RE

ESEARCH R

Stco A

C

REPORT

tabilityonsoli

Authors

Confidentia

No VTT-R

y of codation

ality

R-08112-12

olloidan in nu

Iva Beto

Public

28.1

al partuclear

ova, Martin

1.2012

ticles apowe

Bojinov, T

and der plan

Timo Saario

epositnts

o

t

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Preface

This literature survey was compiled as part of the project “Water chemistry and plant operating reliability” (WAPA 2012) within the SAFIR 2014 –research programme. Espoo, 28.11.2012 Authors

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Contents Preface 3 

1  Introduction 6 

2  Goal 8 

3  Description 9 

4  Steam generator fouling mechanisms 9 

4.1  Corrosion phenomena in the secondary side 9 

4.1.1  General corrosion 9 

4.1.2  Flow-accelerated corrosion 10 

4.1.3  Stress corrosion cracking 11 4.2  Consequences of corrosion: description of the fouling phenomena 12 

4.2.1  Definition of the fouling phenomenon 12 

4.2.2  Mechanisms and influence of critical parameters 12 

4.2.3  Quantity and localization of deposits 15 4.3  Influence of physic-chemical factors on the phenomena 16 

4.3.1  Role of magnetite and redox reactions 16 

4.3.2  Impact of hydrazine and other amines on corrosion phenomena 16 

5  Composition, physical properties and forms of colloidal oxides within the coolant circuits 17 

5.1  Introduction 17 5.2  Reactivity at solid-liquid interfaces 17 

5.2.1  Characterization of the interface 17 

5.2.2  Surface charge 18 

5.2.3  Interfacial double layer 19 

5.2.4  Zeta potential 20 5.3  Acid-base properties of oxy-hydroxides 21 

5.3.1  Point of zero charge and iso-electric point 21 

5.3.2  Modeling of acid-base properties 22 5.4  Sorption mechanisms 22 

5.4.1  Sorption via ion-exchange 23 

5.4.2  Sorption by surface complexation 23 

5.4.3  Sorption by precipitation/dissolution 24 

5.4.4  Sorption by surface precipitation 24 5.5  Influence of temperature on surface charge 25 

5.5.1  Temperature dependence of the point of zero charge 25 

5.5.2  Temperature dependence of the iso-electric point 26 5.6  Influence of ion adsorption and water chemistry on the surface charge 27 

5.6.1  Ion adsorption 27 

5.6.2  Influence of water chemistry 29 5.7  Colloidal particles in recirculation systems 29 

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5.7.1  Definition 30 

5.7.2  Formation of colloids by corrosion in recirculation systems 30 5.8  Dielectric properties of colloidal systems 31 

5.8.1  Introduction 31 

5.8.2  Main mechanisms of dielectric dispersion in colloidal systems 31 

5.8.3  Dielectric properties of iron oxide suspensions 35 5.9  Interaction between colloids and charged surfaces 36 

5.9.1  Surface molecular interactions 36 

5.9.2  Contact interactions 37 

5.9.3  Parameters influencing the interactions 37 

5.9.4  Influence of the zeta potential and the ionic strength on the interaction between charged surfaces 37 

5.9.5  Effect of temperature on the interactions between charged surfaces 38 5.10 Influence of the colloid-surface interactions on the fouling mechanisms 38 

5.10.1 Deposition of colloidal particles 39 

5.10.2 Description of the re-entrainment phenomenon 41 

5.10.3 Summary of the interactions involved in fouling 43 

6  Consolidation of deposits 43 

6.1  Introduction 43 6.2  Stages of the deposition process 44 6.3  Definition of the consolidation process 45 6.4  Factors influencing consolidation 45 

6.4.1  Temperature and thermal gradients 45 

6.4.2  Influence of boiling 46 

6.4.3  Inhibitors and crystal habit modifiers 46 6.5  Deposition and consolidation modeling 47 

6.5.1  General 47 

6.5.2  Review of fouling models 47 

6.5.3  Modeling magnetite deposition and ageing 51 6.6  Discussion on consolidation 54 

7  Summary 55 

8  References 56 

 

 

1

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The low blow-down efficiency of most SGs, i.e., typically < 10%, implies that the vast majority of corrosion product that is transported with the feed water remains in the SG. Unless mitigating action is taken, the steady accumulation of corrosion products in the SG will eventually lead to some form of material and/or performance degradation. The low blow-down efficiency of RSGs is a consequence of the high surface area of the tube bundle which makes deposition onto the tube bundle a more effective “sink” for particle removal than blow-down.

For minimization of the corrosion product transport into the steam generators a high pH in the overall system is required. This high pH yields to a decrease of general corrosion and flow-accelerated corrosion (FAC) rates, which occurs mainly at the wet steam areas (HP turbine outlet, cross under, moisture separator re-heaters (MSR)). The state of knowledge is that to minimize FAC, the pH at the water film in contact with system surfaces at these locations (T ~ 190°C) must be pH (190°C) > 6.4, while the neutral pH190C = 5.67. A conditioning agent must be therefore provided to achieve this goal. The high- AVT chemistry treatment is using ammonia for adjusting the necessary pH. Applying high-AVT chemistry has the advantage that only one chemical has to be dosed to ensure on the one hand reducing conditions inside the steam generator and on the other hand to maintain a sufficiently high pH value in final feed-water. For both purposes hydrazine is dosed into the main condensate, where it reacts with oxygen to nitrogen and water, and at high enough temperature decomposes producing ammonia.

Beside the use of ammonia obtained directly by thermal decomposition of hydrazine other alternative amines (morpholine (MO), ethanolamine (ETA) etc) are used. They generally have a higher distribution coefficient between the water and steam phase and might provide a better protection against FAC in two phase flow systems. The generally considered main advantage of morpholine (C4H8ONH) is its ability to protect all of the secondary system against FAC, even in presence of copper alloys and at a pH (25°C) of 9.2. One of the most cited advantages of morpholine is its steam-water-distribution coefficient, which is close to 1, ensuring an approximately constant concentration throughout the steam/water system. The main disadvantage of morpholine is the relatively high molar concentration that is required for giving the desired feed-water pH, increasing the cost and the concentration of unwanted organic acids, the decomposition products of morpholine. Ethanolamine (ETA) is an alternate amine, largely used in an increasing number of countries with PWR units (Figure 2). ETA was selected, because laboratory data was promising that pHT values would be increased more significantly in wet steam areas and also organic acid production would be less when compared to morpholine. The distribution coefficient is less than 1 in the temperature range 150°C < T < 280°C, i.e. ETA stays preferentially in water phase, which will not give a constant concentration in the different parts of the secondary side system. Over the past 20 years, nuclear plants have also started to make use of advanced amines to reduce corrosion and deposit precursor formation. Recently, also anti-flocculation

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elaboration of an integrated model for the dissolution/deposition reactions in nuclear power plants.

3 Description

Magnetite is formed in the secondary circuit mainly from corrosion of carbon steel tubing. Magnetite particles are transported with the flow and deposit e.g. in the steam generator tube support plate, tube sheet and re-heater cassette area creating flow and corrosion problems. The source term, magnetite dissolution is rather well known from flow-assisted corrosion (FAC) models developed to predict wall thinning and to prevent tube rupture. Therefore, the main target of the present survey is the mechanism of the deposition process mainly of the colloidal form of magnetite and analogous oxides present in the coolant circuits. Therefore, a short overview of the fouling mechanisms of steam generators is given first, including a concise description of general corrosion, FAC and stress corrosion cracking. Next, the consequences of corrosion, i.e. the fouling phenomena, are assessed, and several individual process steps such as deposition, re-entrainment, structural re-organization etc. are discussed. The next part that constitutes the main body of the survey, concerns the composition, forms, physical and chemical properties and therefore stability of colloidal oxides in nuclear power plant coolant circuits. Theoretical approaches to the reactivity of solid/liquid interfaces, such as acid-base properties, sorption mechanisms, and interaction between colloidal particles and charged surfaces are described and illustrated with relevant experimental data, emphasizing the effect of temperature on key parameters such as the point of zero charge and iso-electric point. And last but not least, consolidation of deposits which is believed to be one of the key stages in the fouling process is discussed with regard to its inclusion in a quantitative integrated model of the deposition process.

4 Steam generator fouling mechanisms

The present literature study concerns an increased understanding of the behavior of corrosion products implied in the problem of corrosion and fouling taking place in the secondary circuit. This section envisages the different types of degradation of the SG materials due to corrosion. The general corrosion and FAC are phenomena that affect the carbon steel parts and result in the formation of corrosion products composed essentially of iron oxides. On the other hand, the nickel alloys constituting the SG tubes suffer from stress corrosion cracking that seems to be favored by the presence of corrosion products.

4.1 Corrosion phenomena in the secondary side

4.1.1 General corrosion

In this paragraph, only the processes taking place in the secondary circuit in the temperature range up to 275 °C (typical for the SG operation) in deaerated medium are briefly described. From thermodynamic point of view, the stability of iron (the main constituent of carbon steel components) in water depends on pH, redox potential and temperature. In the temperature range 30-275 °C, the

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oxides formed by iron corrosion in water are magnetite Fe3O4, goethite -FeOOH and hematite -Fe2O3. At oxidizing potentials, the main species is thought to be hematite even if the energies of formation of -Fe2O3 and -FeOOH are rather close to each other. At lower temperatures, hematite is not precipitated [2], instead, the formation of iron oxide starts with the precipitation of amorphous iron hydroxide that is subsequently dehydrated to form goethite. The direct precipitation of hematite is observed for temperatures higher than 200 °C [3]. In the absence of dissolved oxygen (in practice, for concentrations lower than 0.94 µmol l-1, i.e. 15 ppb) or other oxidizing species, the redox potential is situated normally in the stability area of magnetite. Thus the general oxidation reaction can be formulated as 2 3 4 23 4 4Fe H O Fe O H

In fact, this process is the result of the superposition of two oxidation reactions and a reduction reaction

2

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As a result of this reaction, the carbon steel becomes covered by a double layer magnetite type oxide. This oxide consists of two sub-layers

An internal fine-grained sub-layer (grain size, 50-200 nm) that grows into the metal and occupies a volume identical to that of the consumed metal – this sub-layer is compact, continuous and adherent

A coarse-grained external sub-layer (500-5000 nm) composed of tetrahedral and octahedral crystallites, which is not continuous and less adherent.

More detailed information on the mechanisms of formation of the deposit will be given in chapter 5.10.1 dedicated to the study of deposition of colloidal particles.

4.1.2 Flow-accelerated corrosion

Flow-accelerated corrosion (FAC), also denoted as erosion-corrosion, of carbon or low-alloyed steel piping occurs when the rate of dissolution of the protective oxide film that forms on the internal piping surface into a stream of flowing water or wet steam is enhanced, leading to an increased wall thinning rate. In general, the FAC process consists of two steps: the first step is the production of soluble iron at the oxide/water interface, while the second step is the transfer of the soluble and particulate corrosion products to the bulk flow across the diffusion boundary layer. Although FAC is characterized by a general reduction in pipe wall thickness for a given component, it frequently occurs over a limited area within this component due to the local area of high turbulence. A summary of the processes involved in the FAC phenomenon is presented in Figure 3.

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4.2 Consequences of corrosion: description of the fouling phenomena

As mentioned above, the products of both general and flow-assisted corrosion lead to the formation of deposits in the SGs decreasing the efficiency of their service. The consequences of the deposit formation depend essentially on their nature and localization in the SG. The presence of deposits parallel to the external walls of the tubes and in the confined zones, called SG fouling, is responsible for two types of problems:

Establishment of concentrated media responsible for the enhanced susceptibility to SCC of the secondary side of SG tubes

Degradation of heat transfer from the primary to the secondary circuit which leads to decreased performance of the respective section.

