Int. J. Therm. Sci. 41 (2002) 682–692
www.elsevier.com/locate/ijts
Scale formation in tubular heat exchangers—research priorities ✩
Anastasios J. Karabelas
Department of Chemical Engineering, Aristotle University of Thessaloniki and Chemical Process Engineering Research Institute,
Univ. Box 455, GR 540 06, Thessaloniki, Greece
Received 29 October 2001; accepted 11 February 2002
Abstract
The common case of CaCO3 scale formation in pipe flow is considered in this paper. Results of experimental studies, mainly by the author
and his collaborators, are reviewed from the standpoint of the main mechanisms involved, in order to identify key issues that require additional
research. The discussion is focused on the initial deposition rate as well as on the morphology of growing crystalline deposits as a function
of various process parameters. A critical supersaturation ratio (Sc ∼ 7 for CaCO3 ) represents a significant transition from one type of scale
formation process to another, including the dominant mechanism, the growth rate, and the morphology of scale. As regards generic topics
that need clarification, it is suggested that high priority should be placed on (a) the attachment phenomena of nuclei/crystals on the substrate
and (b) the effect of particulate/colloidal matter on scale characteristics. Significant gaps also exist in our understanding of the effects of
fluid physical and chemical properties, and of fluid mechanics, on elementary processes (e.g., crystal growth and morphology) and on scale
characteristics. Clarifying these aspects of scale formation would facilitate the development of fouling mitigation methods. Modelling efforts
addressing elementary processes as well as system (global) evolution are considered essential for developing improved predictive tools, and
reliable techniques for estimating physical parameter values difficult to obtain by other means. 2002 Éditions scientifiques et médicales
Elsevier SAS. All rights reserved.
Keywords: Calcium carbonate; Scale characteristics; Tube flow; Incipient scale growth; Induction period
1. Introduction
Understanding, and being able to predict, the characteristics of scale formation is required for reliable design and
smooth operation of heat exchange equipment. However, despite a great deal of work over the past 30 years, the state of
the art in this area is unsatisfactory. Indeed, it is impossible
at present to predict (with a satisfactory degree of reliability)
the temporal variation of fouling resistance Rf which is the
relevant parameter for engineering calculations.
For a fixed set of conditions, the temporal evolution of
Rf (Fig. 1) reflects the variation of scale characteristics. Two
features of this variation deserve our attention:
• Induction period ti , observed under some conditions,
and associated with nearly zero (or even negative) values
of Rf [1,2].
✩
This article is a follow-up to a communication presented by the authors
at the ExHFT-5 (5th World Conference on Experimental Heat Transfer,
Fluid Mechanics and Thermodynamics), held in Thessaloniki in September
24–28, 2001.
E-mail address: karabaj@cperi.certh.gr (A.J. Karabelas).
• Behavior at long time, i.e., constant, varying, or asymptotic (Rf∗ ) fouling resistance observed in many published
data sets [3,4].
The practical implications of predicting and/or controlling these characteristics are obvious: extending the induction period ti , as long as possible, is desirable because it is
associated with high heat transfer coefficients and with reduced equipment cleaning costs. Furthermore, the possibility that a system tends to an asymptotic value (Rf∗ ) is helpful in designing the heat exchanger as it affords a (safe) upper limit of fouling resistance. Unfortunately, reliable predictions of the occurrence and of the magnitude of both ti
and Rf∗ are impossible to make at present, despite considerable research efforts over the past 20–30 years [5].
