Value pricing of surface coatings for mitigating heat exchanger fouling
L. Gomes da Cruz1,2, E.M. Ishiyama3, C. Boxler4, W. Augustin4, S. Scholl4 and D.I. Wilson1,*
1
Department of Chemical Engineering & Biotechnology, University of Cambridge, New
Museums Site, Pembroke Street, Cambridge CB2 3RA, UK
2
Department of Chemical Engineering, Polytechnic School, University of São Paulo, Av.
Prof. Luciano Gualberto, 380, trav. 3, 05508-010, São Paulo, SP, Brazil
3
IHS Downstream Research, 133 Houndsditch, London EC3A 7BX, UK
4
Institute for Chemical and Thermal Engineering, Technische Universität Braunschweig,
Langer Kamp 7, 38106 Braunschweig D, Germany
*Corresponding author: diw11@cam.ac.uk
ABSTRACT
Surface modification has been proposed as an attractive mitigation strategy for combatting heat
exchanger fouling in the food industry and other sectors. Antifouling coatings manipulate the
interactions between the surface and fouling precursors or fouling deposit to either extend the
induction period before appreciable fouling starts and/or reduce the rate of deposition. A
successful surface treatment should extend the time between cleaning operations, thereby
reducing the operating cost of the system. A modified exchanger will, however, incur
additional capital costs for replacement and this needs to be compared to the anticipated savings
during operation. This paper considers the economic attractiveness of replacing existing
exchangers by units with modified surfaces in a retrofit. Three cases are considered, which are
modelled using fouling rates taken from studies in the literature. Antifouling performance is
expressed in terms of (i) extended induction period before fouling starts, and/or (ii) reduced
fouling rate. The annualised total cost (operating + annualised capital spend) is mapped for
different combinations of these parameters to establish the economically favourable region for
a coating at different coating prices. This allows the value pricing margin to be identified,
where the expected benefits have to be split between the cost of the coating and the benefit to
the manufacturer and operator. The case studies are (a) DLC-related surface modification to
reduce aqueous crystallization fouling; (b) fluorocarbon-based coatings which offer antifouling
performance but can reduce heat transfer, for crystallization fouling; and (c) fluorocarbonbased coatings in a dairy pasteurizer application. A novel strategy, of replacing stainless steel
with fluorocarbon coated carbon steel, is also considered for case (b).
Key words: heat exchanger, fouling mitigation, cleaning, coating, techno-economic analysis
1
1. Introduction
Fouling is a widespread problem in process heat transfer systems and necessitates regular cleaning
and/or costly mitigation measures. It is a challenge for sustainable manufacturing as it incurs additional
equipment, energy, treatment chemicals and downtime with associated costs as well as increasing the
environmental impact of the process. Fouling can be mitigated (see Müller-Steinhagen et al., 2011) by
modifying the process streams (e.g. softening hard water), manipulating process conditions (e.g.
temperatures and flow rates/shear stresses, using alternative apparatus such as fluidised bed heat
exchangers), and by modifying the heat transfer surface to reduce (or eliminate) fouling and/or enhance
cleaning. The latter strategy, which may be labelled as the search for the ‘Holy Grail’ or antifouling
surface, has attracted a considerable amount of research effort in recent years (Santos et al., 2013).
Coating a surface to reduce fouling or other deposition processes involves modifying the interaction
between the surface and the process fluid and thus the attachment, adhesion, retention and removal of
depositing species. These interactions determine the strength of adhesion of any fouling layer and the
cleanability of the surface. An ideal coating would prolong the fouling induction period, improving the
plant operating efficiency. If deposition did occur, it would also require less effort for cleaning (lower
concentration and temperature of cleaning solutions, shorter cleaning times), increasing the plant
productivity and reducing the consumption of natural resources.
Coatings
There is a wide variety of processes available for coating metal substrates, including electrochemical
deposition, thermal spraying, contact welding, plating, ion implantation or sputtering, physical and/or
chemical vapour deposition, and hybrid methods. These differ in the deposition options (e.g. coating
devices, coating species and precursors, coating rate), film properties (tribological and energetic
properties, thickness and surface topography) and cost (equipment purchase and maintenance price,
power consumption, space and personnel requirements).
The choice of coating material and method will depend on the nature of the surface to be coated as well
as the nature of the species causing fouling. Tables 1 and 2 summarise the results of recent experimental
studies on the effect of surface coatings on heat exchanger fouling in water scaling and milk-related
liquids, respectively. These tables do not provide a comprehensive account of each study, as their
purpose is to illustrate the breadth of types of coating tested, the range of fouling fluids (usually
solutions), and the variety of outcomes. Details such as the method of manufacture, mode of heat
transfer, and testing conditions can all be found in the original paper(s). The studies vary in terms of
characterisation of the coatings (e.g. roughness, surface energy, thickness and uniformity), so
comparing coatings is not always straightforward. A recent review of the effectiveness of different
antifouling coatings has been published by Banerjee et al. (2011).
2
Some of the contradictory results in Tables 1 and 2 can be attributed to the diversity in experimental
conditions, differences in methods for preparing coatings, composition of fouling solutions and
monitoring/analytical methods. It is noteworthy that many workers have reported surface coatings to
have a stronger effect on cleaning than on fouling. This indicates that assessments of surface coating
performance should consider their contribution to the whole fouling-cleaning cycle.
Coatings in practice
A key aspect of surface coatings is the durability, stability and cost effectiveness of the coating over
repeated operating (fouling and cleaning) cycles. Al-Janabi et al. (2010), Bani Kananeh et al. (2010)
and Mauermann et al., (2009) reported that the coatings studied were not suited for the continuous
thermal and mechanical stress which would be experienced during extended operation. This aspect is
not addressed in many studies. Some, such as Barish and Goddard (2013), have reported the coating
performance over several fouling and cleaning cycles. If the coating loses integrity, this limits the asset
lifetime and this will be shown to determine the economic attractiveness of this mitigation option.
In order to be acceptable for process applications, antifouling surfaces – whether imparted by coatings
or new materials of fabrication – have to function effectively under normal process conditions as well
as other ancillary scenarios (such as cleaning, sanitisation, processing different products), consistently
over the lifetime of the unit. There has been considerable interest in their application in the food and
drinking water sectors, as the ability to modify the feedstock, flow rates and temperatures are limited
as these may be set by separate criteria such as consumer/legal requirements or pasteurisation kinetics.
Furthermore, the substances being processed are usually low margin products so there is limited scope
for capital to replace existing equipment.
The dairy sector is an important example in the food manufacturing area where fouling and cleaning
present significant challenges for manufacturing and need to be addressed to improve the sustainability
of milk processing operations (Xu and Flapper 2009; Carbon Trust, 2011). Plate heat exchangers (PHX)
are standard items for pasteurisation and high temperature sterilisation applications: these units are often
subject to acute fouling and require cleaning on a daily basis. Additional energy is needed to counter
heat transfer inefficiencies caused by fouling, and to heat cleaning solutions. The latter requires volumes
of clean water and cleaning chemicals, the treatment of which adds to the environmental impact burden
of the plant (Guignard et al., 2009).
This has prompted the investigation of surface coatings and antifouling treatments for stainless steel
PHX plates since the mid 1980s, and Table 2 summarises some of the key studies in this area related to
dairy processing. The EU-funded MODSTEEL project (Beuf et al., 2004; Rosmaninho et al., 2008;
Santos et al., 2006) considered a range of coating methods for stainless steel PHX plates and reported
mixed results for fouling performance but noticeable reductions in cleaning time. A noticeable feature
3
of recent studies is the extended testing of surface coatings over several fouling and cleaning cycles
(e.g. Barish and Goddard, 2014), replicating standard practice in membrane research (e.g. Weis and
Bird, 2001) where it is recognised that surfaces age noticeably over the first few operating cycles.
4
The innovation gap
Antifouling coatings, like other inventions, must cross the ‘innovation gap’ in order to become adopted
in manufacturing practice. The new coating (or replacement material) must demonstrate a suitably large
advantage in performance, and incremental return on investment, in order to justify the capital
expenditure and risk associated with its implementation. This requires a techno-economic analysis of
the process subject to fouling and cleaning before and after implementation, which has not, to the
authors’ knowledge, been considered by researchers in this area. This is particularly important for
coatings based on fluorocarbons as the coating introduces an extra insulating layer into the heat transfer
considerations, so that more PHX plates are needed for a given heat duty. These calculations also allow
vendors of coating technologies to conduct value pricing analyses, i.e. to establish the profit margin
(based on savings) achievable with a given coating and thus the maximum price that an operator would
be prepared to pay.
In this paper, a general techno-economic model is described and then applied to three case studies. The
case studies are taken from the water and food sectors, with stainless steel as the standard material of
construction. Three coating scenarios are considered, illustrated by three case studies: (i) where the
coating has negligible impact on heat transfer, typical of surface modifications such as diamond like
carbon (DLC) (Case Study I); (ii) where the coating introduces an insulation effect, reducing the rate of
heat transfer while mitigating fouling (Case Studies II and III); (iii) as (ii), but where the coating
provides complete corrosion protection, so the substrate can be substituted with carbon steel, offsetting
the heat transfer penalty associated with the coating (Case Study II). Scenario (iii) is suitable for
fluorocarbon-based coatings which provide good corrosion protection (Ebnesajjad and Khaladkar,
2005) and adhere to carbon steel more readily than stainless steels.
5
2. Model formulation
The techno-economic model requires a quantitative description of the effect of fouling on the
performance of a heat exchanger, which includes the effect of a coating on heat transfer, fouling and
cleaning. Its outputs are fed into a cost model which allows optimal operating strategies to be developed,
and compared. Lumped parameter models are used to predict heat exchanger performance, to illustrate
the concepts. More complex, distributed models could be used (e.g. Coletti et al., 2010), but the aim of
this paper is to establish the nature of the solution landscape and this is best achieved without detailed
models (which may in turn be difficult to parameterise). Similarly, the cost models do not consider the
time value of money nor inflation.
2.1. Heat exchanger performance with fouling
Fouling of heat transfer surfaces leads to increased pressure drop and reduced heat transfer. Only the
latter effect is considered here: pressure drop (and changing flow rate) considerations, as discussed by
Ishiyama et al. (2009) could be added as required. The thermal impact of fouling is quantified via the
fouling resistance, Rf, which is related to the thickness of the deposit, δf, and its thermal conductivity,
λf. Assuming that the thin-slab approximation holds gives
𝑅𝑓 = 𝛿𝑓 ⁄𝜆𝑓
(1)
As the deposit layer grows, 𝑅𝑓 increases and the temperature at the deposit/process stream interface will
change. This will affect the rate of deposit formation, as discussed by Ishiyama et al. (2008). The
sensitivity to temperature is determined by the species and mechanisms involved in deposition. For the
purposes of this paper, the rate of change in Rf with time (the fouling rate) is taken to be constant, at 𝑅̇𝑓 .