In the following, a synthesis of the present knowledge concerning the different mechanisms of fouling is first presented. The experience related to the nature and quantity of deposits formed in the secondary circuit, as well as to the soluble and suspended species present in the SG is then summarized.

4.2.1 Definition of the fouling phenomenon

The fouling of the internal surfaces of the SGs is related to the progressive formation of a deposit layer from the impurities contained in the water, essentially corrosion products. The impurities that form the deposit at the secondary side of SGs are introduced in the feed-water in the form of dissolved species and particulate matter. Since both of those forms are practically non-volatile, they tend to accumulate in the SG and are subsequently precipitated and deposited on the tube walls. The locations and the characteristics of the deposits formed are non-uniform and depend on the thermo-hydraulic and chemical properties of the bulk water flow. This is a generic problem for all the SG fleet and is amplified with service life.

4.2.2 Mechanisms and influence of critical parameters

The dissolved species and particulate matter in the secondary circuit represent the source term of the SG fouling. The mechanisms of constitution of the source term have been briefly described above and are connected to the degradation due to general corrosion, FAC and ammonia-assisted corrosion of components fabricated from copper containing alloys, as well as to impurities that originate in the feed-water. The fouling phenomenon is the result of the superposition of two opposed processes – the formation and the destruction of the deposit. The actual degree of knowledge does not permit to distinguish if these two processes take place simultaneously or sequentially. Even so, the fundamental mechanisms intervening in these two processes seem to be similar, namely

Deposition – re-entrainment of particles Precipitation-dissolution of species Structural reorganization of the deposits.

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4.2.2.1 Deposition-re-entrainment of particles This mechanism is pertinent to the solid particles suspended in the moving fluid and can be split in three stages. The first is related to the movement of particles by the turbulent motion of the fluid, the second to the interaction forces that could exist between the particles and the wall and the last to the diffusion forces of matter in the presence of gradients, most notably thermal. The particles present in the fluid are transported by convection and diffusion towards the walls limiting the flow. The particles interact with the limiting turbulent layer situated in the zone closest to the wall giving rise to particular hydrodynamic phenomena. In close proximity to the wall, the physico-chemical interaction forces (mainly the electrostatic Van der Vaals forces, chapter 5.8) become predominant face to inertial forces and will either cause adherence of the particles to the wall or prevent this adherence, i.e. repulse them towards the centre of the flow. In the case in which there is effective adhesion of the particles to the wall by means of the physic-chemical interaction forces, the fluctuating motions of the fluid within the boundary dynamic turbulent layer could favor the re-entrainment of the particles that are returned to the centre of the flow. Similarly, a modification of the interaction forces that ensure the cohesion of the deposit by variation of the local chemical forces could lead to an analogous result. In addition, thermo-phoresis, generated by the temperature difference between the particles and the wall could also play a role in the mechanism of deposition – re-entrainment. The importance of such a mechanism is strongly determined by the magnitude of the thermal gradients, the physical and chemical properties of the particles and the flow and thermo-phoresis is found to assist fouling only in the case in which the particles have a temperature superior to that of the wall. Thus such a mechanism will not favor fouling on SG tubes whereas it will favor it on condenser or cooler tubes. Summarizing, the process of deposition – re-entrainment depends in principle of the following factors:

Flow characteristics – velocity, structure of the dynamic boundary layer, temperature

Properties of the solution – pH, redox conditions, ionic strength Properties of the walls and particles – temperatures, presence of chemical

compounds modifying the repartition of surface charges, characteristics of the materials that constitute the particles and the walls in terms of repartition of the surface charges.

4.2.2.2 Dissolution/precipitation of species

This process concerns the species dissolved in the moving fluid and can be regarded as composed of two stages. The first is related to local variations of solubility of the species in question due to spatial and/or temporal variation of the local physical (temperature) or chemical (pH, redox,...) conditions. The second stage is related to the evaporation of the solvent. If this evolution of chemical and physical conditions leads to a solubility that is inferior to the actual concentration of the species in question, they will precipitate in solid form. Several cases can be distinguished:

Variation of the solubility in the core of the flow – this leads to precipitation at this location and the formation of particles suspended in

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the flow itself. These particles are subsequently subject to the process of deposition – re-entrainment described above.

Variation of solubility in proximity of the wall – the particles precipitate in the limiting layer or on the wall itself.

Variation of solubility within a pre-existing porous deposit: the soluble species precipitate in the actual pores and lead to their plugging. As an example, during a shutdown/start-up period, an insufficient hydrazine/oxygen ratio leads to oxidizing conditions in which magnetite is transformed into hematite solubility of which is lower. Thus such an oxidation process would provoke the precipitation of iron that is initially soluble in equilibrium with magnetite and the hematite formed would plug the empty spaces in the porous deposits on the external surface of the SG tubes with the formation of a denser and thermally more resistive deposit.

Summarizing, the process of dissolution/precipitation depends in principle of the following factors:

Flow characteristics – temperature distribution Properties of the solution – pH, redox conditions, concentration of

soluble species Intrinsic properties of the soluble species – solubility.

4.2.2.3 Structural reorganization of the deposit

The mechanism of structural reorganization of the deposit is in principle a viable cause to explain the fouling phenomena, but it has been little studied so far. It would concern a solid present in the form of a pre-existing deposit on a surface, which, taking into account the local chemical conditions, would transform into another solid with different physical (density, thermal conductivity) and chemical (e.g. solubility, surface charge, zeta-potential...) properties. This mechanism could modify the thickness of the deposit, its rugosity, its thermal and physic-chemical characteristic and therefore its future evolution. Such a mechanism can be operational during transients when due to the introduction of oxygen, the redox potential would increase, which would lead in a variation of the oxidation state of iron in the oxide deposited on the SG tubes (e.g. a quasi-reversible transformation of magnetite to hematite). Such a change would explain the increase of the thermal resistance and the decrease of pressure in the SG which is consistent with field observations.

4.2.2.4 Discussion on the fouling mechanisms The mechanisms described above (deposition – re-entrainment, dissolution-precipitation and structural reorganization) could be considered as independent, but this remains to be established. In certain cases, their effect could be contrary to what is generally expected. For example, the fluid velocity by turbulent motion could take away a particle from the deposit even if the local chemical conditions or the temperature gradient are favorable to the precipitation of the dissolved species in the same fluid. It is thus difficult to distinguish a priori the mechanism that would be predominant in order to predict the global evolution of the deposit.

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4.2.3 Quantity and localization of deposits

Numerous results of chemical cleaning of SGs indicate that the average quantity of deposits is about 3100 kg with a minimum of 2400 kg and a maximum of 4500 kg. Such quantities correspond to an accumulation of ca. 200 kg per cycle per SG. These values are in general agreement with the measurements and mass balances between solid impurities entering via the feed-water and those evacuated by purging, comprised from 40 to 170 kg per cycle per SG. A deposit of 200 kg distributed uniformly over the area of the SG tubes (around 5000 m2) corresponds to a deposit of ca. 10 µm per year. In fact, the thickness of the deposit varies strongly from location to location. Plant evidence points to thicknesses of up to 30 cm on the spacer plates, whereas on the tubes themselves, the deposit is in the form of thin layer. Maximum thicknesses have been found in the lowest parts of the tubes on the hot leg side. The mean rate of thickness increase on the tubes is of the order of 1 µm/month with possible variations from 0.1-10 µm/month depending on the service life of the SGs. Concerning the chemical nature of the deposits, a large number of compounds have been identified. The weight percentage of the 10 most important compounds in the layer on SG tubes is shown in Table 1.

Table 1 Main compounds in the deposits on SG tubes [9]

Compound Mean content / wt.%

Min/max content / wt%

Fe3O4 59.6 16.5/94.9 Fe2O3 10.0 0.1/27.9 ZnO 7.3 0.3/19.1 SiO2 7.0 0.0/26.5 Cu 5.9 0.0/28.1 Al2O3 3.4 0.1/24.3 CaO 3.0 0.0/15.0 PO4

3- 2.4 0.0/15.1 MnO 2.1 0.4/5.8 NiO 1.5 0.1/8.8

Regarding the morphology of the deposits, it has been reported [9] that deposits on the free surface of the tubes can comprise several sub-layers with different properties. The internal sub-layer is less porous (0-30%) than the external layer (30-70%). Certain species are preferentially enriched close to the tube surface, as is the case of copper. The external layer consists chiefly of magnetite which can exhibit a particular structure with large pores (diameter 5-10 µm) open towards the surface of the deposit and connected with a system of finer pores in the interior of the deposit (diameter 0.1-1 µm).

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4.3 Influence of physic-chemical factors on the phenomena

4.3.1 Role of magnetite and redox reactions

Due to the relatively small occupancy of cationic sites and the interchange ability of Fe2+ and Fe3+ in octahedral sites, magnetite possesses electro-catalytic properties. For example, it has been demonstrated that this oxide can reduce sulfates to sulfides [10]. This could explain the presence of elemental sulfur, thiosulfates and sulfides on the surface of extracted SG tubes. Further, the possibility of reduction of U (VI) to U (IV) has been evidenced [11] and in a sorption study of uranyl ion on magnetite, Missana et al. [12] have shown that the sorption kinetics is rapid and followed by an electron exchange as a rate limiting step, which has been confirmed by Scott et al. [13]. Analogous results have been presented by Yoojin et al. [14] within the frames of a decontamination study of subterranean waters – it has been shown that Cr (VI) can be eliminated by its reduction to Cr(III) on magnetite surface. A similar reaction was observed by White and Peterson in anoxic conditions [15].

4.3.2 Impact of hydrazine and other amines on corrosion phenomena

Hydrazine is used in the secondary circuit to minimize the corrosion of materials by controlling the level of oxygen in the medium and establishment of reducing conditions. The reductive effect of hydrazine could also lead to the increased susceptibility towards certain types of corrosion such as FAC and SCC. Hydrazine reduces sulfates to sulfites, thiosulfates and sulfides up to a pH of 8.5-9.2 [16]. The reduced sulfur-containing species lead to an increase of the susceptibility to SCC. In reducing conditions, hydrazine can replace hydrogen in the reactions of reductive dissolution of magnetite which are assumed to control the kinetics of FAC 2

3 4 2 4 2 22 12 6 8Fe O N H H Fe H O N

Thus an increase of hydrazine concentration could lead to a larger rate of FAC. The thermal decomposition of hydrazine proceeds at a significant rate for temperatures above 200 °C. The products of this reaction, especially ammonia and hydrogen can be harmful because

Ammonia is deleterious for copper containing alloys as well as ion exchange resins and changes the pH of the medium

Hydrogen, in analogy to hydrazine itself, lowers the redox potential and leads to the establishment of reducing conditions that favor FAC.

In the present chapter, a short overview of the corrosion fouling of steam generators has been presented. In the next section, the properties of colloidal species in the coolant circuits will be reviewed.

