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Optimal Conditions for Magnetic Anti-scale
Treatment in Heat Exchangers
L.C. LIPUS1, J. KROPE2, D. GORICANEC2
1
Faculty of Mechanical Engineering,
2
Faculty of Chemistry and Chemical Engineering
University of Maribor
Smetanova 17, 2000 Maribor,
SLOVENIA
Abstract: The efficiency of magnetic anti-scale treatment of water is investigated as a function of over-saturation
degree, crystallization surfaces of dispersed particles and of the hydrodynamic flow regime. On the basis of
proposed calculations, and also based on data by other authors, optimal conditions of magnetic anti-scale treatment
are discussed
Key-Words: Magnetic Water Treatment, Anti-scale, Heat Exchangers
1 Introduction
Scale formation is the precipitation of salts, mainly
calcium carbonate, which form an encrustation on
susceptible surfaces. This usually occurs as a result
of temperature rise. Other minor scale-forming
components are magnesium carbonate, calcium
sulphate, silica and various iron hydroxides, all of
which occur naturally in raw water supplies.
Anti-scale water treatment using traditional
chemical methods substantially changes the solution
chemistry and can be very expensive. Especially
under conditions of high circulation flow rates, which
are characteristic for large thermal power plants, the
reagent methods of water conditioning are not
economically and ecologically justified. Thus, it is
important to use waste-free physical fields, which are
of various types depending on water composition.
In water processing, magnetic water treatment
(MWT) plays an increasing role as an alternative
physical method amongst chemical water
conditioning methods regarding scale control. Low
investment cost, easy installation and water quality
maintenance enable cheap and non-polluting
application for hard scale prevention. When magnetic
device is properly designed for the particular
supplied water and technological system, we can
expect following changes in scale precipitation:
- the precipitation is occurring mostly in
suspended form,
- linings are brittle and can be easily removed,
-
crystals have modified size, shape and
structure,
- previously formed linings can be gradually
removed after the installation of the magnetic
device.
In world literature, many practical, laboratory
and some theoretical researches have been reported
for different operational conditions and different
water systems [1-13]. The goal is to establish a
theoretical model for designing a magnetic device
with assured efficiency.
The problem of reducing the scale formation in
heat-exchanger equipment is of great importance in
many branches of industry. In recent times, physical
methods are frequently used. On example of these
methods is fine dispersed suspension (FDS), where
fine powder is added to supply water to stimulate the
precipitation of hardness-forming salts in the bulk of
the solution. The crystallization nuclei, when passing
through a heat exchanger, accept the scale and
consequently reduce the precipitation on heated
walls. MWT method is in principle similar to this
method.
2 Anti-scale Efficiency for Heat
Exchangers
The calculation of anti-scale efficiency of MWT
relates equally to the efficiency of FDS. We define
the efficiency  as the relative change in the mass of
scale depositing on the surface of a heat exchanger
during a working time t :
(1)
where m0(t) is mass of scale that has been deposited
on the surface of the heat exchanger during the
period t without magnetic field (B=0) or without
introducing dispersed powder, respectively. We
assume that m(t) is the same when MWT or FDS is
included.
If we define crystal growth rate, rS, as
corresponding mass of scale deposited in a time unit
on a surface unit of the heat exchanger and rV as mass
of scale-forming component crystallized on dispersed
powder in a time unit and a volume unit of the heat
exchanger, assuming spatial homogeneity on the
surface and in the volume of the stationary working
heat exchanger, the efficiency (1) can be written in
following form:

rV V
1 rV


rS S S HE rS
(2)
The parameter SHE = S/V is a specific surface of
heat exchanger. Lower the value of SHE is better the
anti-scale efficiency will be.
Oppositely, high values for SHE are recommended
to ensure quick heat exchange as it can be seen from
heat balance equation (3) (high dT1/dt). An optimal
value for SHE should be found. At modern heat
exchangers, SHE practically extends from 102 to 103
m2/m3.
S HE (T2  T1 )  c
dT1
dt
(3)
where T1 is temperature of water and T2 of HE walls.
Other parameters are given in appendix Symbols.
Crystal growth rate depends mainly on following:
- over-saturation degree of crystal-forming ions
(e.g. ion concentration, thermodynamic
stability of growing phase),
- presence of other ions (i.e. threshold
inhibitors),
- available surface and its quality (i.e.
composition, morphology) and
- temperature.
For CaCO3 as main scale component, the crystal
growth rate is experimentally determined by
following expression [14]:
rV  MSk 0 exp  G / RT 
(4)
  cCa 2  cCO 2  K S
(5)
3
Here, the over-saturation degree, , is defined by
(5), where c is ion activity (or concentration in the
case of diluted solutions) and Ks is equilibrium
constant, which decreases with increasing
temperature [15]. Other parameters in Eq. (4) are
given in appendix Symbols. Introducing index 1 for
crystal growth in the bulk of the solution (on
suspended powder) and index 2 for crystal growth on
HE walls, anti-scale efficiency can be expressed from
(4) and (2) as:
 β  S 
 G2 G1 

