Model for seawater fouling and effects of temperature, flow velocity and surface free energy on seawater fouling☆

Dazhang Yang ,Jianhua Liu ,2,*,Xiaoxue E ,Linlin Jiang

1 School of Energy and Power Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China

2 Shanghai Key Laboratory of Multi-phase Flow and Heat Transfer,Shanghai 200093,China

1.Introduction

The coastal plants such as petrochemical engineering and power stations use seawater as cooling water for saving fresh water and operation cost.A statistic shows that 42%of power stations use seawater as cooling water in USA[1].The cooling seawater for a 500 MW nuclear power station is about 30 m3·s-1[2].

However,the heat exchangers using seawater is easy to get fouled.Firstly,there are a lot of inorganic salts in seawater such as Mg2+,Al3+,and pH of seawater is between 7.2 and 8.6,which results in crystallization fouling in heat exchangers.The electrical conductivity of seawater is 4.788 s·m-1,while drinking water's is 0.0005-0.05 s·m-1.The higher electrical conductivity of seawater causes more corrosion fouling in seawater.Besides,the surface layer of ocean has high BOD(biochemical oxygen demand)and COD(chemical oxygen demand).In some places near the sewage draining exit,the BOD reaches 200 mg·L-1[3],so the bio-fouling can be easily formed in seawater.Rubio et al.[4]found that the nature of the seawater fouling was predominantly inorganic,containing over 70%of total fouling.

The seawater fouling decreases the heat transfer efficiency and increases the pressure drop of heat exchangers[5,6].The designing and the operation of heat exchangers have to contemplate redundancy area and equipment cleaning.According to statistics,the condenser fouling of a 550 MW coal- fired power station can cause a loss of 0.4-2.2 million U.S.dollars every year because of the additional fuel and reduced productivity[7].The economic loss due to fouling in heat exchangers is about 0.25%of GDP in the industrial developed countries[1].

For all the above reasons,people must estimate the fouling process to clean heat exchangers and design anti-fouling methods.Therefore,an accurate and practical kinetic model is important for predicting the fouling process of seawater heat exchangers.Several models for fouling deposition in fresh water were proposed in the literature[8].However,most of them are not appropriate for seawater heat exchangers.Hasson et al.[9,10]proposed a diffusion model for calcium carbonate deposition without removal behavior.According to our investigation,the seawater fouling is quite different from common fouling in fresh water.The main composition of seawater crystallization fouling is not calcium carbonate but rather magnesium hydroxide.Nebot et al.[11]proposed a model for fouling on power plant steam condensers cooled with seawater.The model has two parameters(Rf∞and t0.5)to describe the fouling process,but the model cannot distinguish the effects between deposition and detachment.

In this paper,a kinetic model for seawater fouling was proposed based on the Kern-Seaton model[12]with deposition rate refined using an Arrhenius equation.The experimental setup was built for application and validation of the model.Based on the model and the experiments,the effects of temperature, flow velocity and surface free energy on fouling process were investigated.The fouling model can be efficiently helpful to improve the coefficient of heat exchangers and reduce operating consumption.The study helps for industrial operation using seawater as cooling medium.

2.Kinetic Model

People always hope to design an anti-fouling heat exchanger for seawater and clean them timely with an appropriate method.It is necessary to build a model for seawater,which could supply an estimation of seawater fouling process,so that the optimization of heat exchanger operation can be done easily.The famous model for interpreting the fouling process was proposed by Kern and Seaton[12].They put forward that fouling proceeds with two mechanisms:deposition and removal.The net mass of fouling is the difference between deposition and removal rates:

The Kern and Seat on model is the most popular model of fouling,but it did not propose the definite and appropriate expressions of the deposition and removal rates for different kinds of fouling.Now,most of expressions describing the deposition and removal rates are from data fitting.Our model includes a new expression for the deposition of seawater fouling.We found the seawater fouling is actually a process of crystallization,and the crystallization could be described by the Arrhenius equation.Therefore,we used the Arrhenius equation to express the growth mass rate of depositional fouling:

The parameters kgand E due to the seawater crystallization is determined by seawater and metal surface properties,such as fouling-ion concentration in seawater and the surface free energy of metal.

