessick (1987) have studied the rheological behavior of different crude oil emulsions and have concluded that, whereas many of these behave like Newtonian fluids, 0920-4105/91/$03.50
some show definite non-Newtonian properties. Of the latter most are pseudoplastic, a few are dilatant, many are thixotropic, and a few are rheopectic. The main reasons for this wide variation of emulsion types are the emulsion's composition and conditions under which each type exists and flows. These investigators have suggested several correlations relating the emulsion viscosity to the dispersed phase concentration or shear rate, using either the Richardson equation or the power-law model (Govier and Aziz, 1982 ). In as much as the rheological characteristics of Saudi crude oil emulsions vary with temperature a n d / o r dispersed phase concentration, a method for checking this variation is needed which is capable of producing a general rheological correlation. A suitable way to ensure this is by using a statistical analysis method such as the t-test (Volk, 1969; Parsons, 1978 ). This method was used to investigate the effect of both the dispersed phase (oil) concentration and the t e m p e r a t u r e - o n the
© 1991 Elsevier Science Publishers B V All fights reserved
150
AE OMARETAL
Nomenclature K N NI,N2 n t o It
~app O"1,O"2
Consistency index ( N / m2 / s ~ ) Number of viscosity data points Number of data points of viscosity data set-I and viscosity data set-2, respecuvely Flow behavior index Calculated and tabulated values of t-test Arithmetic mean values of viscosity data set-1 and viscosity data set-2, respecuvely Apparent viscosity (N s / m 2) Shear rate (s L) Standard deviations of wscoslty data set-l and viscosity data set-2, respectively Shear stress ( N / m 2)
rheological behavior of the non-Newtoman emulsions.
Experimental Saudi crude oil emulsions were generally prepared by measuring the four constituents: brine, emulsifier, crude oil and hydrochloric acid into a flask and stirring. The Saudi crude oils used in this study were heavy ( 18.9 API ), m e d m m (25.1 API), light (33.7 API) and extra-hght (51.1 API). The percentage volumes of the dispersed oil phase in emulsions were selected to be 30, 40, 50, 60, 70, 80 and 90. The concentration of NaC1 in brine was fixed at 15 wt%, which is the average salinity of Saudi formation waters. Although many kinds of emulsifying agents were used to prepare crude oil emulsions, a commonly used one is Triton X-100 (Camy et al., 1975). The emulsifier concentration was 0.50 wt%. To dissolve the inorganic materials present in the crude oils, 2 vol% HC1 (36% concentration) was added to the prepared emulsions. Before measuring the rheological characteristics of the emulsions, a test of emulsion stabihty was conducted. The emulsions described in this study exhibited no phase separation when stored over a period of days in an airtight container. Twenty-eight samples of Saudi crude od emulsions were prepared, and their rheological characteristics were measured with a
Brookfield Synchro-Lectnc Vlscometer (Model LVT 70590, speed settings were 0.3, 0.6, 1.5, 3, 6, 12, 30 and 60 tom) at temperatures of 10 °, 20 °, 30 ° and 40 ° C.
Results and discussion
The rheological characteristics of the emulsions measured at temperatures of 10 °, 20 °, 30 ° and 40 oC were plotted in Figs. 1-16. These data were correlated with Newton's law of viscosity (Govier and Aziz, 1982) to be classified into Newtonian and non-Newtonian flmds, as shown in Table 1. The non-Newton1an data were statistically treated using the ttest (Volk, 1969; Parson, 1978 ) to investigate the effects of both temperature and concentration of the dispersed oil phase on the rheologlcal behavior of the emulsions. The t-test is usually carried out to decide whether or not a statistical d~fference between two set of data exists. This can be done by calculating (tc) from the following equation (Volk, 1969 ):
to= IXl -.¢21/{ [a2( N, - 1 ) + G 2 ( N 2 - 1 ) ] × >((N~+N2)/[N,
N2(NI+N:-2)]}
°5
(1)
where the arithmetic mean value (X) and the standard deviation (a) of any viscosity data are given by: TABLE 1 Classification of the experimental data into Newtonlan and Non-Newtonian behavior Type of Crude Oii
Oll Concentration ( vol% ) 30-70
Heavy Medmm
80
Non-Newtoman Newtoman Newtonlan Non-Newtoman Non-Newtoman Non-Newtondl
Light Extralight
90
lan
I-= 10cC Non-Newtoman Non-Newtonian Newtoman Non-Newtoman Non-Newtoman Non-Newtonlan
RHEOLOGICAL CHARACTERISTICS OF SAUD1CRUDE OIL EMULSIONS 10000 Oil 09 •
g g
08
•
1000
07 06
05
•
>
04 03
A
@ ca
100
<
10
. . . . . . . .
|
. . . . . . . .
i
1
. . . . . . . .
lO
i
. . . . . . . .
lOO
lOOO
S h e a r Rate, ,=-1
Fig 1. R h e o l o g l c a l c h a r a c t e r i s t i c s o f S a u & h e a v y c r u d e o l l e m u ] s l o n s a t IO°C. 1000 Oil
"
I-".-.le---.e.~
o
-
o
---I="--
09
¢
08
[]
07
•
05 04
•
03
_
m¢~==~;:l~,,,,,~
100
~ ~
n
I0
........
,
........
1
,
lO
lOO
lOOO
S h e a r Rate, s -1
Fig. 2 Rheolog~cal c h a r a c t e n s t l c s o f Saudi heavy crude oll emulsions at 20°C. 1000 0,1 Q,
u ~, m
m
~
g ~'
~
---B'--
100
09
s
08
-'me---
07
.--e---
06
•
~
05 04
,L
03
Q.
<
10
........
,
1
........
,
........
10
,
1 O0
........
1000
S h e a r Rate, s 1
Fig. 3. Rheological c h a r a c t e n s t l c s o f Saudi h e a v y crude oll emulsions at 30 ° C.
151
152
A E OMAR ET A:
1000 Oil 09 o
08
>,
07 06
o :>
05 IO0 04 03
10
........
,
........
1
,
........
10
,
........
100
1000
Shear Rate, s
Fig_ 4. R h e o l o g l c a l c h a r a c t e n s t t c s o f S a u d l h e a v y c r u d e oil e m u l s i o n s at 40 ° C 1000 Oil ~
09
•
08
[]
07
w
•
06
o
•
05
•
04 03
Im
100
~
~
P <
10
........
i
i
........