   1  1  exp

 β1  S 2 
 RT2 RT1 
(6)
Temperatures at HE surfaces, T2, are higher than
in the bulk of HE volume, T1, therefore, according to
(5) the over-saturation degree is higher at HE
surfaces: 2  1. Calcium carbonate encrusts the
walls mainly as calcite, while magnetically treated
water usually has increased portion of aragonite or
vaterite in powder form, which have slightly lower
values of activation energy G. For practical values
of G and T, the exponential function in (6) is
approximately 1 and at the request for high anti-scale
efficiency request (i.e.   1), Eq. (6) can be
simplified: S1 / S2  2 / 1 > 1. From this can be seen
that powder surface should be greater or at least
comparable to HE surface. This can be achieved by
FDS or MWT method.
The mechanism how magnetic field influences
on the water as solution/dispersion system is complex
and not completely known. Leading hypothesis are:
- the magnetically modified hydration of ions
and surfaces of dispersed particles [3-5]. and
- Lorentz force effects [9-13].
When ions and dispersed particles, which are
present in treated water and electrically charged,
move through the magnetic field, Lorentz force (7)
acts on them. Lorentz force causes the flow of
crystal-forming ions to the surfaces of dispersed
crystals, overcoming the electrostatic barrier in
electric double layer. The result can be acceleration
in nucleation and crystal growth processes [9-13].
From this point of view, the necessary condition
for magnetically modified crystals over-saturation of
water during the treatment. Values of over-saturation
degree are high for nucleation process (as presented
in Fig.1), but much lower for growing process. The
Lorentz force is:

 
FL  e  v  B
flow through the working channel of MWT device
and B is magnetic field density. According to (7), for
intensive MWT effects, the following is
recommended:
- perpendicularity of magnetic field to direction
of water flow through the channel,
- high vB values and
- long retention time of water in working
channel,  or introducing the recirculation
system.
From few-decade practical experiences with
MWT devices, efficiency region is: v from 0.5 to 2
m/s, B from 0.05 to 1 Vs/m2 and  higher than 0.05s.
(7)
where e is electrical charge of the ion or surface
charge of the dispersed particle, v is velocity of water
n BT
140
ARAGONITE
120
= 20
100
80
CALCITE
= 30
60
40
=200
=150
=270
20
a (nm)
0
0.2
0.4
0.6
0.8
1.0
1.2
(9) (5)(9) (5)
1.4
1.6
(1)
(1)
Fig. 1: Free Gibbs energy, Gn, for hypothetically spherical nuclei of aragonite and
calcite in solution with following values of ion product cCa 2  cCO 2 :
3
110-7 mol2 / l2 - curves (1),
510-7 mol2 / l2 - curves (5),
910-7 mol2 / l2 - curves (9).
Further increasing of magnetic field density gives
no higher efficiency, while further increasing of
water flow velocity retards the efficiency. The last
was explained with particles deaggregation due to
turbulence pulsations [16].
If we assume that energy which is necessary for
particle deaggregation to be 10kT per particle (where
k is Boltzmann constant) than we can estimate
critical radius. Kinetic energy of pulsation per
volume unit shall be higher than deaggregation
energy per volume of the particle (with radius a):
v2
10kT

2
4a 3 / 3
(8)
Pulsation velocity, v , can be determined by
relationship (9) and pulsation length by (10), where
Dh is hydraulic diameter of working channel and Re
is Reynolds number [17].
 
v  0.17v
 Dh
  207 Dh
1/ 3



Re1/ 4
log Re/ 7
Re7 / 4
Re  vDh / 
(9)
(10)
(11)
Taking  = 10-3 Ns/m2 for viscosity of water,  =
103 kg/m3 for density of water, T = 200C, Dh = 10-2
m and v = 2 m/s, the critical radius is  = 0.1 μm.
Bigger particles than this are deaggregated and fine
dispersed powder is maintained on that way.
3 Conclusion
MWT has positive influence on scale formation with
smaller amounts of deposits on heat exchange
surfaces and making the deposit softer. In principle,
MWT method is similar to FDS method. It gives
modified crystals, which remain in suspended form
and in HE act as nuclei for scale precipitation in the
bulk of the water flow.
The anti-scale efficiency (6) depends mainly on
ratio of over-saturation degrees and ratio of surfaces
of HE walls and suspended powder. High efficiency
can be achieved if surface of the suspended powder is
at least comparable to the surface of HE walls.
Nomenclature:
a
Radius of nucleus or dispersed particle, m
B
Magnetic field density, Vs/m2
c
Ion concentration, mol/l
cp
Heat capacity of water, J/kg K
Dh Hydraulic diameter of working channel, m
e
Electrical charge of ion or dispersed particle,
As
G Activation energy for crystal growth, J/mol
Gn Free Gibbs energy for nucleation, J
kB
Boltzmann constant =1.3810-23 J/K
k0
Empirical constant for crystal growth, mol/sm5
KS
M
m
rS
rV
R
S
SHE
t
T
V
v
vλ







Solubility constant, mol2/l2
Molar mass of calcium carbonate, g/mol
Mass, kg
Mass growth rate per volume unit, kg/s m3
Mass growth rate per surface unit, kg/s m2
Universal gas constant = 8.3 J/mol K
Surface area, m2
Relative area of heat exchange surfaces per
volume of heat exchanger, m2/m3
Time, s
Absolute temperature, K
Volume, m3
Flow velocity of dispersion through the
channel of MWT device, m/s
Pulsation velocity, m/s
Heat transition coefficient at HE wall, W/m2K
Super-saturation degree, Viscosity of water, Ns/m2
Pulsation length, m
Mass density of water, kg/m3
Retention time in working channel, s
Anti-scale efficiency, -
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