FP7-SME-2010-1 262205/ INTHEAT
29/11/2011
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Project no.: 262205
Project full title: Intensified Heat Transfer Technologies for Enhanced Heat Recovery
Project Acronym: INTHEAT
Deliverable no.: D1.2
Title of the deliverable: Report on experimental fouling investigation and CFD research on
heat transfer enhancement
Contractual Date of Delivery to the CEC: 30/11/2011
Actual Date of Delivery to the CEC: 30/11/2011
Organisation name of lead contractor for this deliverable: UNIBATH
Author(s): Barry Crittenden, Mengyan Yang
Participants(s): P1, P2, P3, P6, P7, P8, P9
Work package contributing to the deliverable: WP1
Nature: R
Version: 1.0
Total number of pages: 30
Start date of project: 1st December 2010
Duration: 24 months
Project co-funded by the European Commission within the Seventh Framework Programme (2007-2013)
Dissemination Level
PU Public
PP Restricted to other programme participants (including the Commission Services)
RE Restricted to a group specified by the consortium (including the Commission Services)
CO Confidential, only for members of the consortium (including the Commission Services) X
Abstract:
Fouling and scaling experiments have been conducted on crude oils and water, respectively, using
the batch stirred cell at the University of Bath. The effects of temperature and velocity on the
fouling and scaling phenomena have been interpreted with the help of CFD modelling using
COMSOL. Crude oil fouling threshold conditions have been obtained. They may provide useful
guidance to the avoidance of fouling by optimising operational parameters. CFD simulations of
fluid flow and heat transfer in tubes fitted with inserts and flows around a wired test surface have
helped to gain understanding of the effects of the geometric alternatives on turbulence
enhancement, and hence on fouling mitigation techniques.
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THEORETICAL AND EXPERIMENTAL INVESTIGATION OF FOULING
Fouling; heat transfer, crude oil, scaling, heat exchangers, threshold plot, mathematical models.
Table of Contents
BIBLIOGRAPHY ............................................................................................................................... 3
NOMENCLATURE ............................................................................................................................ 4
1. EXECUTIVE SUMMARY ............................................................................................................. 5
2. INTRODUCTION ........................................................................................................................... 6
3. EXPERIMENTAL INVESTIGATION ........................................................................................... 7
3.1 APPARATUS, MATERIALS AND EXPERIMENTAL METHOD ......................................... 7
3.2 RESULTS AND DISCUSSION - CRUDE OIL FOULING .................................................... 9
3.2.1 Effect of temperature and velocity on fouling rate –fouling threshold ............................................. 9
3.2.2 Fouling threshold conditions .......................................................................................................... 11
3.2.3 Effect of turbulence enhancement on fouling ................................................................................... 12
3.3 RESULTS AND DISCUSSION – CASO4 CRYSTALLISATION FOULING ....................... 12
3.3.1 Mitigation effect of wire attachment on fouling .............................................................................. 13
3.3.2 Influence of surface materials ......................................................................................................... 14
3.3.3 Asymptotic fouling ........................................................................................................................... 14
4. CFD SIMULATION AND MODELLING ................................................................................... 14
4.1 CFD SIMULATION OF FLOW IN THE STIRRED CELL WITH A WIRED PROBE .......... 15
4.1.1 Effect of shear stress ....................................................................................................................... 15
4.1.2 Effect of temperature ...................................................................................................................... 17
4.2 CFD SIMULATION FOR HEAT TRANSFER IN TUBE FITTED WITH AN INSERT ....... 18
4.2.1 Temperature field in tube fitted with insert ..................................................................................... 18
4.2.2 Average heat transfer coefficient .................................................................................................... 20
4.3 RESEARCH ON FOULING MODELS .................................................................................. 22
4.3.1 Fouling rate and fouling thresholds ................................................................................................ 22
4.3.2 Compensation plot ........................................................................................................................... 24
4.3.3 Modelling of fouling induction periods ........................................................................................... 24
5. CONCLUSION .............................................................................................................................. 26
6. REFERENCES............................................................................................................................... 27
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BIBLIOGRAPHY
The following bibliography has been assembled during the project to provide a wide-ranging
account of the principles underlying the problem of fouling as well as the approaches which have
been adopted for its mitigation. The research element required in finding solutions to the problem is
significant, and accordingly the bibliography is invaluable in assisting organisations to find
practical solutions to individual fouling problems.
Books
• Somerscales, E. F. C. and Knudsen, J. G., (1981), Fouling of Heat Transfer Equipment,
Hemisphere Publishing Corporation, Washington.
• Suitor, J. W. and Pritchard, A. M., (1984), Fouling in Heat Exchange Equipment, American
Society of Mechanical Engineers, New York.
• Garrett-Price, B. A., Smith, S. A., Watts, R. L., Knudsen, J. G., Marner, W. J. and Suitor, J.
W., (1985), Fouling of Heat Exchangers: Characteristics, Costs, Prevention, Control and
Removal, Noyes Publications, New Jersey.
• Melo, L. F., Bott, T. R. and Bernardo, C. A., (1987), Fouling Science and Technology,
Kluwer Academic Publishers, Dordrecht.
• Bott, T. R., (1990), Fouling Notebook, Institution of Chemical Engineers, Rugby.
• Bott, T. R, (1995), Fouling of Heat Exchangers, Elsevier Science & Technology Books.
• Müller-Steinhagen, H., (2000), Heat Exchanger Fouling: Mitigation and Cleaning
Technologies, Institution of Chemical Engineers, Rugby.
Major Biennial Conferences (available on-line)
• Heat Exchanger Fouling and Cleaning: http://www.heatexchanger-fouling.com/index.htm
Commercial Reports
• IHS ESDU, Heat Exchanger Fouling in the Pre-Heat Train of a Crude Distillation Unit,
Report ESDU 0016, London (ISBN: 978 1 86246 119 2).
• IHS ESDU, Fouling in Cooling Systems Using Seawater, Report ESDU 03004, London
(ISBN: 978 1 86246 220 5).
• IHS ESDU, Fouling in Cooling Systems Using Fresh Water, Report ESDU 08002, London
(ISBN: 978 1 86246 618 0).
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NOMENCLATURE
A Pre-exponential factor in Arrhenius expression m2K kJ
-1
A Dimensioned constant in fouling model
B Dimensioned constant in fouling model
C Dimensioned constant in fouling model
Cb Foulant precursor concentration in the bulk kg m-3
Cf Drag coefficient
E Activation energy or apparent activation energy kJ mol-1
Cε1 Parameter in k-ε turbulence model
Cε2 Parameter in k-ε turbulence model
f Friction factor
k1 Rate constant in induction period model s-1
k2 Removal rate constant in induction period s-1
keff Effective thermal conductivity W/(K m)
ko molecular thermal conductivity W/(K m)
kT turbulent thermal conductivity W/(K m)
u Velocity ms-1
u* Friction velocity ms-1
R Universal gas constant kJ mol-1
K-1
Re Reynolds number
Rf Fouling resistance m2K kW
-1
Rf*
Asymptotic fouling resistance m2K kW
-1
Tf Film temperature K
Ts Surface temperature K
t Time s
Greek symbols
α Dimensioned constant in fouling model
β Constant in fouling model
β Time constant s-1
γ Dimensioned constant in fouling model
θ Fractional surface coverage
µ Dynamic viscosity Nm s-2
ν Kinematic viscosity m2 s
-1
ρ Fluid density kg m-3
τ Shear stress N m2
κ Turbulent energy m2/s
2
� Turbulent kinetic energy dissipation rate m2/s
3
η Dynamic viscosity Pa.s
ηT Turbulent dynamic viscosity Pa.s
σε Parameter in k-ε turbulence model
σk Parameter in k-ε turbulence model
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1. EXECUTIVE SUMMARY
Fouling experiments have been carried out over a wide range of experimental conditions using a
batch stirred cell system which is flexible and easy to operate up to pressures of 30 bar and surface
temperatures of 400oC. The system is suitable for use with hydrocarbons such as crude oils and with
aqueous systems when CaSO4 scaling can be studied. The outside surface of the heated test probe
can be modified to study heat transfer and fouling on certain configurations of enhanced surface.