Various types of fouling have been identified in the
literature [6,7], depending mainly on the composition of the
heat exchanging fluids. This paper is focused on scaling,
caused by sparingly soluble salts in water. In particular, the
common case of CaCO3 scale formation in pipe flow will be
dealt with. Work carried out in this Laboratory will be briefly
reviewed in an attempt to outline the main mechanisms
1290-0729/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
PII: S 1 2 9 0 - 0 7 2 9 ( 0 2 ) 0 1 3 6 3 - 7
A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
683
Nomenclature
Ksp
ke
Ke
Rf
Rf∗
S
SrC
calcium carbonate solubility product . . mol·m3
rate constant of polynuclear crystal growth
kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . mol·s·m−2
dimensionless parameter in polynuclear
(exponential) growth kinetics
thermal fouling resistance . . . . . . . . . . m2 ·kW−1
asymptotic value of thermal fouling
resistance. . . . . . . . . . . . . . . . . . . . . . . . . m2 ·kW−1
supersaturation ratio, defined in Eq. (1)
critical supersaturation ratio, signifying change
of precipitation/deposition mechanism
ti
u
induction period for measurable fouling
resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s
average axial fluid velocity . . . . . . . . . . . . m·s−1
Greek symbols
γsl , γcs , γcl components of interfacial tension between
phases at equilibrium, defined in Fig. 12 J·m−2
Gcrit critical excess Gibbs free energy for
homogeneous nucleation . . . . . . . . . . . . . . . . . . . J
G crit critical excess Gibbs free energy for
heterogeneous nucleation . . . . . . . . . . . . . . . . . . J
θ
contact angle (Fig. 12) . . . . . . . . . . . . . . . . . . . rad
The morphology of growing crystalline deposits is also discussed. In the next section, attention is paid to surface nucleation and to incipient growth of deposited/surface crystals. Modelling efforts are also summarized, concerning initial deposition rates, detachment of growing scale elements,
and overall (temporal/spatial) system evolution.
Fig. 1. Possible variation of thermal fouling resistance with time; induction
period ti .
involved and to identify some key issues that seem to require
special attention in future research activities.
Even for the restricted case of a single depositing species
(i.e., CaCO3 ) there is a multitude of factors, responsible for
scale formation in industrial processes, that may be classified
as follows:
• Fluid composition including dispersed solid matter (colloidal, other);
• Substrate surface properties; i.e., material properties,
surface conditions (including roughness);
• Flow field (fluid bulk and solid/liquid interface conditions);
• Thermal field (heat flux, substrate surface temperature,
bulk fluid temperature).
The interaction of the main variables involved in these
categories complicates matters immensely, and necessitates
extra care in efforts to isolate and systematically study
various mechanisms. Here we only touch on the above
first and third categories of factors. The substrate material
examined is stainless steel. Isothermal conditions are studied
over the temperature range ∼15 ◦ C to ∼45 ◦C, mainly
to examine the effect of temperature of flowing water
(supersaturated in CaCO3 ) on scale characteristics.
In the following, after an overview of elementary processes responsible for scale formation, selected experimental
data are reviewed as regards the effect of main parameters.
2. Elementary processes
As is well-known, departure from equilibrium (i.e., supersaturation) leads to crystallization from solution. In this
presentation, the supersaturation ratio S is defined as
1/2
(Ca2+ )(CO2−
3 )
(1)
S=
Ksp
where the quantities in parentheses denote activities and Ksp
is the solubility product of calcite, the dominating polymorphic CaCO3 phase encountered in the scale. For wall crystallization or bulk precipitation to occur, a supersaturation ratio
significantly greater than unity is usually required. With regard to crystalline scale formation, the following processes
contribute directly or indirectly [8,9].
(1) Nucleation onto the substrate and (at relatively higher S)
in the fluid bulk. Ostwald ripening may be considered as
part of this process.
(2) Diffusion of solvated ions, molecules or small particles
to the surface.
(3) Surface Phenomena is a general term to designate
various elementary steps such as adsorption of solvated
ions or molecules on an existing crystal surface, the
ensuing surface reaction, and the incorporation of ions
or molecules into the crystal surface. Any of these steps
may control crystal growth, or surface “reaction”, which
may be described by a phenomenological reaction rate
coefficient.
(4) Attachment of clusters, nuclei, or colloidal particles onto
the substrate might be classified as a category, separate
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A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
from surface phenomena responsible for individual
crystal growth.
(5) Detachment of crystalline matter/particles from the
surface by flow imposed forces.
(6) Agglomeration (or breakage) of developing, in the bulk,
nuclei or particles.
Aging phenomena of deposited/surface crystals, through
phase transformation (possibly aided by heat transfer),
that may harden or weaken the scale.
The intensity of the aforementioned factors (e.g., degree
of supersaturation, flow velocity, heat flux) would tend to
enhance some of the above processes over others. Under
any circumstances, however, it appears that several of
these processes (often taking place simultaneously) are
responsible for scale formation and scale characteristics.