........
i
........
100
10
1
1000
Shear Rate, s- t
Ftg 5 Rheolog~cal c h a r a c t e n s t t c s o f S a u d l m e d m m c r u d e o d e m u l s i o n s at 10 ° C 1000
Oil 09
o
•
08
[]
07
•~
06
[]
05
100
04 ,I,
03
c
Q.
10
........
i 1
........
i 10
........
i 1 O0
....... 1000
Shear Rate, s '
Fig 6 R h e o l o g l c a l c h a r a c t e n s U c s o f S a u d ] m e d m m c r u d e o l l e m u l s l o n s a t 2 0 ° C
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS 1000 Oil 09 08
• 0
07
g
~
06
o
05
•
== 10o
.~
~
04 03
A
10
. . . . . . . .
l
. . . . . . . .
1
i
. . . . . . . .
i
10 Shear Rate, s -1
. . . . . . . .
100
1000
Fig. 7 Rheological characteristics of Saudi medmm crude oil emulsions at 30°C. 1000 Oil o.
~
o
~
~
09 =
08
~
100
07
o
----e---
N
--
06 05 04
•.
~.
03
lO
1
.
.
.
.
.
.
.
.
i
.
.
.
.
.
.
.
1
.
t
.
.
.
.
.
.
.
10
.
i
.
.
.
.
.
.
.
100
.
1000
Sheer Rate, s-1
Fig. 8. Rheo]oglca] charactenstlcs of Saudl medzum crude off emulsions at 40 ° C 1000
Oil O9
o.
8
08
U
07
~
06
D......~_
U
•~
~
_
-
100
.~ .o
--
05 04
A
03
~ ~
_
i 10
. . . . . . . .
i
1
. . . . . . . .
i
. . . . . . . .
10
i
100
. . . . . . . .
1000
Shear Rate, s-~
Fig. 9 R h e o l o g i c a l c h a r a c t e r i s t i c s o f S a u d i light c r u d e oll e m u l s i o n s at 1 0 ° C .
15 3
154
AE OMAR ETA
1000 Oil ~
09
D,, o 100 U
>
•
08
•
07
1~
06
•
05
~
04 03
A
c
10 ,<
. . . . . . . .
i
.
.
.
.
.
.
.
1
i
. . . . . . . .
10
i
. . . . . . . .
100
IOO0
S h e a r Rate, s
Fig. 10 Rheologlcal charactenstlcs of Saudl light crude oil emulsions at 20°C 1000 011
O9 ta. o 07 :p.,
100 '
06
o
•
O5
04 03
{=
ol
10 ¸
Q. Q. <
. . . . . . . .
i
. . . . . . . .
1
i
. . . . . . . .
10
i
. . . . . . . .
1 O0
1000
S h e a r Rate, s-
Fig 11. Rheologacal charactenstms of Saud~ light crude oll emulsions at 30 ° C. 1000 011
" U ~ =
~
08 07 100
06
>
m
=
05
------o-----
04
,t,
03
10
. . . . . . . .
i
1
. . . . . . . .
i
. . . . . . . .
10
!
100
. . . . . . . .
1000
S h e a r Rate, s
Fig. 12. Rheologlcal characteristics of Saudi light crude oil emulsions at 40 ° C.
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS 1000
0,1 09 08
I;3,, t~
07 >' 100
06 05
U al
04 03
¢=
IO a
.
.
.
.
.
.
.
.
I
.
.
.
.
.
.
.
.
I
1
.
.
.
.
.
.
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10
I
.
.
.
.
.
.
.
.
100
1000
Shear Rate, s -~
Fig. 13. Rheologlcal characteristics of Saudl extra-light crude oil emulsions at 10 ° C. 1000
o,, ]
~.~ m m O
• ~
%.\
100
g
09
/
0,
i
07
I
--.-oo I
m
-~..~_.
~
o~ I
.= 10 D.
. . . . . . . .
!
. . . . . . . .
..... ~
I
. . . . . . . .
10 ~0
.......
Shear Rate,
I
100 . . . . . ~0o
......
,1000
s -1
Fig. 14. Rheologdcal glcal charactenstlcs of o f Saudi extra-hi extra-hghtt cr crude J o l l emulsions at 20 ° C. 1000 O,I 09
% -~ ""
1 /
,
0~ /
.
07
/
o/
I00,
05
•
04
.= ~.
10-:
.
.
.
.
.
.
.
.
,
1
.
.
.
.
.
.
.
.
|
.
.
.
10
.
.
.
.
.
!
100
.
.
.
.
.
.
.
.
1000
Shear Rate, s-1
F]g 15. RheologlcalcharactenstlcsofSaudiextra-hght crude oll emulsions at 30oc.
155
A E OMARETAL
156 1000 Oil 09 8
08 07
100
06
o
• ~> t.Q.
05 04
~,
03
10
........
!
........
1
i
........
10
i
........
100
1000
Shear Rate, s
F~g 16 Rheologlcal characteristics of Saudl extra-hght crude od emulsions at 40 ° C.
X = ~ (~'~app)/ t=l
(2)
II measured at a certain oil concentration were not statistically different.
Heavy crude oil emulswns
To compare between two sets of viscosity data measured at two different temperatures or oil concentrations, the values of (XI) and (al) for the first data set and (Xz) and (az) for the second one are calculated from Eqs. 2 and 3, and are then used to determine (to) from Eq. 1. The value of (to) was then compared with the value of (t,) which was determined from statistical tables (Volk, 1969). If the value of (tc) was less than or equal to (tt), the two sets of data were not statistically different.
