AN ABSTRACT OF THE THESIS OF
LACHHMAN DEV
(Name)
in
for the
CHEMICAL ENGINEERING
DOCTOR OF PHILOSOPHY
(Degree)
presented on
(Jv ,&, /Y72
(Date)
(Maj or)
Title: MOMENTUM AND HEAT TRANSFER CHARACTERISTICS OF
LIQUID-LIQUID DISPERSIONS IN TURBULENT FLOW IN
AN ANNULUS
Abstract approved:
Redacted for privacy
James G. Knudsen
The momentum and heat transfer characteristics of liquidliquid dispersions flowing turbulently in an annulus were investigated.
The study was made on the annulus with fully developed velocity pro-
files and constant heat flux on the inner surface. Water and various
liquids, with a wide range of viscosities and interfacial tensions, were
studied using water as one of the phases in each case. Experiments
were conducted to obtain friction factors and local heat transfer
coefficients for dispersions of various concentrations.
The annulus was constructed of a 1.239 inch I. D. acrylic plastic
tube and 0. 508 inch 0. D. stainless steel tube. A sliding thermocouple was developed for the measurement of wall temperature of the
inner tube. The liquids used were Shell solvent (with a viscosity of
1. 0 centipoise and interfacial tension (with water as second liquid) of
49 dynes/cm), iso-octyL alcohol (9 centipoise arid 12 dynes/cm), light
oil (15 centipoise and 54 dynes 1cm), and heavy oil (ZOO centipoise and
48 dyries/cm). Reynolds number ranged from 10, 000 to 100, 000,
It was found that the friction factors could be expressed by
Rothfus and coworkers' equation for single phase fluids. An effective
viscosity was obtained from the friction factor data at three tempera-
tures. Heat transfer data were correlated by Monrad and Pelton's
equation in the following form.
(St)(Pr) /
=
0. OZ (D2 /D1)°'
(Re)°
Z
AlL properties were evaluated at the bulk temperature. The Reynolds
number was based on the effective viscosity. The Prandtt number and
C
p
used were those of the continuous phase.
For the prediction of effective viscosity, a correlation was
developed that takes into account the variation of relative fluidity with
temperature.
The thermal entry length was found to depend on the continuous
phase Prandtl number. There was no systematic variation of the entry
length with respect to the Prandtl number based on the mixture proper-
ties.
The heavy oil dispersions behaved differently particularly at
high concentrations and high temperatures. Use of predicted effective
viscosities in the calculation of friction factors and heat transfer
coefficients resulted in large deviations from the experimental values.
These deviations were attributed to the difference in drop size and
drop size distribution of the heavy oil dispersions.
A study was made of a water-in-solvent dispersion containing
about 94 percent solvent by volume. The viscosity of this dispersion
was found to be very close to that of the pure solvent indicating that
it behaves differently compared to a dispersion having water as the
continuous phase under the same conditions.
Momentum and Heat Transfer Characteristics of
Liquid-Liquid Dispersions in Turbulent
Flow in an Annulus
by
Lachhman Dev
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
June 1972
APPROVED:
Redacted for privacy
Redacted for privacy
Head of Department of Chemical Engineering
Redacted for privacy
Dean of Graduate School
Date thesis is presented
()&M
,
Typed by Mary Jo Stratton for Lachhm3n Dev
DEDICATION
To the memory of my daughter Amita
ACKNOWLEDGMENTS
I wish to extend my grateful appreciation to the following:
To Dr. James G. Knudsen, associate dean of engineering for
his generous assistance and useful suggestions during the course of
this investigation.
To the National Science Foundation for its financial assistance.
To the department of Chemical Engineering, Charles E. Wicks,
head, for the use of its facilities.
To Mr. William B. Johnson for his helpful suggestions and aid
in construction of the equipment.
To Sudershana for her patience and encouragenent.
TABLE OF CONTENTS
Page
INTRODUCTION
1
LITERATURE SURVEY AND THEORETICAL
BACKGROUND
Flow of Single-Phase Fluids
Two-Phase Flow
Turbulent Flow of Non-Newtonian Fluids
Heat Transfer to Single Phase Fluids
Heat Transfer to Liquid-Liquid Dispersions
Heat Transfer to Non-Newtonian Fluids
3
9
13
16
19
21
EXPERIMENTAL PROGRAM
24
EXPERIMENTAL EQUIPMENT
26
Supply Tank and Pump
Piping System
Test Section
28
28
29
Temperature Probe
33
EXPERIMENTAL PROCEDURE
37
SAMPLE CALCULATIONS AND ERROR ANALYSIS
40
Pressure Drop and Friction Factor
Heat Transfer
Analysis of Experimental Errors
DISCUSSION OF RESULTS
Friction Factor Data
Heat Transfer
Thermal Entry Length
Water in Oil Dispersions
40
44
48
57
57
72
79
81
CONCLUSIONS
84
RECOMMENDATIONS FOR FURTHER WORK
87
Page
BIBLIOGRAPHY
88
APPENDICES
Physical Properties
Relationship Between Wall Temperatures
on the Inside and Outside of the Core Tube
Heat Loss from the Test Section
Mean Deviation of Dispersion Concentration
Thermal Entry Length Data
Observed and Calculated Friction Loss and
Heat Transfer Data for Water, Solvent,
andSS94.1
Progress of Mixing Data
V1II. Observed and Calculated Data for Dispersions
Having Water as the Continuous Phase
Computer Programs
Nomenclature
93
100
102
105
107
111
117
119
153
162
LIST OF TABLES
Page
Table
1
Summary of experimental program.
25
2
Effective viscosities and relative fluidities.
62
Comparison of Nusselt numbers predicted by
Quarmby, Monrad and Pelton at Pr = 10,
R2/R1 = 2.88.
72
4
Thermal entry lengths.
80
5
Physical properties of heavy oil.
95
6
Physical properties of iso-octyl alcohol.
96
7
Physical properties of light oil.
97
8
Physical properties of Shell solvent 345.
98
9
Effective density of the manometer liquid.
99
3
10
Mean deviation of dispersion concentration.
106
11
ThermaL entry length data.
108
12
Observed and calculated friction factor data
for water, solvent, and SS94. 1.
112
Observed and calculated heat transfer data
forwater, soLvent, and SS94. 1.
114
14
Progress of mixing data.
118
15
Observed and calculated friction factor data.
120
16
Relative fluidities.
130
17
Predicted outerwall friction factors.
134
18
Observed and calculated heat transfer data.
143
13
LIST OF FIGURES
Page
Figure
1
Schematic flow diagram.
27
2
Detail of test section.
30
3
Temperature probe.
35
4
Friction factor plot for water.
58
Outer wall friction factor plot for water,
solvent and SS94. 1 dispersion.
59
6
Progress of mixing.
60
7
Error plot for outer wall friction factor
using experimental effective viscosities.
63
8
Relative fluidities.
65
9
Error plot for outer wall friction factor
using Equation (23) for effective viscosity.
66
versus
68
5
10
Plot of
11
Corrected relative fluidities.
12
Errorplot for outer wall friction factor
e2
using Equation (78) for effective viscosity.
13
14
15
70
71
Heat transfer results for water, solvent
and SS94. 1 dispersion.
73
Error plot for heat transfer using experimental effective viscosities.
75
Error plot for heat transfer using Equation
(23) for effective viscosity.
77
Page
Figure
16
17
Error plot for heat transfer using Equation
(78) for effective viscosity.
78
Temperature profile along the heated length
for SS4. 7 dispersion.
82
MOMENTUM AND HEAT TRANSFER CHARACTERISTICS
OF LIQUID-LIQUID DISPERSIONS IN TURBULENT
FLOW IN AN ANNULUS
INTRODUCTION
The flow and heat transfer characteristics of two iminiscible
liquids moving in a duct are of fundamental as well as of practical
interest. Such systems are encountered widely in the chemical and
petroleum industries. The design of tubular reactors, liquid-liquid
extraction equipment and liquid transport systems depends upon a
knowledge of the flow and heat transfer characteristics of these liquidliquid mixtures. Fundan-iental knowledge of the heat, mass and
momentum transport between the phases as well as between the two
phase liquid and the tube wall is necessary and depends on the
physical properties of the liquids and the state of division of the
dispersed phase.
While much attention has been given to the gas-liquid mixtures,
little has been devoted to the liquid-liquid situation. Literature
references on the latter are less by at least one order of magnitude
than are available for the former. All the previous work on liquidliquid dispersions has been restricted to the study of the flow and heat
transfer in pipes. The effect of temperature on the properties of the
dispersion has not been investigated to an appreciable extent.
The present work is concerned with the study of dispersions in
2
turbilerit flow in an annul.us. This is a flow geometry of considerable
technical interest. Equipment was designed and built for the measurement of friction factors nd local heat transfer coefficients. The
study has been made on an annulus, of radius ratio R1 /R2 of O 41,
with fully developed velocity profiles and constant heat flux on the
inner surface (core). Four organic liquids were investigated to cover
a wide range of properties (viscosity and surface tension). These are:
a commercial solvent, iso-octyl alcohol, a light oil and a heavy oil.
The study was made over a temperature range of 70-160°F. The
friction factor measurements were made to evaluate the effective
viscosity of the dispersion. This viscosity was then used for the
correlation of heat transfer data. A relationship is proposed for the
prediction of relative fluidity. The expression takes into account the
variation of relative fluidity with temperature.
3
LITERATURE SURVEY AND THEORETICAL BACKGROUND
Flow of Single-Phase Fluids
In analyzing flow problems the energy, momentum and continuity
equations are solved with given boundary conditions. For steady, iso-
thermal, fully developed incompressible flow energy equation for
macroscopic flow may be written as follows for a unit mass of flowing
fluid.
(Va)
+
p
zrg
+
=
Equation (1) is frequently referred to as Bernoulli's equation when w
and 1w are zero.
For one-dimensional flow in the z direction, the continuity
equation may be written
d(pAV)
d
For a conduit of uniform cross-section containing nopumps or
turbines, equation (1) can be reduced to
- + -EP
p
-
z = - 1w
(3)
A large number of experimental determinations on turbulent flow
of fluids have led to the following quadratic resistance law;
F -
fpVA'
2g
fpV2Lp
-
(4)
4
where F is the resisting force at the wall of the conduit, A' is surface
area of the wall at which F acts, L is the length of the tube, p is the
wetted perimeter, and f is a proportionality factor known as the
Fanning friction factor.
The energy required to overcome the frictional force in moving
the fluid through the tube a distance 6 L is F 6 L. This energy is
dissipated in a mass of fluid pA&L. Hence, the energy dissipated
as friction losses per unit mass of flowing fluid is
1w =
FÔL
pAÔL
(5)
ZfLV2
-.
g(4A/p)
Substituting this expression for 1w in the energy equation (3) one
obtains
LhP +
ZfLV2 p
tg z
-
g(4A/p)
For the case of a horizontal pipe of diameter D, this reduces to the
familiar Fanning equation,
-p =
f
ZfLV2
Dg
= the pressure drop due to friction in force per unit area.
where
The term 4Afp in equation (6) is known as the equivalent diameter, D, for
the conduit. For an annulus, consisting of an outer tube with inside
diameter D and an inner tube with outside di3meter D ,
2
1
D
e
is D 2
The friction factor may be defined for annuli using this equivalent
diameter.
D
-g(D2 - D1)
P
(8)
2
ZpV L
-
Pf is the pressure change due to frictional effects alone and may be
written as
f
pgz
=
(9)
By dimensional analysis i,t can be shown that for smooth annuli
the friction factor is a function of the Reynolds number and the dia-
meter ratio D2/D1. However, extensive investigation has failed to
produce a satisfactory correlation involving the diameter ratio.
In the discussion which follows, the Reynolds number for annuli
is based on the equivalent diameter D2 (D2 - D1 ) Vp
(10)
Re
Davis (1943) made a comprehensive study of all existing annular
friction-factor data and proposed the following equation:
D2/D -1
D2''D
-0. 1
=
0. 055(Re)
02
(11)
1
According to this reLationship, f has a higher value than for plain tube
at the same Reynolds number. Davis' expression has the drawback
that it does not reduce to the value for the parallel plate channel as
D2/D1 approaches unity.
Rothfus, Monrad, Sikchi and Heideger (1955) defined inner- and
6
outer-wall friction factors for annuli and correlated friction-loss data
over a Reynolds-number range from 10,000 to 45, 000. The inner- and
outer-wall friction factors are, respectively,
2 T1 g
=
pV
2
2
=
pV
2
is expressed as
(R2 - R2 ) g
2
m
R2pV
c
(Pf/L)
where R 2 is the inner radius of the outer tube and Rm the radius
corresponding to the point of maximum velocity.
Rothfus and coworkers report that for 10, 000 <Re2 <45, 000 and
for long annuli
1
-
4, 0 log (Re2 '[) - 0. 40
where
2(R
Re 2
-
R2)Vp
R2
(16)
Equation (15) is identical to Nikurads&s (1932) well known
friction factor relationship for smooth tubes.
Deissler and Taylor (1955) made a theoretical study of flow in
eccentric and concentric plain annuli and showed that the friction factor
7
decreases as the eccentricity of annulus is increased.
Recently several interesting theoretical (Meter and Bird, 1961;
Macagno and McDougall, 1966; Rothfus, Sartory and Kermode, 1966;
Levy, 1967; Clump and Kwanoski, 1968; Quarmby, 1968; Randhawa,
1969) and experimental (Brighten and Jones, 1964; Jonsson and
Sparrow, 1966; Quarmby, 1967) studies of turbulent flow in annuli
have been made. Brighten and Jones (1964), in what appears to be a
careful and extensive study on flow in annuli with smooth walls,
conclude that the friction factor depends only on the Reynolds number
and is independent of the radius ratio, a, at least for a > 0. 0625.
These workers obtained friction factors slightly higher (1 to
10
percent) than friction factors for pipe flow at corresponding Reynolds
numbers for the ReynoLds number range 4000 - 327, 000. The Bias ius
(1913) equation
f
=
0.079
Re°
(17)
for pipe flow was used for comparison.
Of particular importance is their study in the region of rnaxi-.
mum velocity and the result that the location of the point of maximum
velocity is nearer the inner pipe wall than that for laminar flow. The
point of maximum velocity can be calculated from the following
equations obtained by Clump (1968) who applied standard polynomial
curve-fitting techniques to the data of Brighton and Jones. Although
the data indicate a slight Reynolds number effect at small core-to-shell
8
ratios, this effect was excluded.
R2-R
R
m
=
R + (
1
2
1)11.08 (R lB )3 - Z.Z0(R /R
12
12
)2
(18)
+ 1.65 (R1 /R2) + 0.48]
for core-to-shell ratios between 0. 0625 and 1, and
Rm
B1 [18.1(R2-R1)J(R11R2)
(19)
for core-to-shell ratios less than 0.0625,
The results of Quarmby (1967) agree with Brighten and Jones
relative to the independence upon radius ratio but Quarmby's correla-
tion is closer to the relation for the plain tube (f
0.079
Re°' 25) than
those of Brighten and Jones and are in agreement with the upper limit
of f =
0.087
Re°
25
of the latter's data.
Macogno and McDougall (1966) extended the Prandtl-Karrnan
expression for the resistance coefficient of turbulent flow in circular
pipes to turbulent flow in both smooth and rough annular conduits and
obtained expressions for location of maximum velocity and average
as well as inner- and outer-wall resistance coeffidents. Their results
are in agreement with the experimental findings of brighten and Jones.
Quarrnby (1968) employed Von Krmn's similarity hypothesis
together with a description of the sublayer profile proposed by
Deissler to predict the friction factor - Reynolds number relationship
for annuli. His results show satisfactory agreement with the data of
Brighten and Jones.
Two-Phase Flow
The most general approach to the problem of two-phase flow is to
consider each phase separately, with common boundary conditions.
However, the problem can be considerably simplified if the systems
can be handled by the methods already developed for single-phase flow.
By considering the equations of motion, Baron, Sterling and Schueler
(1953) investigated the size of dispersed phase particle such that a
single phase equation might be applicable to the flow of the two phase
fluid. They considered the ratio of inertia forces to the drag forces
acting on the dispersed phase and arrived at the following criterion for
the applicability of single phase treatment.
(Re)c(dp/D)2
d"c <
1
(20)
where d is the particle diameter.
Application of equation (20) to a liquid-liquid dispersion flowing
in a 4-inch pipe at (Re) = 10, 000 indicates that the drop diameter
should be less than 1 mm.
From drop size distribution and effective viscosity measurements, Ward and Knudsen (1967) indicated that a suitable criterion for
the treatment of liquid-liquid dispersions as single phase fluids should
exist in the form
(Re)(d/D)2
d"c
<2
(21)
10
where d is the Sauter mean diameter. Equation (21) states that a
liquid-liquid dispersion can be treated as a single phase fluid if the
at a Reynolds number of 10, 000 and
drop size d is less than 320
100 i at a Reynolds number of 100, 000, Ward and Knudsen found that
well-mixed Shell solvent and light oil dispersions behaved similar to
homogeneous Newtonian fluids. Heavy oil dispersions having heavy
oil volume fractions above 10 percent behaved differently and velocity
profiles indicated non-Newtonian characteristics,
Petroleum solvent (Shell solvent) was also studied by Cengel
etal, (1962) and Faruqui and Knudsen (1962) in laminar and turbulent
flow conditions. Measured friction factors were used to calculate the
effective viscosities. In vertical turbulent flow all dispersions
behaved as Newtonian fluids. The 35 and 50 percent dispersions in
horizontal flow exhibited non-Newtonian characteristics and had effec-
tive viscosities considerably higher than the same dispersion in
vertical flow. This behavior was attributed to phase separation in the
horizontal tube.
Faruqui and Knudsen (1962), and Ward (1964) also measured the
velocity distribution of the flowing dispersions. The effective viscosity
in these cases was obtained by fitting the turbulent core point velocity
data to the equation
yu*
---251n
u* U
V
+5.5
(22)
11
This method provided satisfactory values of the dispersion viscosity
but does require rather extensive velocity distribution data.
Legan and Knudsen (1966) investigated the momentum and heat
transfer characteristics of liquid-liquid dispersions in turbulent flow
in pipes. For the dispersed phase, they used light oil and heavy oil.
They conclude that the friction losses of liquid-liquid dispersions
studied can be treated with existing single phase equations. By fitting
the friction factors to Blasius equation, 1
0.079 Re°
an effec-
tive viscosity of the dispersion was obtained. There was a deviation
of the data from a slope of -0. 25 at low flow rates for most dispersions which was attributed to either a non-Newtonian behavior or a
coalescence of the oil droplets to a size that the dispersion could no
longer be considered a homogeneous, single phase fluid. In analyzing
the data, all deviating points at low flow rates were not used,
The effective viscosity was correlated at room temperature by
the relationship
(23)
o
<4<
0.5 for
o
<4 <
0.1 for - 200
18
12
Data of Ward (1964), Faruqui (1962) and Cengeletal. (1962) agree
with the above relation,
In the case of heavy oil, the viscosity of 21 percent dispersion
was found to be lower than that of the 5 percent dispersion at the same
temperature. This anomaly was explained by a tislipli velocity of the
large drops relative to a fluid element in which they are contained.
Therelative fluidity was found to decrease significantly with
temperature.
Recently Soot (1971) has studied the two-phase liquid-liquid
flow in pipes. He also analyzed the data of Wright (1957), Cengel
(1959), Ward (1964), Faruqui (1962), Finnigan (1958), and suggested
the following empirical relationship for vertical turbulent bubble flow.
2
=
A 2.25 X 2 - 1.20
AcZ.Si (Reco)
c
where
(Red
0. 563
0.475
(24)
and X2 are the Lockhart-Mart inelli parameters defined as
4
follows:
tPf
2
Zft
c
c
2
W2L
c
2f' W2L
d
,
d
DA2p
'
=
d
Rec
o-
d
(26a, b)
DA2pd
DW
DW
Re
(25a, b)
FLA
(27a, b)
13
W is the mass flow rate.
Turbulent Flow of Non-Newtonian Fluids
The phenomenon of turbulent flow in non-Newtonian fluids has not
received nearly the attention accorded to the laminar flow regime.
However, in recent years the discovery of drag reduction in very
dilute solutions of polymers and increased interest in slurry handling
have resulted in the publication of several excellent articles on the
theoretical and experimental aspects of flow in pipes. While completely general solutions have not been developed, equations that may
be used for engineering calculations are available for many classes of
fluids. No work seems to have been done on the turbulent flow of nonNewtonian fluids in annuli.
Dodge and Metzner (1959) have extended the work of Von Karman
on turbulent-flow friction factors to include inelastic non-Newtonian
fluids. They derived an expression for the friction factor,
f, in
terms of the generalized Reynolds number (Re)':
-A
log [(Re)
+ cn
and
(Re)'
=
8(DnVZnP,K)
6n+ Z
(29)
For n = 1 the Reynolds number reduces to DVp4L. By analyzing
the experimental friction factor data for non-Newtonian liquids these
14
authors proposed that
A
For n =
1,
In
=
4.0/n075
=
-0,4/n'
equation (Z8) reduces to the well known Nikuradse equation.
Tornita (1959) developedcorreLations for use with Bingham
plastics and power law fluids. His general equation for friction factor
is
'.JT7
=
4. 0 log{Re x
/2 -0. 40
wheref and Re are given below for two types of fluids.
For Bingham plastics:
DPg
f
Zp L (1-c) V
a
(l-c)(c-4c+3)
]Vp
= Ty/Tw
Value of c is obtained from
V=
Rgc T
Ti
y
p
c 4-4c+3
lZc
where R is the radius of pipe, T is the yield stress and
p
the
"pIastic viscosity for Bingham plastic. For power law fluids:
1=
ZD P g(Zn+l)
(34)
3L p V
(3h+l)
15
11-n
Re
6[(3n+l)/nj
2n[(Zn+l)/nI
x
D
n
(V)
K
2-n
Although the experimental data supporting this last correlation
are much more limited than those of Dodge and Metzner, it does seem
to hold for a wide range of fluid-property parameters.
The preceding discussion dealt with purely viscous fluids, i, e.,
those that showed no elasticity. The phenomenon of drag reduction
in turbulent flow of viscoelastic materials has evinced considerable
interest in recent years, and is of major concern in designing flow
systems for such fluids. Data on a viscoelastic material have been
presented by Seyer and Metzner (1967). The friction factor is as much
as five times less than that predicted by equation (28) for purely
viscous non-Newtonian fluids of similar n. The friction factor shows
the effect of pipe diameter. The authors have also presented an
analysis for the interpretation of these superficially paradoxical
characteristics of viscoelastic polymer solutions.
Meyer (1966) analyzed the existing data and proposed a correla-
tion for predicting the frictional characteristics of turbulent flow of
dilute viscoelastic non-Newtonian fluids in pipes. Their relationship
is
1 /'[f
=
(4 + a /2) log Re ff - 0. 394
a
- -log
2 D u*cr
w
16
Alog2'+ B
B
A
=
BN + a Log
=
5.66
u*
(37)
u*
cr
B
n
=
cr
(38)
6.07
B is obtained from the velocity profile data. a is a fluid property
defined in equation (38). BN is the value of B for Newtonian fluids.
urn is the maximum flow velocity in the pipe. u* is the friction
velocity
sJ
Tw/p.
u*
cr
is the critical value of u*, taken as 0. Z3 ft/sec.
Heat Transfer to Single Phase Fluids
By dimensional analysis it can be shown that for smooth arinuli
under fully developed conditions
Nu
a(Re)b (p)C (Dz/Dl)d
(39)
Wiegand (1945) analyzed a large amount of data on heat transfer in
annuli and suggested the following relationship.
hDe
for Re >
- 0 023
(DeG 0.8
C0
kb
(2)0. 45
D1
(40)
Properties are evaluated at the bulb temperature.
Monrad and Pelton (1942) recommended the following equation,
which gives results close to equation (40)
17
hD
(-s)
k b
-
02
DeG
p.
b
Cp p.1'3 D20
' k 'b '
(41)
Experimental work by Monrad and Peltori was a more systematic study
of heat transfer in annuli than any- preceding work. Calming sections
were used in the experimental apparatus, and the data obtained in this
manner were only slightly affected by entrance.
Knudsen and Katz (1950) did some experimental work on pressure
drop and heat transfer in smooth and modified annuli. Their heat
transfer results for smooth annuli were in agreement with equation
(40).
Barrow (1955) studied heat transfer in an annulus with a heated
core tube. No calming section before the heated sectionwas used to
ensure a well developed velocity profile before the fluid was heated.
Miller, Byrnes and Benforado (1955) and Stein and Begell (1958)
used spacers to ensure the concentricity of the core tube relative to
the outer tube. The spacers served to break up the velocity and
temperature profiles.
Work on turbulent heat transfer in annuli with small cores has
been done by Mueller (1942), Crookston, Rothfus and Kermode (1968)
and Unzicker (1967).
Several theoretical studies (Deissler and Taylor, 1955;
Knudsen, 1962; Kays and Leung, 1963; Wilson and Medwell, 1968;
Quarmby and Anand, 1969) have been made recently on annular heat
18
transfer. Deissler and Taylor (1955) were possibly the first to
publish analytical work on heat transfer for fully developed turbulent
flow in eccentric annuli. Knudsen (1962) has derived expressions for
j factors for turbulent flow in annuli using Colburn's analogy. His
relationships are:
2/3
f/2
=
02( la)O.2 X-a
0.023 Re
a(1-X
l-X
-
h2
I
Ct2
IP
'C G' '
p
k
= 0.023 Re°
2
1
a)0. 2
1 -x
Experimental data agree with these expressions within
10 percent.
Kays and Leung (1963) have presented analytic solutions for
turbulent heat transfer in annuli with fully developed velocity and
temperature profiles and constant heat rate per unit of length for a
wide range of radius ratios, Reynolds numbers, and Prandtl. numbers.
The solutions are based on empirical velocity and eddy diffusivity
profiles. Their analytic results for Prandt], number of 0. 7 agree with
their experimental data on air for Reynolds numbers >30,000.
Wilson and Medwell (1968) have employed a modification of the
velocity distribution due to Van Driest. Their analytic results for
19
Prandtl numbers of 0. 7 and 1 agree with those of Kays and Leung
except at a radius ratio of 0.2. Above Prandtl number of 1, the
analysis of Wilson and MedweU underpredicts the Nusselt modulus.
Analytic results of Quarmby and Anand (1969) for fully developed
turbulent heat transfer in concentric annuli with uniform wall heat
fluxes cover a range of radius ratios from unity to 50, Reynolds
number from 8000 to 500,000, and Prandtl numbers of 0.01, 0. 7,
1,
10, 1000. They report good agreement with experiment of results for
Prandtl number of 0. 7 over most of this range of variables and
satisfactory agreement with some experiments or a few other Prandtl
numbers. The formulation of their analysis takes into account the
dependence of the turbulent ve'ocity profile on the Reynolds number and
the point of maximum velocity.
Heat Transfer to Liquid-Liquid Dispersions
Finnigan (1958) and Wright (1957) studied heat transfer to
liquid-liquid dispersions flowing in a tube using a petroleum solvent
(Shell solvent) as the dispersed phase and water as continuous phase.