The difficulty of determining the true contribution of each
process in a given physical system, is at the heart of dealing
with the fouling/scaling problem and is responsible for the
poor state of our predictive capabilities.
coupons are inserted [10] in the test sections, so that their inner surface exposed to flow is perfectly cylindrical. The material used for the coupons is stainless steel 316 L and 304
and the finished surface roughness, Ra , is less than 0.5 µm.
Data on the initial deposition rate, measured over a period of
several hours, are presented.
3.1. Effect of supersaturation
At small supersaturations (i.e., below what appears to be
a critical value Sc ∼ 7) the deposition rate is quite small
and tends to increase with supersaturation, as shown in
Fig. 2. A sharp rise of the initial deposition rate is observed
at Sc ∼ 7. At greater supersaturations the deposition rate
remains roughly constant for fixed fluid properties and flow
conditions. It is interesting to close examine some typical
3. Overview of experimental data
The data reviewed here are reported in detail elsewhere [10,11]. It is pointed out that these data have been
taken, under constant feeding conditions, in “once-through”
flow of the fluid (through the test-sections), and not by recirculation of a finite fluid volume. In this mode of operation,
only “fresh” fluid of controlled supersaturation and of the
same age comes in contact with the test sections, thus avoiding the possible recirculation of pre-formed colloidal particles that may influence scale formation and complicate data
interpretation. Data taken under isothermal conditions (in
the range ∼15◦ to ∼45 ◦ C) are summarized. Semi-annular
Fig. 2. Deposition rate versus supersaturation ratio at a constant velocity
(u = 0.43 m·s−1 ) and temperature (23 ◦ C).
Fig. 3. Large calcite crystals formed at low supersaturation ratios. u = 1 m·s−1 , T = 30 ◦ C, pH = 8.75, S = 6.9 and time = 6 h.
A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
685
(a)
Fig. 4. Rate of deposit formation at relatively low pH and supersaturation,
indicating induction period.
cases of initial crystal growth on the substrate, below and
above the critical supersaturation, to get an appreciation of
incipient scale formation. Fig. 3 includes a SEM picture,
corresponding to conditions below but near the critical
value Sc , showing that isolated calcite crystals grow on
an otherwise bare substrate. The rate of deposit formation
corresponding to Fig. 3 is shown in Fig. 4. The case depicted
in Figs. 3 and 4 is typical of the “induction period” of
scale formation. Deposition is initiated with heterogeneous
nucleation on the substrate and subsequent growth of
isolated crystals. Ostwald ripening, i.e., dissolution of nuclei
in favor of the larger crystals, may occur in this case. Surface
nucleation under conditions of low supersaturation (usually
encountered in practice) and subsequent crystal growth, is
a process requiring clarification as will be discussed in a
subsequent section.
In Fig. 5, a sequence of SEM pictures clearly shows the
first stages of scale formation for supersaturation S = 15.5,
i.e., above the critical value. It is evident in Fig. 5(a) and (b)
that the nuclei rapidly grow to cover the substrate. Quite
well formed calcite crystals tend to merge as they grow.
Fig. 5(c) depicts the surface “roughness” of the scale in the
early stages of formation. One also observes that the crystals
grow out of a broad base on the substrate. Fig. 6 includes
data on the rate of initial deposit growth under the same
conditions as those of Fig. 5. A linear variation, with no
induction period is observed.
3.2. Effect of flow velocity
This effect is quite clear for supersaturations above the
critical one, as is indicated in Fig. 6, where typical sets
of data, of deposition rate as a function of mean velocity,
for S ≈ 15.5, are plotted. These data display a dependence
on velocity to a power approx. 0.85, which is typical
of convective mass transfer controlled processes. Similar
results (with smaller exponent values) are obtained, under
isothermal conditions, in other studies [8,12].
(b)
(c)
Fig. 5. SEM micrographs depicting the growth of calcite deposits at
relatively high supersaturation ratios: (a) 2 min after the start of the run,
(b) 10 min, and (c) 60 min (T = 17 ◦ C, u = 1 m·s−1 , pH = 10.5, S = 15.5).
It is worth stressing here the apparently significant effect
of flow velocity on the morphology (and the compactness) of
the growing crystalline scale. The SEM picture corresponding to rather low velocity (Fig. 7) reveals that, at S ≈ 15 and
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A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
temperature 25 ◦ C, crystal formations protrude outward into
the flow. Evidently, such scale layers are not very compact.
