VALUE PRICING OF ANTIFOULING COATINGS IN HEAT EXCHANGERS

Transcription

1 Proeedings of International Conferene on Heat Exanger Fouling and Cleaning (Peer-reviewed) June 07-12, 2015, Enfield (Dublin), Ireland Editors: M.R. Malayeri, H. Müller-Steinagen and A.P. Watkinson Publised online VALUE PRICING OF ANTIFOULING COATINGS IN HEAT EXCHANGERS O.M. Magens 1, J. Hofmans 2, M. Pabon 3 and D.I. Wilson 1* 1 Department of Cemial Engineering and Biotenology, University of Cambridge, Cambridge, CB2 3RA, UK 2 Cemours/DuPont de Nemours BVBA, A. Spinoystraat 6A, B-2800 Meelen, Belgium 3 Cemours/DuPont de Nemours International S.A., 2, Cemin du Pavillon, PO Box 50, CH-1218 Le Grand-Saonnex, Geneva, Switzerland * Corresponding autor. diw11@am.a.uk; Tel. +44(0) ; Fax. + 44(0) ABSTRACT Fouling redues te termal and ydrauli performane of eat exangers over time, requiring regular leaning. A wide range of anti-fouling oatings as been proposed, but attempts ave only reently been made to quantify teir finanial attrativeness rigorously. Weter or not it is attrative to install a oated exanger depends on trade-offs between apital and operating osts over te lifetime of te unit. Te teno-eonomi value priing analysis of oating performane introdued by Gomes da Cruz et al. (2015) is applied ere to a eat exanger wit more realisti eat transfer and fouling performane, speifially distributed temperatures and temperature sensitive fouling rates. Calium arbonate rystallisation fouling is modelled using te surfae growt model and parameters reported by Pääkkönen et al. (2015). Te performane of oatings are ompared wit te unoated ase and te envelope were a oating is finanially attrative is identified. Te data needed to perform tese alulations are disussed. INTRODUCTION Fouling deposits on eat transfer surfaes redue te termal and ydrauli performane of eat transfer equipment over time. Deposits wi grow and deta an, moreover, lead to blokage, as well as ompromising ygieni operation and produt quality if te proessed streams are funtional materials (e.g. food, parmaeutials, fine emials). Tis gives rise to te need to lean eat exangers on a regular basis. Cleaning ations are not instantaneous, requiring te unit to be taken out of servie. Cleaning inurs furter eat transfer losses, or apital expenditure to provide a bakup faility to substitute for te absent unit. Antifouling oatings sould extend te operating period before leaning is required, and/or improve leaning rates or effetiveness: te finanial benefit of tis needs to be balaned against te ost of installing a new or revamped unit. Tis is te ore of te value priing onept introdued by Gomes da Cruz et al. (2015) and involves a series of modelling and optimisation alulations. Te deision wen and ow to lean a fouling eat exanger is an optimisation problem, first onsidered by Ma and Epstein (1981). Fig. 1 illustrates te underlying problem for a single eat exanger. Operation for a period of lengt t inurs an amount of energy loss. Cleaning restores te eat duty, Q, to te lean state, Q l. However, leaning requires te unit to be taken offline for time τ, and indues furter osts for te leaning operation, C l. Fig. 1 Semati of te fouling-leaning yle in a single eat exanger over time t'. Following an indution period wit negligible deposition of lengt t ind, te duty Q falls from te lean value Q l. After operating for time t te unit is leaned, taking time τ, and performane is restored to Q l. Grey saded area represents energy lost (after Magens et al., 2015) Te objetive funtion to be optimized is te timeaveraged operating ost, φ op, alulated tus: φ op t E = 0 ( Q Q( t' )) l dt' + Qlτ + C t + τ were E is te ost per unit energy. Te optimal proessing period, t opt, is found by setting dφ op/dt = 0, wi yields ( Q Q( t )) φ op( topt ) = E l opt (2) Furtermore, te ondition for a minimum in φ op to exist, d 2 φ op /dt 2 > 0, requires te eat duty to deline: dq/dt < 0. Computation of te operating ost requires knowledge of te fouling beaviour over time, Q(t'). If tis is available, it allows te operator or designer to determine te optimal operating strategy and onfiguration of a eat exanger. l (1) 350