Linear and falling fouling rates are observed, dependent on the system under study. Induction
periods can also be studied. Once fouling has progressed to a significant level, the cell can be used
to study negative fouling rates by changing the processing conditions in a carefully controlled
manner. In this way, the thresholds of surface temperature and surface shear stress can be found,
below which fouling becomes insignificant. Flow and heat transfer in the batch stirred cell are
complex, particularly when enhanced surfaces are used. Computational fluid dynamics (CFD) has
therefore been used to model the fluid flow and heat transfer, and hence to obtain local distributions
of surface temperature, heat transfer and shear stress. CFD has also been used to study theoretically
the fluid flow and heat transfer that arise when wire matrix enhancement devices such as hiTRAN®
inserts are used in plain round tubes.
A new concept developed within this project has been that of the equivalent velocity/Reynolds
number. It allows a fouling model developed for bare round tubes to be extended for use with more
complex geometries. For example, it has been demonstrated that the fouling models of Ebert and
Panchal (1997) and Yeap (Yeap et al. 2004; Yang and Crittenden 2011) can be adapted successfully
to correlate the fouling data of a crude oil (Crude A) obtained using the batch stirred cell, as well as
for tubes fitted with hiTRAN®
inserts. Recently within this project, the equivalent
velocity/Reynolds number approach has been adopted for modelling fouling in plate heat
exchangers by SODRU. Fouling threshold conditions can now therefore be predicted successfully,
auguring well for the development of successful strategies to mitigate the highly energy consuming
fouling problem in systems where intensified heat transfer techniques are being adopted.
CFD simulation confirms that the average heat transfer coefficient for a tube fitted with an insert is
much higher than that for the bare tube operated under the same conditions of surface wall
temperature and average velocity. The increase in the heat transfer coefficient when an insert is
used means that the temperature in the shell side of an exchanger can be reduced for a given thermal
duty, so helping to reduce the fouling problem. The distribution of local shear stresses which have
an important impact on fouling rates can also be predicted by CFD simulation. The CFD method for
predicting the average heat transfer coefficient is valuable in providing critical information on the
design of a heat exchanger which comprises tubes fitted with inserts. The CFD and heat transfer
simulation provides a valuable tool in studies of the effect on fouling of the local fluid temperature
near the wall. This is especially the case for tubes fitted with inserts or others with other types of
irregular geometry.
The generic model which has been developed for fouling induction periods now makes it possible
to describe the fouling process from the start of the induction period up to the steady fouling rate
stage using a single and simple mathematical expression. The proposed term t0.5 which is the time to
reach 50% of the maximum surface coverage, θmax, provides a practical measure of the length of the
induction period. Tested on experimental data for crude oil fouling, calcium sulphate fouling and
whey protein fouling, the model quantitatively describes the influence of the surface temperature on
the length of the induction period for various systems. The model also describes in a semi-
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quantitative manner the influence of velocity on the induction time.
2. INTRODUCTION
Fouling concerns the formation of unwanted material on heat transfer surfaces. In the full range of
processing industries, fouling creates a chronic operational problem that compromises energy
recovery and environmental welfare. Problems manifest themselves as loss or reduction in
production, increased energy consumption, increased pressure losses, flow maldistributions, anti-
fouling chemical costs, cleaning costs, and so on (Bott, 1990). Mitigation of the problem is
frequently restricted by inadequate detailed knowledge of the underlying mechanisms (Ishiyama et
al., 2009), even though the basic principles have been understood for some time (Melo et al., 1987).
Fouling can be classified into scaling (crystallization), reaction, corrosion, freezing, sedimentation,
biological, and so on. In many industrial situations, more than one type may occur simultaneously
depending on the fluid being processed and the operating conditions, thereby making each fouling
situation almost certainly unique. This makes the identification of fouling mitigation strategies a
particularly intractable problem. Indeed, it makes modelling for design and operational strategies
even more challenging.
Ever increasing energy costs have led to the pursuit of heat integration approaches in the process
industries in order to recover as much heat as possible from the product streams so as to improve
energy efficiency. Commonly, multi-pass shell and tube heat exchangers are used as heat recovery
units, particularly in oil refineries. Due to the complex nature of crude oils, heat exchangers in oil
refinery crude preheat trains are prone to fouling but the fouling process is slow with a large time
constant. Crude oil fouling is generally believed to be caused by impurities in the crude oil such as
corrosion products, water and salt, the precipitation of insoluble asphaltenes, as well as the thermal
decomposition, or auto-oxidation, of reactive constituents in the oil.
Research using actual plant data is slow, subject to a variety of logistical and operational
requirements which do not lend themselves well to fundamental scientific studies (Crittenden et al.,
1992), and can create difficulties in the interpretation of the thermal data (Takemoto et al., 1999). A
number of laboratory methods have been developed to study liquid phase fouling (Epstein, 1981)
including for crude oils the use of the stirred batch cell (Eaton and Lux, 1984), or the use of a
recycle flow loop with either a tubular cross section (eg Crittenden et al., 2009) or an annular cross
section (eg Watkinson and Wilson, 1997; Bennett et al., 2009). For the current project, fouling
experiments at the University of Bath have been carried out using a batch stirred cell. The cell
design follows closely that of Eaton and Lux (1983, 1984) and was chosen since it offers
extraordinary flexibility. Crude oils or water based fluids can be changed easily, as can the fouling
fluid chemistry (eg by adding asphaltenes, metal salts, etc). Computational fluid dynamics (CFD)
software also allows the thermal and fluid flow characteristics of the complex batch stirred cell
geometry to be predicted and validated (Yang et al., 2009a).
In-tube inserts, such as hiTRAN®, have been shown to be effective in mitigating crude oil fouling
and enhancing heat transfer (Crittenden et al., 1993; Ritchie and Droegemueller, 2008). Increasing
interest in their use in such applications is being shown by the oil industry (Krueger and Pouponnot,
2009) as well as by the water industries (Bott, 2001; Wills et al., 2000). A good review of the
applications and benefits of tube inserts in heat exchangers is provided by Ritchie and
Droegemueller (2008). Nonetheless, the use of inserts creates a challenge in the design of a heat
exchanger, due to the insufficient understanding of the fouling behaviour and the lack of practical
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methods for the estimation of some critical design parameters, the heat transfer coefficient in
particular. Fouling of the heat exchanger depends, amongst other things, on two key operational
parameters, namely the wall shear stress and the surface temperature. The use of inserts, moreover,
raises a challenge in the application of fouling models, namely in the determination of the Reynolds
number and the wall shear stress. Indeed, current fouling models are not capable of taking into
account the complex variation of the surface shear stress along the length of the insert. Whilst the
wall shear stress is easily calculated for bare round tubes using the friction factor approach, this
method cannot be used with hiTRAN® inserts. CFD simulation can offer a possible solution to this
challenge, such that a suitably modified fouling model can then be used to predict the fouling rate
and threshold conditions for tubes with and without inserts fitted. This approach can be further
developed in terms of the equivalent velocity/Re number, which is defined to be the velocity/Re
number in a bare tube that gives the same wall shear stress in a tube of the same internal diameter
fitted with inserts and operating at a different average fluid velocity.
Part of the fouling process is induction, initiation or delay in which no fouling appears to take place.