On the contrary, Fig. 8 shows quite compact scale formation
for nearly the same supersaturation but at a higher velocity (U = 2 m·s−1 ). Another notable feature at high velocities is the much smoother top surface of the growing scale
layer (Fig. 8), as also reported by Hasson [8]. Apparently,
the rather high mass fluxes, prevailing under these conditions, tend to influence the morphology of growing calcite
crystals resulting in the peculiar rounded cups at the surface.
3.3. Effect of temperature
Aside from its effect on supersaturation, temperature
directly influences the CaCO3 polymorph phase develop-
ment [13]. In the tests reviewed here it was found that below 30 ◦ C, calcite is essentially the only polymorph present,
mainly in prismatic form (Fig. 5), exhibiting typical rhombohedral faces on the top (not at high velocities). Above
∼35 ◦ C, aragonite appears to be stable, exhibiting characteristic dendritic formations (Fig. 9) emerging out of (and adhering onto) the metallic substrate. However, as pointed out
by Andritsos et al. [11], with time (even under these higher
temperatures) small calcite crystals tend to cover the substrate forming a coherent “base layer”, on top of which the
dendritic pattern of aragonite develops. The latter, characterized by poor coherence and tenacity and by low density, may
be (at least partially) removed by increased flow velocities,
especially after growth at long times. The practical implications of such a removal need not be emphasized.
3.4. Effect of particles on CaCO3 scale formation
Fig. 6. Rate of deposit formation at a constant pH and temperature for
various liquid velocities (pH = 10.5, T ∼ 18 ◦ C).
In several papers reviewed elsewhere (e.g., [5,14]), there
is evidence that dispersed fine particles tend to increase the
thermal fouling resistance. There are also studies (e.g., [15])
suggesting that the addition of particles (seeding) may be
used as a method to prevent significant wall crystallization.
Data were taken [14] in the same experimental setup employed for fouling studies, to examine the effect of
small amounts (∼40 and ∼100 mg·lit−1 ) of added particles
on CaCO3 scale formation at 25 ◦ C. Commercial calcium
carbonate particles (of mean size 5–10 µm) and colloidal
silica nanoparticles (mean diameter 21 nm) were employed
for tests in the velocity range 0.43 to 1.5 m·s−1 . No
significant effect on the initial deposition rate was found
with the silica particles. Only a reduction of the mean calcite
Fig. 7. Top view of calcite growth at low flow velocity (u = 0.43 m·s−1 ); T = 25 ◦ C, pH = 11, S = 15.
A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
687
Fig. 10. Effect of particulates on deposit formation with tap water at pH 10
and 8.8 and with demineralized water at pH 10 (particle concentration ∼ 40
mg·L−1 ).
Fig. 8. Side view of calcite deposits 5 hours after start of the run; T = 18 ◦ C,
u = 2 m·s−1 , pH = 10.5, S = 15.5.
crystal size, growing on the substrate, may have been caused
by those particles.
Very significant enhancement of deposition rate was
measured with added CaCO3 particles, at the smallest
velocity tested (0.43 m·s−1 ), as shown in Fig. 10, with a
tendency to diminish at higher flow rates. At low velocities,
similar results (with enhanced deposition rate) were obtained
by Watkinson [16] and Watkinson and Martinez [4]. Bansal
et al. [17] experimenting with the CaSO4 system also
obtained significant enhancement. However, Hasson and
Karmon [12] under conditions different than those of our
tests, report that at high velocities, particles seem to hinder
the growth rate and to have a pronounced effect on the
deposit structure, with a general tendency to increase its
porosity. To account for these effects, Hasson [5] argues
that particles residing only temporarily on the substrate
(eventually detached by flow-imposed forces) may offer
their surface for crystal growth, thus augmenting deposit
porosity and acting to reduce the net deposit growth rate.
At present there is no clear explanation for the strong
synergistic effect, exhibited by Fig. 10, due to a rather
small amount of added particles. The morphology of the
deposits suggests that the enhancement is due to augmented
wall crystallization (possibly aided by deposited CaCO3
particles) but not due to increased mass deposited from the
bulk. This issue of particle (positive or negative) influence
on scale formation certainly deserves more attention, and
requires additional R&D work, as it may be one of the
effects leading to asymptotic fouling resistance under certain
conditions.