2 Magens et al. / Value Priing of Antifouling Surfae Coatings in Heat Exangers Gomes da Cruz (2015) onsidered te linear fouling ase, were te fouling resistane, R f, inreases at a onstant rate. Tey quantified te attrativeness of anti-fouling oatings to mitigate fouling using a teno-eonomi analysis of te optimal operating performane of an individual eat exanger and ompared tis wit te ost of installation of a oated unit. Te upper prie tat an be arged for a oating is set by its ability to redue deposition and enane leaning, wile te lower limit is set by manufaturing osts. Quantifying tis prie range, werein value is reated for te vendor and puraser, sould ideally be performed early in te deision proess as it elps to set targets for te oating performane as well as manufaturing ost. Magens et al. (2015) extended te above approa to onsider asymptoti fouling beaviour, wi is more ommon. Tey presented analytial solutions for te ase were te eat exanger ould be modelled using lumped model metods. Tis paper extends teir work furter by onsidering spatially and temporally dynami fouling beaviour. Canges in te proessing onditions and te onditions at te eat transfer interfae influene te loal fouling rate and ause preditions from lumped models to be inaurate, wi in turn affets φ op. Geddert et al. (2009) identified proessing onditions influening fouling as inluding te nature and soure of te foulant, additives, bulk temperature, flow veloity and flow regime. Te loal surfae temperature, its surfae energy, rougness, topograpy and number of nuleation sites (partiularly for rystallization fouling) are also important. Coatings to mitigate fouling (inrease Q) and/or enane leaning (derease τ and C l) are te subjet of mu effort in industry and aademia. Gomes da Cruz et al. (2015) reviewed te different metods for oating eat transfer surfaes wit anti-fouling properties, often by manipulating surfae energy and adesion. From te eat transfer perspetive, oatings an be lassified as tose wi impose extra termal resistane and tose wit negligible impat on eat transfer. For example, fluoroarbon-based polymer surfaes provide low surfae energies, but tend to ave low termal ondutivity (Zao et al., 2002). Considerable effort as been spent on improving teir abrasion resistane and adesion to te substrate. Teir non-stik properties ave set te benmark in ouseold appliations and are effetive even after years of ars termal onditions and leaning proedures. An idealised fluoroarbon oating is onsidered ere. SPATIALLY DISTRIBUTED MODEL Te temperature distribution witin a single pass ounter-urrent eat exanger is alulated over time. A loal rystallisation fouling model sensitive to proessing and interfae onditions is inorporated using te approa presented by Fryer and Slater (1985). More omplex simulations su as tat reported by Coletti et al. (2010) ould be used, if desired. Similarly, oter types of fouling ould implemented (Fryer and Slater studied emial reation fouling by milk). Figure 2 sows a differential element of area of te eat exanger: da = Aδz/L. Entalpy balanes on te ot and old streams yield te following onstitutive partial differential equations for te (well-mixed) bulk fluid temperatures at axial position, z, and time, t : Hot side fluid T (t, T t' UAv = LW ( T T ) Cold side fluid T (t, T t' UAv = LW ( T T ) T + v z T v z Here, U is te loal overall eat transfer oeffiient, A is te total eat transfer area, v and v are te loal bulk fluid veloities, L is te lengt of te unit and W and W are te eat apaity flow rates. U inludes te film eat transfer oeffiients, te wall and any fouling resistanes. Fig. 2 Elements of te entalpy balane on eiter side of an inrement of lengt for a ounterurrent eat exanger (after Fryer and Slater, 1985). Bot streams are aqueous. Water property variation wit temperature is interpolated from te VDI database (VDI, 2010). Tis approa allows te loal deposit interfae temperature and transport oeffiients to be evaluated and