Deposit ageing, which also complicates the effect and rate of deposition over time (see Ishiyama et al.,
2011) was not considered here: 𝜆𝑓 is also assumed to remain constant over time, giving
𝑑𝑅𝑓
1 𝑑δ𝑓
≡ 𝑅𝑓̇ =
𝑑𝑡
𝜆𝑓 𝑑𝑡
(2)
For some processes and surfaces, there may be a delay before there is a discernible increase in 𝑅𝑓 . This
induction period, 𝑡𝑖𝑛𝑑 , may be extended by the use of a coating and is modelled as an initial lag, giving
0,
𝑅𝑓 (𝑡) = { ̇
𝑅𝑓 × (𝑡 − 𝑡𝑖𝑛𝑑 ),
𝑡 < 𝑡𝑖𝑛𝑑
𝑡 ≥ 𝑡𝑖𝑛𝑑
(3)
The heat exchanger is modelled using a lumped parameter approach, where the rate of heat transfer is
calculated using an average temperature driving force and an overall heat transfer coefficient, 𝑈. As
deposition proceeds, U is related to its deposit-free (clean) value, 𝑈𝑐𝑙 , by
6
1
1
=
+ 𝑅𝑓
𝑈 𝑈𝑐𝑙
(4)
The overall heat transfer coefficient for a clean heat exchanger can be calculated from
1
1
𝛿𝑚𝑒𝑡𝑎𝑙
1
=
+
+ 𝑅𝑐𝑜𝑎𝑡 +
𝑈𝑐𝑙
ℎℎ 𝜆𝑚𝑒𝑡𝑎𝑙
ℎ𝑐
(5)
where ℎℎ and ℎ𝑐 are the hot and cold stream film heat transfer coefficients, respectively, 𝛿𝑚𝑒𝑡𝑎𝑙 is the
thickness of the heat transfer surface , 𝜆𝑚𝑒𝑡𝑎𝑙 is its thermal conductivity, and 𝑅𝑐𝑜𝑎𝑡 is the thermal
resistance of the coating. In Eqn [5] the internal and external heat transfer areas are assumed to be equal.
𝑅𝑐𝑜𝑎𝑡 is calculated from the coating thickness, 𝛿𝑐𝑜𝑎𝑡 , and its thermal conductivity, 𝜆𝑐𝑜𝑎𝑡 , using
𝑅𝑐𝑜𝑎𝑡 = 𝛿𝑐𝑜𝑎𝑡 ⁄𝜆𝑐𝑜𝑎𝑡
(6)
Differences in surface roughness between a coated and standard surface are assumed to be negligible.
The following assumptions are made in the calculation of heat exchanger unit performance:
i.
The thermal and physical properties of both the hot and cold process streams remain
constant within the heat exchanger. Each value corresponds to the arithmetic average of
the stream inlet and outlet temperatures;
ii.
Cleaning actions remove all deposit material, so Rf is reset to zero after cleaning;
iii.
The coating layer is homogeneous, durable, free of defects and its fouling mitigation
properties do not change over its lifetime;
iv.
The thickness of the deposit is small compared to the duct dimension, so there is no change
in flow area, average velocity and film heat transfer coefficients of both streams during
operation;
v.
Fouling deposits are uniformly distributed.
The heat duty, Q, is evaluated using the effectiveness-NTU method (Kays and London, 1964), where
the effectiveness, ε, is defined by
𝜀=
𝑄
𝑄𝑚𝑎𝑥
=
𝑄
(7)
(𝑚̇𝐶𝑝 )𝑚𝑖𝑛 (𝑇ℎ,𝑖𝑛 − 𝑇𝑐,𝑖𝑛 )
where 𝑄𝑚𝑎𝑥 is the maximum heat duty achievable from the process, (𝑚̇𝐶𝑝 )𝑚𝑖𝑛 is the minimum heat
capacity flow rate, 𝑚̇ is the mass flow rate and 𝐶𝑝 is the specific heat of a given stream. Stream
temperature 𝑇 is labelled with subscripts ‘in’ and ‘out’ referring to the inlet and outlet location, while
‘h’ and ‘c’ refer to the hot and cold stream, respectively.
The case studies consider examples of single phase (liquid-liquid) heat transfer. The change in
temperature of each stream is related to the heat duty by
7
𝑄={
𝑚̇ℎ 𝐶𝑝,ℎ (𝑇ℎ,𝑖𝑛 − 𝑇ℎ,𝑜𝑢𝑡 ),
for the hot stream
(8)
𝑚̇ 𝑐 𝐶𝑝,𝑐 (𝑇𝑐,𝑜𝑢𝑡 − 𝑇𝑐,𝑖𝑛 ),
for the cold stream
(9)
The effectiveness, 𝜀, depends on the number of transfer units, 𝑁𝑇𝑈,
𝑁𝑇𝑈 =
𝑈. 𝐴
(10)
(𝑚̇𝐶𝑝 )𝑚𝑖𝑛
and the heat capacity flow ratio, 𝐶𝑟 ,
𝐶𝑟 =
(11)
(𝑚̇𝐶𝑝 )𝑚𝑖𝑛
(𝑚̇𝐶𝑝 )𝑚𝑎𝑥
where 𝐴 is the effective heat transfer surface area and (𝑚̇𝐶𝑝 )𝑚𝑎𝑥 is the larger of the two streams’ heat
capacity flow rates. The functional relationship,  = f(NTU, Cr) depends on the type and contacting
configuration of the exchanger.
The performance of the exchanger is evaluated over time, t (see Figure 1). At each time instant, Rf is
evaluated, giving U (via Eqn [4]) and Q (via Eqn [8]). Figure 1 shows that as Rf increases, U and Q both
decrease. Eventually it will be more profitable to take the exchanger off-line for a period of time of
length  for cleaning, resulting in U being restored to its clean value, Ucl. There will be an optimal
operating period before cleaning, the evaluation of which is described below.
It should be noted that the presence of a coating will change the overall heat transfer resistance (via Eqn
[4]), usually reducing U, and NTU (Eqn [10]). If the clean heat duty is to be maintained at a target level,
this reduction in U is usually countered by increasing the heat transfer area, A. Coating the heat transfer
surface is therefore likely to require a larger heat exchanger in the absence of ‘fouling factors’. This has
an effect on the response of the exchanger to fouling, as NTU includes the product UA: the extra heat
transfer surface reduces the impact of a given Rf value and appears to mitigate fouling. This is one of
the benefits of the ‘fouling factor’ approach in designing heat exchangers for fouling service, where the
exchanger is oversized based on a presumed amount of deposition occurring at some point in the future.
In practice, such exchangers tend to foul more quickly owing to inappropriate operating protocols, as
expressed in Bott’s ‘self-fulfilling fouling prophecy’ (Bott, 1995), quantified by Ishiyama et al. (2008).
Oversizing exchangers based on fouling factors is not included in the process models here, and could
be readily added as desired.
2.2. Cost model and economic optimisation
In considering any process improvement, the capital cost for implementing the change must be
compared with the expected improvement in operating costs. For heat exchangers subject to fouling,
8
the operating cost needs to be evaluated over the fouling-cleaning cycle shown in Figure 1. Fouling is
assumed to repeat itself with similar rates over each cycle. The approach presented by Ma and Epstein
(1981) is used to identify the optimal cleaning cycle (OCC), with a processing period of length tp, and
down-time for cleaning, 𝜏. The influence of ageing, discussed by Ishiyama et al. (2011) and choice of
cleaning methods (see Pogiatzis et al., 2012) are not considered here.
The costs due to fouling incurred over the cycle are:
i.
Compensation for reduced heat transfer, e.g. additional heating/cooling cost of the
process stream to achieve temperature target(s), CH, discussed below.
ii.
Heating/cooling during the time the heat exchanger is off-line for cleaning, with cost
= cE Qcl, where cE is the cost per unit energy.
iii.
Cost of a cleaning operation, Ccl, including disposal of cleaning chemicals etc.
iv.
(For completeness, but not considered here) increased pumping costs or penalties
associated with loss of throughput
Additional heating or cooling, CH
The reduced rate of heat transfer caused by fouling can be compensated for in different ways, depending
on the design and operation of the exchanger. For example, an overdesigned heat exchanger (one with
excess area) can be operated with a flow bypass in order to achieve the desired outlet temperatures, and
fouling only has a marked effect when the bypass is fully closed. This mode is not considered here.
The two modes considered are:
I
Providing additional heating/cooling to adjust the process stream from its exit
𝑐𝑙
temperature, Ti,out, to the desired value, obtained when the unit was clean, 𝑇𝑖,𝑜𝑢𝑡
. In this case,
(12)
𝐶𝐻 (𝑡𝑝 ) = 𝑐𝐸 ∫𝑡𝑝(𝑄𝑐𝑙 − 𝑄(𝑡))𝑑𝑡
0
where tp is the duration of the processing period.
II
Adjusting the heating/cooling utility inlet temperature, 𝑇𝑗,𝑖𝑛 , from its value when the
𝑐𝑙
exchanger is clean, 𝑇𝑗,𝑖𝑛
, in order to maintain the process stream outlet temperature at its
target value. In this case
(13)
𝐶𝐻 (𝑡𝑝 ) = 𝑐𝐸 ∫𝑡𝑝 𝑄𝑎𝑑𝑑 (𝑡)𝑑𝑡
0
where 𝑄𝑎𝑑𝑑 is the additional heat duty required to pre-heat or cool the utility stream, given by
(14)
9
𝑄𝑎𝑑𝑑 (𝑡𝑝 ) = {
𝑟
𝑐𝑙
𝑚̇ℎ 𝐶𝑝,ℎ (𝑇ℎ,𝑖𝑛
(𝑡𝑝 ) − 𝑇ℎ,𝑖𝑛
), 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 ℎ𝑒𝑎𝑡𝑖𝑛𝑔 𝑖𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑
𝑐𝑙
𝑟
𝑚̇ 𝑐 𝐶𝑝,𝑐 (𝑇𝑐,𝑖𝑛
− 𝑇𝑐,𝑖𝑛
(𝑡𝑝 )),
(15)
𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑖𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑
Optimal operating period
The optimal operating cost (and OCC length) is found by minimising the time-averaged operating
cost, 𝜙𝑜𝑝 , which is the sum of the above three costs divided by the total cycle time, tcyc, which is the
sum of tp and  viz.
𝜙𝑜𝑝 (𝑡𝑝 ) =
𝐶𝐻 (𝑡𝑝 )+ 𝐶𝐸 𝑄𝑐𝑙 𝜏+ 𝐶𝑐𝑙
(16)
𝑡𝑝 + 𝜏
Since  is here assumed constant and not time dependent, Eqn [16] can be differentiated with respect
to tp. The optimal operating period, 𝑡𝑝,𝑜𝑝𝑡 , is when
𝑑𝜙𝑜𝑝
𝑑2 𝜙𝑜𝑝
= 0:
>0
𝑑𝑡𝑝
𝑑𝑡𝑝 2
(17)
The annual total energy loss, 𝐸𝑙𝑜𝑠𝑠 , due to fouling can then be calculated, from:
𝑡
𝐸𝑙𝑜𝑠𝑠 = {
𝑛 [∫0 𝑝,𝑜𝑝𝑡(𝑄𝑐𝑙 − 𝑄(𝑡))𝑑𝑡 + 𝑄𝑐𝑙 𝜏] , 𝑓𝑜𝑟 (𝐼)
𝑡
𝑛 [∫0 𝑝,𝑜𝑝𝑡 𝑄𝑎𝑑𝑑 (𝑡)𝑑𝑡
+ 𝑄𝑐𝑙 𝜏] , 𝑓𝑜𝑟 (𝐼𝐼)
(18)
(19)
where n is the number of cleaning cycles in a year.