Finnigan correlated his data by the use of a Dittus-Boelter type equat ion
() = 0.023 (DG)0.8 (Pc)O.4
where subscript c refers to the continuous phase. Wright used the
(44)
20
Colburn equation to correlate his data
(cG
k213 = 0.023
(DG)-0.2
(45)
Heat capacity C in equation (45) was the weighted average of the
mixture. There was considerable scatter in the data. Both investi-
gators used the dispersion properties to evaluate the Reynolds number.
Faruqui and Knudsen (1962) measured the velocity and temperature
profiles of unstable liquid-liquid dispersions in vertical turbulent flow
in a tube using Shell solvent as the dispersed phase and water as the
continuous phase. From an analysis of the velocity profile data they
concluded that the dispersions could be treated as Newtonian fluids.
The temperature profiles indicated that the dispersion behaved as a
single phase fluid with a Prandtl number equal to that of the contin-
uous phase at the film temperature. They correlated the heat transfer coefficients with the usual Colburn heat transfer j-factor equation
using the Prandtl number of the continuous phase at the film temperature and the Reynolds number based on effective dispersion viscosity.
Legan and Knudsen (1966) investigated the momentum and heat
transfer characteristics of unstable, liquid-liquid dispers ions flowing
turbulently in a circular tube. Two mineral oils, a Light oil with
viscosity of 15 centipoise, and a heavy oil with viscosity of 200 centi-
poise were used as the dispersed phase with water as the continuous
phase. At Reynolds numbers above 60, 000 the heat transfer
21
coefficients follow the relation
= 0.023 Re°
2
where the Prandtl number is that of the continuous phase evaluated
at the film temperature and the Reynolds number is based upon the
viscosity of the dispersion evaluated at the film temperature. Below
a Reynolds number of 60, 000 individual curves were obtained for each
light oil dispersion and the curves lie much below equation (46). Heat
transfer results for heavy oil agreed reasonably well with equation
(46) over the range of Reynolds numbers investigated. Deviations
occurred at high temperature in case of heavy oil. Legan and Knudsen
suggest that under these conditions either the dispersions do not
behave as Newtonian fluids or that droplet coalescence causes the
dispersion to behave as anon-homogeneous fluid.
Heat Transfer to Non-Newtonian Fluids
Metzner and Friend (1959) have given a correlation for purely
viscous non-Newtonian fluids in turbulent flow in tubes for small
driving temperature difference. It is based on the analogy between
heat and mass transfer in turbulent flow proposed by Reichardt (1957)
and extended to non-Newtonian fluids by Metzner and Friend (1958).
f/Z 9
(St)
irn
1
m
+
m
11.8fT7[(Pr)wb -iJ
1/3
(Pr)wb
-.
22
where the Stanton number is given by h Im ICpG. h Im is the log mean
heat transfer coefficient.
is the ratio of the bulk mean velocity
to the centerline velocity.
0
m
is the ratio of mean to maximum
temperature difference. The Prardtl number (Pr) wb is evaluated at
the shear stress at the wall and at the average bulk temperature of the
fluid.
Petersen and Christiansen (1966) have improved this correlation
considerably and extended its applicability to large temperature
differences by redefining the Pranitl number to be used, and by
introducing a viscosity ratio term of the type proposed by Kreith and
Summerfield (1950). Their equation for pseudoplasticfluids is:
f
'20
St
=
1
,11ww
'1 wb
.
m'
-0. 1
11.8 ,JTZ{(pr)-i]
(48)
+
where the Prandtl number (Pr) is defined as:
p
(Re)
(Pr)
=
(Pr)Wb x
wc
The Reynolds number (at the wall shear stress and the critical flow
rate), (Re), was derived from the stability parameter developed by
Flanks (1963):
(Re)
wc
1, 616
(n+
)
4n+2)(n+l)
(3n+1)
23
The viscosities r ww and ri wb are evaluated at the wall shear stress,
and at the wall temperature and the bulk fluid temperature,
respectively. Equation (48) is only valid for Re > 10, 000.
EXPERIMENTAL PROGRAM
The research described in this report is part of a project being
conducted at this university to study the momentum and heat transfer
characteristics of two phase liquidrliqui.d systems. Previous work has
been confined to the investigations of flow in pipes. The annutus,
being an important industrial geometry, was therefore selected for the
present investigation. It also has some advantage from an experi
mental standpoint. The results reported by Legan and Knudsen (1966)
have indicated a need to study friction factors and heat transfer coef-
ficients to determine the effect of the physical properties of the liquids
on the dispersion, as well, as the effect of temperature. They also
reported that the region of Reynolds number below 50, 000 needed
further study. In addition to these goals, it was desired to develop a
sliding thermocouple to measure the local heat transfer coefficients
and entrance lengths.
Four organic phases were chosen to provide a wide range of
properties (viscosity and interfacial tension): the Shell solvent (with
a viscosity of 1.0 centipoise and interfacial tension (with water as the
second liquid) of 49 dynes 1cm), iso-octyl alcohol (9 centipoise and
12 dynes /cm), and heavy oil (200 centipoise and 48 dynes /cm). The
heavy oil was studied most extensively. A Reynolds number range of
l0-l0 was investigated. A summary of all the experimental runs is
given in Table 1. The following system was used in identifying the
25
runs. The first two letters designate the organic phase: SS for Shell
solvent, 10 for iso-octyl alcohol, LO for light oil, and HO for the
heavy oil. The numbers following the two Letters signify the actual
concentration of the organic phase in volume percent. Thus a run
labeled 1023. 6 would indicate an iso-octyl alcohol dispersion of 23. 6
volume percent.
Table 1. Summary of experimental program.
Dispersed
phase and
concentration
Temperature
range
(°C)
L 025
L04. 6
H032. 5
H014. 1
H07. 5
H02. 1
23-59
Friction
factor
8 flow rates
between 1.5-4
lb/sec and at 3
temperatures
bounding the
temperature
range
At 2 tempera-
1023. 6
SS19. 2
SS4, 7
20-37
SS94.l
20.5
tures in case
of 1023.6 and
Heat
transfer
7 flow rates
between J.5-4
lb/sec at room
temperature.
Readings at
higher tem-
peratures taken
at 4 lb/sec at
intervals of 7°C
SS 19. 2
4 flow rates
3 flow rates
26
EXPERIMENTAL EQUIPMENT
The experimental apparatus is shown schematically in Figure 1.
The organic phase and water were mixed in the stainless supply tank
and were kept in dispersed state through the combined mixing action
of two variable speed mixers and the fluid returning to the tank. The
dispersion was circulated from the tank to the orifice, vertical test
section, heat exchanger and back to the tank. A short flexible rubber
hose was provided at the end of the return line so that the liquid could
be diverted to a weighing tank for measurement of the mass flow rate.
The test section was equipped for pressure drop and heat transfer
measurements. Flow rate through the test section was controlled by
diverting a portion of the dispersion to the tank through the bypass line
provided at the pump. Four different liquids were used as the organic
phases: Shell solvent 345 (a commercial solvent marketed by Shell Oil
Company), Iso-octyl alcohol, Light oil (white oil No. 1), Heavy oil
(white oil No. 15), The last two were the highly refined oils supplied
by Standard Oil of California. The physical properties of these liquids
along with the methods used for their determinations are given in the
Appendix. Thermocouples were provided for measurement of bulk
temperature before and after the test section. Wall temperature of the
inner tube of the test section was measured by a sliding thermocouple.
The test section was connected to the main piping system by four
FLEXIBLE
HOSE
POLYETHYLENE TUBES +
TH
CORE TUBE
MIXERS
PLEXI
GLASS
L. TUBE
SUPPLY
TANK
2
-OP
DRAI N
lxi
P PRESSURE GAUGE
TH THERMOCOUPLE
WATER FLUSH
PRESSURE TAP
-TH
-
PUMP
HEAT EXCHANGER
Figure 1. Schematic flow diagram.
28
polyethylene tubes 1 /2 inch I. D. and 1/6 inch thick, The important
individual components of the system are described below in detail.
Supply Tank and Pump
The 80-gallon, stainless steel supply tank and the pump were the
same as used by Finnigan (1958) and have been described by him in
detail. Two propellor-type agitators with variable speed drive were
provided to ensure complete mixing of the dispersion. The bronze
turbine pump was driven by a three horse power electric motor, A
pressure gauge on the discharge side of the pump indicated the pump
discharge pressure. In order to prevent leakage of air into the system,
this pressure was always maintained above 15 psig by partially closing
the valve (valve number 4 in Figure 1) at the end of the return line,
Piping System
To avoid corrosion problems, the materials in contact with the
dispersion were only stainless steel, copper, brass, plexiglass,
polyethylene, or rubber. All the piping system, except the test section and its connecting tubes, was constructed of standard 2-inch and
1-1/4 inch brass pipe, and a section of flexible synthetic rubber hose.
The 2-inch pipe was located on the suction side ofthe pump. A 2-inch
gate valve was inserted in this line so that the piping system could be
drained independently of the tank. Flexible hose was a 2-1/2 foot
29
length of heavy wall synthetic rubber located at the efflux point of the
system. This rubber material was found to be resistant to alL of the
liquids used in this investigation. A number of unions were used for
ease in assembly and dis-assembly. Provision for drainage was made
at the low point of the system. The entire system was washed with a
water solution of sodium tripolyphosphate and then several times with
water.
A 20-gallon stainless steel weighing tank was placed on a
calibrated platform scale close to and approximately at the same height
as the supply tank. The flow rate was measured by diverting the flow
stream from supply tank to the weigh tank by means of the flexible
hose and noting the time required to collect a known weight1 101.2
lbs of the liquid.
Test Section
The outer tube of the vertical annular test section shown in
Figure 2 was made out of two pieces of 1.239 ± .004 inch I. D.
plexiglass pipe. The two pieces were provided wtth a flange at each
end and then joined together with bolts. The flanges were fixed with
weld-on No. 3 acrylic adhesive. Gaskets in all the flanged connections
were made out of Vellumoid sheet packing. This material supplied by
the Vellumoid Company, Worcester, Mass., is good for oil, gasoline
and water service. The inner core tube was made out of 1 /2 inch
30
TENSION
BOLTS
'SI
1/4"
BRASS
FLANGE
1/4"
,
3/8"
,,
:
__, ,,,,..,
PLEXIGLASS
FLANGE
is"
.1/2"
FLUID
j
COPPER TUBE
PRESSURE
PLEXIGLASS
TAP
39 1/8'
INLET
4,1/4" BRASS PIPES
IiU
1/2"
TUB E
PLEXIGLASS
FLANGE
1/2"
STAINLESS STEEL
PRESSURE
TAP
r2W
?,.vwt
TUBE
uI
FLUID
9 1/8"
WflflJfltflflflfltffflflfl. OUTLET
4 1/4" BRASS PIPES
PLEX IGLASS
FLANGE
3/8"
3/8"
1/4"
BRASS FLANGE
3 3/8"
DIA
COPPER TUBE
Figure 2. Detail of test section.
31
stainless steel tube with 1/2 inch coppertubes at the ends. The
0. 508 ± 0. 002 inch 0. D, stainless steel tube was 39. 12 inches long
with 0.010-inch wall thickness. The copper tubes of the same 0. D. as
the stainless steel tube having a wall thickness of 0. 065 inch served as
conductors (leads) for the electric current and also ensured fully
developed flow in the test section. The upper copper tube was 39-1/8
inches long and the lower one 9-1/8 inches. These tubes were joined
to the stainless steel tube with silver solder and then machined to
ensure uniformity of diameter, The lower copper tube had a brass
flange 1/4 inch thick and 3-3/8 inch diameter welded to it 1-1/4 inch
from the lower end. This flange was bolted to the lowest flange of the
outer plexiglass pipe to close the lower end of the annular test section.
An 0 ring arrangement was used to close the upper end. This is shown
in Figure 2, To make the test piece concentric it was found necessary
to stretch the inner core. As shown in Figure 2, a brass flange,
1 /4
inch thick with four threaded holes, was soldered to the upper copper
tube. Tightening of the bolts through the holes provided the necessary
tens ion.
Two 1/4 inch pipe taps facing the copper-stainless steel joints
were drilled and threaded 39. 12 inches apart in the outer tube, thus
defining the length of the test section for pressure drop measurements.
Because of the silver in the joints, the length of the test section for
heat transfer was only 38, 170 inches. Heat generated in the copper
32
tubes was 0. 5% of the total energy input. The dispersion entered and
left the annular section of the test piece through four polyethylene
tubes, 1 /2 inch I. D. and 1/16 inch thick, arranged equidistant around
the circumference. This ensured uniform flow conditions at the
entrance and exit. Four 1/4 inch pipe taps, equally spaced around the
circumference, were drilled into the outer tube at each end. Pieces
of 1/4 inch brass pipe threaded at one end were fixed into these taps
and polyethylene tubes were clamped on. The other end of the poly-
ethylene tube was connected to the 1-1/4 inch brass pipe as shown in
Figures 1 and 2. This arrangement provided a flow entry section of
length 35-i /8 inches (or 49 diameters) at the top and a calming section
of length 6-1/2 inches (9 diameters) at the bottom.
In order to measure heat transfer coefficients, heat was generated in the stainless steel tube by passing direct current through the
core. The power was supplied by a rectifier with 220 V A0 C0 input
and a rated D. C. output of 28 volts at 1000 amps. The electrical
connections between the rectifier and the core tube were made with
copper cable 1 /2 inch diameter, A resistance (a piece of stainless
steel tube) was placed in series to vary the energy input in the test
section0 The resistance could be varied by connecting the cable on the
tube at different positions. This vertical stainless steel tube was
supported by insulated clamps and cooled by passing water through it
to dissipate the heat generated.
33
The inlet and outlet bulk temperature of the dispersion and the
wall temperature of the stainless steel tube in the test section were
measured with copper-constantan thermocouples. All the thermocouples were made from the matched spools of number 30 B & S
gauge wire supplied by the Leeds & Northrup Company. Voltages
generated by these thermocouples were checked at 0°C, 100°C and
were found to agree closely with the values supplied by Leeds &
Northrup Company. The thermocouple wire was held approximately
in the center of a 1/4 inch copper tube 5 inches long with the help of
Hysol 1 C white epoxy, supplied by Hysol Division of Dexter Corporation. The epoxy was found to be highly resistant to the fluids under
investigation. The thermocouple bead projected outside the epoxy on
one side of the tube and the thermocouple wires coming out on the
other side were lead to a potentiometer. The thermocouple was
checked to make certain it was insulated from the tubing. The 1/4
inch copper tubes carrying the thermocouple were installed with
standard fittings into the 1-1/4 inch brass pipe with thermocouple bead
meeting the fluid in the center of the stream.
Temperature Probe
A temperature probe was specially constructed to measure the
inside wall temperature of the stainless steel tube. The thermocouple
in this probe was held in a copper piece that was in contact with the
34
inside of the stainless steel tube. The arrangement is shown in
Figure 3. The side of the copper piece in contact with the stainless
steel tube was machined to match its curvature with that of the tube
wall. The thermocouple bead was inserted in the small hole, drilled in
copper piece and the hole closed by pressing the piece followed by
application of Devcon epoxy resin. The copper was held in a cylin-
drical plexiglass piece with a spring underneath. The action of the
spring ensured contact of the copper with the stainless steel tube.
Thermocouple wires came out of a hole 3/32 inch diameter drilled in
the plexiglass piece. In another hole 1/8 inch diameter, one end of a
stainless steel rod 4-1/4 feet long was fixed with Devcon epoxy to
facilitate the movement of the thermocouple up and down and along the
circumference of the stainless steel tube from outside the test piece.
The thermocouple wires were wound along this rod to avoid the
possibility of damage to the wires by their getirig trapped or dragged.
As the outside diameter of the plexiglass piece was greater than the
inside diameter of the copper tube, the temperature probe was inserted
into the stainless steel tube before silver soldering the lower copper
tube to the stainless steel tube.
All the thermocouples were connected through a multi-position
selector switch to a Leeds & Northrup (No. 737621) potentiometer.
The cold junctions of the thermocouples were inserted in a thin glass
tube filled with oil and the glass tube was immersed in a bath of
r
A
THERMOCOUPLE
H7/64-
0477"
DIA
I
WIRES
r
/
COPPER
PIECE
3/32" DIA
PLEXIGLASS
STAINLESS
STEEL
TUBE
7/I,J/3 24
11/16"
I"
I
I/8"DIA
STAIN LESS
STEEL ROD
Figure 3. Temperature probe.
SECTION AT AA
36
crushed ice to maintain a constant temperature of
O°C
The voltage across the core was measured by a Simpson 270
VOM meter. A DB-1Z G.E. ammeter was employed to measure the
current flowing through the core. A 1200 amp 50 my shunt was placed
in series with the circuit after the core and the ammeter connected
across it.
The pressure drop across the test section was measured with a
five-foot long U-tube manometer filled with carbon tetrachioride under
water. A thermometer installed on the manometer board indicated the
ambient temperature. The threaded taps on the outer tube of the test
section were connected to the manometer through 1/4 inch tube fittings
and Crescent precision instrument 0. 25-inch 0 D. PVC tubing. Water
was used as the pressure transmitting fluid. The lines were horizontal for a distance of about five feet at each pressure tap to prevent
the dispersion from getting into the vertical portion of the tubing due
to the movement of the manometer columns. Water connections,
shown in Figure 1, were provided for flushing.
37
EXPERIMENTAL PROCEDURE
A run was started by charging a weighed amount of continuous
phase to the supply tank and allowing this to circulate for a few
minutes through the entire piping system. The manometers were
flushed with water to remove any entrained air or organic phase.
Care was taken to ensure that the return hose was mairitained under
the liquid level at all times. The power to the inner core of the test
section and the cooling water to the heat exchanger were turned on.
Cooling water was adjusted to attain constant bulk temperature of the
fluid entering the test section. It took about 15 minutes to attain
equilibrium with water. The required amount of dispersed phase was
then added to the supply tank and allowed to mix through the combined
action of pump, stirrer and the fluid returning to the tank. The mixing
was continued until the equilibrium was attained as evidenced by no
change in pressure drop and temperature readings. This required two
to three hours.
When a uniform dispersion had been obtained heat transfer data
were obtained. The thermocouple readings of wall temperatures and
inlet, outlet bulk temperatures, volts across the inner core, current
flowing, and the flow rate were recorded. The flow rate was mea
sured by diverting the flow to the weighing tank noting the time to
collect a known weight, usually 101.2 pounds of the liquid. Flow rate
38
was then adjusted and further heat transfer data taken. Wall temperature was studied in detail for one flow rate (usually 4 Ib/sec) to obtain
the entrance length. At other flow rates wall temperatures in the fully
developed region (from X = 50. 5 to 74, 5 cm) only were recorded. To
avoid problems of axial conduction from the stainless steel tube to
the copper tube of the core, the power input to the core was reduced
at low flow rates to keep the difference between wall and bulk temperature below 20°C. The reduction in power was achieved by connecting
another resistance (stainless steel tube) in series with the circuit and
dissipating the heat with cooling water.
After completing the heat transfer data at room temperature, the
flow rate was raised to its maximum value, and the manometers were
flushed with water. Power was discontinued and cooling water adjusted
for isothermal conditions in the test section. The temperature of the
dispersion was kept within 0. 5°F. Pressure drop data were then
taken at several flow rates. Manometer deflection across the test
section, temperature of the manometer board and the flow rate were
recorded.
At this point the flow was again increased to its maximum value
and power was applied to raise the temperature of the emulsion. Heat
transfer data were taken at this flow rate under steady state conditions
after each increase of about 7°C in the bulk temperature. Pressure
drop data were taken at several flow rates at the highest temperature
39
and one intermediate temperature. The highest temperature was
usually 370C for systems containing Shell solvent or iso-.octyl alcohol
and 59°C for systems containing light oil or heavy oil. For pressure
drop data at the highest temperature, the temperature variation of the
mixture was maintained within ± 1°F by adjusting the amount of heating
time. After the dispersion was heated to the desired temperature a
few minutes were allowed to pass before the manometer readings were
taken.
A one-liter sample was taken from the return line at least twice
during a series of runs for each dispersion. The samples were sea.led
and allowed to separate overnight so that the composition of the
dispersion could be obtained. The deviation of composition from the
average concentration is given in the Appendix. To obtain a clear
separation of the heavy oil dispersions the samples had to be heated
to about 75°C. Before the next run the system was thoroughly flushed
several times with water and drained. When changing from heavy oil
to light oil and from light oil to iso-octyl alcohol, the system was
rinsed with Shell solvent and then flushed with water. Before switching
over to 100% Shell solvent or dispersions with Shell solvent as con-
tinuous phase, the system was completely drained, rinsed with Shell
solvent and again drained.
The observed and calculated data are given in the Appendix.
40
SAMPLE CALCULATIONS AND ERROR ANALYSIS
Pressure Drop and Friction Factor
The pressure drop across the test section,
T'
was ca1cu-
lated from the manometer deflection, HT, and the effective density of
the manometer fluid, p
by the expression
-.
T
= K(HT)(p)
(51)
where K converts HT from inches to feet. Since the test section was
vertical with liquids of different densities in the pressure transmissiori lines and the test section, part of the pressure drop,
P,,, was
If the length of the test
due to the static pressure difference,
section is L, the density of the liquid in the test section is p and the
density of the pressure transmission liquid (water) is p, then
PS
KL(p-p)
(52)
Since in this case dispersions were flowing in the test section,
was
the density of the organic phase and water comprising the dispersion.
Pf was then
The friction loss,
Pf
+
=
K(HT)(p) + KL(p
"wy
(53)
The friction factor is calculated by
gD
c
;
ZpVL
(_Pf)
e
The outer wall friction factor, f2, is given by
(54)
41
-
(R
f
R
m
2
R2)g(-Pf)
(55)
2
=
R2PeV L
is calculated by Clump's (1968) equation
R
m
= R +{(
R-R
2
2
1
1
(1.08 (R1/R2)3
2.Z0(R1/R
)Z
+ 1.65 (R1/R2) + 0.48)1
-
RRR-
Let
then
R2)
RD
2
e
-
(57)
(RRR) £
=
Since the velocity, V. is related to the mass flow rate, W, by
V = W/Ace
p
(58)
- D)
(59)
and
A
=
(71
/4) (D
Thus
De A2
e
2WL
2
Given
= 0.508 inches, D2 = 1.239 inches,
L = 39. 12 inches and R2 = D2/2, R1 = D1/2,
De =D2 -D
then
R
= 0. 411 inch, RRR
0. 948, A = 0.00696 It2,
(60)
42
and
Pf - -j{HTp
f
R
e
Re2
) + 39.12
(61)
e
=
1.458 (10)(- Pf) Pe/W
(62)
=
0. 948 1
(63)
DW
e
(10)
=
Ai
ce
2 (R2 - R2 ) W
2
m
= AR
2
c
=
(16)
e
(RRR) (Re)
The relationship suggested by Rothfus and coworkers was used for
evaluation of effective viscosity
1
- 0. 4
=
4. 0 log (Re2
=
4. 0 log (RRR x Re x
=
4. 0 log (RRR x
- (0. 4 + 4. 0 log
De:
(15)
0. 4
x
f2)
)
(64)
The pressure drop, friction factor, Reynolds number, and the
dispersion viscosity were calculated and analyzed with the aid of a
CDC 3300 digital computer. The program performed a least square
analysis to find m and b in the equation
DW
e
=
m
log
(RRR
x
x..112)+b
1/"./
A
(65)
43
The slope m was then fixed at 4.0 (assuming Rothfus and coworkers'
equation) and a new intercept was obtained by a second least square
analysis. This value was then used for the calculation of an effective
viscosity for the dispersion.
=
10
-(b + 0.4)/4.0
(66)
A least square analysis of run HOZ. 1 (23. 3) gave an effective
lb/ft sec. A sample calculation for this run
viscosity of 6.38 x
showing the use of equations (61), 62), (63), (10), and (16) is given
below.
Given: HT = 32.46 in C Cl4
W = 4.04 lb/sec
Temperature of dispersion
23.
Ambient temperatire = 27. 7°C
62.28 lb/ft3
Density of heavy oil at 23. 2°C
pm
54.06 lb/ft3
=36.52
therefore,
=
(0.21)(54.06) + (.979)(62.28) = 62.11 lb/ft3
-Pf = -j[(32. 46) (36. 52) + 39. 12(6. 11 -62.28)]
-
P
= 98,23 lb/ft3
f
=
1.458 (10
f
=
.00544
) (98. 23) (62. 11) / (4.04)2
44
f2
=
.948 (.00544)
=
.00515
(.731 /12) (4. 04) / [(.00697) (.000638)
Re
Re
= 55400
Re2
=
II
0. 948 (55400) = 52500
Heat Transfer
The heat transfer coefficient, h, was obtained from the expression
q = hALT
(67)
T is the temperature difference between the wall and the fluid.
where
A=
A
(0. 508/12) (96. 95/30. 48)
D Lh
0. 4203 ft2
where Lh is the heated length, 96. 95 cm. The he3t transferred,
is
calculated by
RSS
q = 3,4129 VC RSS+RCU
(68)
where C is the current, and V is the voltage across the inner core.
Factor 3. 4129 converts watts into Btu/hr. The term RSS /(RSS + RCU)
corrects for the losses in copper leads. RSS is the resistance o the
stainless steel core in the test section and RCU is the resistance of the
copper tubes on the two sides of the stainless steel core
RSS = .0732, RCU
RSS
RSS + RCU
995
.00344
45
A check on the energy balance can be made by the following
express ion:
q = 3600 w C (TBZ - TB1)
The Stanton number was calculated from
St=
h
p
where C is that of the continuous phase.
p
The sliding thermocouple measured the wall temperature, TWI,
on the inside of the core tube. For evaluation of the heat transfer
coefficient, the wall temperature on the outside of the core tube must
be known. The relationship between these two temperatures has been
derived in the Appendix and is
TWO
TWI
q III
Zkss
(r0/2 - r. 2/2 - r. 2In r 0 /r.)
(71)
1
L
The heat generated per unit volume of the core, q", is calculated by
qW
=
2,
lr{r 2 - r.j Lh=
=
.000346 ft
= q/v
254'l2)
(72)
2
244"2) 2-9695
30:48
(73)
then
= TWO-TB
TB = TB1 + (TBZ - TB1) X/96. 95
(75)
where X represents the Iength in cm of the test piece up to the point
where TB is required, with zero length corresponding to the point
46
where heat transfer begins. The total length of the heated core is
96.95 cm.
The Prandtl number used was that of the continuous phase at the
bulk temperature. The Reynolds number was calculated by equation
The effective viscosity at the bulk temperature was obtained
(10).
from the isothermal pressure drop data assuming that the logarithm of
the viscosity (lb/ft sec) versus the logarithm of the absolute tempera-
ture (R°) is a straight line.
Monrad and Pelton's equation was used for correlation of heat
transfer data.
D
oz (-)
Re
(St)(Pr)213
=
.
