N09505211
ARNE OLAV FREOHEIM
NEI-NCJ--563
THERMAL DESIGN OF COIL-WOUND
LNG HEAT EXCHANGERS
SHELL-S:OE HEAT TRANSFER AND
PRESSURE DROP
DOKTOR INGENl0RAVHANDLING 1994:15
INSTITUTI FOR KULDETr.KNlKK
TRONDHEIM
DISTfliBlJTlON OF THIS DOCUMENT IS UNUMiTEO
Thermal Design of Coil-Wound LNG Heat
Exchangers
Shell-Side Heat Transfer and Pressure Drop
by
Arne Olav Fredheim
A Thesis Submitted for the Degree of
Doktor ingeni0r
The Uni~e:rsity of Trondheim.
The Norwegian Institute of Technology
Department of Refrigeration Engineering
February 1994
MASTER
DISTRIBUTION OF THIS
UOCUM~NT
IS UNLIMITED
}tct
1
Summary
The main objectives for the work presented in this thesis has been to develop
calculation models for LNG heat exchangers and LNG liquefaction cycles, in
order to do realistic simulations of LNG plants.
The thesis consists of three different parts :
• Description of procedures for thermal design of LNG heat exchanger
• Description of a test facility for measurements of heat transfer and
pressure drop in a coil-wound heat exchanger
• Presentation of measured data and models foi' calculation of heat transfer and pressure drop
A detailed model for thermal design of a multi-stream heat exchanger is
given. The mcdel is based on a step-by-step integration procedure, in order
to establish the temperature profile in the heat exchanger. The minimum
temperature difference is adjusted by variation of the shell-side pressure.
Different criteria for calcuiation of split point between the cold a.nd the warm
hea.t exchanger bundle are given given. A procedure for calculation of lay-out
parameters on the shell-side is presented, with a review of different methods
for calculation of minimum flow area. A brief description of different methods
for calculation of thern:J.~physical properties is also given.
The test fa.cility consists of a small test heat exchanger, where the heat transfer coefficient and pressure drop are measured in evaporating down flow.
Parameters such as flow rate, vapour quality, pressure and composition are
varied. The geometrical parameters and the instrumentation are described in
addition to data acquisition, data reduction and treatment of measurement
uncertainty. Heat transfer and pressure drop are measured in superheated
vapour flow, film flow and shear flow. The onset point for nucleate boiling is
also measured. The measured data are compared to methods from reference
literature, and some parameters have been adjusted to own measurements.
Acknowledgments
This thesis sum up some of the results from a research project carried out.
at The Division of Refrigeration Engineering, at the Norwegian Institute of
Technology. The project has been financed by Statoil, and I would like to
thank the responsible project managers who made this work possible.
Professor Einar Brendeng has been my supervisor.
Mr. Bengt O. Neeraas wrote his MSc.-thesis on measurements from a early
version of the test facility, and requirement for reconstruction was identified.
The test facility was ready for operation late 1989. Both the test heatexchanger and part of the instrumentation had been changed. The work on
construction, instrumentation and commissioning have been carried out as
parts of the work on this'thesis. I would like to thank Mr. Havard Rekstad
and the laboratory personnel for excellent assistance during the reconstruction and commissioning period. The measurements used in this thesis have
been carried out in the period from 1989 to 1992. Mr. Harald M;ehlum has
performed the measurements on binary mixtures.
The LNG heat-exchanger model was developed and implemented in CryoPro
in the p~riod from 1990 to 1992. I would like to tank Dr. Geir Owren for his
support during this period.
Mr. Hamid MGehlum and Mr. Havard Rekstad have made the AutoCad
drawings.
I would also thank my family for their patience during a rather long preparation period for this thesis.
ii
Contents
1
Thermal design ::.f LNG heat exchangers
1
1.1
1
Introd uctior
.. . .. .. ..
...............
1.2 Process considerations
2
1.3 Design procedure . . .
6
1.3.1
Basic design principles
1;3.2
Heat exchanger mode::
1.3.3
Optimum split point .
1.3.4
Optimum suction pressure. .
14
..................
18
1.4 Geometrica.lla.y-out
6
..
.........
1.5 Thermodynamic and physical properties
11
24
1.5.1
Selection of calcula".:ion methods
24
1.5.2
Equilibrium da.ta . . . . . . . ..........
27
1.5.3
Thermodynamic properties
28
1.5.4 Physical properties . . . . .
2
7
Test facility for LNG heat exchangers
29
30
Introduction. . . . . . ..
30
2.2 Description of test facility
30
2.3 Test heat exchanger ...
33
2.1
2.4
Estimat.ion and treatment of errors
iii
36
Contents
IV
2.5 Instrumentation, calibration and uncertainty
2.5.1
Tempera.ture
37
2.5.2
Pressure.
40
2.5.3
Flow rate
44
2.5.4
Heat flux
46
2.5.5
Composition
49
2.6 Data acquisition and data reduction
3
37
-. . -
49
49
2.6.1
Data acquisition
2.6.2
Pressure drop in section
49
2.6.3
Fluid temperature in section
50
2.6.4
Wall temperature in section
52
2.6.5
Total flow rate
53
2.6.6
Vapour quality
54
2.6.7
Heat-transfer coefficient
55
Heat transfer and pressure drop
56
3.1
Introduction . . . . . . . .
56
3.2 Su perheated vapour flow .
57
3.2.1
Test conditions ..
57
3.2.2
Heat-transfer coefficient
58
3.2.3
Pressure drop .
61
3.2.4
Heat leakage
64
3.3
Film flow
......
65
3.3.1
Parameters in gravity-controlled flow .
3.3.2
Test c.onditions
. -. -.
67
3.3.3
Heat-transfer coefficient
69
65
Contents
v
3.4
Onset of nucleate boiling.
75
3.5 Shear flow . . . . . . ... .
82
3.5.1
Parameters in shear-controlled flow.
82
3.5.2
Test co!:aitions . . . . .
86
:3.5.3
Heat-transfer coefficient
88
3.5.4
Pressure drop . . . . . .
96
A Thermal desfgD of LNG heat exchangers
107
A.I Geometrical data ..
107
A.2 Reference flow area .
114
A.3 Vapour pressure for pure propane ..
116
A.4 Corresponding state method for density
118
A.5 Corresponding state method for viscosity
...........
B Test facility for heat exchanger
123
B.1 Geometrical data .. __ . . . .
B.2 Estimation and treatment of errors .
121
123
.............
127
..
127
B.2.2 Systematic errors .
129
B.2.3 Propagation and combination of errors _
130
B.2.1
Random errors
B.3 Test for outliers in measurements . .
132
B.4 Student's-t statistics. . . . .
133
B.5 Location ofthermocoupies .
-134
B.6 Thermocouple reference equation
136
B.7 Thermocouple off-site calibration
137
B.8 On-site calibration of thermocouples
140
Contents
VI
B.9 Pressure transmitters . . . . . . . . . . . . . .
141
B.lO GeometricaJ data for the orifice meters .. .
144
B.ll Calibration da.ta. for turbiue meter
145
B.12 Measurement of heat flux ..
148
C Examples of measured data.
150
C.1 Superheated vapour flow . . .
151
C.2 Film flow "
153
C.3 Sh@af flow . .
155
Nomenclature
vii
Nomenclature
Latin
All
Ah.e
B
Cp
dX
D
DP
E
E
f
Fr
g
h
K
m
m
M
M
n
N
N
Nu
P
Pr
Pr
PI
q
Q
R
Ru
-Re
S
5
S
t ...,P
T
Flow area
Heat transfer surface
Estimated uncertainty from systematic error
Specific heat capacity
Longitudinal element
Diameter
Pressure difference in test facility
Electrical potential
Exergy loss
Fugacity
Froude number
Acceleration due to gra.vity
Enthalpy
Equilibrium constant (K-V<Ilue)
Number for last tube layer
Mass flow velocity
Mass flow rate
Number of set of measurements
Number for first tube layer
Number of items ( general )
Number of replicated readings
Nusselt number
Pressure
Radial distance between tube centers
Prandtl number
Longitudinal distance between tube centeiS
Heat flux
Heat transferred to fluid
Resistance
Universal gas constant
Reynolds number
Distance between tubes
Slip factor
Standard deviationStudent-t vab.e
Temperature
m2
m2
J/kgK
m
m
Pa
V
W
Pa
m/s2
J/kg
kg/m 2s
kg/s
Pa
m
m
W/m2
W
n
Nm/kgK
m
°C orK
Nomenclature
VIll
Velocity
Total heat-transfer coefficient
Est~mated total uncertainty interval
Wattmeter signal
Length
Vapour quality
Liquid _composition array
Vapour composition array
Total composition array
mjs
W/m 2 K
W/m 2 K
8
8
Heat-transfer coefficient
Inclination angle for all tubes
True uncertainty from systematic error
Film thickness
Heat of evaporation
Increase in number of tubes
Temperature difference
Step length for integration
Angle between identical configurations
True uncertainty from random error
Void fraction
Mass flow rate pr _ unit length
Thermal conductivity
True mean value for a normal distribution
Dynamic ~osity
Degree of freedom
Kinematic viscosity
Density
Surface teusion ccC::
Peripherical angle' Fugacity coefficient
Subscript
a
bu
calib
cb
Acceleration
Bundle
Calibrated -..alue
Cold b!i.ndle
u
U
VI
W
X
i
X
y
Z
W
m
Greek
Q
Q
f)
0
LlhLV
LlNT
LlT
LlX
Ll(}
E
e
r
).
J.£
J.£
v
v
p
(j
0
!D
J/kg
K
m
0
kg/ms
WjmK
Ns/m 2
m 2 /s
kg/m3
N/m
0
Nomenclature
co
com
cs
f
g
iJ
i-I
In
lam
lay
10
Is
L
m
n
oh
onb
or
P
ref
sat
sh
st
tp
tu
tui
vo
vs
V
w
wb
ws
Core
Component
Cold strea~
Friction and drag force
Static head or gravity
General number
Relative value between stream i and stream 1In-lirl.o:cuutiguratlon
Laminar
Layer
Liquid only
Liquid superficial
Liquid phase
Measured
Step number
Superheated
Onset of nucleate boiling
Orifice
Probability
Reference value
Saturated
Shell or jacket
Staggered con1iguration
Twcr-phase
Tube
Inside t'!!be
Vapour only
Vapour superficial
Vapour phase
VVall
VVarm l-n"dle
VVarm ~t.ream
IX
x
Nomenclature
Mathematical
Function parenthesis
()
Gradient of X with respect to Y
4X/dY
Acronym
SRK-EOS
PR-EOS
G-EOS
CSP
GPA
CWHX
MCR
LNG
MITA
PTFE
EMF
IPTS-68
Soave-Redlich-K wcng equation-of-state
Peng-Robinson equation-of-state
Cubic eq~atioD-of-state
Corresponding state principle
Gas processors association
COil-WOUD_d heat excha.nger
M ultico.:D p-cilent refrigerant
Liquefied natural gas
Minimum temperature approach
Teflon
Electromotive force
The International Practical: Temperature '5cale of 1968
1 Thermal design of LNG heat
exchangers
1.1 Introduction
Coil-wound heat exchangers ( CWHX ) have been used as main heat exchangers i:J. most of the LNG production plants built until now. The main
application areas for CWHX are as natural gas condensers in LNG production
plants, as steam boilers in nuclea.r power production plants and occasionally
as heat exchangers in petrochemical. or cryog€nic plants. Use of CWHX
in !:!'fG plants is based on the advantages of multist~eam capability, high
compactness, efficient heat transfer, high flexibility with regard to design
temperature and pressure and robustness with regard to rapid changes in
temperature and pressure.
CWHX may be constructed with one or several tube-side streams. Two
or three tube-side streams ue normal for LNG application. These streams
exchange heat with a common shell-side stream. The fluid ma.y be in onephase flow or in two-phase flow, both on the tube-side and on the shell-side.
The shell-side stream for the Ll'iG application is a.n evaporating multicomponent mixture which produces cooling duty for the condensing and subcooling
streams on the tube-side. The two-phase flow on the shell side is limited to
the cryogenic LNG application. The design pressures may be up to over 200
Bar on tube-side, but a normal design pressure for LNG appliC<'.tion is in
the range of 30-50 Bar on tube side and 2-10 Bar on shell-side. The areato-volume ratio is in the range of 150 to 250 m2 /m 3 in t!:.e heat exchanger
bundle, depending on tube diameter and radial and longitudinal tube spacing. High compactness combined with efficient heat transft:r due to local
cross-flow and total counter-current flow, make it possible to build la...rge heat
exchanger units, which are utilized in LNG plants.
1
2
1 Thermal design of LNG heat exchangers
The direct capital cost for the main neat exchanger may be about 30 % of tne
total investment cost pro liquefaction train [1], [2J. The energy consumption
<j.ue to exergy loss :n the main heat exchanger could be about 25 % of the
total energy consumption pro liquefaction train. Optim~J design of the main
heat exchanger is therefore important with regard to investment costs and
energy consumption during operation.
A simulation program, CryoPro, has been developed in order to carry out
thermal design and simulation of the liquefaction cycle and the main heat
e.'(changer in an LNG plant. The computer program was developed at The
Division of Refrigeration Engineering, at the Norwegian Institute of Technology, with financial support from StatoiL The design procedure for LNG
heat exchangers, described in this chapter, have also been implemented in
CryoPro.
1.2 Process considerations
Figure 1.1 shows a flow diagram for a natural gas liquefaction process. The
process is a propane precooled MCRI process, the most widely-u~ process
for LNG production worldwide.
A complete description of the process is given by Newton et al. in references
[3], [4], [5]. The process consists of a pretreatment system, a liquefaction sys,tem and a compressor/driver system. Heavy hydrocarbons, water, CO 2 , HzS
and Hg are removed down to a specified limi.t in the pretreatment system.
The limits for maximum content of these components are normally given in
order to prevent freeze-out and blocking in the main heat exchanger. The
design specification for the fractioning system would be given by the inlet
composition of the natural gas and the freeze out limit in the main heatsxchanger. The liquefaction system consists of a PI':COCling system which uses
a propane cycle or a binary-fluid cycle (Dual-mix), aud a main liquaaction
system which uses an MCR cycle. The pretreatment system and tha precooling system are normally incorporated into the same process block. The main
heat exchanger consists of two bundles built together in one shelL The two
bundles are called the warm bundle and the cold bundle respectively.
The natural gas and the MCR mixture are precooled before they are conI
Multi Component Refrigerant
3
1 Thermal design cif LNG heat exchangers
_-
..........
-
-
rrr~
I
II
I
(
Figure 1.1: Flow diagram for a na.tural gas liquefaction process [3).
4
1 Thermal design of LNG heat exchangers
dense<! in the warm bundle and subcooled in the r.old bundle. The MeR
fluid is separated into liquid and gas, before entering the warm bundle, in
()rder to obtain different compositions of the evaporating fluid in the warm
and the cold bundle. The MeR mixture is totally evaporated in the warm
bundle before being compressed and recondensed again. The natural gas and
the MeR are multicomponent mixtures, and will therefore condense at decreasing temperature. The MeR mixtures will also evaporate at increasing
temperature.
The natural gas enters the main heat exchanger with specified composition,
flow rate and pressure. The flow rata of the fuel gas is specified from the
total demand in the plan'!;. The natural gas temperature at the outlet of the
cold end in the main heat exchanger will be a function of this fuel-rate.
The selection of the remaining process parameters for the MeR refrigerant
has to ~ done in close ccnnectir,m with the thermal design of the liquefaction cycle and the main heat exchanger. These process parameters could be
summarized. as :
• Composition of the MeR fluid
• In!et temperature to the
wan::J.
end of the heat exchanger
• Suction and delivery pressure for the MeR compressors
• Pressure drop on each stream in the heat exchanger
• Temperature at the split point between the warm and the cold bundle
•
US(;
of expander as throttle device
The inlet temperature to the warm end of the heat exchanger is a function
of the temperature in the precooling loop. If a propane cycle is used, this
temperature may only vary v.ithin a narrow range. If a duel-mixture cycle
is used the flexibility will be much greater with respect to selection of inlet temperature and distribution of cooling duty and driver capacity in the
precooling cycle and the MeR cycle.
The exergy loss in the liquefaction loop may always be minimized by changing
the MeR composition. The local exergy loss due to heat tIG.!'!.sfer of a duty
Q between a warm and a cold stream with temperatures Tws and Tes may
1 Thennal design of LNG heat excha:agers
5
be calculated from Equation 1.1. The temperature is assumed to be constant
for both streams. Tref !s the reference temperature for exergy.
E
Tref
[T
"' ]
Q = Tcs. Tws· ws -.L cs
(1.1)
The loss is an inverse function of the stream temperature and a function of
the temperature difference between the warm and the cold stream. Equation 1.1 is used to calculate the temperature difference for a constant relative
exergy loss of 0.05 as function of temperature. The result is given in Table
1.1. The MCR composition should be optimized in such a way that temperature profiles in the heating and the cooling curves are similar to each other,
with decreasing temperature difference at decreasing temperature, in order
to obtain a constant, relative exergy loss.
Table 1.1: Temperature difference as function of temperature with a
relative exergy loss of 0.05.
Tes [K]
240.0
200.0
150.0
100.0
T uts
-
con~tant
T es [K]
10.00
6.89
3.85
1.69
The exergy loss in the main heat exchanger will also be a function of the
delivery pressure from the MeR compressors. Expanders may also be used
as throttle devices for the natural gas stream and the two MCR streams, in
the main heat exchanger. Use of expanders entails a reduction in exergy loss
in the liquefaction unit.
6
1 Thermal design of LNG heat exchangers
1.3 Design procedure
1.3.1 Basic design principles
The design procedure for the main heat exchanger is based on two main
principles.
• The total surface in the main heat exchanger will depend on the location
of the split point between the warm and the cold bundle. The location
will always have an optimum solution .
• A specified minimum temperature in the main heat exchanger can always be obtained by cha.nging the pressure on the shell side.'
The first statement is only valid for design purpose, where the geometrical
lay-out has to be established. The last statement may be used both for design
and for simulation.
A design procedure for the main heat exchanger is summarized in Figure 1.2.
The specification contains process parameters for the inlet natural gas stream
and the outlet LNG product, specified minimum temperature difference in
the heat exchanger, specified temperature difference in the warm end of the
heat exchanger and an object function for the optimization. The object
function could, for iI!stance, be exergy loss, investment cost or a combination
of investment cost and operational costs.
The design starts with a heat balance around the main heat exchanger with
given process conditions in order to calculate MeR flow rate. The hea.t
exchanger length is estimated by use of a step-by-step calcula.tion from the
warm to the cold end, with a heat balance on each step. The length of the
warm bundle is settled by use of a. split criterion, and the specified minimum
temperature difference is obtained by control of suction pressure. A new
total heat balance and a new ftow rate are calculated every time the suction
pressure is updated. The change of suction pressure and the location of split
point, and tile calculation of surface in the heat excilanger bundle will be
described in detail.
A procedure for simulation of the main neat excha.nger is given in Figure
1.3. The heat transfer area is fixed, and the operational conditions, such as
natural gas :flow rate and gas composition may be varied. MeR :flow ra.te
1 Thermal design of LNG heat exchangers
7
With given process specifications and object junction
Change MeR composition and delivery pressure
Change MeR ·suction pressure
Change location of split point between warm and cold bundle
Calculate surface in warm and cold bundle
TJ ntil optimum location is reached
U uti! specified minimum temperatu1'C difference is reached
Until optimum design solution is rmched
Figure 1.2: Ba.sic procedure for design of the main heat exchanger.
and high pressure is established by the compressor. Such simulations could.
be used in order to achieve optimum operation conditions. The procedure
described in Figure 1.3 uses a shooting technique on the temperature of the
low-pressure refrigerant in the warm end and on the suction pressure. The
optimum control of the MeR compressor is not considered in the procedure.
With given process specifications and object junction
Change MCR composition.
Change MCR S1.lCtior. pressure
Change refrigerant temperature out of warm. end
Calculate warm and cold bu.ndle
Until total heat balance is reached
Until specified LNG conditions is reached
Until minimum power input is reached
Figure L3: Basic procedure for simulation of the main heat exchanger.
1.3.2 Heat exchanger model
Figure 1.4 shows a simplified sketch of a multistream heat-exchanger bundle
with N st number of streams. The first stream is the shell-side stream and
the (N st-1) tube-side streams exchange heat with the shell-side stream only.
1 Thermal design of LNG heat exchangers
8
.
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
·
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
,
I
I
I
.
I
I
I
I
I
I
··
·, ·,,
·
···
. , ·,
I dX I
Len gt hO
I
I
I
I
I
I
I
I
Stream Nst
Stream·· .
Stream 2
•,
I
I
Stream 1
I
I
Len gt.h
X
Figure 1.4: Simplified sketch of a 1X.ultistream. heat exchanger with N st
streams.
A steady-state heat balance for a small longitudinal element dX, between a
tube-side stream, i, and the shell-side stream, 1, leads to Equation 1.2 and
1.3. The longitudinal heat conduction is ignored in this heat balance.
i
dh
N~, dh
M·
dX
;=2 dX
Ml
= 2···Ns i.
(1.2)
[-h=2,)-k-'
(1.3)
A. momentum balance over a longitudinal element dX leads to Equation 1.4.
i= l···Nst
(1.4)
51, S2 and 52 are integer constants with values of -lor 1 depending on integration direction, flow direction and direction of phase change. An adiabatic
1 Thermal design of LNG heat exchangers
9
flash method for calculation of temperature as function of enthalpy and pressure for a given composition is also needed as given by Equation 1.5, in order
to obtain a closed equati~n system.
i=1···Nst
(1.5)
Equations 1.2 to 1.4 express the enthalpy and the pressure for each stream
through the heat-exchanger bundle by first-order differential equations. The
right-hand side of the equations has to be calcdated from a set of algebraic
equations and constants. The constants are given by the geometrical layout such as heat transfer area pro unit length and cross-sectional area for
each stream. The algebraic equations, sach as heat-transfer coefficient for
each stream and pressure gradient for each stream will vary through the heat
exchanger, as the temperature and pressure vary. The total heat-transfer
coefficient is calculated from the local heat-transfer coefficients by the same
method as for a shell and tube heat exchanger [6].
The total mathematical model consists of (2· Nst - 1) independent differential
equations and a set of independent algebraic equations. A solving procedure
for the equations is given in Figure 1.5. The geometrical lay-out refers to
parameters such as radial and longitudinal tube spacing, number oftubes for
each stream and tube length. .
With given stream data and design limitations
Change geometrical lay-out
Change guessed values at length 0.0
Change for next step by integration
Enthalpy, pressure and temperature.
Heat-transfer coefficient and total surface
Until stop criterion is reached
Until residuals at length X are minimized
U nti! optimum design is obtained
Figure 1.5: Solution procedure for a bundle in a multistream heat exchanger.
..I\.s described in Chapter 1.3.1. all of the input streams to the heat exchanger
are known or guessed in the wa.rm end. These streams are considered as
10
1 Thermal design of LNG heat exchangers
specified input values. There will also be design limitations such as ma.ximum
pressure drop, maximum length and so on. These limits could be based on
J;Danufa.cturing, transport, or process considerations. The design starts ,..lith
a choice of geometrical lay-out for the bundle. k soon as these values are
established the heat transfer area pro unit length and the cross-sectional area
for each stream can be calculated. The geometrical parameters are constant
throughout the heat exchanger bundle.
The solution of Equation 1.2 to Equation 1.4 is based on a numerical integration of the differential equations from length 0 to length X of the heat
exchanger. Different numerical methods may be used to integrate equations
1.2 to 1.4. The simple first-order Euler method is given by Equation 1.6. The
method is a. step-by-step method, where 11. refers to integration step number
and i refers to stream numb~r. LlX is the length of each integration step.
The pressure and the enthalpy at the next integration step are calcula.ted
from equations 1.2, 1.3 and 1.4. The temperature is calculated from Equation 1.5 and the rigbt-hand sides of equa.tions 1.2 to 1.4 a.re updated in order
to calculate yet another integration step.
(1.6)
The integration proceeds until a specified stop criterion is reached. Specified
length or specined temperature and pres'Oure on an output stream may be
used as stop criterion. The procedure is generalized to solve the situation
where some of the input streams have unknown values at length 0 and known
values at length X. The residuals are defined as the difference betw~ the calcula.ted stream temperature a.nd pressure at length X and the known stream
temperature and pressure at length X. The guessed values at length 0 are
changed in order to minimize these residuals. In the last part of the design,
the geometrical lay-out may be changed in order to meet the design-limits
given at the start of the calculation.
A simplined solution may also be obtained for Equation 1.2 to Equation 1.47
by assur::ling that all of the warm streams follow the same temperature profile
thro1igh the heat exchanger. The total cooling curve may then be divided into
a number of grid points or section:;, where the temperature for the sa ell-side
1 Thermal design of LNG heat exchangers
11
stream is estimated by use of a heat balance. This gives a faster calculation
and the U . Aile value is then post-calculated for each stream and each grid
point. Such an approach. may be used for preliminary studies of the design
and the process parameters.
The accuracy of the design depends on many parameters, such as adiabatic~
l1ash calculation and correlations for calculation of heat-transfer coefficients
and pressure drop. The temperature difference in an LNG heat exchanger
may be as low as 2 to 3 K at the pinch point. Accurate prediction of temperature from specified enthalpy and pressure values is therefore important.
The total calculated surface is also sensitive to the pressure on the shell-side.
The prediction of the pressure drop may therefore affect the prediction of the
temperature difference and the total surface.
1.3.3 Optimum split point
Different design criteria may be used in order to establish the split point
between the warm and the cold bundle. Figure 1.6 shows an example on the
temperature difference in the warm and the cold bundle as a function of relative length. The split point must be within the range of relative length where
both the warm and the cold bu~dle have a positive temperature difference.
This range will vary with composition and suction pressure. The profile is
generated with the assumption of equal temperature on each warm. stream
at each grid point.
Different criteria for detection of split point may be :
L Given length of warm bundle or temperature of one stream out of warm
bundle
2. Minimizing surface in heat exchanger
3. Maximizing
~T
in the split point
The first criterion may not be obtainable due to the actual range with positive
temperature differences for both bundles.
Figure 1.7 shows an example for the total heat transfer surface in a main heat
exchange!" as a function of the relative length at the split point between the
warm and cold bundles. A decrease in the warm bundle length will reduce
12
1 Thermal design of LNG heat exchangers
::.::
8.0
OJ
Warm bundle - - •
{J
C
OJ
1-1
OJ
Cold bundle ___ .
6.0
I
"-l
"-l
-rI
'0
I
'.
4.0
I.
OJ
1-1
:l
J.J
<0
1-1
~- .....
,,
I"
'
I
,
"I
,
.... J
I
,
I
2.0
,
\,I
I
OJ
0.0
~
QI
E-t
0.7
0.8
0.9
1.0
Relative length [-]
Figure 1.6: Temperature djfferences in the warm and cold bundle.
the total surface because the total heat transferred is reduced due to the
fact that there are more streams in the warmb-undle than in the cold bundle
and because the temperature difference in the warm bundle is increased. The
surface in the cold bundle will increase at the same time since the temperature
difference is reduced. The minimum surface will be at a length where these
two effects balance each other. The possible split range is narrow for this case
and the temperature difference in the cold bundle increases very rapidly with
respect to relative length. The split point for minimum surface is therefore
located very close to the lowest range limit. The criteria for minimum surface
is set up in Equation 1.7. The optimum po!nt for minimum surface is given
in Figure 1.7.
(1.7)
The use cf the minimum surface criterion PN~UCes a lower Ll T for the cold
bundle than for warm bundle. If the pinch point for the heat exchanger is
located in the split point, the suction pressure will have to be kept lower
than necessary in crder to obtain the specified, minimum pi.nch point. The
13
1 Thermal design of LNG heat exchangers
40000
r---~r-r---...,...----"----'
N
I
E
•
~
~
36000
ItS
""':II-<
til
32000
Surface - Minim1.lJ.iI ---Max_ DT ----
2800 0
'--_---J~
0.85
_ _.....J,..._ ___L_ _
0_87
0.89
0_91
~
0.93
Relative length [-]
Figure 1.7: Total h eat- transfer surface as a. fun ctian of th e split pai:Jt between
the warm and coid bundle.
