Scaling Growth in Heat Transfer Surfaces and Its Thermohydraulic Effect Upon the Performance of Cooling Systems

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1 799 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 017 Guest Edtos: Peta S Vabanov, Rongxn Su, Hon Loong Lam, Xa Lu, Jří J Klemeš Copyght 017, AIDIC Sevz S..l. ISBN ; ISSN The Italan Assocaton of Chemcal Engneeng Onlne at DOI: /CET Scalng Gowth n Heat Tansfe Sufaces and Its Themohydaulc Effect Upon the Pefomance of Coolng Systems Hebet Lugo-Ganados, Matín Pcón Núñez* Depatment of Chemcal Engneeng, Unvesty of Guanajuato, Noa Alta s/n, Guanajuato, Gto., Mexco, C.P pcon@ugto.mx A new theoetcal model to pedct the buld-up of scalng on the heat tansfe suface of cooles s developed. Scalng foulng s ognated as a laye of cystals of nvese solublty salts such as calcum cabonates pesent n coolng wate, s fomed on the heat tansfe suface. Even though foulng cannot be fully avoded, ts detmental effect can be mnmsed by accuate pedcton of foulng ates. Most cuent models fo the pedcton of scalng ae based on a mechansm that consdes mass tansfe though the lamna laye and the chemcal eacton between ons to fom the salt. It has been obseved that wth such models, the velocty of deposton of cystals augments as the flud velocty nceases wthout a tendency to an asymptotc behavou. Theoetcally, at hghe flud veloctes, t s expected that a emoval phenomenon to take place wth the consequent educton n the ate of deposton. Besdes, even wth tme, the ate of deposton cannot be mantaned snce velocty nceases as the coss-sectonal aea of a tube s educed and the netal and fcton foces tend to mantan the on speces n soluton dampenng the eacton. In ths pape, a new model s poposed to account fo the emoval tem. The model s valdated aganst expemental data and ts pefomance s compaed aganst extng models avalable n the open lteatue. 1. Intoducton Scalng s a common type of foulng that takes place n coolng systems and s assocated to wate hadness. Ths type of foulng happens as cystals deposts gow on a heat tansfe suface becomng a laye that dmnsh heat tansfe. The most common type of scalng s the one fomed fom calcum cabonates and sulphates. These salts have the chaactestc that ts solublty deceases at nceased tempeatues, thus eachng the condton of ovesatuaton untl cystals stat to depost on the suface (Pugh et al, 007). Scalng s stongly dependent on tempeatue, velocty, concentaton and ph. Once fomed t can only be emoved on an acdc envonment (Bott, 1994). Among the vaous wate dssolved salts that ognate foulng, ths wok focuses on CaCO 3 snce t s the compound that s found n the lagest popoton n most souces of coolng wate (Pӓӓkkonen, 015). The mpotance of studyng foulng les n the fact that not only heat exchanges educe ts themal effectveness (Zahd et al., 016) but that the downsteam consequences ceate huge economc losses as epoted by Alabudznsk et al. (016).. Methodology Hasson et al. (1968) poposed a foulng mechansm based on the lamna laye whee mass tansfe by dffuson and chemcal eacton take place. Mass tansfe by dffuson can be expessed by Eq(1) and Eq(): m = β ([ Ca ] [ Ca ] ) + + b 3 ] b [ CO3 ] (1) m = β ([ CO ) () Please cte ths atcle as: Lugo-Ganados H., Pcón Núñez M., 017, Scalng gowth n heat tansfe sufaces and ts themohydaulc effect upon the pefomance of coolng systems, Chemcal Engneeng Tansactons, 61, DOI: /CET