Effect of temperature The data o f heavy, medium, light and extralight crude oil emulsions given in Figs. 1-16 were used to calculate the values of (to). The values of (&) were then compared with the corresponding values of (tt) which were determined from the statistical Tables (Volk, 1969 ). The results are given in Table 2, which shows that two statistically different groups resulted. The viscosity data of either Group I or Group
Results of the t-test of heavy crude oil emulsions listed in Table 2 clearly indicate that the rheological characteristics of the 30% oil concentration emulsion were not statistically different at all test temperatures. This means that the variation of temperature (from 10 ° to 40 °C) did not affect the rheological behavior of the emulsion having 30% oil concentration. For oil concentrations varying from 40 to 60%, the effect of temperature became significant to the extent that the rheological characteristics measured at 10 ° and 20°C (Group I) were statistically different from those measured at 30 ° and 40°C (Group II). It was also found that the rheolog~cal characteristics of the emulsion with 70% oil concentration emulsion measured at 10 °C were statistically different from those measured at 20 °, 30 ° and 40oc
Medtum crude otl emulstons Results of the t-test of the emulsions listed in Table 2 show that, at 30, 50 and 90% oil concentrations, the change in temperature from 10 ° to 40 °C did not affect the rheological behavior of the m e d i u m crude oil emul-
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS
157
TABLE 2 Effect o f temperature on rheolog~cal behavtor o f crude oil emulsions O11 concentratlon (vol%) 30 40 50
Heavy
Medium
Group I
Tlo,/'2o Tlo, T20
G r o u p II NSDE* Tat~ T40
Group I ~ TI o, T20
T30,T40
Light G r o u p II
Extra-light
Group I
NSDE T30, T40 NSDE
Group II NSDE-NSDE--
G r o u p II
~ N S D E ~ N S D E - - - N S D E - -
~o
Tip, T2o,
Group I
T3o 60
Tt o, 7"2o
T30, 7"4o
Tlo
T20, Tao,
~ N S D E
--NSDE
- - N S D E
~ N S D E
T4o 70
Tlo
T20, T30
Tlo, T20
T30, 7"4o
T~o
Newtoman
/'40 80
~
90
--Newtonian
Newtoman - - -
~
NSDE - -
NSDE ~ --.Newtonian
Tip --
T~o
~o, ~o, ~o ~o,~o, ~o
*NSDE = N o statistical difference exists at all test temperatures. Tx= Data measured at x ° C
sions. At 40 and 70% oil concentrations, the rheological characteristics measured at 10 ° and 20°C (Group I) were statistically different from those measured at 30 ° and 40 °C (Group II ). It was also found that the variation in temperature (from 20 ° to 40°C) did not affect the rheological behavior of the emulsion having 60% oil concentration, whereas, for an oil concentration of 80%, the emulsion exhibited Newtonian behavior.
Light crude oil emulsions Light crude oil emulsions exhibited nonNewtonian behavior at oil concentrations of 30, 40, 50, 60, 70 and 80%. There had been an inversion from oil-in-water to water-in-oil emulsion, however, at an oil concentration of about 50%. The rheological characteristics of the light crude oil emulsions were not statistically different at the test temperatures.
Extra-light crude otl emulsions Although extra-light crude oil emulsions exhibited non-Newtonian behavior at all concentrations of the dispersed oil phase, the change in temperature only affected their rheological characteristics at oil concentra-
tions of 80 and 90%. This is expected, because the extra-light crude oil contains a high relative amounts of wax.
Effect of od concentration The t-test was carried out for the data of heavy, medium, light and extra-light crude oil emulsions to investigate the effect of the dispersed oil phase concentration on their rheological characteristics. The results are given in Table 3, which shows the following generalizations: (a) For heavy oil emulsions, no statistical difference existed between the measured data (Group I or Group II) for oil concentrations of 40 and 50% as well as the 60 and 70%. (b) For m e d i u m oil emulsions, the measured data for the emulsions having 60, 70 and 80% oil concentration (Group I ) as well as the 60 and 70% concentrations (Group II) were not statistically different. It was also observed that no statistical difference existed between the measured data for the emulsions having 40 and 50% oil concentration emulsions. (c) For light oil emulsions, no statistical difference existed between the measured data
AE OMARETAL
158 TABLE 3 Effect of oil concen tration rheolog~cal on behavior of crude oli emulsions Combination data under comparison
Type of crude oil Heavy
Medium
Group I 30"&40 30&50 30&60 30&70 30&80 30&90 40&50 40&60 40&70 40&80 40&90 50&60 50&70 50&80 50&90 60&70 6 0 & 80 6 0 & 90 70&80 70& 90 80&90
G r o u p II
SDE** SDE SDE SDE NSDE*** SDE SDE SDE SDE NSDE -
Light
Group I
G r o u p II
SDE SDE SDE SDE SDE SDE NSDE SDE SDE SDE SDE NSDE SDE SDE SDE NSDE NSDE SDE NSDE SDE SDE
SDE SDE SDE SDE SDE NSDE SDE SDE SDE NSDE SDE SDE NSDE SDE SDE -
Group I
Extra-hght G r o u p II
Group I
SDE SDE SDE SDE NSDE SDE NSDE SDE NSDE NSDE SDE NSDE SDE SDE -
G r o u p 1I SDE SDE SDE SDE NSDE NSDE NSDE SDE SDE SDE SDE SDE SDE SDE SDE NSDE SDE SDE SDE SDE NSDE
*30 = The measured data of 30% (by v o l u m e ) oll concentration emulsion **SDE = Statistical difference exists ***NSDE = N o statistical &fference exists - = No combination b e t w e e n the t w o sets o f data since one of them is N e w l o m a n TABLE4 G r o u p s of n o n - N e w t o m a n emulsions data Data group
Heavy oil (% concentration )
1 2 3 4 5 6
30 40 40 60 60
and and and and
50 50 70 70
(Group (Group (Group (Group
1) II ) I) II )
M e d i u m oil (% concentration)
Light oll (% concentration)
Extra-light oll (% concentration)
30 40 40 60 60 90
30 50 ( G r o u p I) a n d 4 0 50 ( G r o u p II ) 60 and 70 80
80 40 60 80
( G r o u p ll) ( G r o u p I) and 50 and 70 ( G r o u p II ) and 70 ( G r o u p I) and 80
for the emulsions having 50% oil concentration (Group I) and the data for the emulsions having 40, 60 and 70% concentration. It was also observed that, the measured data for the emulsion having 70% oil concentration were not statistically different from the data of the
and and and and
90 ( G r o u p I I ) and 30 50 70 90 ( G r o u p I )
emulsions having 40 and 60% concentrations. (d) For extra-light emulsions, no statistical difference existed between the measured data (Group I or Group II) of the 30, 80 and 90% oll concentration emulsions. It was also noticed that the measured data of the emulsions
RHEOLOGICALCHARACTERISTICSOF SAUDICRUDEOIL EMULSIONS
159
TABLE 5 The values of K and n for the fitted rheological models Data group
1 2 3 4 5 6
Medium
Heavy
Light
Extra-hght
K ( N / m 2 / s -n)
n
K (N/m2/s -")
n
K ( N / m 2 / s -n)
n
K (N/m2/s -")
n
0.048 0270 0 061 0 433 0 125 -
0 735 0808 0 741 0 910 0 885
0 273 0015 0 060 0.032 0.067 0.277
0 3069 0.944 0.866 0.878 0 925 0.329
0.138 0.036 0.016 0.039 0.154
0.418 0.737 0.873 0 866 0232
0010 0.097 0.054 0 024 -
0.828 0.355 0 582 0 882 -
having 40 and 50% oil concentration, as well as the data of the emulsions with 60 and 70% concentration were not statistically different. E m u l s io n s correlation
The use of Richardson equation (Richardson, 1958 ) in correlating the measured viscosity to shear rate and temperature resulted in twenty-eight empirical equations. Statistical analysis was used to group the non-Newtonian data which are not statistically different. Resuits presented in Tables 2 and 3 were used to prepare Table 4. This table shows that the number of groups of heavy, medium, light and extra-light crude oils data were equal to 5, 6, 5, and 4, respectively. Thus, the total number of the rheological models, which fit the data of these groups, is equal to twenty. In as much as these data demonstrated pseudoplastic behaviour at the test conditions, they can be correlated with the so-called power-law model (Govier and Aziz, 1982): z=K# n
(4)
The values of the consistency index (K) and the flow behavior index (n) for the twenty rheological models were calculated and the resuits are given in Table 5.