The subject is poorly understood and poorly modelled. Better knowledge might mean that induction
periods could be extended indefinitely. Accordingly, a generic model of the fouling induction
period has been developed and extended to a variety of fouling systems (Yang et al. 2009). The
model allows the effects of both surface temperature and velocity on the induction time to be
studied and interpreted.
3. EXPERIMENTAL INVESTIGATION
Experimental investigations for both crude oil fouling and calcium sulphate scaling have been
carried out using the batch stirred cell. The effect of surface enhancement has been studied using
wires attached to the otherwise plain heated surface. The effects of the wires on heat transfer and
surface shear stress have been simulated using CFD.
3.1 APPARATUS, MATERIALS AND EXPERIMENTAL METHOD
The general arrangement of the cell is shown in Fig. 1. The cell comprises a pressure vessel made
in-house from a block of 304 stainless steel, together with a top flange. The base of the vessel
houses an upwards pointing test probe heated internally by a cartridge heater, the heat flux from
which is controlled electrically (Fig. 2a). The fluid, crude oil or aqueous solution (≈ 1.0 litre), is
agitated by a downwards facing cylindrical stirrer mounted co-axially with the test probe and driven
by an electric motor via a magnetic drive. External band heaters are incorporated to provide initial
heating to the vessel and its contents. An internal cooling coil uses a non-fouling fluid (Paratherm)
to remove heat at the rate that it is inputted via the cartridge heater during the fouling run. The
vessel is fitted with a pressure relief valve and there is a single thermocouple to measure the fluid
bulk temperature. A wire nest comprising 8 vertical wires of 0.7 mm fabricated by Cal Gavin can be
attached to the probe, allowing the effects of attached wires on turbulence, heat transfer and fouling
to be evaluated. Figure 2b shows this configuration schematically. The actual number of wires used
is not the same as shown in the figure.
The cell can be sparged with various gases, eg oxygen and nitrogen, and the heat transfer surface is
easily inspected and changed. Computational fluid dynamics (CFD) software also allows the
thermal and fluid flow characteristics of the complex batch stirred cell geometry to be predicted and
validated (Yang et al., 2009a). The heated probe surface for the crude oil fouling experiments was
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refinery grade mild steel. In order to evaluate the influence of surface properties on CaSO4 scaling,
three new probes were made using mild steel, copper, and stainless steel.
The properties of the crude oil used in the fouling experiments are listed in Table 1. The aqueous
CaSO4 solution was prepared by weighing 4.10 g Ca(NO3)2 and 8.00 g Na2SO4·10HO2 and
dissolving each salt in 0.5 L of distilled water. Then the two solutions were mixed slowly with
agitation. The solution made in this way contains 3.4 g CaSO4 in 1 L water.
t wb t ws
t bulk
© 2008 University of
Bath, England
t wm
Fil Level
Fig. 1 The batch stirred cell
Fig. 2a Heated test probe Fig. 2b Probe with wire nest
twb, twm, and tws: embedded thermocouples
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Table 1 Properties of the Crude Oil Blend Tested
Crude A
API 27.5
Viscosity (cst) @ 80 oC 15
Viscosity (cst) @ 260 oC 1.74
Total Sulphur (% wt) 2.82
Iron (ppm) 4
Nickel (ppm) 42
Vanadium (ppm) 226
Saturates (%) 28.36
Aromatics (%) 56.87
Resins (%) 6.8
Asphaltenes (%; IP143) 8
CII 0.56
3.2 RESULTS AND DISCUSSION – CRUDE OIL FOULING
In virtually all experiments to date, the fouling resistance has been found to vary linearly with time.
An induction period is usually seen when a well-cleaned probe is used, but not when the surface has
not been cleaned thoroughly. A typical crude oil fouling resistance curve is shown in Fig. 3.
Fig. 3 Typical fouling curve for Crude B
3.2.1 Effect of temperature and velocity on fouling rate – fouling threshold
Keeping the stirrer speed constant, but increasing the initial surface temperature by increasing the
power input to the cartridge heater results, as expected, in a higher fouling rate. Figure 4 shows the
effect of surface temperature on fouling rate for four stirrer speeds.
Previous work (Young et al. 2011) has demonstrated the effect stirred speed, or the wall shear stress
has on the fouling rate. That is, keeping the surface temperature constant but increasing the stirrer
speed results in a lower fouling rate. The effect of surface shear stress on the removal of deposits
has now been studied in a different, and novel, manner. After a significant of fouling has been
accumulated, the stirrer speed is then increased and maintained constant at the elevated value for a
reasonably long period whilst maintaining the other key parameter, namely surface temperature,
constant. Under such circumstances, it becomes possible to observe negative fouling rates, as
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0 1 2 3 4 5 6 7
Time (hour)
Rf
(Km
2/k
W)
Rf = 0.0177 t - 0.0185
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shown for example in Figure 5. The power input to the cartridge heater shown in this figure
confirms that the heating power, and hence heat flux, has been maintained constant.
Fig. 4 Effect of surface temperature on fouling rate
Fig. 5 Negative fouling rate at increased stirrer speed
Figure 6 summarises the new method of obtaining the fouling threshold when the fouling rate is
equal to zero. The locus of surface shear stress and surface temperature at which the fouling rate
becomes zero is obtained easily from Figure 6. The surface shear stress for any given stirrer speed is
obtained by CFD simulation (Yang et al. 2009a). The surface temperature is obtained by
measurement.
Fig. 6 Fouling rate against surface shear stress for various initial surface temperatures
0.00E+00
1.00E-09
2.00E-09
3.00E-09
4.00E-09
5.00E-09
6.00E-09
610 630 650
dR
f/d
t (m
2K
/J)
Ts (K)90 rpm 160 rpm 300 rpm 400 rpm
y = -1.9631E-05x + 4.4701E-05
-0.00018
-0.00014
-0.0001
-0.00006
-0.00002
0.00002
0 2 4 6 8 10
Time (hour)
Rf (m
2K
/W )
100
120
140
160
180
200
220
240
Po
wer
(W)
Fouling Resistance Power
-1.00E-08
-5.00E-09
0.00E+00
5.00E-09
1.00E-08
0 0.5 1 1.5 2
Surface shear stress (Pa)
Fo
uli
ng
ra
te (
m2K
/J)
600 K 610 K 620 K 630 K 640 K 650 K 660 K
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3.2.2 Fouling threshold conditions
The concept of fouling threshold conditions, which was introduced by Ebert and Panchal (1997), is
particularly interesting since if the loci of surface temperature and surface shear stress for which
fouling will not occur can be found, then the fouling problem is, in principle, solved. In practice,
fouling threshold conditions, if identified, may provide a guide to avoid fouling or at least to
minimise the impact of fouling by operating a heat exchanger under the non-fouling conditions.
Normally, the fouling threshold would be determined by extrapolating plots of fouling rate versus
surface temperature (at constant shear stress) back to the point at which no fouling occurs (Panchal
et al., 1997; Knudsen et al., 1997). To obtain reliable threshold data in this way, it is necessary to
carry out a large number of fouling runs, including some tests being run at very low fouling rates to
improve the accuracy of locating the zero fouling conditions. Experiments in which very low
fouling rates need to be studied would, however, be extremely time-consuming. In the present work,
given that negative fouling rates can be observed by judicious choice of operating conditions after a
deposit has been laid down on the surface, it now becomes possible using the new method described
in 3.2.1 to identify the fouling threshold conditions by interpolating the plots of fouling rate –
surface temperature (at constant shear stress) to find the points at which the fouling rate becomes
equal to zero. Figure 6 shows fouling rate plots, both positive and negative, at a series of shear
stress values.