(St)(Pr)2' 3
=
.031971 Re
-.2
or
-.2
(76)
An example showing the numerical calculation of the heat
transfer coefficient, the Stanton number, and the Reynolds number is
given below. The dispersion considered is L04. 6. The observed
data were: W = 3.92 lb/sec, TB1 = 42. 1°C, TB2 = 43. 0°C, TWI =
54. 7°C at X = 62.5 cm, C = 292 amperes, V = 22.8 volts.
(3.41) (22.8) (292) (.995)
q
q = 22600 Btu/hr
r
=
0.508 / (2 x 12), r. = 0.488 / (2 x 12)
From equation (71), TWI - TWO
2. 43°F
1.4°C
47
TWO = 54.7 - 1.4 = 53.3°C
TB
=
42, 1 + (43.0 - 42. 1) (62,5) I (96. 95)
=
42.7°C
53,3 - 42.7
10. 6°C
= 22600 / (0. 423 x 1.8 x 10.6)
h
= 2790 Btu/hrft2 °F
hA C
h
St
GC
-
3600CW
p
(2790) (.00697)
(3600) (3.92) (1,0)
=
p
.00137
The viscosity and thermal conductivity of water were obtained
from Perry (1950). For water, C = 1. Prandtl number of water at
42. 7°C is 4. 13.
(St) (Pr)213
(.00137) (4.13)2/3
=
.00353
To calculate the Reynolds number the dispersion viscosity at the bulk
temperature (42. 7°C) is required. To approximate this viscosity
pressure drop data were taken at three bulk dispersion temperatures:
26. 1, 42.2, and 59. 0°C. The viscosity at these temperatures of the
dispersion was found by the previously discussed method to be
.000716,
.
000567, and .000448 lb/ft sec, respectively. Assuming that
the logarithm of the viscosity in lb/ft sec versus the logarithm of the
absolute temperature (°R) is a straight line, the viscosity of run
48
L04. 6 as a function of temperature is
9. 193 - 4,517 Log (°R)
Log
Using this equation
at 42.7°C = .000562 lb/ft sec
and
=
(.731/12) (3. 92) / (.00696 x .000562)
Re = 61,100
and
.032
Re2
.00353 comparedwith (St)(Pr)2'3 of .00354.
=
Analysis of Experimental Errors
The experimental errors can be estimated by taking the differentials of the quantities involved. The error in friction factor is
estimated by taking the differential of equation (60)
g(D2 - D1)
2
(D
D)2
-
f
P1)
e
(60)
32W2 L
e
(D2 - D1)3 (D2 + D1)2 (- Pf)
32 W2 L
There is negligible error involved in measuring L since it is a
large quantity, Then
df
dp
e+
d(D-D)
D2-D1
[
'
dD1
'dD+
1
d(D-D1)
dD2
'dD]
2
49
+
dD1
D2+D1
d(-z. Pf)
-Pf
+
dD1+ dD2
dD2]
dW
-
dD1
dPe
df
d(D2+D1)
d(D2+D1)
2
-
+
dD1
dD2
+
=
dD2
+ZD+D +
Error in
d(Pf)
-Pf
2
aw
results from the error in composition f the dispersion and
the density of the organic phase. It is of the order of ± 0.2 percent.
D2-D1
D2-D1
dD2
D2+D
- .006 or ± 0,6 percent
-
dD1
D2+D1
- .003 or ± 0.3 percent
-
-
(A)
.VVL
1.747
.001 or - 0. 1 percent
0.004 - .002 or ± 0.2 percent
1.747
100
- D2D1)dDz
D2+D1
=
± 1.2 percent
The error in manometer readings was approximately ± 0. 5 percent
and hence a maximum error of
±
0. 5 percent in - Pf . The error in
the total weight of the fluid was negligible since it was estimated
50
accurately by measuring the volume of water and temperature and the
same weight was used in each run. Assuming an error in time of 0. 1
0.1 x 100 percent or 0. 4 percent.
sec, the error in W is ---x 100
=
± (0.2 + 3 x 0.3 + 1.2 + 2 x 0.1 + 0.5 + 2 x 0.4)
=
± 3.8 percent
The error in calculating f is of the order of ± 3. 8 percent.
R2-R2m
2
R2(R2-R1)
2(R2-R2
2
m
RRR
RD
2
e
dR
ZR2
d(RRR) -
R2(R2-R1)
dR
ZRm dR
+{
dRm
dR1
(R-R2)
ZRm dR2
- 1 +{(
R-R
2
22
(R2Rm) (R2,
+
(R2(R2R1))2
l/2(l.08(R1/R2)3
+ 1. 65(R1 /R2) + 0.48)11
0.68
dR
1
1) (3,24(R1/R2)3 /R1-4.4(R1/R2)2 /R1
+ 1.65 1R2)
=
d R2
[R2(R2-R1)]
m
R2(R2-R1)
(2R2-R1)
-
2.20(R1/R2)2
51
2
::
1)
[-3. 24(R1 /R2)3 / R2+4. 4(R1 /R2)2
/R211 + i/2[1.08(R1/
-
-
3
)
2.20(R1/R2)2 + 1.65(R1/R2) + 0.48 1
0.38
= 0.411
RRR = 0.948
d(RRR) = -. 042 dR2 + 0. 106 dR1
d(RRR)
RRR
- -.044dR2+.1l19dR1
d(RRR) x 100
RRR
cm1 = .001
.002
dR2
=
± (.0088 + .0112) percent
=
± .02percent
The error in RRR is negligible. The error in f2 is of the order of
3.8 percent. The error in effective viscosity is estimated by taking
the differential of equation (64)
i/'f
DW
=
4.0 log (RRR x
x
- (0.4 + 4log)
(64)
or
DW
=
(RRR)(
From equations (60) and (63)
exp[-2
303 ((1/2 + 0.4)1
(77)
52
(RRR) g(D-D1) 2(D-D)
2
Pf)
32W2L
Substitution for A.
c
=
c
,
f
2
, De in (77) results in
(RRR)
3/2
exp[- 2.303
(D2-D1)
- 1/2
(f2
3/2
+0.4)1
Error in RRRI L is negligible
d
e
d(D2-D1)
3
-
d
+
2
2.303 -3/2
+
8
1e
+
1
2
d(- Pf)
-
Pf
df2
All the right hand side terms except the last one have been evaluated
already. They are
dD2
d D1
-
D2D1
D2-D1
=
±0.009
d(D2-D1)
D2-D1
d
= 0.002
d(-
-
Pf)
Pf
The last term is
0. 005
- ± (0.006 + 0.003)
53
f2dfa
1/a x error in f2
fl/a
___
a
f2 -
=
0. 038
f' /2
Setting f2 = . 00469 (minimum value of f2) results in an estimate of
maximum error. This maximum error is
(2. 303) (.038) (004)l/'Z
d
e
± [(3/2) (.009) + (1/2) (.002) + 1/2 (.005) +
=
is of the order of 19 percent.
DW
e
-
Ac
d(Re)
Re -
. 161
±.19
The error in
Re
.16
e
4W
-
dW
(D2+D1)
d(D2+D1)
e
dLe
W
dD1
dD2
-
W-
=
±
=
± .20
dPe
-
(.004 + .002 + .001 + . 19)
The error in Reynolds number is of the order of ± 20 percenL
Monrad and Pelton's equation for heat transfer is
(St)
(Pr)2/3
=
.oz (D2/D1)
.53 Re -.2
1
54
Error in .02 (ID2 /D1Y
Re
2
is
d(D2 ID )
D21D1
- (1/5)[ W d(D2 'ID1)
d(D7 ID.1)
d(D2/D1)
D1+
dD 1
=
dL
d(D2+D1)
dID2
dID2
d D2
(D2/D12) d D1 +
-
D
1
dD1
d(D2/D1)
D21D1
-
dID2
-
ID2
Error in .02 (D2/D1Y
Re
=-.53
+ .2
dID
2
1+53
dID1
=( D2+ID1 -
+ .2
D2
D2+ID1
+ .2
-.2+.2
dD2
W
dLe
.53 d ID1 +
dID2
=
dID2
ID1
.2
=
is
dID2
ID2
-
.2 dW
--
due
± (.002 + .002 + .001 + .001 + .038)
. 044 or 4. 4 percent
55
22
h(D-D)ir
hA
St
= h/GC
q
=
=
4WC
RSS
3. 4129 VC
RSS + RCU
The errors in reading voltage and current were 0.5 and 1.0 percent
respectively. Assuming negligible error in the ratio of resistances,
the error in q was therefore of the order of 1. 5 percent.
h = q / (A x
A= 1TD1L
Error in
and hence in A is ± 0. 4 percent.
TWI - TWO
q II?
2k
(r
2
2
/2
r.
/2
r.
in r0 /r.)
o
2
1
i.
Assume an error of 5 percent in the expression on the right hand side.
Because of its small magnitude, it contributes at the most an error of
0. 5 percent in TWO. The errors in reading thermocouples were
of
the order of ± . 025°C.
TWO-TB
tT is of the order of 10-15°C.
Error in thermocouple readings TWI and TB results in an error
of
.025+.025 x 100 or 0.5 percent in AT
10
Total error in
T
0.5 + 0. 5
the test section has negligible effect on h.
1 percent
Heat Loss from
56
Error in h = ± (1.5 + 0.4 + 1)
2. 9 percent
22
q
LxT
-
St
d(St)
St
22
d(St)
St
2
q
d(D2-D1)
2
4WC
d(DD)
4a+
d(D-D) =
2
(D2-D1)
dD1
d(tT)
W
2
(2D2) d ID2 - (2D1) d ID1
2dD2-
2
2D1
2
2dD1
D2-D1
ZD
q
p
ID2
2D2
=
iT
2D
2
1
dD2-(-j5--+
D2-D2
2
d(LT)
1
1
2
D2-D1
1.
dW
W
± (.0150 + .008 + .006 + .01 + .004)
= ±.043
The Prandtl number itsed is that of water and does not involve
any experimental measurements.
The error in St and henze in St Pr2
percent.
is of the order of 4, 3
57
DISCUSSION OF RESULTS
Friction Factor Data
To test the validity of the system and the experimental method,
friction factor data were obtained for water, The results are shown
in Figure 4. Also shown are the upper and lower limits of the data of
Brighten and Jones (1964). The present data fall well within resuLts
of these workers. Therefore, It was concluded that the apparatus, as
well as the experimental technique, were satisfactory. A plot of
versus Re2 for the data on water and Shell solvent is shown in Figure
5.
The results are in good agreement with equation (15), proposed by
Rothfus and coworkers (1955). This equation was used for the least
square analysis of friction factor data and evaluation of efective
viscosity of dispersions, as discussed in the previous chapter. The
Reynolds number was based on the effective viscosity. The observed
and calculated data are given in the Appendix.
The progress of mixing in the circulation system as a function of
time following the addition of a second liquid phase to the system can
be observed in Figure 6. The second liquid phase in this case was
25 percent by volume light oil. Pressure drop (manometer reading)
and heat transfer coefficient are plotted as a function of time witk zero
time being the instant that a second liquid phase is added to the agL
tated tank. Total mass flow rate through the test section remained
58
1
0
t
I
I
EXPERIMENTAL
0087 Re025
200
0079R1°25
100
m
80
- p_ - - -
0
X6.O
-
.-9 OIy
40
I
0'8 I0
20
40
I
I
60 80 100
Re X104
Figure 4. Friction factor plot for water.
WATER
N
V
SOLVENT
0
SOLVENT(NE W)
0
SS941 DISPERSION
I
401o9(Re2.Jç)-O4
oo
I
&
2
4
I
I
I
6
8
(0
Re2 X IO
Figure 5
Outer wall friction factor plot for water, solvent and SS94. 1 dispersion.
38
U)
PRESSURE DROP
36
w
3:
z
C-)
(;34
z
w
28
cr32
I-
000
Iii
0
3O
0
0
0
HEAT TRANSFER COEFFICIENT
I
0
I
I
I
I
I
I
10
20
30
40
TIME, MINUTES
Figure 6. Progress of mixing.
50
60
70
6i
constant. The heat transfer coefficient has accomplished 90 percent
of its total change in six minutes while the pressure drop requires
about twice as long for the same percentage change. The mixing
phenomenon was not investigated in detail.
Figure 7 is an error plot of the outer wall friction factor data on
dispersions compared to equation (15). The value of 'f2 Predicted' is
obtained from equation (15) using the Reynolds number based on
experimental effective viscosity. The predicted values have a stan
dard deviation of 1.0 percent. These results are indicative of the
general experimental accuracy of the data since experimentally mea-
sured viscosities are used to predict friction factor and these were
obtained from the experimental friction factor.
The effective viscosities and relative fluidities are shown in
Table 2. Effective viscosity increases with increasing dispersed
phase concentration for dispersions containing isooctyi. alcohol,
solvent, and Ught oil. This would be expected from theories on the
viscosity of dispersions. The results for H07, 5, H014. 1, and H032, 5
indicate that the effective viscosity does not change appreciably with
the addition of more dispersed phase liquid. This is in agreement
with the findings of Ward (1964) and Legan (1965). Ward explained
this unusual behavior by examining the drop size and drop-size
distribution fo the heavy oil dispersions. These distributions were
characterized by a large number of drops occurring in the diameter
62
Table 2. Effective viscosities and relative fluidities.
Run
Temperature
Viscosity x 10
(lb/ft sec)
1023. 6
24. 707
1023.6
35, 33
12.217
12.266
SS4. 7
19. 775
7,5730
SS4. 7
27. 800
6. 2930
SS4. 7
36. 900
5.3830
86886
SS 19. 2
21. 122
9. 4090
.69851
SS 19. 2
35. 452
6. 8260
70495
L04. 6
26. 146
7. 1570
.81761
L04. 6
L04. 6
L025
L025
42. 186
5. 6660
.74711
59. 000
4. 4770
7 142 1
42. 209
9. 6740
43739
L 025
58, 907
8. 0560
39748
1-102. 1
23. 290
6.3810
97864
H02. 1
41. 360
4. 5450
94562
H02. 1
55. 540
4. 2020
.80291
H07. 5
22. 675
H07. 5
42. 000
7.0410
5,2640
H07. 5
58. 745
4. 7410
.67707
H014. 1
23. 780
7.5120
.82193
H014. 1
42. 160
5. 1900
.8 1602
H014. 1
58. 300
4.4810
.72125
H032. 5
24. 610
7. 3470
82455
H032. 5
42. 070
78703
H032. 5
58. 628
5.3900
5.1180
26. 755
11.739
'1c "e
49477
39323
89659
O
89652
.49177
O
O
89972
80691
62832
63
r
I
/
x HEAVY OIL
- ALCOHOL
LIGHT OIL
' SOLVENT
6
5
X IO
7
EXPERIMENTAL
Figure 7. Error plot for outer wall friction factor using experimental
effective viscosities.
64
range 1 /2 to 10 i but the remaining drops, accounting for quantity of
the volume, having diameters as large as 300 and in some cases 600 p
The unusual behavior of the friction factor was explained by a 'slip
velocity of the large drop relative to a fluid element in which they are
contained.
The relative fluidity,
ce' of the dispersions is plotted as a
function of the dispersed phase concentration on Figure 8, The
relationship
2.54
(23)
used by Legan and Knudsen (1966) for correlation of relative fluidities
at room temperature is shown for comparison. Legan and Knudsen
indicated that in case of heavy oil dispersions, the applicability of this
relationship is limited to volume fractions of heavy oil below 10
percent. Present results show a similar type of behavior to those of
Legan and Knudsen.
A second error plot of the data on dispersions compared to
equation (15) is shown on Figure 9. In this case the Reynolds number
is based on the effective viscosity calculated by equation (23)
Exclud-
ing the heavy oil results, the predicted friction factor has a standard
deviation of 3. 30 percent.
As the temperature increases the relative fluidity decreases at
constant concentration, a phenomenon also observed by Legan and
10
'D23
41 D
20,28
370
08 560
023
4 2V
5 9V
250
24
420
42
58
059
420
35
a
21
590
0 HEAVY OIL
o ALCOHOL
25Q V27
V42
V LIGHT OIL
350 V59
O SOLVENT
02
NUMBERS INDICATE
TEMPERATURES(°C)
01
RELATIVE FLUIDITY=e254
02
VOLUME FRACTION DISPERSED PHASE
Figure 8. Relative £luidities.
03
66
8
x
HEAVY OIL
- ALCOHOL
LIGHT OIL
5
+ SOLVENT
5
X
6
7
EXPERIMENTAL
Figure 9. Error plot for outer wall friction factor using
Equation (23) for effective viscosity.
67
Knudsen. Interfacial tension changes slowly with temperature and,
therefore, would not be expected to cause this appreciable variation.
changes rapidly with
Viscosity ratio of the two phases
temperature and was considered as a parameter affecting the variation
of fluidity with temperature.
versus the viscosity ratio
Figure 10 is a plot of (/i)e'
d'cTB
/
dc70
.
TB is the tempera.
ture at which the measurement is made, subscript 70 denotes 70°F,
and
c
is the viscosity of the continuous phase. The variation of
with
d'cTB
was not as systematic as the one shown on
Figure 10. The choice of 709F as the reference temperature was
arbitrary. Most of the previous room temperature results were
obtained at or close to this temperature
None of the relationships
described by Ward and which involved the ratio d'c were found to
represent the effective viscosity of dispersions since the observed
variation with temperature was in the opposite direction to that pre
dicted by these equations. The results of Legan, Ward, Cengel (1959),
and Wright (1957), Faruqui (1962), and Finnigan (1958) are also
included in Figure 10, The data, excluding that of heavy oil, were
fitted by simple linear regression with a standard deviation of 8. 35
percent to the relationship
e
c
2,5
038 + 0.61
=
1
/ FACTOR
dcTB
dc70
(78)
68
-0
U HEAVY OIL
o ALCOHOL
I7
V LIGHT OIL
O SOLVENT
15
2?%HEAVY 011.0
- . .-
-o
.D
IF
,
/__
.,.
----0
141%$EAVYOIL
O9
up
07
F
_-1
-o
02
V
1
04
06
Figure 10. Plot of
08
\
a 0510
I
10
e25 versus
'4
12
dcTB
/
dc7O
69
Where FACTOR is defined by the reciprocal of the right hand side of
equation (78) for convenience,
- (FACTOR) =
e
-2.54)
(79)
A plot of ceACTO versus the volume fraction, 4), is shown
on Figure 11. From here on (
/)(FACTOR) is referred to as
corrected relative fluidity for convenience. The ReynoLds number
based on the effective viscosity calculated by equation (78) was used to
obtain outer wall friction factor f2 by equation (15). These predicted
values of f2 are plotted against the experimental values in Figure 12.
Excluding the heavy oil results, a standard deviation of 2 percent was
obtained.
The variation of relative fluidity with temperature could be due
to change in drop size and drop size distribution at the higher tempera-
tures and further investigation is necessary. For the prediction of
effective viscosity and hence the friction factors, there are three
alternatives. These are equation (66), equation (23), and experimental
values. Each alternative predicts friction loss within reasonable
engineering accuracy.
In case of heavy oil dispersions, particularly at high concentrations and high temperatures, the predicted viscosities show large
deviations from the experimental results0 This is explained by the
different drop size and drop size distribution reported by Ward for
I
14
o
HEAVY OIL
O ALCOHOL
>I-
V LIGHT OIL
-il2
O SOLVENT
LL
LU
>
O8
Lii
()
LU
a:
00
00
I
01
02
03
04
O5
VOLUME FRACTION DISPERSED PHASE
Figure 11. Corrected relative fluidities.
/
8
x HEAVY OIL
- ALCOHOL
LIGHT OIL
5
+ SOLVENT
5
6
7
X tO EXPERIMENTAL
Figure 12. Error plot for outer wall friction factor using
Equation (78) for effective viscosity.
72
heavy oil dispersions. For better accuracy, experimental effective
viscosity should be used for systems with
d'c'
°°
Heat Transfer
To check the apparatus and procedure, heat transfer results
were obtained for water, Shell solvent and compared with Monrad and
PeltonTs (1942) equation (Figure 13). Close agreement is seen to exist.
However, at the lowest Reynolds number of 9912, the heat transfer
coefficient was too low compared to Monrad and Pelton's equation.
This Reynolds number appears to fall in the transition region between
laminar and turbulent flow.. The change in the behavior of heat trans-P
fer coefficient can be observed in Figure l4-1 in Knudsen and Katz
(1958) and in the following table where Quarmby's (1969) results for a
radius ratio of 2.88 and a Prandtl number of 10 are compared with
Monrad and Pelton's equation for three Reynolds numbers.,
Table 3. Comparison of Nusselt numbers predicted by Quarmby,
Monrad and Pelton at Pr 10, R2 /R1 2,88,
NU
Re
Q uarmb y
Monrad
Pelt on
Difference
(%)
10, 184
100. 49
121
-17.2
73, 035
595. 95
587
1.5
122, 275
918.27
887
3. 6
73
WATER
SOLVENT
SOLVENT(NEW)
SS94I DISPERSION
4
Re XIO'4
Figure 13. Heat transfer results for water, solvent and
SS94. 1 dispersion.
74
In Table 3, the percent difference is calculated by
Difference (%)
NUQNUM
NUM
where Q refers to Quarmby and M to Monrad and Pelton
The heat transfer data on dispersions were correlated with
Monrad andPelton's equation (76), using Prandtl number of the
continuous phase and Reynolds number based on the effective viscosity. Friction factor data were taken at three temperatures (two in a
few cases) bounding the temperature range of the heat transfer run,
The effective viscosity at the bulk temperature was then obtained by
interpolation as shown in the section on Sample Calculations, For all
heat transfer runs, the fully developed heat transfer coefficient was
calculated from temperatures at X = 62. 5 cm, i. e. , at a location on
the heated length 62. 5 cm from the point where the heat transfer
begins. At this location, the temperature profile was always fully
developed arid the end effects (axial conduction, etc ) were absent.
This was indicated by the bulk temperature profile being parallel to the
wall temperature profile along the heated length from X = 5O 5 to
X
74. 5 cm.
An error plot of the heat transfer data on dispersions compared
to equation (76) can be seen on Figure 14. The 'St Pr2
Predicted
was calculated by
St Pr 2/3 Predicted = .031971 Re
-.2
(80)
75
46
30
30
34
38
(St)(Pr)213 X IO
42
EXPERIMENTAL
Figure 14. Error plot for heat transfer using experimental
effective viscosities.
76
using experimental effective viscosity in the Reynolds number. The
results show agreement with Morirad and Pelton's equation. The
standard deviation of the predicted results was 5. 5 percent.
A second error plot of the heat transfer results is shown on
Figure 15. The 'St Pr2 /3 Predicted' was obtained from equation (80)
using in this case effective viscosity calculated by equation (23).
Excluding heavy oil results, the predicted results had a standard
deviation of 3,7 percent. Results for runs HO2. 1, H07. 5, and H014. 1
are within about 10 percent and for H032. 5 within about 20 percent of
the experimental values.
In the third error plot in Figure 16, the effective viscosity
calculated by equation (78) was employed in the calculation of the
predicted results. Excluding heavy oil, the standard deviation in this
case was 4. 3 percent. The heavy oil results are within about 30
percent.
The error plots show large deviations from Monrad and Pelton's
equation in case of heavy oil, particularly at high concentrations and
high temperatures. This is explained again by the different drop size
and drop size distribution reported by Ward for heavy oil. In general,
the heat transfer coefficient can be predicted by Monrad and Peltons
equation using any of the three methods described above for obtaining
effective viscosity. However, in case of lJd/IL
200, it is suggested
that for better accuracy the experimental effective viscosity be used.
77
50
46
LU
0
LU
a:
a.-
HEAVY OIL
ALCOHOL
LIGHT OIL
30
SOLVENT
30
34
38
(St)(Pr)213 X O4
42
46
EXPERIMENTAL
Figure 15. Error plot for heat transfer using Equation (23)
for effective viscosity.
78
50
46
o HEAVY OIL
o ALCOHOL
V LIGHT OIL
o SOLVENT
30
30
34
38
42
46
(St)(Pr)213X 1O4 EXPERIMENTAL
Figure 16. Error plot for heat transfer using Equation (78)
for effective viscosity.
79
Thermal Entry Length
Thermal entry length is the heated Length up to the point where
the local Nusselt number becomes equal to the fully developed Ntisselt
number. Thermal entry lengths for water and dispersions are shown
in Table 4. In this table
x+
X
D
(Pr)
(69)
e
is the Prandtl number calculated from the properties of the
mixture and (Pr) is the Prandtl number of the continuous phase.
Thermal conductivity in (Pr)
is the volumetric average of the
thermal conductivities of the components in the mixture. The heat
capacity of the mixture (dispersion) was obtained from the heat transfer data.
q
LTxW
An average value was calculated from the several sets of data for a
particular dispersion and temperature. It is interesting to note that
the entry length shows systematic variation with respect to (Pr)c but
not with respect to (Pr). Faruqui and Knudsen (1962) measured the
temperature profiles for Shell solvent dispersions and reported that
these profiles depended on the Prandtl number of the continuous phase.
The present observations are in agreement with Faruqui and Knudsen0
Also shown in Table 4 are the theoretical entry lengths reported
Table 4. Thermal entry lengths.
System
Re
Water
1023. 6
7. 18
7. 18
7. 06
7. 12
7. 09
6. 93
17.5
17.5
17.5
17.5
15.9
27, 500
6. 01
14. 3
5.81
5,81
6,79
13.3
13.3
7.37
6, 30
6,39
7.09
7.79
17.5
17.5
17.5
8. 15
20. 7
56, 000
51, 000
46, 200
47, 800
**for
17.4
16,7
20.7
H02. 1
H07. 5
H014. 1
H032. 5
=
Quarmby
24. 0
47, 600
(NU)d
Present
4.50
SS4. 7
x
x+
3. 85
48, 300
29, 111
(NU)
(Pr) m
88, 100
75, 800
51, 000
45, 400
41, 300
30, 900
27, 900
20, 000
L04. 6
L025
*for
(Pr) c
1.05
1,5
6.43
6. 33
6. 05
& Anand*
13.5
at
Pr = 7. 1
26 for
Pr = 1
Re = 50, 000
21 for
Pr = 10
Re = 50, 000
15. 9
20.7
20,7
20.7
Lee * *
14.8
at
Pr = 5.8
17.5
14.6
at
Pr = 6
81
by Lee (1968) and Quarrnby and Anand (1970). Quarmby's figures are
based on NU /Nd = 1,05, i.e., the length up to the point when local
Nusselt number is 5 percent higher than the fully developed Nusselt
number. Leets results are for a radius ratio of 1.5. The present
results are between those of Lee and Quarmby.
Wall and bulk temperatures obtained on SS4. 7 for Re = 47600
and (Pr)= 6.79 are shown on Figure 17 as a function of X, the distance
along the heated length, from the point where the heat transfer begins.
The abnormal increase in the wall temperature in the entrance region
(X = 2.5 to X
14.5) is probably due to some defect in the tube wall
or the connection between the tube and the power terminal since it
occurred around the same location in all the cases. The wall tem-
perature profile becomes parallel to the bulk temperature profile at
X = 32. 5 cm. Therefore, in this case, the entrance length is 32. 5 cm,
The bulk temperature profile was calculated from TB1 and TBZ
assuming a linear variation.