14
1 Thermal design of LNG heat exchangers
maximum obtainable ~ T in the split point wi.ll be for relative length where
temperature difference is equal for the warm and the cold bundle, as
given in Equation 1.8.
th~
(1.8)
The optimum point for maximum temperature difference is also given in
Figure 1.7. The variation in minimum temperature difference between the
two different split points is about 0.4 °C in Figure 1.7. The optimum curve
is :fiat in this region, so the increase in surface between the two split points
is small compared to the change in temperature difference and, eventua.lly,
suction pressura, for this case.
All of the three methods are im plemented in CryoPro, but the method which
maximizing the !!J. T is used in most cases.
1.3.4 OptimUm suction pressure
Figure 1.8 shows the temperature difference through the heat exchanger as a.
function of relative length at different specifications for minimum temperature approach (MITA ). The split point between the warm and cold bundle is
ca.Iculated from the criterion of maximum temperature-difference in the split
point. The profiles are generated with the assumption of equal. temperature
on each warm stream. The change in MITA specification creates a. change
in suction pressuro:;. The different temperature ?rofiles have a parallel displacement to each othe:.r with respect to change in suction pressure or MITA
specification. There are six different pinch points in this example, four-in the
warm bundle and two in the cold bundle. The last one in the warm :,undle
and the first one in the cold bundle are located in the split point. These two
are similar due the specification of maximum temperature difference. Two
of the different pinch points are in position to be a MITA point.
Figure 1.9 shows a trace of the different pinch points as a function of suction
pressure. The pinch points are detected from the definition given in Equation
1.-9.
dT
[dXbu];
= 0.0
(1.9)
15
1 Thermal design of LNG heat exchangers
::.::
~
10.0
MITA
(!)
u
t:
(!)
8.0
l-l
(!)
....,
...., 6.0
"'-- ..
.
= 1.5
= 2.5
= 3.5
I
I
"
•
•
.
.,.,j
'0
4.0
0.0
0.0
0.2
0.4
0.6
D.B
1.0
Relative length [-]
Figure 1.8: Temperature profile as a function of specified MITA.
The MITA specification is located at the pinch point which gives the lowest
suction pressure. Each of the pinch points has to be traced during iteration
on suction pressure due to the fact that the MITA point jumps from one pinch
point to another when the pressure is varied. At a given suction. pressure,
the MITA point is located at two different pinch points.
The slo.,-.a of the dinerznt pinch traces is a strong function of pressure drop
on the shell side. If the eqQations are solved without the assumption of equal
temperature on each v;ann stream, the number of pinch points increase:::, as
shov.,,!!jn Figure 1.10. The total heat-transfer coefficient is assumed to be
constant for each stream through the heat exchanger in this example. There
are about 10 different pinch points in the figure.
Heating and cooling curves for the main heat exchanger in an MeR,
precooled, liquefaction system are given in figure l.li.
propa.n~
Figure 1.12 shows the total heat transfer surface and the exergy loss in an
LNG heat exc.h.ar.ger as a function of the suction pressure to the MeR compressor. A change of ~:uction pressure will lead to a pa.rallel displacement of
the heating and cooling curves in figure L 11. The optimum solution has to
16
1 Thermal design of LNG heat exchangers
~
~
10.0
(!)
()
Split point pinch
Warm #1
,
Warm *2
' • .c:-.-".",
Warm #3
, .............------,'::.~
Cold #::!.
....-:::........
....~---
W 8.0
1-1
(!)
:!j 6.0
• ..-1
'0
(!)
J..J
ItS
----
-:::-............... ---..:::--..
4.0
.......
1-1
;:!
.-.-.-.:~:::~
.
2.0
.
>-I
(!)
0:
e:Q}
8
0.0
I
L
1.9
2.1
2.3
2.7
2.5
2.9
Suction pressure [Bar]
Figure 1.9: Pinch trace as a function of specified MITA.
~
~
15.0
(!)
()
liquid. - vapour ----
!1CR
MCR
W12.0
Natural gas
1-1
..' ,,
Q}
I
::::
9.0
,
• ..-1
\,
"
'0
"
6.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Relative length [-]
Figure 1.10: Temperature profiles in an LNG heat exchangel".
17
1 Thermal design of LNG heat exchangers
Temp=mre [KJ
240.00
230.00
,
1\\.
I
I
I
~, I
~
220.00
I
I
I
I
200.00
I~,
190.00
I
II~-,-
I
180.00
I
I
170.00
i
I
~ ~\.
I
I
I
150.00
140.00
I
130.00
II
I
120.00
I
I
110.00
I
0.00
0.20
II
I~\
I
I
I
I
I
I
"\ 1
\.1
\l\
I
160.00
HotTii~-­
ColdSbCilPaSs - .
coidTiibcPaSSC
CcldTuiid'iSsr
I
I
HotSheIlFass
HotTlibePassl
HOlTi!beP"aSSi---
!
I
I
I
210.00
I
!
I
1
I
I
I
I
I
0.40
0.60
0.80
I
\\ I
\'
';~
\1
1
I
Re1:uive Length [-]
1.00
Figure 1.11: Heating and cooling curve for for the main heat exchanger in
an MeR, propane precooled, liquefaction process.
18
1 Thermal design of LNG heat exchangers
be based on economical considerations.
til
til
o
.-l
60
50
Area
Exergy loss
40
30
20
M
E
10
o ~----~------~----~----~
1.0
1.5
2.0
2.5
Suction pressure [Bar]
Figure 1.12: Total heat transfer surface and exergy loss as a functioD. of
suction pressure.
1.4 Geometricallay--out
A sk~-:-~h of a CWHX bundle is shown in Figure 1.13. The heat exchanger
consists of tubes coiled in layers around a cylindrical core. The coiling direction alternates for each la.yer and the number of parallel tub~ in each layer
increases by a constant number from layer to layer toward the outside of the
heat exchanger. The radial distance between each layer is held constant by
use of longitudinal space bars.
The longitudinal distance between tubes in one layer and the tube inclination are also kept constant for all the layers. All of the tubes in one bundle
have equal length because of the constant distances in the radial and longitudinal directions and the constant inclination. The tubes are connected to
tubesheets at each end of the heat exchanger_ The ratios of tubes from all
of the different streams are constant for each layer in order to avoid maldistribution for the :fluid Oil the shell side introduced by differences in heat load
1 Thermal design of LNG heat exchangers
19
ELEMENTS 0" CONSTRUCTION
t-'1t.-:~_--
8
I. CD!L
2. MANDREL,3. TuBE L~Y:RS
4. SPACER5
5. JACKET
6.. PIGTA:L-ENDS
7. TuBE-SHEET
~. NOZZLES
«. ':''I£LL
USUALLY COUNTER-CURRENT
RANGE 0, BUllT UNITS
AREA
;.ElGHT
DIAMETER
WElGH'
,
0.3 -
11000 m 2
0.6 - 20m
I
o ;: -
201:'
0.0-4- 150 'tons
A-A SHELL SIDE FLOW
B
B-B 1. TUBE SIDE ~LOW
C-C 2. TUBE SIDE FLOW
0-0 TUBE SlOE FLOW
Figure 1.13: Sketch of a .:oil-wound hea.t exchanger bundle OYith four streams,
LINDE A.G. [8}
20
1 Thermal design of LNG heat exchangers
for each stream. The bundle is covered by a. jacket on the outside in order to
avoid a by-pass stream on the shell side.
A uniform two-phase flow distribution on {;he shell-side is crucial in a heat
exchanger used for LNG production in order to achieve constant temperature on each layer at a given length. Maldistribution may result in reduced
production capacity or increased power consumption.
The distribution system in a heat exchanger used for LNG production may
be constructed as given in Figure 1.14 as a separator and a perforated plate
spray tower [7]. The liquid phase is distributed over the entire CfO<:S section
ofthe tube bundle by gravity force, through the perforated plates; and :8.ows
as a thin film on the tube wall. The vapour is distributed in between the
liquid phase by pressure differences. The liquid and the vapour are in thermal
equilibrium a.t the top of the bundle, downstream the distribution system.
INTEIUUU.
SEPJlRATOR
DISTRIBUTOR TRATS
FOR UQU\D
Figure 1.14: Two-phase :Bow distribution system for a CWHX, Bukacek [7}
Description of a. the geometrical lay-out, performance and manufacturing of
1 Thermal design of LNG heat exchangers
21
coil-wound heat exchangers are also given ir. references [3], [7] and [9].
The main objective for the geometrical calculations in CryoPro is to establish
the bundle geometry, and to calculate variables which influence on the heat
transfer and the pressure drop. The geometrical data are classified in three
different categories, given in Table 1.2. The input data which have an initial
estimate may be changed during the calculation.
Table 1.2: Geometrical data for the main heat exchanger in CryoPro.
Fixed input data
Inside and outside tube diameter
Radial tube pitch
Longitudinal tube pitch
Input data with initial estimate
Core diameter
Number of tubes for each stream
Output data
Shell diameter
Bundle length
Heat transfer surface for each stream
Flow area for each stream
Number of layers
Tube inclination
The shell-side configuration varies continuously between in-line and staggered
as a function of position. Figure 1.15 shows the tube configuration between
four different layers at peripherical angle 0, 20 and 40 degrees. All of the
layers have in-line configuration at the starting position, (J = 0.0. The second
and the fourth layer are coiled in the right direction, and the other layers are
coiled in the left direction. The calculation of geometrical data is reviewed
in Appendix A.I.
Two of the most important parameters for calculation of heat transfer and
pressure drop are the characteristic flow area, and th,! characteristic radial
distance between neighboring tubes. The flow area for a tube side stream, j,
22
1 Thermal design of LNG heat exchangers
40
0000
0000
0000
degrees
s::
....0
"'u"'
Q)
....'0
l-;
.....
60 degrees
0°00
00
00°0
400
6
III
....'0s::
::s
...."'"'
OJ
s::
0
..J
o
degrees
20 degrees
0000
0000
0000
o 00
0°0
0~08
Radial direction
Figure 1.15: Local tube configuration at different periphe;-ical angles.
23
1 Thermal design of LNG heat exchangers
may be calculated from Equation LID.
(LID)
The cross-flow area on the shell-side may be calculated from Equation 1.11,
where SreJ is the radial reference distance between to neighboring tubes,
calculated from one of the different methods reviewed in Appendix A.2.
(Lll)
The different methods calculate different values for the reference distance
and the lIow area. Comparisons between the methods are given in Table 1.3,
for four different cases. The methods are compared on a relative basis with
respect to the in-line flow area for given values of Pr, PI and Dt... These
parameters are also given in Table 1.3 and represent a reasonable range of
choice with respect to geometrical data in an LNG heat exchanger.
Table L3: Rel:;,:'ive Bow area on shell side, calculated by four different methods.
Case 1 : D tu = 10.0 mm, Pr = 13.0 mm, PI = 12.D mm
Case 2: D tu = 10.0 mm, Pr 13.0 mm, PI
11.0 mm
Case 3 : Dtu = 10.0 mm, Pr = 15.0 mm, PI = 12.0 mm
Case 4 : Dt'OL = 10.0 mm, Pr 15.0 mm, PI = 11.0 mID.
=
=
- ..c!'
Method
In-line
Staggered
Glaser [13]
Gilli [14]
=
Relative flow area
Case 2 Case 3 Case 4
1.0000 1.0000 1.0000
1.3719 1.2311 1.1953
1.1206 1.0782 1.0659
1.1961 1.1220 1.1032
Case 1
1.0000
1.4393
1.1493
1.2313
The heat-transfer surface for each stream, j, may be set up as a function of
the shell-side length, as given in Equ ation 1. 12. The total surface is calculated
24
1 Thermal design of LNG heat exchangers
as a sum of the surfaces for each stream.
(1.12)
The total tube length and the total bundle length are calculated as a result
from the integration. The two length parameters are related as given in
Equation 1.13.
Xiru. = sin{o:) . X t ...
(1.13)
1.5 Thermodynamic and physical properties
1.5.1 Selection of calculation methods
Accurate calculation of thermodynamic and physical properties is important
both for the design and simulation of heat-transfer equipment. The main aim
for the review in this section is to describe general methods which may be used
for calculation ofthermodynamic and physical properties in relation to design
and simulation of LNG heat exchangers. The thermo-physical properties are
also of great importance for data reduction and for data modeling in the test
facility, described in Chapter 2 and Chapter 3.
.
The properties and methods used in connection with models for thermal
design of heat exchangers and models for calculation of heat transfer aIid
. pressure drop may be classified into three different grQUPS as given in Table
1.4. A brief description of the different calculation methods is provided.
The thermodynamic and physical properties must be calculated for both
the liquid and vapour phase. The two key parameters used for selection of
calculation methods are the claim for high accuracy and the claim for general
application on mixtures. The main objective is to use the same Calculation
methods both for pure component and for mixtures in o::der to achieve a
smooth transition for the measured properties in the test facility with regard
to composition. The methods are selected for use on light hydrocarbons or
hydrocarbon mixtures. Some special methods are chosen for nitrogen gas in
order to obtain high accuracy in the test facility.
1 Thermal design of LNG heat exchangers
25
Ta.ble ! .4: TherlIlodynamica.l and physical properties used for design of the
main heat exchanger and da.ta. reduction in the test fa.ci1ity.
I Property
Calculation method
Equilibrium. data
Pure component
Vapour pressure or C-EOS
Multicomponent
C-EOS
Solid-liquid
GPA
Thermodynamic properties
Enthalpy
CSP (C-EOS in test facility)
Heat of evapora.tion . CSP (C-EOS in test facility)
Entropy
CSP (C-EOS in test facility)
Heat capacity
CSP (C-EOS in test fwlity)
Density
CSP
Physical properties
Cet>
I
Viscosity
Thermal cond.lcti\"ity
CSP
I Surface tension
CSP
....
26
1 Thermal design of LNG heat exchangers
A review of the chosen methods is given with emphasis on accuracy. The
review is related to the measUi<=lments and the data reduction in the test
f?rility, and is not c')mplete with r,>spect to the different da.ta given in Table
1.4.
A computer program for calcula.tion of thermodynamic and physical properties has been developed at SINTEF, Division of Refrigeration Engineering
[10J. This program, TP-lib, is used as a subsystem in CryoPro. The propert!es are calculated from a given temperature, pressure and composition. A
view of the different layers in TP-lib is given in Figure 1.16.
Enthalpy
APPUcmON LIVEL
t
FIASR CAI.CULUIONS
PHASE SEARCBlNG
ENTBALPY !'l'C..
RESIDUAL
FtlNCl'JONS IDEAL GAS
FOIL
PROPEiTlES
m!"J2Es
ImiNG ~!I
I
I
,CSP~
,.
Entropy
Compositions
'!P.Jib left! 0
BesidlI8l flmctioD
cas flmctiODS
TP_lib left! 1
tIdal
t
1
I
~panmeters
TP.Jib left! 2
Pure eomJlC!ll.ent
parameter!
TP_lib level 3
PtmE COMPONENT
CONDmONS
Figure 1.16: The layers ofTP-lib used for calculation of thermodynamic and
physical properties [10]-
The program consists of different layers and the interface between CryoPro
and TP-lib is on the application level. The system is also used as a basis for
the data reduction in tbe test facilities.
1 Thermal design of LNG heat exchallgers
27
1.5.2 Equilibrium data
The isothermal equilibrium in a vapour-liquid system may be calculated by
us<; ofEqi,iation 1.14, [il]. The equation is solved by iteration, and is applied
to calculate t-he vapc~r quality ~d the composition for each phase.
(1.14)
The equ3tion for adiabatic equilibrium may be obtained by adding a heat
balance around the two phases, as giveli in Equation 1.15. This is a calculated equilibrium with given enthalpy and pressure. This equation may
also be solved by iteration with respect to temperature, in combination with
Equation 1.14.
htp
-
i· hv(T, P, Y) - (1- x) . hL(T, P, X)
= 0.0
(1.15)
The vapour quality is influenced by th~ K-value for each component, which
is the equilibrium constant that describes the distribution of a component
between the two phases. The K-~ues are functions of temperature, pressure
and composition and a.re obtained from the definition of thermodynamic
equilibrium, given in Equation 1.16, where the fugacity for a component, i,
is equal in both phases. The temperature and the pressure are also equal in
the two phases.
fL,i
= IV.i
(1.16)
Different models may be used for calculation of the fugacity, and a G-EOS
is normally used for both phases in light hydrocarbon systems with small
amounts of polar components present. The K-value for a component, i, may
then be calculated from Equation 1.17.
Ki
= Yi = (h,i(T,P,X"r
Xi
BV,i(T, P, Y)
(1.17)
The CWHX design is based on Equations 1.2 to 1.5, and the accuracy in
the calculations depends on the C-EOS model, in turn dependent upon the
28
1 Thermal design of LNG heat exchangers
K-values and the enthalpy-temperature relationship. High accuracy may
be obtained for multicomponent equilibrium by use of binary interaction
parameters.
The same equilibrium model may be chosen for calculation of pure-component
vapour pressure. This gives a smooth transition between a pure component
arid a mixture, which is of importance for the measurements in the test facility. Pure-component vapour pressure for propane is compared with different
calculation methods in Appendix A.3. The deviation for the Peng-Robinson
equation-of-state ( PR-EOS ) is estimated to be within ± 0.2 °C within the
t~IUperature range of 230 K to 350 K. A detailed description of different
ii.&odels for calculation of K-values is given in Reference [11]. Different equations of sta.te for calculation of equilibrium in binary and multicomponent
mlxt)lres have also been reviewed in Reference [15].
.
.
Estimation of freeze-out for C02 and heavy hydrocarbons in LNG heat exchanger:; is an important part of the equilibrium calculations because these
calculations set the limit for the pretreatment system. These calculations
have been reviewed by Owren [12], with given recommendations. The GPA
Cryogenic Solubility program, developed by Kahn and Luks, may be used for
such calculations [12].
1.5.3 Thermodynamic properties
The density for pure or mixed hydrocarbons is calculated by a cCJ."l'esponding
state method as described by Ely et al. [16] and Stephan et aI. :[17]. The
method is based on statistical thermodynamics and relates the properties of
a mixed or pure fluid to the same properties for_a P1J!'e reference fluid by use
of a set of functions. Methane is used as reference fluid, and the density for
pure methane is calculated by a very accurate correlation. The P ..... p - T
data for pure methane may be c:alculateJ by use of a quasi-vinal equation
of state as given by Younglove et aI. [18], [19}. The equation is used both
for saturated and subcooled liqUid and for saturated and superheated gas
and is quoted to be very accurate. Evaluation of uncertaint)~ in calculated
density by the corresponding state method is based. on data for pure and
mixed hydrocarbons. The uncertainty for the calculated density is regarded
to be within ± 2 % for light hydrocarbons. A detailed description of the
comparisons is given in Appendix A.4.
1 Thermal design of LNG heat exchangers
29
Density and thermodynamic properties for pure nitrogen gas is calculated
from the same quC!Si-virial equation-of-state used for methane and propane
[18]. The uncertainty ill the calculated density is quoted to be within ±
C.2 % for fluid above critical temperature. This method is used for data
reduction in the test facility, for gas measurements. The uncertainty for the
calculated thermodynamic properties for nitrogen gas above critical temperature is quoted to be within ± 5 % for calculation of specinc heat at constant
pressure or volume, and within ± 1 J/mole for calculation of enthalpy [18].
1.5-4 Physical properties
Viscosity and thermal conductivity for pure or mixed hydrocarbon fluids are
estimated o;>r use of a corresponding state method similar to the method used
for calculation of density. A complete review of the method is given by Ely
et aI. [16]. The method has been implemented in TP-lib as a part of the
work on the thesis.
The uncertainty in calculated dynamic viscosity and thermal conductivity
for pure hydrocarbons and hydrocarbon mbctures is evaluated to be within
± 8 % for this method [16]. A def::illed comparison is performed in Appendix
A.5 for pure component dyna-..lic viscosity. The uncertainty in calculated
dynamic viscosity for pure propane is regarded to be within ± 3 %.
Thermal conductivity and viscosity for a pure component are given by YOllDglove et aI. [18], [19]. The uncertainty for the calculated properties for
nitrogen gas above critical temperature is quoted to be within ± 6 %, both
for viscosity and thermal conductivity.
2
Test facility for LNG heat exchangers
2.1 Introduction
Design- and simulation results for LNG heat exchangers are sensitive to the
loeal heat-transfer coefficient and pressure gradient on the shell side, due to
small temperature differences between warm and coLd streams and a high
~ gradient on the shell side. No commercial computer program is available
to calculate such an exchanger. Information regarding heat transfer and
pressure drop are normally proprietary for manufa...-turers I)f such exchangers.
Two different test facilities have baen built in order to verify and improve
the simulation program CryoPro. The test facility described here is built for
measurement on down-flow evaporation on the shell side.
The local heat transfer coefficient and pressure gradient are measured, and
the whole shell-side range, in an LNG heat exchanger, may be covered by
.::hanging different parameters in the test facility. The test fluid may be
pure or mixed hydrocarbons and the test facility are operated at realistic
pressures and temperatures. Different parameters which affect the measured
heat-transfer and pressure drop are varied.
The construction of the test heat-exchanger, and the commissioning of the
test facility have been performed in connection to this thesis.
2.2 Description of test facility
A flow diagram for the test facility, including the major parts of equipment
and instrumentation, is presented in Figure 2.1. The facility consists of a
test circuit, a propane brine circuit and a methane cooling cirC1!it.
The local hea.t-tra.nsfer coeilicient and the pressure gradient are measured
30
31
2 Test facility for LNG heat exchangers
I
I
I
I
I
I
I
I
I
I
I
I
H~
I
.
_~ __ ~___Lj~~r, ~fl~'"
~
I
)---L~"""J.:T5
-------liliI-L--LrO;- ....
@yI..N
Figure 2.1: Flow diagram for the test facility.
(A)(C)(E)(G)(1)(K)(M)-
Test heat-exchanger
Vapour blower
Vapour cooler
Turbine-meter
Propane pump
Propane cooler
Methane expansion drum
(B)- Sepa.rator
(D)- Orifice-meter
(F)(H)(J)(L)(N)-
Pump
Liquid cooler
Temperature regulator
Propane expansion drum
Philips cryogenerator
32
2 Test facility for LNG heat exchangers
in the test heat exchanger. The test fluid is circulated through the test
heat exchanger as gas- , liquid- or two-phase flow. When measurements are
Rerformed at two-phase conditions, the fluid is separated into a liquid stream
and a vapour stream, after the test heat exchanger. The flow rate and the
composition are measured for the two different phases. The V3.pour stream is
circulated by use of a gas blower and cooled before it is mixeJ with the liquid
in the test he:~,t exchanger. The liquid stream is cooled after the separator
and circulated by use of a pump before it is mixed with the gas in the test
hea.t exchanger again.
The liquid and the vapour streams in the test circuit are cooled against the
propane in the brine ci,rcuit. The propane is circulated by use of a pump
a.nd cooled against evaporating methane in the main cooling circuit. The
brine circuit is branched into three courses; one for cooling of liquid, one
for cooling of vapour and one for recirculation of brine. The main cooling
circuit operates by thermosyphon circulation. The methane is conde!lsed in
a cryogenerator, which is the cold-supplier in the plant.
The vapour- and the liquid flowrates are changed by means of frequency regulation on the gas blower- and the pump motor, and by means of recirculation
of liquid from the pump to the separator. This system provides a smooth
regulation of flow rate through the test heat exchanger. The flow rate in the
brine circuit is changed by means offrequency regulation on the pump motor
and by means of regulation of the split ratio between the different courses.
The brine temperature is set by regulation of the cooling duty in the cryogenerator and by regulation of the electrical heat-input. The temperature in the
test heat exchanger follows the brine t~mperature. The pressure in the test
heat exchanger is a function of the temperature and the total composition of
the nuid in the test circuit.
The test facility may be operated at temperatures from 0 to -150 0 C, and
pressures from 1 to 15 bar. The mass-flow velocity in the test section may
be varied from 20 to 200 kg/m 2 s. The whole quality range from superheated.
vapour flow to liquid film flow may be covered for a particular mixture,
by changing the temperature and the flow rate of liquid and vapour in the
test circuit. Pure-component or mixtures of nitrogen, methane, ethane and
propane would normally be used as test fluid.
2 Test facility for LNG heat exchangers
33
2.3 Test heat exchanger
The test heat exchanger consists of a gas-liquid mixing system, a two-phase flow distribution system and the test section. A sketch of the hea.t exchanger
is gl1T<ln in Figure 2.2.
The liquid- and the vapour strea!:lS have different temperature and composition before mixing into a two-phase fiow. The purpose of the mixing system
is to bring the two-phase flow to thermodynamic equilibrium. The system
consists of series of bends and T junctions.
It is important to obtain uniform distribution of the two-phase flow in the
test heat exchan~er. The :flow distribution system consists of a plate with 30
vertical tubes, placed in a circle over the central coil in test heat exchanger.
Each tube has two slits, 0.5 mm wide and 100 mm long. The two-phase now
is separated by gravity, and the liquid forms a level over the partition pla.te
before it is drained through th.e slits in th.e tubes. The vapour is drained
directly through the center of the tubes, and the two-phase flow forms an
annular flow pattern through the distribution tubes. The expansion at the
outlet of the tubes generates a uniform spray of liquid over the whole flow
area in the test section.
The distribution system and the heat exchanger were tested with air-water
mixtures as test fluid. Visual observations were performed. The flow rate
and the vapour quality were changed over a large range. Dye was added at
different locations in order to observe the iluid :Bow through the d.istributi.on
system and in the heat exchanger. The testing gave satisfactory results, both
for two-phase distribution and for film flow down through the heat e.'Cchanger.
The dye was traced around the whole periphery of the test excha.nger in a.
distance of 6 to 8 rows downstream the injection point. The heat exchanger
is normally operated with light hydrocarbon mixtures, where the density and
the viscosity ra.tios are much smaller than for air and wa.ter. The degree of
mixing and the :Bow distribution will therefore be better for such mixtures.
The test section is a model of a coil-wound hea.t exchanger, and consists of
one central coil and two half-tube coils on the inner and outer walls. The
center coil consists of four parallel tubes and the inner and the outer coils
consist of respectively three and five parallel half-tubes. The half-tabes on
the walls are inserted in order to obtain right flow performance around the
center coil where the heat-transfer coefficient is measured. Tha main layer is
2 Test facility for LNG heat excha'lgers
34
Figure 2.2: Test heat exchanger.
(1)(3)(5)(7)(9)-
Tubes with vertical slits
Outer half-tubes
Flow inlet
Pressure tapping
Partition plate
(2)- Heated palt of test section
(4)- Inner half-tubes
(6)- Flow braker
(8)- Separator plate
35
2 Test facility for LNG heat exchangers
coiled to the right and the two half-tube layers are coiled to the left. Three
longitudinal space bars are inserted between each of the layers. The tubes in
the center coil are also separated by space bars in the longitudinal direction.
The core and the half-tubes on the inner wall are cut on the lathe with high
accuracy, from one piece of metaL Five parallel half-tube hollows with correct
inclination and longitudinal distance were made on the outer walL The tubes
was squeezed down into t:,~ hollows in order to form the ~uter half-tubes
on the walL
The test section consists of a flow stabilization zone, an isothermal zone and
a heated test zone. The total heat exchanger consists of 24 succ~ing tubes
in the flow direction. The flow-stabilizer zone consists of 6 succeeding tUDes
where a correct velocity profile and flow distribution are esta.blished.
The heated zone corresponds to one round for each tube in the coil, which
again corresponds to four succeeding tubes in the flow direction. Outside
tube diameter, heated area, longitudinal tube pitch, radial tube pitch and
tube inclination have been measured directly or calculated from indirect measurements. The geometrical data are used in date reduction and in models for
heat transfer and pressure drop. An uncertainty limit for each of the geometrical parameters is estima.ted. The geometrical data for the test section are
cited in Table 2.1, and reflect a normal geometrical choice for a coil-wound
heat exchanger. The determination of the different geometrical parameters
and the relation between the different parameters are shown in Appendix
B.1.