The threshold conditions are easily obtained by interpolating the plots shown in Figure 6 when the
fouling rate equals zero. Figure 7 shows the fouling threshold conditions for the four surface
temperatures for which the fouling rate – surface shear stress curve crosses from being a positive
fouling rate to a negative one: 620K (347°C), 630K (357°C), 640K (367°C), and 650K (377°C).
The shear stress values were obtained by CFD simulation based on the physical properties of the
crude oil, the stirrer speed and the bulk temperature used in the experiments (Yang et al., 2009;
Young et al., 2011). Figure 7 seems to show that the fouling rates, when plotted in this way,
decrease linearly with increasing shear stress. It is also worth noting from Figure 6 that the
gradients of the plots of fouling rate against shear stress seem to be constant regardless of the
surface temperature. As a comparison, results from the new interpolation method have been
compared with those from the more time-consuming extrapolation method (reported previously by
Young et al. (2011)) in which zero fouling rates were obtained by extrapolating fouling rate data
back to zero. The comparison is shown in Figure 7.
Fig. 7 Threshold temperature
◊: this work; ●: previous work (Young et al., 2011)
2 4 0
2 6 0
2 8 0
3 0 0
3 2 0
3 4 0
3 6 0
3 8 0
4 0 0
0 0 .5 1 1.5 2
Shear stress (Pa)
Th
resh
old
tem
pera
ture
(°C
)
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Agreement of the two methods is surprisingly good, bearing in mind the previous method
potentially suffered from inaccuracy as the fouling rate curves were extrapolated back to the origin.
Any differences could be due not only to difficulties in extrapolation but also to the fact that the
crude oil used in this work has been subject to fouling for relatively long periods, and accordingly,
some its properties may have changed slightly.
Although the threshold conditions have been obtained using a batch stirred cell system, it could be
argued that they might not bear close resemblance to the industrial situation. However, to counter
this argument it should be borne in mind that they would have a significant value in understanding
the industrial situation provided that a fouling rate for a particular crude oil was determined solely
by the surface temperature and the surface shear stress. That is, the fouling behaviours should be
similar at the same temperature and under the same shear stress, i.e. at the same equivalent
Reynolds number regardless of the geometries of the surface (Yang et al., 2009a).
3.2.3 Effect of turbulence enhancement on fouling
Fins and/or wire inserts fitted in a flow path may enhance the fluid turbulence, and hence increase
the wall shear stress. This can effectively mitigate fouling. To investigate this effect, a test probe
fitted with the wire nest shown schematically in Figure 2b was used in the crude fouling
experiments. Figure 8 shows a typical fouling curve using this probe.
Fig. 8 Fouling resistance versus time using a wired probe
Test condition: bulk temperature 258°C; surface temperature 399 °C
stirring speed 160 rpm, heat flux 79 kW/m2
The fouling data is seen to be rather scattered. This could be due to irregular removal of the foulant
from the surface under elevated shear stress due to presence of the wires. Table 2 lists the fouling
rates and shows that the fouling rate using a wired probe is lower even at higher temperatures when
compared with that using a bare probe.
3.3 RESULTS AND DISCUSSION – CaSO4 CRYSTALLISATION FOULING
Experiments on calcium sulphate scaling have been included for three reasons. Firstly, the aqueous
solution provides much more certainty in its composition than crude oil. Secondly, experiments are
y = 5.47E-10x - 8.37E-06
-0.000015
-0.00001
-0.000005
0
0.000005
0.00001
0.000015
0 5000 10000 15000
Fo
uli
ng
re
sis
tan
ce
(m
2K
/W)
Time (S)
FP7-SME-2010-1 262205/ INTHEAT
carried out under much milder conditions than those for crude oil. Thirdly, experiments can be
carried out more quickly, so that an understanding of the effects of process parameters, including
enhancement of the heat transfer surface, can be gained more quickly. Fouling experiments were
conducted using both bare and wired probes made of mild steel, copper and stainless steel.
Table 2 Fouling Rate C
Probe
Bare probe
Wired probe
Wired probe
Bulk temperature 258
3.3.1 Mitigation effect of wire attachment
Figure 9 shows the increase in surface
stirring speeds with the calcium sulphate system
directly proportional to the rate of fouling in the batch stirred cel
3, demonstrate that the fouling rate, which is proportio
probe than for the bare probe. However the mitigating effect of the wires seems
significant as for the case of crude oil fouling.
expected, lower at a high stirring speed.
Fig. 9 Surface temperature increase with time due to CaSO
♦: bare probe
▫: wired probe, 130 rpm
Bulk temperature: 55
Table 3 Summary of CaSO
Fouling rate on bare probe
Fouling rate on wired probe
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carried out under much milder conditions than those for crude oil. Thirdly, experiments can be
carried out more quickly, so that an understanding of the effects of process parameters, including
heat transfer surface, can be gained more quickly. Fouling experiments were
conducted using both bare and wired probes made of mild steel, copper and stainless steel.
ouling Rate Comparison for Crude Oil – Bare Probe vs Wired P
Surface temperature
(°C)
383.7
385.5
399.3
Bulk temperature 258 °C; Stirring speed: 160 rpm; Crude A
attachment on fouling
increase in surface temperature with time using bare and wired probes at two
with the calcium sulphate system. The rate of increase in surface temperature is
directly proportional to the rate of fouling in the batch stirred cell. The results,
, demonstrate that the fouling rate, which is proportional to the gradient, is lower for
. However the mitigating effect of the wires seems
significant as for the case of crude oil fouling. The results also show that the fouling rate is, as
high stirring speed.
Fig. 9 Surface temperature increase with time due to CaSO4 fouling
bare probe, 130 rpm; x: bare probe, 300 rpm
wired probe, 130 rpm; +: wire probe, 300 rpm
Bulk temperature: 55 °C; Initial surface temperature: 85 °
Summary of CaSO4 Scaling Rates on Bare and Wired P
Stirred speed 130 rpm Stirred speed 300 rpm
5.2E-5 m2K/kJ 4.
4.1E-5 m2K/kJ 2.9E
Confidential
carried out under much milder conditions than those for crude oil. Thirdly, experiments can be
carried out more quickly, so that an understanding of the effects of process parameters, including
heat transfer surface, can be gained more quickly. Fouling experiments were
conducted using both bare and wired probes made of mild steel, copper and stainless steel.
Bare Probe vs Wired Probe
Fouling rate
(m2K/J)
1.10 x 10-9
Not detected
5.47 x 10-10
°C; Stirring speed: 160 rpm; Crude A
using bare and wired probes at two
The rate of increase in surface temperature is
e results, summarised in Table
nal to the gradient, is lower for the wired
. However the mitigating effect of the wires seems not to be as
show that the fouling rate is, as
fouling
°C
on Bare and Wired Probes
Stirred speed 300 rpm
4.2E-5 m2K/kJ
2.9E-5 m2K/kJ
FP7-SME-2010-1 262205/ INTHEAT
3.3.2 Influence of surface materials
Table 4 summarises the fouling rate data obtained using
stainless steel. The fouling rate on the probe of stainless steel was
mild steel or copper, even at a significantly higher
found to be similar in level for the mild steel and
Table 4 Summary of Fouling Rate Data Obtained Using Probes of Different M
Probe material and initial surface temperature
Mild steel, 78 °Copper 78 °C
Stainless steel, 90
3.3.3 Asymptotic fouling
The increase in fouling resistance
form (Figure 10). This trend can
provided by Kern and Seaton (1959), as shown in Figure 10 in which the solid line is the Kern and
Seaton model.