When comparing a mitigation strategy such as coating with the performance of existing equipment,
the capital cost of replacing an existing plant asset has to be considered. The annualised capital cost,
𝜙𝑐𝑎𝑝 , is calculated from
𝜙𝑐𝑎𝑝 =
𝛼𝐶𝑒𝑞𝑢𝑖𝑝 (𝐴)
𝑡𝐿𝐹
(20)
where 𝐶𝑒𝑞𝑢𝑖𝑝 is the installed price of an uncoated unit with area A, 𝛼 is the cost multiplier associated
with the coating, and tLF is the asset lifetime for accounting purposes. The coating must remain effective
over this period.
In the techno-economic analysis the annual operating cost of an existing, uncoated heat exchanger
subject to fouling, 𝜙𝑜𝑝,𝑢𝑛𝑐 , is compared with the cost of a new coated unit, 𝜙 𝑇,𝑐𝑜𝑎𝑡 , which includes the
annual operating cost, 𝜙𝑜𝑝,𝑐𝑜𝑎𝑡 , (which is expected to be lower than 𝜙𝑜𝑝,𝑢𝑛𝑐 ) and the capital costs
associated with replacement, 𝜙𝑐𝑎𝑝,𝑐𝑜𝑎𝑡 . The alternative scenario, of applying a coating to an existing
unit, is not considered here. This may not be possible in practice. Considerations of the time dependency
10
of money, e.g. net present value and inflation, are not included in the calculations but could be added
as desired.
All calculations were performed using MATLAB® on a desktop PC. The calculation sequence is
summarised in the Appendix.
3. Case studies
3.1 Case Study I. DLC coating of a shell and tube heat exchanger to combat water scaling
Crystallisation fouling caused by hard water, or scaling, is a common industrial problem where the
water contains significant amounts of ions of inverse solubility salts such as calcium and magnesium
sulphates and carbonates. Scaling mitigation techniques have been studied widely (Kho et al., 1997;
Naik et al., 2010; Tijing et al., 2011) and antifouling coatings have been shown to be quite effective in
reducing water scaling, as summarised in Table 1.
Geddert et al. (2009) reported an improvement in the performance of a heat transfer mini-plant treating
synthetic hard water using surfaces with thin diamond-like carbon (DLC) coatings prepared by plasma
enhanced chemical vapour deposition (PECVD), including DLC, Si-DLC, SICAN and SICON®. The
modified surfaces gave negligible differences in clean heat transfer performance and affected crystal
adhesion, prolonging the induction period and reducing any subsequent rate of fouling. The economic
attractiveness of such coatings is considered in this case study.
It is assumed that the coatings retain their effectiveness over the financial lifetime, tLF. Geddert et al.
(2011) subsequently reported that some of the coatings exhibited changes in composition following
several cleaning cycles using different cleaning agents. The effect of tLF is considered in this case study
as it can be manipulated to represent the durability of the coating, and quantify how long a coating must
remain effective in order to justify replacement of an uncoated unit.
The performance of two shell-and-tube heat exchangers are compared here based on the Rf-t data
reported by Geddert et al. (2009). The units have identical design, with one shell pass and two tube
passes. Rcoat is set at zero, as the 3 µm thick DLC coating had negligible effect on heat transfer. Both
are fabricated from stainless steel (SS304), one with no coating and the other having SICON®-coated
heat transfer surfaces. Both process streams are aqueous liquids, and one is prone to fouling. For the
SICON® unit the fouling stream will have to be on the shell-side as coating techniques for tube internals
are not commercially available at present. Fouling streams are usually put on the tube-side in order to
facilitate cleaning. The choice of shell- or tube-side is not considered further here: it is assumed that
there is no difference in fouling behaviour or heat transfer.
11
Equation [12] is used to evaluate the additional operating cost due to fouling, assuming that the streams
can be heated elsewhere in the process. The effectiveness is given by Incropera et al. ( 2001):
𝜀 = 2 {1 + 𝐶𝑟 + (1
+ 𝐶𝑟2 )1/2
1 + 𝑒𝑥𝑝[−𝑁𝑇𝑈(1 + 𝐶𝑟2 )1/2 ]
×
}
1 − 𝑒𝑥𝑝[−𝑁𝑇𝑈(1 + 𝐶𝑟2 )1/2 ]
−1
(21)
Table 3 summarises the unit design and performance parameters. They represent an industrial unit
operating at conditions similar to those in Geddert et al. (2009)’s experiments. In the latter study the
SICON® surface extended the fouling induction period from 5 h to 72 h and the fouling rate was reduced
to less than a third of the uncoated value. In this case study the time taken to clean the exchanger is
fixed, at 4 days. The timescale associated with fouling can be gauged by the time taken for U to fall to
half its clean value, Ucl/2, corresponding to a fouling Biot number (= Ucl×Rf) of 1, is 62 days for the
uncoated heat exchanger and 235 days for the SICON®-coated unit.
The plot of overall operating cost in Figure 2 shows that there is an optimal processing time which gives
a minimum in op. The optimum is not symmetric and is shallow, particularly at higher tp. The optimal
processing time before cleaning for the uncoated exchanger is 40 days whilst that for the SICON®coated unit is 71 days, representing a 77% extension to the operation period. The effectiveness values
decreased from 0.30 to 0.20 and 0.25 for the uncoated and coated surfaces, respectively, indicating that
the optimal operating condition does not correspond to a common value of U. The coating reduces the
optimal annualised operating cost by 43%, from 235.4 to 133.5 US$ day-1.
The capital cost of a new heat exchanger, given in Table 3, was obtained from data in Peters et al.
(1990) adjusted to December 2012 using a chemical engineering plant cost index of 572.7. The cost of
the SICON® coating is not considered here, so 𝛼 = 1. The life-time, tLF, is set at 5 years. This gives an
annualised capital cost for the replacement unit, 𝜙𝑐𝑎𝑝 , of 38.7 US$/day, i.e. 16% of the operating cost
of the uncoated HEX.
‘Value pricing’
The summary of the costs in Table 4 shows that the total annualised cost of the coated unit is 62.8
kUS$/yr, which is 23.1 kUS$/yr less than the uncoated unit. This difference represents the maximum
return on investment for the coating and can be used in either (i) assessing the economic attractiveness
of a coating by the operator, or (ii) establishing the costing space in a ‘value pricing’ calculation for the
coating by its vendor. As an example of the latter, the 23.1 k$/yr difference in total annualised costs is
1.65× the capital cost, indicating that the maximum value of  at which the coating can be sold is close
to 2.5. This in turn can be compared with the cost of manufacturing the coated unit. The values will be
determined by the inputs to the calculation: size of unit, material of construction, duty, impact on
12
fouling, and costing parameters (particularly tLF). These will vary from sector to sector. The remainder
of this case study compares the impact of different fouling parameters on the attractiveness of replacing
an existing unit with a coated surface.
Fouling parameter sensitivity
When comparing the effect of fouling parameters on the performance and costs of coated and uncoated
units, it is helpful to present the results in terms of ratios based on the uncoated (i.e. base case)
exchanger. The dimensionless performance indices are:
[i]
∗
𝑡𝑐𝑦𝑐
= 𝑡𝑐𝑦𝑐,𝑐𝑜𝑎𝑡 ⁄𝑡𝑐𝑦𝑐,𝑢𝑛𝑐
Ratio of the optimal cycle times
[ ii ]
𝜙 ∗ = 𝜙 𝑇,𝑐𝑜𝑎𝑡 ⁄𝜙𝑜𝑝,𝑢𝑛𝑐
Ratio of the total annualised cost for the coated unit
divided by the operating cost for the uncoated one
[ iii ]
∗
𝐸𝑙𝑜𝑠𝑠
= 𝐸𝑙𝑜𝑠𝑠,𝑐𝑜𝑎𝑡 ⁄𝐸𝑙𝑜𝑠𝑠,𝑢𝑛𝑐
Ratio of the energy losses due to fouling
Table 4 shows that 𝜙 ∗ = 0.73 for the example in Figure 2, representing a 27% reduction in total cost.
In terms of energy consumption, which may attract tax benefits, the coating delivers a 44% reduction
in energy losses due to fouling.
The results of parametric sweeps are now presented. The ranges considered are
(a) Fouling rate, 𝑅𝑓̇ , varying from near 0.1× to 1.5× the uncoated rate. The latter values represent
a poor coating in terms of fouling rate, but this could be offset by extending the induction period
and/or increasing the cleaning rate.
(b) Induction period, tind, ranging from 0 to 5 days. tind for the uncoated HEX is set as 5 hours.
(c) Cleaning times, , of 2, 4 or 5 days, representing possible improvements or extension of
cleaning time as a result of the coating. for the uncoated heat exchanger is fixed, at 4 days.
No assumptions are made about the nature of the coating beyond it not affecting the overall heat transfer
resistance. The coated and uncoated exchangers in this instance have the same area and the results
apply to any coatings with these characteristics. The calculation outputs are summarised in 3-D plots in
Figure 3, where the fouling rate is presented as the fraction of the rate in the uncoated case. The
horizontal plane in each plot corresponds to the performance of the uncoated exchanger for its original
values of 𝑅̇𝐹 , tind and .
The calculated optimal cycle times in Figure 3(a) shows that increasing the induction period over the
range of values considered shortens tcyc* slightly, while a lower fouling rate results in a longer operating
period and cycle length. tcyc* is more sensitive to fouling rate: for example, the point where tcyc*
13
approaches 1 is most sensitive to fouling rate, followed by cleaning time and then induction period.
Finally, a shorter cleaning period also gives shorter cycle times.
Figure 3(b) shows families of results for different cleaning times plotted as planes of total annualised
cost. Some general trends are evident, namely (i) reducing the cleaning time reduces 𝜙 𝑇 , particularly
when tcyc is short; (ii) increasing tind reduces 𝜙 𝑇 , albeit relatively weakly, and (iii) 𝜙 𝑇 is most sensitive
to the fouling rate, with a lower fouling rate than the uncoated case required to give 𝜙 𝑇 < 1. The capital
cost contribution to 𝜙 𝑇 means that the fouling rate required to give * = 1 is lower (i.e. better mitigation
performance) than that required to give tcyc* = 1. Reducing the cleaning time, , to 2 days also has a
significant effect.
The effect of the coating on energy losses in Figure 3(c) shows benefits for all cases where the fouling
rate is reduced from the base case, and also where the induction period is extended. Reducing the
cleaning time also gives noticeable improvement in Eloss*. Comparing the region where Eloss* < 1 in
Figure 3(c) with that for * < 1 (Figure 3(b)) indicates that the latter requires better antifouling
performance (lower fouling rate, longer induction period and/or shorter cleaning time) in order to be
economically favourable. Figure 3(b) suggests that the fouling rate should be reduced to less than 40%
of that in the uncoated unit in order for coating to be economically attractive to the operator with this
costing ( = 1). This is a sizeable reduction and arises from the cost of installing a new unit: it illustrates
the balance between capital costs and energy prices. Significantly better performance will be required
if the coating is expensive to manufacture or the vendor wishes to negotiate a mutually attractive price
for the coating.
3.2 Case Study II. Fluorocarbon coating of a shell and tube heat exchanger to combat hard
water scaling
This case considers a fluorocarbon or similar coating which can introduce a noticeable thermal
resistance. Oldani et al. (2013) reported a 40% reduction in linear fouling rate for water-based fouling
with a perfluoropolyether (PFPE) film on tubes in a shell-and-tube heat exchanger. This performance
is subjected to the above techno-economic analysis and further factors considered.