In the process of seawater fouling,the decreasing mass rate of fouling-ions in seawater is equal to the growth mass rate of depositional fouling in heat exchangers,so Eq.(2)can be expressed as

In our experiments,we found that the induction period(t0)was quite short compared to the whole time of fouling,thus the induction period can be ignored.In this case,the constant value(c)is equal to the logarithm of(M0-S).The mass of depositional fouling can be expressed as

The differential of the mass rate of depositional fouling can be calculated by

The detachment of fouling is complex and mutative.Taborek et al.[13,14]proposed that the removal rate of fouling has great relevance with flow velocity,fouling mass and intensity,corresponding to the following expression:

In fact,the integrated kinetic rate of removal is hardly equal to the integrated kinetic rate of deposition.Therefore,we took no account of the situation of kr=kd.Eq.(13)shows that the process of seawater fouling is a asymptotic curve,which is also proved in experiments.

3.Methods and Experimental Setup

3.1.Experimental methods

In order to obtain the kinetic parameters of the model and validate the new model,a monitoring method for heat exchanger fouling was adopted[15-17].The fouling resistance was used to represent the fouling on heat transfer surface.As shown in Eq.(14),the amount of fouling is directly related to the heat transfer resistance of fouling on the heat transfer surface[18]:

Therefore,the mass of seawater fouling could express by the thermal resistance conveniently.

In our experiments,the fouling ions in seawater became fouling depositon the surface of a heating rod when seawater was heated,and the fouling on the surface was an additional heat transfer resistance.The fouling resistance can be determined by calculating the difference in heat transfer resistance between fouled and clean conditions by

According to the thermodynamic equilibrium,the calorific value of heating rod is equal to the heat transferred to seawater.The overall heat transfer coefficient of rod surface can be calculated with

where Q is the calorific value of heating rod,and ΔT is logarithmic mean temperature difference between seawater and heating rod.The thermal resistance of seawater fouling is calculated as

In our experiments,the voltage and the current of heating rod,wall temperature,the inlet and outlet temperature of seawater can be measured in the test device.Monitoring the fouling thermal resistance can indicate the variation of sea water fouling in the heat transfer process.

3.2.Experimental setup and procedure

The schematic diagram of the experimental setup for monitoring seawater fouling process is shown in Fig.1.In order to observe the real-time fouling process,a glass tube was used to the test section.The length of glass tube is 1000 mm,and the inside diameter is 21 mm.An electric heating rod made of 304 stainless steel or copper is fixed in the center of glass tube.The length of heating rod is 800 mm and the outside diameter is 12 mm.The seawater flowed between the glass tube and the heating rod.75 L of seawater was stored in the tank and circulated through the experimental setup.The thermostatic water tank has independent cold and heat sources in order to maintain the seawater temperature at(32±0.5)°C.The max thermal power of the heating rod is 3 kW,and the heat flux density to seawater is adjusted accordingly to match the seawater flow velocity so that the temperature on the heat transfer surface can be kept in a certain range.The test device can perform experiments in different conditions with the scheduled flow velocity and surface temperature.

Fig.1.Schematic diagram of the seawater fouling test device.

The seawater fouling in heat exchangers is a composite behavior.The composition of seawater fouling has a correlation with seawater sample[19].We collected the seawater sample in the Yellow Sea of China.The composition of the seawater sample was showed in Table 1,which showed that the highest amount of metal elements is magnesium in the seawater.