17 (61)

5 Composition, physical properties and forms of colloidal oxides within the coolant circuits

5.1 Introduction

As described in the previous chapter, the presence of corrosion products in the secondary circuit of nuclear power plants has deleterious consequences on their service. On one hand, magnetite that is deposited on the SG tubes is able to fix sulfates present in the nominal medium by sorption. This could lead to the reduction of these species and the formation of compounds containing reduced sulfur that enhance corrosion. On the other hand, the transport and adhesion of such particles on the tube material in SG leads to a reduction of the thermal performance and favors SCC. The particles in question are most likely in colloidal form. The colloid science has made tremendous progress since the development of the theory of inter-particulate forces coupled to experimental techniques that allow a direct and precise measure of the size, form, concentration and attraction/repulsion forces between surfaces separated by several nanometers only. The surface of a solid in contact with a liquid presents a certain reactivity that is expressed by several processes: transfer of species from the solid to the liquid, or in general dissolution/corrosion, transfer of species from the liquid to the solid, that is, sorption when the species in question is soluble, or adhesion when the species is suspended. In the present chapter, first the solid-liquid interface is described in a general way. The different sorption phenomena that take place in this zone are then discussed. The nature of colloids and the interactions between charged surfaces that characterize them are emphasized in order to understand and eventually predict their behavior in the coolant circuits of the NPPs. The different stages of fouling that involve the properties and behavior of colloidal particles are implicitly presented.

5.2 Reactivity at solid-liquid interfaces

5.2.1 Characterization of the interface

A material enters in contact with the surrounding medium via its surface. The atomic scale organization at the surface of a solid (and also to a certain extent a liquid) is different from that in its core. The atoms or ions present at the surface of a solid are neighbored by less parent atoms/ions of the solid than those in the bulk of the material. Thus the surface atoms/ions are freer to interact with the atoms/ions of the surrounding medium. From a physic-chemical point of view, a surface is a system that reacts with the environment, in our case the electrolyte. The solid/liquid interface is defined as the intermediate zone between the two bulk non-perturbed phases. When the liquid phase is an aqueous solution, the surface of the solid is hydrated. This hydration process generates functional groups at the surface of the material [17,18]. A common example is the hydration of silica the

Figure

5.2.2

mechachemitype. hydrooxide

e 4 Propose

Surfa

The hionizeto theamphthe eq

In theaqueothe su Otherthe scompcan be

The spH. Inon thepH raion. Tcreatiof thesurfac

anism of wisorption ofThe stage (

oxyl groups.s.

ed mechanis

ace charge

hydroxyl gred, i.e. protoe 2-pK modoteric chara

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ese reactionous protons.urface of the

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M

M

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f the charge, e.g.

M

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sented in Flecules thatonds to theof hydration

ydration of a

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M O H

presents a mquilibrium aroxide, K+ an

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Figure 4. Tht create func

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M O

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he stage (a) ctional grouion of watebe generally

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metallic oxyng a surfacegs of the M

of surface c

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n in a surfaed the dissoectively.

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1/2H H

ntration in tin solution

rption proceof the surfacribution of

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as an exam

y-hydroxidese charge. Ac

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USIC) consnds on the19,20]. Thi

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18

ds to the hydroxyl es on the e to most

mple).

s can be ccording have an

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(0)

(0)

d H+ are stants of

ider that mutual s charge

(0)

n, i.e. the emselves lace in a adsorbed solution function sult, the

8 (61)

5.2.3

Figureof Gou

Interf

At thinteradenotof thedependeveloand tothe sadsorporigincan bdiffusdiffusStern their pthe sudiffus

condi

e 5 Scheme uy-Chapman

facial doub

he interface act with the ted as the ele surface andent on thoped to deso calculate urface. Thption of ion

nal diffuse sbe regarded se layer modse layer andlayer. The

positioning urface charse layer. If

tion can be

of the solidn-Stern (GC

ble layer

of the chasurface cha

lectric douband the fixihe electric pscribe the dthe electros

he model ons or molestructure of

as a combdel. The add constitutespecific affat the Ster

ge. The othf is the

written as

d-liquid interCS). Stern la

arged particarges to for

ble layer. Thing of protpotential ofdistribution static term tof Gouy-Checules at thf the layer abination of dsorbed ionse an additioffinity of indrn plane andher part is e charge a

0 d

rface (denoayer denote

cle with thrm a structuhis layer moons by thef the surfacof charges

that influenhapman-Stee vicinity oas proposed

the constas are inserteonal monomdividual iond to the comcompensat

at the Stern

d .

oted by solided by dash-d

e solution, ured layer oodifies the a

surface whce. Several s at the vicices the acidern (Figureof the surfa

d by Gouy ant capacitaned between molecular lans towards tmpensation ed by the

n plane, th

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the dissolvof a few nanacid-base pr

which becommodels ha

inity of thed-base prope 5) considace which and Chapm

ance model the surface

ayer denotethe surface of a certainions presen

he electro-n

rding to the

19

ved ions nometers roperties

mes then ave been e surface perties of ders the alter the

man. i.e it and the

e and the ed as the

leads to n part of nt in the neutrality

e model

9 (61)

Figureof GraHelmh

5.2.4

Figureat thesurfacHelmwhichGenerplacedat the

e 6 Scheme ahame-Parsholtz plane (

Zeta

Whenother,The mseparainterfasurfac

e 6) introdue so-called ce. The elec

mholtz plane h, at a distarally, the ld at the innexternal pl

of the solidsons. Inner H(OHP) deno

potential

n a solid pa, a part of thmobile andated by the

face in two zce charge ca

The model

uces chemisinternal H

ctro staticalthat corresp

ance d fromless stronglner plane whane.

d-liquid interHelmholtz poted by a da

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l of Graham

sorption of Helmholtz plly adsorbedponds to th

m the surfacly hydratedhereas more

rface (denoplane (IHP)ashed line.

a liquid areontaining thee parts of hear, or sliphich accumro-neutrality

me-Parsons

ions and/orplane situatd counter-io

he Stern plance of the pad ions (moe strongly h

oted by solid) is denoted

e in relativee counter-iothe liquid

pping, planemulation of c

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(

r moleculested at a dions are situne in the prarticle, the dst frequent

hydrated cat

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rding to theotted line an

with respectined by the ng the parture 7). It divs to compenated (it is on

20

e placed from the external

del, from er starts. ons) are

py places

e model nd outer

t to each particle.

ticle are vides the nsate the nly valid

0 (61)

Figure

5.3

5.3.1

for thpotendenot

e 7 Scheme

The pthe mnanom(Debystrengshear potenstrengchargwill bcharg

Acid

The vacid-bprotonpresumarea. differ

Point

The pchargproton

e whole intential differented as the ze

of the movi

position of tmedium. Expmeters fromye length) gth of the m

plane prantial at this gths (smallee at the inte

be equal to e of the soli

-base pro

variation of base titrations fixed ormed to be pAccording

rence of the

t of zero ch

point of zere becomes ns that are a

erface). Durnce betweeeta-potential

ing liquid-pa

he shear plaperimental

m the exterand the po

medium. Whactically coplane and t

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operties o

the surfaceon of a sor leaving thproportiona to the 2-surface con

harge and

ro charge (zero [22]. Dadsorbed an

ring the disen the sheal, , or elect

article inter

ane is a funstudies [19rnal Helmh

osition of thhen the ionoincides withe zeta-po

01 mol l-1) holtz plane e potential, and the char

of oxy-hy

e charge of olid suspenshe surface ial to that co-pK model,ncentration

iso-electric

(PZC) correDuring an and desorbed

placement oar plane antro-kinetic p

rface.

nction of the9] have shoholtz plane.he shear pl

nic strength ith the ext

otential are in the absenis negligiblwhich leadrge in the di

ydroxides

a solid in fsion duringis estimated

oncentration, the surfaof 2MOH a

c point

esponds to cid-base titr

d can be zer

of the particd the bulk potential.

e physic-chewn that it i. The diffulane both vis inferior

ternal Helmthen equal.nce of specle [19]. Thus to an equiffuse doubl

function of g which thd. The surfn reported tace charge and MO .

the pH forration, howeo at certain

cles, this ressolution, w

emical propis situated use layer thvary with tto 0.01 mo

mholtz pla. At very locific adsorpus the zeta-puality of thele layer.

pH is meashe concentrface chargeto the oxide

correspond

r which thewever, the ba

pH (pH of

21

sults in a which is

perties of at a few hickness he ionic

ol l-1, the ane. The ow ionic

ption, the potential e surface

sured by ration of e is then e surface d to the

e surface alance of f the zero

(61)

22 (61)

net proton charge, PZNPC) at which the surface charge is non-zero, due to the initial charge determined by the adsorption of ions other than H+. Thus one way to estimate the PZC is to measure titration curves at different ionic strengths which are expected to cross each other at a point denoted as point of zero salt effect (PZSE) which can be considered as a viable estimate for the PZC. Another way to estimate the evolution of surface charge with pH is to measure the mobility of particles in a suspension in an electric field (zetametry). In this case, the variation of the zeta-potential with pH is assessed. As a result, the iso-electric point (IEP) is defined as the value of pH at which the mobility is zero which corresponds to a zero charge. Normally the PZC and IEP should coincide, however, due to adsorption of cations and anions from the solution, this is not always observed.

5.3.2 Modeling of acid-base properties

The modeling usually consists of a numerical simulation or fitting of the titration curves by optimization of the characteristic parameters of the acid-base properties of the oxide and the double layer. Within the frames of the 2-pK model, these parameters are the acidity constants K+ and K-, as well as the surface concentration of adsorption sites, or the maximum value of the surface charge corresponding to saturation of all the available surface sites. To these parameters one should add the parameters defining the double layer, i.e. the capacitance C in the constant capacitance model (in the diffuse layer model, there is no adjustable double layer parameter).

5.4 Sorption mechanisms

The term sorption is employed when the atomic scale is considered, i.e. when the particle fixed at the surface is an atom, ion or a simple molecule. This process represents the transfer of atoms, ions and/or molecules from the liquid phase to the solid phase implying or not the formation of a surface layer of a known thickness or diffusion in the solid. According to the type of interactions that enter into play, two sorption categories can be distinguished:

Physisorption due to interactions between atoms, ions or molecules of the type of Van der Waals (e.g. hydrogen bonds) or electrostatic. These interactions are most often reversible.

Chemisorption which implies the formation of surface chemical bonds. The interaction involves electron exchange between the liquid phase and the surface. The formed bonds are selective in what concerns the adsorption sites and are usually irreversible.

Different sorption mechanisms can be identified at the solid/liquid interface, as follows

Ion exchange Surface complexation Dissolution/precipitation Surface precipitation.

23 (61)

5.4.1 Sorption via ion-exchange

This mechanism is generally applicable to solids that are characterized by a fixed electric charge (ion exchange resins, argyles, zeolites), which are capable to retain oppositely charged ions. The fixed charges can be due to vacancies or substitutions in the crystal lattice. In a more general way, the model of ion exchange is applied to systems in which the sorption process comprises an equivalent exchange of ions between the two phases.

5.4.2 Sorption by surface complexation

The surface complexation approach describes the sorption of anionic, cationic or neutral species on a specific material reactivity of which is surface dependent. This model takes into account the interactions between the adsorbed ions/molecules with the solid in analogy to complexation in the solution. These interactions can be both electrostatic and covalent. The sorption of numerous anionic or cationic species, including H+ and OH-, that take part in the acid-base equilibriums, can be treated in terms of specific adsorption by surface complexation. Accordingly, two types of complexes can form (Figure 8):

External sphere complexes formed by electrostatic interactions with species located at the Stern or external Helmholtz planes

Internal sphere complexes – in this case, the bonds established between the surface sites and the species in solution are chemical involving OH groupings at the surface. The species forming internal sphere complexes are situated at the surface of the solid [57], and could be both mono- and bi-dentate.

The modeling of sorption via surface complexation is effectuated by defining equilibriums between surface sites and species in solution coherent with the acid-base properties of the surface, e.g.