Conclusions Based upon the experimental observations and statistical analysis of the results, the fol-
lowing conclusions were formulated. ( 1 ) Saudi heavy crude oil emulsions exhibited Newtonian behavior at 80 and 90% oil concentrations, whereas emulsions of medium crude oil exhibited such behavior only at 80% oil concentration and test temperatures greater than 10°C. Light crude oil emulsions exhibited similar behavior at 90% oil concentration. ( 2 ) The variation of temperature (from 10 ° to 40 oC ) did not affect the rheological behavior of heavy crude oil emulsion having 30% oil concentration, and the medium crude oil emulsions having 30, 50 and 90% oil concentrations. (3) The rheological behavior of the light crude emulsion (50% oil concentration) and extra-light crude emulsion (80 and 90% oil concentrations) varied with temperature. (4) The concentration of the dispersed oil phase was strongly affecting the rheological behavior of Saudi crude oil emulsions to the extent that, 50 out of 67 possible combinations of the data under comparison were statistically different. (5) The non-Newtonian emulsions exhibited pseudoplastic behavior and their characteristics were correlated with power-law.
Acknowledgements The critical review of the manuscript by Prof. Dr. S.S. Marsden is greatly appreciated.
160
References Alvarado, D_A and Marsden, S.S, 1979 Flow of oil-mwater emulsions through tubes and porous media. Soc Pet. Eng. J , 19(6). 369-376. Camy, J P , Marsden, S.S, Hung, J E., Anhara, N , Casse, F,J, Alvarado, D A , Mandel, L , Mobarak, S., Gonzales, H.O., Mao, M L., Samamego, F , Romero, R~vera, E J and Marius, C.G., 1975 The rheology of crude oil dispersions Proc. Int Symp. Oil Field Chemistry_ Soc Pet Eng., Pap 5299: 51-66_ Chllinganan, G.V_ and Vorabutr, P., 1981. Drilling and Drilhng Fluids. Developments in Petroleum Science, 11 Elsevier, Amsterdam, 767pp. Flock, D.L_ and Stelnborn, R , 1982. The rheology of heavy crude oils and their emulsions Annu. Tech Meet. Pet Soc. CIM, Pap. 82-33-60 246-251_ Gogarty, W B., 1967. Rheological properties of pseudoplastic fluids m porous media. Soc. Pet Eng. J., 7(2) 149-159.
A E OMAR ET AL
Govler, G W. and A z I z , K , 1982 The Flow of Complex Mixtures in Pipes. Van Nostrand Reinhold, New York, N Y , 792 pp_ Marsden, S S, Jr and Raghavan, R , 1973 A system for proceeding and transporting crude oil as an oil/water emulsion. Inst Pet., 59(570) 273-278_ Marsden, S S and Chlllngarlan, G V., 1978. New methods of petroleum transportation. Energy Sources, 3 ( 3/ 4): 389-394_ Parsons, R , 1978 Statistical Analysis, 2nd ed Harper and Row, New York, N.Y, 456 pp Richardson, E.G, 1958_ The flow of emulsions. J Colloid Scl, 8 367-373 Simon, R and Poynter, W . G , 1968. Downhole emulsification for improving vtscous crude production J. Pet. Technol., 20(6) 1349-1353. Volk, W., 1969. Applied Statistics for Engineers, 2nd ed. McGraw-Hill, New York, N Y_, 362 pp. Wyslouzd, B E and Kesslck, M.A, 1987. Pipeline flow behavlour of heavy crude oil emulsions. Can J. Chem Eng., 65(3) 353-360
149
Elsevier Science Publishers B.V., Amsterdam
Rheological characteristics of Saudi crude oil emulsions A.E. Omar, S.M. Desouky and B. Karama Kzng Saud Umverstty Collegeof Engmeermg, P 0 Box 800, Rtyadh 11421, Saudt Arabta (Received February 20, 1990; accepted after revision November 20, 1990)
ABSTRACT Omar, A.E, Desouky, S.M. and Karama, B., 1991 Rheologlcal characteristics of Saudl crude oll emulsions J_ Pet Set. Eng., 6 149-160 Rheologtcal charactensttcs of Saudl crude oli emulsions were measured with a Brookfield wscometer at temperatures of 10 °, 20 °, 30 ° and 40°C. The Saudl field crude oils used m the present study were: heavy, medium, light and extrahght. The emulsion consntuents were crude od, brine, emulsifier (Triton X- 100) and dilute hydrochloric acid. The measured data were first classxfied into two groups for Newtonian and non-Newtonian fluids. The results showed that the non-Newtoman emulsions exhibit pseudoplast~c behavior and their rheolog~cal characteristics can be described by the power-law model. Then, the effect of dispersed phase (oil) concentration and temperature on the rheologlcal behavior of the emulsions were thoroughly investigated using statistical analysis (t-test)_
Introduction The study of the rheological characteristics of crude oil emulsions has received attention in petroleum research laboratories during the past twenty years. The development of new methods of secondary recovery and the potential application of crude oil transportation through pipelines as stable emulsions have leaded to a number of research works dealing with emulsions (Gogarty, 1967; Simon and Poynter, 1968; Marsden and Raghavan, 1973 ). There are two types of crude oil emulsions: oilin-water ( o / w ) and water-in-oil ( w / o ) . The latter is the form of the most produced crude oils of the world and is usually more viscous than either of its constituents. Carny et al. ( 1975 ), Alvarado and Marsden (1979), Flock and Steinborn (1982) and Wyslouzil and Kessick (1987) have studied the rheological behavior of different crude oil emulsions and have concluded that, whereas many of these behave like Newtonian fluids, 0920-4105/91/$03.50