anges wit time aounted for. CRYSTALLISATION FOULING MODEL Te old stream is assumed to ontain dissolved alium arbonate wi auses rystallization fouling. Solubility is a funtion of te onditions at te loation of rystal formation, in partiular te temperature (Bott, 1997). Te effets of ph, pressure and te presene of oter emial speies are not onsidered ere but ould be inluded if desired. Assuming te solid pase to be alite, te solubility, C s (in kg/m 3 ), at te deposit-solution interfae temperature, T i, is alulated using te orrelation reported by Pääkkönen et al. (2015) (were T i is in C) i Cs = T Ti T (5) i Aragonite and vaterite ave iger solubilities and are not expeted to partiipate (Helalizade et al., 2000). Te temperature distribution and flow onditions are assumed to 7 2 (3) (4) 351

3 Heat Exanger Fouling and Cleaning 2015 favour surfae integration ontrolled deposition (Bott, 1997; Bansal et al., 2008) Te integration step is a ompliated proess, involving te pysis of eterogeneous nuleation, emistry of te solid-liquid interfae and loal termo- and ydrodynamis (Pääkkönen et al., 2015). Rater tan modelling all tese proesses in detail, te rate of deposition into te rystal lattie is alulated via. dm dt E f a j = kd 'exp ( Ci Cs ) ' RT (6) i wit te dependeny on te differene between te saturation onentration, C s, and te onentration at te interfae, C i, being set as j = 2 (Helalizade et al., 2000; Mwaba et al., 2006; Bansal et al., 2008; Pääkkönen et al., 2015). E a is te ativation energy and R te gas onstant. If te integration step ontrols fouling, te onentration of speies at te wall, C i, is pratially equal to te bulk onentration, C. Te interfae temperature is alulated using te internal film eat transfer oeffiient,, via. U T i = ( T T ) + T Te deposition rate fator, k d, is expeted to be a funtion of loal flow veloity or residene time. Te stiking fator formulation suggested by Epstein (1994) is used: k d = k d μ l/(ρ lv 2 ), were μ l denotes te visosity of te liquid and ρ l is te liquid density evaluated at interfae temperature. V is te frition veloity, estimated using te Blasius orrelation (7) be te largest satisfying te Courant-Friedris-Lewy riterion for te two stiff equations wen using an expliit integration metod (Press, 1986). Fryer and Slater were interested in fast fouling, reaing an asymptote in about one our. For slower fouling rates wit a ig spatial resolution, multistep metods su as tose in Matlab ode15s, are more effiient and are used ere. Equations (3) and (4) are integrated numerially over time. Te spatial derivatives are approximated wit a first order upwind seme and finite Δz, giving for te ot stream T z + T z T ) (9) z z and for te old stream T T z z T ) (10) z z Tis upwind seme is preferred over entral differening semes sine advetive entalpy transfer dominates diffusive transfer and eat an only propagate in te diretion of bulk flow. Te ontinuous oordinates, t and z, are disretized wit a mes of temporal, k = 1, 2 K, and spatial, n = 1, 2 N, nodes. Figure 3 sows a semati of te spatial mes. N, was set at 150, as larger values gave no appreiable inrease in auray. τ i f V = = v = v ρ Re (8) Here, τ i is te sear stress imposed on te fouling layer and Re is te Reynolds number of te old stream evaluated at te interfae temperature. Inorporation of additional material into te deposit beomes more diffiult as te rystal layer grows and long rystals are likely to be less robust against removal fores (Bott, 1997). A suppression or term ould be inluded to address tis, but is negleted ere. Te fouling layer is assumed to be omogeneous and fouling slow, so tat te bulk onentration of fouling preursors does not ange wit z. Te loal fouling resistane is alulated from R f = m f/(ρ fk f) and te fouling Biot number is given by Bi f = R fu l. Te loal dut diameter anges as a result of layer growt (tikness δ f = m f/ρ f) so T i, V, C s and fluid properties vary wit position and time. Hene te fouling rate and Bi f vary as f(z, t ). SOLUTION METHOD Fryer and Slater (1985) used te metod of arateristis to onvert