24 2 2 22( ) 2 ( ) 2 aqM OH SO H M O SO H O (0)

to which corresponds a stability constant of the respective complex Kc. As the example demonstrates, the sorption via surface complexation can modify the surface charge.

Figurecontai

5.4.3

5.4.4

e 8 Schematining KCl an

Sorpt

Whenand fmechareducstablewith condi

Sorpt

Surfacno sumodifbetwethe dian ada comperiodprecipisotheconce The dvisiblconceiron o

tic represennd Na2SO4 [

tion by pre

n the solid iform insolanism can be on the su

e in the solsulfides antions becom

tion by sur

ce precipitaurface saturfied by theeen that of istinction bsorbed mon

mplex kinetd indicatespitates can erms corresentration of

distinction e, the mo

entration of oxy-hydrox

ntation of th[24,25].

ecipitation/d

is partly soluble phasebe also assourface of oxution in redd carbonate

me oxidizing

rface precip

ation is a soration of site formationthe initial setween pre

nolayer is notics and nons the formalso be de

sponding tothe adsorbi

between suore the m

the adsorbxides such

he magnetite

dissolution

luble in thees with spociated to rexy-hydroxidducing cones that coug again, Fe

pitation

orption mectes is obse

n of a newsolid and th

ecipitation aot always en-equilibriu

mation of etected by to the increaing species.

urface precmechanism

ing speciesas goethite

e/water inte

n

e liquid, thepecies presedox procesdes which

nditions. Hould be prese

(II) can be

chanism tharved. The

w phase,thehat of the sand surface vident [26]

um conditiosurface pr

the absencease of the s

cipitate andof sorptio, e.g. durine [27]. The

erface in an

dissolved isent in thesses. For exleads to dis

owever, Fe ent in the moxidized to

t can becomcompositioncompositiourface preccomplexat

. In generalons persistinrecipitates. e of a platesurface cov

d surface con varies wg adsorptioe adsorptio

aqueous so

ions can pre electrolytxample, Fe ssolution of(II) can pr

medium. W Fe (III).

me effectiven of the suon of whiccipitate. In ption which l, the observng for a lo

The preseau in the

verage with

omplex is with pH

on of phospon obeys a

24

olution

recipitate te. This (III) can f Fe (II)

recipitate When the

e even if urface is h varies practice, assumes

vation of ong time ence of sorption volume

the less and the hates on

surface

4 (61)

25 (61)

complexation mechanism at low concentration of phosphorus and a precipitation mechanism at high concentration.

5.5 Influence of temperature on surface charge

5.5.1 Temperature dependence of the point of zero charge

The studies of the effect of temperature on the PZC are relatively few due to the technical difficulties in measuring acid-base titrations and pH at elevated temperatures. They are summarized in Table 2.

Table 2 Studies of the temperature dependence of PZC for relevant oxides.

Temperature range (°C) Oxide/hydroxide Source 5-95 TiO2 [28,29] 25-90 Al2O3 [30] 25-90 Fe3O4 [30,31] 5-70 - Fe2O3 [29] 25-80 Co(OH)2

Co3O4 NiO

[32]

25-250 TiO2 [33] 25-290 Fe3O4 [34] 5-320 Fe3O4

NiFe2O4 CoFe2O4

[35]

25-290 ZrO2 [36] 25-290 TiO2, ZrO2 [37,38]

The first obtained results indicate a decrease of PZC with increasing temperature. This evolution is comparable to that of ½ pKW (the ionic product of water). The difference between PZC and ½ pKW is more or less constant in the studied temperature ranges for most of the studied oxides with the exception of magnetite for which this difference increases with temperature and intersects the curve of neutral pH of water to become superior to the latter at 250 °C according to ref. 35 An analogous result has been obtained for cobalt ferrite (Figure 9) for temperatures higher than 150 °C. The results show that the parallelism between PZC and pH of neutral water is not anymore valid above a certain temperature.

Figurevariati

5.5.2

e 9 Influencion of pH of

Two taforem

The eGibbs

Temp

The eFe3O4

resultbeing

ce of temperf neutral wa

types of calmentioned r

Using thePZC as aassumed reaction ithe produreactions of water

M

pK

evolution of s’ energy of

G

By usingWesolowtemperatu

PZC

perature de

effect of te4, in the rants indicate a more signi

rature on thater (1/2 pK

culation of results, accoe 2-pK moda function othat the chein which thucts. This re

according t

2M OH O

K pK p

f the PZC wf reaction (0

298TG G

g the monwski et al. ure as

0298 2

2.3

H

R

ependence

emperature nge 23-235 °a decrease oificant in the

e PZC of FeKW). pHZNPC

the PZC haording to thdel, Schoonof temperatemical equi

he charge nueaction resuto the 2-pK

aq

W

OH

pK pK

with tempera0) with temp

298 ( 2S T

no-site 1-p[34] mod

298 pC

RT

e of the iso

on the IEP°C has beenof the IEP we case of Ti

e3O4 and coC correspond

ave been proe model em

nen [39] hasture betweeilibrium corumber of th

ults from theK model ((0)

2

M O

PZC p

ature is exprperature

298) (pC

pK model, deled the

0298

2.3pS C

R

o-electric p

P of severan studied bywith increasiO2 in comp

obalt ferrite ds to the PZ

oposed on thmployed: s proposed en 25 and 3rresponds the reactantse combinati) and (0)) an

aq

W

H H

pK

ressed by th

( 298T T

Macheskyvariation

1 ln 298p

RT

oint

al oxides, iy Jayaweerasing temper

parison to m

compared ZC.

he basis of t

a calculatio350 °C. It hto an iso-cos is equal toion of the and the ionic

2 , H O K

he variation

ln )298

TT

y et al. [3of PZC w

ln

2.3pC T

R

including Ta et al. [40,rature, the t

magnetite (IE

26

to the

the

on of the has been oulombic o that of acid-base c product

(0)

of the

(0)

33] and with the

T (0)

TiO2 and 41]. The tendency EP 6.3 at

6 (61)

27 (61)

23 °C and 6.1 at 235 °C). Zhou et al. [42] have studied the evolution of IEP of ZrO2 with temperature in the interval 25 to 200 °C and have shown that the IEP decreases with increasing temperature similarly to ½ pKW, the difference between these two being constant in the whole temperature range. Similar tendency has been observed for TiO2 [43]. Summarizing, it can be stated that the variation of the PZC with temperature is similar to that of the IEP. The observed tendency for most of the studied oxides is a decrease of both values with increasing temperature. This evolution is similar to that of the pH of neutral water. For certain oxides, such as rutile or zirconia, the difference between PZC/IEP and ½ pKW is constant regardless of the temperature, whereas for spinel oxides such as magnetite, nickel and cobalt ferrites this is not the case.

5.6 Influence of ion adsorption and water chemistry on the surface charge

5.6.1 Ion adsorption

The effect of lithium ions and borate species on the surface reactivity of metal oxide particles representative of corrosion products found in primary circuits of PWR has been studied [44]. No effect of lithium ions was observed in comparison to potassium ions. The presence of borate species causes a decrease of the iso-electric point of the three oxides. This effect was attributed to the sorption of boric acid to the surface as a negative surface complex. In order to predict the behavior of oxide particles in the presence of borate ions for different concentrations of boric acid and pH values, a new approach using both theoretical and empirical bases was developed. Zetametry showed the effect of boron and pH on the ζ potential, but did not give direct access to surface acid–base and sorption constants, which are necessary for developing predictive models. In the proposed approach thermodynamic bases to calculate the surface acidity constants of the three solids from the data of acid base titrations were employed. Connection between acid–base titrations and zetametric measurements was achieved through an empirical relation between the surface potential Ψ0 and the potential ζ at the shear plane. The determination of the position of the shear plane and, as a consequence, the relation between Ψ0 and ζ, remains a problem which cannot be solved easily by a theoretical approach. This study also showed that modeling the curves of ζ variation versus pH by assuming that surface potential is equal to ζ for low ionic strength such as 10−4 mol l−1 leads to large errors. However, a general tendency in the presence of borate was deduced from the measurements: a decrease of IEP for cobalt ferrite and an increase of IEP for nickel ferrite. Combined with previous measurements of the PZC in the absence of borate of these oxides up to 320 ◦C [35], a first tool to predict the behavior of oxide particles of primary circuits of PWR was developed. If extrapolation of these data are valid at higher temperatures than those used in the present work, the decrease of boron concentration during the functioning of the reactor should lead to an increase of the surface charge of oxide particles toward their natural PZC, the consequences to adhesion depending on the charge of the materials constituting the primary circuit.

28 (61)

Further, a complete characterization of the magnetite has been performed, including purity, redox and acid–base properties, followed by a study of the sorption of sulfate ions [24]. One of the results is that, in the operating conditions of this work, no redox reactions were observed: any oxidation during storage, no reduction of sulfate ion to pyrite or sulfide contrary to thermodynamic predictions, so that sulfate is the real adsorbed surface species. The predicted reduction is probably retarded by sluggish kinetics, contrary to Pu (V) and U(VI), which are reduced in presence of magnetite [12]. The predicted decomposition into hematite and Fe2+ at low pH affects only a superficial layer of magnetite. The acid–base properties were determined by zetametry, mass titration and acid–base titration. The relatively close values of PZC and IEP indicate that this magnetite is pure and that the surface charge is not affected by specifically adsorbed species. The titration curves were fitted by two different electrostatic models (constant capacitance and Stern model) in the 2pK acid–base model. As usually, the differences between the fitted and the experimental values do not allow discriminating between models. Sorption experiments of sulfate showed a pH dependency typical of anionic species on oxides. The main difficulty in modeling the sorption data resulted in the choice of surface adsorbed species, which could not be done from fitting of sorption curves alone. The choice was guided by the slope of the curves (excluding IS complexes alone) and by the value of ζ potential measured in presence of sulfate. Finally, according to the proposed model, sulfate ions are adsorbed essentially as OS complexes, with a partial sorption as a neutral bi-dentate IS complex below pH 5. It is to be noted, that the values of sorption constants depended on the acid–base parameters, but a consistent set of acid–base and sorption parameters in the BSM models was proposed. All these results could be the basis of the data necessary to understand and predict the behavior of magnetite in the secondary circuits of PWR. To complete the present results, experiments are in progress to get closer to the conditions of PWR, especially by studying the effect of temperature and reducing conditions on the sorption behavior and nature of sulfur species. In a further paper [25], the sorption of aqueous sulfate onto magnetite, studied between 50 and 275 °C, was found to be promoted under acidic conditions when the magnetite surface is positively charged. The effect of temperature on this retention is moderate but complex. From 50 to 125 °C the sorption edge is shifted toward low pH values, according to the variation of the point of zero charge. Above 125 °C, the effect of temperature is inverted, leading to a shift to basic pH values and an increase of the adsorbed quantity. This inversion of the temperature effect is interpreted as related to changes in the nature of the complexes formed, correlated to the evolution of speciation of dissolved S (VI) species. In the absence of hydrogen, redox reactions which are predicted from thermodynamic data were not observed. In presence of hydrogen, sulfate is involved in redox reactions, likely as a consequence of the catalytic effect of the sorption that enhances the H2–sulfate reaction, producing sulfides in the gaseous, liquid, and solid phases. However, this effect is better evidenced at 125 °C than at 275 °C, illustrating the importance of surface speciation, assumed to change with temperature. The experiments provide new insight for the mechanisms and the kinetics of sulfide formation in such environments. They demonstrate the important role of surface catalysis in kinetics of sulfate reduction.