some show definite non-Newtonian properties. Of the latter most are pseudoplastic, a few are dilatant, many are thixotropic, and a few are rheopectic. The main reasons for this wide variation of emulsion types are the emulsion's composition and conditions under which each type exists and flows. These investigators have suggested several correlations relating the emulsion viscosity to the dispersed phase concentration or shear rate, using either the Richardson equation or the power-law model (Govier and Aziz, 1982 ). In as much as the rheological characteristics of Saudi crude oil emulsions vary with temperature a n d / o r dispersed phase concentration, a method for checking this variation is needed which is capable of producing a general rheological correlation. A suitable way to ensure this is by using a statistical analysis method such as the t-test (Volk, 1969; Parsons, 1978 ). This method was used to investigate the effect of both the dispersed phase (oil) concentration and the t e m p e r a t u r e - o n the
© 1991 Elsevier Science Publishers B V All fights reserved
150
AE OMARETAL
Nomenclature K N NI,N2 n t o It
~app O"1,O"2
Consistency index ( N / m2 / s ~ ) Number of viscosity data points Number of data points of viscosity data set-I and viscosity data set-2, respecuvely Flow behavior index Calculated and tabulated values of t-test Arithmetic mean values of viscosity data set-1 and viscosity data set-2, respecuvely Apparent viscosity (N s / m 2) Shear rate (s L) Standard deviations of wscoslty data set-l and viscosity data set-2, respectively Shear stress ( N / m 2)
rheological behavior of the non-Newtoman emulsions.
Experimental Saudi crude oil emulsions were generally prepared by measuring the four constituents: brine, emulsifier, crude oil and hydrochloric acid into a flask and stirring. The Saudi crude oils used in this study were heavy ( 18.9 API ), m e d m m (25.1 API), light (33.7 API) and extra-hght (51.1 API). The percentage volumes of the dispersed oil phase in emulsions were selected to be 30, 40, 50, 60, 70, 80 and 90. The concentration of NaC1 in brine was fixed at 15 wt%, which is the average salinity of Saudi formation waters. Although many kinds of emulsifying agents were used to prepare crude oil emulsions, a commonly used one is Triton X-100 (Camy et al., 1975). The emulsifier concentration was 0.50 wt%. To dissolve the inorganic materials present in the crude oils, 2 vol% HC1 (36% concentration) was added to the prepared emulsions. Before measuring the rheological characteristics of the emulsions, a test of emulsion stabihty was conducted. The emulsions described in this study exhibited no phase separation when stored over a period of days in an airtight container. Twenty-eight samples of Saudi crude od emulsions were prepared, and their rheological characteristics were measured with a
Brookfield Synchro-Lectnc Vlscometer (Model LVT 70590, speed settings were 0.3, 0.6, 1.5, 3, 6, 12, 30 and 60 tom) at temperatures of 10 °, 20 °, 30 ° and 40 ° C.
Results and discussion
The rheological characteristics of the emulsions measured at temperatures of 10 °, 20 °, 30 ° and 40 oC were plotted in Figs. 1-16. These data were correlated with Newton's law of viscosity (Govier and Aziz, 1982) to be classified into Newtonian and non-Newtonian flmds, as shown in Table 1. The non-Newton1an data were statistically treated using the ttest (Volk, 1969; Parson, 1978 ) to investigate the effects of both temperature and concentration of the dispersed oil phase on the rheologlcal behavior of the emulsions. The t-test is usually carried out to decide whether or not a statistical d~fference between two set of data exists. This can be done by calculating (tc) from the following equation (Volk, 1969 ):
to= IXl -.¢21/{ [a2( N, - 1 ) + G 2 ( N 2 - 1 ) ] × >((N~+N2)/[N,
N2(NI+N:-2)]}
°5
(1)
where the arithmetic mean value (X) and the standard deviation (a) of any viscosity data are given by: TABLE 1 Classification of the experimental data into Newtonlan and Non-Newtonian behavior Type of Crude Oii
Oll Concentration ( vol% ) 30-70
Heavy Medmm
80
Non-Newtoman Newtoman Newtonlan Non-Newtoman Non-Newtoman Non-Newtondl
Light Extralight
90
lan
I-= 10cC Non-Newtoman Non-Newtonian Newtoman Non-Newtoman Non-Newtoman Non-Newtonlan
RHEOLOGICAL CHARACTERISTICS OF SAUD1CRUDE OIL EMULSIONS 10000 Oil 09 •
g g
08
•
1000
07 06
05
•
>
04 03
A
@ ca
100
<
10
. . . . . . . .
|
. . . . . . . .
i
1
. . . . . . . .
lO
i
. . . . . . . .
lOO
lOOO
S h e a r Rate, ,=-1
Fig 1. R h e o l o g l c a l c h a r a c t e r i s t i c s o f S a u & h e a v y c r u d e o l l e m u ] s l o n s a t IO°C. 1000 Oil
"
I-".-.le---.e.~
o
-
o
---I="--
09
¢
08
[]
07
•
05 04
•
03
_
m¢~==~;:l~,,,,,~
100
~ ~
n
I0
........
,
........