Although the coating reduced the rate of scale deposition, its relatively low thermal conductivity, of
around 0.1 W m-1K-1, gives a lower Ucl value. In order to achieve the same heat duty as the uncoated
heat exchanger with the same temperature driving force, the existing unit would have to be replaced by
one with larger area, given by
𝐴𝑐𝑜𝑎𝑡 =
𝑈𝑐𝑙,𝑢𝑛𝑐
× 𝐴𝑢𝑛𝑐
𝑈𝑐𝑙,𝑐𝑜𝑎𝑡
(22)
14
This increase in area is assumed to be small enough that installing the replacement unit does not require
major structural changes, e.g. supports, space and associated expense. The increase in area will be
accompanied by higher capital cost.
Table 5 summarises the parameters for this case study. Two stainless steel shell-and-tube heat
exchangers are considered, again with one shell pass and two tube passes each. Oldani et al. (2013)
used a liquid phase coating process so that the tubes could be coated internally and externally. They did
not report whether deposition was limited to one side of the tubes. The design and performance
parameters were taken from Oldani et al. (2013) and typical industry values. Equation [21] was used to
calculate the effectiveness. 𝐶𝐻 was calculated using Equation [13], as in Case Study I.
The effect of coating thickness on heat exchanger area and capital cost for the base case design is
illustrated in Figure 4. Increasing the coating thickness reduces U, and the increase in cap and Acoat
becomes significant when coat > 10 µm for this example. A 100 µm thick layer is unlikely to be
considered for practical use but is included here to convey the impact of such layers on heat transfer
performance. While Figure 4 indicates that coating thicknesses of order 10 µm are desirable for this
application, durability criteria as well as resistance to cleaning agents may require use of thicker layers.
Oldani et al. (2013) did not indicate any effect of the coating on the induction period so tind is set at
zero for both surfaces. The cleaning time for the units is similarly taken to be the same. A tLF value of
10 years is used in the base case calculation. The time taken fouling to cause U to fall to half of its clean
state, Ucl/2, is 157 days for the uncoated heat exchanger and 269 days for the PFPE-coated unit.
The results for the base case, with a coating thickness of 10 µm, are shown in Figure 5 and Table 6. The
coated stainless steel heat exchanger gives an 18% reduction in the operation cost and extends the
∗
operating period by 27%. There is a 17% reduction in energy losses (𝐸𝑙𝑜𝑠𝑠
= 0.83). However, this level
of improved performance is not sufficient to offset the cost of the new exchanger. Even in the absence
of coating costs ( set to 1), the total amortised cost for operating and capital costs is comparable to the
existing unit, with 𝜙 ∗ = 1.01 for tLF =10 yr. This indicates that replacement of the unit with a PFPEcoated one is not economically attractive for this set of input parameters and cost structure. Extending
tLF (requiring the coating to be effective for longer times), higher energy costs etc., could all be explored
in a search of the costing parameter space for economically attractive combinations.
Coating carbon steel?
The scenarios considered to this point have all assumed that the coating is used to improve the fouling
performance of stainless steel surfaces. Stainless steel surfaces are frequently used to avoid corrosion
and contamination problems. Fluorocarbon coatings offer good corrosion resistance (McKeen, 2006).
If the coating is durable and prevents corrosion as well as mitigating fouling, it may be possible to use
15
a cheaper material of construction, such as carbon steel, to provide the mechanical strength needed for
the unit. Carbon steel (CS) also has a thermal conductivity three times that of SS, so the heat transfer
penalty associated with a thick coating can be offset by improved conduction through the steel. CS units
are also considerably cheaper, as shown in Figure 6. The option of using a coated CS unit is investigated
in this scenario.
Results for a coated CS unit for the base case are given in Table 6. The U value for the unit is comparable
to the uncoated SS exchanger and the additional area is small. The time taken to reach a fouling Biot
number of 1 is 262 days for the coated CS unit, representing a reduction of 7 days compared to the SS
unit. The tcyc* and 𝜙𝑜𝑝 values differ slightly from the SS unit owing to the difference in UA. The capital
cost is 13.3 US$ day-1, which is about a third of the cost of the coated SS unit, at 43.6 US$ day-1. This
reduces 𝜙 ∗ to 0.89, at which point the coated exchanger is economically attractive. The maximum cost
of coating can also be calculated, at 101.5k US$ for a 10-year lifetime, representing a maximum  value
of 3.1.
This concept is not considered further here: it is presented to promote discussion and research.
Coating performance
The results reported by Oldani et al. (2013) are now extended in a parameter sweep to establish the
economic attractiveness of a theoretical fluorocarbon coating. The thickness of the coating is varied
from 0.1 to 100 µm, and the associated fouling rate is assumed to vary from 0.1 to 1.5 times that reported
by Oldani et al. (2013) for the uncoated SS unit. A deterministic model of the effect of coating thickness
on fouling behaviour is not offered here: this would be a useful tool as it would guide coating
development into economically feasible regions. The results for coated SS and coated CS units are
presented as 3-D plots in Figures 7 and 8.
Figure 7 shows the effect of fouling parameters for a fixed coating thickness of 10 µm, as in the base
case discussed above. The fouling induction period is varied from 0 to 10 days and two cleaning times
are considered, namely 2 and 4 days. The plots of tcyc* in Figure 7(a) indicate little influence of tind, but
high sensitivity to the fouling rate, as in Case Study I. This is expected as the induction period is
relatively short compared to the operating times. The cleaning time has a significant effect, however,
indicating that the heat lost during the period when the unit is off-line for cleaning is appreciable. This
aspect highlights another target for coatings in fouling service, to promote rapid cleaning, as reported
for dairy pasteuriser units by Beuf et al. (2004) and heat pump systems processing treated sewage water
(Yang et al., 2014).
16
The sensitivity to fouling rate and cleaning period is emphasised in the total annualised cost in Figure
7(b). The influence of material of construction is now evident, with the CS units always lower than the
SS equivalent, and the plane for the CS unit with a 4 day cleaning time comparable to that for a SS unit
with a 2 day cleaning time. The desirability of improved cleaning performance is very evident in this
plot. The fouling induction period does have some effect on ϕ*, evident from where the planes cut the
ϕ* = 1 plane, at higher fouling rates where the optimal operating periods are shorter. When the coating
gives a reduction in fouling rate of 50% or greater, there is little influence of tind.
The Eloss* plots in Figure 7(c) all show a positive benefit of the coating. Reducing the fouling rate has
the strongest effect, followed by shortening the cleaning time. The induction period has a noticeable
effect where the fouling rate is high and close to that of the uncoated exchanger: this is, however,
unlikely to be considered satisfactory for an ‘antifouling’ coating.
Figure 8 shows the effect of coating thickness for a SS and a CS exchanger with fouling induction
periods of 0 days and 5 days. There is little effect of fouling induction period on tcyc* across the
parameter space in Figure 8(a), as expected from Figure 7(a). There is little difference between the two
coating options over the parameter space. The planes for tcyc* are curved, with larger tcyc* values for
thicker layers, indicating improved performance under these conditions. This is the effect of the extra
heat transfer area added to match Qcl as the coating thickness increases.
There is a noticeable col in the 3-D plot where tcyc* = 1 for thicknesses in the range of 1-10 µm. It is an
interesting feature, but only applies to cases where there is little reduction in the fouling rate as a result
of the coating so is not considered further here. For coatings which give reduction in fouling rate, the
increase in tcyc* occurs when coatings are more than 10 µm thick.
Figure 8(b) shows that coating is economically attractive, i.e. 𝜙 ∗ < 1, when the fouling rate is reduced.
There is some sensitivity in 𝜙 ∗ to the fouling induction period at high fouling rates, which are associated
with shorter operating times and hence induction period length. At lower fouling rates (good antifouling
performance) there is negligible sensitivity to tind. The point at which 𝜙 ∗ = 1 is insensitive to coating
thickness, which is attributed to the balance between extra capital cost and improved operating
performance. At low fouling rates there is no effect of coat on 𝜙 ∗ for the CS unit and for the SS unit for
thicknesses less than 50 µm. This suggests that coatings on stainless steel should not exceed this
thickness (for the case study parameters, i.e. heat transfer conditions, costs, etc. considered here).
The plot of energy losses in Figure 8(c) shows that the coatings are attractive for all cases where the
fouling rate is reduced, which is expected. There is a relatively small effect of fouling induction period
as discussed above. The influence of coating thickness on Eloss* is relatively weak for a given extent of
fouling rate reduction until ‘thick’ coatings are used, at which point the cost of the coating on SS
17
outweighs the energy saving to give an increase in ϕ* in Figure 8(b) but for the CS unit the difference
in costs is small and ϕ* is uniformly attractive for good antifouling performance.
3.3 Case Study III. Fouling and cleaning a Ni-PTFE-coated dairy plate heat exchanger
Fouling is a major problem in food and beverage manufacturing operations, not only in terms of heat
transfer and obstruction to flow, but also in affecting product quality and hygiene. Milk pasteurisation
and sterilisation units in dairy processing require cleaning, often on a daily basis (Jun and Puri, 2005),
due to the high rates of protein and mineral deposition on heat transfer surfaces and the associated risk
of microbial contamination. Frequent interruption and the large volumes of cleaning agents required
incur significant productivity losses and cleaning costs.
Fouling mitigation in milk processing has been investigated at some length, and ‘antifouling’ coatings
have been found to be effective on reducing unwanted deposition in heat exchangers, as shown in Table
2. Surface modifications must also be durable as well as resistant to frequent contact with acid, alkali
and oxidising cleaning and disinfection agents. The latter agents may be used for periodic cleaning of
the whole system or switchover to other product streams.
Barish and Goddard (2013) studied the performance of a model plate and gasket heat exchanger (PHX)
with Ni-P-PTFE (nickel-phosphorus-polytetrafluoroethylene) coated plates operating under simulated
pasteurisation conditions and showed a significant reduction in fouling levels. The (anti-) fouling
performance of the coating was similar over several repeated fouling and cleaning actions, indicating a
durable character. This is one of the few studies of repeated cycle PHX performance in the literature
and their data are used here in an evaluation of the performance of such coatings. It should be noted
that many types of fluorocarbon coatings exist and their performance will be determined by the method
of assembly and quality of manufacturing as well as their chemistry (McKeen, 2006). The results
presented here should be interpreted as representing all fluorocarbon coatings.
Consider two stainless steel plate and gasket heat exchangers, one of which has a 10 µm fluorocarbon
layer on the product side. The PHX configuration is a 1-1 pass counterflow arrangement, with raw milk
as the cold stream and water as the hot stream. The effectiveness is given by Kandlikar and Shah (1989):
𝜀=
1 − 𝑒𝑥𝑝[−𝑁𝑇𝑈(1 − 𝐶𝑟 )]
1 − 𝐶𝑟 𝑒𝑥𝑝[−𝑁𝑇𝑈(1 − 𝐶𝑟 )]
(23)
As the outlet temperature of the process stream is critical for pasteurisation, it must be maintained at its
target value. The milk flow rate is also held constant to maintain the mean residence time. As deposition
proceeds, the inlet temperature of the heating water stream is raised in order to achieve the desired duty,
and equations 13 and 14 are used in the model for this Case Study.