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Sorption and zetametry experiments at 25 °C were performed on the Ni2+/CoFe2O4 and Co2+/NiFe2O4 systems in order to determine the behavior of corrosion products in the fluid of the primary circuit [45]. For nickel and cobalt concentrations lower than 10-5 mol l-1, adsorption is the only process occurring, with formation, for both systems, of a positive mono-dentate surface complex (ONi+ or OCo+). The formation of a OMOH complex was assumed for more basic pH. For higher concentrations and at pH higher than 8, hydroxide precipitation occurred in addition to sorption of the surface complex. Differences observed in zetametric measurements between the two solids were thought to result from differences in their IEP, which was found to be higher for nickel ferrite than for cobalt ferrite. For the first solid, IEP was higher than the pH of precipitation, while it was lower for the second solid. Application of these results to PWR nuclear power plants would require performing experiments at higher temperatures, allowing these measurements to be used in a surface complexation model close to those already developed. Moreover, due to the low concentrations of soluble species in cooling circuits, the main sorption process is expected to be the formation of surface complexes that supports the need for better information about this kind of reaction.

5.6.2 Influence of water chemistry

Specific studies detailing the effects of amines, used as pH control agents for corrosion inhibition in power plants, on the surface charge of iron oxides provide data to assess the mechanism of how these amines impact deposition rate. In that context, a recent study [46] was undertaken in order to determine accurately the dissociation constants of the relevant amines in PWR operating conditions and to investigate the effect of sorption of two of these amines (morpholine and dimethylamine) by magnetite. The acid-dissociation equilibriums of morpholine (MOR), dimethylamine (DMA) and ethanolamine (ETA) were measured potentiometrically with a hydrogen-electrode concentration cell from 0 to 290 °C in sodium trifluoromethanesulfonate (NaTr) solutions at ionic strengths up to 1 mol kg−1. Magnetite surface titrations were performed at an ionic strength of 0.03 mol kg−1 (NaTr medium) in the presence or absence of MOR and DMA buffers over a wide range of pH and total amine concentrations at 150– 250 °C. The authors claim to have optimized the opportunity to observe significant effects of amine and/or amineH+ in excess of that due to sodium ions, on the surface charge of magnetite and conclude that there is either no specific effect or that it is insignificant. Furthermore, these studies indicate that if the un-protonated amine molecules adsorb on magnetite surfaces to a greater or lesser extent than their protonated cations, this differential adsorption is insufficient to perturb the proton balance calculations, which are a very sensitive test of the expected amine/amineH+ ratio in solution.

5.7 Colloidal particles in recirculation systems

The acid-base properties of the surface and the sorption phenomena are inherently concerning the colloidal particles as corrosion products in the coolant circuits of the NPPs. Such particles would not only react with the charged species dissolved in the medium, the sorption process aggravating SCC by reduction of sulfur-containing species, or will lead to SG fouling by adhesion. The next part of the current chapter summarizes the state-of-the-art concerning colloidal particles and their connection to fouling mechanisms.

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5.7.1 Definition

Dispersion is considered to be colloidal when the discontinuous phase is subdivided in units with dimensions much larger than those of single molecules but sufficiently small so that the interfacial forces are predominant in determining the properties of such dispersion. The gravity forces on the particles can then be considered negligible. A more general definition of a colloidal dispersion is a stable system of particles in a certain medium with at least one of the particle dimensions in the range 0.001-1 µm. The essential characteristic of a colloidal ensemble is the large surface of the dispersed phase, compared to a similar quantity of matter in a massive solid. The increase of this surface leads in fact to negligible influence of the volume forces with respect to surface forces. The properties of the colloidal dispersions are direct function of their size but mostly of the characteristics of the interfaces with the surrounding fluid. Thus there are two general ways to change the properties of colloidal dispersions:

By changing the distribution of the particles by size Or modifying the nature of the interface by adding an electrolyte or

surfactant. Depending on the conditions prevailing in the medium, the particles can agglomerate under the influence of the electrostatic or Van der Waals forces (and eventually provoke sedimentation) or stay suspended, stabilized by the electrostatic forces. The stability of a colloidal system is frequently correlated to the zeta-potential discussed above in paragraph 5.2.4.

5.7.2 Formation of colloids by corrosion in recirculation systems

In a recirculation loop such as the coolant systems of NPPs, the formation of colloids is a result of the corrosion and surface reactions of the construction materials and is determined by the soluble species present in the circulating fluid. Several phenomena controlled by the variation in thermo-chemical conditions (temperature, pH, redox potential) can affect the oxidation state of a metal, mostly iron, and its distribution between soluble and particulate species. Such variations can lead to

Precipitation of soluble species in the flow or on the walls Dissolution or growth of particles Agglomeration or dissociation of particles (caused by magnetic or

turbulent shear forces…) Oxidation/reduction of particles or their reactions with other species.

Thus colloidal particles are formed either on the surface of the material by corrosion, or by precipitation in the bulk of the flow. The ion-containing species would evolve following the thermo-hydraulic conditions, form or modify deposits. In a general way, the adhesion between solids implies all the phenomena of chemical bonding that contribute to the cohesion of solids, i.e. hydrogen, metallic, covalent or ionic bonds. In fact, the surface bonds tend to be saturated by contaminants and can create further bonding only when the substances enter in contact. In the continuation of the present chapter, the interactions that determine the behavior of colloids in the vicinity of a charged surface will be presented and discussed in view of the fouling mechanisms determined by this behavior with the flow.

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5.8 Dielectric properties of colloidal systems

5.8.1 Introduction

In this chapter, the fundamentals of the phenomenon of dielectric dispersion in aqueous colloidal suspensions, as well as the most recent advances on the subject with regard to oxide particles, are described. Such a description is considered worthwhile in the context of the present survey due to the fact that the permittivity is very sensitive to such quantities as: the particle size and shape, the tendency of the particles to aggregate or not, the equilibrium electric potential at the slip/shear surface (the electro-kinetic or ζ-potential), the concentrations, charges and diffusion coefficients of ions in the medium and the volume fraction of dispersed solids. First, the definitions of the permittivity of a heterogeneous system consisting of a certain volume of a material dispersed in the form of identical spheres (particles) in a liquid medium (electrolyte solution). Attention is also paid to the relationship between the electric permittivity of the suspension and the strength and frequency dependence of the dipole moment induced by the external field. Next, the mechanisms that are typically responsible for the dielectric dispersion of the suspension are outlined, including the contribution from the permittivity of the electrolyte solution, the dispersion determined by the difference between permittivity and conductivity of the particle and the surrounding medium, and last but not least, the Low Frequency Dielectric Dispersion (LFDD) due to the phenomenon of concentration polarization. The short overview is finished with a description of the most recent advances, namely the consideration of suspensions of soft particles and extensions of the standard electro-kinetic model in order to reach a better agreement between theory and experiments.

5.8.2 Main mechanisms of dielectric dispersion in colloidal systems

The frequency dependence of the complex conductivity (or of the permittivity, considering their relationship) of a suspension is characterized by a series of dispersions (regions of variation with frequency), which are determined both by the frequency dependence of the complex conductivity of the electrolyte solution and the frequency dependence of the dipole coefficient. The origin of these dispersions can be easily described considering the simplest case when they are independent of one another: the conductivity and permittivity spectra have the shape of a series of plateaus separated by regions where the conductivity increases and the permittivity decreases. Going from high to low frequencies, these regions are classically called the γ, δ, and α-dispersions [47].

5.8.2.1 Gamma-dispersion

The γ dispersion is associated to the frequency dependence of the aqueous electrolyte solution where the particles are suspended, which is mainly determined by the polar nature of the water molecules [47,48]. The dielectric behavior of electrolyte solutions is very similar to that of pure water, which can be represented by a simple Debye-type dispersion [48]

32 (61)

*0

(0)

1rm rm

m m rme

jj

(0)

The parameters appearing in this expression, valid in the frequency range from 0 Hz to several THz, have the following approximate values at 25 °C:

12(0) 78.4, 5.3, 8.3 10 , 10 / .m rm e ms S m These values weakly

depend on the electrolyte concentration except for the stationary conductivity, which strongly increases with this concentration. The γ dispersion is seldom measured and often ignored in the theoretical and numerical calculations related to the dielectric behavior of colloidal suspensions. This is done by limiting the considered frequency range to the region below 1 GHz, and considering that the relative permittivity of the dispersion medium is frequency-independent.

5.8.2.2 Delta dispersion

The δ dispersion is determined by the Maxwell–Wagner–O'Konski (MWO) relaxation phenomenon: a frequency dependence of the dipole coefficient while the permittivity and conductivity of the particle and of the electrolyte solution remain frequency-independent. At frequencies above this dispersion, the dipole coefficient is solely determined by the relative permittivity values of the particle (εrp) and of the electrolyte solution (εrm), both real, as mentioned:

*

2rp rm

rp rm

C

(0)

This happens because below the γ dispersion the polarization is proportional to and always in-phase with the local field (total field at any point of the suspension). When the frequency is decreased, the ionic current density starts to build an ever increasing charge density on the particle surface. Since this density is out of phase with respect to the local field, it leads to the appearance of an out of phase (imaginary) part of the dipole coefficient. Therefore, the local field becomes complex, which means that an increasing fraction of the ionic current density shifts out of phase with the applied field and, correspondingly, part of the free charge density shifts in-phase with the field. At frequencies below the δ dispersion, the period of the applied field becomes so large that the free charge density shifts in-phase with the applied field and attains a final value that is responsible for the low frequency dipole coefficient. Therefore, at sufficiently low frequencies, the dipole coefficient only depends on the conductivity values of the particle and the electrolyte solution

* 02

p m

p m

C

(0)

The shift from the high to the low frequency regimes relative to the δ dispersion outlined above occurs when the conduction and displacement current densities throughout the system become comparable. The actual expression of the relaxation time of the δ dispersion is

02

2rp rm

p m

(0)

33 (61)

In the above expressions, p should be interpreted as the effective particle

conductivity: a value determined by both its bulk and surface conductivities [49]

2 S

p pb a

(0)

In the simplest situation, the surface conductivity is entirely due to the net charge of the particle: solid particles immersed in an aqueous solution acquire a surface charge (usually negative). While this charge is fixed, so that it cannot directly contribute to the surface conductivity, it attracts ions of the opposite sign that form a diffuse double layer around the particle, shielding its radial electric field. Inside the double layer the counter-ion density is higher than in the bulk electrolyte solution while the co-ion density is lower, but the total ion density is usually much higher than in the bulk. Therefore, when a field is applied to the system, the double layer transports a higher current than an equivalent volume of the bulk solution. This excess can be described by means of a surface conductivity. However, the increased ion density is not the only responsible for the surface conductivity value, which is also due to fluid motion. Another contribution related to the fluid motion but only present at very low frequencies will be discussed in the next section.