te yperboli partial differential equations (3) and (4) into ordinary differential equations. Te arateristi lines assoiated wit te onvetional entalpy transport, wit veloities v and v, onstrain te numerial integration to a distint step size, wi proves to Fig. 3 Seme of te spatial mes of te exanger. N nodes are equally spaed along te pysial lengt L. Cleaning is assumed to remove all fouling. Te initial temperatures of all nodes n at k = 0 are set to te steady state profile for te lean exanger, obtained by running an initial simulation fouling, i.e. dm d/dt = 0. Te temperatures onverge rapidly to te lean distribution. Tis was verified by omparison wit analytial results. To define upwind derivatives at te inlet boundaries, T (k, N+1) and T (k, 0) are arbitrarily set to zero. Tis is a omputational measure as te unit operates wit onstant inlet temperatures. Te boundary onditions 352

4 Magens et al. / Value Priing of Antifouling Surfae Coatings in Heat Exangers T = T z = L, t' (11) in T = T z = 0, t' (12) in are enfored by setting te numerial temporal derivatives at ea inlet to zero, i.e. T ( k, N) T ( k,1) = = 0 t' t' (13) CRYSTALLIZATION FOULING CASE STUDY Pääkkönen et al. (2015) studied saling of CaCO 3 on a flat-plate AISI 316L stainless steel eat exanger surfae and measured initial mass deposition rates under transitional and turbulent flow onditions. No indution period was observed and tey reported tat Equation (6) gave losest agreement wit teir data. Te kineti parameters, experimental onditions and properties of te porous fouling layer are given in Table 1. Te fouling model desribed above was verified against Pääkkönen et al. s results. Table 1: Kineti parameters, experimental onditions and fouling layer properties (after Pääkkönen et al., 2015). Kineti parameters k d Deposition rate fator m 4 /kg s 2 E a Ativation energy J/mol Operating onditions T i Interfae temperatures K C CaCO 3 onentration kg/m 3 D yd Hydrauli diameter 0.03 m v Bulk veloities m/s Re Reynolds number (parallel plates) Fouling layer properties ρ f Density 971 ± 13 kg/m 3 k f Termal ondutivity 0.66 ± W/m K We illustrate value priing of antifouling oatings by omparing an unoated stainless steel and a polymer oated single-pass ounter-urrent sell-and-tube eat exanger operating at onstant flow rates and inlet temperatures. Te oating introdues an additional termal resistane to te overall eat transfer oeffiient, wi is evaluated using 1 Bi U = + U f l δ + k oat oat r + k wall r log r r + r 1 (14) were r and r are te internal and external radii of te tubes, is te internal and te external film eat transfer oeffiient, δ oat te oating tikness, and k oat and k wall are te oating and tube wall termal ondutivities, respetively. Baffles are not onsidered and te flow in te sell is assumed to be parallel to te tubes. Te film eat transfer oeffiients are estimated using te Gnielinski orrelation wit temperature dependent water properties and te approporiate ydrauli diameters (Bergman et al., 2011). Te differene in U values means tat te oated unit requires a larger eat transfer area to aieve te speified lean eat duty. Tis is alulated from te number of transfer units, i.e. A oat = AU l/u l,oat and te lengt of te oated exanger inreased aordingly. For te unoated unit, δ oat is zero. Te design and operating parameters of te two eat exangers are summarised in Table 2. Operating onditions were seleted to be initially omparable to te onditions in te Pääkkönen et al. (2015) experiments. Te fouling model (6) is solved togeter wit te entalpy balanes (3) and (4) in Matlab on a desktop PC. As te fouling layer builds up, te inrease in fluid veloities, aused by dereasing dut diameter, redues te fouling rate signifiantly. Table 2: Design, operating and ost parameters of te oated and unoated (un) eat exangers. Design of te unoated unit A Heat transfer area 96.7 m 2 L Lengt 20.0 m NT Number of tubes 150 r Inner tube radius 5.1 mm r Outer tube radius 6.4 mm s Tube spaing 9.1 mm r sell Sell radius 103 mm k wall Tube termal ondutivity 16 W/m K U l Overall