18
The parameters used in the simulations are presented in Table 7. Barish and Goddard (2013) reported a
90% reduction in fouling rate for their Ni-P-PTFE-coated surfaces, but it was not possible to extract
reliable values of induction periods from their data, so the uncoated and coated surfaces are both
allocated a 𝑡𝑖𝑛𝑑 value of 2 hours. The cleaning-in-place operation was initially considered to be
unaffected by coating, so 𝜏𝑐𝑜𝑎𝑡 =  = 4 hours. The characteristic time scale for fouling is noticeably
faster in this Case Study as the both the fouling rate and Uc are large (Ucl = 7500 W m-2 K-1). The time
taken for the fouling Biot number to reach 1 is 5.5 hours for the uncoated unit and 53 hours for the
coated unit.
Figure 9 shows that the fluorocarbon coating would give a 70 % reduction in operating costs and
extend the processing cycle by more than 3.5 times. The coated CS scenario described in Case Study
II was not considered in this Case Study.
Hygiene restrictions
Food manufacturing processes are subject to regular cleaning and disinfection cycles to ensure product
hygiene. The optimised PHX operating cycle length afforded by coating could be longer than the
maximum hygienic operating period, denoted thyg. The hygiene constraint would then require the unit
to be cleaned before topt, such that the benefit of the improved heat transfer performance is limited by
the need to guarantee product quality and safety.
Figure 9 illustrates this for the base case scenario with thyg set at 48 h (2 days), which is longer than topt
for the uncoated unit so that its optimal op value of is not affected. The thyg constraint reduces the cycle
∗
time for the coated exchanger by 30 % but the effect on performance (see 𝜙 ∗ and 𝐸𝑙𝑜𝑠𝑠
in Table 8) is not
large as the locus is locally quite shallow: the coating still yields around 70 % savings in costs and a 60
% reduction in energy losses. Figure 9 suggests that if thyg was shortened to 24 h the difference between
the optimal and the limited performance for the coated unit would be significant. The summary of
performance in Table 8 includes the results for this case: * increases from 0.34 (for thyg = 48 h) to 0.51
(for thyg = 24 h).
Table 8 shows that the contributions to the total annualised cost are dominated by operating costs due
to regular process interruption and cleaning, at appreciable cost. The capital contribution (calculated
with  = 1) constitutes around 2 % of the total annualised cost, so replacing the existing unit with a
coated one would be attractive. The maximum value of  for thyg = 48 h is 78, indicating a wide margin
for the coating cost (which would be divided between manufacturing cost, vendor profit and incentive
for the purchaser). This margin is reduced to around 55 for thyg =24 h. Microbiological factors, which
set the value of thyg on the basis of anticipated microbial growth, are clearly important. It is quite likely
19
that the value of thyg would differ for a coated unit as the surface coating is likely to affect the adhesion
and growth of micro-organisms. However, the extent to which thyg would be increased is not currently
estimable, and a rigorous microbiological testing regime on an installed unit would be required to
validate a different thyg value in practice.
Fouling parameter sensitivity
The effect of different fouling parameters, i.e. the antifouling performance of the coating, was
investigated for the base case 10 µm thick coating. Figure 10 shows that the coated cycle length is not
significantly affected by an increase in induction period and cleaning time. There is little effect of tind
and τ on total annualised cost, ϕ*, at low fouling rates, whereas there are noticeable differences at high
fouling rates. A decrease in fouling rate will cause an extension of cycle length and will imply cheaper
costs. As the capital cost contribution in this case is small (less than 3% ϕ* for the scenarios in Table
8) due to the high costs of cleaning, a small improvement in fouling performance makes unit
replacement economically attractive. Eloss* values are then similar to ϕ* and are not plotted, for brevity.
Figure 11 demonstrates the impact of the hygiene constraint, thyg, on tcyc* and ϕ* for different coating
thicknesses and fouling rates. As noted above, a deterministic relationship between the coating
thickness and fouling rate would be a valuable addition to this analysis. In the absence of hygiene
limitations, lower fouling rates and thicker coatings give rise to longer cycles and tcyc* approaches 20×
the uncoated value. Figure 11 shows the results for thyg = 1 and 2 days. In Figure 11(a) the thyg limit
truncates the rise in tcyc*, giving rise to a larger value of ϕ*. The cost savings are still favourable for
both thyg scenarios, but thyg = 24 h limits ϕ* to values > 0.5. Microbiological considerations are therefore
critical and may ultimately determine the attractiveness of coatings.
Figure 12 presents the performance for a coated exchanger subject to a maximum cycle length of 48 h
(i.e. without significant microbiological impacts) for different fouling rates, induction periods and
cleaning times. tcyc* is longer and ϕ* is reduced with lower fouling rates and a higher value of tind, as
expected from the results above. There is a noticeable truncation in tcyc* at lower fouling rates owing to
the thyg constraint becoming active but the effect on ϕ* is small. The down-time required for cleaning,
taken as 2, 4 or 5 hours (cf. 4 hours for the uncoated case), causes a shift in tcyc* but the maximum topt
value is the same for all cases. Cleaning downtime only affects ϕ* at high fouling rates. Figure 12(b) also
shows that coating is economically attractive across the range of fouling parameters considered.
Splitting savings: Value pricing and operation cost reduction
20
Table 8 shows that the coated heat exchanger with a 10 µm thick coating subject to thyg = 2 days gives
ϕ* = 0.34, representing a 66 % reduction in costs, if no expenses related to coating are considered in
the capital costs (α = 1). A coated unit will only be manufactured and adopted if it is attractive to both
producers and operators. It follows that α > 1 and ϕ* < 1 so each party can benefit from exchanger
replacement.
The increased performance of the coated exchanger in Table 8 provides cost savings of 82.2 k$/year,
which represents an αmax value of 79 for ϕ* = 1, albeit with no benefit to the operator. Given that there
must be an incentive for the operator to adopt the technology, a saving based on reduction in operating
costs is employed here. For example, for a 25 % reduction in operating costs, the maximum cost
associated with manufacturing this PHX is 51.9 k$/year, giving αmax = 49, and the operator would save
31.3 k$/year. For ϕ* = 0.5, the maximum annualised capital cost falls to 20.6 k$/year and the maximum
cost multiplier αmax is then 20. These values will in turn depend on the lifetime of the coating or the
accounting period, whichever is shorter.
Figure 13 presents the calculated maximum values of α for different fouling rates and induction periods
with set saving fractions. The horizontal plane at the base of the plot represents α =1 and is included to
mark where there is no extra cost or benefit derived by the manufacturer. The uppermost plane shows
the results for ϕ* = 1, where the cost of the new, coated unit matches the savings generated by its
introduction. This represents the maximum price that the manufacturer could expect to market the
coated devices at, albeit with no savings for the customer. The intermediary planes describe αmax values
where the operator gains a prescribed benefit from installing the coated exchanger. At ϕ* = 0.75, the
operator has set a target of 25% improvement in annualised operating costs, and at ϕ* = 0.5 the saving
is twice this. As the operator demands a larger share of the savings (lower ϕ*) the manufacturer is
compelled to manufacture the surfaces more cheaply (or accept a lower profit) and to achieve lower
fouling rates. There is relatively little effect of induction period for this scenario.
Note on application
Several parameters have been set at arbitrary or typical values in order to generate Figure 13, and these
would be replaced by more reliable values based on local experience when modelling particular
applications. The cost factors are particularly important in these techno-economic analyses and will
vary between industrial sector and location, as will the timescales. Figure 13 nevertheless summarises
the key finding from this study, in demonstrating that surfaces for mitigating fouling in processes
subject to repeated fouling and cleaning cycles will require guaranteed long term antifouling
effectiveness (here, with fouling rate reduction by a factor of at least 5× for the * = 0.50 case) in order
to be considered for industrial application.
21
4. Conclusions
The economics of mitigation of fouling by coating heat exchanger surfaces has been investigated using
quantitative models which included both the capital cost of replacing existing units and optimised
operating costs of repeated fouling and cleaning cycles. The effect of the coating on heat transfer and
the surface area of the exchanger for constant duty applications was considered. The increase in
robustness towards fouling resulting from increased exchanger surface area was evident and noted.
For most of the case studies considered here, the annualised costs associated with adding an antifouling
surface were smaller than the benefit (savings in operation costs) resulting from enhanced performance,
in which case replacement of the unit is economically attractive as long as the improved fouling
behaviour lasts the lifetime of the heat exchanger. Coating also extends the length of equipment
operating periods in fouling and cleaning cycles and reduces the additional energy required to
compensate heat transfer inefficiencies.
One Case Study considered the scenario where the coating is able to prevent corrosion completely so
that a stainless steel unit could be replaced by a coated carbon steel one. This both compensated for the
reduction in heat transfer associated with a coating of finite thickness and also reduced the capital cost
of the unit. Another Case Study considered a food processing application wherein the fouling and
cleaning cycle is subject to hygiene-driven cycle length limits. The latter can dominate the financial
attractiveness of such coatings.
The calculations allowed the cost saving benefits and the maximum increase in installed price that a
coated unit could be sold for. This information allows the value pricing margin to be identified and the
associated levels of fouling mitigation effectiveness to be quantified.
Data for the performance of coatings were based on studies in the open literature. The modelling
framework presented here can be used to assess the economic attractiveness of coatings once such data
become available. Alternatively, a deterministic model relating fouling behaviour to coating nature and
thickness could be used to identify performance targets for such coatings and guide coating
development.
Acknowledgements
Funding
for
CB’s
doctoral
studies
by the
Friedrich-Ebert-Stiftung and
Max-Buchner-
Forschungsstiftung is gratefully acknowledged, as a scholarship for LG from the University of São
Paulo Innovation Agency.
22
5. Nomenclature
Roman
A
Heat transfer area, m2
Ccl
Cost of cleaning, US$ unit-1
cE
Energy cost, US$ J-1
Cequip
Cost of the uncoated equipment, US$
CH
Cost of additional heating, US$
Cp
Specific heat capacity, J kg-1 K-1
Cr
Heat capacity flow ratio, -
Eloss
Annual total energy loss, J
∗
𝐸𝑙𝑜𝑠𝑠
Ratio of energy losses due to fouling, -
h
Film transfer coefficient, W m-2K-1
𝑚̇
Mass flow rate, kg s-1
n
number of cleaning cycles per year, -
NTU
Number of transfer units, -
Q
Heat duty, W
Rcoat
Thermal resistance of the coating, m2K W-1
Rf
Thermal resistance of the fouling layer, m2K W-1
𝑅̇f
Fouling rate, m2K J-1
Rmetal
Thermal resistance of the tube metal, m2K W-1
t
Time, day
𝑡𝑐𝑦𝑐
Optimum cycle time, day
∗
𝑡𝑐𝑦𝑐
Ratio of optimum cycle times, -
T
temperature, K
U
Overall heat transfer coefficient, W m-2K-1
Greek

Equipment cost multipilication factor due to coating, -
coat
Thickness of coating, m
f
Thickness of foulant, m
metal
Thickness of tube, m

Effectiveness, -
coat
Thermal conductivity of coating, W m-1K-1
f
Thermal conductivity of deposit, W m-1K-1
metal
Thermal conductivity of tube, W m-1K-1
*
Ratio of the total annualised cost for the coated unit over the uncoarted unit, 23
cap
Time averaged capital cost, US$ day-1
op
Time averaged operation cost, US$ day-1
T
Time averaged total annualised cost, US$ day-1

Time taken to clean a unit, days
Subscript
add
Additional
c
Cold stream
cl
Clean
coat
Coated
h
Hot stream
hyg
Hygienic constraint
in
Inlet
ind
Induction
LF
Life time of the heat exchanger
max
Maximum
min
Minimum
opt
Operating
out
Outlet
p
Processing period
unc
Uncoated
Superscript
cl
Clean state
r
Required condition to achieve the same amount of heat as the clean state
24
Appendix Calculation sequence of economic performance parameters of uncoated and
coated heat exchangers
Step
Equation
1. Initialization. Selection of reference heat
exchanger without coating: surface area, Aunc, clean
overall heat transfer coefficient, Ucl,unc, clean heat
duty, Qcl with an induction period of tind,unc, constant
fouling rate, 𝑅̇𝑓,𝑢𝑛𝑑 and a cleaning period of .