5.8.2.3 Alpha dispersion

The α- or LFDD is a phenomenon characterized by a huge increase of the permittivity of colloidal suspensions at very low frequencies. Its origin is in the asymmetry of these systems with respect to the ion sign: due to the fixed charge of the suspended particles, the behavior of counter-ions under the action of an applied field becomes different to that of co-ions at very low frequencies. Let us consider a negatively charged particle and a DC electric field pointing in the left to right direction that is suddenly switched on (Figure 10). On the right hand side of the particle a very strong flow of positive counter-ions arrives from the left to the outer boundary of the double layer. However, the counter-ion flow abandoning this boundary towards the right is much weaker because there is no excess of counter-ions in the bulk electrolyte solution. This means that the counter-ion density on the right hand side of the particle starts to increase. As for co-ions, their flow arriving from the right to the outer boundary of the double layer is comparable to that of counter-ions in the electro-neutral electrolyte solution. On the contrary, the co-ion flow inside the double layer is much lower. Therefore, the co-ion density on the right hand side of the particle also increases. An increment of both the counter-ion and the co-ion densities means that the electrolyte concentration at the right hand side of the particle increases (it decreases at its left hand side). This phenomenon often referred to as “counter-ion polarization” or “concentration polarization” continues until huge (of the order of the particle radius) neutral regions of increased and decreased electrolyte concentration build up around the particle. At this stage the system attains a stationary state and ceases to evolve in time. This happens because the strong flow of positive counter-ions that arrives from the left to the outer boundary of the double layer has now the same value as the counter-ion flow abandoning this boundary towards the right, because counter-ions are not only driven by the electric field but also by their concentration gradient. Analogously, the co-ion flow arriving from the right to the outer boundary of the double layer

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34

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4 (61)

5.8.3

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35

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5 (61)

5.9

5.9.1

Figureelectro

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Inter

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(left) and

36

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6 (61)

37 (61)

At very short distances between particles (of the order of few nm), other forces have also to be taken into account, e.g. Born repulsion and the interaction due to hydration of surfaces.

5.9.2 Contact interactions

When the particle enters in contact with a solid substrate, its intrinsic characteristics need to be known to estimate the necessary force (pull-off force) to detach the body from contact. These forces are denoted as adhesion forces. The theory of Johnson, Kendall and Roberts (JKR theory) is based on an estimate of the work needed to separate the interfaces taking into account the deformation of the particle [59]. The contact surface leads to adhesion efforts being necessary to overcome in order to separate the contact surfaces. It can be shown that this separation is achieved when the contact radius is smaller than 63% of its initial value, which has been experimentally verified [58]. The JKR model underestimates the surface charge and also predicts an infinite value of the surface tension in the contact zone. To overcome this difficulty, the Derjagin-Muller- Toporov (DMT) approach is used taking into account a Hertz-type deformation of the contact zone and an adhesion due to the surface forces acting out of that zone [60]. This model is applied mostly for low adhesion energies and low contact radii.

5.9.3 Parameters influencing the interactions

The contact conditions can be modified by several parameters, notably: The roughness of the contact surfaces The time of contact and its influence on the pull-off force The kinetics of pull-off The oxidation of the contact surfaces.

However, since the main goal of the present survey is to treat the interaction between particles and material surfaces in the coolant circuits of NPPs, the influence of electric and electrochemical parameters such as the zeta-potential and ionic strength is of chief importance.

5.9.4 Influence of the zeta potential and the ionic strength on the interaction between charged surfaces

In the system consisting of a particle and a surface, both characterized by their zeta-potentials, two regions can be defined as depending on the relative sign of these potentials (Figure 14) – in regions A and C, the two zeta potentials have the same sign, and in region B, their signs are opposite [61]. Region B is more favorable to the adhesion of the particles on the surface since the resulting force is attractive.

Figuredifferethe IEPzone c

5.9.5

5.10

e 14 Schemaent constitueP, (b) two c

comprised b

In thedetermstrengincreaparticzone streng

Effec

AccorDebyedecreadimintempevariatHamadepenfrom tempe(of th

Influmec

The fof twofor th

atic represeents (a) – siconstituentsbetween IEP

e Gouy-Chamines the ragth)-1/2. At ase in ioniccularly impoof pH in w

gth as predic

ct of tempe

rding to thee length thaases with

nishes. Howerature on tion of the aker constannds on temp

the changerature [62]e order of 1

ence of thanisms

fouling pheno opposing e deposition

entation of tingle constitwith differe

P1 and IEP2.

apman-Sternadius of acthigh ionic

c strength wortant ionic

which the zected by the

rature on t

e GCS theorat is a meas

decreasinwever, this

surface chzeta poten

nt that deteperature thres in optic. The variat0%) betwee

he colloid

nomenon isprocesses –

n is then giv

the interactituent, the agent IEPs – h

n theory oftion of the c strengths,will favor thc strength caeta potentiaDLVO theo

the interac

ry of the dosure of the dng tempera

effect is fhemical eq

ntial with teermines therough sevecal and eletion of the Hen room tem

d-surface

s, as already– depositionven by [63]

ions as a fugglomeratiohetero-coag

f the doubleelectrostati, the potenhe adhesionan lead to als are of simory is illustr

ctions betw

ouble layer, diffuse layeature, i.e. far less impquilibriums emperature e strength oeral factors,ectronic proHamaker comperature a

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y mentionedn and re-ent

nction of thon is favoregulation is fa

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ntial barriern of particlean adhesionmilar sign. rated in Figu

ween charg

the temperaer thickness

the electportant thathat repre[44]. On t

of Van der the most operties of onstant is hond 1000 °C

ons on th

d, a result otrainment [6

he zeta potened in the vicfavored in th

e Debye lenaries with thr is low, tes. A mediun of particleThe effect

gure 13 (righ

ed surface

ature influes. The Debytrostatic r

an the influesents 90%the other hWaals inteimportant r

f the materowever rath

C.

he fouling

of the super63,64]. The

38

ntial of cinity of he pH

ngth that he (ionic thus the um with es in the of ionic

ht).

es

ences the ye length repulsion uence of

% of the hand, the eractions resulting rial with her small

g

rposition net flux

8 (61)

39 (61)

fd r

dm

dt (0)

d and r being the fluxes of deposited and re-entrained particles in kg m-2s-1

and mf the mass of the deposit per unit area, kg m-2. The following paragraphs present the state-of-the art of the theoretical knowledge on these two phenomena. They are influenced by numerous parameters that can be grouped in several categories – parameters related to the nature of the particles (granulometric distribution, physic-chemical properties), surface condition (material, roughness, and deformation), nature of the deposit (monolayer, poly-layer, and heap), flow (acceleration, characteristics of the turbulence, shear velocity at the wall), and environmental factors (temperature, humidity, etc.).

5.10.1 Deposition of colloidal particles

The mechanism of formation of such a deposit can be considered to consist of two stages:

Transport stage – from the bulk of the flow towards the surface of the solid wall. This stage depends on the particle size, fluid velocity, temperature and temperature gradients;

Attachment stage – adhesion of the particle on the solid surface, which depends on the surface charge which is in turn a function of pH.

The global deposition flux depends linearly on the particle concentration in the fluid, cb, and is thus given by d d bk c (0)

where kd is the global deposition coefficient in m s-1. Since the process is a two-stage one, this coefficient is expressed as

1 1 1

d t ak k k (0)

where kt and ka are the transport and attachment coefficients, respectively [65]. Several mechanisms of transport of particles in the liquid medium are operative. The predominant mechanism is determined by the relaxation time of the particle which is directly related to its size

2

*218

d

(0)

where is the fluid density, d the diameter of the particle, the dynamic viscosity of the fluid and the shear stress of the fluid at the wall. Effectively, three mechanisms of transport dominate successively for sub-micron particles in a turbulent flow [63,66]

Diffusion – small size particles are entrained by the turbulent fluctuations of the fluid and arrive in close proximity of the wall where they are subject to Brownian agitation and turbulence is suppressed

40 (61)

Inertia – particles that have certain inertia are detached from the turbulence zones of the fluid to impact with the wall without the intervention of turbulent fluctuation (characteristic for particles larger than 1 µm)

Turbulent impact. The parameters that influence these particular transport mechanisms are the diameter of the particle and the fluid velocity. Since the colloidal particles are smaller than 1 µm, the main transport mechanism is diffusion [67]. In a laminar flow, the diffusion coefficient is determined by Brownian motion and is expressed by Stokes equation

6

bB

k TD

r (0)

where r is the radius of the particle and kb is the Boltzmann constant. In the turbulent regime, the effective diffusion coefficient is influenced by the fluctuation of the liquid

teff B

t

D DSc

(0)

where the Schmidt number is Sct = 0.9 and t is the viscosity in the turbulent

regime. In addition, the transport of particles is influenced by parasitic effects such as the roughness of the surface and temperature gradients. On an isothermal surface, the particle transport coefficient can be calculated from the relation [65]

2/30.084tk Sc

(0)

Where the Schmidt number is expressed as / BSc D and the shear stress

of the fluid at the wall, as mentioned above. If the surface is subject to a significant heat transfer, the particles have to diffuse with or against the temperature gradient, and the thermo-phoresis effect has to be taken into account. In these conditions, the flux of particles towards the heated surface is estimated from [65]

2th

t t

kk k

(0)

where the thermo-phoretic coefficient is expressed as

1

0.262

lth

l p

k QT

(0)

l and p being the thermal conductivities of the liquid and the particle, T the

temperature of the liquid, and Q is the thermal flux.

41 (61)

On the other hand, the attachment coverage depends on the total potential energy that according to the DLVO theory is in principle equal to the sum of the Van der Waals and double-layer interaction energies. These forces of interaction between the wall and the particles become important in the close vicinity of the latter (ca. 10 nm). If the energy of the double layer is translated into a repulsive force and is sufficiently important, the total potential energy passes through a maximum when the particle approaches the surface. In this case, the particles transported from the bulk towards the surface have to overcome an energy barrier in order to become attached at the surface at which they are attracted by Van der Waals forces. It has been demonstrated that in such circumstances the attachment flux of colloidal particles to the surface for a diluted suspension is given by [68]

/,0

sE RTa s ac k e (0)

cs being the concentration of particles in close proximity to the surface, ,0ak the

pre-exponential factor of the attachment reaction, E its activation energy and Ts the surface temperature. The energy of activation is equal to the maximum of the total potential energy and corresponds to the energy of attachment. Equation (0) shows that the flux of attachment increases exponentially with the surface temperature. This Arrhenius’ type of dependence for the attachment flux is taken into account already in the diffuse part of the double layer due to the repulsion forces between the particle and the surface when the particle is still in suspension rather than after the adhesion when a chemical bond is formed. If the particle and the surface have opposite charges, there is no energy barrier for the attachment and the coverage by the deposit is equal to the flux of transport of particles towards the surface for a dilute suspension. Summarizing, if the charges of the particle and the surface are of the same sign, the global force is repulsive and the coverage by the deposit is controlled by the attachment flux. If the charges of the particle and the surface are of the opposite sign, the coverage by the deposit is controlled by the transport flux. If the deposit process is limited by the transport, colloidal particles are small enough to diffuse following a Brownian motion.

5.10.2 Description of the re-entrainment phenomenon

In analogy to the deposition process, the re-entrainment is also a two-stage event consisting of

Detachment of the particle from the surface Transport of the particle by the flow from the closest wall.

From the point of view of fluid mechanics, the ensemble of these stages takes place in a particular zone of the flow – the dynamic turbulent boundary layer. This is the zone of the fluid that is situated between the wall and the bulk of the fluid that is not perturbed by that wall. Classically, for the sake of modeling, this layer is decomposed in three zones, the laminar sub-layer in contact with the wall where the viscous effects are predominant, the transition sub-layer and the turbulent sub-layer in which the turbulent exchanges are preponderant.

Figure

The cby coincludhydroare no Chiefforce.is thadiffus

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42

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2 (61)

43 (61)

the structures associated to re-entrainment in two categories: ejection-sweep (ES) and macros-sweep (MS), the first events being more frequent than the second and are due to a local and temporary interruption of the viscous sub-layer. The MS are characterized by an erosion of the viscous sub-layer in a time interval larger than that of the ES. Even if the particle is detached from the support, and there is no direct contact between them, the wall still influences the flow and thus the behavior of the particle. This is why the transport in proximity of the wall is an important stage of the re-entrainment process. Most authors retain the drag, lift, gravitational and Brownian motion forces [75] in the modeling of particle transport in close vicinity of the wall within the frames of a re-entrainment situation.