Water in Oil Dispersions
Because of the high Prandtl number of light oil, heavy oil, and
iso-octyl alcohol, and hence low h and high
T, low power is needed
for a study of the dispersions containing one of these liquids as the
continuous phase. It was not possible to obtain that low power from
the present power source.
36
INSIDE WALL TEMPERATURE
o
- 0
o
0
0
0
0
0
35
BULK TEMPERATURE
20
'9
J0
20
30
40
60
70
80
X, CENTIMETERS
Figure 17
Temperature profje along the heated length for SS4 7 disperj0
90
83
Outer wall friction factor data for a dispersion containing 94. 1
percent Shell solvent are shown on Figure 5. The effective viscosity
of this dispersion was very close to that for the pure solvent in agreement with Finnigan (1958) who reported the effective viscosity of 90
percent Shell solvent dispersion to be equal to that of the pure solvent.
Ward also studied the water in solvent dispersions and reported that
such dispersions did not behave as single phase fluids.
Heat transfer results for SS94. 1 are shown on Figure 13. New
Shell solvent was used in the preparation of this dispersion. Although
the new and the old materials had the same density and viscosity, the
heat transfer results differed. This was attributed to the possibility
of a different thermal conductivity.
Water-in-solvent dispersions with dispersed phase concentrations
greater than about 10 percent exhibited erratic behavior, Steady state
and a uniform composition couLd not be attained. This difficulty was
also reported by Finnigan.
84
CONCLUSIONS
The friction losses of dispersions studied can be treated with
Rothfus and coworkers' equation for single phase systems and an
effective viscosity can be obtained. The outer wall friction factors
calculated from this effective viscosity had a standard deviation of
1 percent from the experimental values which is indicative of the
scatter of the experimental friction loss data.
The effective viscosity of heavy oil dispersions does not change
appreciably with composition at oil concentrations above 7, 5 percent.
This anomaly is explained by a difference in drop size and drop size
distribution as indicated by Ward (1964) and Legan (1965).
The relative fluidity decreases with increase in bulk temperature
and was correlated by equation (78) using viscosity ratio
dc7O
d'CTB /
as a parameter. The effective viscosity for Shell solverit
light oil and iso-octyl alcohol dispersions can be predicted by equations
(Z3) and (78).
The outerwall friction factors obtained by using effec-
tive viscosities calculated by these equations had standard deviations
of 3, 3 and Z, 0 percent respectively. It is suggested that for heavy oil
200) the experimental effective viscosity be used. However,
if equations (23) and (78) are used to predict outer wall friction factors
for heavy oil the standard deviations from the heavy oil experimental
data are 6. 3 and 7. 4 percent respectively
85
The water in solvent dispersion containing about 94 percent
solvent had an effective viscosity very close to that of the pure solvent.
A dispers ion with solvent as continuous phase behaves differently from
those with water as continuous phase having the same concentration
of
continuous phase. Water-insolvent dispersions behave erratically and
the small amount of data obtained were not sufficient to draw firm
conclusions.
The heat transfer coefficient can be predicted from the Monrad
and Pelton equation using Prandtl number and heat capacity of con
tinuous phase and the Reynolds number based on the effective viscosity.
The heat transfer coefficients evaluated in this manner using the
experimental effective viscosity had a standard deviation of 5. 5 per
cent from the experimental values. Excluding heavy oil, the predicted
heat transfer coefficients using equations (23) and (78) for effective
viscosity had standard deviations of 3. 7 and 4. 3 percent respectively.
In case of heavy oil dispersions the corresponding deviations were
8.8 and 11.3 percent respectively.
The thermal entry length depends on the Prandtl number of the
continuous phase and does not show systematic variation with respect
to the Prandtl number based on the mixture properties.
In summary, the friction factor and heat transfer coefficient for
dispersions with water as the continuous phase can be predicted from
the single phase equations using the Reynolds number based on the
86
effective viscosity. For heat transfer the Prandtl number and the heat
capacity of the continuous phase should be used.
The effective viscosity can be predicted from equation (23) or
(78), the latter equation being more reliable for temperatures above
70°F. For better accuracy in case of dispersions with d'c > 18,
particularly at high concentrations and temperatures the effective
viscosity should be obtained experimentally.
In case of dispersions with F1d/.L
200, the effective viscosity
does not change appreciably with composition at oil concentrations
above 7.5 percent. An estimate of the effective viscosity for concentrations above 7. 5 percent may be obtained from equation (23) or (78)
using4 = P075.
87
RECOMMENDATIONS FOR FURTHER WORK
The dispersions in which the organic phase is the continuous
phase require further investigation
One way to obtain a steady
composition and a stable system would be to introduce the immiscible
phases separately into a small mixer at the inlet of the test section
Photographic studies should be made to determine the effect of
the temperature on the drop size and drop size distribution of the
dispersions
It is possible that the decrease in relative fluidity with
temperature can be explained by changes in the dispersed phase drop-
let size and size distribution
Increased pumping capacity should be utilized to extend the
range of Reynolds numbers achievable with high viscosity liquid-
liquid dispersions.
Study of dispersions having high Prandtl number fluids as the
continuous phase should be made.
Annuti of various diameter ratios should be used in the study of
dispersions to make the resuLts more general.
88
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APPENDICES
93
APPENDIX I
PHYSICAL PROPERTIES
94
Physical Properties
The physical properties of the four organic phases are listed in
Tables 5-8. The density of each liquid was measured with a Cenco
16752 hydrometer set. The viscosity was determined by means of a
Cannon-Fenske viscometer set. The interfacial tension was measured with a Du Nuoy ring tensiometer according to ASTM method
D97l-5O. The heat capacity was obtained from the heat transfer data.
Thermal conductivity measurements were made by Heat Transfer
Research Inc., Alh3mbra, California.
The effective densities of the manometer liquid are listed in
Table 9. This density represents the difference between the carbon
tetrachloride density and that of water. The carbon tetrachloride
density was obtained from Hodgman (1960) and Marsden (1954) and a
linear variation with temperature was assumed.
95
Table 5. Physical properties of heavy
Temperature
T emperature
Density
(Ib/ft3)
(F)
(F)
54.25
54,24
54. 19
54. 19
54. 13
54. 09
53. 94
53. 70
53. 58
53. 32
53, 14
52. 99
52. 82
52. 56
52. 40
71.0
73. 8
79. 0
91.0
97. 2
111.0
119.0
126, 0
135.0
148. 0
157. 5
154. 1
148. 9
63. 0
64, 1
67. 0
70. 0
73. 0
80. 5
54. 32
62. 0
64. 4
65. 6
67. 0
67. 5
Viscosity x 10
(Lb/ft sec)
130.6
118.2
105. 4
80. 65
64. 13
45, 55
87.5
98. 7
31,99
21,70
15.91
13.74
10.81
111.5
127.0
140. 7
147. 0
155.5
Viscosity was fitted to log10 = 43. 05 - 16. 14 log10 (T, °R) where
T, °R is the temperature in degrees Rankine.
80
Thermal conductivity
(Btu/hr ft F)
0.0822
230
0.0775
Temperature
(°F)
Temperature
(°F)
Heat capacity**
(Btu/lb °F)
48
77
100
0. 448
300
0.559
Taken from Ward (1964)
Taken from Legan (1965)
Interfacial tens ion*
(dyne/cm)
96
Table 6. Physical properties of i,so-octyl alcohoL
Density
(lb/ft3)
Temperature
62,0
65,0
66.2
66.7
68,5
71.7
72.7
75.2
79,2
84.7
93,7
118. 5
51.89
51.82
51.76
51.69
51.62
51.30
51.28
51.03
50.83
50.77
50,63
50.52
126.0
50. 32
106.5
111.5
114.5
118.2
Temperature
(°F)
62.0
64.2
66.2
68.7
71.7
86.0
87.5
98.7
107.0
108.0
113.0
Viscosity was fitted to log10
(°F)
80
97
117
2,434
2,331
2.144
Thermal coiiductivity
(Btu/hr ft °F)
0,0805
0.07275
225
77
76
6,491
6.204
5.717
5.573
5.205
4.783
4.204
3.469
3.077
2.686
= 30.31 - 11.94 log10 (T, °R)
(°F)
(°F)
7,284
6,787
6.587
99. 5
Temperature
Temperature
Viscosity x 1O3
(lb/ft sec)
Heat capacity
(Btu/Ib °F)
0.726
Interfacial tension
(dyne /cm)
12,2
11.9
11,4
97
Table 7. Physical properties of light oil.
Temperature
Temperature
Density
(lb /ft3)
(°F)
62. 0
64. 2
66. 6
67, 0
68. 0
72. 0
74. 0
80. 5
90. 5
101.2
120. 0
144. 5
160. 0
(F)
54. 24
54, 19
54. 14
54. 14
62. 2
63. 8
67. 0
68. 0
54, 11
54. 03
53, 98
53. 84
53, 62
53. 39
52, 98
52. 46
52. 13
71.0
72,0
Viscosity x 10
(lb/ft sec)
11.97
11073
10. 93
10, 57
9, 791
9. 583
8. 194
6. 705
79. 5
88. 7
98. 5
109. 7
5,555
4. 535
3, 756
3, 111
3. 039
2. 568
2. 330
120.7
133.0
135,0
145.0
151.0
155,5
2. 174
Viscosity was fitted to log10 jt = 26.34 - 10.40 log10 (T, °R)
Thermal conductivity
(Btu/hr ft °F)
Temperature
(°F)
000675
0. 0642
80
225
Temperature
(°F)
100
300
76
114
144
From Legan (1965)
Heat capacity*
(Btu/lb °F)
0.450
0. 560
Interfacial tension
(dyne/cm)
52,6
47.5
42.9
98
Table 8. Physical properties of Shell soLvent 345.
Densy
Temperature
(lb/ft
(°F)
62. 0
64. 0
66. 0
68. 0
70. 4
73. 2
79. 5
81.6
86. 0
90. 0
91.0
100. 0
108. 0
Viscosityx
(lb/ft sec)
Temperature
(°F)
)
49. 80
49. 75
49, 70
49. 66
49. 59
62. 0
63. 5
66. 7
70. 0
72. 7
49,53
81.0
49. 34
49. 30
49. 18
49. 07
49. 04
86. 8
94. 0
96. 0
99. 1
0. 6820
0,6781
0. 6585
0, 6418
0.6310
0.5921
0. 5678
0.5359
0. 5196
0. 5073
0. 4454
117.5
48. 8 1
48. 62
48.40
Viscosity was fitted to log10
117.5
8. 4395 - 4.2696 log10 (T, °R)
Temerature
Thermal conductivity
(Btu/hr ft °F)
0,0682
F)
80
0, 062
230
Temperature
(°F)
73.2
95,5
77
From Ward (1964)
Heat capacity
(Btu/lb °F)
0.444
0,461
Interfacial tens ion*
(dyne /cm)
49
99
Table 9. Effective density of the manometer
liquid.
Temperature
Effective density
(°F)
(lb lit3)
60
37.78
68
37.30
70
37. 18
80
36.60
90
36.04
100
35,53
100
APPENDIX II
RELATIONSHIP BETWEEN WALL TEMPERATURES ON THE
INSIDE AND OUTSIDE OF THE CORE TUBE
101
The relationship between these two temperatures, TWI and TWO,
is established by considering the applicable energy equation (see
Arpaci, 1966)
hr d/dr (r dT/dr) =
(81)
where
=
energy generated per unit volume of the stainless
steel wall.
The boundary conditions are
at r = r.
(82a)
T
TWIatrr.
(82b)
T
TWOatrr 0
(82c)
dT/dr
0
1
where r. and r are respectively the inside radius and outside radius
of the core tube.
Solution of the differential equation (81) and application of the
boundary conditions results in
TWI - TWO
qW
Zkss
Z
(r /2
r2/2
-
r
2
In r /r
102
APPENDIX III
HEAT LOSS FROM THE TEST SECTION
103
Heat was lost from the outer tube of the test section due to
natural convection. An estimate of this loss is obtained by considering the resistance to heat flow given by the following equation taken
from Arpaci (1966)
1/U o
(R2 /R 1 ) /h. + (R2/k) In (R2/R1) + 1/h
=
(83)
L
where k is the thermal conductivity of the outer tube of the test
section,
From Perry (1963)
h
0
0.25
0,5 (At 5 /D1)
0
(84)
for long vertical pipes.
At
is the temperature (°F) of the exposed surface less that of
the ambient air in the room and D' is the outside diameter of the pipe
in inches.
0. 12 Btu/hr ft °F.
k for acrylics
Maximum value of A t encountered at the highest bulk temperature =
60°F
1.74 inches
=
then
0.5 (60/1.74)0.25
h
1/u 0 =
and
1,74/1,24
2600
1.03
+
1,2 Btu/hr ft2 °F
1.74
in (1.74/i. 24) + 1/1.2
2 x 12 x 0. 12
104
= 0.97 Btu/hr ft2 °F
U
Heat lost q1 is given by
q
1
= U0 A 0 ,t S
where A is the outside surface area of the outer tube seven feet long
0
A
q1
=
iT x (1. 74/12) x 7
=
3.18 ft2
= 0,97x3,18x60
=
185 Btu/hr
Heat received by the fluid from the inner core was of the order of
24, 000 Btu/hr. Therefore,
Heat lost
=
(185/24,000) x 100 percent
=
0.8 percent
The increase in bulk temperature due to the heat received from the
inner tube of the test section was of the order of 1. 7F. Therefore
the change in bulk temperature caused by the heat loss is 1. 7 x
(0. 8 /100) °F, or 0. 01°F, This has negligible effect on the heat
transfer coefficient h for heat transfer from wall of the inner tube
to the surrounding fluid since
t in this case was of the order of 15°F.
105
APPENDIX IV
MEAN DEVIATION OF DISPERSION CONCENTRATION
106
Table 10. Mean deviation of dispersion concentration.
Run
Mean deviation of
concentration
(%)
HO2. 1
0. 1
H07. 5
0. 7
H014. 1
0. 9
H032. 5
1.4
1023. 6
0. 1
L04. 6
1.0
L025
0.8
SS4. 7
0, 5
SS19. 2
0. 6
107
APPENDIX V
THERMAL ENTRY LENGTH DATA
Table 11. Thermal entry length data.
Water
1
2
3
4
5
6
7
8
1023.6
L04.6
L025
SS4.7
H02. 1
H07.5
H014. 1
H032,5
Thermal entry
TB1
TB2
(Ib/sec)
(°C)
( C)
(cm)
3,97
3.94
4.11
3.66
3,27
2,47
2.22
1.56
3,84
45,7
37.83
46,6
38.76
17.70
17.75
18.25
17.67
17.77
19.07
24.71
18.65
18.80
19.42
19.22
19.45
44.5
38.5
32.5
32,5
3,94
3.89
4.00
25.70
26.15
19.82
22.82
22.00
22.60
24.39
W
Run
3. 96
4.01
3.89
3.84
(Continued on next page)
20.00
25.75
26.63
27.22
20.80
23. 76
22.97
23.58
25,52
length
32. 5
32.5
29. 5
29. 5
38.5
38. 5
38.5
32, 5
32,5
32,5
32.5
38.5
Table 11. (Continued)
Run
Water
x= 0.6
1
1023,6
L04, 6
L025
SS4,7
H02. 1
H07, 5
H014. 1
H032. 5
2,5
58.02
51,02
34.50
35.05
37.61
42,05
35, 17
35,43
36.00
38.62
43,50
42, 14
44. 40
30.39
36.19
38.81
37.73
34,54
31.98
37.44
39.83
38.69
35,45
33,12
38,02
36. 43
39. 05
43. 86
44. 62
33, 57
36. 09
5752
2
3
50,22
4
33.90
5
36. 17
39. 19
40, 43
6
7
8
Wall temperature (°C)
11.5
8.5
32. 90
35 12
35,64
37. 15
(Continued on next page)
5,5
58,50
51,72
59.05
51. 91
59. 16
52. 12
35, 57
36. 59
14.5
59. 16
51.95
39.31
35. 57
36. 28
38. 83
440 14
43.31
44. 76
33, 93
440 57
33. 17
370 58
39. 98
390 88
39,24
35.86
38. 79
37. 07
36. 09
37. 68
36. 57
36,62
38,26
37.41
39.24
37. 68
36. 57
37. 02
38. 55
35,71
17.5
58.65
51.54
35.19
36.61
39.48
44,53
44.76
34.71
20.5
58,28
51,58
34.80
35,88
38.79
43,33
44.50
34.49
Table ii. (Continued)
Run
X = 23,5
Water
1
2
3
4
5
6
7
8
1023,6
L04.6
L025
SS4.7
H02. 1
H07. 5
H014. 1
H032, 5
26.5
58.58
58. 65
-
51.60
34.73
35.57
38.33
42.63
43.98
33.81
34,68
35,71
38.50
43,10
-
33.76
37.90
39.29
39.05
35.24
37.02
36.40
37.12
38.81
32.5
58.67
51.60
34.78
35.93
38.57
43,12
44.24
33. 19*
38.09
40,17
39.29
35.74
37,59
36.76
37,32
39,69
Wall temperature at X = 29 5 was 33. 17°C.
Wall temperature (°C)
44,5
50.5
38.5
59. 14
58.84
59.09
51.88
51.86
51.77
34.85
36.02
38.67
43.07
44.29
33.29
38.36
40.24
39.50
35.59
37.46
36.83
37.37
40.09
34.98
36.02
38.64
43.12
44,45
33.31
38.52
40.33
39.57
35.88
37.51
36,88
37.41
40.19
35.00
36.14
38.76
43.19
44.45
33,35
38.59
40.36
30. 64
35.90
37,54
36, 95
37.46
40.26
62.5
74.5
86. 5
59,25
52,00
35.10
36.28
38.97
43.36
44,79
33,45
38.71
40,48
39,79
35.98
37.68
37.07
37.61
40.40
59. 38
59.52
52.21
35.33
36.50
39.21
43.83
52.10
35.21
36,41
39.12
43.62
45.0
33,57
38.83
40.60
39. 90
36,09
37.81
38.91
40.69
40,02
35,89
37,88
37, 17
37,73
40.52
37.83
40.60
111
APPENDIX VI
OBSERVED AND CALCULATED FRICTION LOSS AND
HEAT TRANSFER DATA FOR WATER,
SOLVENT, AND SS94. 1
Table 12,
Run
Water
Shell
solvent*
Observed and claculated friction factor data for water, solvent, and SS94. 1
TB
T
W
HT
(inch)
Re
fx 10 3
Re2
f2 x 10 3
4.821
4.568
4.971
5.103
5.189
5.364
5.490
5.673
5.685
5.858
5.841
6.135
6.242
6,544
7.147
7,750
8.130
94780
86460
78970
71710
65990
56640
48880
46040
43510
39840
36660
32190
27730
22890
17220
11780
9361
5.715
5.951
6.038
5.989
6.215
6.441
6.680
40520
37540
35060
32980
29340
26100
22750
5.415
5.639
5.722
5.675
5,889
6,104
6,330
(°C)
mb
(°C)
52.5
30.0
(Ib/sec)
4.054
47. 0
29. 1
4. 054
29. 64
41.8
36.7
32.5
25.4
18.2
18,2
18.2
18.2
18.2
18.2
18.2
18.2
18,2
18.2
18.2
28.4
28.0
27.2
26.0
25.8
25,8
25.8
25,8
25.8
25,8
25,8
25,8
25,8
25.8
25,8
4.064
4.064
4,064
4.064
4.165
3,922
3.707
3.394
2.742
2.362
1.950
1.467
1,004
0.797
29.97
30.65
31.06
31.93
34.25
31,40
28.10
24.27
20.50
16.60
12.53
8.95
5.53
2.81
1.86
100000
91260
83350
75690
69650
59770
51600
48590
45920
42040
38700
33980
29270
24160
18170
12440
9880
21.6
29.0
3.213
2.977
2,780
2.615
2.326
2.070
1.804
40.61
37.75
34.99
32.38
29.04
26.28
23.61
42760
39610
37000
34800
30960
27540
24010
(Continued on next page)
3. 123
29.18
4. 922
4. 664
4.710
4.835
4.917
5.083
5,202
5.376
5,387
5.551
5,535
5,814
5.915
6,201
6,772
7,344
7.704
Table 12. (Continued)
Run
TB
(°C)
T
mb
(°C)
Shell
solvent*
(con't)
Shell
solvent
21.3
25,1
20.6
25.0
(new)
SS94.l**
*
W
HT
(lb /sec)
(inch)
1.373
0.985
0.780
19.78
17.11
3,213
3.003
2.827
2.618
3.286
3.095
2.883
2.594
40,44
37.71
35.27
32.17
40.54
37,62
34.65
31.06
15. 94
Viscosity of Shell solvent was 6.571 x 10 -4 lb/ft sec.
Effective viscosity of 5S94. 1 was 6,797 x l0 lb/ft sec.
Re
fxlO 3
18280
13110
10380
7.078
7.720
43830
40970
38570
35760
5.779
5,944
6.031
6.028
5.811
5.864
5,952
6.150
42280
39820
37100
33380
8. 114
Re2
f2xlO 3
17320
12430
9833
6.707
7.315
41540
38820
36550
33850
40060
37730
35150
31630
7. 689
5,476
5,632
5.715
5,712
5,507
5.557
5,640
5,828
Table 13. Observed and calculated heat transfer data for water, solvent, and SS94. 1.
W
Run
Water
TB2
TB
TWI
TWO
C
V
(°C)
(°C)
(°C)
(°C)
(°C)
(amp)
(volt)
1
(ib/sec)
3.922
55.00
55.92
55.60
67.40
66.07
22.9
2
3. 969
45. 70
46. 63
46. 30
59. 23
57. 87
3
3.941
37.83
29.00
17.70
38.78
38.44
52.00
29. 58
18.31
18. 44
50.62
42.06
33.67
17. 75
29. 90
18.65
18. 82
1.562
0.761
18.25
17.67
17.78
19.08
19.52
19.44
19.24
19,50
20.01
20.60
3.138
3.184
34,95
29.56
35,50
30.12
19.02
18.68
18.89
19.68
20.22
35.30
29.92
43. 35
35. 10
36. 28
38. 98
300
307
310
302
320
320
320
320
316
200
150
11.1
11.1
3. 184
22. 30
22, 85
2.994
2.762
22,45
22.53
22,43
22.43
22.50
22,55
22,67
23,05
138
138
138
138
138
130
122
122
118
107
3. 932
4. 114
3. 651
4
5
6
3.275
2.470
7
8
9
10
11
Shell
solvent
TB1
2.21.9
1
2
3
4
5
6
7
8
9
10
2, 586
2. 364
.2. 081
1.801
1.464
(Continued on next page)
34. 85
37. 54
43.40
44.79
33.45
35.33
49.21
44.74
41.97
43.38
32.92
35.02
48.90
44.43
22. 66
37. 46
37. 16
38.05
39.26
37.73
37.00
38.69
39.57
37.74
38.96
37.47
23.24
22.84
22.94
22.81
22.81
22.93
23,00
23. 37
23. 12
39. 64
23. 17
23.02
23.02
23. 17
36. 77
38.46
39.36
39,46
22, 9
23.0
22, 1
23. 1
23, 1
23,2
23. 1
23,0
13.7
10.4
10. 9
10.9
10.8
10. 1
9.5
9,5
9.0
8.4
Table 13.
(Continued)
TB
TWI
TWO
C
V
(°C)
(°C)
(°C)
(°C)
(amp)
(volt)
20.10
20.25
20.18
20.63
20.83
20.80
20.44
20.62
20.58
33.60
34.61
35.31
33.26
33.91
33.31
34.32
35.02
133
133
133
32.98
33.62
35. 17
34. 88
132
132
132
10.7
10.7
10.7
10.6
TB1
TB2
Shell
solvent
2
(new)
3
w
(Ib/sec)
3.213
3.003
2.780
1
3. 277
20. 30
20. 83
20. 64
3.021
2.735
20.33
20.33
20.88
20.93
20.68
20.71
Run
SS94. 1*
1
2
3
Re
Run
Water
1
2
3
4
5
6
7
8
9
10
11
101800
88250
75920
63330
51110
45500
41410
30960
27970
20070
9912
(Continued on next page)
(°C)
Pr
3,202
3,796
4.441
5,396
7.139
7,114
7.005
7.068
7.030
6,885
6.839
h
(Btu/hr ft2)
2925
2711
2612
2385
2147
2009
1788
1416
1324
930
470
StxlO3
1.444
1.323
1.283
1.175
1.010
1.066
1.057
1.110
1. 155
1. 153
1. 195
NIJ
470,5
443.0
432.7
401.4
368.6
344.9
306.6
243,0
227,0
159.3
81.0
(St)(Pr)2 3
x iO3
3. 133
3,218
3. 468
3,614
3, 746
3.941
3, 868
4. 089
4. 237
4, 173
4. 303
io,6
10. 6
Table 13.
(Continued)
Re
Run
Shell
solvent
1
2
3
4
5
6
7
8
9
10
Shell
solvent
2
(new)
3
SS94. 1*
1
1
2
3
Pr
St x
h
(Btu/hr ft
502.6
NU
)
1St'1Pr
'
x 10 3
415.0
6.728
6.313
6.336
6.553
6.548
453.2
422.2
411.4
400.4
369.2
3.701
3,599
3.794
3,920
3.914
14. 63
399. 7
6. 737
355. 5
4. 030
14.63
14.61
14.60
14.58
370.5
333.0
6.833
329.5
4.087
6, 973
7. 007
296. 3
257. 6
4. 168
4. 186
218.3
4.357
43290
40570
37540
15.00
14.97
14.97
493. 3
437. 6
4. 100
14.96
411.1
390.0
448.8
4.112
4.215
44180
40720
36870
463.3
349,5
505.8
7.300
6.742
6,771
6.939
6.773
14. 96
14. 95
482. 2
440. 4
7. 005
7. 065
428. 0
390. 8
52210
49140
44300
41770
38590
36060
32960
29080
25180
20510
12.90
13.61
14.66
14.63
14.61
471.0
462.6
450. 1
289. 6
245.3
Dispersion SS94. 1 was prepared from new Shell solvent,
4. 113
4. 252
4. 288
117
APPENDIX VII
PROGRESS OF MIXING DATA
Table 14. Progress of mixing data.
Run
W
V
C
(lb/sec)
(volt)
(amp)
L025
3.907
23.0
304
h
HT
Time
TB1
TBZ
TB
TWI
TWO
(Bt u/hr
(mm)
(°C)
(°C)
(°C)
(°C)
(°C)
ft2 °F)
(inch)
0 (water)
25.97
26.15
26.15
26.95
27.22
27.22
27.22
27.22
27.22
27.22
27.22
26.60
26.84
26.84
26.84
26.84
26.84
26.84
26.84
42.32
40.99
40.44
40.06
39.89
39.83
39.79
39.79
40.91
39.59
39.04
2180
2400
2512
2590
2630
2647
2652
2652
30.44
33.60
35.85
37.00
37.70
37.91
38.13
38.21
38.38
38.41
38.57
38,64
38.68
38.68
2
4
6
8
10
15
20
25
30
45
60
75
90
26. 15
26. 15
26.15
26.15
26.15
38. 66
38.49
38.43
38.39
38.39
119
APPENDIX VIII
OBSERVED AND CALCULATED DATA FOR DISPERSIONS
HAVING WATER AS THE CONTINUOUS PHASE
Table 15. Observed arid calculated friction factor data.
