Proceedings of the 7th International Symposium on Fresh Water from the Sea Vol. 1, 399-406, 1980
SUMMARY
An analytical investigation of resulting from
seeding particles
Generation of scale formation restriction on
heat transfer surfaces is carried out. with that end in view, material balance
of substances in the treated water is considered, taking into account heat and
mass transfer, as well as physico-chemical aspects of scale formation process.
A criterial equation is obtained making a calculation of scale preventing
efficiency of the magnetic treatment and the crystal-seeding technique
possible.
Some results of an experimental investigation of
magnetic treatment influence on scale formation are given. A similarity is
found between the magnetic treatment method of scaling inhibition and the usual
crystal seeding technique. Recommendations are presented, determining optimal
conditions and limits of saline water magnetic treatment directed to inhibit
scale formation.
Due to very strict environment protection
requirements, wastes from saline waters chemical softening plants are rather
difficult to dispose oft. That is why for pretreatment of high salinity waters
some physical treatment methods are proposed and applied again and again,
though the obtained results vary in a broad range. So, because of this urgent
necessity to have available a comparatively simple method of water softening
without using any chemicals for this process, it seemed worthwhile to return in
particular to the much disputed though nevertheless used method of magnetic
water treatment of special interest for pretreatment-softening before passing
the water in evaporators. But the
influence of the magnetic field on the treated water is not quite clear.
So, resulting from a lot of laboratory, pilot
plant and industrial experience, as well as some mathematical analysis, the
following processes may be considered to take place during magnetic treatment
of industrial water, i.e. its flowing through the gap of an magnetic apparatus
with a certain Intensity [1, 2 ].
1. In
the gap during the flow through of large water volumes, a highly porous layer
of ferromagnetic iron oxides is formed (fig. l), detained by the magnetic
field. There are always iron oxides in every kind of industrial water.
The
detained in the gap of the magnetic apparatus quantity of ferromagnetic iron
oxides Gm is approaching its maximal value.
Fig. l.
Forming in the magnetic apparatus – gap porous layer of ferromagnetic water
impurities.
Gm
max during some hours or days after the magnetic field is switched on.
Thus
Gm
max = a*B*lg (Wm lim/Wm) |
(1) |
2. If
the entering the magnetic apparatus water is unstable, i.e. supersaturated on some
salt or gaseous compound, the latter will discharge from the solution on the
highly developed surface of the ferromagnetic particles in the gap. This
concerns the Usual scale formation compounds – calcium carbonate, magnesium.
hydroxide, calcium sulfate, as well as dissolved gases – carbon dioxide,
nitrogen, oxygen etc. The discharge of soluted in water supersaturated
compounds from the solution on the surface of fixed by the magnetic field
filter layers results in accumulation of those compounds in the apparatus gap
in a new phase condition (solid, gaseous). The originating and growing
crystals (or gaseous bubbles), reaching some certain dimensions, are washed oft
by the water flow and out from the Magnetic apparatus. Finally a certain
dynamic equilibrium is established characterizing processes of the supersaturated
compound discharge and carrying out from the magnetic apparatus into the heat
exchanger in solid or gaseous state:
P =
7,2 104 jm*Fm / (Qm*Hc) (2)
Fig.2. to
derivation of the expression specifying magnetic water treatment
influence on scale formation rate in heat exchangers systems:
1 – magnetic apparatus;
2 – heat exchanger;
3 – feed water tank;
4 – pump;
5 – consumption of the heated water (leakage from the re circulation system).
3.
Due to the mentioned processes in the water flow after the magnetic apparatus
supersaturation degree of the dissolved impurity decreases and its
concentration in the new (solid, gaseous) phase increases. Besides, the
characteristics of the ferromagnetic impurities (surface properties, dispersity
degree etc.) change too, due to the impact of the magnetic field magnetic
coagulation of the iron oxides takes place as well as crystallization on their
surface of soluted in the water salts. In this way the magnetic treatment can
influence the properties of supersaturated water systems in a way, to a certain
degree similar to heterogeneous catalysis. Examination of processes proceeding
in the mentioned above magnetic apparatus' gap made some mathematical
specification of the magnetic water treatment antiscaling phenomena possible.