Fig. 10 Asymptotic scaling
4. CFD SIMULATION AND MODELLING
CFD simulation and modelling stud
software package, Comsol 4.2. The velocity and temperature distribution in the stirred cell
with a wired probe and in a round tube fitted with a hiTRAN insert have both been
Based on the simulation results,
the average heat transfer coefficient between the wall and fluid in a tube fitted with inserts
obtained. The CFD simulation for
(Yang et al. 2009a). The basic equations
manual 2006a), but are briefly described
momentum are in similar forms to
turbulent dynamic viscosity term to the viscosity expression. The equations of the turbulent kinetic
Page 14 of 30
Influence of surface materials
Table 4 summarises the fouling rate data obtained using bare probes made of mild steel
The fouling rate on the probe of stainless steel was significantly lower than on either
a significantly higher surface temperature, whilst fou
in level for the mild steel and copper probes.
Table 4 Summary of Fouling Rate Data Obtained Using Probes of Different M
and initial surface temperature Fouling rate
°C 4.33E
C 5.58E
Stainless steel, 90 °C 8.33E
Bulk temperature: 55 °C
fouling resistance with time for the CaSO4 system tends to follow an
form (Figure 10). This trend can be correlated quite well using the simple and original model
(1959), as shown in Figure 10 in which the solid line is the Kern and
Fig. 10 Asymptotic scaling of CaSO4 in the batch stirred cell
SIMULATION AND MODELLING
CFD simulation and modelling studies on fouling have been conducted using a commercial
The velocity and temperature distribution in the stirred cell
a round tube fitted with a hiTRAN insert have both been
the shear stress distribution over the surface of a wired probe,
the average heat transfer coefficient between the wall and fluid in a tube fitted with inserts
The CFD simulation for the stirred cell with a bare probe can be found
The basic equations for the turbulent flow can be found elsewhere (Comsol
described as follows. The equation of continuity and the equation of
momentum are in similar forms to the normal Navier-Stokes equations but with the addition of the
turbulent dynamic viscosity term to the viscosity expression. The equations of the turbulent kinetic
Confidential
made of mild steel, copper, and
significantly lower than on either
surface temperature, whilst fouling rates were
Table 4 Summary of Fouling Rate Data Obtained Using Probes of Different Materials
Fouling rate (m2K/kJ)
4.33E-6
5.58E-6
8.33E-7
to follow an asymptotic
simple and original model
(1959), as shown in Figure 10 in which the solid line is the Kern and
in the batch stirred cell
conducted using a commercial
The velocity and temperature distribution in the stirred cell fitted
a round tube fitted with a hiTRAN insert have both been simulated.
he shear stress distribution over the surface of a wired probe, and
the average heat transfer coefficient between the wall and fluid in a tube fitted with inserts, can be
can be found in previous work
for the turbulent flow can be found elsewhere (Comsol
The equation of continuity and the equation of
Stokes equations but with the addition of the
turbulent dynamic viscosity term to the viscosity expression. The equations of the turbulent kinetic
Page 15 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
energy (k) and the dissipation rate of turbulent energy (ε) are as follows (Comsol, 2006; Wilcox,
2000):
( ) ( )[ ] ρεησ
ηηρ
ρ−∇+∇+
∇
+⋅∇=∇⋅+
∂
∂ 2T
T
k
T uukkut
k (1)
( ) ( )[ ]k
CuukCCut
TT
2
2
2
1
ερρε
σ
ηηερ
ερεµε
ε
−∇+∇+
∇
+⋅∇=∇⋅+
∂
∂ (2)
Here, ηT = ρCµk2/ε is the turbulent dynamic viscosity. Values of the k-ε model parameters are given
in the literature (Comsol 2006). For the heat transfer equations, the turbulence results in an effective
thermal conductivity keff (Comsol, 2006):
keff = ko + kT (3)
kT = CpηT (4)
4.1 CFD SIMULATION OF FLOW IN THE STIRRED CELL WITH A WIRED PROBE
The CFD model geometry is set to be three dimensional. The properties of Crude A have been
given in Table 1, and more details, such as density and viscosity can be found in Yang et al.
(2009a). For the CaSO4 – water system, given the low salt concentration, the physical properties for
water built into the Comsol material library can be used directly.
4.1.1 Effect of shear stress
Figure 11 shows the velocity field for the flow of Crude A in the batch stirred cell fitted with the
wired probe.
Fig. 11 Velocity field in the stirred cell with a wired probe
Fluid: Crude A; Stirrer speed: 200 rpm
Bulk temperature: 523 K
FP7-SME-2010-1 262205/ INTHEAT
Figure 12 shows the shear stress distribution over the probe surface around a circle, 0
middle height of the probe. It is see
probe due to the interference to the flow by the wires.
probe are also shown in this figure.
is higher than that over the bare probe. This helps to explain
given previously in Tables 2 and
Fig 12 Comparison of shear stress over th
Fluid: Crude A; Stirrer speed: 200 rpm
Figure 13 shows the vertical distribution of shear stress in front
probe surface. Given the clockwise flow
than behind it. This may suggest that fouling is more likely behind the wire. A photo
probe after a fouling test confirms this prediction
Figure 13 Vertical distribution
Left: Diagram of appropriate
Red point – wire location; B
Right:
Page 16 of 30
shows the shear stress distribution over the probe surface around a circle, 0
It is seen that the shear stress varies in a periodical manner around
probe due to the interference to the flow by the wires. For comparison, shear str
lso shown in this figure. It can be seen clearly that the shear stress over the
t over the bare probe. This helps to explain the comparative
3 for crude oil and the calcium sulphate solution, respectively.
Comparison of shear stress over the probe surface – around a circle (0
Fluid: Crude A; Stirrer speed: 200 rpm
Bulk temperature: 523 K
shows the vertical distribution of shear stress in front of and behind the wire
. Given the clockwise flowing direction, the shear stress is higher in front of th
. This may suggest that fouling is more likely behind the wire. A photo
confirms this prediction (Figure 14).
distribution of shear stress in front of and behind the wire
Left: Diagram of appropriate locations around the probe
wire location; Blue points – positions where shear stress values are calculated
Arrow: flow direction
Right: Vertical distribution of the shear stress
Confidential
shows the shear stress distribution over the probe surface around a circle, 0 - 2π, at the
periodical manner around the
For comparison, shear stress data for a bare
that the shear stress over the wired probe
comparative fouling rate results
3 for crude oil and the calcium sulphate solution, respectively.
around a circle (0 - 2 π)
and behind the wire over the
tion, the shear stress is higher in front of the wire
. This may suggest that fouling is more likely behind the wire. A photograph of the
and behind the wire
locations around the probe
shear stress values are calculated;
Page 17 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
Fig. 14 Photograph of the probe after CaSO4 fouling test
Fluid flows clockwise when viewed from the top
4.1.2 Effect of temperature
Figure 15 shows the temperature field of the CaSO4 – water fluid in the stirred cell with the wired
probe. Figure 16 shows vertical distributions of the temperature over the positions where the
thermocouples are located, and over the probe surface. The temperature readings given by the
thermocouples were in good agreement with those obtained by the CFD model simulation. This can
be regarded as a good validation of the model. The fouling layer thickness on the bare probe was
measured using a Proscan 2000 machine (Yang et al. 2009a). Figure 17 shows the fouling layer
thickness profile. It can be seen that the fouling layer thickness profile over the probe surface is
strikingly similar in form to the temperature profile shown in figure 16, with their maximum
occurring near to the middle of the heated probe surface.