4. Modelling CaCO3 scale growth
Fig. 9. Morphology of deposits formed at 45 ◦ C after 60 min. Conditions:
u = 0.41 m·s−1 , pH = 9.5, S = 12.
Hasson et al. [18] have proposed an ionic diffusion model
to predict the rate of CaCO3 deposition for a set of condi-
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A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
tions, including pH, Ca concentration, total alkalinity, fluid
velocity, and temperatures (wall and bulk). The formation of
deposits is considered to be a combination of the mass transfer from the bulk to the interface (of the chemical species
involved in the calcium and carbonate equilibria) and of
the ensuing surface reaction. Although satisfactory order of
magnitude estimates are obtained with this model, there is
a need for improvement at relatively low pH values (<10)
which are of practical interest.
Andritsos et al. [19] have presented an improved model
leading to better predictions of CaCO3 scaling rate in the
entire pH range. Scale growth is assumed to be controlled
by both the mass transfer of active ions to the solid/liquid
interface, and the surface (crystallization) reaction. To represent the latter, it was found that the “polynuclear growth”
model [20] has advantages over the “parabolic” one, yielding better predictions of the experimentally observed sharp
increase of deposition rate near the critical supersaturation
Sc ≈ 7. Fig. 11 shows a comparison of experimental data
on initial deposition rate with model predictions. The data
of Fig. 2 have been replotted here. It will be noted that the
polynuclear model parameter values, for ke and Ke , shown
in Fig. 11 are close to those of other substances reported by
Nielsen and Toft [21].
The rather sharp change of controlling mechanism indicated by the preceding experimental data, i.e., from surface
reaction controlling at small supersaturations to convective
transport controlling above Sc , seems to be confirmed by the
model predictions. There is certainly a need for more work to
better understand the processes taking place near the critical
supersaturation. However, further model improvement may
be obtained if one employs the actual surface area available
(to ionic species) for crystallization below Sc , where surface
reaction controls. More specifically, as already discussed and
clearly shown in Fig. 3, only a small portion of the tube surface (covered by growing crystals) is essentially available
for deposit growth during the induction period. By substituting the apparent deposition rate (plotted in Fig. 11), which
is based on the total inner tube surface area, with a “real”
one, using the total surface of growing (isolated) crystals,
better agreement is expected between data and predictions.
Similarly, a more realistic estimate of the “rough” scale surface may be required, when the substrate tends to be totally
covered at supersaturations right above the critical value and
the surface area available for the crystallization reaction is
greater than the tube inner surface.
5. Interfacial forces—incipient scale growth
The interplay of surface nucleation and of particle/ substrate adhesion forces [22] on one hand, and of the fluid
mechanical forces acting to detach particles on the other,
is responsible for the extent of the induction period and for
the incipient scale formation. Understanding these phenomena and controlling the respective forces may provide the
means to mitigate scale growth or to facilitate scale disbonding/removal.
Scale formation starts with “surface nucleation” which is
a typical heterogeneous nucleation process, poorly understood. According to the classical theory (e.g., [23]) it is described in terms of the excess Gibbs free energy as follows
G′crit = φ Gcrit
Fig. 11. Measured and predicted [19] deposition rates for a combined
convective transport/polynuclear growth mechanism. ke in mol·s·m−2 and
Ke = 10; u = 0.43 m·s−1 .
(2)
where Gcrit is the free energy change associated with
the formation of critical nuclei in homogeneous nucleation
which is normally greater than the critical excess free energy
G′crit associated with heterogeneous nucleation. The factor
φ tends to increase from zero to unity with increasing
contact angle θ between the crystalline deposit and the solid
substrate (Fig. 12). By considering the interfacial tensions
between phases at equilibrium one obtains
γsl − γcs
(3)
cos θ =
γcl
Fig. 12. Interfacial tensions between phases and contact angle θ .
A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
As usual, θ is considered a measure of the affinity of
the deposit phase with the substrate. Large contact angles
indicate small affinity. Furthermore, small θ angles are
associated with reduced critical supersaturation for surface
(heterogeneous) nucleation.