Table 1 The composition of seawater

When the heating rod and pump were turned on,the seawater fouling appeared on the surface of the heating rod gradually.Simultaneously the temperature differences were monitored every hour.The fouling thermal resistance was evaluated using Eq.(18).The experiments were conducted under different conditions in order to study the effects of surface temperature and flow velocity of seawater on seawater fouling process.In order to investigate the effect of flow velocity in fouling process,it varies in the range from 0.37 m·s-1to 0.185 m·s-1,and for the effect of surface temperature it is either 80°C or 100°C.The effects of corrosion and bio-fouling were neglected in the study.

4.Results and Discussion

4.1.Material phase analysis of the seawater fouling

SEM(scanning electron microscope)and EDX(energy dispersive X-ray)analyses were performed on the seawater fouling sample,which was scraped from the rod surface after about 100 h.The EDX results are showed in Table 2.The main elements of the sample were oxygen and magnesium,which account for over 60%in mass.The atomic percentage of oxygen and magnesium is over 70%.The second amount of metal is aluminum,which accounts for 9.0%in mass.The calcium was hardly detected in the seawater fouling.There are two reasons for the calcium loss.Firstly,the concentration of calcium in seawater sample is much low,which is 0.16 g·L-1.Then,the calcium was easy to become calcium carbonate and deposit in the tank or tubes,which hardly absorbed on the surface of the heating rod in the test device.The SEM results shown in Fig.2 clarify that there are various crystals.The main crystal shape is acicular and the crystals grew together.The micro-scale images of main crystals are similar as the images of magnesium hydroxide obtained by Ning et al.[20].According to the SEM and the EDX analyses,it could be concluded that the main component of seawater fouling is magnesium hydroxide and aluminum hydroxide.(See Table 2.)

Table 2 The elemental composition of seawater fouling

4.2.The fitting results and control analysis

Fig.2.Micro-scale images of the seawater fouling after 100 h experiment.

The experimental data were fitted into the model with the transformation between fouling mass and thermal resistance as Eq.(15).As the material phase analysis,the main composition of seawater is magnesium hydroxide and aluminum hydroxide.The solubility of magnesium hydroxide is 0.4 mg·L-1in 100°C,and the solubility of aluminum hydroxide is 1 mg·L-1in 25°C.The concentration of magnesium ion and aluminum ion in the seawater sample is 1272 mg·L-1and 164 mg·L-1respectively.The solubility of magnesium hydroxide and aluminum hydroxide is much less than M0of the fouling ions in seawater.Therefore,the solubility of seawater fouling compounds was ignored,and the(M0-S)is replaced by M0in the experimental data fitting.M0is 3.57 g·L-1obtained by the experimental data,and it consists of amount of Mg2+,Al3+in seawater and OH-associated with fouling formation.

Fig.3.Examples of proposed model and their fitting to experimental data.

The experimental data was fitted to the model through regression analysis.Fig.3 shows four comparisons between the experimental data and the model prediction.A suitable model must have the physical significance,and make it possible to interpret the kinetic parameters[10].In the new model,three kinetic parameters were proposed.The integrated kinetic rate constant of deposition(kd)represents the overall speed of the depositional process.The integrated kinetic rate constant of removal(kr)represents speed of removal subjected to a reasonable variation with respect to the flow velocity.The initial mass of fouling ions(M0)in seawater represents the characteristics of seawater sample.

In the different conditions,the crystallization has two kinds of control mechanism,which are diffused control and chemical reaction control.The nature of control mechanism is crucial to determine the anti-fouling treatments and the operating conditions.The control mechanism could be inferred from the apparent activity energy of crystallization,as calculated by

As the experimental fitting,the kdwas 2.8×10-5h-1in 100°C of surface temperature and the kd′is 2.8×10-5h-1in 80°C of surface temperature.Thus,the activity energy of seawater fouling was 1.84×104J·mol-1,which fell in the range of apparent activity energy of diffusion in the seawater.Therefore,the process of seawater fouling was diffusion-controlled in the present experimental condition.It is more effective to mitigate the fouling accumulation that the treatment for decreasing the diffusion rate is used,such as lower salinity and temperature.