Table 2.1: Geometrical data for the test heat excha.1ger.
Parameter
Outside tube diameter
Longitudinal distance between tube center
Radial distance between tube center
Winding angle
Heated tubelength
Heated area
Value
12.00 ± 0.05
13.94 ± 0.09
15.91 ± 0.06
7.938 ± 0.06
1688.5 ± 3.00
63655.0 ± 288
mm
mm
mm
0
!Ilm
mm 2
Each of the four aluminium tub~ in the center layer is heated with electrical
heating elements at the center of the tu bes. The heated test zone is separated
36
2 Test fadlity for LN G heat
excha.ng~rs
from the rest Cif the heat exchanger by PTFE plugs in order to prevent heat
leakage. The heat flux from the tubes may be varied from 0 to 10 kW 1m2 •
A mixing chamber is insta.lled after the heated test section in order to bring
the fluid back to isothermal conditions before the temperature is measured.
The mixing chamber consists of saddle pocking, as used in distillation columns.
2.4 Estim.ation and treatment of errors
Measurement and calculation of physical properties involves errors. The main
aim for the error analysis is to estimate uncertainty intervals ror the measured
heat transfer, the measured pressure drop, the parameters used for modelling
purposes and the models used for calcu lation of heat transfer and pressure
drop.
The uncertainty interval, UI, is defined as the range around a mean value,
which can be expected to inclllde the true mean vabe of the property
with a. specified confidence level or probability, P. A result may be stated as
x±Ulp.
x,
Errors are divided into three main groups. Spurious errors, random errors or
precision errors, E, and systematic errors, /3, also called fixed errors or bias
errors. Spurious errors, such as human errors and instrument malfunction,
are not incorporated into the uncertainty intervaL A statistical outlier test is
used in order to detect and reject measurements affected by spurious errors.
The Dixon outlier test [26] is described in Appendix B-3. The total uncertainty interval is estimated by a combination of j3 and E. The error analysis
for the measurements involves ;
L Identification of all independent sources of errors
2. Identification and rejection of spurious errors
3. Estimation of uncertainty associated with systema.tic errors
4. Estimation of uncertainty associated with random errors from repeatoo
measurements a.nd statistical analysis
5. Estimation of uncertainty intervals for the measured results due to
propagation of systematic and random errors
2 Test facility for LNG heat exchangers
37
6. Estimation of uncerta.inty interval for the calculated results due to propagation of errors
The main sources for uncertainty in measured values are calibration, data
acquisition and data reduction. Methods for estimation of errors and uncertainty interval are given in Appendix B.2.
3.5 Instrumentation, calibration and uncertainty
2.5.1 Temperature
The locations of the different points for measurements of temperatures are
shown in Figure 2.1. Fluid temperatures in the test section are measured
at eight different points. All of these points are regarded as isothermaL
Surface temperatures are measured in the tipper and lower parts of the heated
test section, by four thermocouples on each of the four heated tubes. The
location of the wall points and the fluid points are given in Appendix B.S.
Temperatures in the test fluid are measured at three points along the liquid
part of the circuit and at four points in the vapour part of the test circuit.
A description of the different elements is presented in Table 2.2.
The temperatures TIl to T 1., T31 to T~ and all of the surface temperatures
are measured with sheathed and insulated thermocouple elements. The rest
of the temperatures are measured with ba.re thermocouple elements. All of
the thermocouples are of type E made with chromel-constantan wires. An
ice ba.th is used as reference junction.
An instrumentation diagram for the thermocouple element is given in Figure
2.3. The chromel-constantan wires in the thermocouple elements are connected to shielded and twisted copper wires at the reference jUilction. All of
the copper wires from the reference junction are connected to an isothermal
input connector on the data logger. The shield is connected to earth ground.
The shield on the input connector is connected to earth ground through a
100 kQ resistance in order to prevent noise in the measuring chain.
The signals from the thermocouple elements are converted to temperature by
use of Equation 2.1, where the electrical signal is represented as a temperature
38
2 Test facility for LNG heat exchangers
DATAE..OGGER
VOLTMETER
CONNECTOR
MEASUREMENT
+
POINT
G
CONSTANTAN
SHIELD
100 k
Figure 2.3: Instrumentation diagram for temperature measurement.
39
2 Test facility for LNG heat exchangers
Table 2.2: Thermocouple elements in the test circuit.
Identifier
TIl - T14
TSl - T 3•
TZAl - TZAa
T2Bl - T2B8
T4
Ts
'1'6
T7
Ts
T9
TIO
Tn
TI2
Tlcb
Location
Fluid temperatures before the heated test section
Fluid temperatures after the mixing chamber
Wall temperatures in the upper part
Wall temperatures in the lower part
Liquid temperature at the outlet of the separator
Liquid tempera.ture at the outlet of the liquid cooler
Liquid tempera.ture at the inlet of the mixing system
Vapour temperature at the outlet of the separator
Vapour temperature before tr.e orifice meters
Vapour temperature at the inlet of the mixing system
Propane temperature at the outlet of the p'lmp
Propane temperature at the outlet of the liquid cooler
Propane temperature at the inlet of the pl\mp
Laboratory temperature
function.
E(T} = EreJ(T) + Ecalib(T}
(2.1)
Erei is the electromotive force, EMF, calculated from a standard thermocouple reference table. Ecalib is a correction for the EMF based on calibration
data. The reference table is given by an equation in Appendix B.6. Equation
2.1 is solved by iteration. Six of the sheathed elements and the bare wire
are calibrated off-site by a comparison method described in Appendix B.7.
Individual equations for Ecalib are given. Total uncertainty, in EquatioI:. 2.1,
due to off-site calibration of the elements is estiinated to be within ± 0.07
°e, both att~e calibration points and in the int€!"Val between the points.
The calibration curve for the rest of the sheathed elements is estimated by
bulk calibration as described in Appendix B.8. An equation for Eeelib is given.
The elements are also checked on-site by use of isothermal me<lSurement. The
uncertainty due to calibration for these elements is estimated to be v..':ithin ±
0.1 DC. The main error sources in the data acquisition system for temperature
are summarized in Table 2.3.
2 Test facility for LNG heat exehangers
40
Table 2.:3: Error sources for measurement of temperature.
Source
Reference junction
Data logger
Function of reading
Function of resolution
Calibration
Fluid temperature
Wall temperature
Uncertainty
± 0.01 °C
± 0.01
%
± 8.00
p.V
± 0.07 °C
± 0.10 °C
Status
Dependent
Dependent
Independent
Dependent
Dependent
The inaccuracy for the data logger is based on a.n air temperature !n the range
of 15 - 35°C and recalibration of the logger once a year. The total uncertainty
limit for each measured. temperature is estimated by use of Equa.tkl !! B.17
without dependency between the different sources. The uncertainty limit
will vary with respect to tem~rature. The total uncertainty interval for two
thermocouple elements is given in Figure 2.4, as a funct!on of temperature.
Element one corresponds to measur~ment of fluid temperature and element
two corresponds to measurement of wall temperature.
The last column in Ta.ble 2.3 describes dependency status for different error
sources when different temperatures are combined into a result. The different
sources a.re random with respect to each other for a single measurement. The
small random part for the calibration error is neglected..
2.5.2 Pressure
The location of the different pressure transmitters is shown in Figure 2.1.· A
further description is given in Table 2.4.
The liquid level in the separator is measured in order to evalua.te plant sta.·
bility. Specification data for the different pressure transmitters a.re given in
Appendix B.9.
An instrumentation diagram for the measuring chain is given in Figure 2.5.
P sec, DPsl and DP52 are installed in the isothermal part of the test section.
The lower pressure taps are located about 70 mm above the heated. part of
41
2 Test facility for LNG heat exchangers
0.25
,
'-
u 0.20
>.
~
-- ---:------_._------------'-
0.15
• .-j
ttl
t
Element one
Element two
0.10
Q)
u
§ 0.05
0.00
-150
-120
-90
-60
-30
o
Temperature [C]
Figure 2.4: Uncertainty interval for two thermocouple elements as a function .
of temperature.
Table 2.4: Pressure transmitters in the test orc!.lit.
Identifier
P sec
DP s1
Por
DP or
-
DPm.cr
DP s2
Location
Absolute pressure in the test section
Differential pressures in the test section
Absolute pressure before the orifice-meter
Differential pressure through the orifice-meter
Liquid level in the separator
42
2 Test facility for LNG heat exchangers
DATALOGGER
VOLlMETER
P1
R
+
PorDP
4-20mA
P2
Figure 2.5: Instrumentation diagram for pressure measurement.
2 Test facility for LNG heat exchangers
43
the test section. and about 126 mill above the end of the heated test section.
The longitudir.al distance between the pressure taps is 126 ± 0.5 mm which
corresponds to nine succ~ive tubes in the flow direction. The upper pressme
taps are located about 84 mm below the entrance of the test section. which
corresponds to si.... successive tubes in the flow direction. The difference in
peripherical angle between DP.. 1 and DP.. 2 is about 90 0. p ..ec is connect~
to one of the lower tappings. The tappings are located between two parallei
tubes in the outer half-tube layer.
The tra.nsmi~ters ~;ve; a 4-2(1 !IlA outliut signal as a function of pressure.
This signal is convc:-ted to a v"luge signal by use of a precision resistance, in
order !!) achie....~ ('. higher degr~ C(~ accuracy in the data-Iogge!". The signal is
regardl'"C! to be linear OVt:!i" the calibrated range. The measured voltage signal
is converted to pressure or differential pressure by use of Equation 2.2.
(2.2)
a and b are constants estimated from individual of-site calibration. The constants and the precision resistances for the different transmitters are given in
Appendi.x B.9, along with a detailed description of the calibra.tion procedure
for the different transr.litters.
The main error sources for the measurement of pressure and differential pressure are given in Ta.ble 2.5. The accuracy for the trans"itters is given in Table
B.17.
Table 2.5: Error sources for measurement of pressure.
Uncertainty
Source
Data logger
function of reading
±O.Ol %
Function of resolution
±0.8 mV
Precision resistance
±O.l n
Transmitter
I Table B.17
Status
-1I
Dependent
Independent
Independent
Independent
I
The total uncert~inty limit for each measured pressure is estimated by us('
of Equation B.17 without dependency between the different sources. The
sensiti ..;ty coefficients are calculated from Equation 2.2. The uncertainty
44
2 Test facility for LNG heat excha"\gers
limit will vary with respect to measured pressure level. The uncertainty due
to reading in the data logger is treated as dependent when pressure data are
c~mbined.
2.5.3 Flow rate
Vapour flow rate may be measured by use of one of the orifice meters at the
point DPor in Figure 2.1. The choice between the different meters depends on
the total vapour flow rate and the pressure drop through the orifice meters.
The lower limit for differential pressure is set to about 500 Pa in order to
adlieve a high degree of accuracy. Geometrical data for the orifice meters
are presented in Appendix 8.10. Data for the different pressure transmitters
are given in Appendix B.9.
Flow rate through an orifice meter may be calculated by use of Equation 2.3.
The differential pressure through the orifice and the upstream temperature
and pressure are measured [30].
Mv
= a: • E •
i .D~ . ";(;:;.2-.'D"'P.;:::-or-·-p
(2.3)
ThE flow coefficient, 0:, is a function of the diameter ratio, m = Dor/Dtui,
and the Reynolds number[31]. The equation used for calculation of 0: has a
maximum deviation of 0.11 %. The expansibility coefficient, E, 3s a functio!l of
diameter ratio, pressure ratio through the orifice and the isentropic coefficient
for the fluid. The equation used for calculation of E has a. mean deviation
of 0.11 % [31]. Equation 2.3 has to be solved by iteration. Uncerta.:nty in
measured flow rate is calculated by numerical perturbation of the independant
variables, given in Table 2.6. These variables are based on the analysis in
Reference [26]. The sensitivity coefficients are calculated from Equation 2.3.
The magnitude of the different error sources will vary with flow conditions.
The liquid flow rate is measured by use of a turbine meter at the point ML
in Figure 2.1. The measuring chain for the turbine meter is given in Figure
2.6.
The turbine meter gives a pulse-rate signal as function of volume flow. This
signal is converted to a 4-20 rnA signal by a pulse-rate converter, and to a
voltage signal by a precision resistance. The turbine meter is calibrated from
the factory and recalibrated in-site by use of water. The calibr.:.ted range
2 Test facility for LNG heat exchangers
45
Table 2.6: Independent sources of error in :Bow calculation through orifice
meter.
Variable
To
Ts
Par
DP ar
J.L
p
K
Dar
Dtui
E
a
I
Variable name
Reference temperature for diameters
Fluid temperature before orifice
Fluid pressure before orifice
Differential pressure across orifice
Fluid viscosity
Fluid density
Isentropic exponent for fluid
Diameter in orifice plate
Diameter in orifice tube
Expansibility coefficient
Flow coefficient
DATALOGGER
YOL"IIIETER
FLOW
R
F'ULSE-RA1E
CONVERTER
4-20mA
Figure 2.6: Instrumentation diagram. for turbine meter.
+
46
2 Test facility for LNG heat exchangers
may be divided into different sections where the function between the 4-20
mA signal and the flow rate is assumed to be linear. The signal is converted
t.o flow rate by use of Equation 2.4.
(2.4)
a and b are constants estimated from the calibration data. The constants
in Equation 2.4 and the precision resistances are giver. in Appendix B.ll,
along with a detailed description of the calibration procedure for the turbine
mete!".
The uncertainty limit for the turbine meter is estimated to be within ±
0.5 % of the reading. The limit includes precision and bias error from the
data logger, the turbine meter, the pulse-rate converter and the precision
resistance. The turbine is calibrated, and used within a narrow range, and
the calibration is not affected by the full scale nonlinearity in the turbine
meter.
2.5.4 Heat flux
The heat flux in the test sectio!l is measured by use of a wattmeter and
by use of voltage measurement and effect calculation as a control method.
The measuring chain for heat flux is given in Figure 2.7, where both met;hods are illustrated. The control method uses the measured voltage and a
temperature-corrected resistance in order to calculate the effect. The control
method is described in Appendix. B.12.
The wattmeter is calibrated and the observed value is corrected as given
in Equation 2.5. The W ca.lib function is assumed to be linear between the
different calibration points. Calibration data for the wattmeter are given in
Appendix B.12.
Vl' = Wm
+ W calib
(2.5)
The different error sources for measurement of heat flux are given in Table
2.7. The sources are regarded to be independent.
47
2 Test facility for LNG heat exchangers
Q1
Q2
R3
Q3
R2
Q4
R1
DATALOGGER
VOLTMETER
WATTMETER
U
R4
-
+
Figure 2_7: Instrumentation diagram for heat-flux measurement_
48
2 Test facility for LNG heat exchangers
Table 2.7: Error sou:-ces for measurement of heat Dux.
Calculation from resistance
Source
Uncertainty
D,\ta logger
Function of reading
±O.O2
Function of resolution
±4
Pr,.rision resistances
Table B.21
Heating elements
Table B.22
V\Tattmeter
Source
Uncertainty
Calibration and nonlinearity
±O.5
Resolution/reading
±O.05 times scale factor
%
mV
W
W
I
2 Test facility for LNG heat exchangers
49
2.5.5 Composition
The fluid refered to as pure propane has a composition of 99.71 %-propane,
0.22 % n-Butane and 0.07 % i-Butane. The composition is measured by use
of gas chromatograph. The influence f!"om the contaminations of butanes is
taken into account by use of the PR-EOS, as given in Appendix A.3.
2.6 Data acquisition and data reduction
2.6.1 Data acquisition
Voltage signals from temperature, pressure and flow measurements are collected by use of a FLUKE 2280B data. logger, and transferred to a VAX-730
computer by means of the LABSYS data sampling system. The data from
the wattmeter is transferred manually. The measured data a.re combined with
geometrical data and thermophysical data by use of a computer program in
order to calculate output data such as heat-transfer coefficient and pressure
drop.
The calculation of different output data from measured data will be described
along with an estimation of uncertainty limit.
2.6.2 Pressure drop in section
The total pressure drop through the test section is a combination of pressure
drop by friction, static head and acceleration. The mea.n total pressure drop
is calculated from the measurements in DP sl and DP s2, by use of Equation
2.6.
DPf = 0.5· (DPs1 + DPs2 )
-
DPCOT'T" - DPe. - DPg
(2.6)
The measured pressure drop is corrected fOT static head. due to a difference
in location of pressure taps, by using Equation 2.7.
DPcorr = 0.126· g. p(P.. ec , Tlcsb. Y)
(2.7)
50
2 Test facility for LNG heat exchangers
The uncertainty in the correction is calculated. from the uncertainty in the
longitudinal distance between the pressure taps and from the uncertainty in
~alculated density.
The pressure drop due to a change ir. static head m;::.y be calculated by use
of Equation 2.8.
DPg = 0.126· g. (e:. pv
+ (1- e:) . PL)
(2.8)
The pressure drop due to acceleration may be calcula.ted by use of Equation
2.9. The ch~Jlge in conditions through the test exchanger is small and the
pressure change due to acceleration or evaporation is smalL
_
.. 2 . ..!!:..[~
D p... - 0.126 m
dX
Pv'c
(1 - X)2 1
+ (l-c) 'PL
J
(2.9)
The void fraction may be calculated by use of Equation 2.10.
e:=
1
------~~~-
1 + E::!...
p,
(1-:-;;) .
S
(2.10)
~
The slip factor, S, is defined as the ratic between vapour- and liquid velocity.
The slip will be small at small vapour fractions with a liquid film fow on
the wall and a small amount of vapour :flOwing in the free space between the
tubes. As the vapour quality increases the vapour velocity will be higher
than the liquid velocity and 5 > 1. At high vapour quality the shear rate
will be high a.nd the flow will tend to flow at homogeneous conditions with
5 = 1. P_ slip rat!o of 1 ± 0.5 is used for data reduction.
2.6.3 Fluid temperature in section
The fluid temperature may vary througho::.t the heated test section due to
variations in enthalpy and pressure. A representative mean value is estimated
at the center of the heated test section. The heat transfer COefficient calculated from the measured data is based on the assumption of thermodynamic
equilibrium in the fluid. It is impos..,.jble to measure a representative mean
fluid temperature in the heated part of the test section, and the majority of
2 Test facility for LNG heat exchangers
51
computer programs use the assumption of fluid equilibrium in design of heat
exchangers.
A representative mean ftuid temperature, T:b may be calculated from the
measured values Til to Tl4 and T3 l to T34 directly. The mean fluid temperature before the heated test section and after the mixer may be estimated by
use of Equation 2.11 and 2.12.
"1\ =
1
4
LT
-.
4 .=1
1,
(2.11)
(2.12)
The temperatures may vary due to random error in the measuring chain
and due to actual variation in temperature in the section. The standard
deviation for the mean value may be estimated using Equation B.lS where
the covariance between the measurements is taken into account. The total
uncertainty interval is estimated by a combination of bias and random error.
Common bias errors for each of the measured temperatures are considered.
The cha.nge in temperature from point 1 to point 3 is a function of pressure
drop, heat input in the test section and heat leakage from the surroundings.
The pure propane temperature is only affected by pressure drop. For nit~en
gas and two-phase mixtures the change in temperature is also affected by heat
input.
The length from point 1 to the outlet of the section is about 240 mm. The
height of the mixer is about 160 mm. The total length which creates pressure
drop is about 400 mm, and the pressure drop profile is assumed to be linear.
The total length between point 1 and point 3 is about 700 mm. The length
from point 1 down to the center of the section is about 210 mm. The profiles
for heat input and temperature in the heated part of the test section are
assumed to be linear. The mean fluid temperature in the center of the test
section may be estimated by use of Equation 2.13.
(2.13)
The constant L Jra.c ma.y be set to 0.5 due to pressl!re drop and heat input from
the test section. The influence from heat leakage will require a lower constant,
2 Test facility for LNG heat exchangers
52
but this !nfiuence is smaller than for the other two, and the constant is set
to 0.5 ± O.L The standard deviation for the mean value may be estimated
by use of Equation B.15.
The mean temperature may also be estimated from equilibrium calculation
with specified pressure, vapour quality and total composition as described in
Equa.tion 2.14. The method is only used as a. control method.
(2.14)
The bias error for the mean temperature is estimated by a combination of
bias errors for each element.
2.6.4 Wall temperature in section
The mean wall temperature in the test section, Tw, is based on measurements
at 16 different points. A mean wall temperature is estimated in the upper
and the lower part of the heated test section, and the temperature approach
is assumed to be linear between these two points. A representative mean wall
temperature may therefore be estimated by Equation 2.15.
_
Tw
1
8
1
8
8
;=1
8
i=l
= 0.5· [_. :L T 2A. + - . LT2BJ
(2.15)
Figure 2.8 shows a plot of the measured wall temperatures in serie B7 where
the heat flux is varied. The repeated measurements for each point may be
regarded as normally distributed, but the total distribution of each mean
value has bias errors with respect to the grand average. An uncertainty limit
for each point may be calculated by a combination of bias error and precision
error for each point.
The actual wall temperature will vary due to :
- Maldistribution of heat flux.
- Variation of heat transfer coefficient around the tube.
. Variation of fluid temperature through the section.
2 Test facility for LNG heat exchangers
58
.-.
u
c
0
.r-i
JJ
C1l
.r-i
0-4
0.2
;>
(l,)
'0
0.0
Q)
l-i
='
JJ
-0.2
!G
l-i
Q)
0.
5:
OJ
E-t
-0.4
0
2
4
6
8
1u - 12 14 16
Wall point
Figure 2.8: Measured wall temperature in serie B7.
2.6.5 Total flow rate
The total flow rate may be calculated by use of Equation 2.16. The equation
is set up from a mass balance around the test section and the separator.
The vapour and liquid holdup in the system ma.y be neglected as long as the
level in the separator is constant, and the temperature and the pressure are
constant.
(2.16)
The vapour flow rate is calculated directly from the measurements by use
of EG1;ation 2.3. The density in the turbine meter is calculated from the
estimated temperature and pressure after the pump. The temperature is
me-"l.Sured at Ts, located 3.2 m downstream the turbine meter, and corrected
due to heat input from the surroundings. The corrected temperature Tst is
estimated from Equation 2.li, by use of a maximum heat fluX. The A -value
for the insulation is estimated to be 0.05 ± 0.02 W jmK. The tube diamete~
2 Test facility for LNG heat exchangers
54
is 40 mm and the outside insulation diameter is about 140 mm.
'T'
_
'T'
.LS'-.LS-
16.0 . ). • (11lab- Ts + Ts')
ML-CPL
2
The differential pressure over the pump is about 0.5 ± 0_1 bar during operation. The pressure will decrease from point 1, where the section pressure
is measured, to point :3, and increase from point 3 to point 5 at the pump
suction_ The total pressure variation will be within 0_01 bar_ The pressure
in the turbine meter may therefore be estimated from Equation 2_18.
The uncertainty in total flow rate is calculated during data reduction.
2_6.6 Vapour quality
The vapour quality in the test section may be estimated on weight basis by
use of Equation 2.19. MV2 is the local vapour flow rate in the test section .
. -
MV2
X=-M tp
The local vapour fiow rate may diiler from the measured vapour flow rate,
and a heat and a mass balance is set up around the test section in order
to estimate the local vapour quality_ The heat balance is given in Equation
2.20_ Point 6" is the recirculated liquid from the pump.
lvlL-z - hL-z
+ Afv2 . hV + Ms" - h 6, + Q;ec + Qlo$$
2
Mv . h7 + M4 . h4
=
(2.20)
The mass balance is given in Equation 2.21.
M4 = Mstl+ML
Ah + Mv = M~
M tp =
+ MV2
(2.21)
2 Test facility for LNG heat exchangers
55
The different equations may be combinf:d to Equation 2.22. The different
constants are given in Equa.tion 2.23 to Equation 2.23.
(2.22)
c _ h4 ,
2 -
c ,
4 -
hL2
!:lhLv
Q""+Q
2
loss
!:l.hLv
(2.23)
The correction for vapour flow rate depends on the heat input and the variation in fluid condition from the test section to the separator. The constant
C3 may be set to 0.0. This assumption depends on the variation in fluid temperature from point 4 to point 6", and it is made due tG the fact that Ms"
is unknown. The liquid at point 4 and the vapour at point 7 are regareled to
be in equilibrium. The change in fluid condition between point 2 and point
(4,7) depends on pressure drop. The measured condition downstream,the
mixer is used in order to estimate change in fluid conditions. The heat loss
is estimated from Equation 2.24, where the). -value is 0.05 ± 0.02 W /mK.
(2.24)
2.6.7 Heat-transfer coefficient
The local heat-transfer coefficient in the test section may be calculated from
Equation 2.25. Qsec is measured as described in Chapter 2.5.4. A temperatu.Te difference based on the fluid temperature aft2r the section, and the
mean wall temperature in the lower part may also be used.
(2.25)
The total uncertainty in the measured hea.t-transfa- eoeflicientisa ftmctian
of uncertainty in estimated heat supply, estimated heat transf€! area and
estimated temperature difference.
3
Heat transfer and pressure drop
3.1 Introduction
The two-phas~ flow distribution system in coil-wound heat exchangers is
gravity-drained, as described in Chapter 1. The vapour quality in the top of
the cold bundle is normally low, in the range of 0.02 % to 0.07 %, and the
iiuid iiow in this part of the exchanger ",ill mainly be annular with a liquid
film on the tube wall and a vapour iiow in the annular space between the tube
layers. The low-quality liquid film :flow on the tube wall is gravity-driven. As
the quality a.nd vapour velocity increase down the exchanger, the shear force
between the liquid and the vapour increases. This shear force will enha.nce
both the velocity of the liquid film and the entrainment rate. At the hot end,
in the bottom of the heat exchanger, the fluid is superheated a.bout 5 tc 20
°C.
No obsen-ations on shell-side flow patterns in coil-wound heat exchangers
have been reported :'n the literature, and no observations have been performed iLl the test exchanger. The description of fluid hydrodynamics in
coil-wound heat exchangers is therefore based on the limited work published
on observing flow patterns in ordinary shell and tube heat exchangers used
for shell-side condensers or shell-side evaporators. The compu:!sons are restricted to unbafBed devices with horizontal or inclined tubes where there
are a continuous downflow of :fluid film on shell side. Effects of pa.rticular
importance for fluid flow are tube inclina.tion, inundation, vapour shore ana
entrainment.
The description of different heat-transfer mechanisms is based on the fillid
hydrodynamics. A coil-wound heat exchanger may be divided into four different zones according to the ma.in driving force for fluid liow. The fluid
entrainment increases in zones 2 and 3 as the slip rate increases.
56
3 Heat transfer and pressure drop
57
Zone 1 Gravity-drained environment, with a liquid film on the wall and
low-va.pour velocity in the annular space between the tubes.
Zone 2 Transient environ~ent where both gravity force and vapour-share
force contribute t~ the fluid flow.
Zone 3 Share-controlled environment, with a high-vapour velocity which
enhances the !iuid flow and the entrainment ra~<:.
Zone 4 Superheated vapour-tlow.
Different m~thoJ5 for calculation of heat transfer and pressure drop are reviewed from the li~eratl>.e.
3.2
Sr...""&~ '. ~·.·'1ated
3.2.1 Test
vapour flow
condit:~~ns
Heat-transfer coeffir...;l :s and frictional pressure gradients in vapour flow are
measured r.y use of pure nitrogen. Two different series are performed. The
test cO!lditions are given in Table 3.1, with now v::]ocity calculated from
i;t-line flow area...
Table 3.1: Test conditions for vapour flow.
Temperature
[0C)
Series VI
Series V2
-10.8 - -11.8
-11.7 - -18.3
I
P!"essure Flow velocity
[Bar}
[kgjm2 s]
27 - 56
4.6 - 4.71
8.9 - 9.1
29 - 95
The Pr number is about 0.7 for both series. The dimensionless Re, Nu and
Pr numbers are used for presentation, as givei' in Equa.tion 3.1. The in-line
area is used for measured and calculated values in the presented graphs. The
d::tferent calculation models may employ other definitions.
R e=
m·Dt...
p.
_
, .Nu _
(X •
Dt'U.