Using classical nucleation theory and the Young equation (3), Foerster and Bohnet [1] argue that one may influence the deposition rate (at incipient scale formation)
by modifying the surface free energy γsv of the substrate,
because the interfacial free energy γsl is directly affected
by γsv . Thus, to mitigate fouling and prolong the induction period, they propose to employ low energy surfaces
which would effectively reduce nucleation rate and crystal/substrate adhesive strength. By experimenting with a
flowing calcium sulphate solution and with several metallic
and low energy materials, Foerster and Bohnet [1] present
data showing significant prolongation of the induction (essentially “no scaling”) period. Moreover, they conclude that
DLC (Diamond-Like Carbon) coatings of surfaces offer an
interesting option, superior to other materials they have
tested.
Müller–Steinhagen and associates (e.g., [24]) have pursued a similar approach, experimenting with ion-implanted
metal surfaces and with various types of sputtered surfaces
(with AC, DLC, DLC-F); they suggest that the treated surfaces have energies much lower than the untreated ones. In
several publications from that Laboratory, summarized by
Müller–Steinhagen and Zhao [24], data are presented, with
the CaSO4 system and with treated surfaces, showing significant reduction of fouling.
Another approach for treating the effect of surface forces,
on the initial stages of fouling, has been followed by
Visser [25] who took avantage of relevant work by van
Oss [26] on the interfacial forces and in particular on
the so-called “Lewis acid/base interaction” of neighboring
species. The latter is attractive in aqueous media and tends to
combine with the Lifshitz–van der Waals forces to overcome
the common electrostatic repulsion at usual pH values. In
terms of Gibbs free energies, the total energy of interaction
between a colloidal particle and a metal surface can be
written as follows
GTot =
GLW +
GEL +
GAB +
GBr
(4)
Here the four terms correspond to Lifshitz–van der Waals
component (LW), electrostatic double layer component (EL),
Lewis acid/base component (AB) and Brownian motion
(Br) contribution, respectively. Obviously, scaling is considered to take place only if the interaction of these components leads to a negative total free energy change GTot .
Visser [25] summarises the techniques (proposed by van
Oss) to make relevant measurements and to predict the
individual contributions in Eq. (4) and outlines difficulties thereof. It is concluded that for the system calcium
phosphate-stainless steel (which bears some similarities to
the CaCO3 system studied here) the main driving force for
attachment resides in the Lewis acid/base component of the
689
overall interaction energy. Furthermore, it is recommended
that an effective way to reduce that component would be to
alter the characteristics of the heat-transfer surface. For the
particular system studied by Visser, it is suggested to modify the surface by making it more hydrophilic. Such an approach is currently pursued in the context of a collaborative
EC-funded R&D project, under the acronym MODSTEEL.
It must be pointed out, however, that several aspects of the
above modified DLVO theory are still unproven and that
judgement on its applicability to real situations should be
withheld until sufficient new and reliable data, with “modified” surfaces, become available. It will be further noted that
the above efforts to modify surfaces are focused on stainless
steel surfaces which are fairly smooth and corrosion resistant. The case of mild steel, widely used in industry, appears
to be quite different; Keysar et al [27] have shown that the
surface roughness of mild steel has a strong effect on the
adhesion and morphology of calcite scale, leading to more
compact and tenacious deposits.
6. Particle detachment
6.1. Detachment from flat surfaces
The adhesion forces, between nuclei/crystals and substrate, evidently play a key role in scale formation. Particle detachment occurs when such forces are overcome by
hydrodynamic forces. If extensive detachment occurs in the
early stages of scale growth, the induction period would be
prolonged. Quantitative predictions of detachment rates are
impossible to make at present, mainly due to the effect of
some parameters that cannot be easily quantified; e.g., surface inhomogeneity, microroughness etc.
Experiments carried out under well controlled conditions
with monodisperse (micron size) spherical particles [28]
were aimed at clarifying some issues of detachment from
a fundamental point of view. It was pointed out in that
paper that, for particles in the colloidal size range, tangential
forces dominate, and not lift forces often invoked in the
literature. Some experimental results of relevance to this
review may be summarized here:
• Smaller particles require higher shear stress for effective
removal, as expected.
• A continuous distribution of stresses, and not a singlevalued critical stress, is required to detach a population
of monodisperse particles
• pH exerts a significant influence on the adhesive strength.
Predictions based on DLVO theory are in qualitative
agreement as regards observed pH effects.