1 20
ISO-OCTYI. ALCOHOL
.236
PHI
TB
RHOM
24.71
TIME
MT
38.59
35.54
33.02
30.21
27.07
23.84
20.80
17.06
11.06
7.88
26.40
27.66
29.04
30.60
32.52
35.46
39.30
44.46
60.48
80.22
CL
1.1249E 01
VISL
t.2239E-03
3.8333
3.6587
3.4848
3.3072
3.1119
2.8539
2.5949
2.2762
1.6733
1.2615
27440.6
26190.6
24946.0
23674.2
22276.5
20429.5
18575.2
16294.0
11978.3
9030.6
SLOPE
SCL
1.4235E02
4.0117E 00
27.42
28.20
29.34
31.32
33.18
36.30
40.08
45.30
61.56
77.46
CL
1.1257E 01
YISL
1.2186E-03
W
3.6907
3.5887
3.4492
3.2312
3.0500
2.7879
2.5250
2.2489
1.6439
1.3065
SCL
k.6172E-02
VESIi
1.2266E-03
F
.0064542
.0064822
.0065961
.0066640
.0066461
.0068528
.0070948
.0073105
.0078580
.0085378
RE2
F2
26301.9
24817.4
23638.1
22433.0
21108.5
19358.4
17601.3
15439.7
11350.0
8557.1
.0061158
.0061423
.0062502
.0062957
.0062976
.0064935
.0067228
.0069272
.0074460
.0080902
RE2
F2
24935.2
24245.5
23303.5
21830.3
20606.5
18835.4
17059.0
15193.9
11106.6
8826.8
.0062360
.0062137
.0061873
.0063246
.0063554
.0066315
.0067201
.0068742
.0074939
.0080355
SB
1.1949E-01
2.4120E-05
TB
36.97
34.99
32.41
29.36
26.58
23.53
20.03
16.78
10.94
8.31
RHOW
62.25
EVISL
VlSI.
t.2217E-03
TIME
RHOE
59.69
RE
W
35.33
MT
36.49
RHOM
36.30
RE
26314.9
25587.1
24592.9
23038.2
21746.7
19877.6
18002.9
16034.6
11721.2
9315.2
SLOPE
3.9545E- 00
EVISI
3.2393E-05
RHOW
RHOE
59.48
62.07
F
.0065810
.0065575
.0065297
.0066745
.0067070
.0069984
.0070920
.007251+5
.0079085
.0084801
SB
1.6542E-01
121
LIGHT OIL
PHI = .250
TB
RHOPI
26.76
TIME
HT
36.68
35.47
32.51
29.05
26.28
23.28
20.23
16.49
25.98
27.30
28.80
30.78
32.92
35.64
38.64
44.22
3.8953
3.7070
3.5139
3.2876
3.0741
2.6395
2.6190
2.2886
29320.5
27617.3
26178.9
V.494.9
22902.6
21154.7
19912.2
17350.0
VIS4
36.77
32.97
30.52
27.36
24.90
21.96
16.75
15.57
11.56
26.34
28.38
29.34
31.50
33.42
36.30
40,14
45.10
55.74
CL
1.16538 01
VISL
9.69738-04
RHOM
3,8421
3.6040
3.4492
3.2127
3.0281
2.8111
2.5212
2.2489
1.8156
3t.3&
33.10
37,14
41.40
46.44
58.20
64.92
CL
1.19318 01
VISL
8.26448-04
27498.9
26169.3
24806.3
23210.6
21701.6
20045.5
18489.2
16156.1
.0060166
.0060579
.0061406
.0062117
.0061706
.0065340
.0065655
.0068083
RE2
F2
32912.9
33873.4
29547.6
27521.5
25940.3
24081.3
21597.6
19265,0
15553.0
.0057748
.0058389
.0058651
.0060026
.0060929
RE2
F2
38991.1
37234.0
35701.8
33176.0
30709.8
28030.8
25146.5
22417.4
17887.7
16036.1
.00558 36
.0055318
.0055678
SB
RHOW
RHOE
61.81
59.67
F
.0060943
.0061620
.0061896
.0063349
.0064301
.0064896
0067491
.0068402
.0073179
0061493
.0063952
.0064816
.0069342
SB
1.59578-01
EVISL
V154
9,6740E-04
26.70
27.96
29.16
F2
2.1224E-01
SLOPE
4.01548 00
2.54488-05
TB
35.35
32,17
29.95
26.53
24.14
20.44
17.69
14.76
10.64
9.30
36.03
34734.0
32581.7
31182.5
29044.2
27375.6
25413.7
22792.6
20331.0
16413.6
SCt.
4.55838-02
TIME
0064806
.0065554
.0067231
.0068955
.0069287
0071850
RE
W
56.91
HT
.0063495
.0063931
RE2
EVISL
TB
TIME
F
4.50118-05
1.1739E-03
42.21
HT
RHOW
62.22
SLOPE
3.9157E 00
6.7607E-02
VISL
1.1563E-03
RHOE
60.12
RE
W
SCL
CL
1.1348E 01
36.23
W
3.7901
3.6195
3.4705
3.2253
2.9853
2.7248
2.4444
2.1792
1.7388
1.5586
SCI
6.86338-02
V154
8.0558E-04
RHOM
RHOE
RHÜW
35.74
59.21
61.42
RE
41148.6
39294.2
37677.2
35311,7
32409.0
29581.8
28537.8
23657.8
18877.4
16923.4
SLOPE
k.1912E 00
EVISL
3.28608-05
F
.0058925
.0058378
.3058759
.3059593
.0062655
.0062393
.0065697
0066805
.0369895
.0072792
SB
2.65488-01
.0056469
.0059370
.0059122
.0062252
.0063303
.0066230
.0068976
zzT
iHI1
IHd
$1
ST9
WI1
662
9
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9991
01T99'7
299S00
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'76T12'7
TSL
ST00'7
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9$747900
99022
96L3900
59002
52
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95 01
662L92
16900
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62091
LL+7'iLUO
05
13
135
TO
3d015
S59b2
0-308+7+7
'SIA
'i0-3695LL
1SIA
47O-32471L
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5061
299609
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6
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13
36SST
929S'i
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+70-3L+747
+799L
+79LTL
20ffL9
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1909L0
99OTS
9cO0.
I9LTSOO
2047S0O
9Z5OO
9657S00
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151A3
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096L4700
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92L1S00
9T+7SO0
47'7SO0
123
SHELL SOLVENT 345
PHI =
.192
TB
21.12
Hi
TIME
37.25
30.54
22.82
16.20
12.06
6.32
25.62
29.22
34.80
43.50
54.00
72.30
CL
1.1.6896 01
VISL
9.50246-04
F
36717.3
32193.6
27031.6
21477.1
17420.3
13065.3
3.9500
3.4634
2.9080
2.3105
1.8741
1.4056
SCL
3.9004E-02
SLOPE
4.0795E 00
VIS4
9.40866-04
EVISL
2.13376-05
TIME
34.29
29.80
23.05
15.62
12.05
25.98
28.92
33.42
43.62
52.26
CL
t.2234E 01
VISL
6.94156-04
H
3.8953
3.4993
3.0281
2.3200
1.9365
SCL
RHOW
62.38
RHOE
59.91
W
TB
35.45
Hi
RHOM
36.80
RHOM
36.56
RE
49906.3
44832,8
38796.1
29724.1
24809.9
1.52036-01
SLOPE
4.11BBE 00
VIS4
6.8263E-04
6.0827E-05
EVISL
.0059431
.0062325
.0063953
.0068099
.0071940
.0077193
RE2
F2
34792.3
30505.7
25614.3
20351.1
16507.0
12380.2
.0056315
.0059057
.0060600
.0064528
.0068168
.0073146
R62
F2
47289.7
42482.2
36762.0
28165.7
23509.1
.0052083
.0055356
.0055492
.0059970
.0062242
SB
1.52666-01.
RHOE
59.50
R'IOW
62.05
F
.0554965
.0056419
.0058562
.0063288
.0065686
SB
5.66076-01
124
SHELL SOLVENT 345
PHI =
TB
19.78
TIME
NT
25.25
28.50
33.79
27.58
tC.82
13.83
10.12
5.61
4.55
33.42
42.30
51.00
73.80
85.44
VISL
7.5674E-04
4.0063
3.5509
3.0281
2.3924
1.9843
1.3713
1.1845
40999.8
34363.9
27623.9
22911.6
15533.2
13676.2
SLOPE
3.3205E-02
3.9907E 00
VIS4
7.571.4E-04
1.4466E-05
TIME
25.20
28.20
33.24
43.20
55.58
83.70
H
4.0159
3.5887
3.0445
2.3426
1.8078
1.2091
VlSI.
25.20
27.56
33.36
42.60
53.82
77.22
CL
1.2664E 01
VISL
5.4195E-Q4
RE2
F2
.005471+1+
52882.2
.0055746
.0057707
.0061723
.0065582
.0072205
47256.1+
.0051873
.0052823
.0054682
.01362928
.0069225
.0073082
SB
1,3903E01
RHOE
RHOW
61.66
62.20
F
40091.2
30547.9
23805.5
15921.5
.00581+87
.006211+4
.0068419
SB
7.3820E-02
EVISL
6.6295E06
TB
32.04
26.50
19.78
13.16
8.88
4.95
.0053893
.0055762
.0057452
.0060192
RHOM
3.9732E 00
5.2933E-0l.
TIME
63833.3
38550.1
33130.7
26175.6
21710,4
15003.1
12959.1
.0056875
.0058847
.0060630
.0063523
.0066410
.0073056
.0077125
36.58
55808,2
49871.2
42309.5
32554.8
25122.7
16802.5
36.90
HI
F2
SLOPE
1.8354E-02
VlSI.
6.2747E-04
RE2
F
RE
SCL
CL
t.2410E 01
RHOW
62.31
EVISL
TB
32.80
26.78
20.10
12.94
8.40
4.43
RHOE
61.73
1+6258.6
27.80
NT
RHOM
36.70
RE
H
SCL
CL.
1.2084E 01
.047
H
4.0159
3.6195
3.0611
2.3756
1.8803
1.3105
SCL
5.4298E02
VIS4
5.3830E-04
RHOM
RHOE
RHOW
36.40
61.29
61.90
RE
65245.8
58805.2
49733.6
38596.1
30549.9
21292.3
SLOPE
4.0609E 00
EVISL
1.6942E-05
F
.0052739
.0053464
.0055311
.0060048
.0063039
.0067761
SB
2.2294E0i
RE2
61826.9
55722.1
47125t
36572,5
28945.1
20176.0
.0049974
.0050660
.0052411
.0056930
.0059734
.0064208
125
HEAVY OIL
PHI =
TB
RHOM
24.61
HI
TIME
34.51
31.62
28.65
25.34
22.11
16.63
15.32
12.51
26.46
27.90
29..0
32.34
34.74
39.12
44.76
51,54
VISL
?.iS7lE-04
3.8246
3.6272
3.4422
3.1586
2.9131
2.5869
2.2609
1.9635
45530.2
43180.3
40977.2
37600.5
3i.678.5
30795.7
26915.3
23374.6
3.8541E 30
VlSi.
7.3466E-04
EVISI
2.5276E-05
TB
HI
TIME
32.31
29,26
26,58
23.08
20.43
17.00
13.83
11.52
26.35
28.32
30.00
32.64
36.00
40.50
46.32
53.88
3.7691
3.5734
3.3733
3.1005
2.8111
2.4988
2.1848
1.8782
V154
27.19
28.90
30,94
33.56
37.32
41.88
28.30
25.74
22,45
19.36
16.25
CL
t.2697E 31
VISL.
5.3183E04
3.7233
3.5017
3.2815
3.0055
2.7117
2.4164
SCL
V154
5.1176E-04
F2
.0057458
.0058044
.Qi57791
.0059818
.0060209
.0062528
.0064648
.0066345
43143.1
40916.3
38328.8
35629.4
32860.3
29181.1
25504.1
22149.1
.0054445
.0055001
.0054761
.0056682
.0057052
.0059249
.0061258
.0062867
SB
2.2216E-Q1
RHOE
RHOW
59.10
61.89
RE
F
RE2
F2
61157.6
57983.1
54736.0
50308.9
45613.4
40545.2
35453.8
30476.6
.0054066
.0053891
.0054305
.0054745
.0057811
.0058776
.0059485
.0063334
57951.1
54943.0
51866.2
47571.2
43221.9
39419.4
33592.1
28878.1
.0051231
.0051065
.0051458
.0051875
.0054780
.0055695
.0056367
.0060013
RE2
F2
63293.9
56705.4
53138.4
48686.5
43911.8
39130.5
.0050311
.0050358
.0051530
.0052483
.0054239
.0055277
SB
4.2194E-Q1
RIIOM
RHOE
RHOW
36.26
58.60
61.43
RE
W
9.1153E-02
RE2
3.3138E-05
TB
31.57
F
EVISL
5.3899E-0'.
TIME
RHOM
36.49
4.0362E 00
58.63
HI
RHOW
62.26
SLOPE
1.0622E-01
VISL
5.4164E-04
W
SCL
CL
RHOE
59.55
SLOPE
6.1032E-02
42.07
1.2665E 01
36.74
RE
W
SCL
CL
1.2174E 01
.325
63630.
59843,0
56078.6
51380.4
46341.5
41295.7
SLOPE
4.2518E 00
EVISL
2,7919E-05
F
.0053095
0053144
.0054382
.0055387
.0357240
.0058335
SB
3.3531E-01
126
HEAVY OIL
PHI
.325
TB
58.63
HI
TIME
13.0k
10.63
16.25
50.40
59.40
41.98
CI.
t.2064E 01
VlSI
7.6548E-0k
RHOPI
RHOE
RHOW
36.26
58.60
61.43
F
w
2.0079
1.7037
2.4164
SCL
t.5638E-01
VIS4
5.9992E-0k
29272.2
24837.0
35227.2
SLOPE
7.7626E 00
EVISL
6 .9001E-05
.006335
.0067377
.0058335
SB
1.2734E 00
E2
27737.4
23534.8
33380.3
.0063583
.006384k
.0055277
127
HFAVY Oil.
PHI =
TB
23.78
TIME
HT
33.59
30.54
27.72
23.84
21.10
17.52
14.06
25.50
27.30
28.32
31.1'.
33.0
37.30
43.12
'.9.20
55.18
1i%51
9.67
VlSI..
7.5024E-04
3.9225
3.7070
3.4993
3.2498
2.9853
2.6772
2.3361
2.0569
1.8274
VISL
5.2208E-04
3.8685
3.7316
3.4422
3.2250
2.9030
2.5996
2.3010
1.9567
1.7886
55,62
CL.
1.297iE 01
VISL
'..5'.IOE-0&.
F?
61773.3
59586.6
54965.6
51497.4
'.6356.5
40807.8
36743.7
31245.0
28561.1
.0050727
.0049989
.0051130
.0051330
.0051821
.0055386
.0056886
.0098615
.0059021
RE2
F?
71549,7
67377,?
63534.9
57769.7
53785.6
47699.8
40672.3
33652.3
.001.8229
.0049551
.0348927
.0050905
.0050810
.0052843
.0066tq3
.0068860
SB
Z.l.896E-Qi
RHOW
61.90
F
.0053533
.0052755
.0053959
.0054170
.0054688
.0058451
.3060034
.0061858
.0062286
SLOPE
2.8335E-05
46.2
RE2
.0055922
.0058310
.0060731
.0061907
.0064041
RHOE
VlSI.
5.1898E-01.
32.40
34.50
39.24
.0054281
.0055048
.0055832
.0055253
.0057547
.0058661
.0060684
.0062722
.0065250
60.62
4.0458E 00
26.16
27.78
29.46
43270.5
40893.0
35632.3
35850.3
32931.5
29533.8
25770.5
22690.6
20158.5
.0058091.
RHOM
65191.3
62883.6
58006.9
54346.8
48921.5
43065.7
38776.8
32973.8
30141.5
N
RHOM
RHOE
RHOW
36.18
60.20
61.44
RE
3.8685
3.6429
3,4352
3,1235
2.9080
2,5790
2.1990
1.8195
SCL
SB
3.804tE-01
EVISL
TB
30.13
27.57
24.37
21.15
18.48
15.36
11.96
8.92
.005728'.
36.44
9.'.236E-02
TIME
F?
RE
W
58.30
HT
RE2
EVISL
SCL
CL
F
SLOPE
2.9120E-05
26.16
27.12
29.40
31.38
34.36
39.60
43.98
51.72
56,58
1.2729E 01
'.5664.7
'.3155.6
'.0738.2
37833.9
34753.6
31168.0
27196.4
23946.1
21273.9
VIS'.
7.5121.E04
TIME
10.20
8.80
RHOW
62.27
3.9909E 00
TB
31.23
28.75
25.20
22.37
18.55
15.60
13.22
RHOE
61.12
6.7'.09E02
42.16
HI
RHOM
36.68
RE
W
SCL
CL
t.2099E 01.
.1.1.1
75508.6
71105.3
67050.4
60966.2
96761.6
90339.1
42922.7
35514.3
SLOPE
7.0485E-02
4.1002E 00
VlSI.
4.L.807E-Qi.
1.6'.30E-05
EVISL
F
.0050898
.0052293
.0051634
.0)53722
.0053622
.0055766
.0058100
.0060573
SB
2.8171E-0i
.0055054
.0057397
128
HEAVY OIL
PHI =
TB
22.68
HI
TINE
33.34
29.98
25.32
26.91+
22.59
18.57
28.30
31.26
35.58
14.1.7
1.0.32
10.52
6.68
49.74
66.30
26.1+9
Ct.
i.2189E 01
VXSL
7.1245E-04
.0056335
.0057222
1+361+7.3
0057617
3.2371.
2.81.43
40212.5
35330.0
31176.7
25272.3
18959.9
.00576'.0
.0060997
.0060421
.0065690
.0071355
2.5099
2.0346
1.5261.
SLOPE
1+.C835E 00
VIS'.
7.0409E-0k
41464E-05
31.13
28.24
24.35
20.40
16.80
12.82
9.30
25.33
26.94
29.46
32.52
36.36
42.84
51.78
k.0000
3.7565
3.4352
3.1119
2.7381
2.3623
SLOPE
VIS4
VlSI
.0053381
RE2
F2
62968.4
59135.2
48988.4
43103.4
37187.2
30766.7
.0048995
.0050272
.0051617
.0052380
.0055278
.0055876
.0057869
RE2
F2
69344.2
65129.3
60331.2
54596.0
49466.2
41175.8
.34004.4
.0048384
.0048740
.0050101
.0052493
.0051+222
.0051+596
.0051+618
.0057799
.0O57253
.0062246
.00676i4
F
.0051706
.0053051+
.00541+73
.0055278
.0058337
.0058968
.0061071
51+376.8
SB
4.0358E01
EVISL
3.3404E-05
5.2643E-0l.
H
3.9500
3.7261
32.1.0
3.1235
2.8300
2.3557
1.9454
4.8674E-04
RHOW
61.90
k.C831E 00
25.62
27.16
20.32
CL
RHOE
61.22
32469.1
TB
1.2851E 01
RHOM
3921.4.9
1.944
1.0803E01
35.76
42.96
52.32
47043.3
'.1.214.4
41358.9
38104.2
33477.7
29542.1
23947.3
17965.9
SB
36.59
66452.6
62407.2
57068.9
51698.9
45488.4
58.75
30.36
27.29
24.15
20.82
17.17
12.45
9.26
F2
3.7055E-01
RE
H
TIME
RE2
EVISL
SCL
Cl.
F
4961+6.3
1+6660.8
501
TIME
MT
RHOW
62.28
t.0105E-0t
HI
VlSI
RHOE
61.68
3.9968
3.7565
3.5139
TB
5.3286E-0k
RHOM
36.73
RE
W
42.00
1.269'.E 01
.075
3.1.516
SCL
RHOM
RHOE
RHOW
36.38
60.78
61.43
RE
72864.'.
68732.9
63669.4
57616.9
52203.2
43454.1
35885.9
SLOPE
t.1915E-01
k.1833E 00
VIS4
4.7411E-Ok
3.3412E-05
EVISL
F
.0051062
.005141.5
.0052871.
.0055397
.0055241
.0056879
.0060760
SB
4,4931E-01
.005231+5
.0053897
.005757'.
129
HFAVY OIL
PHI =
TB
23.29
HI
TP4E
32.1.6
25.02
2'.76
29.34
25.62
22.09
18.55
13.93
24.05
7,23
28.32
31.32
35,10
40.90
46.23
58.90
55434,9
51830.4
49499.7
4,01.1.8
3.7818
3.6117
3.2312
2.8832
41.284,2
39515.1
33994,6
30021.2
23588.1
2.1.801.
2.1905
1.7211
SLOPE
3,8937E 00
1.6350E-01.
VlSI.
VISL
6.2836E-01.
30.35
27.09
23.53
19.89
16.01
12.33
8.07
6.50
25.26
26.94
28.93
31.63
36.35
1.2.36
52.92
51.26
CL
1.2973E Si
VlSI
.5381E-04
I..Q363
3.1.921
3.1944
2.8111
2.3890
1.9123
1.6520
1.5968.6
36795.?
31786.3
SLOPE
SCL
S.7763E'02 3.9875E 00
VlSi.
25.32
26.91.
28.56
31.30
36.)tI
2.48
54,63
CL
0054362
.0056175
.0053732
.0057818
.0066382
.8061571
.00621.09
.0065559
RU
F2
52528.5
37443.4
2212.3
23447.2
22351.4
.0051512
.0053230
.0050915
.0054787
.0057690
.0058363
.0059137
.0062122
RE2
F2
73045.8
68490.6
63669,3
.001.8454
1.9112.9
&9o4.'.
1.1962.4
SB
5.9725E01
RHOW
RHOE
61.7'.
61.92
F
.0051135
.0051875
.0352354
.0052532
.0051.47!
.0057872
.0058617
.0062890
5821.2.9
51253.8
1.3558.5
.0049156
.0049353
.0049778
.0051617
.0051.837
34866.5
30119.8
.005551.1.
F
RE2
F2
.0049515
.3351031
.0053639
.0051870
.0655406
.0055221
.3059629
79767,6
74082.6
69880.5
62760.6
55438.5
.001,6919
.005959!
SB
3.5129E-01
EVISL
Z.935E-05
1.,S1.53E0i.
TB
30,27
26.93
23.80
19.70
16.45
11.83
7.80
RHOM
36.29
77087.5
72280.2
67192.2
61465.6
54089,7
3.7565
TIlE
F
RE
W
55.54
MT
RHOW
62.28
EVISL
TB
TIME
RHOE
62.11
5.9260E-05
6.3813E-0l.
41.36
HI
RHOM
36.52
RE
W
SCL
CL
i.2L.07E 31
.021
W
4.0448
3.7565
3,543L
3.1824
2.8111
2.3823
1.8535
SCL
RHOM
36.16
RE
84181.2
78181.7
73747,0
66233.2
58506.0
1.9581.3
38575.4
SLOPE
i.3063E 01
i.2873E-01 4.1778E 00
VlSI
4.30 89E'31.
4.2322E-04
VlSI.
EVISL
3.1959E-35
RHOW
RHOE
61.50
61.32
SB
1..8718E-01
1.6931.8
35552.9
.0046356
.0047981.
.0049156
.0052501
.0052325
.0056502
Table 16. Relative fluidities.
Run
H032. 5
H032. 5
H032. 5
H0l4. 1
H014. 1
H014. 1
H07, 5
H07, 5
H07 5
TB
x 104
d 1cTB
e25
(°C)
(lb/ft sec)
24.61
42.07
7. 347
58. 63
23. 78
42, 16
58. 30
5. 118
7.512.
5. 190
4.48 1
0.8219
0.8160
0.7213
22,68
7.041
5,264
0. 8997
0. 8069
0. 9527
0. 5118
4, 741
0,6771
6.381
4.545
0.2938
0. 9786
0. 9456
0. 8029
0. 9346
0. 5227
0. 3269
0. 4948
0. 3932
0. 9408
0. 7760
0. 8926
0. 7094
0.8176
0.7471
0.7142
0.4918
0.4374
0.9417
0.9161
0,8371
42. 00
5.390
H02, 1
H02, 1
H02, 1
58,75
23.29
41.36
55.54
1023. 6
1023. 6
24, 71
35, 33
L04. 6
L04. 6
L04. 6
26. 15
42. 19
7. 157
59.00
4. 477
L 025
L 025
L 025
26. 76
42. 2 1
58.91
(Continued on next page)
4. 202
12. 22
12.27
5,666
11,74
9, 674
8. 056
d
0. 8246
0. 7870
0. 6283
0, 3975
70
0. 8968
0. 5106
0. 2949
0. 9204
0.5091
0.2981
0. 7566
0. 5836
0. 9347
0. 7563
0. 5836
1. 858
1.774
1.416
1. 169
1. 161
1.026
1.084
0.9721
0.8157
1,031
0,9961
0. 8462
0. 8003
0. 9188
0.8172
0, 7426
Corrected
fluidity*
0.8908
1.141
1,126
0.8744
1.185
1.288
0.9375
1.169
1.215
1.032
1.356
1.390
0.5195
0.4616
0.8579
0.8895
0.9726
0.5184
0.5208
0.5413
e -2.54
0.4438
0,4438
0,4438
0.7029
0.7029
0.7029
0.8301
0.8301
0.8301
0.9489
0.9489
0.9489
0,5543
0,5543
0.8925
0.8925
0.8925
0,5353
0,5353
0,5353
Table 16. (Continued)
Run
SS19. 2
SS19. 2
SS4. 7
SS4. 7
SS4. 7
TB
x 10 4
(°C)
(lb/ft sec)
21. 12
9.409
6.826
35.45
27.80
7. 573
6, 293
36. 90
5.383
19. 78
I.Lc
d'CTB
e2'5
-2. 54
fluidity*
e
1. 129
1. 139
0. 7065
0. 6657
0. 6188
1,008
1,008
0,9142
1.059
0. 8752
0. 8896
0. 8896
1. 125
0. 9767
0.8161
0.8896
1.019
0. 7966
0. 6691
0. 6884
0. 6828
0. 7788
70
0. 6985
0. 7050
0. 8966
0. 8965
0. 8689
Corrected
1.000
1. 115
0. 9872
0.6188
Legan's data
LOb. 0
LOb. 4
LOb. 4
LOb, 4
20. 00
L018. 0
21. 11
42. 22
LO18, 0
L018. 0
L020. 0
L033. 0
L033. 0
L032. 0
L035. 0
20.00
8. 508
10, 13
42. 22
7.319
60.00
6. 330
60.00
20. 00
21.11
42. 22
60.00
20.00
20.00
H04. 5
42, 22
H04. 5
60.00
H04. 5
20. 00
H021, 0
39. 44
HO2L 0
H021, 0
54,44
(Continued on next page)
10.85
8.207
6, 677
0. 7937
0. 6667
0. 5780
0. 4975
0. 6061
0,5155
0.4717
10.67
0, 6329
14. 73
10. 28
0.4464
0.4115
0.3718
8.472
15,06
8.238
5.880
5. 165
7.901
5.791
5. 150
0. 4484
0.8197
0.7194
0. 6098
0. 8547
0. 7692
0. 6667
1.013
1.013
0, 7561
0. 5743
1.000
0,7561
0. 5743
1.013
1,000
0.7561
0. 5743
0. 8646
0. 7497
0. 6452
0. 9505
0. 8084
0. 7398
0.7711
0.7711
1.044
1.019
0. 6353
0, 7711
0. 6376
0. 6376
0. 6376
0. 6065
0.4516
0.4382
0. 9391
0. 8273
0. 4901
0.4501
0. 4382
0. 4493
0.6131
0.6139
0.6474
1.013
1.035
0.5081
0.2817
1.076
0. 4501
0.4169
0.9173
0. 8117
1.045
1. 109
0. 8936
0. 8936
0, 8936
1. 035
1.445
1,300
0.8464
1. 127
1. 140
0.5916
0.5916
0.5916
0. 5566
0. 3390
0. 8051
0. 6824
1.072
Table 16. (Continued)
Run
TB
(°C)
e
x 1O
(lb/ft sec)
-
d'cTB
d'c70
e
-e e2.54)
c
Corrected
-2. 54)
fluidity*
e
0. 9783
1. 104
0. 8397
0.8762
0. 8869
0. 6862
0. 3580
0.6157
0. 9130
0. 9839
0. 9630
0. 9873
0. 7545
0. 8086
0. 6126
0. 4232
0. 2923
Cengel and Wright's data
SS4. 8
SS19. 4
SS34. 2
21.39
21.39
22. 67
7. 526
9.610
17. 74
0. 8677
0. 6796
0.3571
1.003
1.003
1.015
0. 4253
Faruqui's data
SS8. 5
SS19. 6
SS34. 4
SS49. 2
19.44
19.44
19.44
11.36
16.80
19. 44
23, 72
9, 274
0. 7382
0. 6028
0. 4075
0. 2886
0. 9834
0. 9834
0. 9834
0. 9834
0.6161
0.4165
0. 2939
Finnigan's data
SS49. 2
SS24. 8
SS63. 1
17. 22
21.23
1. i66
0.3531
14.31
0. 3407
0. 5055
0. 9615
17.22
0.9615
0. 9397
0. 5238
19. 72
32. 05
0,2122
0. 9854
1.027
0.2166
(Continued on next page)
0. 2923
0. 5379
0. 2065
Table 16.