1
,
lO
lOO
lOOO
S h e a r Rate, s -1
Fig. 2 Rheolog~cal c h a r a c t e n s t l c s o f Saudi heavy crude oll emulsions at 20°C. 1000 0,1 Q,
u ~, m
m
~
g ~'
~
---B'--
100
09
s
08
-'me---
07
.--e---
06
•
~
05 04
,L
03
Q.
<
10
........
,
1
........
,
........
10
,
1 O0
........
1000
S h e a r Rate, s 1
Fig. 3. Rheological c h a r a c t e n s t l c s o f Saudi h e a v y crude oll emulsions at 30 ° C.
151
152
A E OMAR ET A:
1000 Oil 09 o
08
>,
07 06
o :>
05 IO0 04 03
10
........
,
........
1
,
........
10
,
........
100
1000
Shear Rate, s
Fig_ 4. R h e o l o g l c a l c h a r a c t e n s t t c s o f S a u d l h e a v y c r u d e oil e m u l s i o n s at 40 ° C 1000 Oil ~
09
•
08
[]
07
w
•
06
o
•
05
•
04 03
Im
100
~
~
P <
10
........
i
i
........
........
i
........
100
10
1
1000
Shear Rate, s- t
Ftg 5 Rheolog~cal c h a r a c t e n s t t c s o f S a u d l m e d m m c r u d e o d e m u l s i o n s at 10 ° C 1000
Oil 09
o
•
08
[]
07
•~
06
[]
05
100
04 ,I,
03
c
Q.
10
........
i 1
........
i 10
........
i 1 O0
....... 1000
Shear Rate, s '
Fig 6 R h e o l o g l c a l c h a r a c t e n s U c s o f S a u d ] m e d m m c r u d e o l l e m u l s l o n s a t 2 0 ° C
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS 1000 Oil 09 08
• 0
07
g
~
06
o
05
•
== 10o
.~
~
04 03
A
10
. . . . . . . .
l
. . . . . . . .
1
i
. . . . . . . .
i
10 Shear Rate, s -1
. . . . . . . .
100
1000
Fig. 7 Rheological characteristics of Saudi medmm crude oil emulsions at 30°C. 1000 Oil o.
~
o
~
~
09 =
08
~
100
07
o
----e---
N
--
06 05 04
•.
~.
03
lO
1
.
.
.
.
.
.
.
.
i
.
.
.
.
.
.
.
1
.
t
.
.
.
.
.
.
.
10
.
i
.
.
.
.
.
.
.
100
.
1000
Sheer Rate, s-1
Fig. 8. Rheo]oglca] charactenstlcs of Saudl medzum crude off emulsions at 40 ° C 1000
Oil O9
o.
8
08
U
07
~
06
D......~_
U
•~
~
_
-
100
.~ .o
--
05 04
A
03
~ ~
_
i 10
. . . . . . . .
i
1
. . . . . . . .
i
. . . . . . . .
10
i
100
. . . . . . . .
1000
Shear Rate, s-~
Fig. 9 R h e o l o g i c a l c h a r a c t e r i s t i c s o f S a u d i light c r u d e oll e m u l s i o n s at 1 0 ° C .
15 3
154
AE OMAR ETA
1000 Oil ~
09
D,, o 100 U
>
•
08
•
07
1~
06
•
05
~
04 03
A
c
10 ,<
. . . . . . . .
i
.
.
.
.
.
.
.
1
i
. . . . . . . .
10
i
. . . . . . . .
100
IOO0
S h e a r Rate, s
Fig. 10 Rheologlcal charactenstlcs of Saudl light crude oil emulsions at 20°C 1000 011
O9 ta. o 07 :p.,
100 '
06
o
•
O5
04 03
{=
ol
10 ¸
Q. Q. <
. . . . . . . .
i
. . . . . . . .
1
i
. . . . . . . .
10
i
. . . . . . . .
1 O0
1000
S h e a r Rate, s-
Fig 11. Rheologacal charactenstms of Saud~ light crude oll emulsions at 30 ° C. 1000 011
" U ~ =
~
08 07 100
06
>
m
=
05
------o-----
04
,t,
03
10
. . . . . . . .
i
1
. . . . . . . .
i
. . . . . . . .
10
!
100
. . . . . . . .
1000
S h e a r Rate, s
Fig. 12. Rheologlcal characteristics of Saudi light crude oil emulsions at 40 ° C.
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS 1000
0,1 09 08
I;3,, t~
07 >' 100
06 05
U al
04 03
¢=
IO a
.
.
.
.
.
.
.
.
I
.
.
.
.
.
.
.
.
I
1
.
.
.
.
.
.
.
.
10
I
.
.
.
.
.
.
.
.
100
1000
Shear Rate, s -~
Fig. 13. Rheologlcal characteristics of Saudl extra-light crude oil emulsions at 10 ° C. 1000
o,, ]
~.~ m m O
• ~
%.\
100
g
09
/
0,
i
07
I
--.-oo I
m
-~..~_.
~
o~ I
.= 10 D.
. . . . . . . .
!
. . . . . . . .
..... ~
I
. . . . . . . .
10 ~0
.......
Shear Rate,
I
100 . . . . . ~0o
......
,1000
s -1
Fig. 14. Rheologdcal glcal charactenstlcs of o f Saudi extra-hi extra-hghtt cr crude J o l l emulsions at 20 ° C. 1000 O,I 09
% -~ ""
1 /
,
0~ /
.
07
/
o/
I00,
05
•
04
.= ~.
10-:
.
.
.
.
.
.
.
.
,
1
.
.
.
.
.
.
.
.
|
.
.
.
10
.
.
.
.
.
!
100
.
.
.
.
.
.
.
.
1000
Shear Rate, s-1
F]g 15. RheologlcalcharactenstlcsofSaudiextra-hght crude oll emulsions at 30oc.
155
A E OMARETAL
156 1000 Oil 09 8
08 07
100
06
o
• ~> t.Q.
05 04
~,
03
10
........
!
........
1
i
........
10
i
........
100
1000
Shear Rate, s
F~g 16 Rheologlcal characteristics of Saudl extra-hght crude od emulsions at 40 ° C.
X = ~ (~'~app)/ t=l
(2)
II measured at a certain oil concentration were not statistically different.