Cp· J1
,\.' Pr=-,\.-
(3.1)
58
3 Heat transfer and pressure drop
3.2.2 Heat-transfer coefficient
Measured and calculated Nu numbers are given as function of Re number,
in Figure 3.1. The difference between the two series of measurements is
negligible.
300
2S0
l-l
IV
-§
-
200
-
;l
Z
150
-
100
10000
Vl
Vl
¢
V2
V2
+
..•....~
......<i-+-
.~
........ +
.....++
/~*
;l
s:
I
I
Series
HEDH
Series
HEDH
/
-
I
I
30000
SOOOO
70000
Re number [-]
Figure 3.1: Measured and calculated heat-traIJsfer coefficients.
A model developed by Gniellinski et ale for calculation of the heat-transfer
coefficient for single phase -fiO\\i in a tube bank is given in Equation 3.2 [40].
(3.2)
The turbulent and laminar Nu numbers are given in Equation 3.3 a.nd E<;.uatio!! 3.4.
N Ula.m = 0.664 . v'['i; . Pr1 / 3
.
]v Uturb
(3.3)
8
0.037· ReO. . Pr
= -----.....".~...,.-__:_:~-1 + 2.443· Re-O•1 • (Pr(2/3) - 1)
(3.4)
3 Heat transfer and pressure drop
59
The Re number is given in Equation 3.5, and the characteristic length is
defined by X = Dtt< ·,,/2 which is the stream 1ength of a single tube. u is the
veiocity in the empty cro~ section of the channel, and the void fraction "'I is
used to calculate the average velocity between the tubes.
Re =
_'l£_'_X_'-,-P
(3.5)
'Y'p.
-y for an in-line tube bank and the arrangement factor fA, are given in Equation 3.6, where Pr and PI denotes the radial and longitudinal distances be-
tween tube centers.
1i •
D tu
"'1=1- 4.0.Pr'
0.7· (PIj Pr - 0.3)
fA=l+ 'Y 1.5 .(PljPr+O.7)2
(3.6)
Deviations between measured and calculated values are given in Figure 3.2.
There is a small increase in deviation as a function of increased flow rate,
but the overall deviation is small, generally within 5 %. The estimated
uncert2inty for the measured values is given in Figllre 3.3. Th~ uncertainty
is generally within ± 2 %. Th-e method is expected to predict heat transfer
within 10 %.
60
3 Heat transfer and pressure drop
10.0
dfJ
s.o -
Series 'Vl
Series V2
,
~
+
-
t:;
-'
•..-i
oW
0.0 .............................................................
III
.
g>- -5.0
..-\
~
¢ot-~ <)~ .f;1 ~~
-++
+
-10.0
10000
-
+++=t
,
I
30000
50000
70000
Re number [- ]
Figure 3.2: Deviation between measured and calculated heat-transfer coefEdents.
10.0
.
Ser~es
dfJ
>.
oW
.t:
8.0
~
6.0
f-
4.0
...
..-\
Ct\
.:...J
\..I
'Vl
Series V2
u
<>
-
+
-
+
-
+
OJ
t:
=:J
,
2.0
f-
0.0
10000
<)K><>~~~+~ ++ + ++=+
I
I
30000
50000
70000
Re number [-]
Figure 3.3: Uncertainties in measured heat-transfer coefficients.
61
3 Heat transfer and pressure drop
3.2.3 Pressure drop
Measured and calculated frictional pressure gradients are given in Figure
:~.4, as functions of Re number. The free flow area is calcuiated by use of the
method from Gilli [14J for the calculated pressure drop.
6000
+
:r.-t. .
o
J.J
§ 4000
i
~
2000
f
~'
10000
Co.
+,:1=.....
..
:it ...
~/ 4 t-:f... "Series
¢/
~."'."
Q>'" •.••~...
+ ..,
0 ______
~
-b....
0,,-
¢,/
.
~~
VI
EARBE VI
Series V2
E.z:~RBE
V2
______
30000
~
¢
+
______-L__
50000
~
70000
Re number [-]
Figure 3.4: Measured and calculated pressure drop.
The pressure drop for single phase flow in a tube bank may be calculated by
use of Equation 3.7.
.
(3.7)
Barbe et al. [32] have developed a method for calculation of single-phase
pressure drop in coil-wound heat exchangers. The friction factor, F, is calculated as a weighted value betwe~n the friction factors for in-line and staggered
configurations as given in Equation 3.8.
F
=
2
1
1
..n:r;.+"ff;;
{3.8)
3 Heat transfer and pressure drop
62
The in-line and staggered pa.rt of the function may be calculated by use of
Equation :3.9. The equations must be solved by iteration.
(3.9)
The friction factors for in-line or staggered tube bank may be calculated by
use I)fa method dev~loped by Idel'cik [29J, given in Equation 3.10 to Equation
3.12. The 30w area and the Re number are calculated by use of the method
developed by Gilli [14].
Pr
Pi
a=-, b=D tu
D tu
m
= 0.27
(3.10)
(3.12)
If Pr :5 PI :
If Pr
FiTVJ = 1.52· (a - 1)-0.7. (b - 1)0.2. Re- n
(3.13)
n=O.2
(3.14)
> PI :
(3.15)
b-1
a-I
n=0.2· [--] 2
(3.16)
Deviations between measured and calculated values are given in Figure 3.5.
The deviation is generally within 15 %. The estimated uncertainty for the
measured values are given in Figure 3.6. The uncertainty varies as a function
of:fl.ow rate, and increases rapidly at low rate, due to lower measured pressure
drop. The method is expected to predict pressure drop within ± 20 %.
3
Beat
transf~,'t'and
63
pressure drop
20.0 r-------~--------~------__,
10.0
riP
c
o
0.0
·M
.w
n:!
·M
>
~
Series Vl <)
Series V2 +
-10.0
-20,0
10000
30000
50000
70000
Re number [- 1
Figure 3.5: Deviation between measured and calculated pressure drop.
20.0
dP
~
15.0 r-
>.
.w
C
·M
co
1!)'0 r-
.oJ
Q)
u
c
=>
Series Vl <:>Series V2 + -
<:>-
+
¢
+
<>
\...0
5.0 t0.0
10000
I
I
++
++-\.r
<:>
O
00
++ +
I
I
30000
50000
-
++ of
70000
Re numbey [-]
Figure 3_6: Uncertainty in weasured pressure drop.
64
3
Heat transfer and pressure drop
3.2.4 Heat leakage
-:'he heat leak-d.ge into the test section is estima.ted from the nitrogen data,
as a deviation between the heat input to the test section and the j;:~...ased
temperature or enthalpy for the iluid.
/~
The :esults are given in Figure 3.7, as a function of tl.ow fa."te. The leakage
increases 3S a function of fio,~' rate, t1~,~ to increased .!ie~.t transfer. Tne
leakage may be estimated fmm Equation 3.17. Thp equation may also be
used to estimate the effective leak area in the section, Aler:.;;.
(3.17)
30
:::
Q)
til
25
20
/'Cl
~
u
t!l
Q)
.-i
15
10
LJ
/'Cl
OJ
5
I
II
+
[
~
[
...L.4> +* ++
00
*0
.J..~
+t.'
*
+-i
+
Series V1 <;>
Series V2 +
:J:;
0
10000
30000
50000
Re nu.'Tlber [-]
Figure 3.7: Heat Jeakage in test section.
70000
3 !Ieat transfer and presSUI"e drop
65
3.3 Film flow
3.3.1 Parameters in gravity-controlled flow
Studies performed on falling-fUm h;;>.at transfer outside horizontal tubes have
shown that the :Bow regime and the ho~dup in the vertical space between
the tubes changes with the liquid load. At low-liquid :Bow rate the film faUs
from one tuc.e to a.nother as droplets. The drip-off points are located with
very regular spacing. .~ the liquid rate increases the droplets become stable
columns of liquid now; a-ad :at extremely high -fiow rates the film is expected
to fall from on~ tube to th-=- next as a continuous sheet [35}, [36J, [44], [41].
The tubes in coil-wou:ad heat excllangers have a inclination of about 5 to 10
O.
The inclination entails a horizontal flow of liquid film along the tubes,
and the film will no longer drip off from the tubes as a stable column or as a
sheet, as for horizontal tubes. The main rearrangement on :flow regime with
respect to inclination takes place in the bottom layer of each tube, whera the
inclined flow involves a thickening of the the fihll, held at the underside by
surface tensions [461The const<>.nt radial tube spacing is obtained by longitudinal spacers. These
spacers may act as a restrain on the longitudinal :flow along the tubes, a.nd
drain the liquid from one tube to another. This may also form maldistribution in bundle, as the liquid tend to :flow down along the spacers instead
of a.long the tubes. Some reports of la.rge liquid columns :flowing down the
heat excha.r,ger may be caused by such effects which may be obtained a.t high
turndow!l ratios_ The inunda.tion effect, ;>.5 reported on horizontal shell-side
condensers, will be reduced due to the tube inclination, as the liquid drip-off
from tlibe to tube occurs a.t fewer places [41]. The fluid flow will also be
influenced by the alternated coiling dire..::tior! for each layer in a coil-wou~d
heat excha.nger_ Bennett et al. [34] performed a study on an in-line tube bundle, v..ith R-ll as test fluid. They used a gravity-drained distribution system
and observed the fluid flow in the test section. No flow pattern map was
given, but they reported to have a thin-film :flow boiling with an increasing
entrainment rate at increasing vapour quality.
The film flow may be described with similar parameters as single-phase flow.
66
3 Heat transfer and pressure drop
The Reynolds number for the liquid film is defined in Equation 3_18_
4-r
ReL=-J.LL
r is the mass 'ffow rate pro unit length, calculated from Equation 3.19. The
liquid is distributed on both sides of the tubes.
(3.19)
The total tube-iength in a coil-wound heat exc..lJ.anger, perpendicular to the
fiow direction, may be calculated by use of Equa1;iQn 3.20.
Xt'l.!
= "ii • Nca.y • [Dco +2 Dsh]
(3.20)
The now in the film wiD var'J from laminar through wavy-laminar to turbulent
as a function of How ra.tE:. The transitiOn range from laminar to turbulent
;nay be observed for a Re,L number in the range from 1000 to 20GO for a fiat
plate [44}. A ReL number of 1600 has been used as transition criterion. The
Re number for the film flow in an LNG heat exchanger will normally be :n
the range of 1,000 - 10,000, which is in the laminar-wavy or slightly turbulent
region. The drip-off from tube to tube may also create agitation effects for
the film f!O"il!, which enhance the heat-transfer coefficient.
The heat-transfer coefficient for film flow may be described by the Nusselt
number as ce:finecl by Equation 3.21 where the ·111m thickness equals the
characteristic lec.gth.
a·§
iVUL
•
1
=>"1.,-
(3.21)
The real fillL thickness may be difficult to estimate and the Nu number is
often chara.cterized by the reference film thickness, as given by Equation 3.22.
Both representations have been :.Jsed in the liter::.ture in order to characterize
the Nusselt number in the :film flow.
(3.22)
3 Heat transfer and pressure drop
67
The reference nlm thickness is defined in Equation 3.23.
(3.23)
The dimensionless tube diameter and the dimensionless vertical tube spacing
is defined in Equation 3.24.
(3.24)
(3.25)
The real film thickness and the film velocity may be difficult to estimate,
because they are a function of parameters as total flow rate, quality, vapour
share and entrainment. The thickness will also vary around the tube. The
liquid holdup in the vertical space between the tubes will also affect the film
thickness. The average -film thickness for laminar film flow on a vertical plate
may be calculated by Nusselt film analysis a.E given :n Equation 3.26 [42].
5Iam =[
3· VL· r
g·PL
I
]3"
3
!
= [-]3"·5
c · Ret
4
I
(3.26)
The film thickness for wavy laminar or turbulent "flow is difficult to predict
and a normal approad, is to use an analogy as given in Equation 3.27, as reviewed by Seban [43]. Most previous studies have been performed on vertical
plates and the results may not be transferred to horizontal tubes, where the
i11m is redistributed for each tube row.
o
b
--=a·ReL
- .
li1am
(3.27)
3.3.2 Test conditions
Heat-tra.nsfer coefficients for film flow have been measured by use of pure
propane and of mixtures of propane and ethane. Film flow has been obtained
by circulation of liquid or low-quality two-phase !low through the test section.
68
3 Heat transfei" and pressure drop
The main objective has been to vary the Reynolds number for the film by
varying the flow rate. Some series performed at low vapour quality have also
Qeen classified as film !low. Test conditions for the measurements with pure
propane are given in Table 3.2. The test section is too short to measure
pressure difference in film flow. The flow velocity refers to the in-line flow
a.rea. and it is used to compare film measurements to shear fiow measurements.
The variation in Prandtl number was only within 10 %, due to the variation
in temperature and pressure.
Table 3.2: Test conditions for fjim-flow with propane.
Series
Fl
. F2
F3
I
I
F4
F5
!I Temperature
[0C]
-5.0 - -5.1
-9.9 - -10.1
-19.9 - -20.0
-29.9 - -30.0
-9.8 - -ID.1
II
I
Pressure
Flow velocity
Heat flux
Vapour quality
[Bar]
(kg/m 2s]
[kW/m:!]
[kg/kg]
4.u
33 - 108
64 - 99
28 - 120
33 - 115
53 - 98
3.96
3.9E>
3.li -3.97
3.18
3.17 - 3.98
0.0
0.0
0.0
0.0
0.05 - 0.09
3.4
2.4
1.6
3.4
I
I
.
Test conditions for the measurements with binary propane-ethane mi.xtures
are given in Table 3.3. Series BFl to BF3 have been performed with mixtures
of 10 % ethane and 90 % propane. Series BF4 has been performed with a
mixture of 15 % ethane and 85 % propane. The pressure is given as a mean
value and may vary within ± 0.1 bar for a series. All of the measurements
are without nucleate boiling heat transfer.
Table 3.3: Tpst conditions tor film-tlow with propane-ethane mixtUies.
Series
Temperature
[0C]
I
BFI
BF2
BF3
L BF4
-14.6 -]8.9 -29.5 -]6.9 -
-14.8
-19.4
-29.7
-18.7
Pressure
[Bar]
3.6
3.2
2.3
3.6
Flow velocity
[kg/m2s]
36 - 93
43 - 92
43 - 97
33 - 85
Vapour quality
Heat flux
[kW/m2]
3.18
3.18
3.18
5.54
(kg/kg]
I
0.02 0.00 0.00 0.05 -
0.06
0.01
0.02
0.11
69
3 Heat transfer and pressure drop
3.3.3 Heat-transfer coefficient
The measured heat transfer coeffici.ents for pure propane a.re given in Figure
:3.8 by the Nu~ number as a function of the ReL number. The measured
heat-transfer coefficients for propane-ethane mixtures are given in Figure 3.9.
Some of the measurements at low Re number may be very close to the laminar
transition range with decreasing influence from liquid flow rate. The overall
uncertainty for the measured Nu numbers are given in Figure 3.10. The
estimated uncertainties are within 5 to 10 % and increase with increasing
flow rate.
0.40
I
I
Xl
G
X
I
~
0.35
El&¢
I-
~
~
(j)
~0.30 I~
s::
~
0.25
z-
-
0.20
0
~
¢
+
Fl ¢
F2 +
F3 8
F4 X
F5 A
I
I
I
2000
4000
6000
8000
Re numbar [-]
Figure :t8: Nusselt number in film :Bow for propane.
The heat transfer in film flow is influenced by different parameters. A general
model, of;;en used for film flow outside orizontal tubes, is given in Equation
3.28 [42], [41], [44], [34J.
(3.28)
The tube number, n, is included in order to cover the thermal developing
range [44]. The heat transfer will be greatest for the top tube a.nd will
70
3 Heat transfer and pressure drop
0.40
I
~
0.35
H
W
..q 0.30
-.
-5
I
I
~
-
0.20
0
-
)¢J+
~
-
I
xa+0
~
BF1
BF2
BF3
BF4
0
+
G
X
I
I
I
2000
4000
6000
Re number
8000
[-]
Figure 3.9: Nusselt number in film Bow for propane-ethane mixtures.
15.0
a;; 12.5
+
+
+ :1-+ 0+. <)
+ ~~~+ ~
>. 10.0
.w
c
7.5
~-r~~()
H
III
5.0
0 00
C
2.5
• ..-j
rtl
.w
Propane
U
::>
I
()
¢
()
1
Mixtures +
0.0
0
2000
4000
6000
8000
Re number [-]
Figure 3.10: Uncertainty in measured Nusselt number for film flow.
3 Heat transfer and pressure drop
71
decrease until the thermally fully-developed region is reached. The film Sow is
treated similar to single phase flow, as a combination of heat conduction and
heat convection. The cOD:?tants w!l] therefore vary from region to region. The
Nu. number decreases with an increasing Re number for laminar flow, wnere
heat conduction and film thickness govern the heat transfer. ..0\5 the flow
becomes turbulent the Nu number a.ugments with an increasing Re number
and convection governs the heat transfer. The heat-transfer is also increased
v.ith a growing Pr number as for single phase flow. The dimensionless group
Dc: reiates the flow length over one tube to the heat transfer; and Lc: relates
the holdup 'in the free vertical space and the inertia. effect for the falling film
between the tubes to the heat transfer.
Bennett et al. hav ~ developed a model for calculation of heat-transfer coefficient for downward film flow in a tube bank with horizontal tubes [34]. The
equation "''as developed by use of Rll with one heated tuDe. The original
model is given in Equation 3.29. All of the thermo-physical properties are
calculated for the liquid.
2
Q
= 0.886. [ '
A2
.;./3
.P
•g
2/3
... Dtv. . 1-'1/3
.
C
4 r
P]i/3. [.£..]lJ4. [_·_]1/9
JLw
jJ-
(3.29)
The ratio between the bulk and the wall viscosity may be set to l.0, due to
low tempera,ture difference. The equation may be re-structured to its general
form by introducing the Pr numb~r and the dimensionless tube diameter.
Kocamustafaogullari et al. have also developed models for calculation of the
heat-transfer coefficient for dowm....ard film How in a tube bank with horizontal tubes [45]. A model was developed from hydrodynamic and thermal
theoretical analysis by a finite difference method. The model was used to
generate data fOT pazameter variation. The results were :fitted in order to
estimate the constants in the general equation 3.28. The constants from
Bennett et al. an~ Kocamustafaogullari et al. are given in Table 3.4 for
different conditions. Only turbulent flow is consi.dered. All of the thermophysical properties are calculated for the liquid. The transition Re number
is used to choose between the constants in the thermal developing region,
and constants for fully develo~d flow for the Kocamustafaogullari equation.
The Ku number for fully developed fio ....; is used as asymptotic value in the
thermai dev~loping region. The transition Re number is calculated by use
of Equation 3.30. The two equatioIls are equal for n in the range of 8 - 9.
72
3 Heat transfer and p:ressure drop
Benn'=!tt et al. also investigated the thermal developing length by using three
heated tubes in the experiments. They concluded with a reduction of about
2. - 4 % for the third tube.
(3.30)
Table 34: Constants -f"or ~r,ation 3.28.
Bennett
Kocamustafaogullm
I
a
b
c
d
e
f
0.7622
-0.3.3
0.0
0.33
0.111
0.0
Re < Fhtr
0.033
-0.28
0.08
0.46
0.39
-0.28
Re > Retr
0.018
-0.28
0.08
0.46
0.39
0.0
KocamuStafaoguUa.ri et al. used numerical solution in combination with linear regression in order to establish the values for different constants for horizontal tubes [44], [45]. Their results were also compared to measured data.
from different sources. Bennett et aL performed measurements by use of
pure RII and developed a model which included all of the terms except Lc
and n.
Influence from inclination has been investigated for conde:asation outside
tubes [41] [46]. The influence is within 1 % "!"or angles bellow 18°, and may
therefore be neglected.
A full fit of the constants a, b, c, d, e and f requires extensive experiraental
data- The conSl:ants are also interconnect.ed. The use of b and c will change
the ,ralue for a and e, and the range for the Pr number will also influence
the constants. The mea.stlrements in the test facility are on1y varied v.ithin
a narrow range for the Pr number, the Dc number and the Lc nU!llber. All
of the heat-transfer coefficients are calculated from data in the lower part of
the test section. The difference between the upper a.nd lower value lies in the
range of 5 to 10 % and increases with reduced flow rate. Tne measurements
3 Heat transfer and pressure drop
73
are tho::refore assumed to be in the fully developed region even though Kocamustafaogullari et aL predicted a higher thermal developing rang~ [44J. The
measured values aiso correspond to the measurements taken by Bennett et
al.
All of the measured values have been compa.red to the two models, and the
results are given in Figure 3.11. The overall agreement with the Bennett
model is good but the influence from Re number is underestimated, ar,d the
deviation is also influenced by variation in Pr number.
The deviation from the Koca.mustafaogullari is higher, and the moriel underpredicts for all of the measurements. This model includes more effects and
the de"iation is ne?-rly constant. A new a constant is developed from thE:
measured data. The constant is set to 0.031 and does not V'dory between data
measured ""-ith pure propane and data measurw with binary mixtures. The
results are presented in Figure 3.12. The agreemem l;es generally v,.;thin ±
10 %, ill accord with the uncertainty for the measurements. The slope for
the Nu numbe!" as a function of the Re number is low, and the uncertainty
will propagate into a fit for the constants.
50
B (pure)
dP
:::
.....0
"-'
.....
'">
Ql
0
~"T"+
R
K
K
2000
4000
30
.....
10
(mix)
(pure)
(mix)
0-
+
[]
X
..............~... ~;~.~~......... .
-10
-30
-50
0
6000
8000
Re number- [- ]
Figure 3.11: Deviation between measured and calculated Nl.lsselt number for
film flow. B = Bennett. K = KocamustafaoguJlari.
74
3 Heat transfer and pressure drop
20
dP
t:
0
·ri
.u
I
o
10 -
0
+
<f' -¢,..
.....
>
Q)
-
~
~
.... :t-~ 00
0 - .......... -H-+..~..... ~~ .................-
ttl
Q
I
I
-10
~
i-
8
0
0
+
Pure
Mix.
<:> -
+
-20 ~----~I~----~I------~I----~
o
2000
4000
6000
8000
Re number [-]
Figure 3.12: Deviation between measured and calculated Nusselt numbers
for film BotJ.t with modified Kocamustafaogullari model.
75
3 Heat transfer and pressure drop
3.4 Onset of nucleate boiling
The onset point for nucleate boiling must be detected in order to establish a
total heat transfer modeL In the state of nucleate boiling vapour bubbles are
produced over cavities on the hot surface. The bubbles enlarges to a certain
diameter, depart from the surface and rise to the liquid-vapour interface.
The initiation and growth of the bubbles require a superheated surface with
respect to the saturation temperature at a given pressure. The flow around
the tubes has a laminar sublayer near the tube wall, and the heat :flux in this
layer may be expressed using Equation 3.31.
(3.31)
Wall temperature and temperature gradient increases with increasing heat
flux. An increasing heat-transfer coefficient reduces the wall temperature and
the superheat, and increases the minimum heat :flux for the onset of nucleate
boiling. The temperature gradient may be regarded as linear with respect
to the distance X, from the wall in the sublayer, and the temperature in the
sublayer may be calculated by use of Equation 3.32.
(3.32)
The necessary superheat, in order to produce a bubble from a cavity with
radius r, ma.y be calculated by use of Equation 3.33, established by Davis
et al. [38]. The equation is derived from ideal gas law and the ClausiusClapeyron equation.
'T'
J.
oh
_
T
_ Ru . Tol-. • Tsa.t.l [1 0
sa.t -
"h
!..l.
LV
n
.
+ P2··rCT]
(3.33)
. The two equa.tions are visualized in Figure 3.13. Equation 3.33 represents
the minimum liquid temperature which maintains a bubble with radius r.
The touch point between the two equations may be calculated from (dToh!dr)
= (dTL/dX). The equation gives the necessary cavity radius in order to
maintain a growing bubble. The heat flux for the onset of nucleate boiling
76
3 Heat transfer and pressure drop
TSClt
I I
• I
Bubble equ.librium
It-'"'"
I
Figure 3.13: Visual presentation of equations for onset of nudeate boiling
[40].
3 Heat transfer and pressure drop
11
may be calculated with Equation 3.34, which is obtained by setting T oh =
TL in Equation 3.33 and introducing the necessary cavity radius [38].
.
_ .6..hLv . Pv . :XL . (T _ T )2
8 T
'UJ
sa.t
qonb -
.
(3.34)
sd·"
Equation 3.32 represents a set of curves as a function of distance from wall,
with increasing gradient at increasing heat :fiux. A major assumption is that
the surface contains cavities with various sizes. A.s the heat flux increases, T L
and T ok become equal; and the superheat is then sufficient to prod uce bubbles
from the cavities with radius rcrit. As the heat flux increases more and more
cavities grow active. The active size range is represented by the interval
between the cross points for the two lines, rmin and I m =. At low heat-transfer
coefficient, as for film flow, the heat :fiux and the- temperature gradient will
be low, and the predicted cavity size may be larger than the largest available
cavity size of the surface. The superheat qonb is then underestimated and the
equation may be regarded as a lower limit for the onset of nuclea.te boiling.
Frost et al. [39] used the same theory but assumed that two temperature
curves share a touch point at distance PrL· rc instead of at rc. The minimum
temperature difference between the wall and the saturated :fi uid for onset of
nucleate boiling may be calculated using Equation 3.35. The equation was
tested on a wide range of boiling :fluids.
(3.35)
Equation 3.35 may be rewritten to Equation 3.36 in order to introduce the
heat-transfer coefficient. The suppression of nucleate boiling caused by:fluid
flow is taken into account in Equation 3.36 by applying the convective heattransfer coefficient a = IJ/(Tw - TSC1t).
(3.36)
Eight ~ries with varied heat ftux ha.ve been ca.rried out in order to estimate
the onset point of n!lcleate boiling. Pure propane has been used as test
fluid. The heat-transfer coefficient varies among the different series due to
78
3
Heat transfer and pressure drop
variation in flow rate and vapour quality. The measurements have been
divided into film flow and shear flow, and the results are presented in Table
3_.5 as a function of vapour quality and flow velocity. The measured results
a.re also compared with the :predicted value by use of Equation 3.36. The
measured and predicted results are in good agreement for shear flow, but the
method underestimates the minimum heat flux for film flow. These results
a.re generally in agreement with the theory.
Table 3.5: Measured and calculated onset point for nucleate boiling.
Series
B1
B2
[ B3
B4
I B5
B6
B7
B8
x
[kg/kg]
0.00
0.00
0.00
I 0.05
0.:35
0.38
0.38
0.47
m
[kg/m 2s]
70
70
70
53
110
62
63
48
i
T
q<mo,c
1]-0,,,.
[0C]
[WJ
[W]
-10.0
-20.0
-30.G
-10.0
2400
3500
5200
2300
17700
5900
6200
3700
5500 - 6000
6500 - 7000
> 8000
4500 - 5000
> 8300
6000 - 6500
6000 - 6500
3900 - 4200
-10.0
-10.0
10 0
.
-5.0
1-
The variation in heat-transfer coefficient with respect to heat flux is given
in Figure 3.14 for film flow and in Figure 3.15 for shear flow. The measured
onset point for nucleate boiling may be estimated v.1thin a limit of ± 500
[W /m2]. The nucleate boiling part of the heat transfer is up to 20 % of
the total heat transfc_ 'or the measurements. The measurements are in the
transient region betw( L\· convective boiling and fully nucleate boiling. The
maximum heat flux in the test facility is about 10 kW 1m2 and the results
may not be used for development of nucleate boiling heat-trcllsfer models.
The onset points for pure propane, estimated by use of Equation 3.36, are
given in Figure 3_16 for different fluid conditions. Two lines for constant heattransfer coefficients are also give!l. These two curves represent the minimum
and maximum values for the heat transfer on the shell side. The onset points
are given at the cross-point between the curve ca.iculated by \\1th Equation
3.36, and the curve for constant heat transfer. The nucleate boiling v..ill
occur for heat flux higher than for the cross-point. The minimum point for
the onset of nucleate boiling will increase as the heat transfer increases, for
79
3 Beat transfer and pressure drop
0.25
~
81~
0.20
0.15
c
o
-.-I
.w
82
-+--
83
-E}-
0.10
(tl
-; C. 05
(])
o 0.00
-0.05
o
2500
5000
7500
10000
Heat flux [W/m2]
Figure 3_14:
heat flux.