4.3.Effect of surface temperature on seawater fouling

The investigation of the effect of surface temperature on seawater fouling was performed by the model analysis and experiment.Based on Eq.(13),the derivative of fouling mass with respect to the surface temperature of fouling can be written as

Based on the extreme value analysis,the expressionis determined by the values of kdand krin the fouling process.The value of kdhas a correlation with surface temperature,and the value of krhas no correlation with surface temperature.After the extreme value analysis,the surface temperature has different effects on the fouling in the process of fouling.The demarcation point is t=2kd-1.When fouling time is less than 2kd-1,the derivative of fouling mass with respect to the surface temperature is positive,an increase of the surface temperature deteriorates the seawater fouling.In our experiments,the fouling process was slow and the integrated kinetic rate of deposition(kd)was between 3×10-5h-1and 4×10-5h-1,so the value ofwas quite large.Generally,the working time of the seawater heat exchangers before cleaning is far less than.Therefore,a decrease of surface temperature is beneficial to alleviate seawater fouling in the general case.

Fig.4.The effect of surface temperature on fouling resistance in experiments(seawater velocity=0.37 m·s-1,inlet temperature=32°C).

By comparison the experiments of 100°C with 80°C,the results of the effect of surface temperature on fouling behavior was shown in Fig.4.The higher thermal resistance was obtained under the higher temperature,indicating the faster growth of fouling as increasing surface temperature.The relationship between surface temperature and thermal resistance could be due to the fact that higher surface temperature accelerated the crystallization.

In order to investigate the effect of temperature on the fouling deposition,the fouling experiments of different metals in 60°C and 80°C were done without the removal behavior(stagnant seawater).The pieces of metals(50 mm×32.5 mm)were put in the beakers of 100 ml filled with seawater.In order to fix the seawater temperature,the beakers were placed in the thermostatic seawater tank for 100 h.Due to the removal missing,the fouling accumulation is quite great than the flow experiments.The total solids extracted from the metal surface were measured as the solids mass of fouling per cm2and shown in Fig.5.The results clarify that a positive correlation between the temperature and the fouling deposition.In the 35‰salinity seawater,a temperature of 80°C increased the amount of fouling by 35%compared to a temperature of 60°C on the galvanized iron surface.The increment of fouling increased with the increasing salinity of seawater.The increase of salinity seawater also increased the amount of fouling.The fouling deposition on the copper and stainless steel surface was much less than that on the galvanized iron.Accordingly,the high surface temperature and high salinity were harmful to mitigate the seawater fouling on the metal surfaces.

Fig.5.Mass of seawater fouling at different temperature and salinity without removal behavior.

Fig.6.Effect of seawater velocity on seawater fouling resistance(surface temperature=80°C,inlet temperature=32°C).

4.4.Effect of seawater flow velocity on seawater fouling

The flow velocity is in a negative correlation with the fouling accumulation.A high flow velocity enhances the fouling removal to reduce the fouling accumulation.Furthermore,a high flow velocity improves the heat transfer to decrease the surface temperature of the heat exchangers.In the paper,the effect of seawater flow velocity on the seawater was analyzed by the model and experiments.

Based on Eq.(13),the derivative of fouling mass with respect to the flow velocity of seawater can be derived as

Based on the extreme value analysis,the expression(kr-kd)t)is always negative.Therefore,the derivative of fouling mass with respect to the flow velocity is always negative,showing an inverse correlation between the fouling mass and the flow velocity.

The experimental data also indicate the same result as the extreme value analysis.As shown in Fig.6,the fouling resistance-time curves show that a higher thermal resistance was monitored for the flow velocity of 0.185 m·s-1compared to the flow velocity of 0.37 m·s-1.The results show that the thermal resistance of seawater fouling was lower with the higher flow velocity,because the higher flow velocity caused the greater hydrodynamic shear,and induced a greater removal behavior.It is prone to mitigate the fouling that the flow velocity decreases as a complementary treatment along with other methods.