Fig. 15 Temperature field of CaSO4 fluid in the stirred cell with a wired probe
Bulk temperature 55°C; Average heat flux from the probe surface: 31 kW/m2
Stirrer speed: 130 rpm
FP7-SME-2010-1 262205/ INTHEAT
Figure 1
Blue line: actual probe surface temperature
line where the thermocouples are
thermocouple twm; ♦: temperature reading by
temperature: 55°C; Average heat flux: 31 kW/m
Fig. 17 Fouling layer
The shear stress over the bare probe surface where the fouling zone is located was relatively
constant, as illustrated in Fig. 12
temperature. Accordingly, the similarity of the temperature and the fouling layer thickness profiles
provide a qualitative explanation for
4.2 CFD SIMULATION FOR HEAT TRANSFER
The CFD simulation was focused on
results of the velocity field and the shear stress distribution have been
Crittenden 2011).
4.2.1 Temperature field in tube fitted with insert
The hiTRAN®
inserts comprise a series of loops equally spaced with a helical pattern and
periodical pattern in the axial dimension. For CFD
round loops whose diameter and thickness are set to be the same as for the actual insert.
300
310
320
330
340
350
360
0
Tem
pera
ture
(K
)
Vertical position from the probe shoulder
Page 18 of 30
Figure 16 Vertical distribution of temperature
probe surface temperature (by simulation); Red line: temperature over the vertical
are located in the probe (by simulation); ■: temperature reading by
: temperature reading by thermocouple twb. Stirrer speed:
temperature: 55°C; Average heat flux: 31 kW/m2
Fouling layer thickness profile obtained using Proscan 2000
he shear stress over the bare probe surface where the fouling zone is located was relatively
Fig. 12. Hence the fouling behaviour is solely determined by the surface
temperature. Accordingly, the similarity of the temperature and the fouling layer thickness profiles
explanation for the fouling behaviour in the experiment.
HEAT TRANSFER IN TUBE FITTED WITH
FD simulation was focused on heat transfer in tubes fitted with hiTRAN
the shear stress distribution have been reported elsewhe
Temperature field in tube fitted with insert
inserts comprise a series of loops equally spaced with a helical pattern and
periodical pattern in the axial dimension. For CFD simulation, the inserts are represented by closed
round loops whose diameter and thickness are set to be the same as for the actual insert.
0.02 0.04 0.06 0.08Vertical position from the probe shoulder
(m)
Confidential
; Red line: temperature over the vertical
: temperature reading by
speed: 130 rpm; Bulk
obtained using Proscan 2000
he shear stress over the bare probe surface where the fouling zone is located was relatively
. Hence the fouling behaviour is solely determined by the surface
temperature. Accordingly, the similarity of the temperature and the fouling layer thickness profiles
AN INSERT
hiTRAN inserts, whilst the
reported elsewhere (Yang and
inserts comprise a series of loops equally spaced with a helical pattern and a
, the inserts are represented by closed
round loops whose diameter and thickness are set to be the same as for the actual insert. The model
FP7-SME-2010-1 262205/ INTHEAT
tube is divided into three sections, namely pre
sections as shown in Figure 17. The boundary conditions for all walls of the solid domains/metal
phases in the pre- and post- insert sections are set to be as for thermal insulation. The outer wall in
the insert section is set to be at constant temperature (250°C or 5
thermal wall function. This arrangement would simplify the calculation of the average heat transfer
coefficient using the temperature distributions obtained from the simulation, which will be
described later. Figure 18 shows the resulting temperature field.
Fig. 17 Division of the tube length for simulation purposes
Fig. 18 Temperature field in tube fitted with inserts
inlet linear velocity: 1m/s; bulk temperature: 423K
It is notable that the fluid temperature is higher at the location just behind the wire loop, where the
shear stress is lower according to Yang and Crittenden (2011).
temperature and the film temperature (which is simply an
have both been used in previous fouling research investigations. Nonetheless, little attention has
actually been paid to the effect of the local fluid temperature near to the wall. This local fluid
temperature near to the wall may play an important role in the crude oil fouling process, as it can
have a significant influence on the phase
believed to be a key aspect of the crude oil fouling process (Macchietto e
no experimental results are available to demonstrate the effect of fluid temperature near
on fouling either in the case of bare round tubes or
It is interesting to plot the local surf
Pre-insert section.
Thermal insulation
-0.02 m 0.0 m
Page 19 of 30
tube is divided into three sections, namely pre-insert (insulated), insert, and post
shown in Figure 17. The boundary conditions for all walls of the solid domains/metal
insert sections are set to be as for thermal insulation. The outer wall in
the insert section is set to be at constant temperature (250°C or 523K), and the inner wall
This arrangement would simplify the calculation of the average heat transfer
coefficient using the temperature distributions obtained from the simulation, which will be
s the resulting temperature field.
Fig. 17 Division of the tube length for simulation purposes
Temperature field in tube fitted with inserts
inlet linear velocity: 1m/s; bulk temperature: 423K
It is notable that the fluid temperature is higher at the location just behind the wire loop, where the
shear stress is lower according to Yang and Crittenden (2011). The effects of both wall surface
temperature and the film temperature (which is simply an average of wall and bulk temperatures)
have both been used in previous fouling research investigations. Nonetheless, little attention has
actually been paid to the effect of the local fluid temperature near to the wall. This local fluid
wall may play an important role in the crude oil fouling process, as it can
have a significant influence on the phase behaviour of asphaltenes present in the oil, a phenomenon
believed to be a key aspect of the crude oil fouling process (Macchietto et al.,
no experimental results are available to demonstrate the effect of fluid temperature near
on fouling either in the case of bare round tubes or the tubes fitted with inserts.
It is interesting to plot the local surface temperature over the wall as a function of the local shear
Horizontal slice
Vertical slice
Temperature scale (K)
Insert section, Surface
temperature Ts Post-insert section. Thermal
insulation
0.0 m 0.033 m 0.08 m
Confidential
insert (insulated), insert, and post-insert (insulated)
shown in Figure 17. The boundary conditions for all walls of the solid domains/metal
insert sections are set to be as for thermal insulation. The outer wall in
23K), and the inner wall to be a
This arrangement would simplify the calculation of the average heat transfer
coefficient using the temperature distributions obtained from the simulation, which will be
Fig. 17 Division of the tube length for simulation purposes
It is notable that the fluid temperature is higher at the location just behind the wire loop, where the
The effects of both wall surface
average of wall and bulk temperatures)
have both been used in previous fouling research investigations. Nonetheless, little attention has
actually been paid to the effect of the local fluid temperature near to the wall. This local fluid
wall may play an important role in the crude oil fouling process, as it can
present in the oil, a phenomenon
, 2011). Unfortunately,
no experimental results are available to demonstrate the effect of fluid temperature near to the wall
tubes fitted with inserts.
ace temperature over the wall as a function of the local shear
insert section. Thermal
0.08 m
Page 20 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
stress, and to compare this plot with the fouling threshold conditions reported elsewhere by Yang
and Crittenden (2011). As seen in Figure 19, the local conditions of surface temperature and surface
shear stress fall in the fouling zone for operation at an outer wall temperature of 523K and an
average inlet velocity of 1 m/s. In contrast, the local conditions fall within the non-fouling zone for
the same outer wall temperature but at the higher average velocity of 3.6 m/s. These results are
confirmed by the experimental results (Phillips, 1999) in which fouling did occur at this surface
temperature with an average velocity of 1 m/s for the tube fitted with a mid-density insert. The
experimental results also showed that fouling occurred for the bare tube at this temperature and an
average velocity of 3.6 m/s, though no experimental results were obtained under these conditions
for the tube fitted with the insert. These results indicate that the simulation is indeed able to help in
identifying the appropriate operational conditions to eliminate or reduce fouling by taking into
account the actual local conditions.