• The mean hydrodynamic wall shear stress required for
detachment, which is representative of adhesion forces,
is found to be proportional to particle diameter to the
−1.8 power. This finding suggests that particle rolling
is the most likely removal mechanism.
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A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
6.2. Modeling of removal processes
A modeling effort was undertaken [29] in order to suggest
a rational mechanism that may account for the removal
aspects of the fouling process and may offer a framework for
predicting the temporal evolution of scaling rate. The main
premises involved may be summarized as follows
(a) Roughness elements or “out-growths” such as agglomerated crystals, crystal dendrites and branches, are more
likely to be detached by the action of flow shear forces.
(b) Removal occurs when the hydrodynamically imposed
stress on these roughness elements exceeds an intrinsic
adhesive or breakage strength determined by various
physicochemical factors (previously outlined).
(c) A dynamic situation is envisioned whereby roughness
elements grow due to deposition and suffer breakage
when they reach a limiting size. Thus, the kinetics of
removal is linked to the growth process and to the
polydispersity of strength of the deposit.
In order to obtain a complete description, several simplifying assumptions were introduced regarding the roughness elements (shape, growth rate, number density) and their
breakage strength distribution. Despite these simplifications,
encouraging results were obtained such as asymptotic fouling behavior and flow effects in qualitative accord with experimental data. In particular, the often observed reduction
of asymptotic fouling resistance Rf∗ with increased flow velocity is predicted by the model. Fig. 13 shows a comparison
of model performance against the data on CaCO3 scaling by
Hasson [30]. Here the fouling resistance was adjusted for the
lowest velocity and calculated for the other cases. A mean
value for the deposition rate was estimated from the data and
used to find the time scale.
Fig. 13. Comparison of data on CaCO3 fouling by Hasson [30] with
model [19] predictions. High-Rf curve u = 39 cm·s−1 ; low-Rf curve
u = 125 cm·s−1 .
7. Comprehensive modeling of precipitation and fouling
in pipe flow
In preceding sections, the focus was mainly on elementary processes contributing to scale formation. However, supersaturation triggers several precipitation-related phenomena that may occur along the flow path. The interaction between fluid dynamics and physicochemical processes (i.e.,
nucleation, particle growth, agglomeration) leads to an axial
variation of bulk fluid properties and of ionic and particulate deposition rates at the pipe wall. Fig. 14 provides an
overview of the various processes that may be classified into
two main categories, i.e., ionic and particulate processes. In
the case of sparingly soluble compounds, such as calcium
salts, the rates of most of these individual processes tend to
be of the same order of magnitude. Therefore, the respective
processes may occur concurrently, creating very serious difficulties in studying separately each one of them as well as
in modeling and predicting the outcome of their complicated
interaction
Significant efforts have been made in this Laboratory
to simulate such complicated systems [31,32]. Simple plug
flow hydrodynamics is combined with rather comprehensive
modeling of physicochemical phenomena. A population
balance type of formulation is employed for modelling the
particulate processes involved. Using modern and optimized
(for such problems) computational techniques, efficient
numerical algorithms have been obtained to cope with these
demanding tasks. The methodology and the tools developed
are appropriate for simulating precipitation phenomena,
with emphasis on pipe wall fouling in turbulent flow. The
usefulness of those tools is twofold: (a) to predict the axial
Fig. 14. Physical processes occurring in pipe flow of supersaturated
solutions.
A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
and/or temporal variation of scale and fluid characteristics,
and (b) to provide a reliable computational framework
for estimating those system parameters that cannot be
determined with reliability by simplified experimental or
other procedures. Although satisfactory results have been
obtained so far with these tools, further improvements are
required.
8. Concluding remarks
The supersaturation ratio S is clearly the most important
parameter affecting the scale growth process. In the case
of CaCO3 deposition/precipitation, a critical supersaturation
ratio (Sc ∼ 7) appears to represent a significant transition
from one type of scale growth process to another. The main
features of each regime may be summarized as follows:
S <7
S >7
An induction period is observed in the scale growth
process, which tends to increase with decreasing S.
This is a direct consequence of the fact that (at such
small supersaturation) only heterogeneous wall nucleation takes place, at relatively small rates. Furthermore, “surface reaction” appears to control the
initial growth of nuclei/crystallites which are isolated and distributed on the substrate. Under these
conditions, individual crystal growth, and in particular substrate surface coverage are relatively slow.