0, 𝑡 < 𝑡𝑖𝑛𝑑
𝑅𝑓 (𝑡) = { ̇
𝑅𝑓 × (𝑡 − 𝑡𝑖𝑛𝑑 ), 𝑡 ≥ 𝑡𝑖𝑛𝑑
2. At a given time instance, t, calculate fouling
resistance, Rf
1
3. Calculate overall heat transfer coefficient, U
𝑈
=
1
𝑈𝑐𝑙
+ 𝑅𝑓
Eq. (3)
Eq. (4)
Ucl is the clean overall heat transfer coefficient
4. Calculate exchanger effectiveness, 
𝜀 = 𝑓(𝑁𝑇𝑈, 𝐶𝑚𝑖𝑛 , 𝐶𝑚𝑎𝑥 )
Here Cmin and Cmax are the minimum and maximum
heat capacity flow rates, respectively. NTU is given
by
𝑁𝑇𝑈 =
𝑈𝐴
Eq. (10)
𝐶𝑚𝑖𝑛
𝑄 = 𝜀𝑄𝑚𝑎𝑥
5. Calculate operating heat duty
based on Eq. (7)
Here Qmax is the maximum heat duty given by
𝑄𝑚𝑎𝑥 = 𝐶𝑚𝑖𝑛 (𝑇ℎ,𝑖𝑛 − 𝑇𝑐,𝑖𝑛 )
Th,in and Tc,in are the hot stream and cold stream
inlet temperatures.
6. Calculate the additional energy cost, Ch(tp) during
an operating period of tp, due to fouling. If the
process achieves the target operating conditions by
(a) supplying additional heating, integrate steps 2 to 5
(a) 𝐶𝐻 (𝑡𝑝 ) = 𝑐𝐸 ∫𝑡𝑝(𝑄𝑐𝑙 − 𝑄(𝑡))𝑑𝑡
Eq. (12)
(b) 𝐶𝐻 (𝑡𝑝 ) = 𝑐𝐸 ∫𝑡𝑝 𝑄𝑎𝑑𝑑 (𝑡)𝑑𝑡
Eq. (13)
0
0
Here, CE is the energy cost.
(b) modifying inlet temperature
𝑄𝑎𝑑𝑑 (𝑡𝑝 ) =
𝑟
𝑐𝑙
𝑚̇ ℎ 𝐶𝑝,ℎ (𝑇ℎ,𝑖𝑛
(𝑡𝑝 ) − 𝑇ℎ,𝑖𝑛
),
𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 ℎ𝑒𝑎𝑡𝑖𝑛𝑔 𝑖𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑
𝑐𝑙
𝑟
𝑚̇ 𝑐 𝐶𝑝,𝑐 (𝑇𝑐,𝑖𝑛
− 𝑇𝑐,𝑖𝑛
(𝑡𝑝 )) ,
{𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑖𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑
7. Calculate the time averaged operating cost, 𝜙𝑜𝑝
25
𝜙𝑜𝑝 (𝑡𝑝 ) =
𝐶𝐻 (𝑡𝑝 )+ 𝐶𝐸 𝑄𝑐𝑙 𝜏+ 𝐶𝑐𝑙
𝑡𝑝 + 𝜏
Eq. (16)
8. Evaluate optimum operating time, tp,opt
tp,opt is when:
𝑑𝜙𝑜𝑝
𝑑𝑡𝑝
= 0:
𝑑 2 𝜙𝑜𝑝
𝑑𝑡𝑝 2
>0
Eq. (17)
This gives an optimum cycle, tcyc of:
tcyc = tp,opt + 𝜏
9. Calculate the optimum averaged operating cost
𝜙𝑜𝑝 (𝑡𝑝,𝑜𝑝𝑡 ) (from step 7)
10. Calculate the time averaged capital cost
𝜙𝑐𝑎𝑝 =
𝛼𝐶𝑒𝑞𝑢𝑖𝑝 (𝐴)
Eq. (20)
𝑡𝐿𝐹
 is a cost multiplier associated with coating. If no
coating is applied,  = 1. tLF is the asset lifetime.
11. Calculate the total time averaged cost, 𝜙 𝑇
𝜙 𝑇 = 𝜙𝑐𝑎𝑝 + 𝜙𝑜𝑝
Calculate annual total energy loss, Eloss
(a) 𝐸𝑙𝑜𝑠𝑠 = 𝑛 [∫0 𝑝,𝑜𝑝𝑡(𝑄𝑐𝑙 − 𝑄(𝑡))𝑑𝑡 + 𝑄𝑐𝑙 𝜏] Eq. (18)
𝑡
𝑡
(b) 𝐸𝑙𝑜𝑠𝑠 = 𝑛 [∫0 𝑝,𝑜𝑝𝑡 𝑄𝑎𝑑𝑑 (𝑡)𝑑𝑡 + 𝑄𝑐𝑙 𝜏]
Eq. (19)
12. Follow steps 2 to 11 for uncoated heat exchanger
to obtain tcyc,unc, 𝜙𝑜𝑝,𝑢𝑛𝑐 , 𝐸𝑙𝑜𝑠𝑠,𝑢𝑛𝑐 .
13. Calculate new area for the coated unit, Acoat, to
give the same operating condition with a coating
thickness of coat and a coating thermal conductivity
of coat. The coating gives an induction period of
tind,coat, constant fouling rate, 𝑅̇𝑓,𝑐𝑜𝑎𝑡 and a cleaning
period of .
𝐴𝑐𝑜𝑎𝑡 =
𝑈𝑐𝑙,𝑢𝑛𝑐
𝑈𝑐𝑙,𝑐𝑜𝑎𝑡
× 𝐴𝑢𝑛𝑐
Here Ucl,coat is the clean overall heat transfer
coefficient of the coated unit given by
1
𝑈𝑐𝑙,𝑐𝑜𝑎𝑡
=
1
ℎℎ
+
𝛿𝑚𝑒𝑡𝑎𝑙
𝜆𝑚𝑒𝑡𝑎𝑙
+ 𝑅𝑐𝑜𝑎𝑡 +
𝑅𝑐𝑜𝑎𝑡 = 𝛿𝑐𝑜𝑎𝑡 ⁄𝜆𝑐𝑜𝑎𝑡
14. Follow steps 2 to 11 for the coated heat
exchanger to obtain tcyc,coat, 𝜙𝑜𝑝,𝑐𝑜𝑎𝑡 , 𝐸𝑙𝑜𝑠𝑠,𝑐𝑜𝑎𝑡 .
15. Calculate dimensionless performance indices
∗
𝑡𝑐𝑦𝑐
= 𝑡𝑐𝑦𝑐,𝑐𝑜𝑎𝑡 ⁄𝑡𝑐𝑦𝑐,𝑢𝑛𝑐
𝜙 ∗ = 𝜙 𝑇,𝑐𝑜𝑎𝑡 ⁄𝜙𝑜𝑝,𝑢𝑛𝑐
∗
𝐸𝑙𝑜𝑠𝑠
= 𝐸𝑙𝑜𝑠𝑠,𝑐𝑜𝑎𝑡 ⁄𝐸𝑙𝑜𝑠𝑠,𝑢𝑛𝑐
26
Eq. (22)
1
ℎ𝑐
Eq. (5)
Eq. (6)
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30
Tables
Table captions
Table 1: Experimental studies of the effect of surface coatings on stainless steels for mitigation of
aqueous crystallization fouling (scaling).
Table 2: Experimental studies of the effect of surface coatings on stainless steels for mitigation of
fouling, or enhancement of cleaning, of milk-related deposits.
Table 3: Input parameters for Case Study I (DLC coating, water scaling). Shell-and-tube heat
exchanger, one shell pass, two tube passes.
Table 4: Case study I. Comparison of optimal cleaning times, annualised costs and annual energy
losses for uncoated and SICON®-coated heat exchanger unit. Fouling parameters in Table 3.
Table 5: Input parameters for Case Scenario II. Fluorocarbon coating, water scaling. Shell-and-tube
heat exchanger, one shell pass, two tube passes.
Table 6: Case study II. Comparison of optimal performance indices and process parameters for base
case (values in Table 5)
Table 7: Input parameters for Case Scenario III for fluorocarbon coating in milk pasteurization PHX
Table 8: Case study III. Comparison of optimal performance indices and process parameters for base
case (operating parameters in Table 5). Fluorocarbon coating thickness 10 µm.
31
Table 1: Experimental studies of the effect of surface coatings on stainless steels for mitigation of aqueous crystallization fouling (scaling).
Coating type
Coating
CaSO4
Influence on
fouling
0
CaSO4
-
Zettler et al. (2005)
CaSO4
-
Zhao et al. (2002); Zhao et al. (2005a,b)
Ca3(PO4)2
-
Rosmaninho and Melo (2006)
Ni-P, Ni-P-BN
CaSO4
-
Al‐Janabi et al. (2010)
FEP
CaSO4
-
Förster and Bohnet (2000)
FA, FP, FS, TC, TC/TF
CaCO3
- for FA, TC
&TC/FS
DLC
CaSO4
-
Förster and Bohnet (2000)
DLC
CaSO4
-
Zettler et al. (2005)
DLC, Si-DLC, Si-O-DLC
(prepared by PECVD)
CaSO4
-
Geddert et al. (2009)
CaPh
-
Boxler et al. (2013b)
SiOx
CaPh
+
TaC sputtered
CaSO4
+
Zettler et al. (2005)
CrN
CaSO4
-
Geddert et al. (2009)
Si+, F+, H+, SiF+, SiF4+
CaSO4
except H+
MoS2, SiF3+
CaPh
-
C, N
CaSO4
-
PTFE
PTFE-based
Electroless nickel film
Polymer-based
CVD
PVD
Ion-implanted
Carbon nitriding
Ni-P-PTFE
Foulant
Influence on
cleaning
Source(s)
Förster and Bohnet (2000)
Dowling et al. (2010)
+
Rosmaninho and Melo (2006)
Müller-Steinhagen and Zhao (1997); Zettler et al. (2005)
-
Rosmaninho and Melo (2006)
Zettler et al. (2005)
+, increase; -, reduction deposition or cleaning effort compared with non-coated surface; 0, no influence. Null entry indicates data not available.
Acronyms: CaPh: calcium phosphate; CVD – chemical vapour deposition; DLC – diamond-like carbon; FA – Fluoroalkene; FEP – perfluorethylenpropylen
FP – Fluoropolymer; FS – Fluorosiloxane; Ni-P-BN – Nickel phosphorous boron-nitride; PECVD – plasma enhanced chemical vapour deposition; PVD –
physical vapour deposition; TC – Tomcats (tetramethylcyclotetrasiloxane); TC/FP – Tomcats + fluoropolymer:
32
Table 2: Experimental studies of the effect of surface coatings on stainless steels for mitigation of fouling, or enhancement of cleaning, of milk-related deposits.