\I~u-jation
in heat-transfer coefficient for iilm flow with varied
0.4
0.3
c
0
-.-I
S4
B5
~
-+--
B6 -EJ-B7 -x--B8 ~.
0.2
JJ
~
..... 0.1
:>
(])
0
0.0
0
2500
5000
7500
10000
Heat flux [W/rn2]
Figure 3.15: Variation in hear-transfer coefficient for shear flow with varied
heat flux_
80
3 Heat transfer and pressure drop
a given fluid condition. The onset point will aiso increase for decreasing
pressure.
10000
C"l
E
'-
/
7500
I
3
,,
I
,
I
x
::s
5000
!
.-l
~
.w
ttl
,
.
.
.
...
,
2500
(1.'
::I:
o
0.0
1.0
2.0
0 C
-20 C
-40 C
H = 2000
E. = 8000
,
,,
,,
.
3.0
4.0
5.0
DT [C]
Figure 3.16: Predicted onset point for nuclea.te boiling for pure propane.
The same method has been used for calculation of onset point for a rnulticomponent mixture used as a refrigerant in an LNG heat exchanger. The results
are given in Figure 3.17 as a function of vapour quality. The probability for
nuc1~te boiling is reduced for increasing vapour quality as the heat transfer
increases, and necessary superheat increases. The method overestimates at
!ow heat transfer. and the conclusion is that the nucleate boiling part ofthe
heat-transfer coefficient is insignifica!'t in an LNG heat exchanger.
81
3 Heat transfer and pressure drop
lOOOO
N
........
E
3:
7500
5
5000
I
.-i
oW
I'll
OJ
--
i
~
,
I
2500
I
/x
x
0.2
= 0.5
x = 0.9
= 2GOO
:r:
8000
0
0.0
1.0
2.0
DT
3.0
·LD
5.0
[el
Figure 3.17: Predicted onset point for nucleate boiling in a refrigeration
.:nixtur-e '?lith different vapour qualities. Pressure 3 bar.
82
3 Heat transfer and pressure drop
3.5 Shear flow
3.5.1 Param.eters in shear-c.ontrolled flow
Is is important to distinguish between a sheer-controlled em·ironment and a
gravity-controlled one, as both liquid d~abing and inundation may differ a
lot in the two environm~ts. At low vapour shear the ftow tends to separate
into two distinct phases, and at high vapour shear the gravitatjoIlal effect
is negligible and the two phases tend toilu''; together. The heat transfer
and the pressure drop models differ a lot iil the two regimes, and parameters
which identify the different regimes must be established.
The variation of vapour velocity and vapour '!Jow rate over the cross section
are cor. .trolled by the pressure drop. The pressure-drop per unit length is
assumed constant over the cross section.
The mean thickness of the liquid film is small acd the vapour velocity in
the heat exchanger may be represented by the superficial velocity defined in
Equation 3.37. The velocity is based on a mean cross section.
Uv3
z·m
(3.37)
=-Pv
The Wallis dimensional gas velocity parameter is given in Equation 3.38 [41].
This parameter is a measure of the relative importance on gravity and vapour
shear en the :flow conditions.
x·rn
iv=
JDtu.pv'9'(PL-pV)
(3.38)
The Froude number for the flow at liquid-only conditions is given in Equa.tion
3.39 (33].
...,
m-
.c'rlo
Figure
= """"-2---
:~"'8
PL' 9 ·D t 1.J.
(3.39)
shows principal sketches of the now down the heat exchanger.
3 Heat transfer and pressure drop
83
GRAVITY DOMINATED FLOW:
TRANSrENT FLOW:
SBEAR DOlfl"!NATED FLOW
GrPity dnmed film !ow.
Shea: .... d gn~ c:nmed!ow.
Mist flo....
Low ,-..pour velocity.
Hig!> _pour vcIocity.
c::;rl
.~
),
Figure 3.18: Principal sketches of the shell-side flow.
3 Heat transfer and px-essure drop
84
The energy- and mass transfer between the liquid film and the gas is strongly
affected by the entrainment and deposition rate in the :Bow. The geometry on
t.he shell-side ~th successive contraction and enlargement may also enhance
the entrainment due to vapour velocity accelerating in the contractions.
Ishii et al. [37J proposed start criteria for droplet entrainment in two-phase
concurrent film flow. They reported four different entrainment mechanisms
with respect to concurrent flow. The four types are shown in Figure 3.19,
and described. below.
1. Roll wave, where the tops of large amplitude roll waves are sheared off
from the wave crests by the turbulent gas flow.
2. Wave undercut, where the gas flow undercutting the liquid film and
tears off droplets of liquid.
3. Bubble burst, where fine droplets are generated. when bubbles rise to the
interface where they burst. The bubbles may result from gas injection,
turbulent wavy motions or heavy nucleate boiling.
4. Liquid lmpingement, where drops of liquid impinge the film surface
ana. -produce new droplets. This mechanism may also be related to
inundation effects when the liquid film falls from one tube to another.
~he
first and second mecb.a.n.isIIis are the most important for concurrent flow,
and the analysis on inceptio~ from Ishii et al. [37j is based on these two
mechanisms. The fourth mechanism ma;~· also be important in film flow on
shell-side where the liquid falls from one tube to the next. The phenomenon
is well known in shell-side condensers as a splashing or inundation effect.
The minimum gap between the tu bes is small, and the successive contraction
and enlargement play an important part in the detection of entrainment and
deposition rate.
. The phenomenon of inception of entrainment was examined. by Ishii et al.
who plotted the critical gas velocity ag?inst the liquid film Reynolds number.
Three different regimes were reported; 3. minimum Reynolds number regime,
a transition regime and a rough turbulent regime. The minimum gas velocity
for the onset of entra.inment decreases as the film Reynolds number increases
.
for the three regimes.
85
3 Heat transfer and pressure drop
TYPE 1
ROLL WAVE
77>'>'~'»»»»'»»';
TYP£2
WAVE UNDERCUT
TYPE 3
BUBBLE BURST
TYPE 4
LIQUID IMPINGEMENT
Figure 3.19: Different entrainment mechanisms [37}.
In the tr<tnsition regime between the fully laminar and fully turbulent flow
the film interface becomes very rough. The onset of entrainment in this
region is a function of the film Reynolds number, which indicates that the
momentum exchange between the phases is affected by the liquid flow in the
film. In the rough turbulent regime where the :film Reynolds number exceeds
1500 to 1750, the critical gas velocity becomes constant. This creates a
lower gas velocity limit for :fihr. e.."l.trainment, una.ffected by the film Reynolds
number. The hydrodynamics of the film flow in this region are controlled by
the interf~al conditions between ~he gas and the liquid.
86
3 Heat transfer and presSlU'e drop
3.5.2 Test conditions
Heat-transfer coefficient and pressure drop in shear 'flow have been measured
by use of pure propane. The vapour quality, the flow rate and the pressure
have been varied. The different test. runs were arranged in series, as a function
of the three main parameters mentioned above, in order to visualize and
plot the results. Some of the measurements for TIlm 'flow are also included
in the series. Ali of the measurements are \\ithout nucleate boiling heat
transfer. Test conditions for different series with varied vapour quality are
cited in Table 3.6. The variations in temperature are within ± 1.0 °C and
the variations in mass velocity lie within ± 4 kg/m 2s, for these series.
Table 3.6: Test conditions for shear flow at constant- pressure and t10w rare.
I Series
Xl
X2
X3
X4
XS'
X6
Temperature
[0C]
-9.8 -9.7 -9.7 -9.4 -
-Hl.3
-10.1
-11.6
-10.4
I -10.0 - -10.5
i -9.6 - -10.7
I Flow veiocity
I
[kg/m 2 s]
47.6- 55.1
62.i - 65.6
74.6 - 79.9
88.9 - 93.2
102.1- 107.9
115.6 - 121.7
Heat flux
[kW/m2]
3.19 - 7.87
3.19 - 7.87
3.19 - 7.S7
3.97 - 7.87
7.87
7.87
I
Vapour quality
[kg/kg]
il.05 - 0.74
0;04- 0.89
0.07 - 0.91
0.22 - 0.67
0.24 - 0.48
0.20 - 0.40
I
Test conditions for different series with varied mass 'flow rate are listed in Table 3.7. The variations in temperature are within ± 0.5 °C and the variations
in vapour quality are within ± 0.02 kg/kg, for these series.
Test conditions for different series with varied pressure are given in Table 3.8.
The variations in mass velocity are within ± 1 kg/m 2s a.nd the variations in
vapour qUality a~ within ± 0.01 kg/kg, for these series.
A total of 107 meas~reILents have been performed for the heat-transfer coefficient and 136 measurements have been taken for pressure drop. Some of
the measurements do not fit into the series, but are used in the total analysis
for different models.
3 Heat transfer and pressure drop
87
Table ;~.7: Test cO!lditions for film tfow a.t constant- pressure and vapour
quality.
Series
Temperature
[0C]
M1
M2
M3
M4
M5
-10.0 - -10.7
-9.6 - -IDA
-9.8 - -IDA
-9.7 - -10.6
-9.8 - -10.3
Flow velocity
[kg/mls]
50.7 - 118.8
51.2 - i17.9
47.6 - 104.5
53.9 - 85.4
55.1 - 79.0
Heat flux
[kW/m2J
3.19 - 7.87
3.19 - 7.87
3.97 - 7.87
6.33 - 7.87
6.33 -.7.87
Vapour quality
[kg/kg]
0.24 - 0.28
0.36 - 0.40
0.44 - 0.49
0.60 - 0.65
0.71- 0.75
Table 3.8: Test conditions for shear tfow at constant- :flow rate and vapour
quality.
Series
PI
P2
P3
P4
-
Pressure
[Bar]
1.68 - 4.01
1.99 - 4.00
2.86 - 3.94
1.63 - 3.40
Flow velocity
[kg/m2s]
46.8 - 48.1
61.7 - 63.7
76.1- 78.2
63.2 - 63.5
Heat flux: Vapour quality
[kg/kg]
[kW /m2]
3.96 - 7.87
0.46-0048
3.97 - 7.87
0.45 - 0.47
7.87
0.47 - 0.48
3.97
0.32 - 0.34
., ,.
... tl.33 - {l.34
.
1.0;) - 3.~41
(.~ (8.3
~.~o3.-9~'~ (
. 2.41 - 3.39 _ 93.6 - 94.1.
._
0.33
I
-~-
--{ -- I
~~
I
~
3 Heat transfer and pressure drop
88
3.5.3 Heat-transfer coefficient
The measured heat-transfer coefficient in the series Xl to X6 is illustrated
in Figure 3.20 and Figure 3.21. The heat transfer increases with increasing
vapour quality due to increasing vapour velocity and shear ra.te. The increase
in heat transfer is therefore initiated at a lower vapour quality for the highest
flow rate. The series Xl has a constant heat-transfer coefficient up to a vapour
quality of about 0.3. The maximum vapour quality is approximately 0.9. No
dryout effects have been observed. The heat-transfer coefficient will drop
down to the vapour value when the quality approaches 1.0. The dry-out
range may be very narrow, especially for high How-rate, where the mist :How
creates a very effective wetting on th~ wall.
';2 12000
I
+
I
I
I
N
~ 10000
-
;-
3:
l-I
OJ
"-I
til
s::
8000
6000
++
+
fo-
0
fo-
co
l-I
.l..J
4000
f0-
G
+
.l..J
co
OJ
X
+
[J
+
++
<>
+
8
2000
~
0.0
I
$
0.2
~
$
Xl
X3
$
~
$
X5
I
I
1
0.4
0.6
O.B
$
+
8 1.0
Vapour quality [kg/kg]
Figure 3.20: Measured heat-transfer coefficient as a function of vapour quality.
The variations of heat transfer with respect to mass flow velocity are shown
in Figure 3.22, for four of the series. The gradient for increase in heat transfer
due to increased flow rate is highest for the highest vapour quality.
The variations in heat-transfer coefficient with respect to pressure are gi"~n
in Figure 3.23 for some of the series. The measurements show that the heat-
3
89
Heat transfer and pressure drop
~
10000
¢
('oJ
.....E
3:
\.l
(l)
"-4
8000
+
t::
~
\.l
@
:000
E:J
.u
.u
~
(l)
*
e+
6000
til
+
++
¢
¢
0
¢
¢
¢
¢
X2
X4 +
X6 Ei
1000
:J:
0.0
0.2
0.4
0.8
0.6
LO
Vapour quality [kg/kg]
Figure 3.21: Measured heat-transfer coefficient as a function of vapour qual-
ity.
:.::
9000
~
........
3:
7000
OJ
5000
-
~X
E:J
0
0
f-
.p-
C
(t!
~ 3000
f-+
.u
¢
¢
~
~ 1000
40
I
XX
\.l
"'-l
til
I
I
I
M1
+
8
M4
G
p+
¢
M3
0
+
++ MS
X
<P
¢¢
¢
-
0
I
~
I
I
60
80
100
120
140
Flow velocity [kg/rn2s]
Figure 3.22: Measured heat-transfer coefficient as a function of:B.ow velocity.
3
Heat trailSfer and pressure drop
transfer coefficient' increases with increasing density ratio. The variation in
increase due to flow ra.te a.nd vapour quality is low.
:.::
6000
I
I
I
N
e
......
~
5000
-
X
El
+
+
1-1
OJ
~
til
4000
f-
s::
D
<>
X
:f
~t
IV
1-1
~
.u
3000
-
X
P4 <:>
P2
~P5 El
P3 X
-
+.
-
¢
(>
IV
OJ
::c
c
2000
1..0
I
I
I
2.0
3.·.0
4.0
5.0
Pressure [bar]
Figure 3.23: Measured heat-transfer coefficient as a function of pressure.
The estimated uncertainties in the measured heat-transfer coefficiant are
given in Figure 3.24 to Figure 3.25 as a function of the vapour quality and
heat transfer coefficient itself. The increase in uncertainty is due to a reduced temperature difference at increased heat-transfer coefficient. All of
the measurements are within ± 20 %.
The heat transfer in saturated two-phase filni.:.:Oow evaporation consists of
four mechanisms, but only the first two are included in this study.
• Heat transfer by gravity-drained filmfow
• Heat transfer by enha.ncement due to shear flow
&
Heat transfer by nucleate boiling
• Heat transfer reduction due to mixture effects
The model should match the film-flow correlation at low varour quality and
forced convection flow at high vapour quality. Few ccrrelaiions have been
91
3 Heat transfer and pressure drop
25
!
!
·
.
.
.
- ..........;............ j...........+............~.....4>.. ·
..
..
.
·
Of'
20
>.
.u
15 ~
~
C
.........+......~... j............~.~~...~... -
.0-1
ctl
.u
l-I
Q)
u
c
:::::>
:~:
~<;>
~
...
0:
.. *:.~ i:.......... _
10 ~ ......... l~....~ . ~M..<;>
:
. · . . . . """'::
:
•
~~ .........~............ ~.. ........ ~.......... - ..:..........
5
···
...
-
j
i
j
i
o L.-_....L.._--iL........._-'-_
_L-._...J
0.0
0.2
0.4
0.6
0.8
1.0
Vapour quality [kg/kg]
Figure 3.24: Estima.ted uncertainty in measured heat-transfer coetlicient a.s
a function of vapour quality.
.
proposed for the calculation of. heat transfer in combined gravity-drained
and shear-enhanced flow. McNaught [41J proposed a method fo!" shell-side
condensers, given in Equation 3.40.
(3.40)
a J is heat transfer in gravity-drained film flow and Cis is heat transfer in
forced-convection shear flow. A coefficient n=2 v.as used. The forced convection heat-transfer coefficient is given in Equation 3.41.
(3.41)
Xu is the Lockhart-Martinelli parameter given in Equation 3.42. als is the
one-phase flow heat-tra.nsfer coefficient based on the liquid phase flowing
alone in the section..
(3.42)
92
3 Heat transfer and pressure drop
25
riP
>.
.u
c
-.....
<tI
.u
l-I
Q)
u
c
=>
·~
.~
·:
.:
.~
20 I---------~--------------.-+--.--.----------~.--.--------~
15 1---------~--~.----~-.---~.-4----.-~-.----------· a..
'<).'
~: .A.
V(;)<):
~"V
10 I-~.-----~
:<i>:
-
.
<):
.
:
•
-. -----.. ----.----~.--.-----------
:
.:
:
.:
:-------- -- -------;------------ --- --~- -- ---- -------5 1------ ---~
·
.
0
i
.
3000
6000
i
9000
12000
Heat transfer coefficient [W/m2K]
Figure 3.25: Estimated uncertainty in measured heat-transfer coefjjdent as
a function of heat-transfer coefficient_
=
McNaught correlated data to find a = 1.26 and b
0.78. The measured
and calculated data for series Xl are given in Figure 3.26_ The film-flow
correlation dominates at low vapour quality, and the shear-iiow correlation
dominates at high vapour quality. The shear-flow correlation will approach
00 as the vapour quality approaches 1.0. One way to avoid this is to reduce
the heat-transfer coefficient when the vapour quality 1s in the range of 0.95
to 0.98. This creates a smooth transaction towards the vapour value. A corrected heat-transfer coefficient is given in Equation 3.43. No measurements
have been performed in order to verify such an approach.
Otp,c
=
0tp,(=O.95) .
[1.0 -:-- x] + 0V,(=1.0}· x
(3.43)
The deviation between the measured and the eakulated -v--.:du.es as a function
of vapour quality is given in Figure 3.27. The method tends to overestimate
heat transfer at low vapour quality due to an early influence from the shear
flow correlation. A higher n coefficient in Equation 3.40 may reduce this
problem_ The method tends to underestimate at high vapour quality; but
the uncertainty in :neasured value is also high and the number of points are
93
3 Heat transfer and pressure drop
~
7000
~
:s: 5000
~
Meashred
I
/
-
1'5
/~
~ 3000 r
J.J
,~
~
~
I
til
Film flow
Shear flow ---~Total
w
~
I
¢
-
....•.-"6
..-:;~
~- •• ~'
1000 ~
•
0.0
..
-=-----------------*
-
---'
I
0.2
I
I
I
0.4
0.6
0.8
1.0
Vapour quality [kg/kg]
Figure 3.26: Measured and calculated heat-transfer coeiIicient, as function of
vapour quality, for series Xl.
few. Therefore it is difficult to make a clear conclusion on these phenomena.
The Olean deviation is within 1 % for all of the points.
The deviations between the measured and the calculated values as a functicn
of mass flow velocity are given in Figure 3.28. There is a clear trend which
indicates that the calculated single-phase liquid superficial value does not
reproduce all of the effects due to variations in :flow rate.
The deviations between the measured and the calculated values as functions
of the Wallis parameter ( Equation 3.38) are given in Figure 3.29. One
observes clear trend 'with respect to this parameter. An direct use of this
parameter in the correlation may therefore have reduced the deviation. The
a and b parameters in Equation 3.41 have also been adjusted in order to
fit the measurement. The !Lew parameters produces change in deviation, as
illustrated in Figure 3.30. The fit gave the new parameters a
1.32 and b
0.76, which is a very small adjustment compared to the original parameters.
The maximum deviation is about 30 %, and .. ost of the <:lata lie within ±
20 %. The total uncertainty in the measured ,·~lues is also estimated to be
within ± 20 % in general.
=
=
94
3 Heat transfer and pressure drop
40
ciP
20
c::
0
.,-j
.l.J
~
!
> -20
0
-
~<>i~··········­
~~,
It!
<I)
~
,·-t::~···t·:r····l---·-
0 -~·······T··~·
..-f
l
!
..
~~
~
-------~-------:-~-----~-----~---.------.~-----------
-40 ~---~I-----~I:----~I-----~I----0.0
0.2
0.4
0.6
0.8
1.0
Quality [kg/kg]
Figure 3_27: Deviation between measured and calculated heat-transfer coefficient as a function of vapour quality.
40 r-----!~~-.--~--~~-----~!:-----T!:~
~:
:
~
-,-i
~
o
20
0
:
:
:
~·i~Ii"~····~t·-,;·:r·······+···-
e-.<>.~: "-?~i~~::::~---·r··-·: ' ,
~~~Q7'"
-20 ~.- ... -----.~ .. ---...... :.: .. -.. -.... ---~ .......... -.~ .. -.-40
40
i
60
i
80
i
100
i
120
Mass flow velocity [kg/r02s]
Figure 3.28: Deviation between measured and calculated heat-transfer coefficient as a function of mass flow velocity.
95
3 Heat transfer and pressure drop
40
!
!
!
~~~~
<:H>
20
s::
0
'.-i
.w
<tl
0
-.-I
> -20
Q)
Q
~
!
!¢!o
~
~
~
I i ~i ":
"i
f-__ •.•..~ •.•.~••.•.•.• ~ •.•.•.•. ~ ..•.•..• ~ ..•...•. ~ .....•-
~-----+------:: ---
·;·~o;-----··-~¢·~··-·---
ft :
:~::
~o
::
::
f- .•.•.. : ....----:.----.. -: .. ---.. - : ,.•: •....... : .. - .. :
:
:
:
:
:
:
:
.
:
:
~
-40 ~~~___~I·__~i___~I·__~i___.i:__~
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Wallis parameter [-]
Figure 3.29: Deviation between measured and calculated heat-transfer coefficient as a. function of the Wallis parameter_
40
<:H>
20
s::
0
•.-i
.w
<tl
0
!
~ ¢
1
~:
!
!
.
:
<»
7t;~~:ji:··c····-r·--
-
-'....~~ ...- ...
•..-i
>
-_.. _.-... : _._- -_ ..._. --.,. --.- .. .. -..... -.C!)
-20 .............-;-..
..
··
..
-~
Q
···
...
...
~
...
-40 ~---~I·----~I·----~I·----'~--~
0.0
0.2
0.4
0.6
0.8
1.0
Quality [kg/kg]
Figure 3.30: Deviation between measured and calculated heat-transfer coef·
ficient as a. function of vapour quality, with adjusted coefficients.
96
3 Beat transfer and pressure drop
3.5.4 Pressure drop
The pressure drop is measured in the isotheIllJ.al part of the test section and
is not influenced by the heat flux. When the vapour quality is reduced the
pressure drop will approach zero. Measured values of pressure drop at low
vapour quality are rejected from the analysis.
The measured frictional pressure gradients in the series Xl to X6 are given
in Figure 3.31 and Figure 3.32.
E
......
,
6000
4000
-
l-I
::I
B
0
2000
-
til
til
0
+
Q)
l-I
c..
+
X3 +
X5 0
'0
Q)
,
Xl ¢
ItS
c..
%
l-I
,
,
0
0.0
,<:>
0.2
r::J
+
++
<:>
0
+++
-
<:>
-
+
+
<:>¢
<:>
I
I
I
0.4
0.6
0.8
-
LO
Vapour quality [kg/kg)
Figure 3.31: Measured frictional pressure drop as function oiva.pour quality.
The pressure drop increases as the vapour velocity increases, and is produced
both from friction and from drag force. The pressure drop in a two-phase flow
is normally represented by an enhancement factor. The enhancement factor
in Equation 3.44 is preferred in a How where both the single-phase liquid
and vapour phase may be represented, due to the fact t.hat this factor will
appi"oach both single-phase liquid and vapour pressure drop. as the vapour
quality varies from 0 to 1.
.'
(3.44)
97
3 Heat transfer and pressure drop
6000
I
E
.......
I
I
I
Q.
...
'U
0
III
...
:l
4000
...III
e
r§I
2000 ....
++
G
+
til
til
0..
0
+X2
co
0..
+
<>
0
0.0
jr
+
<> <>
I
I
0.2
-J.4
<)
<:>
i
0.6
X4 +
X6 G
<:>
<:>
<:>
-
I
0.8
1.0
Vapour quality [kg/kg]
Figure 3_32: Measured frictjonal pressure drop as function of varied va.pour
quality.
Barbe et al. applied an enhancement factor based on liquid superficial flow,
as given in Equation 3.45 [32]. This factor will approach DC as the vapour
quality approaches unity.
(3.45)
Barbe et al. correlated the factor against the Lockhart-Martinelli parameter, a.s gi,,-en in Equation 3.46, with a = 1.0. The deviation between the
measured-and the calculated frictional pressure drop is given in Figure 3.33,
as a function of now rate. The dependency on ilow rate in the deviation indicates that the liquid superficial, reference value, does not predict the correct
rate dependency.
(3.46)
98
3 Heat transfer and pressure drop
40
dP
20
~ ~8~
·~ ..~...... . ';.:
.¢.
~ .................. ~.~
... ~'$>" ....:
:
t:
0
•..-1
.LJ
!.~
!
<)
.
' . . ~(!j
~ V"
:
:
..............[.....................
·
.............. .................... ..................-
0 ~·········iJ·· .~
ItS
•..-1
>
Q)
-20
~
0
-40
.
:
~
~
"
..
~
~
40
....... h .
~ ~.
.:
·
_________ ____________
~i
70
Flow rate
..
~I·
__________
100
130
[kg/~s]
Figure 3.33: Deviation between measured and calculated frictional pressure
drop as function of flow rate, by the method of Barbe et al.
The variations for the measured enhancement factor <)13, as function of
vapour quality, are given in Figure 3.34 and Figure 3.35 in a log-log scale.
The enhancement factor is a function of both mass ~ow rate and vapour
quality.
Grant et al. [33] proposed the use of the FrIo number to calculate the dependency on flow rate. The a factor in Equation 3.46 is given in Figure 3.36 as
a function of FrIo for the series Xl to X6. The a function is a straight line
with log x scale.
The FrIo contains only data for mass flow velocity and density, and reflects a
liquid velocity. This information has been used to modify Equation 3.46 into
Equation 3.47. The two constants have been fitted using the measured data,
and may therefore be influenced by uncertainty in measurements.
<Pis
02S [1.0 + Xtt]2
= [0.05 + 1.6· Frl~
].
X
tt
(3.47)
The deviation between measured and calculated pressure drop by use of
99
3 Heat transfer and pressUI'e drop
100.0
':
'1
'1
~
I
~
oW
oW
:<
.......
~.
10.0
~
.u
oW
:<
+
~
~fr
~
.-I
1.0
10.0
~+
$'
-:
Xl
X3
X5
¢>
+
B
.
•1
100.0
1000.0
Figure 3.34: Measured enhancement factor for pressure drop as a. function of
vapour quality.
Equation 3.47 is given in Figure 3.37. Most of the dat(!, aTe within
±
10
%.
The estimated uncertainties in measured frictional pressure drop are given
in Figure 3.38 as a function of the vapour quality....0\11 of the measurements
are within ± 25 %.
100
3 Heat transfer and pressure drop
100.0
....,
I
.w
.u
x
...... 10.0
~
~
.w
.w
x
+
, , ""i
' , ""i
~
'j
~
<:>
p+
or
.....
X2
~
X4
x6
r::J
+
LO
10.0
100.0
1000.0
DP_tp/DP_Is [-]
Figure 3.35: Measured enhancement factor fer pressure drop as a function of
vapour quality.
1.4
L2
....,
I
LO
0.8
0.6
0.01
. 0.10
LOO
Figure 3.36: a factor in Equation 3.46 as a function of Froude number.
101
3 Heat transfer and pressure drop
20.0
r-----~----_T----~r_--~
10.0
ttl
.ii~i:~;:,·~i~=-;~:~·
¢.» ..
>
..
~
§
.r-i
0 _0
.LJ
<:>
• .-1
g-10.0
(>'8
~
~¢: ~O~ ~ .
.'
~
¢~..¢".~ ... -....o .. ~.. -............ ;.............
<:> 0 :'J'
:
:
.
;.
~
~
-20.0 ~.----~----~~----~----~
60
80
40
100
120
Flow velocity [kg/m2s]
Figure 3.37: Deviation between measured and calculated pressure drop as a
function of flow rate.
30
<if'
25
.!
~·
!.
!.
::::::::::t::::::~l!:::::t:::::::::L:::::::~
·
.
.
-_
>.