The controlling process here (i.e., surface reaction)
implies that there is no effect of flow velocity on
the intrinsic deposition rate. There is some experimental evidence in support of this observation, although this issue requires clarification. Nevertheless, velocity may still play a role in the overall
scale growth process. The crystals growing in isolation during the induction period (as shown in Fig. 3)
are subjected to significant drag forces at high velocities, and might be detached if crystal/substrate
adhesion forces are not strong enough. It will be
pointed out, parenthetically, that creating conditions promoting such an occurrence (through modification of crystal morphology or weakening of
substrate/crystal adhesion), thus lengthening the induction period, seems to be one of the main approaches to mitigate scaling. It will be also noted
that most of the experimental work on pure CaCO3
scaling reported so far shows that, after surface coverage has taken place, a rather compact and tenacious scale layer develops which is difficult to be
affected by flow induced forces.
In this range, the rate of nucleation is fairly large
and the substrate is rapidly covered by deposited
mass. Thus, there is no induction period. The effect of flow velocity on deposition rate is quite
strong (d ∝ U 0.8 ) suggesting that convective diffusion controls. Another significant velocity effect
691
is also observed. At small velocities prismatic outgrowths of calcite are evident; but at relatively high
velocities the developing scale is quite compact
and tenacious, its top surface exhibiting rounded
cups (e.g., Fig. 8). There is no obvious explanation
for this intriguing effect. It will be added that in
this range of conditions (S > 7) bulk precipitation
phenomena (nucleation, crystal growth, agglomeration) appear to take place along the flow path and
to be intensified with increasing supersaturation.
At and above critical supersaturation, very significant
enhancement of scaling rate is measured with the addition
of a small amount of CaCO3 particles. This effect is
very strong at the smallest velocities tested, being reduced
with increasing velocity. Colloidal particles of a different
type (SiO2 ) have practically no influence on CaCO3 scale
formation. This strong synergistic effect of added CaCO3
particles definitely needs clarification. In fact, a common
argument in the literature, contrary to the above results, is
that the presence of particulates may have a negative overall
effect in scale growth, adversely affecting scale coherence
and facilitating solids detachment. This issue has obviously
significant practical implications.
To summarize, significant knowledge gaps exist, with regard to scale formation, at two levels, i.e., elementary mechanisms/processes promoting scaling and interaction of such
processes which take place concurrently. One of the most
important aspects demanding attention appears to be that of
attachment of nuclei/crystals on the substrate. The influence
of the ionic environment and of the substrate properties on
the adhesion forces between particles and substrate (inadequately understood and insufficiently tested so far) should
be given priority in R & D efforts. Similarly, the conditions
for attachment and/or incorporation of the (ever present in
real systems) dispersed colloidal particles onto the developing scale, and their effect on scale coherence, seems to be
an issue that requires clarification. Understanding and possibly controlling particle/substrate adhesion forces, and the
effect of dispersed matter on scale properties, may be essential for tackling key issues such as the extent of induction period and the occurrence of asymptotic thermal fouling resistance (i.e., the condition of zero net deposition rate). Quantifying the influence of fluid dynamics on other elementary
processes (i.e., nuclei and crystal growth, detachment effects) appears to be another significant issue that should be
given high priority. Finally, better understanding of the effect
of fluid properties (chemical composition, pH, temperature)
on crystal/particle morphology seems to be a pre-requisite to
developing effective scale mitigation procedures.
Modelling elementary processes as well as the entire
flow system evolution can lead to improved predictive capabilities and, more important, can provide reliable methods/framework for interpreting experimental data and for
process parameter estimation.
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A.J. Karabelas / Int. J. Therm. Sci. 41 (2002) 682–692
It is finally pointed out that this brief review of scale formation is restricted to a single depositing species (CaCO3 )
in an attempt to focus on key issues requiring special attention in future research activities. Aside from that restriction,
this paper is also incomplete in other respects, with several
significant contributions to this field not included. In particular, the somewhat different scale characteristics [33] due to
precipitation (or co-precipitation) of other compounds (e.g.,
CaSO4 ) are not treated here despite their importance. Nevertheless, it is clear that considerable research work is still
required to better understand scale formation even in simplified cases.
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