lean eat transfer 234 W/m 2 K oeffiient Q l Clean eat duty 482 kw Modified design of te oated unit k oat Coating termal ondutivity W/m K δ oat Coating tikness 1 10 µm A oat Heat transfer area 99.0 m 2 L oat Lengt 20.5 m U l,oat Overall lean eat transfer oeffiient 229 W/m 2 K Operation w Cold stream mass flow 4 kg/s w Hot stream mass flow 4 kg/s T,in Hot stream inlet temperature K T,in Cold stream inlet temperature K C CaCO 3 onentration kg/m 3 τ Time taken for leaning 3 days v Cold stream bulk veloity, un m/s Re Cold Reynolds number, un Costs E Cost per unit eat US$/J C l Cleaning ost per unit 2000 US$ t lf Asset lifetime (depreiation) 5, 10, 15 years 1 Data taken from Gomes da Cruz et al., 2015 RESULTS AND DISCUSSION Figure 4 sows te temperature distribution in te unoated exanger at different times. Te ange in temperatures of bot streams aross te exanger beomes smaller wit time owing to fouling. Tere is little ange in 353

5 Heat Exanger Fouling and Cleaning 2015 te old stream temperature distribution near its inlet as tere is less deposition ere as te level of supersaturation, wi drives rystallisation (Equation (6)) is smaller. In te seond alf of te exanger tere is notieable ange over time as tis is were fouling, driven by bulk temperature and saturation, is igest for te inverse solubility salt. Figure 5 sows te distribution of deposit in te unoated exanger at different times, expressed as te loal fouling Biot number. Te Biot number at te ot end exeeds 1 at extended time, indiating a signifiant ange in U. Te fouling layer formation kinetis are not trivial as a result of te dynami interdependeny between eat transfer and temperature sensitivities in te fouling model. Tere is a notieable transition from onvex to onave fouling distributions over time, and autoretardation at te ot end. As te fouling layer grows, interfae temperatures derease. Dut narrowing auses te flow veloity to inrease, resulting in a lower fouling rate. Isiyama et. al. (2008) presented a tenique to alulate te mean fouling rates in o- and ounter-urrent eat exangers assuming a linear ange in temperature aross te unit. Tey also assumed tat te fouling layer tikness does not vary onsiderably over te tube lengt: so fouling rates tended to inrease monotonially aross te unit. Figures 4 and 5 sow tat teir approa would not be appliable to tis ase. Te old temperature profile is initially linear but beomes non-linear over time. Figure 5 sows evidene of strong variations in loal fouling rate, generated by different sensitivities to interfae and bulk temperature in te Arrenius rate onstant and te solubility in Equation (6). After long periods of time, it as to be expeted tat te interfae temperature, and ene te fouling layer tikness, beomes more and more uniform. Fig. 5 Fouling Biot number distribution in unoated exanger at seleted times, t. Te effet of fouling on te overall fouling resistane for te unoated unit is presented in Figure 6. Te overall trend ould be desribed as falling rate fouling and arises from two autoretardation meanisms, namely dereasing T i and anges in stiking fator. Tis will be aompanied by an inrease in old stream pressure drop. Asymptoti fouling beaviour as reported by Zao et al. (2002) for CaSO 4 fouling on a stainless steel surfae, would require a suppression or removal term. Fig. 6 Evolution of te overall fouling resistane, R f, of te unoated unit. Fig. 4 Bulk temperature distribution along te unoated eat exanger at different times, t. Te impat of fouling on finanial performane is plotted in Figure 7. Te optimal proessing period, t opt, is reaed after 316 days of proessing, wen te operating ost, φ op, alulated wit Equation (1), equals te termal ost of fouling. At t opt = 316 days, te overall fouling resistane is 2.5 m 2 K/kW, wi orresponds to a mean fouling layer tikness of δ f R f k f = 1.65 mm. Tis is signifiant ompared to te tube radius of 5.1 mm, su tat approximating te fouling layer as a tin slab is not aurate. If deposits of tis tikness were enountered regularly, te assumptions in deriving Equation (14) would need to be revised