Fig. 19 Plot of local surface temperature against local shear stress in the plane of fouling threshold
conditions
♦: inlet velocity 1 m/s; ●: inlet velocity 3.6 m/s
Inlet/Bulk temperature: 423K
Outer wall temperature: 523K
■: threshold conditions (Yang and Crittenden, 2011) converted to shear stress from equivalent
velocity
4.2.2 Average heat transfer coefficient
A simple method has been developed to calculate the heat transfer coefficient based on the
temperature distribution. Assuming a small portion of fluid in an annulus of diameter r, thickness
∆r, and unit height passes a distance L from the bottom to the top as shown in Figure 20, the
amount heat gained by this fluid portion is given by:
)(2 brtrp TTrrcq −∆=∆ πρυ (5)
In this equation Ttr and Tbr are the temperatures at the top (radius r) and bottom (radius r),
respectively, and υ is the linear velocity. The total heat obtained by the fluid contained in a cylinder
of radius R and unit height is therefore given by:
400
450
500
550
600
0 20 40 60
Shear stress (Pa)
Su
rface t
em
pera
ture
(K
)
Page 21 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
∫ −=R
brtrp drTTrcq0
)(2πρυ (6)
Fig. 20 Diagram for calculation of an average heat transfer coefficient
In practice, the calculation is conducted by numerical integration, given that Ttr and Tbr are results
obtained from the model simulation. The heat transfer coefficient can then be calculated as follows:
)(2 bs TTRL
qh
−=
π (7)
Here Ts and Tb are the temperatures at the surface and in the bulk fluid, respectively, which are
assumed to be constant. Figure 21a shows that the temperature distribution over the radius near the
left hand end, that is in the pre-insert section at z = -0.02m, is essentially constant, as expected.
Figure 21b shows the temperature distribution for the same average inlet velocity over the radius
near the right hand end of the insert section, that is at z = 0.08m. It should be noted that at this
location the temperature distribution is almost axially symmetric, with a smooth profile across the
radius, with only 1.6 K difference from the centre to wall.
Table 5 shows a comparison of the average heat transfer coefficients obtained (i) by simulation, (ii)
from the Dittus-Boelter correlation, and (iii) from experiments. The method for calculation of the
heat transfer coefficient based on the experimental measurements of the inlet and outlet
temperatures can be found elsewhere (Phillips, 1999). The Table reveals that the simulated values
of the heat transfer coefficient are in broad agreement with the experimental values. The increase in
∆rr
L
Fig. 21a Temperature distribution over radius in
the pre-insert section (z = -0.02 m)
Outer wall temperature at insert section: 523K
Fig. 21b Temperature distribution over radius near
the end of the post-insert section (z = 0.08 m)
Outer wall temperature at insert section: 523K
Page 22 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
the heat transfer coefficient when an insert is used means that the temperature in the shell side of an
exchanger can be reduced for a given thermal duty, so helping to reduce the fouling potential.
Table 5 Average heat transfer coefficient (W/m2K)
Velocity
(m/s)
h
bare tube
simulation
h
Bare tube
Dittus-Boelter
method
h
Experimental
value
(Phillips
1999)
h
Tube with insert
experimental value
Phillips (1999)
h
Tube with insert
by CFD simulation
0.5 443 391 490 1460 1644
1.0 826 682 780 2150 2292
2.0 1365 1186 1280 3460 3768
4.3 RESEARCH ON FOULING MODELS
4.3.1 Fouling rate and fouling thresholds
The fouling rate in a given heat exchanger is determined by the operational parameters, namely,
velocity and surface temperature. Most established models are for fouling in the tube-and-shell type
heat exchangers, in which the velocity and Reynolds number are well defined. These models are,
accordingly, not straightforward to use in heat exchangers with complicated configurations, for
instance in tubes fitted with inserts or for plate heat exchangers. To extend the application scope of
these fouling models, the concept of equivalent velocity or equivalent Reynolds number has been
introduced (Yang et al. 2009a, Yang and Crittenden 2011). It is defined to be the velocity/Re
number in a bare tube that gives the same wall shear stress in a tube of the same internal diameter
fitted with inserts and operating at a different average fluid velocity. The shear stress and velocity
data can be obtained from the CFD simulation or from empirical correlations, as has been carried
out for plate heat exchangers by INTHEAT project partner SODRU.
A modified version of Yeap’s model (Yeap et al. 2004) has been used to correlate the fouling rate
data of Maya crude oil (Yang and Crittenden 2011):
8.0
3/23/13/123
3/43/23/2
)/exp(1uC
RTETCuB
TuCA
dt
dR
ssf
sff−
+=
−−
−
µρ
µρ (8)
This model, initially developed for crude oil fouling, is capable of taking into account the effects of
both mass transport and chemical reaction in fouling (Yeap et al. 2004), but at the expense of a little
complication. This model has successfully been applied to predict fouling of other fluids in plate
heat exchangers by SODRU. The original Ebert and Panchal (1997) model, shown in equation (9)
has also been used to fit the fouling rate data including both the positive and negative rates shown in
Figure 6 in section 3.2.1:
γτα β −=−
f
A
RT
E
feRe
dt
dR (9)
Page 23 of 30
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Figure 22 shows that the quality of the model fit is reasonably good. Departing from the practice in
Ebert and Panchal, the surface temperature was used in the present study rather than the film
temperature Tf. Also, as explained earlier in this report, the equivalent Reynolds number (Young et
al., 2011), was used in the model. The parameter γ was obtained from the gradient of the plots of
fouling rate versus shear stress shown in Figure 6. It should be recalled that all the gradients can be
considered to be the same and the value was found to be 3.85 m2K/JPa. The remaining parameters
in the Ebert and Panchal model were then obtained by curve fitting. The parameter values that gave
the best fittings were 1190 m2K/J, -0.88 (non-dimensional), and 98.4kJ/mol for α, β, and EA,
respectively. The predictions correspond well with the experimental threshold values, as shown in
Figure 23.
Fig. 22 Comparison of the experimental data and the model fit for the fouling rate
Fig. 23 Comparison of the threshold conditions between the model prediction and experimental
result
▲: experimental result; ■: model prediction
It should be noted that whilst the fouling rate data can be correlated reasonably well by the Ebert
and Panchal model, this model is not necessarily the sole or unique one that is able to interpret the
observed fouling behaviour. Indeed, the experimental fouling rate data can be correlated just as
successfully using other models, such as the modified Yeap model (Yang and Crittenden 2011),
-1.20E-08
-6.00E-09
0.00E+00
6.00E-09
1.20E-08
-1.2E-08 -6.0E-09 0.0E+00 6.0E-09 1.2E-08
Fouling rate - experimental (m2K/J)
Fo
ulin
g r
ate
- m
od
el fi
ttin
g (
m2K
/J)
500
550
600
650
700
0 0.5 1 1.5 2
Shear stress (Pa)
Th
res
ho
ld t
em
pe
ratu
re (
K)
Page 24 of 30
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though details of these models’ fit are not provided. Given its simplicity, a model of this type with
the parameters generated was passed onto the project partner at the University of Manchester.
4.3.2 Compensation plot
It had been initially thought that the compensation plot might provide an opportunity to create a
single modeling method to account for all crude oil fouling (Young et al., 2011), and to account for
all calcium sulphate scaling. Both these types of fouling show strong dependencies on both surface
temperature and fluid velocity (shear stress). The compensation plot stems from the Arrhenius plot
which is the linear relationship between the logarithm of the fouling rate and the reciprocal of the
absolute temperature. Whilst good Arrhenius plots are indeed found in both crude oil fouling and
calcium sulphate scaling, the slopes of the plots are seen to be dependent upon velocity or Reynolds
number. Hence, the apparent activation energy seems to increase with the degree of turbulence.