20
t:
15 r---••••.• -+-.----.-tf>-¢~-.~ ...-----..-~--.-----.--
.LJ
• .-1
til
.w
l-I
Q)
: 0 0
t:
~.
.0:
,...
o<;t~:o~~:
:
:
........
10 ~- ... ~~~.
.Q..,j.
<)9 ~
v ..... ~
. .... - ...
()
~
:
5
~ __ ._m ••
o
0.0
·
:_
i
0.2
.
'.:
' . <§>
:¢ ~:
~m __ ~___ ~___ _
i i~
0.4
-
.
0.6
i
0.8
~
1.0
Vapour quality [kg/kg]
Figure 3.38: Estimated uncertainty in measured pressure drop as a. function
of vapour quality.
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Gas Symposium, Nigeria., Sep. 198!.
[2] DiNapoli, R.N., Evaluation in,!-NG project costs
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[4] Newton, C.L., Kinard G.E., Liu, Y.N., C3 -MR processes for baseload
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[10] Owren, G., How to use the results from the SPUNG flow calorimeter in
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D~ign
Handbook, Hemisphere Publishing Corporation,
1983.
[41J Marto, P.J., Fundamentals of condensation, Two-phase flow heat exchanger. Thermal-hydraulic fundamentals and design. PI'. 221 - 291,
1987.
[42] Chun, K.R., Heat transfer to evaporating liquid films, J. of Heat Transfer,
Nov., pp. 391 - 395, 1971.
[43] SeDa.n, R.A., Transport to falling film, 6.th Int. Heat Transfer Conference, vol. 6 , pp. 417 - 428, Toronto 1978.
[44] Kocamustafaogullari, G., Chen, LY., Falling film heat transfer analysis
on a bank of horizontal tube evaporator, AIChE Journal, VoL 34, No.9,
pp. 1539 - 1549, September 1988.
[45] Kocamustafaogullari, G., Chen, LY., Horizontal tube evaporators. Part
I : Theoretically based correlations, Int. Com. Heat Mass Transf., Vol.
16, No.4, pp. 487 - 499, 1989.
106
Bibliography
[46] Shklover, G.G., Buevich, A.V., Investigation of steam ;;ondensation in
an inclined bundle of tubes, Thermal Eng., Vol. 25, No.6, pp. 49 - 52,
1978.
A Thermal design of LNG heat
exchangers
A.1 Geometrical data
Figure A.I shows the location of the tube center.for two neighboring layers
as a function of peripherica.I angle 9, between 0 and 360 degrees. Tubes with
coiling direction to the right assume a positi~e inclination. The two layers
have four and five parallel tubes, indicated with solid lines. The dotted lines
indicate the same tubes in different coils. The crossing of two lines indicates
in-line configuration. Staggered configuration is obtained at angles between
two crossings. The minimum radial distance between two neighboring tubes
will vary as a function of 9.
The longitudinal distance between each occurrence ofa given tube in a layer,
at a constant peripherical angle, may be calculated from Equation A.I, where
i denotes the layer number.
(A.I)
flLtu..i = Ntu,i . PI
The location of each tube may be described by a spiral line in cylindrical coordinates. Figure A.2 shows a spiral line for a tube center viewed. in cartesian
coordinates. The Hne is drawn for a layer with four parallel tubes.
The diameter on a general layer i may be calculated from Equation A.2. The
layer number starn. from one, but only the layers with diameters greater than
Dco are active.
D/a.y,i = 2 . Pr . i
(A.2)
The first active layer is numbered n and the last layer is numbered m, n
107
>
A Thermal design of LNG heat exchangers
108
~
~ 100
(l)
(J
I::
III
oW
Ul
--I
80
60
"0
.-I
III
c:
40
--I
'0
::l
.u
20
..-I
01
c:
a
0
0
...:I
50 100 150 200 250 300 350
peripherical angle
Figure A_I: Location of tube center for two layers as a fun ction of peripherical
angle..
~ 250
(l)
(J
I::
III
200
oW
to
--I
150
'0
.-I
ttl
I
I
~
::
100 r-
I::
!
I
I
:I
-
:::>-
c:::
--I
"0
::l
-01....
c:
a
...:I
>-
50 rc:::::::
oW
0
,
-'
-60 -40 -20
•
0
20
40
60
X projection
Figure A_2: Spiral line for a tube center viewed in cartesian coordina.tes.
109
A Thermal design of LNG heat exchangers
1. The number of parallel tubes in a layer i is C<l.lculated from Equation A.3.
!II . - Ll NT . . _ !l.NT· Dlay,;
- tu,. Z 2 . Pr
(A.3)
The difference in number of parallel tubes from one layer to the next, LlNT,
is normally equal to 1. The inclination is constant for all of the tubes in the
different layers, and may be calculated from Equation AA. The inclinatioil.
is set up as the ratio between longitudinal and peripherical displacement for
a tube in a coil.
tan
Ct =
<}
Nt':!. i . PI
l!J.NT . PI
.
= ---7r • Dlr:zy,;
2 . 7r • Pr
(AA)
The longitudinal and radial tube pitches a!ld the tube inclination cc.nnot be
chosen independently, as indicated in Equation A.4. The distances between
the core and the first tube layer, and the outward jacket and the last tube
layer are normally chosen to be Pr/2 in order to a.void bypass flow. The core
and the jacket diameters are calculated by Equation A.5 and A.6, whe:-e n
and m are the layer numbers for the first and the last la.yers.
Dco = (2· n -1)· Pr
Dsh
(A.5)
= (2· m+ 1)· Pr
(A.6)
The total number of tubes and layers may be ca.lc111ated by use of Equation
A.7 and A.8.
. (N
'"
_ N-
N lay
=m- n+ I
1Vt" -
lay
t..,n
_.Ll N-T)
-
+....."NT.
Nl ay - (Nlay
2
+ 1)
(A.7)
(A.8)
Equation A.7 combines with Equa.tion A.3 to give Equation A.9.
Nt" =
~~T . (m -
n
+ 1) . (m + n)
(A.9)
110
A Thermal design of LNG heat exchangers
The connection between the inclination angle a and peripherical angle 9 is
given by Equation A.1O.
9.DIa.lI,i=~
2
tan(a)
(A.I0)
=
=
() is given in radians and z 0.0 when (} 0.0. Equations A.4 and A.I0 may
be combined to give Equation A.ll for calculation of longitudinal displacement for a layer i as a function of 9. The angle is converted to degrees in the
equation.
Ntu.,i . PI . ()
Zi
=
(A.ll)
360
The tubes in la.yer i will incline a longitudinal distance az.; and th~ tubes
in layer i + 1 will decline a longitudinal distance LlZi+1 between two in-line
conngurations, as shown in Figure A.1. The total displacement is equal to
PI. Equation A.l1 may be used to calculate this displacement as described
in Equation A.12 to A.14.
dz;
I -dZO+1 I ·.6.8· =
I -dB I ·Lll)·+
•
dB
•
PI . Ntu..i . ~9'
360
•+
(A.12)
Pl
Pi . (Ntu..i + 6.NT) . 6.(}. = Pl
d(}. =
360
• 2 . Ntu..i + flNT
360
•
(A.13)
(A. 14)
d(}i gives the peripherical angle between two identical configurations for layer
i a.nd i + I. If the configuration is in-line at e = 0, the in-line configuration
will be repeated at angles j . 6.9i and the staggered configuration at :angles
j. flBi/2 where j goes from 1 to (2· Ntu.,i + 6.NT).
The minimum distanCE between tubes in two la.yers will vary with fJ. The
path for minimum distance between two neighboring layers is located along
lines through the points of tube-crossing shown in Figure A.1. These lines
are in the following called tube-crossing lines. The geometrical layouts for
A Thermal design of LNG heat exchangers
111
four tubes at peripnerical angles of 0, 20 and 40 0 are shown in Figure A.3.
Layer 2 is coiled to the left apd declines with positive (), and layer 3 is
coiled to the right and hlclines with positive fJ. The position for observing
minimum distance alternates between different pair of tubes at the point
w!.:. ~ the configuration is staggered. The distance between tube 3 and tubp.
6 lV• .is a minimum distance at 0 0 _ The layout becomes staggered when the
angle is increased to 20 0, and the distar..ces between tube 3 and tube 6 and
between t-r.:oe 2 and tube 6 become equal. When the angle :'ncreases further,
the minimum distance is obtained between tube 2 and tube 6. The path
for the minimum distance between these two layer.; is drawn in Figure A.4.
The minimum distance path forms a zig-zag pattern alternating between two
tube-crossing lines.
Equation A.I5 may be used to calculate the longitudinal distance between
tube centers in layer i and i + 1, for a tube-crossing line, where j varies from
1 to (2· Nt ....i + flNT); and change values for angles equal to j . flO . The
line starts in the middle between two cross points.
1\ ~
..z,.,..in
° .+ .;)
I
= 2 '';'-"<. ":£:.9
- J
0-)
(A.I5)
The tube-crossing lines incline or decline and the inclination mz.y be calculated from Equation A.I6. This equation gives a constant, longitudinal displacement for all of the minimum path lines and for all of the tube-crossing
lines.
(A.I6)
Fig-<.lre A.5 shows the minimam distance between two tube centers as a function of 0, along the tube-crossing line. The distance is drawn for two crossing
tlnes, and the path for minimum distance follows the minimum. of the two
lines. The layer dia.meter may vary from 2 to 5 meters in a CWHX and the
inclination of the pa!h line for miniIllum distance may be neglected. The
minimum and the maximum points in the curves are located for in-line configuration, and the crossing point for the two curves is located for sta.ggered
configaration. The tu!:le disknce varies from maximum to minimum for a
constant angle 0, and the minimum distance path, shown in Fi!;Ure AA, a.lters locatiO:l_ The fluid flow will be forced by this change in restrictions, and
the flow velocity will change in radia.! direction.
A
112
Thermal design of LNG heat
40 degrees
i:::
.....0
J.J
0
(])
....lo<
'U
......
60
0000
0000
0000
lIS
i:::
....'U
:I
J.J
.....
ljl
i:::
0
..J
o
degrees
exchanger~
d.~grees
OG\~)O
00
6
o0~8
20 degrees
0000
0000
0000
8~~8
00 0
Radial direction
Figure A.:3: Geometrica1lay-out at different angles.
113
A Thermal design of LNG heat exchangers
~
~
OJ
()
s::
<0
.L>
rfJ
60
50
40
.,-i
~
30
.-j
<0
s::
.,-i
't:l
....='
.I...l
20
10
0'1
s::
50
0
:J
1.00 1.50 200 .250 300 350
Peripherical angle
Figure A.4: Path for minimum distance between two neighboring layers.
24
22
20
18
16
14
o
50 100 150 200 250 300 350
Peripherical angle
[deg]
Figu.re A.5: Minimum distance between tube centers as a function of peripherical angle along a tube-crossing line.
114
A
Thermal design of LNG heat exchangers
A.2 Reference flow area
Different methods have been proposed for calculation of the shell-side flow
area in a CWHX. The cross-flow area may be calcul~.ted by use of Equation
1.11, where SreJ is calculated from one of the different methods reviewed in
this chapter.
.
The simplest methods involve using the minimum or maximum radial distance between two neighboring tubes as the reference length. The minimum
distance is located for the in-line configuration, as given in Figure A.3 at 8
= 0.0, and ma.y be calculated from Equa.tion A.17. The in-line connguration is only obtained for a small part of the exchanger and is located at the
minimum points of the curves in Figure A.5.
Sin
= Pr-
(A. 17)
D tu
The maximum distance is located. for the staggered connguration as given
in Figure A.3. The distance for ~ staggered configuration may be calculated
from Equation A.18. The connguration in an CWHX will alternate regularly
between in-line and staggered as shown in Figure A.5 and Figure A.3.
(A.I8)
Glaser proposed a method for calculation of the net cross-flow area based on
a mean gap width Sg!a.s as given.in Equation A.19 [13].
PI
Sg!r:..s =
:1'
loT S·dX
==
2
Pl'
10 {JX2 + Pr2 -
PI
2
D:.. } . dX
(A.19)
X equals the longitudinal distance between the tube centers in two neighboring layers. The configuration varies from in-line at X = 0 to staggered at X =
~l. The gap widt!! is integrated between these two configurations in order to
calculate a mean gap width. The equation integrates th.e minimum-distance
path line froc a minimum point to a cross point, and this gives the referenC2 distance for the minimum path line. Th2 minimum p.ath line consists of
A
115
Thermal design of LNG heat exchangers
many equal curve elements, as identified by the Glaser equation. The result
is given in Equation A.20 [13].
Sgla.$
=
.or
Pl
(1+--)2+
2· Pr
Pi
(1
+ 2. Pr)2} -
(A.20)
Dt",
GilIi proposed a similar methoo for calculation of the net cross-ilow area
[14], but he used both the sma!lest and largest diagonal distance between
tube centers in two neighbori!l!S iayens in the integration. ':fhe reduction in
free space due to the tube inclination was also taken into account. The result
is given in Equation A.21 [14]. a, b , Q and P are defined in Equation A.22.
Sgilli
=
~'Dn{b+2'P}-2'I.ln{ b+2·Pl }]+
b
2 . (b + Q)
2.a
~. [po (0.5-1) +2. I .Q+~' (a3 _Q3) -1]
(A.21)
p_R~2
a + ,
2
(A.22)
3·P
a
pr
a=-,
D
tu
_cos{a).PI
,
b_
D tu
Q~
- va
+ OM
M
I is an interpolation factor between the smallest and largest diagonal freeflow gap. Gilli employed this factor in order to convert heat transfer and
pressure drop obtained for straight tubes to coil-wound !leat exchangers. This
factor take into consideration the variation in velocity due to the alternating
minimum path line. Gilli proposed a factor I = 0.3 ± 0.1 for calculation of
mean flow area and mean velocity, for use in heat-transfer coefficients and
pressure-drop correlations for tube bundles with straight tubes. The equation
reduces to the Glaser equation when I 0.0, and it is only valid for the case
where b S;; .J4 . a + 1. The transversal spacing is then large compared to the
iongitudinal spacing, which is the normal case for LNG heat exchangers.
=
The two methods produce different results and they are closely related to the
chosen heat-transfer and pressure-drop methods. It is therefore not possible
to say tha.t one of the methods is more correct than the other.
116
A Thermal. design of LNG heat exchangers
-----------------------------
A.3 Vapour pressure for pure propane
Four calcula.tion methods have been compared to experimental data collected
by Goodwin [22]. 138 data points from 12 different sources are collected.
The calculation methods are the Peng-RobinSQn equation-of-state (PR-EOS),
a modified Soave equation-of-state (SRK-EOS), a vapour-pressure method
given by Younglove [18] and a vapour-pressure method by Goodwin [22]. The
last method is represented by the zero deviation line. The SRK-EOS and the
PR-EOS method may also be used for mixtures. The deviations between the
different methods are large, in pa-:ticular at high and low vapour pressure.
The de"lations between the different data sources collected by Referen~ [22]
a.re also high, and it is difficult to validate the quality of the different data.
The deviatior..s between the pure component data and the different methods
a.re cited in TabJe A.I. The mean deviation (BIAS) and the maximum deviation (MAX) are given. Restricted comparisons have been made within
the temperature range from 230 K to 350 K. The accuracy for calculation
of saturation temperature for pure propane by the PR-EOS is estimated to
be ± 0.2 °C within this temperature range. The PR-EOS method is chosen
because of multicomponent application and low deviation for pure propane,
whicll is of importance for data reduction in the test facility. Figure A.6
shows the difference between the satur;;.tion temperature for pure propane
and the bubble-point and the dew-point t·emperatT.re for the contaminated
propane-butane mixture in the test facility. The deviation is calculated by
use of the PR-EOS.
A
Thermal design of LNG heat exchangers
117
Ta.ble A.I: Deviation between calculated and measured saturation temperature for pure propane.
BIAS
Method
°C
-0.043
NBS
-0.174
PR-EOS
SRK-EOS
-0.333
Younglove
-0.077
-0.060
NBS for restricted range
PR for restricted range
-0.098
-0.413
SRK for restricted range
Younglove for restricted range -0:140
0.5
I·
I
I
MAX
°C
-0.903
-0.863
-1.274
0.942
-0.903
-0.863
-1.274
0.942
I
Boiling-point
Dew-point ---- -
u
0.4
I-
oC
0.3
1-------------------------------
0.2
I-
0.1
tr__- - - - - - - - - l
• .-1
JJ
<0
• .-1
-
:>
(J)
Q
0.0
-40
I
I
I
I
1
-30
-20
-10
o
10
20
Temperature [C]
Figure A.6: Deviation between saturation temperature for pure propane and
bubble- and dew-point temperature for contaminated propane, calculated by
use of the PR-EOS.
U8
A Thermal design of LNG heat exchangers
AA Corresponding state method for density
The corresponding state method, as given by Ely et al. [16], relates the
compressibility for a fluid to the corresponding compressibility for a pure
:fluid, and is claimed to be very accurate. Methane is used as a pure reference
fluid in the model.
Calculated density is compared to reference data for pure methane vapour
and liquid in Figure A.7. The reference data are given by Buhner et al. [20]
and Younglove et aI. [19]. Both sources claim to have data accur-...cy within
± 0.5 % for reduced temperature below 1.0.
Calculated density is also compared to reference data for pure ethane in
Figure A.8, and for pure propane in Figure A.g. All of the data are given by
references [20] and [19].
s::
.,.,o
0.0
.l.J
.,.,tIS-1.0
f-
o -2.0
I-
+
>
Q)
-3.0
+
Liq-Bubner
Liq-Younglove
Vap-Bubner
vap-Younglove
~~I--~I~--~I----~I--~I--~
100
120
140
160
180
200
TemperaturE [K]
Figure A.7: Density calculations for pur': methane.
Calculated density is compa.red to reference data for different LNG mixtures
in Figure A.lO. The reference data is given by Haynes eta.l. [21]. The data
a.ccuracy is claimed to be within ± 0.05 %. The corresponding 5tate method
is expected to predict density within ± 2 % for light hydrocarbon vapour
A Thermal design of LNG heat exchangers
119
6.0 r-~I-~.--+r-~.---~.--~r-X-~~X--~
Of'
3.0
c
o
• .-1
.w
0.0
XX
+
~
X
+X
-
x+ +++++:.
~
~
f-·~-9-·@·~~·~-@·~·6·a·"fr·g··~···x.
cd
~
X . Liq-Bubner
• .-1
~ -3. a ....
Q
•
I
Liq-Youngl.
+
Vap-Bulmer
\3
VfP-Y~ungf·
~
G
0
-
I
- 6 . 0 '--""--.....".--........- -....--~-""--.........-~
160 180 200 220 240 260 280 300
Temperature [K]
Figure A.S: Density calculations for pure ethane.
6. 0 '---L-i-q"T_.Buhn.--er-...,.r---.-~-T'""
.---,.r--"1¢
<1P
3. 0
~
c:
O. 0
(!)
-3 _ 0
Cl
¢
++
.....o
w
.....cd
:>-
+
Liq-Younglove +
Vap- Bulmer
D
Vap- Younglove X
-6.0
¢¢x
f-········ce~~~g"tlG~·xX
~
~
150
___
xX
_______
~~
200
~I
250
~
____~'____i~
300
350
Temperature [K]
Figure A.9: Density calculations for pure propane.
120
A
Thermal design of LNG heat exchangers
and liquids.
2.0
aP
1.5
s::
.....0 1.0
.I.J
I
I
-
~
--
.~~
,
••
Ii3
.....
>
QJ
0.5
Q
0.0
17
I
I
-
8
••
I
I
I
~
18
19
20
21
22
Molecular weight.
Figure A.lO: Density calculations for LNG mixtures.
121
A Thermal design of LNG heat exchangers
A.5 Corresponding state method for viscosity
The corresponding state method given in Section A.4 is also used to calculate
physical properties as dynamic viscosity ond thermal conductivity. Dynamic
viscosity data for methane, ethane and propane given by Younglove et al.
[19] are compared to calculated data in Figure A.11, Figure A.12 and Figure
A.11. Data accuracy is claimed to be within ± 2 % for reduced temperatures
below 1.0.
2. 0
dP
r - - r - -........--.,...,.~oft--.....,~-...,
<>
~¢
~+
1.0
¢
+++ <>
++t++++ ¢
++
<>
++
c:
0.0 •••=F •..••••.••••••••••......... -.............-.-..... --o
++
<>
..-j
<0-1.0
¢
<>
..-j
:>-
OJ
r:l
-2.0
-3.0
Liquid· data
Vapour data
<>
+
1
~~_o_~_~__~__~___~
100
120
140
160
180
200
Temperature [K]
Figure A.11: Viscosity calculations for pure methane.
122
A Thermal design of LNG heat exchangers
tiP
4.0
0
s::
.....o
J,.l
III
-rl
2.0
<:>
+ ++
¢
+
<:>
O¢<:>
+
•.....,f.........................•.........................
0.0
:>
+
~ -2.0
-4.0
+
+ 0
+
+
Liquid data
Vapour data
¢
+
L...._L-.....J'----'_--L_--L_--L.....
180 200 220 240 260 280 300
Temperature (K]
Figure A.12: Viscosity calculations for pure ethane.
r--""
2.0 .----...,Ir----T"T"""----r-
tiP
1.0 +¢
o
0.0 -········O:·~;-O·¢.-~·"$";-·-·~+········-····--
§-1.0
-
¢
- 'rl
~ -2.0 .....
~ -3.0 -
o
++
+
+ +-rF
+
-
-
Liquid data <:>
VaI:-our data +
-4.0 -
-
-5.0 ,--_ _-,I_ _ _L-I_ _-,'_ _- - ,
200
240
280
320
360
Temperature [X]
Figure A.13: Viscosity calculations for pure propane.
B
Test facility for heat exchanger
B.l Geometrical data
The outside tube diameter, D t .. , was measured to be 12.00 ± 0.05 mm. The
diameter was not affected by the coiling. The length for each tube in the
heated part of the test section was measured after coiling. The results are
given in Table B.l, together with a mean tube l-ength for each tube and a total
mean tube length. The mean value is regarded equal to th~ length along the
center line. The estimated accuracy is a maximum limit for the combined bias
and random errors. The error propagation to the total length is calculated
by use of Equation B.17 without dependency between the variables.
Table B.1: Measured tubelengths in the test section [mmJ.
Coil
1
2
3
4
Total
Inside
382± 2
379 ± 2
375 ± 2
335± ~
Outside
467 ± 2
465 ± 2
459 ± 2
465 ± 2
Mean value
424.5 ± 1.4
422.Q ± 1.4
4i7.0 ± 1.4
425.0 ± 1.4
1688.5 ± 3.0
The total heated area is calculated by use of Equation B.I to be 63655.0 ±
288 mm 2 • The estimated accuracy is about 0.5 %. The error propa.gation is
calculated by use of Equation B.17.
(B.1)
The mean radial distance between the tubes is calculated from measurements
of the coiling diameter on the inner and the oute. half-tube layers. The
123
124
B Test facility for heat E:xceanger
diameter at the tube top on the inner half-tube layer, Di, was measured
to be 108.0 ± 0.05 mm. The inner-layer diaIileter on the outer half-tubes
~as measured at nine different places around the heated part of the test
section. The accuracy for each value may be regarded as a bias limit due
to uncertainty in the measurements. The layer diameter varies from tube to
tube, and each of the measurements represents a ....'3lue for the diameter. The
results are given in Table B.2.
Table B.2: Measured inside-layer diameter on the outher half-tube layer
[mm).
Point
1
2
3
Angle 1
141.7 ± 0.5
147.6 ±Q.5
147.8 ± 0.5
Angle
147.6 ±
147.6 ±
147.7 ±
2
0.5
0.5
0.5
Angle 3
147.6 ± 0.5
147.6 ± 0.5
147.5 ± 0.5
The mean inner-layer diameter may be calculated by use of Equation 8.2.
1
Do=
9
'9 ~Do.i
(B-2)
=1
The uncertainty in thE' mean layer diameter is influenced by the variation
in the measured values. The random error is estimated by use of Equation
B.5 to Equation B.8, and the total inaccuracy is estimated by a combination
of bias error- on each measurement a.nd random errors due to variation in
diameter. The mean value for Do is estimated to be 147.63 ± 0.2 mm.
The radial distance between the tube centers, Pr, is calculated by use of
Equation B.3, to be 15.9] ± 0.06 mm.
Pr
=
Do - Di
4
1 D
+ 2'
tu
(E.3)
The longitudiul distance betwE!--:!n tubes is kept constant by use of spacer
rings, with a diameter of 1.85 ± 0.15 rem. The longitudinal distances between
the tubes in the teSt se-ction are measured at eight points, perpendicular to
four and nve parallel tubes:_ The longitudinal distance ma.y vary from one
B
125
Test facility' for heat exchanger
tube pair to another as a function of peripherical angle. The longitudinal.
distance perpendicular to the tube centers, PIp, may be calculated by use
of Equation B.4, where L is the measured distance and N is the number of
parallel tubes in the measurement.
PI = L-Dtu
p
N-1-
(BA)
The results are given in Table B.3. The error limit for each L represents a
bias error due to uncertainty in measurements, and not a random error due
to actual variatic..n in tube distance. The uncertainty in Pip is estimated
as a random error from the eight measurements by use of Equation 8.5 to
Equation 8.8. The longitudinal distance is corrected due to inclination by
the relation PI = Plp!cos{et), where 7.928 0 is used as inclination angle. The
mean value for PI is estima.ted to be 13.94 ± 0.09 mm. The longitudinal
tube distance oX! the inner and the outer half-tube layers is measured to be
14.0 ± 0.05 mm. The center diameters for the three layers are given in Ta.ble
B.4. The tube inclina.tion has been estimated by use of Equation A.4 to be
Ct = 7.938 ± 0.06 o. Cross-flow area, estimated from the different methods
described in Chapter lA, is given in Table B.5. The area is corrected for
longi!:udinal spacers and tubes used for temperature instrumentation. The
total correction is estimated to be 109.0 ± 0.2 mm 2 •
Table B.3: Measured longitudinal tube distances [mmJ.
Point
1
2
3
4
Five tubes
PIp
L
67A ± 0.5 13.85± 0.13
67.7± 0.5 13.93± 0.13
67.4± 0.5 13.85 ± 0.13
66.8 ± 0.5 \13.70 ± 0.13
Four tubes
PIp
L
53.3±0.5 13.77± 0.18
53.3 ± 0.5 13.77± 0.18
53.5±0.5 13.83± 0.18
53.4±0.5 13.8!J± 0.18
126
B Test facility for heat e.xchanger
Table B.4: Estimated center diameter for each layer [mmJLayer
Inner half tubes
Central tube layer
Outer half tubes
Diameter
96.0±O.O7
127.82 ± 0.11
159.63 ± 0.21
Table B.5: Cross-flow area in test section [mm 2J.
Method
In-line area
Staggered area
Gilli's method
Glaser's method
Flow area
3031.2 ± 63.0
4203.6 ± 62.0
3428.9 ± 62.0
3637.9 ± 62.0
B Test facility for heat exchanger
127
B.2 Estimation and treatment of errors
B.2.l Random errors
Random errors a.re alwa.ys estima.ted from replicated measurements a.nd the
errors will show up as a scatter around the mea.n value for the measurements.
The data points are assumed to deviate from the mean in accordance with
the laws of chance in such a way that the distribution approaches the normal
distributio!l when the number of replicated measurements is increased. The
scattp.r may be caused by cha.racteristics of the measuring system and by
changes or instability in the quantity being measured. The random uncertainty is derived by statistical analysis of repeated measurements as described
in ref~rences [23J, [25], [26].
The best value for a. property, x, in a series with N replicated measurements
is the average value x calculated by Equation B.5.
(B.5~
The uncertainty from random erroiS is quantified by the estimator for the
standard deviation, S, often called the precision index. For a single set of
measurements with a small N, S may calculated by Equation B.6.
s=
"N
(.