4.5.Effect of surface free energy on seawater fouling

The physical properties of metal have great effects on the fouling accumulation,especially the surface free energy,which is deemed to have a direct relationship with the seawater fouling accumulation[21-23].The low surface free energy could reduce the adhesion of particulates and the number of free ions near the surface.Du et al.[24]got the better anti-fouling behavior by the micro-swelling treatment for decreasing the surface free energy.Metals having different surface free energy were tested in the present experiments.The surface free energy was calculated by the contact angles of pure water and glycerol on the metal surface.The angle was measured using an OCA 15 PLUS optical angle measurement system from Data Physics Instruments GmbH.The integrated kinetic rates of fouling deposition were fitted from experimental data.The results listed in Table 3 show a comparison with copper,stainless steel and galvanized iron.The stainless steel has the lowest surface free energy compared to other metals,which attributes to the lowest amount of kdand average fouling thermal resistance.The galvanized iron has the highest kddue to the highest surface free energy.The correlation of kdand fouling resistance with surface free energy is very obvious.The results clarify that a decrease of the surface free energy declines the adhesiveness of crystals,contributing to a decrease of attached fouling.In addition,the lower surface free energy could make more removal of seawater fouling.

5.Summary and Conclusions

Based on the Arrhenius equation for depositional and Taborek model for removal,the kinetic model for seawater fouling prediction was proposed in the paper.The depositional behavior and removal behavior of seawater fouling were presented in the new model with the clear physical significance.Base on the present model,the effects of temperature and flow velocity were analyzed.

The experimental investigation of seawater fouling was performed with a monitoring device of the seawater fouling.The experimental conditions were adjusted to study the effects of surface temperature and flow velocity on fouling process.The seawater fouling was collected to SEM and EDX analyses.The results show that the seawater fouling is mixed crystals and the main components of seawater fouling are magnesium hydroxide and aluminum hydroxide.

The model fitted to the experimental data quite well.The higher surface temperature aggravated the fouling under the certain condition.An increase of salinity could aggravate the effect of temperature on the fouling accumulation.High flow velocity also decreased the fouling accumulation.The experiments clarify that the removal behavior is greater than the diffusion improvement due to the increase of flow velocity.In addition,the low surface free energy is prone to mitigating the seawater fouling accumulation.Accordingly,the order of metal with good anti-fouling ability in seawater is stainless steel,copper,followed by galvanized iron.

Table 3 The metal surface free energy and the parameters of fouling accumulation on metal surfaces

[1]S.J.Pugh,G.F.Hewitt,H.Müller-Steinhagen,Fouling during the use of seawater as coolant—The development of a user guide,Heat Transfer Eng.26(1)(2005)35-43.

[2]K.K.Satpathy,A.K.Mohanty,G.Sahu,S.Biswas,M.V.R.Prasad,M.Slvanayagam,Biofouling and its control in seawater cooled power plant cooling water system—A review,in:P.Tsvetkov(Ed.),Nuclear Power,InTech.2010,pp.192-242.

[3]H.Z.Li,Y.Zhang,H.C.Shi,J.L.Wang,Application of BOD biosensor for marine monitoring,Mar.Environ.Sci.21(3)(2002)14-17(in Chinese).

[4]D.Rubio,C.López-Galindo,J.Casanueva,E.Nebot,Monitoring and assessment of an industrial antifouling treatment.seasonal effects and influence of water velocity in an open once-through seawater cooling system,Appl.Therm.Eng.67(2014)378-387.

[5]A.Z.Sahin,S.M.Zubair,A.Z.Al-Garni,R.Kahraman,Effect of fouling on operational cost in pipe flow due to entropy generation,Energ.Convers.Manage.41(2000)1485-1496.