The compensation plot is a graph of the logarithm of the pre-exponential factor against the apparent
activation energy. Because the compensation plots show very high correlation coefficients it has
always been suspected that the effects for both crude oil fouling and calcium sulphate fouling have
been “false” rather than “true”. Indeed, a recent paper presented at the 2011 Heat Exchanger
Fouling and Cleaning Conference, presented an elegant mathematical reasoning to suggest the
falseness of the compensation plot in fouling applications.
4.3.3 Modeling of fouling induction periods
A mathematical model to correlate fouling resistance data in both the induction period and the
process thereafter was presented at the International Conference on Heat Exchanger Fouling and
Cleaning 2009 (Yang et al. 2009b), and has been further developed since then by the team at the
University of Bath.
Fouling on a heat exchanger surface may be described in the following manner. Firstly, in the
induction period, the active fouling species adhere to the heat transfer surface and gradually cover it
from a fractional coverage of θ = 0 to total coverage at θ = 1. This pre-conditioning layer is very
thin, though not necessarily a single molecular layer and so the increase in fouling resistance Rf is
negligible. Changes in surface roughness are ignored. Secondly, in the fouling period the fouling
layer may start to grow immediately on the covered/pre-conditioned surface when it may be
assumed that the growth rate is proportional to θ. The overall rate of fouling resistance growth can
therefore be expressed as:
′= f
fR
dt
dRθ (10)
Here, Rf′ can be any form of established fouling rate expression, such as those proposed by
Crittenden et al. (1987a and 1987b), Epstein (1994), Ebert and Panchal (1997), etc. These models
describe the fouling rate in a near linear form. In the early stage of surface pre-conditioning, active
species can be captured and adhered to the surface. The following relationship may then apply:
)1( θθ
−∝dt
d (11)
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Meanwhile, the particles that stick to the surface act as seeds, attracting more foulant around them,
such that fouling proceeds in a micro-growth manner. The growth rate is assumed to be first order
in fractional surface coverage θ:
θθ
∝dt
d (12)
Combining the two aspects gives the coverage growth rate as follows:
Growth rate = k1θ(1-θ) (13)
Adopting the concept of removal or release from the surface as in adsorption science, the removal
rate of the surface coverage is assumed to be proportional to the surface coverage. That is:
Removal rate = k2θ (14)
Combining Eqs. (4) and (5) yields the net growth rate:
θθθθ
21 )1( kkdt
d−−= (15)
Integrating Eq. (15) gives:
tkkeck
kk)(
1
21
211
1−−+
−=θ (16)
Given the growth of θ reaching its maximum at 0.5 θmax, the time, t0.5 at which θ reaching 0.5θmax is
defined as the induction time. According to Eq. 16, t0.5 is given by:
21
5.0
ln
kk
ct
−= (17)
In cases of significant fouling, i.e. k1>>k2, the value of k2 in Eq. (17) may be negligible, and k1 is a
lumped growth rate constant which may be assumed to depend on the surface temperature
according to the Arrhenius equation:
RTE
iieAk/
1
−= (18)
Taking logarithms of Eq. (17) gives the temperature dependency of the induction period:
RT
EAct i
i
−−−= ln)ln(lnln 5.0
(19)
It was demonstrated that this model is capable of interpreting the effect of temperature on induction
time for both crude oil and protein fouling (Yang et al. 2009b). Further development of the model
Page 26 of 30
FP7-SME-2010-1 262205/ INTHEAT Confidential
allowed the effect of velocity to be predicted. Adopting the concept given by Polley et al. (2007)
and Yeap et al. (2004), the removal term is proportional to the 0.8 power of velocity, and hence the
removal parameter k2 in the induction period model may be expressed as follows:
8.0
2 uk γ= (20)
Figures 24 and 25 shows the model fittings of the experimental data by Mwaba et al. (2006), and by
Geddert et al. (2009), respectively, revealing that good fits for the fouling curves can be obtained.
Table 6 summarises the model parameters for the data of Geddert et al. (2009), and shows that the
predicted induction times match those observed experimentally quite well.
Table 6 Model Parameters for Fitting of the Data of Geddert et al. (2009)
Coating Re
k1
(1/hour)
k2
(1/hour)
γ
c
t0.5 (hour)
observed
t0..5 (hour)
model
No coating 1030 2.57 0.33 0.0013 1400 3 3.2
No coating 3010 2.57 0.79 0.0013 1400 4 4.1
SICON 1030 0.66 0.196 7.61E-4 251000 23 26
SICON 3010 0.66 0.462 7.61E-4 251000 65 63
Fig. 24 Effect of velocity - model fittings for the data of Mwaba et al. (2006)
From left to right: 0.3 m/s, 0.6 m/s, 1.0 m/s
Symbols: Mwaba experimental data; Lines: model fittings
Fig. 25 Model fittings for the data of Geddert et al. (2009)
From left to right: Stainless steel Re 1030, Re 3010, SICON coating Re 1030, Re3010
Symbols: Geddert et al. data; Lines: model fittings
0
2
4
6
8
10
12
14
0 2000 4000 6000
Time (min)
Fo
ulin
g r
ate
(x10
-4 m
2K
/W)
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 20 40 60 80 100
Time (hour)
Fo
ulin
g r
ate
(*1
0-4
m2K
/W)
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5. CONCLUSION
Fouling is fundamentally a complex phenomenon and a broad range of basic fouling mechanisms
exist, and hence a range of experimental technologies need to be developed for the investigation of
fouling and its mitigation. At Bath, fouling experiments have been carried out over a wide range of
conditions using a batch stirred cell system. Negative fouling rates are observable if the surface
temperature is reduced and/or the stirring speed is increased after the test surface has undergone a
significant amount of fouling, i.e. the fouling resistance has increased to a significant level. The
fouling rate data for both positive and negative fouling rates can then be utilized to identify the
fouling threshold conditions relatively quickly.
It has been demonstrated that CaSO4 crystallisation fouling can be investigated using the stirred cell
system. The results of both crude oil and calcium sulphate fouling have been successfully
interpreted by CFD simulation, including the effects of shear stress and surface temperature on
fouling rates.
With the help of CFD simulation, the concept of equivalent velocity / equivalent Reynolds number
is developed such that a fouling model developed for bare round tubes can be extended for use with
more complex geometries. It has been demonstrated, for example, that the Ebert and Panchal model
(1997) and the Yeap model (Yeap et al. 2004; Yang and Crittenden 2011) can both be adapted
successfully to correlate the fouling data of a crude oil obtained using the batch stirred cell.
Recently this approach has been adopted for modelling fouling in plate heat exchangers by
INTHEAT partner SODRU. Fouling threshold conditions can be predicted successfully, auguring
well for the development of successful strategies to mitigate the highly energy consuming fouling
problem.
CFD simulation has confirmed that the average heat transfer coefficient for a tube fitted with a
hiTRAN insert is much higher than the bare tube operated under the same conditions of surface wall
temperature and average velocity. The CFD simulation can be used to help determine the optimum
design of insert for a particular application, whether fouling or non-fouling. The increase in the heat
transfer coefficient when an insert is used means that the temperature in the shell side of an
exchanger can be reduced for a given thermal duty, so helping to reduce the fouling potential.
The model for fouling induction makes it possible to describe the fouling process from the start of
the induction period up to the steady fouling rate stage using a single and simple mathematical
expression. The induction period model has been demonstrated with applications in crude oil
fouling, calcium sulphate fouling and whey protein fouling. The model is able to describe
quantitatively the influence of surface temperature on the length of the induction period for the
crude oil and whey protein fouling systems, and to describe the influence of velocity on the
induction time in a semi-quantitative manner. The proposed term t0.5 which is the time to reach 50%
of the maximum surface coverage, θmax, provides a practical measure of the length of the induction
period.
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