6 Magens et al. / Value Priing of Antifouling Surfae Coatings in Heat Exangers performane of te unoated exanger in Figure 7. In general, a derease in time required for leaning as a limited effet on te operating ost as te operating periods are very long: tis is evident from Equation (1) if τ is small ompared to t opt. A redution in deposition rate onstant, gives an appreiable differene in operating ost. Tis provides guidane for te development of oatings, sine innovations in oter ontexts often sow a diminising marginal benefit. In tis ase te indution period would ave to be long, in order to influene φ op signifiantly. Not sown in Figure 8 is te assoiated value of t opt, wi will be longer tan 316 days. Tis also onstitutes important guidane as te oating must maintain its integrity (e.g. not spall off) and performane over te extended period if it is to be onsidered for use in pratie. Alternatively, tese alulations an provide indiations of te minimum life expetany required of su oatings. Fig. 7 Effet of proessing period lengt, t, on te annualised operating ost, φ op, and te termal ost of fouling for te unoated eat exanger. Te ross (at t opt = 316 days, φ op,opt = $/day) indiates were Equation (2) is satisfied. Pääkkönen et al. (2015) only studied alite deposition on stainless steel so te antifouling performane of a series of fititious oatings is examined ere in a sensitivity analysis. Te parameters of te fouling model are varied to represent improved fouling arateristis: (i) Geddert et al. (2009) looked at fouling on modified surfaes at iger Reynolds numbers and reported tat te deposition rate onstant was smaller for surfae modifiations wit anti-fouling properties. Tis is investigated by speifying te ratio of deposition rate onstants, in te range 0.1 (good antifouling) k d,oat/k d 1 (no benefit). Te lower limit an be osen as needed: if k d,oat = 0 tere is no need to lean! (ii) Mayer et al. (2012) found tat anti-fouling surfaes exibited lower adesion fores between CaCO 3 rystals and surfaes, wi is likely to failitate leaning. Tis would primarily redue te time taken for leaning, τ, and is investigated for 0.1 τ oat/τ 1. (iii) A oating providing fewer nuleation sites and wit surfae energy indering eterogeneous nuleation is expeted to promote longer indution periods at low flow veloities. However, reliable predition of indution periods is diffiult so is not onsidered ere (see Gomes da Cruz, 2015, for examples). Sine te rystallisation meanism is unaffeted by te oating after an initial rystal layer is formed, te ativation energy, E a, is unlikely to be affeted. Te oated eat exanger is presumed to be operated for te optimum proessing period, ten leaned. Fig. 8 sows te effet of different levels of oating performane (deposition rate and leaning time) on te dimensionless optimal operating ost, alulated by referene to te Fig. 8 Effet of antifouling oating performane (deposition rate and leaning time) on te ratio of optimal operating ost to tat of te unoated exanger. Capital osts are now onsidered. A oated exanger ould be onsidered to replae an existing unit, in a revamp or retrofit, or as an alternative to an unoated unit for a new plant. Te latter, greenfield, senario, is onsidered ere. Exluding te ost of te oating, te apital ost of te base unit, C ap, is alulated as an amortised ost, φ ap = C ap/ t lf, assuming straigt line depreiation over te unit (or oating) lifetime, t lf. Oter depreiation poliies ould be onsidered, depending on te aounting pratie to be used. Te total optimised annualised ost is ten φ T = φ ap + φ op,opt. Aording to Hewitt et al. (2007), a 100 m 2 arbon steel TEMA BEM type eat exanger ost approximately 140 GBP/m 2 in Conversion into US$ and updating it wit te emial engineering plant index to Deember 2013 yields an installed ost of 332 US$/m 2. Taking tis ost as an estimate and assuming 10 years asset lifetime, te 355