-'-'j=l X, -
N-l
x-)2
(B.6)
For a small sample it is necessary to correct the statistical results based on
normal distribution by use of Student-t values. The Student-t values are
gi ....en in Appendu.: B.4 as functions of probability, P, and degrees offreedom,
v. The value tv,P . S give the uncertainty interval for a single observation,
x, which includes the true mean value, p., with a given probability. The 95%
probability is normally used for physical experiments. The random error is
always reduced by taking replicated measurements and using the mean value
as the best estimate for the true value. The estima.ted standa.rd deviation for
mean value may l:..e calculated from Equa.tion B.7.
sr;;;r
s- = vN
(B.7)
128
B Test facility for heat exchanger
The vclue tv,P . 5 gives an uncertainty interval arounci. the estimated mtan
value, x, which includes the true mean value, f.L, with a given probability. The
best interval which contains the true average is th~n given from Equation B.B.
The degree of freedom is given by v = N - 1.
_
x±tv, p
5
(B.8)
.IN
.--
Use of different instrumentation for measurements of the same property is
ca.lled multi-sample measurements. The best value for a measured value
where multiple sets of instruments are used is the grand average, calculated
by Equation B.9. M is the number of sets involved. It is assumed that the
number of observations is common for each set.
x
= _
X-
~M
L.Jj=l
N j ' Xj
-
M
2:j=1
Nj
~M
-
_
L.Jj=l Xj _
-
-
M
~M·N
L.Ji=l Xi
(B.9)
!vi . N
The precISIOn index, or the estimator for the standard devia.tion in the
multiple-set experiment, may be calculated from Equation B.IO.
,\,M
L.Jj=l
N j ' (=x -
Ef=,l Nj
-)2
Xj
,\,M (=
L.Jj=l X -
M
- .)2
x]
(B.IO)
The estimated standard deviation for mean value from multiple set experiments is given by Equation B.Il.
-=-
5
Sm.
5
= -.jM- = --:.JM=.N=-
(B.ll)
A weighted average of the estimated standard deviations in Equation B.ll is
often used. This average may be represented by Equation B.12 in case of N
common observations in all sets.
(B.I2)
B Test facility for heat exchanger
129
Tl!<! best interval which contains the true average with a given probability
for a mUltiple set experiment is now given from Equation B.13. The de,~ee
offreedom is v = M·N - M.
(B.13)
B.2.2
Syst~!Datic
errors
Systematic errors are fixed errors and give a measured result which either are
constant-to-high or constant-to-low with respect to the true value. Systematic errors may be constant or variable, and can be of unknown sign and magnitude, known sign but unknown magnitude, or known sign and magnitude.
Systematic errors may be reduced by calibration r such as for thermocouple
element wire. Systematic errors are estimated by non-statistical methods as
described in references [23], [25] and [26]. Uncertainties from systematic errors may be quantified by maximum limits or by the 95 % confidence level.
These limits may be distributed symmetrically or non-symmetrically around
the true value of the measurement.
The treatment of systematic errors depend on the nature of the error itself
and may be classified into four different groups;
L Errors with known magnitude and sign. The measurements may be
corrected, and the uncertainty limit set to zero. An example of such
errors is the calibration of a single thermocouple element, where the
results are corrected with respect to a standard curve.
2. Errors with known sign and estimated magnitude. The error may be
estimated 'within an interval with a upper and a lower limit. The results
are corrected with the mean value of the error, and the uncertainty limit
is taken as one-half of the error interval. An example of such error is
the heat leakage into the test plant.
3. Errors with experimentally assessed magnitude. Such errors are treated
as random errors, with a statistically estimated uncertainty. An example of such an error is the calibration of a batch of identical thermocouple elements by use of a selected number of the elements. A mean
value and a standard deviation for the batch are calculated from the
calibration.
130
B
Test facility for heat exchanger
4. Errors with unknown sign and magnitude assessed by judgement. The
results are not corrected with respect to such errors. This is the normal type of systematic errors in data acquisition- and data reduction
systems.
Systematic errors in instruments and data acquisition system are generally
stated at a 95 % confidence level [27].
B.2.3 Propagation and combination of errors
Measured and derived parameters are in most cases combined by functional
relationships into the results. The estimated errors for each parameter must
therefore also be propagated into the results.
A result, R, is derived from J number of variables with different average
values, Xj, as given by Equation B.14. Each Xj may contain both systematic
and random errors. The a.im is to estimate a total uncerta.inty interval for
the resul;;, ?.nd the variables should, as fa.r as possible, be independent of
ea.ch other.
(B.14)
Propagation of random errors is calculated by estimation of the standard
deviation for th~ result. It is often impractical or impossibJe to use only
independent variables, and the formula for calculation of the standard deviation must take into account dependency or covariance between variables. The
estimated standard deviation for the result may be calculated from Equation
B.15, [26].
(B.15)
The covariance may be calculated by use of Equation B.16, [26].
(B.16)
B
Test facility for heat exchanger'
131
The covariance is zero for independent variables. The function R and its
derivatives with respect to the different varia.bles have to be continuous
around the given values .. The sensitivity ~~ may be estimated analytically
or numerically. Propagation of systematic errors is treated in the same way,
as given in Equation B.l7. The covariance between variables is neglected.
B:&j is the estimated uncertainty due to systema.tic errors for the variable Xi.
(B.17)
Two different approaches are recommended for combination of errors. The
Root Sum Square approach as given by Equation RI8 and the Add '..:.' approach as given by Equation B.19 [23], [24].
(B. IS)
(B.19)
B is the estimated total error from systematic error sources, ~d S is the
estimated total standard deviation from random errors. The two types of
errors are kept separated until the final result. The 95 % probability is
recommended to be used for the Student-t value. The degree of freedom for
the final result may be calculated by use of the Welch-Satterthwaite formula
in Equation B.20 [25].
(B.20)
132
B
Test facility for heat exchanger
B.3 Test for outliers in measurements
The Dixon test is used in order to detect outliers in the measurements [26].
The test may only be used for normally distributed populations. The observations are ranked and function values for each observations are calculated.
The function depends on the sample size. The function value is compared to
a critica.l value and the data point is rejected if the calculated value is higher
than the critical value. The test function and the critical values are given
in Table B.6 and Table B.7. The measured data are ranked by increasing
values when high values are tested and by decreasing values when low values
are tested.
Table B.6: Test functions for the Dixon method.
Sample size
Test functions
3-7
(xn - xn-d/(z" - Xl)
(x,.. - %"-1)/(%,, - X2)
(x" - %"-2)/(%,, - X2)
(z,.. - %"-2)/(Z,, - X3)
8 - 10
11 - 13
14 - 25
Table B.7: Critical values for the Dixon method.
N
3
4
5
6
7
8
9
10
Critical value
0.941.
0.764
0.620
0.560
0.507
0.554
0.512
0.477
N
11
12
13
14
15
16
17
18
Critical value
0.576
0.546
0.521
0.546
0.525
0.507
0.490
0.475
N
19
20
21
22
23
24
25
Critical value
0.462
0.450
0.440
0.430
0.421
0.413
0.406
133
B Test facility for heat exchanger
B.4 Student's-t statistics.
The values for the Student's-t statistics are given in Table B.8 as a function
of degree of freedom and confidence level for a normal distribution. The 95
% confidence level is used in this thesis.
Table B.8: Student-t Sta.tistic for a. nor.mai distribution as a function of
degree offreedom v.
v
tgo'70
1 6.314
2 2.920
3 2.353
4 2.132
5 2.015
6 1.943
7 1.895
8 1.860
9 1.833
10 1.812
11 1.796
12 1.782
13 1.771
14 1.761
15 1.753
tgS'70
tgg'70
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.626
2.228
2.201
2.179
2.160
2.145
2.131
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
v
16
17
18
19
20
21
22
23
24
25
30
40
60
120
00
tgo'70
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.697
1.684
1.671
1.658
1.645
tss'70
too%
2.120 2.921
2.110 2.898
2.101 2.878
2.093 2.861
2.086 2.845
2.080 2.831
2.074 2.189
2.069 2.807
2.064 2.797
2.056 2.787
2.042 2.750
2.021 2.704
2.000 2.660
1.980 2.617
1.960 2.576
134
B Test facility for heat exchanger
B.5 Location of thermocouples
The thermocouples for measurement of fluid temperature in ~he isothermal
part of the test section are installed in 1.8 mmOn prob2S, inserted from
the end of the test section. The distance from the end of the probe down
to' the heated part of the test section extends about 180 mm. Two probes
are installed in each of the two free spaces between the layers. Two of the
thermocouples balow the mixing chamber are also installed in probes inserted
from the end of the test section. The other two elements are installed in
probes inserted through the tube wall. The distance from the end of the
mixing chamber down to the four points is about 200 mm.
A sketch of the tubes in the test section, before and after coiling, is given in
Figure B.l. The bending of the tubes entailed a displacement of the instrumentation points, as shown in Figure B.l. The elements on the inside were
twisted downwards and the elements on the outside were twisted upwards.
The points at the lower end have been twisted about 15 0, and the points at
the upper end have been twistee. about 45 o.
HEATED iUSE
tt---- t\
+r~~
.12
,
t=- 107.6:0.~
216.1
~-~
=r
~
~a--
98.4:0.7~
r-~---------422.1·1.4 -------~---!
uPPER PA!lT
LOWER PART
Figure B.l: Tube in the heated part of test section, before and after bending.
The location of points for measurement of wall temperatures is given in Table
B
Test facility for heat exchanger
135
B.9. The points are located about one-fourth of the total tubelength from
the upper and lower end. The mean value is calculated both for each tube
and for all of the tubes. The uncertainty in the mean value is estimated from
the bias error only. The distance between the mean value for the upper and
the lower points is 216.1 mm.
Table B.9: Location of points for measurement of wall temperature [mm].
Measured from lower end
Coil Inside
Outside Mean value
1
99.5
89±2
1l0±2
2
96.0
87±2
105±2
107±2
98.5
3
90±2
10S±2
4
91±2
99.5
Mean value for all tubes
98.4± 0.7
Measured from upper end
Coil Inside Outside Mean value
1
101±2 115±2
10S.0
2
101±2 116±2
lOS.5
105.0
3
93±2
117±2
4
109.0
101±2 117±2
Mean value for all tubes 107.6± 0.7
B Test facility for heat exchanger
136
B.6 Thermocouple reference equation
The reference table for the E-type thermocouple wire is given as a power
series equation, based on IPTS-68 [28]. The equation represents the defined
true temperature. Equa.tion B.21 gives a. relation between the temperature
in °C and the EMF in /LV.
13
E.rlClna.
= 2: aj . Tj
(B.21)
i=l
The constants aj are given in Table B.I0 for a temperature range from -270
to 0
ae.
Table B.IO: Constants for type-E thermocouple in Equa.tion B.21.
j
1
2
3
4
5
6
7
a;
5.8695857799E+01
5.1667517705~02
-4.4652683347E-04
-1.7346270905E-05
-4.8719368427E-07
-8.8896550447E-09
-1.0930767375E-1O
j
8
9
10
11
12
13
a;
-9.1784535039E-13
-5.2575158521E-15
-2.0169601996E-17
-4.9502138782E-20
-7.0177980633E-23
-4.3671808488E-26
The numerical representation is very accurate due to the degree and the
number of significant figures in the constants for Equation B.21. The number
of significant figures in the calculated temperature is therefore higher than
the actual accuracy in IPTS-68. The equation is used because it gives a
smooth representation for the temperature-E:M:F relation, and because it is
recommended as a standard reference [28].
B
137
Test facility for heat exchanger
B.7 Thermocouple off-site calibrat.ion
Off-site calibration of th€ thermocouple elements is done by use of a comparison method. A reference temperature, T ref, is established by the cooling
of an insulated copper block. The thermocouples are installed in the CO]r
per block. T reJ is measured by use of a platinium resistance thermometer,
and the EMF in the thermocouple elements is measured by use of a digital
voltmeter. An ice bath is used as a reference junction for the thermocouple
elements. Different elements are connected to the voltmeter by way of a manual switch. The difference between the measured EMF a.nd the standardized
EMF is calculated as a function of measured reference temperature in every
calibration point i by nse of Equation B.22.
(B.22)
The uncertainty for the calibration is caused by errors in the measured temperature and errors in the measured voltage. The result from the calibration
is given in Table B.ll. 1'r ef = 0.0 °C has not been measured, and this point
will not re:fl.ect the uncertainty in the calibration loop.
Table B.U: Off-site calibration results for the thermocouple elements.
Calculated
~
Tref
EstanC:
Tl
Tl
0.0
-37.85
-62.61
-89.00
-124.11
-141.07
0.0
-2138.11
-3438.78
-4730.16
-6277.26
-6947.47
0.0
-20.81
-:33.48
-44.36
-66.06
-76.67
0.0
-21.11
-33.78
-47.16
-65.86
-77.97
T3
0.0
by use of Equation B.22.
-25.01
-39.38
-50.46
-69.86
-81.27
T.;.
0.0
-24.51
-38.58
-51.96
-72.96
-84.17
Ts
T6
0.0
0.0
-24.21 -21.61
-37.98 ' -34.78
-50.46 -45.46
-69.86 -64.66
-81.27 -75.57
Wire
0.0
-3.81
-7.38
-4.76
-6.06
-8.87
The uncertainties for the measured E and T ref are divided into bias error
and precision error. The precision errors are affected by temperature instabilities in the copper block, and by random errors in the measuring chains
for temperature and voltage. The measurement have not been repeated for
every calibration point, and the uncertainty is therefore estimated asa bias
limit. The uncertainty interval is dependent on the temperature and the total
uncertainty is estimated by use of Equation 8.17.
138
B
Test f <lcility for heat exchanger
A list of the different error sources, with an estima.ted uncertainty interval,
is presented in Table B.12. The total uncertainty is estimated at -140.0 °C,
'l/'hich is reg<>,rded to be a minimum value. The voltage errors are converted
to temperature errors by use of the reference equation.
Table B.12: Uncertainty interval [oroff-site calibration of E-type thermocou-
ple element.
Uncertainty in the measured reference temperature
Source
Uncertainty
Platinum resistance thermometer
±0.05
Bridge for measurement of resistance
±O.OO125
Temperature stability of copper block
±0.01
Uncertainty in the measured voltage
Source
Uncertainty
Reference junction
±O.Ol
Digital voltmeter
Function of reading
±0.005% or ±O.35
Function of full scale
±0.0005% of 100 m V or ±().5
Function of resolution
±1.0
Scanning system
±l.G
Combmed errors from all sources
± 3.;) JLV or :::t: 0.07
-
Of"'
'V
°C
°C
°C
p,V
j.LV
j.LV
.uV
°C
The polynomial equation for Ec<>iib is generated hy using the least Squar~s
technique, from the sets of calibration points given in Table B.11. The degree for the equation is chosen in such a way that the number of distiact
calibration points available is greater or equal to 2 . ( degree + 1 ) [28]. All
of the experimental data points must also be held within theunc~-tainty interval when the interval is centered around the most probable interpolation
equation. Ecalib is given by Equation B.23, with values for b o, b l and h:!
given in Table B.13. All of the calibration points are within the estimated
uncertainty interval.
2
ECtllib
=L
j=O
bj . Ti
(B.23)
B
IZ9
Test facility for beat e..xchaPgcr
Table B.13: Constants in Equation B.23.
Element
Tl
T2
T3
T4
Ts
T6
Wire
bo
-7.30.10- 1
-5.1:~ .10- 1
-9.23.10- 1
-6.47 -10-1
-7.24 -10- 1
-7.05.10- 1
-4.67.10- 1
b1
4.83 .10- 1
5.12.10- 1
6.06.10- 1
6.03 ·lO-l
5.97 ·lO-l
5.25 ·lO-1
9.76 ·lO-2
b2
-3.59.10-1
-2.03.10-4\
2.57 ·10-4
1.22 ·lO-4
2.42 ·10-4
1.40 ·lO-5
3.36·10-
140
B Test facility for heat
exchaDg~
B.8 On-site calibration of thermocouples
All of the thermocouple elements were delivered at the same time and it
is assumed that all of the elements come from the same reel. 7 of the 23
elements were calibrated individually. 6 of the calibrated elements are used
in the test facility_ The results from the individual calibratio:l are used to
estimate a mean calibration curve. This curve represents the 16 elements
used for measurements of wall temperatures. The !Dean deviation from the
standard curve is calculated from the results in Appendix B.7. The standard
deviation for the mean value is also calculated. The results are given in Table
B.14.
Table B.14: Mean calibration result for the therm0couple
TreJ
0.0
-37.85
-62.61
-89.00
-124.11
-141.07
!
Estc.nd.
~E
S
0.0
-2138.11
-3438.78
-4730.16
-6277.26
-6947.47
0.0
-22.77
-36.32
48.56
0.0
0.66
0.90
1.09
1.21
1.23
-68.75
-80.00
elem~ts.
The uncertainty in the mean value depends on the total bias uncertainty in
each point and the random uncertainty due to variation from element to element. Most of the different error sources in Table B.12 are not independent,
because the elements are calibrated at the sar::J.e time. A common bias error
is therefore used for the mean value. The total random uncertaiety is estimated from the standard deviation for the mean value. The total uncertainty
interval is estimated to be within 0.1 °C at -140.0 0 C.
The equation Ecalib for the mean value is generated by the procedure described in Appendix R7. The constants for Equation B.23 are given in
Table B.15.
Isothermal checks have been performed with propane as the test fluid in twophase flow. The r::lea.n fluid temperature and the deviation from the mean
were calculated for each point in the test section. The results are given in
Figure B.2. Point numbers 1 to 4 represent the fluid temperatures prior to
B
141
Test facility for heat exchanger
Table B.15: Constants in Equation B.23 for the mean calibration curve.
1
bo
15.55~\0 -3.2~~ 10 61
the test section, point numbers 5 to 12 represent the waIl teClperatures in the
upper part, point numbers 13 to 20 represent the wall temperatures in the
lower part and point numbers 21 to 24 correspond to the fluid temperature
after the mixing chamber. The deviation from the mean reflects all of the
different error sources in the. temperature measurements.
CJ
0.20
a
c::
0.15
.&.J
0.10
?
0.05
.,-i
...,ttl
III
'd
..
~
~
~
$
.~ •• ' .....• " •...•x.:L:t!....................... .
0.00
~-O.05
~
~
series
series
-0.10
~
+
<)
~
(>
~
t~
~ -0.15
p.
al
Eo<
-0.20
0
5
10
15
20
25
Point
Figure B.2: Deviation from mean temperature for each point in the test
section at isothermal conditions.
H.9 Pressure transmitters
The different pressure transmitters are described in Table B.16. The cali·
brated span is the initial range set by the manufacturer. The accuracy is
142
B Test facility for heat exchanger
often related to this range, especially for the Honeywell transmitters.
Table 8.16: Technical description for pressure transmitters.
Identifier
P sec
Por
DPs1
DP s2
Fabrication
Honeywell
Honeywell
Honeywell
Honeywell
DPor
DP=cr
NAF
NAF
Type
STG150
STA140
STD120
STD120
ETD-14
ETD-14
Calibrated span [Bar]
0-35.0
0-8.6
0-0.25
0- 0.25
0.05 - 0.25
0.015 - 0.075
Two different reference pressu.res are used for calibration of the transmitters.
For pressures or differential pressures greater than 0.01 bar a dead weight cell
is used. For lower pressures a static water column is applied. The signal from
the trar.smitter is measured by use of a precision resistance and a voltmeter.
The Jp.w. weight cell has a accuracy of 0.03 % of reading and the water column
u.., accuracy of about 0.5 mm or 5 Pa. The accuracy for the voltmeter is high
a.nd will not be regarded in the total uncertainty.
The upper range value ( URV ) is adjusted in order to obtain a given range.
The zero point or the lower range value ( LRV ) is adjusted on the transmitters during calibration. The linearity may also be adjusted for some of the
transmitters in order to obtain the specified accuracy. The reference chara.;:teristic, given by Equation 2.2, is estimated from an end peint 4.<ijustr.:lent
based on the linear cha.racteristic. The constants are only dependent on the
lower and upper range value and their signals; and will not be changed by
re-calibration. The residual for each calibration point is checked against the
reference characteristic.
Equation B.25 c:.::!Q Equation B.24 are used to estimate the cc.nstants a and
b in Equation 2.2. The equations are used both for absolute pressure and
differential pressure.
b = PURV - PLRV
JURV - hRV
a = PLRV - hRV • b
(8.24)
(B.25)
B
143
Test facility for heat exchanger
The accuracy for a and b depends on the accuracy for the calibration equipment, and on the ra.ndom pa.rt of the accuracy for the transmitter itself. The
adjusted end points may. therefore drift due to hysteresis and repeatabilil;y
error in the transmitter.
The accuracy for a and b due to calibration may be estimated from Equation B.17 without dependency between the variables, where the sensitivity is
estimated from Equation B.25 anu B.24. The accuracy for a and b dua to
ra.ndom transmitter error is not estimated, but included in the data reduction; by the specified accuracy for the transmitters. This accuracy involves
combined effects of linearity, hysteresis and repeata.bility.
The constants in Equa~ion 2.2 are given in Table B.17. The lower range value
is zero for a.l.l of the differential transmitters, and 1 bar for the other two.
The specified. transmitter accuracy is also given in the table.
Table B.17: Precision resistances a.,d constants in Equation 2.2.
Identifier
i
P sec
P"r
DPsl
DPs2
DP"r
DPmcr
a,-
-3.72814 . 10:-3.74653.10 5
-3.74977.10 2
-3.75047. 102
-3.75117.103
-1.87617· 10 3
Ri [Q]
b·•
9.38999. 10 7 401.0
9.37364. lOi 399.8
9.37441.10 4 [400.3
9.37617· 104 400.7
9.37606 . 10~ 400.6
4.69041 . 10" 400.1
I
Accuracy
5300
1500
25.0
25.0
37.5
18.8
Unit
Pa
Pa
Pa
Pa
Pa
Pa
The maximum deviations for DP"r, DP 51 and DP s2 are well within the specified 2.ccuracy. It has been observed that the zero point for these two transmitters may drift within ± 10 Pa due to variations in line pressure on one or
both sides. Such drift ma.y be observed. directly after a re-calibration. The
specified accuracy is used in order to establish an upper maximum limit. The
maximum deviations for P sec and P or fall within the specified accuracies.
B Test facility for heat exchanger
144
B.lO Geometrical data for the orifice meters
Geometrical data for the three ori~lce meters and the orifice tubes are cited
in Table B.18. The tube diameters are measured at four points in the large
orifice and at eight points in each of the other two orifices. The uncertainty
in the mean tube diameter is estimated from a combination of estimated
standard deviation from the mean value and bias deviation for each measurement. The bias deviations for all of the measurements are regarded to
be independent. The rest of the geometrical data for the orifice meters lie
within the recommended values in DIN1952 [30].
Table B.18: Geometrical data for orifice meters and orifice tubes [mm].
Meter size
Measurement
1
2
3
4
5
6
7
8
Mean
Orifice diameter DOT
Small
Medium
10.000 ± 0.05 27.997 ± 0.005
Tube diameter, Dtui
Small
Medium
21.35
41.07
21.40
41.08
41.07
21.32
21.31
41.07
21.29
41.09
21.29
41.07
41.09
21.32
21.32
41.07
21.33 :i: 0.04
41.08 ± 0.01
Large
51.993 ± 0.005
Large
81.26
81.26
81.33
81.22
81.27 ± 0.073
The tube and the orifice diameters are corrected with respect to temperature
by use of Equation B.26.
Dcorr
= D· (1 +1"
(T - TreJ)}
(B.26)
Both the orifice plates and the orifice tubes are made of stainless steeL The
reference temperature, Trej, is 20.0 °C, and the expansion coefficient, 1', is
15.10- 6 iPC
B
Test facility for heat exchanger
B.II Calibration data for turbine meter
The liquid flow rate is measured. with a turbine meter from manufactorer
Flow Technology, inc. type FT-16W50-LB. The meter and the pulse-rate
converter were calibrated. in factory by use of a liquid with specific gravity of
0.761 and viscosity of 1.2 cSt. The calibration was performed at 20°C. The
bearings in the turbine had to be replaced after a few hours of operation,
and an on-site recalibration was carried out in order to check drift and onrite ir.stallation effects. Water ';Vjth a specific gravity of 1.0 and viscosity of
about 1.5 cSt was used. The re-calibration was performed a.t a temperature
of about 6°C. A drift of approximately 2 % was observed, over the whole
range, between the two calibrations, and the data from the recaIibration have
been used. for calculation of :Bow rate. The total measuring chain. was used
for the on·site calibration. The 4 - 20 mA signal is transfe:-red to a voltage
signal by use of a 400.5 ± 0.1 n resistance.
The turbine meter is regarded to have a linear correspondence between volume :Bow rate and signal within the 10:100 % range of the maximum-designed
:BoWTate. The characteristic tends to be nonlinear at lower :Bow rate. The
change in characteristic correspond to change between laminar and turbulent :Bow pattern and is therefore a function of Reynolds number. The :Bow
starts to get turbulent at a Reynolds number of about 2300. As the rate increases the :Bow becomes more and more turbulent, and the How is regarded
to be fully turbulent for a Reynolds number greater than 10,000. The fullydeveloped turbulent :Bow corresponds to a :Bow rate of about 0.3 Ijs or a signal
of 2.12 V or 5.3 mA for the recalibration. The :Bow rate may be calculated
by use of Equation 8.27.
ML
= [a+ b· E]. PL
(B.27)
Two linear characteristics Ci.re estimated, one for :Bow rate up to O.3ljs and
one for flow rate higher than 0.3 lIs. The least squares technique is used to
estimate the constants a and b. The constants a.re given in Table 8.19.
The hydrocarbon fluid has a kinematic viscosity in the range of 0.25 to 0.4
cSt. A viscosity of 0.4 cSt a.nd a Reynolds number of 10,000 correspond to
a :Bow rate of about 0.07 lis in the test facility. The fiow will therefore be
turbulent at a much lower How rate during operation than during calibration.
The high-range equation is therefore extrapolated to be used for the whole
146
B
Test facility for heat exchanger
Table B.19: Consta.nts for turbine meter in Equation B.27.
Range
Low
High
a
-0.934291
-0.922246
b
0.581332
0.576161
turbulent regime, even though the constants are estimated for higher flow
ra.tes. The test fa.cility is not operated in regions where the flow through the
turbine meter tends to be laminar.
The volume How rate was calculated by use of Equation B.28 during reca.libration, where G is the measured weight of water, t is the time and PL is the
water density.
G
v=-t· PL
(B.28)
The different error sources for ;:he reca.libration are given in Table B.20. The
error sources for the volume flow rate are given by judgement. The time used
is about 300 seconds for ea.ch measurement, and the total measured weight
va.ries from a.bout 20 kg for the lower How rate to about 400 kg for the higher
flow rate. Each error source is rEogarded to be independent. The uncertainty
interval is estimated to be ± 0.5 %"
B Test facility for heat exchanger
147
Table B.20: Error sources for reca1ibration.
Volume flow rate
Source
Uncertainty
Weight
Function of reading
±O.l
Function of resolution
±O.l
Time
±l.O
Density
±l.O
Voltage signal
Source
Uncertainty
Data logger
Function of reading
±O.Ol
Function of resolution
±O.8
Repeatability for turbine meter
±{).O5
Resistance
±O.l
%
kg
sec.
kgjm 3
%
mV
%
%
148
B Test facility for heat exchanger
B.12 J\1easurement of heat flux
The heating elements are connected in series, and the voltage is measured
by use of precision resistances parallel to the heating elements as shown in
Figure 2.7. The voltage between A and B may be calculated from Equation
R29, where El is the measured voltage. The resistance w1.ain is used in order
to adjust the output voltage to the range for the data logger.
(B.29)
The values for the different resistances are given in Table B.2!. Ru" is the
resistance for the wires between A and B. Ru4 is the resistance for the wires to
the wattmeter. The uncertainty is estimated from measurement of resistances
and from judgement of installation errors.
Table B.21: Precision resistances for heat :flux measurements [Q).
Identifier
Ru,
RU2
RUJ
Total between A a.nd B
Ru.
Resistance
999.2± 0.2
999.6±O.2
2.2±O.4
2001.00 ± 0.5
2.5±0.2
The resistance for the heating elements are measured at two different temperatures. The results are given in Table B.22. The resistance is assumed to
be linear between the two temperatures. The accuracy for the temperatures
is assumed to be within ± 2
ac.