5.10.3 Summary of the interactions involved in fouling

The deposition of particles when they are in the proximity of the wall can be summarized by taking into account the energy barrier at the wall and the attachment force. The energy barrier is a result of the potential energy of interaction calculated by the DLVO model as a function of the distance between the two solids. The Van der Waals force can be estimated a priori from the Hamaker constant or from surface energy calculations. The electrostatic force depends directly on the surface potential, and can be identified if the zeta-potential is measured, or calculated based on models of surface reactivity in which several parameters need to be estimated (PZC, density of sites, acidity constants, double layer capacitance). The relative sign of the zeta potential and its value is important to predict the interaction between the two solids – attraction or repulsion. The ionic strength of the medium is also important since it can influence the surface charges and reduce the electrostatic repulsion. The force of detachment depends on both the adhesion forces that can be calculated from the JKR model subject to an estimate of the surface energies of solids or the DMT model, and the aerodynamic forces that are mainly comprised of the drag and lift force. Lift forces sufficiently high to detach the particles are generated by perturbations of the turbulent layer, so-called bursts. The particle is subsequently transported into the bulk fluid or is re-deposited on the wall following the forces acting on it once it is has been detached from that wall.

6 Consolidation of deposits

6.1 Introduction

At the beginning of plant lifetime, the deposition of corrosion products, creates porous oxide scales on the tube surfaces, which increase the internal tube surface area, resulting in an increase of nucleated boiling, accordingly enhancing the primary to secondary heat transfer. But these oxide scales grow and consolidate with the plant operating time and after a certain time the heat transfer rate begins to decrease, due to the isolation effect of the consolidated tube scales. Consolidation (or ageing) is a process whereby particles become chemically bonded to either the heat-transfer surface or to the pre-existing deposits. Deposit

44 (61)

that has aged, or become consolidated, is strongly bound to the surface and therefore cannot be removed by the fluid. The driving force for the consolidation of deposit is postulated by the precipitation of dissolved species within the pores of the deposit (so-called Ostwald ripening). It is enhanced by the temperature gradient at heat transfer surfaces. The process is thermodynamically favored because it is accompanied by a reduction in surface area and, therefore, by reduction of surface energy. Boiling induced precipitation is also a part of the deposit consolidation mechanism. In the following, the effect of consolidation/ageing on the overall impact of fouling on heat transfer surfaces will be assessed. First, the stages of the deposition process will be briefly recalled to recognize the place of consolidation in the sequence of events that lead to fouling. Second, the consolidation mechanisms will be reviewed and the effect of different factors on the consolidation process will be discussed. Finally, some insights into the potential remedies to fouling that are directed towards deposit consolidation will be given.

6.2 Stages of the deposition process

The overall fouling process can be viewed as consisting of the following five sub-processes [76]:

• Initiation - Conditions that promote subsequent fouling are established during the initiation period, e.g., nucleation sites for crystallization or nutrients for biological growth are developed.

• Transport to surface - Mechanisms that contribute to fouling species transfer to the high temperature surface (HTS) include diffusive phoresis, turbulent diffusion, thermo-phoresis, brownian diffusion, electrophoresis, gravity, etc.

• Attachment - Factors that may influence the adhesion of fouling species are Van

der Waals forces, electrostatic forces and external force fields at wall.

• Removal - Removal of fouling species may occur as a result of spallation, erosion or dissolution, which may or may not begin soon after initial layer is deposited.

• Consolidation (Ageing) - Ageing of the deposit starts as soon as it has been

attached on the HTS. The process of aging includes changes in the crystal and chemical structures of fouling species by dehydration, polymerization, developing thermal stress, etc., which may affect the strength of the deposit and hence the removal process. Ageing is the least investigated step and is usually ignored in the modeling studies so far. The buildup of the fouling deposits as a function of time may be regarded as the result of deposition accompanied by a removal process, which may form one of the four curves shown in Figure 16 [77,78]: • Linear curve: the fouling resistance increases as linear function of time. This is observed for very hard scales with high adhesion and indicates constant deposition and removal rates (or no removal).

Figure

6.3

6.4

6.4.1

• Decdecreaand re• Asyis obincrearate. It is basymp

e 16 Differe

Defin

Consodeposlong pthermlocatelayer inaccube con

Fact

Temp

Surfacimporsurfaccrystafoulinsalts, viscosfoulin

creasing rateasing rate. esults from ymptotic curtained if thases with th

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ent types of f

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olidation orsit, which mperiods, fro

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surface. Ifurately prednstant throu

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a reductionsity betweenng species d

e curve: theThis behava falling derve: the fouhe depositi

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hat the lineavior.

fouling curv

the conso

r ageing phmay result fom a soft sivity of fouthe wall anf an ageingdicted if theughout its th

encing co

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ture, bulk tmeters affectn controlledr polymerizto an increan in the soln the heat tr

due to tempe

e fouling revior is foundeposition ratuling resistanion rate res of the dep

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olidation

henomenon from chemsubstance touling layer,nd the softeg mechanise thermal cohickness.

onsolidati

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temperatureting foulingd fouling przation, highased reactionlubility of ransfer surferature grad

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ing rate mo

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is defined ical reactioo a harder between th

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as a structn, which isone. This l

he hard depis situated clved, the fof deposit

velocity are.g., the ratlving chemtemperatur

in the case os. Also, varlk fluid mays the wall b

s with time mechanical moval rate. s a constant e the remoquals the de

e early stag

tural changs accumulaleads to a posit that isclose to thefouling behlayer is ass

re among tte of foulin

mical reactiore tends to of inverse sriations in ty affect tran

boundary lay

45

but at a strength value. It

oval rate eposition

ge of an

ge of the ted over different s usually e fouling havior is sumed to

the most ng. For a ons, e.g., increase olubility the fluid nsport of yer [80].

5 (61)

46 (61)

Fluid velocity is a critical factor with respect to both deposition and removal processes. Higher velocities will enhance the mass transfer of fouling species from the bulk fluid to the heat transfer surface and the intensity of the removal forces, but tend to reduce the efficiency of surface adhesion for the fouling species. Thus the deposition rate may increase or decrease with velocity depending on the specific mechanisms controlling deposition process [80,81].

6.4.2 Influence of boiling

The presence of boiling on heat transfer surface has a significant impact on fouling rate and deposit characteristics in various industrial applications including steam generators. The main source of fouling species in boiling water systems are dissolved inorganic salts (e.g., calcium carbonate and calcium sulphate) and suspended particles and corrosion products (e.g., iron oxide) [76,82].

Fouling is generally enhanced by boiling heat transfer due to the high temperatures and additional bubble activities involved at heating surface. In a pioneering work, Partridge and White [83] investigated the boiler scale formation by calcium sulfate. The deposit was shown to exhibit characteristic ring structure typical of those formed as a result of micro-layer evaporation at the base of bubble nucleating sites. These results were later confirmed by Freeborn and Lewis [84] and Hospeti and Mesler [85]. Asakura et al.[86] developed a particulate fouling model based on the concept of micro-layer evaporation to describe the deposition of iron oxide particles in boiling water. Good agreement between the measured deposition rate coefficients and model predictions was reported. The effect of boiling on the particulate fouling of iron oxide was studied by Charlesworth [87]. The deposition rate on boiling surface was found to be an order of magnitude larger than that for the unheated surface. The author suggested that the higher fouling rate in the presence of boiling might be caused by fresh water flux to the surface of the deposit layer to replace the departing bubbles. The iron oxide deposit formed under boiling condition was porous in nature probably because of bubble nucleation within the deposit. The rates of crystallization, corrosion and particulate fouling under boiling conditions were strongly dependent on heat flux due to its effect on the rate of bubble generation. The fouling rate depended on heat flux to the power of 1 to 5.5 with the most common values between 1and 2 [76,87,88].

6.4.3 Inhibitors and crystal habit modifiers

Chemical additives developed by many companies have been extensively used to mitigate fouling in the industrial sector. Various additives can be used to prevent scaling [89]. Bott [90] specified that the additives used act in different ways, such as (a) sequestering agents, (b) threshold agents, (c) crystal modifiers and (d) dispersants. Some of the common water additives are EDTA (sequestering agent), polyphosphates and polyphosphonates (threshold agents) and polycarboxylic acid and its derivatives (sequestering and threshold treatment). Sequestering agents such as EDTA complex strongly with the scaling ions thus preventing scaling as well as removing any scale formed previously. They are used effectively as anti-scaling agents in boiler feed water treatment.

47 (61)

Troup and Richardson [91] claimed that their use is uneconomical when hardness levels are high. Polyphosphates and polyphosphonates as threshold agents are also used to reduce scaling in boilers and cooling water systems. Bott [90] said that they prevent the formation of nuclei thus preventing the crystallization and mitigate fouling. Very small quantities of these agents are effective in reducing scaling from supersaturated salt solutions. Crystal modifying agents (e.g. polycarboxylic acid) distort the crystal habit and inhibit the formation of large crystals [92]. The distorted crystals do not settle on the heat transfer surface, they remain suspended in the bulk solution. If their concentration increases beyond a certain limit, particulate fouling may take place. This is prevented either by using techniques to minimize particulate fouling or using dispersing agents along with crystal modifying agents. Though crystallization fouling may not be prevented completely using additives, the resulting crystalline deposits are different from those formed in the absence of any additives. The layer loses its strength and can be removed easily. By controlling pH, crystallization fouling can furthermore be minimized. Additives that modify crystal habit can be divided into the following categories: ions, ionic surfactants, nonionic surfactants like polymers and chemical bonding complexes. Ionic surfactants, for example, are routinely used in industry to control crystal morphology during crystallization. These impurities can compete with the crystallizing molecules for adsorption sites on the faces of the growing crystals. In the absence of additives, the crystal morphology depends on the energy of attraction between the various crystal faces and the depositing molecules, i.e., the relative rates at which growth occurs at individual faces. If adsorption of impurities is selective, i.e., only to specific crystal faces, or to different extents at different faces, significant changes in the growth rates on those faces will lead to habit changes [93,94].

6.5 Deposition and consolidation modeling

6.5.1 General

According to Epstein [76], there are five major types of fouling: particulate, crystallization, chemical reaction, corrosion and biological deposition. Combinations of these types can often occur. Particulate fouling is used to explain the mass transport phenomena of unwanted particles from bulk liquids or gases through boundary layers and eventually deposit on the wall or heat transfer surface. Those particles can be generated by any mechanisms such as crystals formulated by nucleation process in crystallization fouling or products of chemical reaction which occurs in bulk liquid far from the surface. Moreover, this fouling type is considered to play a role in the other deposition mechanisms. There are two important steps involved that generate particulate deposition, transport of the particles to the surface and particle adhesion [80].

6.5.2 Review of fouling models

A brief review of the early fouling models starting with the pioneering work of Kern and Seaton [95] is shown in Table 3.

48 (61)

Table 3 A brief summary of crystallization fouling models.