7 Heat Exanger Fouling and Cleaning 2015 amortised apital osts of te base units are φ ap = US$/day for te unoated unit and φ ap,oat = US$/day for te sligtly larger oated unit, before oating osts are added. Müller-Steinagen et al. (1997) stated te low termal ondutivity of polymers su as PTFE was one of te main disadvantages of polymer based anti-fouling oatings in eat exangers. Tis does not old true for tis ase, possibly beause te oating is tin. Given tat φ op is approximately 28 US$/day for te unoated unit, te ontribution from apital expenditure is modest: tenoeonomi analysis suggests tat te eat transfer penalty is negligible in omparison to te potential savings wen proessing streams prone to serious fouling. Te maximum prie for oating su an exanger an be alulated from oat, max, new φ, ( φt T oat ) tlf Aoat = (15) Tis is te value prie for oating a eat exanger to mitigate fouling. It represents te maximum benefit arising from installing te oated item, to be sared between te operator and te oating vendor. If te oating annot be provided at tis prie or less tere is no inentive for te operator to onsider it. Figure 9 sows a map of potential value pries alulated for te ases in Figure 8. Neiter inflation nor te time value of money is onsidered ere, but ould be introdued to alulate te net present value. oeffiient, a parallel experiment wit a nikel posporus/ptfe oating exibited no fouling over te duration of te experiment. If tis most promising result would apply to te urrent ase, te oating value would greater tan US$/m 2, depending on t lf. Fluoropolymers generally provide good orrosion resistane so a fluoropolymer oated arbon steel unit ould be onsidered as an alternative to a stainless steel unit. Carbon steel is eaper and onduts eat better tan te stainless variety: tis ould ompensate for te additional termal resistane imparted by te oating. Gomes da Cruz et al. (2015) investigated tis senario and sowed it to be an attrative option. Te oating again as to be stable and impermeable for te wole time in servie. CONCLUSIONS 1. Te entalpy balanes of a pure ounter-urrent eat exanger were solved togeter wit a fouling model to predit te eat duty and fouling dynamis in a simple eat exanger subjet to rystallisation fouling. 2. Te eat exanger model was able to demonstrate nonlinear fouling dynamis arising from different temperature dependenies in rystallisation fouling. 3. A metodology for assessing te eonomi value of speifi oatings was demonstrated for various ombinations of antifouling effetiveness. 4. For te ase study onsidered, a sorter leaning period ad a substantial, but limited effet on te operating ost ompared to te termal savings wen reduing te deposition rate fator. 5. Te low termal ondutivity of te polymer oating onsidered ere ad negligible effet ompared to te potential gain from fouling mitigation. ACKNOLEDGEMENTS A PD studentsip for OMM from Du Pont/Cemours is gratefully aknowledged. Fig. 9 Value pries of oating for different ratios of deposition rates, tree asset lifetimes, and four dimensionless leaning period lengts. Te strong effet of asset lifetime, t lf, is evident in te results in Figure 9. In pratie, te asset lifetime is likely to be limited by te oating s durability. Assuming te oating is stable and retains its effetiveness, it reates maximum value if it prevents fouling ompletely. Zao et al. (2002) onduted fouling experiments wit aqueous CaSO 4 solution on stainless steel surfaes. Wile rystal deposits on te stainless steel surfae resulted in a 38% lower eat transfer NOMENCLATURE A eat transfer area (m 2 ) Bi f fouling Biot number ( ) C CaCO 3 onentration (kg/m 3 ) C ap apital ost of te base unit (US$) C l leaning ost per eat exanger unit (US$) oat oating prie per area (US$/m 2 ) E ost per unit eat (US$/J) D yd ydrauli diameter (m) E a ativation energy (J/mol) f fanning frition fator ( ) film eat transfer oeffiient (W/m 2 K) j order of te rystal integration reation ( ) K total number of temporal nodes k termal ondutivity (W/m K) or temporal node 0,1, k K ( ) k d deposition rate fator (m 4 /kg s 2 ) k d deposition rate fator k d = k d μ l/(ρ lv 2 ) (m 4 /kg s) L lengt of te eat exanger (m) m f mass of te fouling layer per overed area (kg/m 2 ) 356