Heavy crude oil emulswns
To compare between two sets of viscosity data measured at two different temperatures or oil concentrations, the values of (XI) and (al) for the first data set and (Xz) and (az) for the second one are calculated from Eqs. 2 and 3, and are then used to determine (to) from Eq. 1. The value of (to) was then compared with the value of (t,) which was determined from statistical tables (Volk, 1969). If the value of (tc) was less than or equal to (tt), the two sets of data were not statistically different.
Effect of temperature The data o f heavy, medium, light and extralight crude oil emulsions given in Figs. 1-16 were used to calculate the values of (to). The values of (&) were then compared with the corresponding values of (tt) which were determined from the statistical Tables (Volk, 1969 ). The results are given in Table 2, which shows that two statistically different groups resulted. The viscosity data of either Group I or Group
Results of the t-test of heavy crude oil emulsions listed in Table 2 clearly indicate that the rheological characteristics of the 30% oil concentration emulsion were not statistically different at all test temperatures. This means that the variation of temperature (from 10 ° to 40 °C) did not affect the rheological behavior of the emulsion having 30% oil concentration. For oil concentrations varying from 40 to 60%, the effect of temperature became significant to the extent that the rheological characteristics measured at 10 ° and 20°C (Group I) were statistically different from those measured at 30 ° and 40°C (Group II). It was also found that the rheolog~cal characteristics of the emulsion with 70% oil concentration emulsion measured at 10 °C were statistically different from those measured at 20 °, 30 ° and 40oc
Medtum crude otl emulstons Results of the t-test of the emulsions listed in Table 2 show that, at 30, 50 and 90% oil concentrations, the change in temperature from 10 ° to 40 °C did not affect the rheological behavior of the m e d i u m crude oil emul-
RHEOLOGICAL CHARACTERISTICS OF SAUDI CRUDE OIL EMULSIONS
157
TABLE 2 Effect o f temperature on rheolog~cal behavtor o f crude oil emulsions O11 concentratlon (vol%) 30 40 50
Heavy
Medium
Group I
Tlo,/'2o Tlo, T20
G r o u p II NSDE* Tat~ T40
Group I ~ TI o, T20
T30,T40
Light G r o u p II
Extra-light
Group I
NSDE T30, T40 NSDE
Group II NSDE-NSDE--
G r o u p II
~ N S D E ~ N S D E - - - N S D E - -
~o
Tip, T2o,
Group I
T3o 60
Tt o, 7"2o
T30, 7"4o
Tlo
T20, Tao,
~ N S D E
--NSDE
- - N S D E
~ N S D E
T4o 70
Tlo
T20, T30
Tlo, T20
T30, 7"4o
T~o
Newtoman
/'40 80
~
90
--Newtonian
Newtoman - - -
~
NSDE - -
NSDE ~ --.Newtonian
Tip --
T~o
~o, ~o, ~o ~o,~o, ~o
*NSDE = N o statistical difference exists at all test temperatures. Tx= Data measured at x ° C
sions. At 40 and 70% oil concentrations, the rheological characteristics measured at 10 ° and 20°C (Group I) were statistically different from those measured at 30 ° and 40 °C (Group II ). It was also found that the variation in temperature (from 20 ° to 40°C) did not affect the rheological behavior of the emulsion having 60% oil concentration, whereas, for an oil concentration of 80%, the emulsion exhibited Newtonian behavior.
Light crude oil emulsions Light crude oil emulsions exhibited nonNewtonian behavior at oil concentrations of 30, 40, 50, 60, 70 and 80%. There had been an inversion from oil-in-water to water-in-oil emulsion, however, at an oil concentration of about 50%. The rheological characteristics of the light crude oil emulsions were not statistically different at the test temperatures.
Extra-light crude otl emulsions Although extra-light crude oil emulsions exhibited non-Newtonian behavior at all concentrations of the dispersed oil phase, the change in temperature only affected their rheological characteristics at oil concentra-
tions of 80 and 90%. This is expected, because the extra-light crude oil contains a high relative amounts of wax.
Effect of od concentration The t-test was carried out for the data of heavy, medium, light and extra-light crude oil emulsions to investigate the effect of the dispersed oil phase concentration on their rheological characteristics. The results are given in Table 3, which shows the following generalizations: (a) For heavy oil emulsions, no statistical difference existed between the measured data (Group I or Group II) for oil concentrations of 40 and 50% as well as the 60 and 70%. (b) For m e d i u m oil emulsions, the measured data for the emulsions having 60, 70 and 80% oil concentration (Group I ) as well as the 60 and 70% concentrations (Group II) were not statistically different. It was also observed that no statistical difference existed between the measured data for the emulsions having 40 and 50% oil concentration emulsions. (c) For light oil emulsions, no statistical difference existed between the measured data
AE OMARETAL
158 TABLE 3 Effect of oil concen tration rheolog~cal on behavior of crude oli emulsions Combination data under comparison
Type of crude oil Heavy
Medium
Group I 30"&40 30&50 30&60 30&70 30&80 30&90 40&50 40&60 40&70 40&80 40&90 50&60 50&70 50&80 50&90 60&70 6 0 & 80 6 0 & 90 70&80 70& 90 80&90
G r o u p II
SDE** SDE SDE SDE NSDE*** SDE SDE SDE SDE NSDE -
Light
Group I
G r o u p II
SDE SDE SDE SDE SDE SDE NSDE SDE SDE SDE SDE NSDE SDE SDE SDE NSDE NSDE SDE NSDE SDE SDE
SDE SDE SDE SDE SDE NSDE SDE SDE SDE NSDE SDE SDE NSDE SDE SDE -
Group I
Extra-hght G r o u p II
Group I
SDE SDE SDE SDE NSDE SDE NSDE SDE NSDE NSDE SDE NSDE SDE SDE -
G r o u p 1I SDE SDE SDE SDE NSDE NSDE NSDE SDE SDE SDE SDE SDE SDE SDE SDE NSDE SDE SDE SDE SDE NSDE
*30 = The measured data of 30% (by v o l u m e ) oll concentration emulsion **SDE = Statistical difference exists ***NSDE = N o statistical &fference exists - = No combination b e t w e e n the t w o sets o f data since one of them is N e w l o m a n TABLE4 G r o u p s of n o n - N e w t o m a n emulsions data Data group