Run
(Continued)
TB
(°C)
e
x 10'
(lb/ft sec)
e
d'cTB
d"c70
c
e
2. 5
e
Corrected
fluidity*
e
-2. 54
Ward's data
L08. 5
L017. 0
L033. 0
L046. 0
H05, 0
H08. 5
H016. 8
H027. 0
20. 00
10, 15
0.7555
0.6655
20.00
20.00
20.00
20,00
20,00
20.00
14.58
0. 4631
22,44
9. 139
9. 139
9, 139
0.3009
0.7389
0.7389
0.7389
8,736
0. 7730
20.00
8.938
*Corrected relative fluidity = (FACTOR) x
Factor = 1.0 / (0. 378 + 0.6106
dcTB
1. 057
0. 9502
0,4648
0. 8086
0. 6538
0. 4382
0. 3020
0,3166
0. 8373
0. 8825
0. 8086
1. 124
0,7316
0.7316
0.7316
1,518
0. 7654
1.013
1.013
1.013
1.013
1.035
1,035
0. 9344
1. 035
1,035
1.018
0.9138
0. 7583
0. 6679
0,6571
0.5092
Table 17. Predicted outer wall friction factors.
134
ISO-OCTYL ALCOHOL
TB
24.71
PHI
.236
F2EXPT
W
3.8333
3.6587
3.4848
3.3072
3.1119
2.8539
2.5949
2.2762
1.6733
1.2615
TB
35.33
w
3.6907
3.5887
3.4492
3.2312
3.0530
2.7879
2.5250
2.2489
1.6439
1.3065
VISL,
.0012217
F2B
.0061158
.0861423
.0062502
.0062957
.0062976
.064935
.3067228
.0369272
.0074460
.0380902
PHI
.236
AD
33.3095
VIS4
.0012266
F2EXPT
.0062360
.0062137
.0061873
.0)63246
.0363554
.0066315
.0067201
.0368742
.0374939
.0080355
.0060774
.0061455
.0062178
.0362969
.0063908
.0365278
.0066833
.0369063
.0074738
.0080558
40
30.3095
F28
.0061386
.006180C
.0062393
.0063387
.0064285
.0065720
.0067356
.0069344
.0075164
.0079887
80
-11.9420
VISR7O
9.0860
F2C
F20
.0059157
.0059812
.0060508
.0061269
.0362171
.0063487
.0064981
.0067122
.0072567
.0078141
.0059842
.0060508
.0061216
.0061989
.0062907
.0064245
.0065765
.0067944
.0073486
.0079163
80
-11.9420
F2C
.0056620
.0056989
.0057516
.0058400
.0059197
.0060471
.0061922
.0063681
.0068821
.0072975
VISR7O
9,0860
F20
.0058777
.3059166
.0059723
.0060656
.0061499
.0062845
.3064378
.0066240
.0071684
.0076092
135
LIGHT OIL
TB
26.15
W
3.9780
3.7761
3.5286
3.2751
3.0065
2.7073
2.3361
1.8039
1.2267
TB
42.19
w
3.950c1
3.6827
3.4843
3.2436
2.9695
2.6815
2 .3 4 59
1.6423
1. 3871
TB
59.00
w
3.9225
3.6747
3.4492
3 .2374
2.9591
2.6150
2 .2 762
PHI
.046
VlSI.
AD
BO
.0007i57
26.3419
-10.4030
VISR7O
15.2550
F2EXPT
F2B
F2C
F20
.0053430
.0053800
.0054839
.0055383
.0056992
.0057610
.0060542
.0063972
.0370572
.0053235
.0053864
.0054699
.0055639
.0056747
.0058148
.0060205
.0064073
.0370539
.0052200
.0052811
.0053623
.0054536
.0055613
.0056973
.0358970
.0062723
.0068990
.0052764
.0053385
.0054209
.0055137
.0056231
.0057613
.0059642
.0063458
.0069833
PHI
.046
VlSI.
AD
90
.0005666
26.3419
-10.4030
F2EXPT
0050196
.0052319
.0052426
.0052348
.0053990
.0054758
.0055610
.0063019
.0065088
PHI
.046
F2C
F28
.0050618
.0051407
.0052042
.0u52883
.0053945
.0055212
.0056938
.0061939
.0064531
AO
VlSI.
.000447?
F2EXPT
.0047980
.3049072
.0349660
.0049641
.0051736
.0052416
.0054442
26.3419
F2B
.0048163
.0048846
.0049522
.0053212
.0051217
.0052645
.0054318
.0048693
.0049439
.0050038
.0050833
.0351836
.0053032
.0054659
.0059369
.0061806
90
-13.4030
F2C
.0045931
.0046569
.0047200
.0047844
.0048780
.0050111
.0051668
VISR7O
15.2550
F20
.0050580
.0051368
.0052002
.0052842
.0053904
.0055169
.0056893
.0061888
.0064477
VISR7O
15.2550
F20
.0049065
.0049767
.0050462
.0051172
.0052203
.0053672
.0055392
136
TB
26.75
PHI
.250
F2EXPT
W
3.8951
3.7070
3.5139
3.2878
3.0741
2.8395
2.61q0
2.2886
TB
42.21
3.6043
3.4492
3.2127
3.0281.
2.8111
2.5212
2.2489
1.8156
TB
58.91
w
3.7903
3.6195
3.4705
3 .2250
2.9853
2 .7 248
2.4 44L
2 .17 92
1.7388
1.5588
.0009674
.0057748
.0058:389
.0058651
.0060028
.0060929
.0061493
.0063952
.3054816
.0069342
.0059970
.0060681
.8061462
.0062453
.0063479
.0064721
.0066023
.0068279
AD
26.3419
.00571+91
.0058356
.0058960
.0359958
.0863808
.0061901
.0063553
.0365356
.0068936
VIS4
PHI
.0008056
80
VISR7O
-10.4C30
15.2550
F2C
f'28
F2EXPT
.250
26.3.19
VIS4
PHI
.250
AD
F28
.0060166
.0860579
.0061438
.0062117
.0063706
.3065340
.0065655
.0068083
w
3,%3L121
VlSI,
.001.1739
AD
26.3419
F2EXPT
F28
.0055836
.0055318
.0055678
.0056469
.0059370
.0059122
.0062252
.0063303
.0065230
.0068976
.0055286
.0055874
.C356417
.0057385
.0058429
.0059699
.0061262
.0062981
.0066566
.0068408
.0058782
.0059472
.0060231
.0u61194
.0062190
.0063396
.0364659
.0066849
80
-10.4030
F20
.005951.6
.0060219
.0060991
.0061972
.0062986
.0061+214
.0065501
.0067732
VISR7O
15.2550
F2C
F20
.0054877
.0055687
.0056252
.0057184
.0057978
.0058997
.0060538
.0062218
.0865551
.0057126
30
-10.4030
F2C
.0051699
.0052232
.0052725
.0053602
.0054549
.0055698
.0057112
.0058661.
.0061897
.0063555
.0057981+
.0058583
.0059571
.0060413
.0061496
.0063132
.0064918
.0068463
VISR7O
15.2550
F20
.0055418
.0056007
.0056553
.0057524
.0058572
.0059846
.00611+15
.006311.0
.0066739
.0068587
137
SHELL SOLVENT 3L5
TB
21.12
N
3.9500
3.L+ 634
2.9080
2.3105
1. 8741
1.1+056
TB
35.45
N
3.8953
3.4993
3.0281
2.3230
1.9365
PHI
.i9
VlSI.
AD
.0009409
8.4395
F2EXPT
F28
.0056315
.0059057
.0060600
.0061+528
.0068168
.0073146
PHI
.192
F2C
.3056755
.0058521
.0060993
.0064482
.0058380
.0060219
.0062797
.0067913
.0070020
.0075413
.0073071
VlSI.
AD
.0006826
8.4395
F2EXPT
.0052083
.0055356
.00551+92
.0059970
.006221..?
BO
''+.2696
F2B
.0052920
.0054216
.0356037
.0059630
.3062260
.00661+37
BD
4.2696
F2C
.0054502
.0055854
.0057756
.0061511
.0064262
VISR7C
.9771+
F20
.0058536
.0060382
.0062970
.0066625
.0070223
.0075638
VISR7O
9771
F20
.0053799
.0055126
.0056992
.0060675
0063371
138
TB
19.77
PHI
.047
VIS4
.0007573
F2EXPT
w
4.0063
3.5509
3.0281
.0053885
2.39214
1.981+3
.0060192
.0062928
.0069225
.0073082
1.3713
1.1845
TB
27.80
.3055752
.00571+52
PHI
.0'.?
VIS4
.0006293
w
F2EXPT
4 .0 159
.0051873
.0352823
.0054682
.0358487
3.5887
3.0445
2.31426
1.8073
1.2091
TB
36.90
w
4.0159
3 .6 195
3. 0 611
2 .3 756
1.8803
1.3105
.006214'.
.0068419
PHI
.047
VIS4
.0005383
F2EXPT
.0049974
.0050660
.0052411
.005690u
3t)59734
.0064208
AO
8.4395
F26
BD
-14.2696
F2C
.0053831
.0055329
.0057400
.0U60675
.0063470
.0069562
.0072211
.0053927
.0355L29
.0057505
.0060788
AD
3D
-14.2696
8.4395
F2B
.0351617
.0352929
.0054935
.0058367
.0062072
.0068530
AD
8.',395
F2B
.01363591
.0069700
.0072357
F20
.0054161+
.0055675
.0057765
.0061070
.0063892
.00700144
.0072719
VISR7O
.9774
F2C
F20
.0351706
.0053021
.0055033
.00511429
.00581+73
.0062189
.0068664
BO
-4.2696
F2C
.0051023
.0052962
.0049615
.0050758
.0052683
.005610'.
.0055.801
.0059246
.0064619
.0539i8
.004987j.
VISR70
.9774
.0061+247
.0052734
.0054730
.0058143
.0061828
.0068248
VISR7O
.9774
F2D
.0048943
.0050664
.0051950
.0055005
.0058058
.0063273
139
HEAVY OIL
TB
24.61
w
3.8246
P141
.0007347
F2EXPT
.0054445
.0U55001
3.1+422
.009476.1
3.1586
2.9131
2.5869
2.2609
1.9635
.0056682
.0057052
.0059249
.0061258
.0062867
w
PHI
.325
VlSI,
.0005390
F2EXPT
.3051231
3 .5 734
.0051065
2 .1848
1. 8782
TB
58.63
.0051458
.0351875
.0054780
.0055699
.0056367
.0360013
PHI
.325
F2EXPT
3.7233
3.5017
3.281,
.0353311
.0050358
.0091530
.0052483
.0054239
.0055277
2 .7 117
2.4164
.0054682
.0055339
.0056444
CO57513
.0059135
.0361056
.0063166
AD
143.0488
.0053584
.0051182
.0351840
.0052826
.0054005
.0355473
.0357219
.0059280
AD
VlSI.
.0005118
w
3 0 865
CO54028
F2B
3.7691
3.3733
3.1005
2.8111
2.4988
43.0488
F2B
3. 62 72
TB
42.07
AD
VlSI.
.325
43.0488
F2B
.0050146
.0350827
.0051563
.0052578
.0053813
.0355242
80
-16.1450
VISR7O
176.8100
F2C
F2D
.0062449
.0063255
.0064067
.0065432
.0066756
.0068769
.0071160
.0073793
.0063630
.0064459
.0065292
.0066696
.0068056
.0070127
.0072586
.0075296
SD
16.150
VISR7O
176.8100
F2C
F20
.0057589
.0058310
.0062898
.0063718
.0064621
.0065977
.0067604
.0069637
.3072064
.0074944
.005910.4
.0060296
.0061725
.0063507
.0365631
.0068147
BD
-16.1450
F2C
.00514189
.0054950
.0055773
.0356911
.0058296
.0059901
VISR7O
176.8100
F20
.0062101
.0063028
.0064032
.0065421
.0067116
.0069084
140
TB
23.78
PHI
.141
F2EXPT
w
3.9225
3.7073
3,1+993
3.2498
2.9853
2.6772
2.3361
2.0569
1. 8274
TB
42.16
w
3. 8 685
3.7316
3.4L422
3.229)
2.9033
2.5556
2.3013
1. 9567
1.7886
TB
58.30
VlSI.
.0007512
F28
.0054281
.0055048
.0055832
.0055253
.005751+7
.0358661
.0060684
.0062722
.3065250
PHI
AD
1+3.0488
.0053990
.0354687
.0055412
.0056363
.0057482
.0358966
.0060903
.0062795
.0064631
AD
VlSI.
.141.
.0005190
F2EXPT
.0053727
.0049989
.0051130
.0051330
.0051821
.0055386
.0056886
.0058615
.0359021
PHI
.141
VIS4
.00C4+81
43.0488
F28
.0049881
.0050275
.0391178
.0051923
.0353159
.0054714
.3056045
.0058193
.0059435
.0056756
.0057505
.0058285
.0059306
.0060912
.0062112
.0064200
.0066242
.0068225
80
-16.1450
.0051546
.0051961
.0052907
.0053689
.0054986
.0056620
.0058018
.0060277
.0061584
80
-16.1450
3.8685
.0048316
.0048947
.0)49576
.0050619
2. 1990
.0048229
.3049551
.0048927
.0050905
.3050810
.0052843
.0055054
1. 8 195
.0357.397
2.5793
.0055952
.0056686
.0057449
.0058451
.0059631
.0061197
.0063240
.0065238
.0067178
AD
F2B
3. 4352
3 .1235
2.9081)
F20
43.0488
F2EXPT
.00511+25
.0052819
.0054757
.0057196
V!SR7O
176.8100
F2C
F2C
w
3 .6 1+29
80
j5,jZ5Q
VISR7O
176.8100
F20
.0056075
.0056543.
.0057612
.0058496
.0059965
.0061818
.0063407
.0065977
.0067466
VISR7O
176.8100
F2C
F20
.01)1+8585
.0055267
.0056334
.0056799
.0058070
.0099051
.0060756
.0063131
.0066131
.0049222
.001+9855
.0050907
.0051719
.0053125
.0055079
.0057539
141
TB
22.6?
VIS4
DHI
.075
.0337341
F2EXPT
w
.3u52933
.0053970
.0354618
.0054548
.3355578
.33572c1
.0262246
.0355963
.0061955
.0066494
.3055576
.0356635
.0358368
.3060115
.0063223
.00676L.
.3051381
.3054222
2.5'gq
2C
1.526L4
TR
42.0)
95L595
.3i67614
2.73'1
2.:1623
1 .9544
TB
53.75
w
3.9503
3.7261
3.'515
3.1235
2.83C0
2.1cc?
1.9454
VIS4
PWI
.075
.0005264
C35i728
.:057264
AD
41.0438
.054735
BO
15.1Ls50
F2EXPT
F28
F2C
Q3L995
.0349672
.3353358
.0249380
w
4.0300
3.756
3.435,
-16.1450
F2C
F2E3
3.9963
3.7565
3.5139
3.27L.
2.344
40
L.3.0t,38
.35272
.0351617
.03.52380
.0055278
.0055576
.0057869
PHI
.075
VIS4
.0004741
F2EXPT
.)0L8354
.0043748
.0C5Q1t'i
.3052493
.0357897
.0057574
0050061
.35±161
.352504
.005105
.0O55859
.0:55543
.0J5287
.0054037
.0353708
3534fj3
.0358034
AD
43.0458
F2B
.3D4368
.0349338
.0350135
.0051253
.0 5 2393
035L+b32
3057u56
-16.1450
VISR7O
176.8100
F20
.0054475
.0055250
.0056103
.0057177
.0058933
.0060706
.0063558
.006356?
VISR7C
176.8100
F20
.0053602
.0054370
.0055490
.3056768
.G058Li86
.0060562
.3063388
VISR7O
176. 81133
F 2C
F2D
0346 22
0052963
.. 0347204
0347934
0050096
3052163
0354464
0 053661
0054633
0055864
.0057152
C 059663
3062455
142
TB
23.29
PHI
.021
w
4.041+8
3.7818
3.6117
3.2312
2.8832
2.1+804
2.1905
1.7211
TB
41.36
w
4.0063
3.7565
.0051512
.0053230
.0050915
.0051691+
.0091+787
.0051+367
.0057690
.0058343
.0059137
.0062122
.0055801
.0057779
PHI
VISL.
.021
.0001+51+5
F2EXPT
.0048451+
3 .19 L 14
.00149778
2.8111
2.3893
1.9123
1.6520
.3051617
w
4.0 41+8
3. 7 565
.00591+90
.006025
AD
1+3.01+38
.001+8100
.001+8773
.001+9552
BO
-16.1450
F20
.0052650
.0052838
.0053388
.0054751
.0056199
.0058198
.0059927
.0363500
.0052666
80
-16.11+50
.0056887
.0058921
.0060682
.006'+320
VISR7O
176.8100
.0052011
.0052765
.0053638
.031+8737
.001+9515
.00501+89
.005861+8
AD
80
-16.11+50
.0001+202
.00551+13
.0048065
.005869'.
1+3.0488
.0054626
F20
.0059593
VIS1+
.0053146?
F2C
.0051+837
.0055541+
PHI
.321
VISR7O
176.8100
F2C
.0050527
.0051977
.0053910
.0056726
.0351937
.0053868
.0056681
.0051+733
.0056361
.0058535
.0061711
.0063935
VISR7O
176.8100
F2EXPT
F2B
F2C
F20
.0046919
.0047202
.0047995
.0048561
.0845563
.0051284
.0052133
.0052818
.301.9708
.001+7943
.001+9245
3.1821+
.001+8356
.0047981+
.001+9156
2.8111
2.3823
1.8535
.0052501
.0052325
.0056502
351434
.0052474
.0053018
F2B
3. 4921
TB
43.0488
F2B
F2.EXPT
.0049156
.0349353
555L
AD
VlSI.
.0006381
.0351080
fb52998
.3056111
.001+6278
.031466514
.0351363
.0054011
.0051+113
.0055666
.0057840
.0061376
Table 18.
Observed and calculated heat transfer data.
143
ISO-OCTYL ALCOHOL
PHI =
1
2
3
4
5
£
7
8
U
I
i.1920E-01
TIH
1.410E 00
2.7i8E 01
2892E 01
9.780E-01
2.688E 01
2.634 01
2.538E 01
9
0
t.452E 00 1.951E CO
1.227E 00 l.742E (0
t.023E 00 1.556E 00
1.021E GO 1.569E CO
1.J1SE 0 i.592E 00
i.312E CO 1.6tkE 00
2.524 01
2.515E 01
2.S10E 01
2.507E 01
9.683E-Oj
TWO
TWI
TOl
T82
CPPI
4.BGTE 01
k.805E 01
4.312E Ut
3.621E 01
9.53?E-01
2.575E 01
2.577E 01
2.563E 01
2.SSSE 01
2.553E 01
2.553E 01
2.555E 01
2.533E 01
9.032E-01
9.102E-03.
9.500E-01
4.133E 01
2,502E 01
3.L.79E 01
3.521E 01
2.980E Ct
3.AT1E 01 2.1.711 01
3.902E 01 2.1.71E Cl
!.957E 01. 2.1.51.E Ci
l..310E 01 2.441E 01
4.076E 01 2.1.32E Cl
4.179E 01 2.1.21.E 01
4.272E Ci 2.1.12E Ci
3.550E Ci 2.446E Ci
2.2824E 00
2.6708E 0'.
2.6884F 04
2.7490F 04
2.66411 01.
2.5039 04
2.3666E 34
2.2228 04
2.0320 04
1.8938E 04
1.6333E 04
I
ST
STPR
I
t.4451.E-03
4.0829E-03
4.2104E-03
4.2727E-03
4.30211-03
3.74B1
4
5
6
7
0
9
10
00
3.7649E 00
3.8421E 00
3.?233E 00
3.1.993E 00
3.3072E 00
3.1062 00
2.8395E 00
2.6461.E 00
2
3
t.377ô-U3
5
6
1.309 3E-03
7
9
tC
1.2922E-03
1.3014E-33
I.3221.-03
1.3372E-3
I.3626E-03
t.37S6E03
1.3535E-03
SLOF
-1 .6686E 31
4.339iE-33
4.38'32E-03
4.4419E-03
4.52811-03
k.5733E-03
4.SOI5E-03
3.OSOE 01
9.495-01
9.636E01
9.61+3E-01
9.91.6E-01
9.574E-01
9.369E-01
NU
PR
2.8302E 03
2.6807E 03
2.5560E 03
2.5044E 03
2.3680E 03
4.7123E 02
4.5471E 02
'..3854E 02
4.28011 02
4.7472E 00
2.tk69E 03
3.6736E 02
3.4i93E 02
3.2173E 02
2.7302E 02
REB
W
2
3
2.29QE 01
9.5L.OE-01.
3.937E 01.
'+.039E 01
2.5OL.E 01
2.990E 02
2.990E 02
3.000E 02
3.000E 02
3.000E 02
3.000E 02
3.000E 02
3.000E 02
3.000E 02
2.120E 02
1.642E 60
4.174E 01
3.732E 01
3.763E 01
3.818E 01
3.870E 01
2.51.CE 01
2.270E 01
2.273E 01
1.685E CO
1.727E CO
1.422E CO
9.0E-01
3.O5E 01
C
i.O11E 00
i.012E CO
1.003E 00
9.620(-0t t.UilE 00
T8
V
THWI
2.290E 01
2.290E 01
2.?90E 01
2.290E 01
2.290E 01
2.290E 01
1.650E 01
9.710E-0l
9.660E-0t
3.060E 01
3.258E 01
3.56'.E 01
3.824E 01
4.434E 01
3.556E 01
3
t.186E 00
9.780E-0t
9,0860E 00
-1.1942E 01
1H92
2.TOOE 01
2
3
5
8
01
THBI
I
L
3.0309
BO
AD
R
A
I
.236
H
2.26U5E 03
1.9998E 03
1.8816E 03
1.5966E 03
STPRPI
4.1632E-03
4.1577E-03
4.1392E-03
4.1653E-03
4.2173E-03
'+.2651E-03
4.3189E-03
4.3972E-03
4.4595E-03
4.5935E-03
SB
AL
3.9503E-02
2. 3323E-02
f+,0479E 32
3.861.6E 02
STPR3
5.31+30E 00
6.0127E 00
6.0103E 00
6.0331E 00
6.0'.65E 00
6.0539E 00
6.0577E 00
6.0617E 00
6.0652E 00
STPR4
3.783E-O3
4.0Q92E-03
4.0586-03
4.0787E-03
4.1042E-03
4.1606E-03
4.2141E-03
k.2909E-03
4.3523E-03
4.4836E-03
4.2052E-03
4.2588E-03
4.3362E-03
4.3980E-03
4.5304E-03
3.9613E-03
4.0339E-03
'+. 1122E-03
SAL
9.50 43-Q3
4.0486-03
4. 1570E-03
802
3 2541-02
144
ISO-OCTYL ALCOHOL
PHI =
A
I
I
t.tg2oE-o1
5.466E 01
?.560E 01
3
I
TB
1
2
3
01
2.513E 01
2.544E 01
2.502E 01
THB2
i.650E 01
2.1ZOE 02
1.j03E 00
Two
iwx
TRI
182
CPM
2.550E 01
9.599E-0l
2.533E 01
9.369E-01
3.692E 01
..i85E 01
3,l.79E 01
I
ST
STPR
I
1.:3826E03
1.3741E-03
1.3530E-03
4.597E-03
SLOPE
4.0394E-03
4.5015F-03
SB
3.43'+5E-02
1.650E 01
1.650E Dl
3.763E 01 2.446E 01
4.256E 01 2.446E 01
3.550E 01 2.446E 01
3
-I.i460E02
C
j.511E 00
t.720E 00
l.422E 00
l.3249E 04
9.0778E 03
i.6333E 04
3
V
t.OIUE 00
1.029E 0
1.338SE 00
2.2824 00
2
THWI
REB
i.51E 00
9.0860E 00
968oE-01
9.680E01
9.680E-01
I
I
RD
AD
-1.1942E 01
THOI
TZME
tlj34
0
3.0309E 01
.236
2.598E 01.
j.966E 03
STPRM
4.7899E-03
5.liiOE-03
4.5935E-03
AL
5.0633E-03
9.10-0l
NU
PR
2.26i9E 02
1.6247E 02
2.7302E 82
6.0487E 00
6.6042E 00
6.0652E 00
STPR3
STPR4
4.6728E-03
4.9791E-03
4.4836E-03
4.7227E-03
5.0355E-03
k.5304E-03
H
1.3230E 03
9.5072E 02
2.120E 02
2.120E 02
SAL
1.6134E-03
A02
3.0094E-02
1HI1
V
0
LOOL-
3497
a
£
30192
4,
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34,97
39T92
9
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34,O92
4,D92
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39292
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33',92
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34,E9
39TS,
366S
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6
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366T
399T
39'T
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3I"2
32022
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3209'2 TO
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30292 TO
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309S2 20
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322L2 TO
34,2L2 TO
34,2L2 TO
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34,2L2 TO
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£O-3L9CT
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3S06 TO
4,0
£O-3O2T
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3SC66 00
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39T4,2
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3T90'T 00
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INI
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O$
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374,97
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3WIi
1
110
=
III
£O-3O'i
£O-B2S
2OV
2O-322iI
2O-S',ST
2O-329T
146
LIGHT OIL
PHI * .046
A
I
I
8
2.5980 01
2.5740 01
2.5800 01
2.5800 31
2.5800 01
2.5620 01
2.7660 31
3.0720 31
9
3.4.300 91
2
3
4.