2 800 Whee β s the mass tansfe coeffcent. As soon as the salt ons each a suface, the deposton pocess stats by the chemcal combnaton to fom the CaCO 3 molecule whch wth tme, gves bth to a cystal laye. The mass tansfe ate can also be expessed as a functon of the ate of eacton, the on concentaton at the nteface and ts solublty: m = k ([ Ca + ] [ CO 3 ] Ksp) (3) Whee K sp s the solublty constant of calcum cabonate, k s the coeffcent of eacton whch s detemned fom the Ahenus equaton. k E RT = k 0 e (4) Whee k 0 s the eacton constant, E s the actvaton enegy, R s the gas constant and T the tempeatue at the sold-lqud nteface. As a laye of cystals s fomed on a heat tansfe suface, t ceates an addtonal themal esstance to heat tansfe. The value of ths esstance depends on vaous paametes, such as on concentaton, tempeatue, and flud velocty among othes. When a theoetcal model s used to pedct the gowth of scalng wth tme, t s commonly found that ts value nceases monotoncally wth tme and even exhbtng geate values wth velocty. Such behavou s contay to theoy snce hghe veloctes ae assocated to tubulent egmes whee patcles ae moe lkely to be emoved mpedng eacton and pecptaton (Bott, 1994). The need then ases to nclude the effects of vscosty, flud densty, damete and oughness on the emoval of Ca + and CO 3 - befoe they eact to fom a CaCO 3 molecule. Fom the P (π) Buckngham theoem (Boylng, 1979), t s found that a dmensonless paamete that affects the ate of deposton s the fcton facto, f. = τ (5) The fcton facto s elated to the flow esstance on the suface of the foulng laye. Now, the effect of velocty can be ncluded by means of the netal foces and vscous foces whch ae epesented by Reynolds numbe. Thus, a new empcal facto (α) expessed by Eq (6) s used. The coelatng paametes a and b ae detemned fom expemental data. ( f Re) b α = a (6) Incopoatng ths coecton facto nto Eq (3) esults: d m = α k ([ Ca] [ CO 3 ] [ Ksp] ) (7) Whee s the mass deposton ate. The convenence of usng a coecton facto such as the one gven by Eq (6) s that any othe type of salt can be analysed o even any combnaton of salts pesent n the coolng wate can be analysed povded the expemental data exsts fo the system unde consdeaton..1 Theoetcal model The fully developed model to pedct the ate of mass deposton ncludng the dffuson and eacton steps s epesented by Eq(8). ( β + ( C + C ) αk ) + 4α k ( Ksp [ C ][ C ]) β β 1 1 = + ( + ) d C1 C (8) αk α k m Whee C 1 y C ae the Ca + and CO 3 - concentatons. The themal esstance due to foulng s expessed by: dr dt f d f m m ρ λ = (9) f

3 Whee ρ f and λ f ae the densty and themal conductvty of the salt; s the mass deposted and s the mass ate emoval fom the suface (Quan et al., 008). 3. Results Fo valdaton puposes, pedcted foulng values ae compaed to typcal publshed foulng esstances n Table 1. Also, esults ae compaed wth values epoted by othe authos usng the own theoetcal models. The am s to demonstate that the new model can poduce elable esults. Fo the puposes of the analyss, the data epoted on Tables and 3 ae used to detemne the foulng ate. Teated wate wth low hadness consstng solely of CaCO 3 flowng though a smooth coppe ppe was consdeed. Table 1: Typcal foulng esstance factos (Bott, 1994) Flud type R f (m K/W) Rve wate below 50 C Coolng wate (teated) Coolng wate (unteated) Table : Data fo CaCO 3 foulng ate calculaton ph Ρ µ R (mol/l) (mol/l) (kg/m 3 ) (kgm/s) (J/mol K) , Ca + CO 3 - Table 3: Data fo CaCO 3 foulng ate calculaton (contnued) ρf λf Dh K 0 E D f (kg/m 3 ) (mol/l) (m) (m 4 /kg s) (kj/kmol) (m /s), E15 115E3 7.90E-10 Expemental data publshed n the open lteatue ae used to valdate the model. Fgue 1 shows the new model plotted aganst mass deposted measued expementally by Pӓӓkkoken (015) and n Fgue, the new model s plotted aganst the expemental foulng esstances detemned by Wu and Cemasch (013). Fgues 1 and show that the new model has good ageement wth the expemental data. In the case of Fgue, t can be obseved that the themal esstance nceases wth tme and educes wth velocty. The esults confm that the new model accuately descbes the eal phenomenon. Fgue 1: Compason between expemental data (Pӓӓkkoken, 015) and the modfed model fo CaCO 3 deposton.