Authors Model equations Remarks Kern and Seaton [95] 1 2 ,

ff t

dxK c m K x

dt

where K1, K2 are constants, xf,t is the deposit thickness at time t, m is the mass flow rate, c - deposit concentration and - the shear stress

Asymptotic fouling model which includes deposition and detachment terms

Taborek et al. [96] 1 2expf n m

d fts

dx EC P C x

dt RT

where C1, C2 are constants, xf is the deposit thickness ; Pd is a fouling probability, - water quality factor, Ts the surface temperature, - the shear stress and a scale strength factor

Criticized for the many unknown parameters and complex combination of particulate and precipitation fouling mechanisms (Valiambas et al., 1993)

Hasson [97] expf

g sts

dm EK A P

dt RT

where, mf is the deposit mass, K is a constant, Ag is a crystal nucleation and growth area, - water quality factor, Pst is sticking probability

The detachment process is not considered, also contains several unknown parameters

Hasson et al. [98] 2 2fr splf lf

dmk M A K

dt

,sp rK k - solubility product and

reaction rate constant

A classical diffusion model explaining the dynamics of scaling mass flux

Müller-Steinhagen et al. [99]

1/22

2

41 1

2f

acM b

bdm

dt a

- mass transfer coefficient, a,b,c – specific constants depending on the chemical nature of the deposit

Using diffusion of ionic species from the bulk to the surface instead of concentrations at the liquid/solid interface

Müller-Steinhagen et al. [99] also represented the variation of the thermal fouling resistance as

0,f w wf

scale

dR T TmR

dt q

where and are the density of the deposit and its thermal conductivity, Tw0 is the wall temperature for clean tubes at the beginning of the process, and q is the heat flux . However, the detachment term has not been taken into account since Hasson et al. [98] because, its mechanism was considered too complex and difficult to capture.

Figure[100].

Figure

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49

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9 (61)

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0 (61)

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6.5.3

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aken to cleaCIP and meincentive fss process b

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gnetite partily described7-110] aime

g.

ends linearlsed by

(assumed ton processes id by attachm

. Accordingsuited for deposit w

er due to denibly aged md by a clea

olvent (e.g.rties). Figuryer remainsFigure 20(c

These methoand are labean dependsechanical c

for CIP actibenefit.

deposit, thileaning-in-pex-situ) clea

icles deposd by Arbeaed at under

ly on conce

o be equivin series – tment – the

51

g to the cleaning ith total eposition material, aning-in- due to re 20(b) s on the c) shows ods often eled ‘M’ s on the cleaning, ion must

ickness place at

aning at

sition on au et al. rstanding

entration,

(0)

valent to transport e overall

(0)

(61)

52 (61)

where kt is the transport coefficient and ka the attachment coefficient. Under isothermal conditions

0.670.084tk Sc

(0)

where is the fluid shear stress at the wall, Sc the Schmidt number ( / pD )

with the density of the fluid, its viscosity and Dp the particle diffusion coefficient. Under non-isothermal conditions such that the particles need to diffuse against a temperature gradient, the transport coefficient is modified with a subtractive term kth, the thermo-phoretic velocity according to equations (0) and (0). To describe the initial processes of deposition, it is assumed that the attachment term in (0) is complex, involving the attachment first of all of a primary layer and then subsequent layers that can be attached on top of the developing primary layer. The rate of attachment of primary particles, in terms of number concentration on the surface is given by

11 11W

dNk N AN

dt (0)

where k1 is the attachment coefficient for primary particles at the wall, Nw is the number concentration in the liquid film at the wall and A is the effective area of a deposited particle. Similarly, the rate of deposition of subsequent or secondary particles is given by

22 1W

dNk N AN

dt (0)

with k2 is the attachment coefficient for particles to themselves. On the other hand, the transport of particles to the wall is expressed by

1 2t b w

dN dNk N N

dt dt (0)

Nb being the number of particles in the bulk, related to the mass concentration as cb=mNb. Assuming a steady-state in the liquid close to the wall, Nw is eliminated and finally

21 2 1 1 1ln 1t

t b

k kk k N AN k k N t

A

(0)

22 1

1 1

1ln

1

kN AN

k A AN

(0)

The results of the modeling concerning growth of the primary and secondary deposit layers and the overall deposit for isothermal and the sub-cooled boiling conditions are presented in Figure 21. In all cases, the primary layer thickness saturates in around 20 to 25 hours, after which time the overall deposition is completely controlled by the growth of the secondary, consolidated layer.

Figure(right)

e 21 Modeli).

A precooledcouldand CregimdeposportiodescriBy coconso In thecouldto this

with k In thlabile

where

nuclea

and tc

the rabe foulabile

ing results a

evious studyd boiling [1

d be removeCussac [109

me, but begsited particlon of the heibes the evaontrast, for olidation sta

e case of bud be employs model, the

m

kr the remov

e case of su portion of

e labilem is

ation site de

c is a criticaate constantund in [109 parameter

applied to su

y by the sam111] led to ed/exchange9] suggestedins only afes are cons

eat transfer saporation rabulk boilin

arts from the

ulk boilingyed, as demoe amount of

d b

fr c

k cm

k k

val rate cons

ub-cooled bthe deposit

com

a function

ensity, heat

al time for s for remov9]. The conand is defin

ub-cooled b

me group onthe conclus

ed, thus cond that consfter a certasolidated. Thsurface thatate of bubbng, Cossaboe beginning

, the deposonstrated byf deposited

cc r

ktk

k k

stant and kc

boiling, a coby Lister an

( )onsolidation t

n of the sur

flux and la

labilem

consolidatioval and consnsolidation ned as

boiling (left)

n magnetite sion that thensolidation dsolidation aain time anhe proposedt is covered

bles as a funoom and L

g of depositi

sition modey Cossaboofouling laye

1 expr

c

k

k

the consoli

onsolidationnd Cussac [

410 labilem

rface area

tent heat of

/site a

vap

A N

q h

on to occursolidation uconstant fo

) and isothe

particles dee entire depdid not occulso takes pld then onlyd model tak

d by active nnction of th

Lister [107] on.

el of Turnerm and Listeer is given b

p r ck k

dation rate

n parameter[109]

1c

t

t

of the nuc

f vaporizatio

r. Details onunder both br bulk boili

ermal condi

eposited durposit was laur. Howeve

place in thisy a fractionkes into accnucleation she boiling in

suggested

r and Klimer [107]. Acby

t

constant.

r was relate

cleation site

on:

n the calculboiling regiing is based

53

itions

ring sub-abile and er, Lister s boiling n of the

count the sites and ntensity. that the

mas [112] ccording

(0)

ed to the

(0)

e, active

lation of imes can d on the

3 (61)

FigurepioneeCussa

6.6

As illuthan t

e 22 Compaering modelc [109].

Disc

ManytransftherefdetermlossesFigurecondiend ohere rof whthe lashear. In mathe lifcoheslayer removcleani

ustrated in Fthose of the

arison betwel by Kern an

cussion o

y heat transffer and limfore cleanemined by as. Fouling ae 20. Thetions for suf the produrefers to fachich contribayer’s respo.

any applicatfetime of thsive, form.

and therefved. Differing efficien

1ck Figure 22, toriginal Ke

een a radiotnd Seaton [9

n consoli

fer systems miting produed regularlyan optimizaand cleanin

e effectivenubsequent fction run de

ctors such aute to the ronse to cle

tions the dehe run fromThe extent

fore the extrent cleaninncy will ther

,labile cm bthe predictioern and Sea

tracer expe[95] and the

dation

are subject uctivity. Hey, with thation involng are, howness of a fouling, whetermines th

as the deposreactivity aneaning agen

eposit underm the initialt of consoltent up to wng methodsrefore be af

5 10cb kgons of this mton approac

eriment by Be consolidat

to fouling, eat exchang

he length olving cleanwever, symb

cleaning oile the statehe nature ansit microstrund rheologynts and me

rgoes consol precursor idation detwhich a fos are availffected by a

2 2/ .g site m s

model are sich.

Basset et al. ion model o

reducing thgers experiof an oper

ning costs abiotic proceoperation de of the found dynamicucture and c

y of the layeechanical ac

lidation, a tform to anoermines the

ouling layerable to an ageing. In s

2

ignificantly

[111], the of Lister and

he efficiencyiencing fourating cycland foulingesses, as shdictates theuling deposcs of cleaninchemical naer, which dection such

transformatother, usuale final statr can be ef

n operator, selecting a

54

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4 (61)

55 (61)

method, the operator must consider whether the method can remove aged as well as freshly formed material. However, accurate prediction of fouling behavior is more and more necessary to offer guidance to the plant personnel on the respective measures to be taken for optimal management of service life of components and systems subject to fouling. Phenomenological/empirical models based on laboratory or plant measurements may be useful as long as the actual fouling process is not significantly different in any major aspect. However, extrapolation to different conditions or general predictions are not possible, because the physical phenomena underlying fouling are so many and complex. They involve the physics of nucleation of crystals on the heat transfer surface, the chemistry of two-phase solid/liquid interfaces, the determination of local chemical, thermodynamic and hydrodynamic conditions. The wide range of possible processes has, even for scale formation alone, led to a substantial number of suggested models and correlations, which all include several simplifications and assumptions and which often predict significantly different values and even trends. One of the reasons for the different predictions that can be found from published models are due to the way that conventional regression methods are used correlate experimental data, in particular inherent mathematical assumptions. An insufficient number of explanatory variables may result in an inaccurate model, which is characterized by a large variance. Some independent variables, which may have critical effects on the dependent variable, here fouling resistance under certain circumstances, may be left out of the correlation. On the other hand, inclusion of non-influential or collinear variables leads to an unstable model. Also, in conventional methods, values of the model parameters always contain consequences of the introduced assumptions and simplifications. As a general conclusion, it can be stated that even if the features of the deposition process involved in fouling of heat transfer surfaces are qualitatively well understood, more attention should be paid to both the experimental study and modeling of the consolidation step which in many cases may lead to low efficiency of conventional fouling mitigation strategies and surface cleaning methods. The present review demonstrates that the transition between a disordered array of individual particles that conserve many of the properties of their colloidal state in the coolant, and a hard, often crystalline, deposit is still poorly understood. To increase the level of understanding in this particular area, a consolidated multi-scale modeling effort supported by experiments benchmarked by comparison between different laboratories is needed.

7 Summary

The formation of deposits in nuclear power plant circuits involves a range of possible physical and chemical phenomena such as turbulent deposition, deposition during sub-cooled boiling, gravitational settling and re-entrainment. It is closely related to the stability of particulate forms of matter in the coolant circuit, such as colloidal oxides. Currently, there are no generally applicable models available for the deposition process. The present survey describes the mechanism of the deposition process of magnetite and analogous oxides present in the coolant circuits in a colloidal

56 (61)

form. First, a short overview of fouling mechanisms of steam generators is given, including a concise description of general corrosion, FAC and stress corrosion cracking. Next, the consequences of corrosion, i.e. the fouling phenomena, are assessed, and several individual process steps such as deposition, re-entrainment, structural re-organization etc. are discussed. The next part, that constitutes the main body of the survey, concerns the composition, structure, electrical and electrochemical properties, and therefore stability, of colloidal oxides in nuclear power plant coolant circuits. Theoretical approaches to the reactivity of solid/liquid interfaces, such as acid-base properties, sorption mechanisms, and interaction between colloidal particles and charged surfaces are described and illustrated with relevant experimental data, emphasizing the effect of temperature on key parameters such as the point of zero charge and iso-electric point. The theoretical approach to interpret the frequency dependence of dielectric permittivity of colloidal suspensions is also described together with available data from such measurements on colloidal iron oxides. And last but not least, consolidation of deposits which is believed to be one of the key stages in the fouling process is discussed with regard to its inclusion in a quantitative integrated model of the deposition process.

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