5
6
7
10
11
I
I
2
3
1.
5
6
7
8
9
10
11
4.0300 31
4.8660 91
2
3
1.
5
6
1
1.271+0 03
1.0580 00
1.3580 00
1.3630 00
1.0870 00
TWO
1W!
6.9280 01
5.8830 01
5.3370 01
4.9010 01
7.0600 Ci
4.8720 01.
4.2720 01
3.7520 31
3.2540 01
2.6300 31
2.6420 31
2.6290 01
2.621+0 31.
2.6210 31
2.7350 01
4.4.550 01
3.9090 01
4.0140, 01
4.1390 01
4.3290 91
4.5980 01
3.9640 01
3.89510 00
3.q3j,O 00
3.92250 00
3.9225E 00
3.9225E 00
3.95030 00
3.65870 00
3.29410 00
2.90830 00
L.05&E 00
1.062E 03
7.70410 0'.
6.66440 04
6.10740 04
5.66720 04
5.26820 04
k.8337E 01.
4.4851.0 0'.
11.
2.07970 00
I
ST
STPR
I
1.5414.0-03
3.2261.0-03
9
10
2
3
4.
5
6
7
8
9
10
ii
2,4801.0 00
1.42560-03
1.3740-03
1.28370-03
1.2445-03
1.16730-03
1.17030-03
i.1811-03
1.18530-03
1.19840-03
1.20750-03
SLOPE
-1.67540-31
3.3991F-03
3.5371.0-03
3.54260-03
3.6671.0-03
3.80330-03
3.80750-03
3.85100-33
3.86610-03
3.91080-91
3.88830-03
SB
2.8600 02
2.8800 02
2.9200 02
2.940E 02
2.980E 02
3.0100 02
3.0030 02
3.0030 02
3.0000 02
3.0030 02
2.1800 02
181
182
CPM
6.0200 01
4.9020 01
4.3)50 01
1.0480 00
1.022E Ot
9.5960-01
9.7290-01
9.6030-01
9.752E-01
9.7490-01
9,8270-01
9.8050-01
9.7590-01
9.7500-01
2.79690-02
1.922E CO
5.9360 01
4.8160 Cl.
4.2120 01
3.693E 01
4.5930 01 3.1930 01
2.5700 01
1+.J1.8E 01
4.1520 01. 2.577E 01
4.2770 01. 2.5570 01
4.4670 01 2.5420 Cl
4.7360 01 2.5250 01
4.0380 Gi. 2.6440 01
4.03050 04
3.55510 04
3.03090 01.
2.57390 04
8
1.6260 00
2.2800 01
2.2300 01
2.289E 01
2.2800 01
2.2600 01
2.2700 01
2.2700 01
2.2700 01
2.2700 01
2.2700 01
1.6800 01
6.0160 30.
5.4720 31.
5.0370 01
ROB
W
C
2.9350 00
2.4740 00
2.2360 00
2.0510 00
1.8610 00
1.6330 00
1.6740 00
1.729E 00
1.8070 00
2.4760 00
1.9930 00
1.7390 00
1.520E 00
1.3130 03
i.018E 00
1.0210 00
1.0130 00
1.0070 00
1.0000 00
1.0480 00
5.9910 Dl
V
THWI
THB2
2.4390 00
1.9560 00
1.7010 03
1.4820 09
1.52550 01
-1.31.030 Cl
TH8I
TB
I
±
2.63420 01
TIME
80
AD
B
-4..51660 39
3.735E 01
3.2880 01
2.6630 01
2.6780 01
2.668E 01
2.668E 01
2.6730 01
2.7390 01
NU
PR
5.04190 02
4.78360 02
4.64310 02
4.36910 02
4.26640 02
4.06720 02
3.7779E 02
3.4338E 02
3.04080 02
3.32820 00
3.6816E 00
4.12740 00
4.58420 00
5.0998E 00
5.88150 00
5.86470 00
5.88330 00
5.8908E 00
5.89510 00
5.77810 00
H
3.10330 03
2.8969E 03
2.78710 03
2.6026E 03
2.52290 03
2.38310 03
2.21390 03
2.01190 03
1.78150 03
1.5363E 03
1.29790 03
STPRM
3.36830-03
3..674E-03
3.5285E-03
3.5816E-03
3.634.30-33
3.69740-03
3.7531E-03
3.83430-03
3.93180-03
4.05920-03
4.19410-03
AL
2.22680-02
2.6224.0 02
2.21270 02
STPR3
3.22140-03
3.33280-03
3.1+0540-03
3.47230-03
3.S4lqE-03
3.63260-03
3.6867E-33
3.76710-03
3.86320-03
3.98860-03
1..1162E-03
SAL
6.79980-03
STPR'.
3.43140-03
3.48760-03
3.52930-03
3.5686E-03
3.61150-03
3.66850-03
3.72390-03
3.80430-03
3.90100-03
4.02750-03
4.16160-03
802
3.15670-02
147
SHELL SOLVENT 345
PHI
.192
B
A
-6.77tE 00
I
1.
2
3
4
5
6
I
I
2
3
4
5
6
TIME
I
-4.2696E 00
THB1
2.80E 01
8.620E-01
8.630E-01
8.770E-01
1.140E 00
3.336E 01
4.452E 01
2.556E 01
2.532E 01
2.255E 01
2.261E 01
2.2?6E 01
2.293E 01
2.931E 01
3.609 01
9.090E-Q1
9.180E-C1
9.210E-Ci.
3.407E 01
3.586E 01
3.729E 01
3.54
01
4.029E 01
4.671E 01
3.548E 01
3.727E CI
3.869E 01
3.636E 01
4.167E 01
4.807E 01
2.190E Dl
2.290E 01
2.302E 01
2.324E 01
2.332E 01
2.966E 01
3.643E 01
9,34BE0i
4.5900E-03
4.'.521E-Q3
4.6771E-03
4.603'3F-03
4.1995E-03
3.83?r,E-03
3
4
5
6
SLOPE
-2.0316E-3t
02
CPM
1.3254E-03
1.2869E-03
1.3551E-03
1.3375E-03
1.3507E-03
1.3631E-03
2
2.41.QE 02
T82
STPR
1.
3.U9O
01
TBI
ST
3.9593E 00
01
1810E
TWI
I
00
2.240E
TWO
3.996E 00
5
2.273i
3.IOOE 02
3,100E 02
01
3.050E 02
3.020E 02
6
1
3.9043E 00
3.513gE 00
3.0335E 00
2.2L40E 01
2.230E
1,L.21E 00
l.496E CO
1.555E DO
i.455E CO
2.230E 01
2.220E 01
3.7479E 04
3.3779E 0'.
2.9262 04
2.2013E 04
4.4295F 04
5.1951E 04
2
3
C
1.683E 00
1.52E CO
i.180E 00
lEO
W
V
1.461E 00
t.421E 00
TB
9.?744E-01
THWI
THB2
8640E-0t 9.O4OE-01
2.592E 01
I
BO
AD
8.4395E OC
7,0821E-02
2.185E 01
2.188E 01
2.222E 01
2.868E 01
3.548E 01
STPRN
3.8904E-03
3.9722E-03
k.0878E-03
k.3273E-03
3.7626E-03
3.6445E-03
AL
3.6752E-02
8.798E-01
9.370E-01
9,2?4E-01
9.276E-0i
NU
PR
4.5902E 02
4.0109E 02
6.4446E 00
6.4347E 00
6.4107E 00
6.3836E 00
5.4830E 00
4.7241E 00
H
2.6745E 03
2.3372E 03
2.1250E 03
1.5718E 03
2.76'.OE 03
2.8157E 03
8.893E01
3.Gt.59E 02
2.6961E 02
4.6964E 02
4.7369E 02
STPR3
3.9847E-03
'..0683E-03
k.1867E-03
4.4320E-03
3.549E-O3
3.7421E-Q3
SAL
2.9619E-02
STPR4
3.9872E-03
4.0107E-03
4.1884E03
k.4329E-03
3.8308E-03
3.6977E-03
A02
3.5555E-02
148
SHELL SOLVENT 31+5
PHI =
A
B
6.0154E 30
I
I
8.4395E 30
TIME
TH8I
7.800E-Oj
7.950E-01
7.990E-31
5
2.508E 01
2.820E 01
3.33EE 01
4.308E 01
5.310E 01
6
2.511+E 01
2
3
1.
7
I
1.
2
3
S.
5
6
7
1.
1+
5
6
7
I.
THB2
THWI
V
C
8.190E-0j.
8.380E-01
8.490E-1,
8.673E-Ci.
2.220E 01
3.OBOE 02
1.143E 00
1.4?OE 00
TWO
TWI
181
T92
CPM
2.045E 01
2.089E 01
3.459E 01
3.593E 01
3.598E Cl
3.732E 01
1.983E 01
2.080E 01.
9.153E-01
9.393E-01
2.142E 01
2.022E 01
2.834E 01
3.630E 01
l+.253E. 01
TB
2.IIOE 01
8.030E-01,
7.700E-01
1.IOOE 33
3.798E 01.
3.332E 01
4.126E 01
4.789E 01
8.100E-1.
4.035tE 03
3.5887E 00
2.02E 01
2.220E 01.
2.220E 01
2.220E 01
1.5BOE 01
2.210E 01
2.2iOE 01
2.127E 01
2.154E 01
2.198E 01
2.057E 01
2.868E 01
3.664E 01
2.030E 01
2.040 01
3.936E 01
4.390E 01
3.1.00E 01
4.263E 01
4.923E 01
REB,
W
i.958E 01
2.771E 01
3.569E 01
1.L.352E 03
3.98?1+E 00
2.3261E 03
2.5529E 03
3.9580E 02
4.2933E 02
ST
STPR
1.031+ 5E-03
3.7113E-03
3. 82?E-O3
1.905E 00
4.0255
00
1.393tE-03
1.t361+E-03
i.1821E-03
5
1.157?E-03
1.118 OE-03
1.2387E-03
4.0 396E-03
1.. 1721E-03
4.1701.03
3.5289F-03
3.4771E-03
SLOPE
SB
-t.9289E-131
2.8364E-02
i.8011E 03
j.1404E 03
STPRM
3.7085E-03
3.7897E-03
3.9088E-03
4.1160E-03
1+.3128E-03
3.539E-03
3.4895E-03
AL
Z.9727E-02
3.000E 02
9.1.83E-01
9.666E-01
9.256E-01
9.C39E-01
9.195E-01
6.7953E 00
6.7200E 00
6.6844E 00
6.6306E 00
2.8276E 04
2.2356E 04
5.5712E Ql.
6.4556E 04
3.6607E 01.
3.OSOE 02
3.711.3E 02
3.4884E 02
3.0979E 02
2.4674E 02
2.3491E 00
3.060E 02
2.120E 02
PR
2.1574E 03
2.C275E 03
3.0611E GO
3.680E 02
3.O7OE 02
NU
H
4.7623E 01.
1+.2733E 04
6
7
9.7741+E-0t
i.430E 00
2.538E 01
I
1
2
3
BO
AD
-4.2696E 00
1.4'.2E 00
1.498E 00
1.583E 00
1.775E 00
1.360E 00
1.723E 00
2.002E 00
I
2
3
.047
1.964E 02
STPR3
3 .7185E-03
3 .7988E-03
3 .q176E-03
4. 1243E-03
1+.3253E-03
3. 5885E-03
3. 4791E-03
SAL
9.0795E-03
6.8363E DO
5.6075E 00
4.7028E 00
STPR1+
3.7299E-03
3.8085E-0 3
3.9266E-03
4.1323E-03
4.3398E-03
3.5693E-33
3. 43 73 E-03
802
3.2056E-02
149
IEAVY OIL
PHI =
325
A
4.3049E 01
THB1
3
6.132E 01
4.9)2E i
4.326E 01
4
3.53'+E 01
5
3.138E
2.844E
2.53k
2.640E
2.640E
2.676E
2.696E
2.7t2E
I
2
6
7
8
9
10
II
12
I
I
2
3
4
5
6
1
IWO
TWI
2.639E 01
2.376E 01
4.020E 01
3.677E 01
2.36E 01
3.5'+3E 01
4.2'.1E 31
4.098E 01
3.75kE Ci
3.619E 01
I
W
I
2
3
4
5
6
7
8
9
10
11
12
THWI
TB
10
11
12
9
THB2
9.730E-61
01
01
01
01
01
31
01
31
01
31
01
01
01
01
01
01
01
1.65040
2.3645E
2.33930
2.86360
3.22530
3.55840
3.84210
3.03330
3.833IE
3.7613E
3.75370
3.73160
4.tO2E
3.983E
3.9040
4.4260
4.9480
5.5180
6.0550
7.009E
01
31
Cl
01
01
01
01
01
1.L+CIE CC
9.1+90EOI
1.011E co
1.310E 00
1.009E 03
j.769E
1.712E
1.560E
1.627E
1.845E
2.071E
2.315E
2.549E
2.970E
jJ
t.Ojjt.
1.247E 00
1.'.96E CO
1.758E 00
2.t326E CO
2.455E 00
4.237E
4.119E
4.3400
4.556E
5.0840
5.6510
6.186E
7.139E
2.320E
2.305E
2.30CC
2.412E
04
04
04
04
04
04
04
o+
04
04
C
1.b'30E 01
2.280E 02
2.2&OE 02
2.260E 02
1,675E 01
1,670E 01
223QE 01
2230E 01
223OE 01
2,230E 01.
2.230E 01
2.230E 01
220E 01
2,220E 01
2220E 01
Ci
01
01
Cl
2.427E Ci
2.4390 Iii
3.0170
3.617E
4.237E
4.8720
5.870E
1.06060
1.2975E
1.429CC
1.71700
1.66840
2.0179E
2.1583E
.3.030E 02
3.000E
3.000E
3.020E
3.003E
3.00)E
2.950E
2.923E
2.890E
Dl
Cl
Ci
01
01
2.459E
2.L15E
2..30E
2.553E
2.550E
2.5kTE
2.5530
3.129E
3.7270
4.3500
4.9790
5.9730
Di
01
01
01
01
01
01
01
01
01
01
01
8.792E-0i
8.799E-01
8.497E-01
8.?70E-01
8.532E-01
8.2060-01
8.1350-01
8.2440-01
8.344E-01
8.086E-31
8.5020-01
8.7950-01
PR
MU
03
03
03
03
03
03
63
2.2'.15E 03
2.36750 03
2.41720 03
2.598E 03
2.66840 03
1.8161E
2.22290
2.4485E
2.93600
3.19480
3.45030
3.69010
3.7998E
3.9782E
4.02450
k.2826E
4.3387E
02
02
02
02
02
02
02
02
CPM
182
2.Le22E 01
01
01
01
01
01
01
01
01
H
2.52870 34
00
CO
CO
CO
CO
CO
CO
00
CO
V
T1
L..376E 01
2.02920 04
2.86180
3.55850
4.00840
4.42280
4.77950
5.08720
5.433.E
5.73230
6.08230
6.6996F
1.651E CO
1.007E 00
9.5OE-G1
REO
00
00
03
00
00
00
00
00
03
00
00
00
80
i7681E 02
-i.6145E 01
9.160E-o1
9.100E-01
9.080E-01
9.540E-Qt
9.580E-o1
9.600E-01
9.650E-01
1.ZO1E 0
1.450E 03
i.712E 03
1.980E 33
2.410E 0)
2.533E
2.5)4E
2.S3SE
2.5120
3.0890
3.6380
k.310E
4.9410
5.9360
8
AD
B
-3.3781E 00
I
TIME
02
32
02
02
02
02
02
02
02
02
02
02
6.20340
6.2545E
6.27170
6.0640E
6.06130
6.0611E
6.05010
5.29640
00
00
00
00
00
00
00
00
4.64.66E 00
4.09650 33
3.63500 00
3.05560 00
I
ST
STPR
STPRM
STPR3
STPR4
I
1.24340-03
1.21610-03
1.18130-03
1.16010-03
4.19830-03
'..3984E-03
'..1281E-33
4.23900-03
4.10610-03
3.93100-03
3.83850-03
3.7637E-u3
3.70580-03
3.65980-03
3.61200-03
3.57350-03
3.53140-03
5.02280-03
4.81030-03
4.69+C0-03
5.09130-03
4.86970-03
4.75000-03
4.55630-03
4.44920-03
4.36250-03
4.29590-03
4.27900-03
4.26140-03
4.25490-03
4.2417E-03
4.21130-03
2
3
4
5
6
7
8
9
10
11
12
1.12OE-03
1.09720-03
1.38690-03
1.13140-03
1.194V-03
1.2367-03
1.338)0-03
1.38360-03
S I. OPE
* 2.93890-01
4.019.0-03
3.85770-03
3.7264.0-03
3.6474.0-03
3.60800-03
3.L.35)E-33
3.3274.0-03
3.16620-03
3.16310-03
2.91340-03
SB
2,994.90-32
3.4.6380-03
AL
8.16080-02
4.4.7950-03
4.37390-03
4.26870-03
4.22190-03
4.11900-03
6.02060-03
3.938.E-03
3.85820-03
3.74160-03
SAL
2.64660-02
A02
3.00510-02
1 50
HEAVY OIL
PHI =
8
A
-4.62930
I
I
2
3
4
5
6
7
8
9
10
11
12
I
I
2
3
4
S
6
7
8
9
10
11
12
I
2
3
4
5
6
7
8
9
10
11
12
I
I
2
3
4
5
6
7
8
4.30490 01
03
TIME
TB
5.8860 31
4.9770 01
4.302E 01
3.5610 01
2.8340 01
2.3240 31
2.3370 01
2.3360 01
2.3400 01
2.3880 01
2.4060 01
2.4170 01
TWO
TWI
181
182
CPM
6.8960 01.
7.0270 01
5.8280 01
4.9190 01
4.2400 01
3.5000 01
2.7710 01
2.260E Cl
2.2670 Cl
5.9180 01
5.0090 01
4.3360 01
3.5950 01
2.8680 01
2.359E 01
2.3760 01
2.3780 01
2.3350 01
2.4200 01
2.4'.4E 01
2.4590 01
9.6320-01
9.6510-01
9.256E-01
9.3470-01
9.2280-Ui
5.4120 01.
4.7560 01
4.1140 01
3.6230 01
3.725E 01
3.8590 01
4.028E 01
3.5340 01.
3.7230 01
3.6990 01
1.i'+OE 03
9.3200-01
9.3900-01
9,4000-01
1.1831.0-03
12
1.2431+0-03
1.17650-03
1.22140-03
SLOPE
-2.33930-01
1..8E 00
9.5700-31
6.1.660 01
5.5470 01
4.891E 01
4.249E 01
3.761E üi
0.862E 01
3.9950 01.
2.2600 1)1
2.2570 01
2.3320 01
2.3370 Cl
2.3410 Cl
4.1640 01
3.6120 1)1
3.81)00 1)1
3.9710 01
ROB
7.80890 01+
6.91.560 04
6.27120 04
5.62020 04
5.00970 34
4.61870 04
4.35690 04
3.90610 04
3.1.5100 34
2.92780 0'.
2.98650-03
3.19510-33
3.36650-33
3.46020-03
3.6381)0-03
3.95920-03
3.90440-03
3.97050-03
k.0397[-03
3.93540-33
4.12580-33
4.19260-03
2.83960 03
2.75200 03
2.66280 03
2.47490 133
4.166'+E 02
1.1)7430 03
4.1+0620-03
SB
AL
3.5808E-02
4.74750-62
3.01+270 02
STPR3
3.3592E-03
3.1.4180-03
3.53980-03
3.58760-03
3.6711E-03
3.731.20-03
3.77500-03
3.85840-03
3.95520-03
4.06740-33
4.23180-03
8.9560-01
9.1460-01
9.532E-01
9.3720-01
9.1460-01
9.6070-01
3.08120 00
3.61110 00
4.10330 00
4.77200 00
5.60750 00
6.33540 00
6.31400 00
6.3157E 00
6.30970 00
6.23510 00
6.20850 00
6.19160 00
4.53730 02
4.43410 02
2.54590 02
2.21540 02
1.83930 32
STPRM
9.3iOE-01.
4.6201+0 02
2.16600 1)3
1.9747E 03
1.77510 03
1.48630 03
1.29370 03
2.260E 02
2.2600 02
2.1930 02
PR
3.95770 02
3.99150 02
3.71290 02
3.3851E 02
2.32590 33
2.32800 03
3.04)0 02
NU
H
STPR
1.16210-03
1.5100 CD
i.552E CD
1.6030 CO
1.6790 CD
9.1+300-01
ST
9
10
11
2.910E 02
2.9530 02
3.0000 02
3.0000 02
3.0230 02
3.0700 02
3.050E 02
3.0500 02
9.7300-01
2.9200 00
2.5400 00
2.2700 00
1.9830 00
1.717E 00
1.1+1+10 00
1.67160 00
1.14'3E-03
C
1.5260 00
1.5930 00
2.4310 00
2.0390 00
1.7520 03
2.46140 34
2.31110 04
1.4104E-03
1.35750-03
1.31350-03
1.22330-03
1.15250-03
1.1.5630-03
V
9.6700-1)1
W
2.01+94E 00
THWI
2.2100 01
2.210E 01
2.2100 01
2.210E at
2.2100 01
2.210E 01
2.2100 01
2.2100 01
2.2100 01
1.6900 01
1.690E 01
1.6300 01
6.0340 01
3.89530 00
3.92250 00
3.92250 00
3.92250 00
3.90430 03
3.89530 00
3.66670 00
3.28730 00
2.90330 00
2.kk4'.E 03
1.76810 02
01
THB2
2.3920 03
2.0000 00
1.7130 00
1.4010 00
1.1000 00
8.920E-0i
8.9500-01
8.9200-01
8.9100-01
9.2100-01
9.2300-01
9.2500-01
6.051+0 01
80
AD
-1.61450
1H81
2.5980 01
2.5600 01.
2.5800 01
2.5300 01
2.5920 01
2.593E 01
2.7600 01
3.0780 01
3.4860 01
4.1400 31
4.9380 01
I
.11+1
3.38890-03
3.4841E-03
3.56720-03
3.66850-03
3.78420-03
3.87360-03
3.9183E-33
4.001+90-03
4.10510-03
6.23930-33
4.38780-03
4.56800-03
SAL
1.85860-02
SIPR4
3.81010-03
3.83390-03
3.85290-03
3.87230-03
3.8958E-33
3.91380-03
3.96100-03
4.0481+0-03
4.15030-03
4.29370-03
4.44710-03
4.63160-03
402
3.13470-02
151
HEAVY Ott.
PHI
.075
I
I
2
3
4
5
6
7
8
9
10
11
12
I
2.395E 00
2.5t'+E 01
2.538E 01
2.526E 01
2.520E 01
2.7)6E 01
1.727E 03
1.'.O1E 00
1.087E 33
4.IiOE 01
5.112E 01
6.120E 01
O.103E-01
TB
TWO
2.50E 01 2,000E C)
4
5
6
1
8
9
10
ii
12
2
3
4
5
6
7
8
9
10
1.?63E 00
i.127E oo
9.t6CE-01
i.586E 00
8.6SOE-01
0. 070E-0l
0.&20E-01
2.234E 01.
2.36AE 01
2.392E 01
2.362E Di
3.963E Cl
3.611.E
01.
3.861E Di.
3.BBOE 01.
3.9'.3E Li
3,962E 01
7.'.0l.E
3.3590E 00
2.9282E 00
'..26q8E 0'.
2.4623E DO
0'.
6.7557F 0'.
6,'+630E 04
0.0'.7kE 0'.
5.L1&2E 0'.
5.00B7E 0'.
'+7509E 0'.
3.?272E 0'.
3lE50E 04
25510E 0'.
I
ST
STPR
1.43O7-03
3.32301-33
3.23231-03
1
.8
9
10
11
1.2
1.3735E-03
i.3C90903
1.202E-03
1.i1'.E-G3
1.1252-03
1.12931-03
1.1621.1-33
1.18331-33
1.14301-33
1.19781-03
1.22571-03
SLOPE
-2.29911-01
2.1241E 0'.
3.324E-03
3,L'IO1E-33
3.53141-33
3.S15E-03
39U'.6E-03
4.01481-03
4,03701-03
3.859E-33
k.0553F-03
4.16981-03
SB
4.1.2291-32
2.900'sE 03
2.78t.6E 03
2.7233E 03
2.5086F 03
2.3054E 03
2.3355E 03
2.1840F 03
2.0186E 03
i.7993E 03
1.4549E 03
1.2256E 03
i.3475E 03
STPRM
3.39i4E-33
3.4577E-03
3.4887E-03
3.54721-03
3.61421-03
3.6082E-03
3.7ii2E-03
3.7903E-03
3.89'+8E-03
k.12'+2E-03
4.20131-03
4.3583E-03
AL
'..3396E-02
3.O1OE 02
3.00E 02
182
CPM
5.920E 01.
1.021E 00
9.570E-01
9.702E-01.
9.361E-Oi
9.004E-Oi
9.197E01
9.122E-01
9.702E-01
9.607E-01
8.688E-01
9.572E-01
9.527E-01
NU
PR
L..T191E 02
3.0792E 00
H
3.9220E 00
3.9225E 00
4.0255E 03
4.0351E 00
'..0063E 00
k.3159E 00
3.139E 00
2.739E 01
2.200E Ci
2.206E 01
2.200E Ci
2.202E 01
2.305E 01
2.320E 01
?.285E 01
3.693E 01
31.
5.012E 01
4.362E 01
3.593E 01
2.837E 01
2.207E 01
2.335E 01
2.3iDE 01
2.329E 01
2.402E 01
2.432E 01
2.405E 01
3.SOOE Cl
3.OiOE 01
4.ICOE Ci
RE9
W
2.930E 02
3.000E 02
3.000E 02
3.000E 02
3.060E 02
3.060E 02
3.050E 32
j.740E 01 2.330E 02
1.7'.OE 01 2.320E 02
1.630E 01 2.200E 02
5.835E Cl
4.919E 01
'..272E 01
60'+1E 01
3.772E 01.