Coating type
Coating material
PTFE
PTFE-based
Ni-P-PTFE
CNT-PTFE
Excalibur® and Xylan®
Polymer-based
polyethylene as well as silicone
and fluorine resins
nylon, PMMA, PS, cellulose
acetate (CA) and agarose
polysiloxane
silica sol-gel
LectrofluorTM and AMC148-18
FEP, PEEK + fluoropolymer and
nanocomposite
epoxy-resin & polyurethanebased coatings
CVD
DLC (prepared by PECVD)
DLC and Si-O-DLC
Foulant
raw milk
whey
milk
raw whole milk
WPC
pasteurised milk
dairy dessert
model fluid
skim milk
WPI in SMUF
raw milk
pasteurised milk
dairy dessert
model fluid
whey
raw whole milk
raw whole milk
WPI
skim milk
WPI
WPC
dairy dessert
model fluid
WPI
Influence on
fouling
+
+
+
+
+
+
Influence on
cleaning
-
-
-
0
-
- (Xylan®)
-
- (PMMA)
Britten et al. (1988)
Kananeh et al. (2010)
Beuf et al. (2004)
+
33
Balasubramanian and Puri (2008, 2009)
Rosmaninho and Melo (2008)
Barish and Goddard (2013)
Rungraeng et al. (2012)
Beuf et al. (2004)
Yoon and Lund (1994)
Santos et al. (2006)
Balasubramanian and Puri (2008, 2009)
Mauermann et al. (2009)
-
- (at pH 6.7)
Gordon et al. (1968)
Dupeyrat et al. (1987)
McGuire and Swartzel (1989)
Yoon and Lund (1994)
Kananeh et al. (2010)
Rungraeng et al. (2012)
Beuf et al. (2004)
Dupeyrat et al. (1987)
0
- (PMMA,
CA)
+
+
+
- except
PEEK +
fluoropolymer
Source(s)
0
Santos et al. (2006)
DLC
PVD
Ion- implanted
Ceramic-based
WPI
+ (at pH 7.8)
- (85 °C)
-
Premathilaka et al. (2007)
Rosmaninho and Melo (2008)
Mauermann et al. (2009)
Patel et al. (2013)
Si-O-DLC (prepared by PECVD)
WPI in SMUF
Si-O-DLC (prepared by PECVD)
doped DLC (prepared by
PECVD)
WPI
+
-
milk, whey
0
0
-, 0
DLC, Si-DLC,
WPI, SMUF and for batch-wise
Si-O-DLC (prepared by PECVD) WPI in SMUF deposition at
120 °C
dairy dessert
model fluid
SiOx
WPI in SMUF
- (at pH 6.7)
DLC
WPI
+ (at pH 7.8)
WPI
+
TiN
WPI in SMUF
+
Ti-DLC
WPI
dairy dessert
silica, SiF+ and MoS2
model fluid
- at pH 6.7,
silica, SiF3, MoS2 and TiC
WPI
except MoS2
silica and MoS2
WPI in SMUF
+ at 85 °C
alumino-silicate
whole milk
chromium oxide and methylated
β-lactoglubulin
+
silica
Boxler et al. (2013a, 2013b, 2013c)
-
+
0
+
0
except SiF3 (-)
0 or +
Beuf et al. (2004)
Rosmaninho and Melo (2008)
Santos et al. (2006)
Premathilaka et al. (2007)
Rosmaninho and Melo (2007)
Mauermann et al. (2009)
Beuf et al. (2004)
Santos et al. (2006)
Rosmaninho and Melo (2008)
McGuire and Swartzel (1989)
Karlsson et al. (1996)
+, increase; -, reduction deposition or cleaning effort compared with non-coated surface, 0, no influence. Null entry indicates data not available.
Acronyms: CVD – chemical vapour deposition; DLC – diamond-like carbon; FEP – perfluorethylenpropylen; PECVD – plasma enhanced chemical vapour
deposition; PEEK – polyethyletherketone; PMMA – polymethylmethacrylate; PS – polystyrene; PTFE – polytetrafluoroethene; SMUF – simulated milk
ultrafiltrate; WPC – whey protein concentrate; WPI – whey protein isolate.
34
Table 3: Input parameters for Case Study I (DLC coating, water scaling). Shell-and-tube heat
exchanger, one shell pass, two tube passes.
Description
Operation
Design
Thermal
properties
Fouling
performance†
Costs
Parameter
Value
𝑚̇𝑐
Cold stream mass flow
30 kg s-1
𝑚̇ℎ
Hot stream mass flow
50 kg s-1
𝑇𝑐,𝑖𝑛
Cold stream inlet temperaturea
42 oC
𝑇ℎ,𝑖𝑛
Hot stream inlet temperature
80 oC
𝐴
Heat transfer surface area
200 m2
𝑈𝑐𝑙
Clean overall heat transfer coefficienta
250 W m-2 K-1
𝑄𝑐𝑙
Clean heat duty
1.42 MW
𝑅𝑐𝑜𝑎𝑡
Coating thermal resistanceb
0 m2 K W-1
𝐶𝑝,𝑐
Cold stream heat capacity
4180 J kg-1 K-1
𝐶𝑝,ℎ
Hot stream heat capacity
4180 J kg-1 K-1
𝑅̇𝑓,𝑢𝑛𝑐
Linear fouling rate, uncoated HEXa
7.5×10-10 m2 K J-1
𝑅̇𝑓,𝑐𝑜𝑎𝑡
Linear fouling rate, SICON®-coated HEXa
2.0×10-10 m2 K J-1
𝑡𝑖𝑛𝑑,𝑢𝑛𝑐
Induction period, uncoated HEXa
5h
𝑡𝑖𝑛𝑑,𝑐𝑜𝑎𝑡
Induction period, SICON®-coated HEXa
72 h
𝜏
Cleaning period
4 days
𝑐𝐸
Energy cost
0.0057 US$ MJ-1
(6×10-6 US$ Btu-1)
𝐶𝑐𝑙
Cost of cleaning a unit
2,000 US$ unit-1
𝐶𝑒𝑞𝑢𝑖𝑝
Unit capital costc
70,600 US$
𝑡𝐿𝐹
Asset lifetime
5 years
𝜙𝑐𝑎𝑝
(from eq. 20)
Unit annualised capital costd
38.7 US$ day-1
a
Obtained from Geddert et al. (2009)
b
Thermal resistance of the SICON®-coating is considered negligible
c
Obtained from Peters et al. (1990) and corrected using Chemical Engineering Plant Cost Index
(CEPCI) of December 2012.
d
No additional capital cost for the coating (𝛼 = 1)
35
Table 4: Case study I. Comparison of optimal cleaning times, annualised costs and annual energy
losses for uncoated and SICON®-coated heat exchanger unit. Fouling parameters in Table 3.
Optimal
cleaning times
Annualised
costs
Uncoated HEX
SICON®-coated HEX
𝑡𝑝,𝑜𝑝𝑡 + 𝜏
40 + 4 days
71 + 4 days
∗
𝑡𝑐𝑦𝑐
-
1.73
𝜙𝑜𝑝 (from eqs. 17, 18)
235.4 US$ day-1
133.4 US$ day-1
𝜙𝑐𝑎𝑝 (from eq. 20)
-a
38.7 US$ day-1 b
𝜙𝑇
235.4 US$ day-1
172.1 US$ day-1
𝜙∗
-
0.73
Total annualised cost
Energy losses
85,930 US$ yr
-1
Energy loss per cycle
1.47 TJ cycle-1
𝐸𝑙𝑜𝑠𝑠 (from eq. 19)
12.2 TJ yr-1
∗
𝐸𝑙𝑜𝑠𝑠
-
a
considering no additional capital costs for the current uncoated heat exchanger.
b
as described in Table 3.
36
62,830 US$ yr-1
1.41 TJ cycle-1
6.86 TJ yr-1
0.56
Table 5: Input parameters for Case Scenario II. Fluorocarbon coating, water scaling. Shell-and-tube
heat exchanger, one shell pass, two tube passes.
Description
Operation
Design
Thermal
properties
Fouling
performance*
Costs
Parameter
Value
𝑚̇𝑐
Cold stream mass flow
25 kg s-1
𝑚̇ℎ
Hot stream mass flow
85 kg s-1
𝑇𝑐,𝑖𝑛
Cold stream inlet temperature†
20 oC
𝑇ℎ,𝑖𝑛
Hot stream inlet temperature†
50 oC
𝐴
Heat transfer surface area
500 m2
ℎ𝐶
Cold side heat transfer coefficient†
500 W m-2 K-1
ℎ𝐻
Hot side heat transfer coefficient†
800 W m-2 K-1
𝛿𝑚𝑒𝑡𝑎𝑙
Metal tube thickness
2 mm
𝛿𝑐𝑜𝑎𝑡
Coating thickness
10 μm
𝑄𝑐𝑙
Clean heat duty
2.12 MW
𝐶𝑝,𝑐
Cold stream heat capacity
4180 J kg-1 K-1
𝐶𝑝,ℎ
Hot stream heat capacity
4180 J kg-1 K-1
𝜆𝑆𝑆
Stainless steel thermal conductivity
16 W m-1 K-1
𝜆𝐶𝑆
Carbon steel thermal conductivity
54 W m-1 K-1
𝜆𝑐𝑜𝑎𝑡
PFPE thermal conductivity
0.1 W m-1 K-1
𝑅̇𝑓,𝑢𝑛𝑐
Linear fouling rate, uncoated HEXa
2.5 × 10-10 m2 K J-1
𝑅̇𝑓,𝑐𝑜𝑎𝑡
Linear fouling rate, PFPE-coated HEXa
1.5 × 10-10 m2 K J-1
𝑡𝑖𝑛𝑑,𝑢𝑛𝑐
Induction period, uncoated HEXb
0 days
𝑡𝑖𝑛𝑑,𝑐𝑜𝑎𝑡
Induction period, PFPE-coated HEXb
0 days
𝜏
Cleaning period
4 days
𝑐𝐸
Energy cost
0.0057 US$ MJ-1
(6×10-6 US$ Btu-1)
𝐶𝑐𝑙
Cost of cleaning a unit
4,200 US$ unit-1
a
taken from Oldani et al. (2013).
b
induction period is set at zero for both surfaces as no effect on the induction period was reported.