The resistance for an intermedia.te temperature T is calculated by interpolation. The total heat input in the elements ma.y be calculated from Equation
B.:30 and B.31 .
(B.30)
(B.31)
B
Test facility for heat exchanger
14:9
Table B.22: Resistances for heating elements [Q).
Elemen"t
Rql
Rq2
R q3
Rq.
Total
Tu = 20°C
3.840± 0.01
3.905 ± 0.01
3.904 ± 0.01
4.004±0.01
15.653 ± 0.08
TL = -196°C
3.753± 0.01
3.824±0.01
3.833 ±0.01
3.910±0.01
15.32±0.08
The total uncertainty interval for W Q may be calculated by using Equation
B.15 to Equation B.18 where the sensitivities are calculated from Equation
B.29 to Equation B.31The wattmeter may be used in different ranges with different scale factors
for current and voltage. Each range is calibrated individually. Four different
ranges have been used for this application. The measured values are corrected
by use of a linear interpolation between the values. The uncertainty due to
calibration and nonlinearity is set to 0.5 W. The uncertainty due to resolution
( reading) is set to [0.05 . scale factor].
C
Examples of measured data.
150
C
151
Examples of measured data.
C.l Superheated vapour flow
SHELL - SIDE
TEST
PAGE:
?IJ\lI'I'
DAte
Pi:ase
15;03:13 ns=n
4-=-1989 Ti:Ir.
2 ·.r-fac:t ~ 31.40 O·fakt:
1.00 I-falct
Measured
.me.
combined variabe1es Siglld1
20
1
5.00 Orifice _ Med.i_
Min
Mean
RAndcm
Bias
186.
103.
5305.
1517.
25.
25.
38.
.0185
.16
.16
T_f1uid after seetiOl1_______C_
T_vap af~er seper4~or_______C_
C_
T_vap before o:rifice
C_
T_V4P af:er coole:
C_
'1'_~...p before mixer
5.4615 907128. 905U4. 906071.
5.5135916387. 915404. 915453.
302.
29B.
300.
2.8832
2.8979
304.
302.
303.
7919.
5.03BB
8226.
8042.
24.7624 49.598 49.588 49.589
-.7994 -13 .90 -13.94 -l3.93
-.7996 -13.93 -13.97 -13.94
-.7982 -13.92 -13.96 -13.94
-.7978 -13.91 -1.3.95 -l3.93
-'l.B3
-7.84
-.4511
-7.81
-7 .~Z
-7.98
-.4585
-7.93
. ; .6~
-7.65
-7.69
-.4424
';7.69
-7'.72
-.4434
-7.67
-1.53
-7.51
-7.55
-.4343
-7,55
-7.53
-7.56
-.4350
-1.47
-7.53
-.4323
-7.50
-7.65
-7.69
-7.66
-.4416
-7.04
-1.02
-7.00
-.4051
-6.97
-6.96
-.4014
-6.94
-6.96
-6.94
-.4001
-6.92
-6.a7
-6.83
-6.85
-.3948
-7.12
-7.11
-7.14
-.4107
-7.00
-7.06
-7.03
-.4056
-6.B7
-6.85
-6.83
-.3~53
-6.71
-6.69
·.3856
-6.67
.-.7466 -13.01 -13.03 -13.02
-.7476 -13.01 -13.03 -13.02
-.7513 -12.98 -13.00 -12.99
-.7561 -13.07 -1!.09 -13.08
-.7388 -12.76 -12.79 -12.77
-8.34
-S,34
-8.33
-.4843
·.8227 -1'.23 -14.27 -14.24
-14.17
-.81a7 -14.14 -14.19
Pa_
DP..;oean in sect-ion
before sec~io,,-C_
C_
'1'-="ea;, in sect.ion
C_
'1'..,:;Ie= Aft.e= seccion
C_
T.:",a11 eo~ect.ion
C_
Tto:_"",an upper
C_
Tto:..;oeal1 [ce=ect:ed)
C_
'iW~an lower
C_
OT' :neasu.::-ed
Q calcula.ted
w_
Q lOeasured
C_
'1' l&borate:y
301.64
-13.94
-13,48
-13.03
.04
-7.71
-7.34
-6.97
6.14
lS7,71
158.69
17.87
P4_
P sect-ion
? orifice
p ....
Pa_
DP se~ion
OP se~ion
DP erifice
O_vol:: seCl:icn
P,,Pa_
be~ore
sec:tioD-C_
T_fluic::!
v_
'1'_fluid befe= s~io,,-c_
'1'_~luid before s~io,,-C_
'1'_fcuid befere sectio,,-c_
'1'.:... 11 tube 1 Opper-outside_C_
':~_11 t:ube 1 ~per-Inside__C_
T_wal1 cube 2 Upper-OUtside_c_
'1'_",al~ tube 2 Opper-Inside--,-_
T_wall tube :3 Opper-OUtside_C_
'1'_101411 tube 3 ~per-Inside__C_
T_wa11 tube 4 Opper-OUtside_C_
T_:.:all eube 4 Opper-Inside__C_
'1'_101411 tul:>e 1 Lower-OUtside_c_
'1'_"",11 tube 1 Lower-Inside__C_
'1'_wall tube 2 Lower-OUtside_C_
~_wa11 tul:>e 2 LOwer-Inside__c_
'1'_101..11 cube 3 Lower~t.side_C_
'1'_wal1 eube 3 !,.ower-~ide_C_
T_wal1 eube 4 Lcwer-outside_C_
'1'_10...11 cube <- Lower-Inside__C_
T_~luid after seetio,,-C_
T_fluid ~~~er
T_!luid after
sec~io~c_
se~io~c_
M<IX
T~an
"'-
COMPOSI'1'!ON
'1'ot:al
N2
1.00000
W1~
Cl
.00000
(;2
.00000
C3
.00000
NC4
.00000
IC4
.00000
l..
C!.
33.
.0014
.01
.01
.01
.01
.00
.00
.01
.01
.01
.00
.01
.01
.01
.01
.01
.01
.01
.01
.01
.01
.00
.:0
.00
.00
.00
.00
.01
.01
.35
.02
.01
.01
.00
.02
.01
.02
.01
.1S
.00
.50
_!.6
.16
.17
.17
.17
.17
.17
.17
.17
.17
.11
.17
.17
.17
.17
.17
.17
.17
.16
.16
.1C
.26-
.16
.16
.:'i
.16
17.6B
.10
.09
.10
.01
.12
.11
.12
.12
1.61
.68
2.00
152
C Examples of measured data.
SHELL - S:D:£
TEST
PACE
P!.A.>r.'
2
Bias
D_tube ::':0 seC1::i.otl.
R.ldial ccl>e pi cc:h
c
"'_
Lang~cudi:l4l cube picc~_
aea~ed cube leagch
m
Tube coiling
dia=e~re~_
FlOiIi' a.:ea in seccion
.012000
.015910
.000050
.000060
.000090
.003000
.0139~0
1.6BBSOQ
.127820
.OOn10
.000063
.000288
_
SeAted are<>. in section-",_
.003031
.063655
DI_orifiee-plate
.027997
.04.1080
.126000
.000005
.000010
.11727:£.02
.161196:£-04
.14248:£.. 01
.118UE+02
.16542E-04
.25072:£-01
.10610:£.04
.23453E.00
.13511E-05
.71239E-Ol
'"
D!_orifice_~ube
Ois~ce be~ee~
Density
i~
~
DP
tapping~_
orifice______kg/~_
Viscosity in
o=ifice~sJ~_
cp/CV ~ orifice____~~~~~
v",O'Our de=. in sect:i0l>..kglJ:U_
Vapou= vise_ i~ seceion~/~_
V4PQur cOlld. ill section_W/mlL
V",pour Cp i.!I Sec::iOD_ _J/kgl';..
Entha1~ before section--J/kg_
Ent~py
.26595:£.06
.26643:£.. 06
~"b41~
.26oSlE.. 06
in sec"ig~J/kg_
after seccioD___J/kg_
V",pour mo1ewei~c___kg/kmole_
Vapour flow rate
kg/s_
Total flow =at:e
kg/s_
F1~ velo=icy
kej~s_
_~ae_ before see~i~kglkg_
lo.nac.
...c.
~n
ae~~
l.ll
sect:io,,-kglkg_
after se~io~kglkg_
leLkage i= seeti0D-----ft_
B"l'C-Pe4SUX"cd
DP_tot.ol
DP~a~ity
W/mlK.-
Pa_
Pa_
Pa_
DP_frictioD
DP_tot ... l 1=adient________P4/~
DP_fr1ctig~ g=... d~eDt _____ Pa/~
~Rf~~~r---------------------
~ ~~~--------------------
.000500
.2368lE.00
• 13314:£-OS
.20058:£-02
.S172.E+02
• 13298E+OS
.13322E+OS
• 13346E+05
.00000:£+00
.28013E.02
.1814
.181;
S9.8~S8
.0004
.0004
.1211
.0000
.0019
.0019
1..3905
.0000
1.0000
l.OOOO
l.0000
15.73
;06.11
288.61
24.6'
.0000
.0000
4.7929
.8266
.3502
27.3089
B.4964
17.6785
303.25
2290.58
24J6.74
.3502
2.7794
2.7793
140.6265
140.6433
.2218
.0009
.0000
87.3203
.70
43152.77
194.37
.oon
.3~S7
.OGOC
.0000
.3107
17.Ge06
.0160
.0868
3610.2664
16.1.173
153
C EX3Jllples of measured data.
C.2 Film :How
=
SHELL • SIDE
Da~e
Phase
=
?LAN'r
:!'~-OCT-l!1H
1 ~-fact
TilDe
= 25.00
15:21:15 DScan
2.00 I-f~
O-fAkt
20
5.00 Orifice
MiD
MeASU=ed. and combined variabe.!.es Signal
i" se<:t:ion
P,a..
o~ifi~e
p~
p~
p
DP seCl: ion_
DE' se~ ion
P4.DP ori~i~e
P4.5ep4re:or lev.. :i._______ ,,~
LiQuiC: volu:;l. rlltl@
U_vol:: B.e1:iotL
1/s_
v_
T_fluid
be=~=e ~e~ioD______C_
'T_fluic!
T'_f.!.u:'d.
b.?~o::, ....: s~~ior'l,
~_!l~id
before
T;.~
T_wal!
sec~i~~
:ide_C_
__C_
:>per-OUtside_C_
Jpper-!r.:i~e
.~<
,,:_w411
______C_
upp~,,,"-("·:':.
1
'.-'
T_w~11
T_wU1.-
'.:.r:x
T_wall
_ _C_
be=~=e .!~io~ _ _C_
...
~IJe=--Icr1de_c_
~c _ Oppe~~~si~e_C_
tube 3 Opper-rcside__C_
T_w~l
T_wa!! ~ube ~ Oppe~~Jeside_C_
T_w4!l cube 4 Oppe=-lAside__C_
7'_W'all
T_wal1
... ~"
-r.:",.o.il
T.-wa.ll
tube ::;. Lowe- • __.;Jt:side_C_
'tuDe 1 Low"~., ~ ..lSide-_C_
t.c.be 2 Low&-, .:lutsideo C
I:w." 2 I.ov, - ':nsicle":C:
':,uQe 3, Lo1_ ,;--OU~sid.e_C_
T_w411 Lube 3 Lawer-~side_C_
:sias
3.3021 400918. 39!1811. 400415.
3.3168 401U5. 40H45. 401U5.
(,.
-14.
1.5::110
-2.
-15.
1.5398
-11.
-:<:1.
1. nos
261.
240.
252.
609.
450.
536.
2. 0578
2.5453
.5456
.5426
• 5442
31. 356!1 62.US 62.768 62.7!15
-5.07
-5.12
-.2!151
-5.11
-.2!161
-5.H
-5.14
-5.12
-.2945
-5.08
-5.U
-5.11
-.2942
-5.0S
-5.12
-S.lO
-.1851
-3.17
-3.25
-3.20
-.1930
-3.31
-3.39
-3.34
-.1903
-3.25
-3.36
-3.29
-.1942
-3.33
-3.42
-3.36
-.1926
-L31
-3.36
-3.33
-.1975
-3.39
-3.44
-3.42
-.1655
-3.18
-3.24
-3.2l
-.1978
-3.42
-3.44
-3.42
-.1928
-3.25
-3.39
-3.34
-) .27
-3.42
-3.36
-.1943
-.1898
-3.25
-3.34
-3.2B
-3.20
-.1848
-3.17
-3.24
-.1709
-2.92
-3.00
-2.96
-.~740
-3.01
-2.!18
-3.0S
-3.1';
-.1828
-3.13
-3.24
~-~l~ Cube 4 ~=-OU~s~de_C_
T_w.o.ll ~ube 4 LoWer-I~ide __C_ . -.1802
T_fluid dfter s~io~C_
-.29 .. 7
-.2912
T_fluid after seec:o=---C_
-.2929
'I"_flwt1. cr:e:- Se-c:t.iOi,-C_
-.2973
T_f1u~d d=ter sectio~C_
T_liq afte~ seperator_______C_
-.2995
-.3097
T_liq ... f= .. r cooler
C_
T_l:'q before mixe:
C_
T_vo&p a.~te: Sepe::-Clt.O::,_ _ _C_
-.2970
-.1070
_______C_
.4291
C_
C_
-.3003
-.2996
-3.08
-3.18
-5.03
-5.02
-5.0!
-5.07
-5.0B
-5.1!
-5.30
-5.08
-5.06
-5.13
-5.17
-5.34
-5.~B
-5.11
-1.80
7.34
-5.13
-5.11
-1.99
7.18
-5.17
-5.17
237.
O.
2.
2.
3.
19 •
.00035
.007)
.01
.01
.01
.01
.01
.01
.02
.01
.Ol
.01
.Ol
.00
-3.!2
_02
.02
_01
.01
.01
.01
.01
.01
5304.
1514.
25.
25.
38.
19.
.00272
.0225
.H
~~6
.l6
.16
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.:1.7
.17
-5.0';
-S.li4
.01
.Ol
.17
.17
.17
.17
.16
.16
-5.05
-5.11
.01
.15
.01
.15
-5.14
.01
-5.32
-5_10
.01
.15
.15
.1.5
-1.84
7.27
.01
.00
.15
.lS
.15
.15
-5.16
-5.14
.02
.01
.01
-8.57
-5.ll
1.69
.02
17.53
T~4::.
.02
.02
.09
T~
-5.0:#
-5.06
.06
-3.39
.00
.01
.12
.ll
.1.2
T_~AP
be~o=~
o=ifi~~
T_V4P 4!"te: coole::T_VAP be!o:e ~e=
::':0 ,'ee=i.oc
P,,-be!'or@ s e c t i o c - C _
T-=ea.c in $.e~ion
C_
DP~
4!~e~
s~c~ioc
_______C_
,!,,_1rial!. co~eC1:ion
"r.....~a.n uppe~
n;-"",,,,, Ic¢__ ect:ecl)
lower
DT ....... =e<1
~~l1!l
Q ~c:u1at:e<1
Q me",,=ed
T l4borato:y
COMPOS!'I':!:OI' 1oo"I'I'H
N2
Total
.00000
[.iqtlici
.00000
Vapour
.00000
C_
C_
C_
e_
C_
W_
w_
C_
Cl
.00000
.OOO~O
.00000
Q
.00000
.00000
.00000
C3
.9971.2
.99712
.99920
NC4
.002l7
.00217
.00054
-3.32
.02
.02
-3.24
.02
1.82
252.51
252.40
.02
23.85
.50
Ie,
.C0072
.00072
.00026
.18
.00
~lO
.10
.14
2.1.7
.!1'
2.00
C Examples of measured data.
154
P:\GE:
2
va.riabo!l
D_t:ube i.e sec'l:ion
m
Radial cube pi cch
"'
Locgitudinal !:\!be piceh--"L
aeated Cube lengtb
"'.
"I'UQe c:oilillg cl.imcel:.:'e
::I
-Flow .a:ea. in seceioll
m
a.aced are... in $ec:t:':'on~
DI.ori!ice-pl ... ce
"'
DI.orifice_tube
m
Dist:oO.Dce becwee:l DO' tappin9JDV.a~ dens. in seC'tion..kg 1!!13_
V...pou= visco in sec:t:io~/=2_
v ...pou: cocd. in sect:ion_\<"~
Vapou: cp ;." seeeioD-J/JcqK...
Liquid decs. in sectioVg 1m3_
:'ic;u..j.d vise. in seet:ion....Ns/m2_
~~d coca. in s~iO~W/mX­
!.iqt!.id Cp 1:> seeeioIl_ _J IJcqK...
ZIlChalpy be!o:e sect:io,,-J!kg_
ED~py ~ sec:ioo_ _ _~/kq_
Enthalpy afee: sectioc__~/kg_
Liquid dellS. in 'Cu=bine.kg 1m3_
Total moleweighc ___kg/kmcle_
V...pou: mo1eweignt ___kg/kmcle_
Liquid mo!eweigct _ _kg/kmcle_
Liquid flc:;J' ra'te
'l'oea.l t2.000 =a~e
FlQIJ vel.ocicy
T_~l1.!ic
estUla1:ed
T_dif! est.i.:lKI.ceO.
H'l'C....me.o.s=ed
DP_eou1
DP..s;r...v.::. t:;(
Icg/s_
kg/s_
kg/..:zs_
C_
C_
W/m2K..,.
P,,P,,-
DP_f=ic~ion
P4_
DP_'Cocal g:.adie:l::
?a/DL
DP_f=ictioc g:4dient ____.Pa/=.
~ ~~~::::::::::::::::::::
N'O' ncmbe:
.012000
.015910
.013940
1.688500
.127820
.003031
.063655
.010000
.021330
.126000
.000050
.000060
.000090
.003000
.000110
.000063
.000288
.000050
.000040
.u00500
.87378£.01
."792£-05
.16419£-01
.16284£.04
.53423£-03
.!2463£-03
.10938£.00
.246291::.0':'
- .11043£·05
- .11000£_06
-.10957E.06
.53432£.. 03
.44137£.. 02
. 44108E·02
.44137£.. 02
.17476£_00
.59834£-06
.ln35E-02
.79380£.. 02
.10685£+02
.9970SE-OS
• 8750SE-02
.12315E+03
-.55210E.c.:.4
-.55000E+0'
-.S4783Z.. 04
.10686E.02
.00000;;:.00
.OOOOOE.OO
.OOOOOE+OO
.2908
.2908
95.9351
-5.31
2.00
2180.87
-18.0':'
660.34
642.30
.0002
.00C2
.0623
.0186
.0186
27.7159
2.6871
. 0257
-14'.~0
13.3897
13.3912
.0001
3.8917
.0045
5097.59
2.81
5810.37
.35
1.6873
.001S
.~015
2.0510
.4162
.41&2
169.1436
17.bi88
2.6242
17.8568
140.3076
14o.n12
.G003
29.5203
.0274
C Examples of m.easured data.
155
C.3 Shear flow
SHEll. - SIDE
PLAIn'·
TEST
2·J1JL-1990
Date
Phase
o ~-fac't
=
NUMBER - AF900702_6
Measured e.:'.": combined vari,u,eles SigDAl
P
se~ion
P~
p
ori~ice
p~
Pa_
!)P SeC1:.io:l
DP seeeioll
P~
DP orifice
P~
SeparAtor level
p~
l.iquid ·~o1_ rate
I/s_
V_
O_volt section
T_fluid b<>fore se=ion_ _ _C_
T_fluid b<>fore seccio~C_
T_fl'-1id before sectio,,-C_
T_fluid b<>fore sectio,,-c_
T_wal1 tube 1 Opper-Ou~ide_C_
T_wall tuDe 1 Opper-Insic:le_C_
T_wall tUb4 2 Opper-Outside_C_
T_wall tube 2 Opper-Insic:l,,--c_
T_wall tube 3 Opper-Outsic:le_C_
T_wall tube 3 Opper-Inside_C_
T_wall tube 4 Opper-Outside_C_
T_wall tube 4 Opper-"Inside_C_
T_wall tube 1 Lower-Outside_C_
T_wall tuDe 1 Lower-"Inside_C_
T_wall tube 2 I.ower-Outside_C_
T_wall tube 2 Lower-Inside_C_
T_wall tube 3 Lower-Outside_C_
T_wall tube 3 Lower-"Inside_C_
T_wall tube 4 Lower-Outside_C_
T_wall tube 4 Lower-"Inside_C_
T_fluid After section_ _ _C_
T_fluid after section______C_
C_
T_fluid after seet:ion
T_fl~id After section ______C_
T_liq after seperAt:or_____C_
C_
T_liq After cooler
T_liq before mixer
c_
T_'-....p After seperator______C_
c_
T_vap before orifice
C_
'T_vap a!'te::- cooler
C_
T_'-"'P before miXer
DP~an in section
T-=eAll before section
l'.JDeAIl in secc.ioa
T,JDe&!l
a...ft:.e= section
T_.... ll co::ec:cio:l
T'Jl_aean upper
lW-"",= (co=e=ed)
'I'W-""' .... lower
O'I' llleas=ed
Q calculated
Q :z>easured
or
COHPOS~TION ~TH
VApour
N2
.00000
.00000
.00000
= Medium
RAndom
Bias
3.0520 342816. 341809. 341S59.
3.0795 346551. 345545. 345947.
70.
1.SS35
60.
66.
73.
1.9054
6S.
71.
1605.
1714.
1695.
2.3<171
835.
642.
2.2501
762.
:"'8499
.1450
.1420
.lU6
31.3165 62.71S 62.70S 62.7H
-.5743
-~.9S
-9.98
-9.97
-.574S
-9.97 -10.00
-9.9S
-.5733
-9.9S -10.00
-9.98
-9.97
-.5733
-9.97
-9.99
-.4970
-S.60
-8.67
-8.63
-B.70
-.4983
-B.61
-8.65
-.5016
-8.68
-8.74
-B.71
-8.77
-.5063
-S.B2
-8.79
-.4680
-S.14
-8.11
-8.12
-B.21
-.4719
-S.16
-B.19
-S.;';O
-8.25
-.4734
-8.22
-8.47
-.4866
-8.42
-8.4S
-.4722
-S.lB
-8.23
-8.20
-.4750
-S.21
-S.26
-6.24
-.4S22
-S.35
-S.40
-9.37
-.4759
-8.23
-8.33
-9.26
-S.25
-S.33
-.4769
-8.<18
-.4S06
-S.30
-S.38
-8.3'
-S.51
-8.60
-8.56
-.49<19
-8.56
-S.61
-.• 4946
-B.59
-.5697
-9.90
-9.91
-9.91
-~.90
-.5694
-9.S7
-~.B9
-9.8S
-.5719
-9.S4
-9.S6
-9.93
-.5755
-9.91
-9.92
-9.97
-9.9S
-.5785
-9.97
-.5901 -10.16 -10.19 -lO.lS
-9.79
-.56S6
-9.81
-9.S0
-9.69
-.5617
-9.67
-9.6S
--:'.97
-5.01
-S.OO
-.2914
-9.37
-9.71
-9.64
-.5595
-.4716
-S.lO
-B.13
-8.12
105.
237.
1.
5304.
1513.
25.
25.
Hi"
68."5
-9.91i
-9.94
-9.90
.06
P~
C_
C_
C_
C_
C_
C_
c_
C_
Cl
.00000
.00000
.00000
1
Hean
Max
-8.53
-8.4S
-8.42
1.'S
251.98
<152.40
2'.19
""C_
l~rat:o::y
Total
Liquid
P:.GE
T:iJDe
1;:17:<10 D.S= :
20
25.00 O-fAkt
<1.00 I-falc: = 5.00 Orifice
C2
.00000
.00000
.00000
NC4
0
.99J,,2 ·.00791
.9a749 .01041
.99677 .0024S
1C4
.00168
.0021~
.00075
o.
23.
22.
.00036
.0023
.00
.00
.00
.00
.01
.01
.01
.01
.00
.01
.01
.00
.01
.01
.01
.01
.01
.01
.01
.01
.00
.00
.00
.00
.00
.00
.00
.00
.01
.04
.00
.6S
.01
.01
.01
.00
.01
.01
.02
.01
.12
.00
.50
38.
19.
.00072
.0225
.16
.16
.16
.16
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.17
.16
.16
.1';
.16
.!&
.16
.16
.16
.15
.16
.16
17.68
.10
.09
.10
.01
.12
.13
.1<1
.14
2.29
.54
2.00
C Examples of measure'l data.
156
SHE!.L - SIDE
TEST
NOMBER -
PUNT
A-~00702_6
Me_
v.o.::iabe1
D_tube in section
~ube piech
a:rea in sect.io~_
DI_ori!ice-p1ace
111DI_orifice_cuQe
III
.012000
. 015910
.01394-0
1.699500
.127820
.003031
.063655
.027997
.041080
OisUlnce bet.ween DP tapping-=-
.126000
RAdial
'"
'"
Locgicudinal cube picch-",_
lI_ced t:ube 1engt:l:
.Tube
~oiling
III
d~e=e~_
s~iQn
Fla..r a:ea in.
m
SeAt.ed
oe~i~
i~
ori:ice______ kg/m3_
.74406E~01
o=ifice~slm2_
.74492E-05
.1l812E.. Ol
.7S217E.01
.73106£-05
.15844E-01
.15976E.04
.54155E+03
.i3192E:-03
.11222E:+OO
.24139E+04
.56294E+05
.57168E.05
.5S043E+OS
.54143E.03
.4423lE+02
• 44149E+02
.U302E+02
viscosity in
~ orifi~e
vapour dellS. in se~ioD_kg/=8_
Cp/Cv
'vapour
Vapour
Vapour
Li<:JUid
Liquid
vise:. in sec:tion.-Ns/:rU._
cond. in seccio,,-W/mK.Cpin seccio~J/k~
dellS . in sect:io"_~/m3_
i~ sec~iQ~s/m2_
vis.e.
"~quid condo in seccio,,-W/mIt.
!.i<:JUid Cp i~ seccio,,___J IkgK....
Ec.t:b.a1py before seccio,,-J Ikg_
Ec.Chalpy i.1l seecio~J Ikq_
~Chalpy af:er $~io,,---J/kg_
!.iquid dellS. ill C=bine_kg/ml_
TO~a1 moleweighc _____kg/kmole_
Vapour moleweigh~____kg/kmole_
Liquid moleweighC____kg/kmole_
kg/s_
.OG65
Liquid flow rate
kg/s_
kg/s_
Toeal flow ra~e
kg/m2s_
Flow ':elocicy
T_!luid es~~~ed
t:_
C_
T_dit: escil:l.:Lted
~a.c. before s~io,,---kg/kg_
""-"?=a.c. in sect:io,,_ _ _ kg/kg_
.0T77
VAPOur flow race
~ac.
4f~er sect:io~kg/kg_
l!T\::..measured
DP_coc4.1
DP-Sr-"vi""
DP_f~i~:iOD
:=a~ion
~~_~o~ g:..dienc
Void
DP_!:i~~on
?It !:umber
it!: nu:me::
NO' number
l<J/m2lt.
Pa_
Pa..
""Pa/m_
g:adiellc_____?a/~
.lU3
47.6085
-9.89
1.42
.4559
.4582
.4621
2684.14
60.46
19.80
80.26
.9841
479.82
636.96
2.81
1476.1S
.44
PAGE
R4ndcm
2
Bias
.000050
.000060
.000090
.003000
.000110
.000063
.00028a
.000005
.000010
.000500
.1498lE·00
.59594E-06
.59059E-01
.15043E+00
.58485E-06
.12676£-02
.7798lE+02
.1093lE.02
.10S53E:-C4
.89772E-02
.12070E:~03
.28147E.04
.28584E+04
.2902lE:.04
.10S29E+02
.00000£+00
.OOOOOE+OO
.OOOOOE+OO
.0005
.0002
.0005
.1623
.0090
.0090
.0018
.0018
.00lS
1~.176S
.6825
.0'749
.6966
.0001
5.4166
5.4488
.0003
3.6813
.0023
.0010
.0004
.0011
1-0527
.2548
.2548
.0032
.0032
.0039
256.48:0
17 .6787
.5387
17.6840
.000S
140.3234
140.3654
.0085
14.2993
.0417