2.220E 01
2.210E 01
2.220E 01
2.220E 01
TOt
TWI
6.ACJCE 01
2.71E 01
C
2.220E 01
2.220E 01
2.220 01
2.220E 01
9.020E0t 0.510E-01 1.59'.E 00
7,022E 01
6.175E Cl
4.330E 01 5t,21F: 01. 5.556E Ci
3.560C 01 '..74'.E 31 4.879E 01
2.802E 01 '..095E 01 4.233E 01
2.263E 01 3.569E 01 3,707E Ci
2.268E 01 3.655E 01 3.793E 01
4.979E 01.
V
2.220E
1.'.82E CO
9.000E-01
1.9707E 00
1.6536E 00
5
6
i.983E CO
j.709E CO
i.'.L.OE 00
11
12
1
2
3
4
2.944E 00
2.274E 00
8.f8E-3i 9.IUOE-01.
3.12E 01 8.600E3i 9.120E-01
3.1.56E 31 8.)0E-01 3.200E-01
I
I
2.qi8E 00
2.L.32E C)
2.O'.OE 03
1.488E 00
i.523E CO
1.572E 00
1.652E 00
I 5.890E 01
2
3
THWI
THB2
THO1
2.550E 31
1.781E 02
l.6145E 01
'..3049E 31
TIME
80
AD
B
A
-3.47AL.E 30
'..5909E 02
4.5329E 02
4.2232E 02
!.9246E 02
'..0079E 02
3.7477E 02
3.4636E 02
3.0867E 02
2.4928E 02
2.O91E 02
1.7949E 02
STPR3
3.2739E-03
3.3708E-03
3.43001-03
3.529E-03
3.61+761-03
3.73571-03
3.78841-03
3.86991-03
3.97531-03
'..099fE-D3
4.27771-03
4.44051-03
SAL
2.13591-02
3.6102E CD
4.0805E 80
4.7135E 00
5.6489E 00
6.'.315E 00
6.'+239E 00
6.4189E 00
6.3974E 00
6.2666E 00
6.2297E 00
6.2751E 08
STPR4
3.6811E-03
3.70941-03
3.70781-03
3.72551-03
3.75091-03
3.76581-03
3.81971-03
3.90231-03
4.OiC6E-03
4.14901-03
4.33311-03
4.49311-03
A02
3.1496E-02
AAV3H 110
6'70'7
00
BWIL
1
0
£
'7
S
9
I
%
6
CT
IT
I
30250
390S2
O22
32052
30252
3%S0
9S92
30S62
320'7C
3'i'7O'7
30925
TO
TO
TO
TO
TO
TO
CT
IT
0
£
'7
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9
L
9
6
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fl
3'7L99
TO
3gL'S
32'7S
TC
TO
3599'7
3'7T'72
20t'7
3O92
TO
3092
31.2'72
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TO
399'70
TO
TO
3026E
3960'7
3T'v'i
L66
0
£
900'7
365T0'7
3'7'7O'7
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0L09
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153
APPENDIX IX
COMPUTER PROGRAMS
154
PROGAM
FRICTION FACTOR
DIMENSION HT(20),TIME(20),PF(20) ,W(20),F(20),F2(20),Y(20),
1 X(2)),REVIS(20),RE(20) ,RE2(20) ,REW(20)
REAL
I..
READ (5, 12) PHI,KINO
12
21
31
22
32
23
33
24
34
25
35
90
91
FORMT(iF8.O,1I3)
GOTO(21,22,23,24) ,KINO
WRITE(6,3i)
FORMAT(iHi,26X,9HHEAVY OIL)
GOTO 25
WRITE(6,32)
FDRM4T(IHI,26x,1THIsQ-OCTYL ALCOHOL)
GOTO 25
WRITE(6,33)
FORHAT(IH1,26X,9HLIGHT OIL)
GOTO 25
WRITE(6,3L)
FORMAT(IH1,26X,1THSHELL SOLVENT 345)
WRITE(6,35)PHI
FORMT(27X,6HPHI
,IFS.3//)
READ(5,91)TB,RHOM,RHOE,RHOW,N
FORMAT(4F8.0,113)
IF(T9 .EQ. 0.)GOTO 115
WRITE (6,92) TB ,RHOM, RHOE, RHOW
92
FORMT(jHQ,23X,2HTB,5x,4HRHOM,4X,4HRHOE,L.X,4HRHOW/
1 19X,L+F8.2/)
Io
98
1=1+1
READ (5,100)HT (I),TIME(I)
too
FORMT(2F8.0)
L39 .12
PF(I=U./t2.)((HT(I)RHOM)+L(RHOE-RHOW))
W(I) 1O1.2/TIME(I)
GC = 32 16
DH= 0.731/12.
AC=0 .0369653
CF=i. .+577E-05
F(I) =(CFPF(I)4RHOE)/(W(I)42.0)
RRR= 0.94757
F2(I)=RRRF(I)
Y(I)1./((F2(I))0.5)
CXO .030800
X(I)=ALOG10((CX)((PF(I)RHOE)0.5))
VISLO(=X(I) -( (Y(I)+O.4)/4.)
VISLGE2. 302585VISLOG
VISB=EXP( VISLGE)
REVIS(I)=(DHW(I) )/AC
RE( I )REVIS (I) /VISR
VISWTR=O.0672/(2.i2((TB-8.435)+(8078.4+(TB-8.k35)
I 2.0)0.5)-123.)
REW( I)=REVIS(I)/VISWTR
IF(I .LT. N)GOTO 98
SIJMX=3.
SI.MY=O.
stJt.lxY=0.
SUMX X=0.
SUMYY=0.
DO 106 J1,N
XYX (J)
Y U)
XX=X(J)X(J)
Yv=Y (J)
Y U)
155
SUMXSU1X+X U)
SUMY=SUMY+Y(J)
SUHX V= SUM XV
V
SUMX XSUMXX+XX
S UM V VSUMYV
106
V
CU4TINUE
ANN
SXX=SUMXX(SUt1X'SUti X) IAN
SVYSUMVY(SUM1(SUIiY) IAN
SXVSUMXY (SUMXSUFV) IAN
SLOPSXVISXX
SVXS:(sYYSLOPESLOPESXx)/(AN-2)
sesQsvxsaisx x
Sf3(SBS
05
CL4 (SUMY00SUMX) IAN
VISL(10)((r)04+CL)/L+0)
SCL (SYXS)/AN+SUr1XSUMXSBSQI (ANAN) )'0
EVISL=005((10.0)(CfCL_SCL)/)(1Q.0.L++CL
I +SCU/L+.))
VISL+(10)4(!J#CLL4)/L+e)
WRITE (6107)
107
FOR
I 3HRE2,X2HF2/)
00 jjL
RE(K)DHW(K)/AC)(VIS'+))
RE2(K)RE(K)RRR
WRTTE(61)HT(K),TI1E(K),W(K),RE(l<),F(KRE2(K),F2(K)
108
I1L+
CONTINUE
WRIT E(6, 109)
log FORMAT(IH,6X,2HCL,gX,3HSCL,8X,HSLOPE2HS
lii
112
113
i1
WRITE(6,111)CL,SCL,SLOPE,SB
FORMAT(4EI24)
WRIT(f1t2)
WRITE(6, 113)VISL,VIS+EVISL
F0RMAT(3Ei.LI/)
GOTO 40
END
1S6
PROGAM HEAT TRMSFER
0IMEtSION W(20),1c31(2C),T82(20),TWI(20),TWO(20),THB1
I (20),THB2(20),THWI(20) ,REB(20),H(2D),NU(20),V(20),
2 C(2)) ,O(2.)) ,TIME(20),T0(20) ,DELTW(20),CPM(20),
3 PR(23) ,ST(20),STPR(20),STPRrI(2)),STPR3(20),STPR4(20)
4 ,Y(?0),X(20)
REAL K,KSS,NU
RM3 .411.3
RRR= ).94757
CM0 .031971
AS=0 .42303
OHZO .731/1.2.
KSS 9.42
R10 .244
R00 .254
RRRO/RI
ROF=].021167
RIF0. 020333
VOL= 3. 000 34559
1. 073192
RSS
RCU= 3 .00 0 3 5 '+15
RFC .9951
AC=0.3069653
READ (5, 12) PHI ,KIND
2
FORMT(1F.0,1.I3)
GOlD (21,22,23,24) ,KIND
21
31
WRIT(6,31)
22
32
WRIT(6,32)
FORMAT(1H1,26X,17HISO-OCTYL ALCOHOL)
23
3
GOlD 25
WRITE(6,33)
FORMAT(IH1,26X,9HLIGHT OIL)
2+
GOb
25
WRITE(6,3'+)
3
25
35
9
103
FORMAT(1H1,26X,9HHEAVY OIL)
GOlD 25
FORPIATC1HI,26X,ITHSHELL SOLVENT 345)
WRITE(6,35)PHI
FORNIAT(27X,6HPHI = ,1F5.3//)
READ (5,99)A,R,AO,BO,VISR70,N
FORMAT(5F8.0,113)
WRITE(6,103)A,B,AO,BD,VISR7O
FORMT(10X,1HA,12X,1HB,12X,2HAO,11X,2HBD,R7C
1 /3X,SEi.3.k//)
DO 103 I=1,N
READ (5, 102) TIME(I) , TH1(I) ,THB2( I)
02
THWI( I) ,V(I) ,C (I)
FOR1AT(6F9.3)
TBi. (I) =F(THP1 (IH
T2( I)F(THB2 (I))
TB(I)=TBI (I)+62.5(T92(I)TB1 (I) )/96.95
TWI ( t)F (THWI (I))
CP=1 .0
TBF= 32. 0+18(I) i.
8
IF(TEW .LE. 100.) (=..363(iU0.TBF).02/68.
IF(T3F .GT. 100.) K=C.363+(TBFiOO. ).03/100.
TBR= T9F+t#3.
VISLOGA+ALOG10 (T3R)
VISLGE2 3025 55VISLOG
VISB=EXP(VISLGE)
Q(I)=V(I)C(I)43.05688360.
QC=RF4Q( I)
157
QCVC)C/VOL
I
(RR) ) /(2.'KSS1. )
TWOC I)TWI( 1) OEL 1W (I)
W(I)lJ1.2/TIME(I)
CP1CI)=Q(I)(5./(9, 36QO,))/(W(I)*(TB2(I)TB1(I)) )
VISW1R=O.672/(2.i.L.82((TB(I)-8.k35)+(8O78.k+(TB(I)-8.435)
2.).5)i2U.)
1
PR(I)VISWTR36JO .1K
GW( 1)/AC
REB(1)DHG/VISO
H(I)=QC/S1Wfl(I1r3fl13)
NU(I)=H(I)DH/K
ST(I)H(I)/(CCP360.)
STPR (I)
STP
S1( 1)
( PR (I)
(I) C1( REf3( I)
(2.13.)
(-0 .2))
VISE3=VISWTPEXP(2.5PHI)
RE3rHG/vISE3
STPR3(I)C(RE2(O.2))
VOLOGAO+3flALO'1 -) ( IBR)
V0L0GE2. 3554VOLOr
VISO=EXP(VDLOGE)
FACT)R=1/(O.377q9+u,6jo627((VISD/VISWTR)fVISR70))
VISE + VISE 3 FACTO R
RE4
GfV1SE+
STPRL(I)CM4(REL44(0. 2))
'HI) ALOG(STPR(I)
X(I) AL0G(RE8 (I))
100
CONTINUE
WRITE(6,21D)
210
FORMT(5x,1HI,L+x,L+HTI,7x,THB1,7X,4RTHB2,7X,
1 sHTI , qX, IHV, lax, IHC/)
00 211 J1,N
212
211
WRITE(6,2l2)J,TIME(J),TIBl(J),TH92(J),THWI(J),V(J),C(J)
FORMAT(lI&,6E11.3)
CONTINUE
WRITE 6 , 214)
214
FORMT(//5X,lHI,5X,2RTB,9X,3HTWO,8X,3HTWI,8X,3HT1
1 ,8X ,3HT13?, 6X , 3HCPMfl
00 21 KK=1,N
WRITE(6,2i.6)KK,T3(KK),TWO(KK),TWI(KK),TB1(KK),TB2(KK)
I ,CP1(KK)
216
215
217
FORM T (116, 6E11 3)
CONTINUE
WRITE(6,217)
FOR1T(//5X,1HI,7X,lW,1lX,3HREB,1jX,1HH,i2X,2HNU,
1 I1X,2HPRI)
DO 219 Ml,N
WRITE(6,220)M,W(M),E8(1)H(1),NU(N1),PR(M)
220
219
FORMAT (116, 5E13.4)
CONTINUE
WRIT(6,221)
221
1 5HSTPR3,3X,5HSTPRL#/
00 222 II19N
WRITE(6,223) II, ST (II) ,STPR( It) ,SIPRM(II) ,STPR3( II)
1 STP.(II)
223
222
FORMAT (1I6,E13.4)
CONTINUE
su xo o
SUMY
J
SWIXY:::0
0
158
SUMXXO.3
SUMYYO.0
DO 240 JJ=i,N
XYX (JJ) Y(JJ)
XX=X(JJ)XCJJ)
yyy (JJ)*(JJ)
SUP1XSUMX+X (JJ)
SUMYSUMY+Y(JJ)
SUMX
SUM XV
V
SUMX=SUMXX+XX
SUMYVSUMVY#VV
CONTINUE
240
ANN
SXX.3UMXX-(SUMXSUP4X) IAN
SVV=SUMYV-(SUMVSU'V) fAN
SXV=3UMXV-(SUMXSUVV) IAN
SLOPESXV/SXX
SYXSQ(SYY-SLOPESLOPESX) / (AN-2.)
S3SQ=SYXSO/SXX
S8=(S')SQ)0.5
CL C SUMXX4SUMV-SUMX SUMXV)/ CAIN*SXX)
CLO2=(SU'IY+O 2SUMX /AN
SCL= CSVXSQ/AN+SUMXsuMXsBSa/ (ANAN))
1
C.5
AL = E X P (CL)
A02=EXP(CLO2)
E1CL+SCL
E2=CL-SCL
SAL
241
(EXP(ESI) -EXP (ER2) ) /2.
WRIT(6,241)
FORMT(//3X,5HSLOP,jrX,2HSO,11X,2HAL,10X,3HSAL,1OX
I ,3H&02)
WRITE(6,243) SLOPE,SF3,AL,SAL, A02
243 FORMAT(3X,5E13.4)
END
FUNCTION FCT)
IF(T .LE. 3.827)F=21.- CO .81-T)/ .04
IF(T T. 0.827 .ANO. T .LT. .868)F=21.+(T-.827)/.041
IF(T .GE. .868 ANO. I .LT. .9C8)F22.+(T-.868)I.04
IF(T .GE. .908 .ANr. I .LT. .gg)F=2.f(T-.gC5)/.041.
IF(T .GE. .99 .ANO. I .LT. 1.0)F=25.+(T-.99)/.O4
IF(T
IF(T
IF(T
IF(T
IF(T
.GE.
.GE.
.GE.
.GE.
.GE.
1.03 .AND. I
LT. i...235)F=26.+(T-i.03)/.041
1.235 .AND. I .LT. 1.277)F=31.(T-i,235)/.042
1.277 SAND. I .LT. 1.3l8)F32.+(T-i.277)/.04i.
1.318 ANOI I .LT. 1.360)F=33.+(T-1.318)/.042
1.360 .AND. I .11. 1.t.OiJF=34.+(T-1.360)/.041
IF(T GE. j.4)j .ANP. I .LT. 1.485)F35.+(T-1.401)I.042
IF(T .GE. 1.485 ,At"D. I .LT. 1.526)F=37.+(T-i.485)/.04i
IF(T GE. 1.526 4P!fl, 1 .11. 1.694)F38.+(T-1.526)/.042
IF(T GE. 1.696 AND, I .LI, 1,737)F42.+(T-1.696)/.043
IF(T GE. 1.737 .AND. I LT. 1.821)F43.+(T-1.737)/.042
IF(T .GE. 1.821 ,4N0. 1.11. j.907)F=45.+(T-i.821)/.043
IF(T GE. 1.907 .4N0. I ,IT. j,949)F=Z+7.+(T-1.907)/.0L+2
IF(T .GE. 1.949 ANO. I .LI. 2.336)F48.+(T-1.949)/.0'+3
IF(T .GE, 2.336 .AF1). I .LT. 2.380)F=57.f(T-2.336)/.044
IF(T .GE. 2.380 SAND. T .LT. 2.423)F=58.+(T-2.380)/.043
IF(T .GE. 2.423 .AtJO. I .LT. 2.775)F=59.+(T-2.423)/.044
lEd
.6E, 2.775 .AND. I .L,T. 2.820)F=67.+(T-2.775)/.0'5
IF(T .CE. 2.820 .4I!3. I .LT. 2.908)F=68.+(T-2.820)/.044
IF(I .GE. 2.908 .AND. T ,LT. 2.953)F70.+(T-2.9)8)/.045
IF(T .GE. 2.953 .AMO. T .LT. 2.997)F71.+(T-2.953)/.044
IF.(T .GE. 2.997 .ANO, 1 .LT. 3.402)F72.+(T-2.997)/.045
159
RETtJN
END
160
PROGRAM PREOICTEO F2
CALCULATES OUTER WALL FRICTION FACTORS USING 3
ALTERNATIVES FOR THE ESTIMATION OF EFFECTIVE VISCOSITY.
C
C
AC=. 3069653
OH=. 731/12
REAO(5,19)KINO
FORMAT(113)
GOTO(21,22,23,21+),KIWO
WRITE(6,31)
FORMAT(iHi,30X,9HHFAVY OIL/)
GOTO 99
WRITE(6,32)
18
19
21
31
22
32
FORMAT(1J-11,26X,17HISO-OCTYL ALCOHOLI)
GOTO 99
WRITE(6,33)
FORMAT(IHI,30X,9'ILIGHT OIL/)
GOTO 99
23
33
21.
WRITE(6,31+).
31.
FOR!IAT(1H1,26X,i7FiSHELL SOLVENT 31.51)
99
100
91
READ(S,100)TB,PHI,VISL4,AD,BD,VISR7O
FORMAT(6F8.0)
WRITE(6,91)TB,PHI,VISL.,A0,BD,VISR7O
FORMAI(/18X,FiTB,SX,3HPHI,6X,L4HVIS1.,8X,2HAO,8X,2HBD,
I 8X,6HVISR7O/t+X,1F8.2,1F7.3,lFti.7,1FIO. 4,2F11.1.//)
WRITE (6, 93)
FORMT(8X,1HW,9X,6HF2EXPT,9X,3HF2B,10X,3HF2C,iOX,
93
I 3HF?O/>
VISWTR0672, (2. i482( (TB-8. 1.35) 4(8078. 44(16-8.435)
2.) -435) -120.)
1
TR=1.92.fi.8TB
VISL0GAr+BOVALOG1C (IR)
VISLGE2. 02585VISLOG
VISDEXP(VISLGE)
VISRVISO/VISWTR
XX=VISR/VISR7O
98
103
FACTJR1. / (37799+. 610627'XX)
READ(5,103)W,F2EXPT
FORMAT(2F.0)
IF(W .EC. 9.)GOTO 18
IF(W .EO. 10.)GOTO 99
IF(W .EO. i1.)GOTO 111
REVIS0HW/AC
REREVIS1VIS4
RE2 .91.757RE
F2flFF2 (RE2)
VISC=VISWTR4EXP (2 .5°HI)
RE2C .91.757REV IS/V ISC
F2CFF2
VI SD
(RE2C)
VI SC F ACT OR
RE2O . 91.757REVIS/VISO
F2t)= FF2 (RE2O)
WRITE(6,105)W,F2EXPT,F26,F2C,F20
105
11.1
FORMAT(3X, 1F9.k,1.F13.7)
GOlD 98
END
FUNCTION FF2(RE)
FF2
.01
10
IF(A3S(FX) .LE, .0001)GOTO 12
FF2=FF2-FX/DFX
161
12
GOTO 10
RETUW
END
162
APPENDIX X
NOMENCLATURE
163
Nomenclature
The fundamental dimensions are: A = ampere; F = force,
L = length, m = mass, T = temperature, and t = time.
Roman Symbols
Meaning
Symbol
area; or constant
A
A
c
surface area of wall of flow channel
A
constant
A
0
LZ
outside surface area of outer tube of
the annulus
radius ratio, R
a
L2
cross sectional area of duct
A'
In
Dim ens ions
1
constant in the law-of-the-wall equation
BN
value of B for Newtonian fluids
current
C
n
constant
C
heat capacity
c
dimensionless plug radius for flow
of Bingham plastic, see Equation (33)
D
diameter
D
e
D'0
A
equivalent duct diameter
outside diameter of outer tube of
the annulus
FL/mt
164
Meaning
Symbol
Dimensions
diameter of inner and outer tube
of annulus, respectively
L
F
resisting force at the wall of the conduit
F
f
friction factor
D1, ID2
friction factor at inner and outer wall
of annulus, respectively
f1,
G
mass flux
m/L2t
g
acceleration of gravity
Lit2
g
gravitational constant
mL1F t2
HT
deflection of friction loss manometer
L
h
heat transfer coefficient
F /LTt
j factor for heat transfer
K
parameter defining shear stress-rate
of shear behavior of liquids or conversion factor for obtaining feet
thermal conductivity, or
Prandtl mixing length constant
F iLt
thermal conductivity of stainless steeL
F/Lt
L
length of test section
L
Lh
heated length of test section
work lost due to friction
L
k
k55
1
w
NU
Nusselt number, hD/k
n
exponent defining shear stress-rate of
shear behavior of liquids
P
pressure
L
LF/m
FIL2
165
Meaning
Symbol
Pf
Dimensions
frictional pressure drop
F/L2
static pressure difference
F/L2
pressure drop across the test section
F/L2
Pr
Prandtl number, C p.1k
p
wetted perimeter
q
amount of heat transferred
FL/t
q1
heat lost to surroundings
FL/t
qHI
heat generated per unit volume
F/L2t
R
radius of pipe
L
R1, R2
RCU
Re
Re2
p
inner and outer radius of annulus,
respectively
electrical resistance of the copper
tubes on the two sides of the stainless steel tube
mL2 IA2t3
Reynolds number DVp/p.
Reynolds number based on point of
maximum velocity, defined by
Equation (16)
R
m
radius of maximum velocity
Re,
Reynolds number based on
superficial velocity
RRR
a factor relating Re to Re2,
L
defined by equation (56)
RSS
electrical resistance of stainless
steer core
mL2/A2t3
r., r 0
inner and outer radius of stainless
steel core tube, respectively
L
i66
Meaning
Symbol
Stanton number, h/G C
St
Dimensions
p
temperature difference between the
wall and the fluid
T
TB
bulk fluid temperature
T
TB1
inlet fluid temperature
T
TB2
outlet fluid temperature
T
T
ambient temperature
T
wail temperature on the inside and
outside of the core tube, respectively
T
temperature (°F) on the exposed
surface less that of the ambient
T
overall heat transfer coefficient
based on outer surface
F/LTt
U
point velocity
L/t
u*
friction velocity, TTIp
L/t
critical value of u*, equal to
0. 3 ft/sec
L /t
maximum flow velocity
L/t
average velocity, or
voltage across the test section
L/t
mLZ/At3
V
volume of heated stainless steel core
L3
W
mass flow rate
m/t
w
work done by a flowing fluid
LF/m
x
distance along test section measured
from the point where heat transfer
begins, or thermal entry length, or
L
mb
TWI, TWO
S
U
u*
0
cr
u
m
V
167
Meaning
Symbol.
Dimensions
Lockhart-Martinelli parameter
defined by Equation (25b)
y
distance coordinate measured normal
to tube wall
z
elevation above an arbitrary datum
L
L
plane
Greek Symbols
a
correction factor in expression for
kinetic energy of fluid or radius ratio
or fluid property defined in Equation (38)
finite difference
viscosity
e
m
ratio of mean to maximum temperature difference
R
V
V
w
p
pw
m/Lt
m /R 2
viscosity
M/Lt
viscosity of continuous phase
M/Lt
viscosity of dispersedphase
M/Lt
effective viscosity of a dispersion
M/Lt
kinematic viscosity
L2 It
kinematic viscosity at wall
L2/t
density
mIL 3
density of dispersion
m/L3
effective density of manometer fluid
mIL3
density of water
mIL
168
Meaning
Symbol
Dimensions
shear stress on inner, outer wall
of annulus, respectively
F/L2
-r
y
yield stress of a Bingham plastic
F/L2
T
w
shear stress at pipe wall
F/L2
T2
4
volume fraction of dispersed phase, or
Lockhart-Martinelli parameter1 see
Equation (25a)
4m
ratio of bulk mean velocity to
centerline velocity
Subscripts
c
cr
continuous phase or cross sectional
critical
d
dispersed phase
e
effective
f
frictional
h
heated
i
inner
lm
log mean
m
manometer fluid or at point of
maximum velocity or refers to
ratio of mean to maximum of a
quantity
mb
ambient
o
outer
p
Bingham plastic or particle
169
Meaning
Symbol
SS
stainless steel
wb
at wall shear stress and bulk fluid
temperature
wc
at wall shear stress and critical
ww
at wall shear stress and wall
temperature
1,2
refer to inner, outer surface of
annulus, respectively
Dimensions
flow rate
Symbols Used in the Computer Printouts
A
constant in the equation relating
viscosity of dispersion to temperature
AD
value of A for dispersed phase alone
AL
least square intercept of heat transfer
AO2
intercept obtained from heat transfer
equation (St)(Pr)2'3 =AL(Re)SLO
equation using SLOPE of -0. 2
B
constant in the equation relating viscosity
of dispersion to temperature
BD
value of B for dispersed phase alone
C
current
CL
least square intercept obtained
CPM
EVISL
F
A
from Equation (65)
heat capacity of dispersion
FL/mt
error on \TISL
m /Lt
f
170
Meaning
Symbol
FZ
Dimensions
fz
FZEXPT
FZB
FZC, FZD
f2 predicted using experimental
effective viscosity
f2 predicted using Equation (23),
(78) for effective viscosity, respectively
F/LTt
H
h
I
serial number
PHI
PR
RE,REB
RE2
RHOE
RHOM
RHOW
SAL
volume fraction of dispersed phase
Pr
Re
Re2
e
m
pw
error on AL
SB
error on SLOPE
SCL
error on CL
SLOPE
ST
least square slope
St
STPR
(St)(Pr)213
STPRM
(St)(Pr)21 obtained from Equation (80)
using experimental effective viscosity
m/L3
m/L3
m/L3
171
Symbol
Meaning
STPR3,
STPR4
obtained from Equation (80)
(St)(Pr)2
using Equation (Z3), (78) for effective
THB1
thermocouple reading of inlet
fluid temperature
THBZ
thermocouple reading of outlet
fluid temperature
THW1
thermocouple reading of inside
wall temperature
TIME
Time taken for the collection of
Dimensions
viscosity, respectively
101. Z lb of fluid in weighing tank
T
T
from the return line
t
VISL
least square viscosity
m/Lt
VIS4
effective viscosity obtained from
Equation (65) using a slope of 4.0
m/Lt
V IS R 70