[6]M.A.I.Said,I.A.Sami,The influence of condenser cooling seawater fouling on the thermal performance of a nuclear power plant,Ann.Nucl.Energy 76(2015)421-430.

[7]M.E.Walke,I.Safari,R.B.Theregowda,M.K.Hsieh,J.Abbasian,H.Arastoopour,D.A.Dzombak,D.C.Miller,Economic impact of condenser fouling in existing thermoelectric power plants,Energy 44(2013)429-437.

[8]Z.K.Liu,Z.R.Wang,H.Z.Tao,Research progress in heat exchanger fouling,Chem.Ind.Eng.Prog.30(11)(2011)2364-2368(in Chinese).

[9]D.Hasson,M.Avirel,W.Resnick,T.Rozenman,S.Windreich,Mechanism of calcium carbonate scale deposition on heat-transfer surfaces,Ind.Eng.Chem.Fundam.7(1)(1968)59-65.

[10]E.Gazit,D.Hasson,Scale deposition from an evaporating falling film,Desalination 3(1975)339-351.

[11]E.Nebot,J.F.Casanueva,T.Casanueva,D.Sales,Model for fouling deposition on power plant steam condensers cooled with seawater:Effect of water velocity and tube material,Int.J.Heat Mass Transf.50(2007)3351-3358.

[12]D.Q.Kern,R.E.Seaton,A theoretical analysis of thermal surface fouling,Chem.Eng.Prog.4(1959)258-262.

[13]J.Taborek,T.Aoki,R.B.Ritter,J.W.Palen,J.G.Knudsen,Predictive methods for fouling behavior,Chem.Eng.Prog.68(7)(1972)69-78.

[14]J.Taborek,T.Aoki,R.B.Ritter,J.W.Palen,J.G.Knudsen,Fouling:the major unresolved problem in heat transfer,Chem.Eng.Prog.68(2)(1972)59-68.

[15]Z.H.Quan,Y.C.Chen,C.F.Ma,Experimental study of fouling on heat transfer surface during forced convective heat transfer,Chin.J.Chem.Eng.16(4)(2008)535-540.

[16]T.Q.Liu,X.H.Wang,Fouling induction period of CaCO3on heated surface,Chin.J.Chem.Eng.7(3)(1999)230-236.

[17]M.Izadi,D.K.Aidun,P.Marzocca,Experimental investigation of fouling behavior of 90/10 Cu/Ni tube by heat transfer resistance monitoring method,J.Heat Transf.133(10)(2011)4770-4773.

[18]S.R.Yang,Z.M.Xu,L.F.Sun,Fouling and countermeasures for heat transfer equipment,Scientific Press,Beijing,2004 279-578(in Chinese).

[19]M.Izadi,D.K.Aidun,P.Marzocca,H.Lee,Integrated experimental investigation of seawater composite fouling effect on the 90/10 Cu/Ni tube,Appl.Therm.Eng.31(2011)2464-2473.

[20]Z.Q.Ning,Y.C.Zhou,L.Q.Sun,H.M.Gu,D.Zhou,D.Xu,Study on the thermal decomposition kinetics of magnesium hydroxide,J.Mol.Sci.25(1)(2009)27-30(in Chinese).

[21]B.Larsson,Ultra filtration membranes and applications,Plenum Press,New York,1980.

[22]D.E.Packham,Surface energy,surface topography and adhesion,Int.J.Adhes.Adhes.23(2003)437-448.

[23]A.Razmjou,J.Mansouri,V.Chen,The effects of mechanical and chemical modification of TiO2nanoparticles on the surface chemistry,structure and fouling performance of PES ultra filtration membranes,J.Membr.Sci.328(2011)73-84.

[24]J.R.H.Du,S.Peldszus,P.M.Huck,X.S.Feng,Modification of membrane surfaces via microswelling for fouling control in drinking water treatment,J.Membr.Sci.475(2015)488-495.