8 Magens et al. / Value Priing of Antifouling Surfae Coatings in Heat Exangers N total number of spatial nodes ( ) NT number of tubes ( ) n spatial node 0,1, n N ( ) Q eat duty (kw) R gas onstant (J/mol K) Re Reynolds number ( ) R f fouling resistane (m 2 K/W) r radius (mm) s tube spaing (mm) t operating period (days) t lf asset lifetime (years) t time, used as variable in integrand 0 t t (days) T temperature (K) U eat transfer oeffiient (W/m 2 K) V frition veloity (m/s) v bulk fluid veloity (m/s) W eat apaity flow rate (J/s K) w mass flow rate (kg/s) z position along te exanger 0 z L (m) Δz spatial step size (m) δ tikness (m) μ visosity (Pa s) ρ density (kg/m 3 ) τ time taken for leaning (days), sear stress (Pa) φ ap amortised apital ost of te base unit (US$/day) φ op annualised operating ost (US$/day) φ T total annualised ost (US$/day) Subsript old stream/internal l lean oat oating/oated f fouling layer ot stream/external i at te interfae in inlet l liquid op operating opt optimal s solubility wall tube wall REFERENCES Bansal, B., Cen, X.D. and Müller-Steinagen, H., 2008, Analysis of lassial deposition rate law for rystallisation fouling. Cem. Eng. Proess., Vol. 47, pp Bergman, T., Inropera, F., 2011, Fundamentals of Heat and Mass Transfer, Wiley, New York. Bott, T.R., 1997, Aspets of rystallization fouling, Exp. Term. Fluid Si. Vol 14(96), pp Coletti, F., Isiyama, E. M. and Paterson, W., 2010, Impat of deposit aging and surfae rougness on termal fouling: distributed model. AICE J., Vol. 56(12), pp Epstein, N., 1994, A model of te initial emial reation fouling rate for flow witin a eated tube, and its verifiation, Pro. 10 t International Heat Transfer Conferene, Brigton, UK. Fryer, P.J. and Slater, N.K.H., 1985, A diret simulation proedure for emial reation fouling in eat exangers, Cem. Eng. J., Vol. 31(2), pp Geddert, T., Bialu, I., Augustin, W. and Soll, S., 2009, Extending te indution period of rystallization fouling troug surfae oating, Heat Trans. Eng., Vol. 30(10 11), pp Gomes da Cruz, L., Isiyama, E.M., Boxler, C., Augustin, W.A., Soll, S. and Wilson, D.I., 2015, Value priing of surfae oatings for mitigating eat exanger fouling, Food Bioprod. Pro., Vol. 93, pp Helalizade, A., Müller-Steinagen, H. and Jamialamadi, M., 2000, Mixed salt rystallisation fouling, Cem. Eng. Proess., Vol. 39, pp Hewitt, G.F. and Pug, S.J., 2007, Approximate design and osting metods for eat exangers. Heat Trans. Eng., Vol. 28(2), pp Isiyama, E.M., Paterson, W.R. and Wilson, D.I., 2008, Termo-ydrauli annelling in parallel eat exangers subjet to fouling. Cem. Eng. Si., Vol. 63(13), pp Ma, R.S.T., and Epstein, N., 1981, Optimum yles for falling rate proesses, Can. J. Cem. Eng., Vol. 59(5), pp Magens, O.M., Isiyama, E.M., and Wilson, D.I., , Quantifying te implementation gap for antifouling oatings. Pro. 3 rd Sustainable Termal Energy Management Conferene, Newastle upon Tyne, UK Mayer, M., Augustin, W. and Soll, S., 2012, Adesion of single rystals on modified surfaes in rystallization fouling, J. Cryst. Growt, Vol. 361(1), pp Müller-Steinagen, H. and Zao, Q., 1997, Investigation of low fouling surfae alloys made by ion implantation tenology. Cem. Eng. Si., Vol. 52(19), pp Mullin, J.W., 2001, Crystallization, Butterwort- Heinemann, Oxford. Mwaba, M.G., Golriz, M.R. and Gu, J., 2006, A semiempirial orrelation for rystallization fouling on eat exange surfaes, Appl. Term. Eng., Vol. 26, pp Pääkkönen, T.M., Riiimäki, M., Simonson, C.J., Muurinen, E. and Keiski, R.L., 2015, Modeling CaCO 3 rystallization fouling on a eat exanger surfae Definition of fouling layer properties and model parameters. Int. J. Heat Mass Transfer, Vol. 83, pp Press, W.H., Teukolsky, S.A., Flannery, B.P. and Vetterling, W.T., 1986, Numerial reipes: Te art of sientifi omputing, Cambridge University Press, New York. VDI e.v., 2010, VDI Heat Atlas, Springer, Berlin. Zao, Q., Liu, Y., Müller-Steinagen, H. and Liu, G., 2002, Graded Ni P PTFE oatings and teir potential appliations. Surf. Coat. Tenol., Vol. 155(2-3), pp