37
Table 6: Case study II. Comparison of optimal performance indices and process parameters for base
case (values in Table 5)
Operation
parameters
Optimum cleaning
times
Annualised cost
Energy losses
a
Uncoated HEX
PFPE-coated SS HEX
PFPE-coated CS
HEX
𝑈𝑐𝑙
296.3 W m-2K-1
287.8 W m-2K-1
295.2 W m-2K-1
𝐴
500 m2
514.8 m2
501.8 m2
𝑡𝑜𝑝𝑡 + 𝜏
84 + 4 days
108 + 4 days
106 + 4 days
∗
𝑡𝑜𝑝𝑡
-
1.29
1.26
𝜙𝑜𝑝 (from eq. 16)
243.6 US$ day-1
200.7 US$ day-1
202.5 US$ day-1
𝜙𝑐𝑎𝑝 (from eq. 20)
-
a
43.6 US$ day-1
†13.3 US$ day-1
𝜙𝑇
243.6 US$ day-1
244.3 US$ day-1
215.8 US$ day-1
𝜙∗
-
1.01
0.89
Annualised total cost
88,900 US$ yr-1
89,170 US$ yr-1
78,770 US$ yr-1
Energy loss per cycle
3.02 TJ cycle-1
3.21 TJ cycle-1
3.17 TJ cycle-1
𝐸𝑙𝑜𝑠𝑠 (from eqs. 18, 19)
12.5 TJ yr-1
10.4 TJ yr-1
10.5 TJ yr-1
∗
𝐸𝑙𝑜𝑠𝑠
-
0.83
0.84
Taken from Figure 4 with no additional capital cost for the coating (𝛼 = 1) and a unit lifetime of 10 years.
38
Table 7: Input parameters for Case Scenario III for fluorocarbon coating in milk pasteurization PHX
Description
Operation
Design
Thermal
properties
Fouling
Performance b
Costs
Parameter
Value
𝑚̇𝑐
Cold stream mass flow
7 kg s-1
𝑚̇ℎ
Hot stream mass flow
13 kg s-1
𝑇ℎ,𝑖𝑛
Hold stream inlet temperature
74 oC
𝑇𝑐,𝑖𝑛
Cold stream inlet temperature a
63 oC
𝑇𝑐,𝑜𝑢𝑡
Cold stream outlet temperature a
73 oC
𝐴
Heat transfer surface area
15 m2
𝑈𝑐𝑙
Clean overall heat transfer coefficient
7500 W m-2 K-1
𝑄𝑐𝑙
Clean heat duty
275.8 kW
𝛿𝑐𝑜𝑎𝑡
Coating thickness b
10.5 μm
𝐶𝑝,𝑐
Cold stream heat capacity
3940 J kg-1 K-1
𝐶𝑝,ℎ
Hot stream heat capacity
4200 J kg-1K-1
𝜆𝑐𝑜𝑎𝑡
Coating thermal conductivity
0.2 W m-1 K-1
𝑅̇𝑓,𝑢𝑛𝑐
Linear fouling rate, uncoated HEX b
10 × 10-9 m2 K J-1
𝑅̇𝑓,𝑐𝑜𝑎𝑡
Linear fouling rate, Ni-P-PTFE-coated HEX b
1 × 10-9 m2 K J-1
𝑡𝑖𝑛𝑑,𝑢𝑛𝑐
Induction period, uncoated HEX b
2h
𝑡𝑖𝑛𝑑,𝑐𝑜𝑎𝑡
Induction period, Ni-P-PTFE-coated HEX b
2h
𝜏
Cleaning period
4h
𝑐𝐸
Energy cost
0.0083 US$ MJ-1
(0.03 US$ kWh-1)
𝐶𝑐𝑙
Cost of cleaning a unit
150 US$ unit-1
a
Typical inlet and outlet temperatures for the hot section of a milk pasteuriser.
b
Taken from Barish and Goddard (2013).
39
Table 8: Case study III. Comparison of optimal performance indices and process parameters for base case (operating parameters in Table 5). Fluorocarbon
coating thickness 10 µm.
Uncoated HEX
Operation parameters
Optimum cleaning
times
Annualised costs
Energy losses
a
coated HEX
coated HEX,
with hygiene
constraint
coated HEX, with
hygiene constraint
0 < tp < ∞
0 < tp < 24 h
0 < tp < 48 h
𝑈𝑐𝑙
7500
5380
5380
5380
𝐴
15 m2
21 m2
21 m2
21 m2
𝑡𝑜𝑝𝑡 + 𝜏
16 + 4 hours
69 + 4 hours
24 + 4 hours
48 + 4 hours
∗
𝑡𝑐𝑦𝑐
-
3.65
1.40
2.60
𝜙𝑜𝑝 (from eqs. 16)
14.30 US$ hour-1
4.50 US$ hour -1
7.10 US$ hour -1
4.80 US$ hour -1
𝜙𝑐𝑎𝑝 (from eq. 20)
-
𝜙𝑇
14.30 US$ hour -1
4.62 US$ hour -1
7.22US$ hour -1
4.92 US$ hour -1
𝜙∗
-
0.32
0.51
0.34
Annualised total cost
125,270 US$ yr-1
40,470 US$ yr-1
Energy loss per cycle
1.2× 1010 J cycle-1
1.8 × 1010 J cycle-1
𝐸𝑙𝑜𝑠𝑠 (from eq. 19)
5.3 × 1012 J yr-1
2.2× 1012 J yr-1
0.6× 1012 J yr-1
1.4× 1012 J yr-1
∗
𝐸𝑙𝑜𝑠𝑠
-
0.41
0.11
0.26
a
0.12 US$ hour -1
Calculated with no additional capital costs for the coating (𝛼 = 1) and a unit lifetime of 5 years.
40
a
0.12 US$ hour 1
63,250US$ yr-1
a
0.12 US$ hour -1
43,100 US$ yr-1
0.2 × 1010 J cycle-1 0.8 × 1010 J cycle-1
Figures
List of figure captions
Figure 1: Heat exchanger performance profiles during operation time. Variation of (a) fouling
resistance; (b) overall heat transfer coefficient; (c) heat duty over an operating cycle.
Figure 2: Case Study I. Effect of tp on annualised operation cost, 𝝓𝒐𝒑 , showing optimal cleaning
times, 𝒕𝒐𝒑𝒕 , for both uncoated and SICON®-coated heat exchangers.
Figure 3: Case Study I. Comparison of the performances of uncoated and SICON®-coated heat
exchanger for different induction periods, fouling rates and cleaning periods of coated-HEX.
(a) optimal cleaning time; (b) ratio of annualised costs; (c) ratio of energy losses. Note change
in base axes between (a) and (b).
Figure 4: Case Study II. Effect of PFPE film thickness on the heat transfer area required for fixed duty
and the capital cost of the coated heat exchanger.
Figure 5: Case Study II. Annualised operation cost and optimal operating time for cleaning, 𝒕𝒐𝒑𝒕 , for
uncoated and PFPE-coated stainless steel heat exchangers.
Figure 6: Case Study II. Estimated capital cost for installed stainless and carbon steel shell-and-tube
heat exchangers. Values obtained from Peters et al. (1990), corrected using the Chemical
Engineering Plant Cost Index (CEPCI) of December 2012.
Figure 7: Comparison of the performance of uncoated and 10 µm thick fluorocarbon coated heat
exchangers made of stainless or carbon steel for different induction periods, fouling rates and
cleaning periods on the coated units. (a) ratio of optimal cleaning times; (b) ratio of
annualised costs; (c) ratio of energy losses. Note change in base axes between (a) and (b).
Figure 8: Case Study II. Comparison of the performance of uncoated and fluorocarbon-coated heat
exchangers made of stainless or carbon steel for different induction periods, fouling rates and
coating thicknesses. (a) ratio of optimal cleaning times; (b) ratio of annualised costs; (c) ratio
of energy losses. Note change in base axes between (a) and (b).
Figure 9: Case Study III. Annualised operation cost profile and optimal cleaning times, 𝒕𝒐𝒑𝒕, for
uncoated and fluorocarbon coated stainless steel dairy PHX, with a hygiene operating constraint
at 2 days (48 h).
Figure 10: Case Study III. Comparison of the performance of an uncoated and a coated dairy PHX for
different induction periods, fouling rates and cleaning periods. 10 µm thick fluorocarbon
coating. (a) ratio of optimal cleaning times; (b) ratio of annualised costs. Note different base
axes.
Figure 11: Case Study III. Relative performance of a coated dairy PHX unit for different fouling rates,
coating thickness and hygiene constraint. tind = 2 hours. (a) ratio of optimal cleaning times; (b)
ratio of annualised costs.
Figure 12: Case Study III. Relative performance of a dairy PHX unit with 10 µm thick fluorocarbon
coating and thyg = 48 h for different induction periods, fouling rates and cleaning periods. (a)
ratio of optimal cleaning times; (b) ratio of annualised costs. Note change in base axes.
Figure 13: Case Study III. Maximum capital cost factor, , for different fouling rates and induction
periods and for selected cost saving ratios.
41
Figure 1: Heat exchanger performance profiles during operation time. Variation of (a) fouling
resistance; (b) overall heat transfer coefficient; (c) heat duty over an operating cycle.
42
Figure 2: Case Study I. Effect of tp on annualised operation cost, 𝝓𝒐𝒑 , showing optimal cleaning
times, 𝒕𝒐𝒑𝒕 , for both uncoated and SICON®-coated heat exchangers.
43
Figure 3: Case Study I. Comparison of the performances of uncoated and SICON®-coated heat
exchanger for different induction periods, fouling rates and cleaning periods of coated-HEX.
(a) optimal cleaning time; (b) ratio of annualised costs; (c) ratio of energy losses. Note change
in base axes between (a) and (b).
44
Figure 4: Case Study II. Effect of PFPE film thickness on the heat transfer area required for fixed duty
and the capital cost of the coated heat exchanger.
45
Figure 5: Case Study II. Annualised operation cost and optimal operating time for cleaning, 𝒕𝒐𝒑𝒕 , for
uncoated and PFPE-coated stainless steel heat exchangers.
46
Figure 6: Case Study II. Estimated capital cost for installed stainless and carbon steel shell-and-tube
heat exchangers. Values obtained from Peters et al. (1990), corrected using the Chemical
Engineering Plant Cost Index (CEPCI) of December 2012.
47
Figure 7: Comparison of the performance of uncoated and 10 µm thick fluorocarbon coated heat
exchangers made of stainless or carbon steel for different induction periods, fouling rates and
cleaning periods on the coated units. (a) ratio of optimal cleaning times; (b) ratio of
annualised costs; (c) ratio of energy losses. Note change in base axes between (a) and (b).
48
Figure 8: Case Study II. Comparison of the performance of uncoated and fluorocarbon-coated heat
exchangers made of stainless or carbon steel for different induction periods, fouling rates and
coating thicknesses. (a) ratio of optimal cleaning times; (b) ratio of annualised costs; (c) ratio
of energy losses. Note change in base axes between (a) and (b).
49
Figure 9: Case Study III. Annualised operation cost profile and optimal cleaning times, 𝒕𝒐𝒑𝒕, for
uncoated and fluorocarbon coated stainless steel dairy PHX, with a hygiene operating constraint
at 2 days (48 h).
50
Figure 10: Case Study III. Comparison of the performance of an uncoated and a coated dairy PHX for
different induction periods, fouling rates and cleaning periods. 10 µm thick fluorocarbon
coating. (a) ratio of optimal cleaning times; (b) ratio of annualised costs. Note different base
axes.
51
Figure 11: Case Study III. Relative performance of a coated dairy PHX unit for different fouling rates,
coating thickness and hygiene constraint. tind = 2 hours. (a) ratio of optimal cleaning times; (b)
ratio of annualised costs.
52
53
Figure 12: Case Study III. Relative performance of a dairy PHX unit with 10 µm thick fluorocarbon
coating and thyg = 48 h for different induction periods, fouling rates and cleaning periods. (a)
ratio of optimal cleaning times; (b) ratio of annualised costs. Note change in base axes.
Figure 13: Case Study III. Maximum capital cost factor, , for different fouling rates and induction
periods and for selected cost saving ratios.
54