Heavy oil (% concentration )
1 2 3 4 5 6
30 40 40 60 60
and and and and
50 50 70 70
(Group (Group (Group (Group
1) II ) I) II )
M e d i u m oil (% concentration)
Light oll (% concentration)
Extra-light oll (% concentration)
30 40 40 60 60 90
30 50 ( G r o u p I) a n d 4 0 50 ( G r o u p II ) 60 and 70 80
80 40 60 80
( G r o u p ll) ( G r o u p I) and 50 and 70 ( G r o u p II ) and 70 ( G r o u p I) and 80
for the emulsions having 50% oil concentration (Group I) and the data for the emulsions having 40, 60 and 70% concentration. It was also observed that, the measured data for the emulsion having 70% oil concentration were not statistically different from the data of the
and and and and
90 ( G r o u p I I ) and 30 50 70 90 ( G r o u p I )
emulsions having 40 and 60% concentrations. (d) For extra-light emulsions, no statistical difference existed between the measured data (Group I or Group II) of the 30, 80 and 90% oll concentration emulsions. It was also noticed that the measured data of the emulsions
RHEOLOGICALCHARACTERISTICSOF SAUDICRUDEOIL EMULSIONS
159
TABLE 5 The values of K and n for the fitted rheological models Data group
1 2 3 4 5 6
Medium
Heavy
Light
Extra-hght
K ( N / m 2 / s -n)
n
K (N/m2/s -")
n
K ( N / m 2 / s -n)
n
K (N/m2/s -")
n
0.048 0270 0 061 0 433 0 125 -
0 735 0808 0 741 0 910 0 885
0 273 0015 0 060 0.032 0.067 0.277
0 3069 0.944 0.866 0.878 0 925 0.329
0.138 0.036 0.016 0.039 0.154
0.418 0.737 0.873 0 866 0232
0010 0.097 0.054 0 024 -
0.828 0.355 0 582 0 882 -
having 40 and 50% oil concentration, as well as the data of the emulsions with 60 and 70% concentration were not statistically different. E m u l s io n s correlation
The use of Richardson equation (Richardson, 1958 ) in correlating the measured viscosity to shear rate and temperature resulted in twenty-eight empirical equations. Statistical analysis was used to group the non-Newtonian data which are not statistically different. Resuits presented in Tables 2 and 3 were used to prepare Table 4. This table shows that the number of groups of heavy, medium, light and extra-light crude oils data were equal to 5, 6, 5, and 4, respectively. Thus, the total number of the rheological models, which fit the data of these groups, is equal to twenty. In as much as these data demonstrated pseudoplastic behaviour at the test conditions, they can be correlated with the so-called power-law model (Govier and Aziz, 1982): z=K# n
(4)
The values of the consistency index (K) and the flow behavior index (n) for the twenty rheological models were calculated and the resuits are given in Table 5.
Conclusions Based upon the experimental observations and statistical analysis of the results, the fol-
lowing conclusions were formulated. ( 1 ) Saudi heavy crude oil emulsions exhibited Newtonian behavior at 80 and 90% oil concentrations, whereas emulsions of medium crude oil exhibited such behavior only at 80% oil concentration and test temperatures greater than 10°C. Light crude oil emulsions exhibited similar behavior at 90% oil concentration. ( 2 ) The variation of temperature (from 10 ° to 40 oC ) did not affect the rheological behavior of heavy crude oil emulsion having 30% oil concentration, and the medium crude oil emulsions having 30, 50 and 90% oil concentrations. (3) The rheological behavior of the light crude emulsion (50% oil concentration) and extra-light crude emulsion (80 and 90% oil concentrations) varied with temperature. (4) The concentration of the dispersed oil phase was strongly affecting the rheological behavior of Saudi crude oil emulsions to the extent that, 50 out of 67 possible combinations of the data under comparison were statistically different. (5) The non-Newtonian emulsions exhibited pseudoplastic behavior and their characteristics were correlated with power-law.
Acknowledgements The critical review of the manuscript by Prof. Dr. S.S. Marsden is greatly appreciated.
160
References Alvarado, D_A and Marsden, S.S, 1979 Flow of oil-mwater emulsions through tubes and porous media. Soc Pet. Eng. J , 19(6). 369-376. Camy, J P , Marsden, S.S, Hung, J E., Anhara, N , Casse, F,J, Alvarado, D A , Mandel, L , Mobarak, S., Gonzales, H.O., Mao, M L., Samamego, F , Romero, R~vera, E J and Marius, C.G., 1975 The rheology of crude oil dispersions Proc. Int Symp. Oil Field Chemistry_ Soc Pet Eng., Pap 5299: 51-66_ Chllinganan, G.V_ and Vorabutr, P., 1981. Drilling and Drilhng Fluids. Developments in Petroleum Science, 11 Elsevier, Amsterdam, 767pp. Flock, D.L_ and Stelnborn, R , 1982. The rheology of heavy crude oils and their emulsions Annu. Tech Meet. Pet Soc. CIM, Pap. 82-33-60 246-251_ Gogarty, W B., 1967. Rheological properties of pseudoplastic fluids m porous media. Soc. Pet Eng. J., 7(2) 149-159.
A E OMAR ET AL
Govler, G W. and A z I z , K , 1982 The Flow of Complex Mixtures in Pipes. Van Nostrand Reinhold, New York, N Y , 792 pp_ Marsden, S S, Jr and Raghavan, R , 1973 A system for proceeding and transporting crude oil as an oil/water emulsion. Inst Pet., 59(570) 273-278_ Marsden, S S and Chlllngarlan, G V., 1978. New methods of petroleum transportation. Energy Sources, 3 ( 3/ 4): 389-394_ Parsons, R , 1978 Statistical Analysis, 2nd ed Harper and Row, New York, N.Y, 456 pp Richardson, E.G, 1958_ The flow of emulsions. J Colloid Scl, 8 367-373 Simon, R and Poynter, W . G , 1968. Downhole emulsification for improving vtscous crude production J. Pet. Technol., 20(6) 1349-1353. Volk, W., 1969. Applied Statistics for Engineers, 2nd ed. McGraw-Hill, New York, N Y_, 362 pp. Wyslouzd, B E and Kesslck, M.A, 1987. Pipeline flow behavlour of heavy crude oil emulsions. Can J. Chem Eng., 65(3) 353-360