4 80 Fgue : Compason between the new theoetcal model and expemental data (40 C) by Wu and Cemasch (013). 3.1 Model pefomance In ths secton, the new model s used fo the pedcton of the themal esstance wth tempeatue, velocty and tme. The esults ae compaed wth the models epoted by Pӓӓkkoken (015) n Fgue 3 and Wu and Cemasch (013) and Fgue 4. Fgue 3: Pedcton of themal esstance due to foulng. Compason between new model and Pӓӓkkoken (015). Fgue 3 shows the compason wth the model poposed by Pӓӓkkoken (015). The data epoted coesponds to foulng ates as a functon of tempeatue fo a velocty of 0.9 m/s. In ths case, t s found that the new model poduces estmatons whch ae moe acceptable compaed to what s expected fom epoted

5 values. Fgue 4 shows futhe use of the theoetcal models to pedct the foulng esstance fo a 6-month peod. Two veloctes ae consdeed: 0.35 m/s and 1 m/s usng data fom Table. Fgue 4 shows the compason fo a tempeatue of 80 C. The themal esstance pedcted by Wu and Cemasch (013) eaches values as hgh as x10 - m K/W whch ae 10 tmes geate than epoted values. Besdes, as the velocty nceases, the themal esstance also nceases whch s contay to what t s expected. The new model, on the othe hand, exhbts foulng esstances n the ange of.5x10-3 m K/W. In ths case the behavou wth velocty s as expected; ths s, as velocty nceases the foulng esstance deceases. Fgue 5 shows the use of the new model to pedct the foulng themal esstance n the tube of a coole n a 6-month opeatng peod. The tube has a length of m; wate entes the tube at 0 C and leaves at 60 C. 803 Fgue 4: Pedcton of themal esstance due to foulng. Compason between new model and Wu and Cemasch model (013). Fgue 5: Use of the new model to pedct the foulng ate n m long tube fo a 6-month opeatng peod. Wate nlet and outlet tempeatues ae 0 C and 60 C.

6 Conclusons Fo a gven flud velocty and concentaton, foulng esstance due to scalng nceases wth tme. Howeve, at hghe veloctes, the ate of deposton s expected to show lowe values. Fo a theoetcal model to accuately pedct such pefomance netal and fcton foces must be taken nto consdeaton and they should affect the ate of chemcal eacton. The atonale behnd ths s that at hghe veloctes, the nceased tubulence educes the lamna laye and takes away the Ca + and CO 3 - peventng them fom eactng to fom cystals whch once fomed adhee to the suface ceatng scalng. A shotcomng of most theoetcal models s that when they ae used to pedct foulng esstances, the pedcted values ae odes of magntude geate than the epoted values n the lteatue. Such ove pedcton endes the use of theoetcal models unelable fo desgn puposes. The model ntoduced n ths wok elmnates these shotcomngs and can confdently be used fo themal pefomance analyss leadng to desgn and opeatng stateges fo systems whee wate s used as a coolng flud. Refeences Alabudznsk S., Makowsk M., Tafczynsk M., Ubanec K., 016, The nfluence of Foulng Buld-up n Condense Tubes on Powe Geneated by a Condensng Tubne. Chemcal Engneeng Tansactons, 5, Bott T. R., Foulng of Heat Exchanges, Elseve Scence B. V., Amstedam, The Nethelands,15, Boylng, J.B., 1979, A shot Poof of the P theoem of Dmensonal Analyss. Jounal of appled Mathematcs and Physcs, 4, Hasson D., Avel M., Resnck W., Razeman I., Shlomo W., 1968, Mechansm of calcum cabonate deposton on heat tansfe sufaces. Ind. Eng. Chem. Fundamentals, 7 (1), Pääkkönen T. M., 015, Modelng CaCO3 Cystallzaton Foulng on a Heat Exchange Suface-Defnton of Foulng Laye Popetes and Model Paametes. Intenatonal Jounal of Heat and Mass Tansfe, 83, Pugh S., Hewtt G., Mülle H., 003, Foulng dung the use of fesh wate as coolant the development of a use gude. In Heat Exchange Foulng and Cleanng: Fundamentals and Applcatons, ECI Symposum Sees, 6-0, <dc.engconfntl.og/heatexchange/3>, accessed Quan Z. H., Chen Y. C., Ma C. F., 008, Heat mass tansfe model of foulng pocess of calcum cabonate on heat tansfe suface. Scence n Chna Sees Technologcal Scences, 51, 7, Wu X., Cemasch L., 013, Effect of foulng on the themal pefomance of condenses and on the wate consumpton n coolng towe systems. Poceedngs of Intenatonal Confeence on Heat Exchange Foulng and Cleanng. Budapest, Hungay Zahd K., Patel R., Mujtaba I., 016, Development of a Dynamc Foulng Model fo a Heat Exchange. Chemcal Engneeng Tansactons, 5,