Fig.2 illustrates these processes, specifically
for a partly closed heat transfer system; high salinity water, treated by a
magnetic field before its entrance in the heat exchanger is used. The heated
water with a flow rate Q is feeded from the storage capacity 3 by a pump 4 to
the user 5, consuming water from the system in quantity Q; the rest (Q – Q,) is
returned to the storage capacity 3 through the heater 2* water losses due to
leakage in the system are restored by teed Qf. At constant water level in the
storage capacity (3), V =const, Q1 =
Qf.
Ahead of the heat exchanger (2) a magnetic
apparatus (I) is installed; according to the summarized above proceedings,
seeding crystals of the scale-forming agent due to transformation of some n
quota of the water's carbonate hardness into crystalline form are generated in
the magnetic apparatus' gap. That means that the latter can be considered as a
control device, feeding calcium carbonate seeding crystals. The efficiency of
seeding crystals teed, causing scale formation rate decrease, can be estimated
quantitatively by considering material balance of the scaling agent in the
heat-exchange tube – 1.
In differential form the scale mass conservation
law can be written as
div
j = J – Jc |
(3) |
Let us consider an elementary heat exchange tube
volume where the solution is supersaturated on some scale forming compound, i.e.
the concentration C being higher than its solubility S. This will cause
precipitation of solid phase on the inside surface of the tube (scale
formation), as well as on the surface of suspended in the flow bulk particles
(crud formation). spontaneous solid phase formation in the solution's bulk in
this case is not likely to take place because of the high energy barrier of a
new phase's formation. Regularities of scale formation on the inside tubes
surface have been established rather well [3, 4 ].
Fick's law for this case is conversed into an
expression.
Js = r*b* (C-S) (4)
In criteria form the scale formation rate can be
expressed as:
Sh = 0.023* Reb * Sc1/3 (5)
Where b= 0,8 (according to [3] and
b = 0,83 according to [4].
This equation describes, to a rather high
precision, the regularities of scale formation on the heat transfer tube wall
in cases when the scale formation rate is defined only by scaling compounds
transfer through the diffusion layer.
While estimating processes of scale (on the heat
transfer surface) and crud (on the suspended in the bulk particles) formation
an important parameter is the ratio of suspended in the flow calcium carbonate
particles' total area and the heat transfer surface area k. Operating with the
notion of an average diameter of the suspended particles scale forming
compounds It can be shown, that
k = 1,5 *Cc* D* r / Dc* rc ) (6)
In equation (3) the value J characterizes the rise
of scaleable components concentration per time unit during chemical react -ions
proceeding. In case of calcium carbonate scale formation this can be the
reaction of bicarbonate thermal decomposition
2HCO3- = CO32-
+ CO2 + H2O (7)
After integration of the equation (3) for an
elementary tube section dL (Fig.2) and substitution in it equations (4-6), the
follow differential equation can be obtained, characterizing processes of scale
and crud formation in the heat exchanger:
-dC/dL=0,092/D*Re(b-1)*Sc-2/3*(1+k)*(C-S)-J/r×w, (8)
Hereby an assumption has been made that jc = j [5]
Examining an beat transfer tube with
insignificant linear temperature gradient, dL/dt, under condition that in the entering
feed water the bicarbonate thermal decomposition process is practically
completed and the suspended particles surface has increased only slightly (S =
const, k = const; J = o) the differential equation can be solved as follows:
C-S=(Cin-S)exp(-0,092)*Re(b-1)*Sc
-2/3*(1+k1*k2)*L/D, (9)
So, the antiscaling efficiency connected with
the presence of suspended scaling compounds particles in the flow, can be expressed
as:
h =
1-exp(-0,138* Re(b-1) Sc-2/3 Cc *L* r /(dc rc)) (10)
An estimation of the magnetic treatment
antiscaling efficiency in closed systems has to consider the process of seeding
crystals accumulation in the recirculating water. The introduction of seeding
crystals into the system partly leads to their concentration increase in the
recirculating water, partly the crystals are removed from the circuit with the
blow-down, as shown below:
5*10-5*Ç*Ðñ*É
= Ññ*É1+ÌâÑñ.âÅ (11)
Taking into consideration the limiting conditions (Cc = 0 at T = 0), the
solution of equation (11) gives:
Cc =5*10-5*P*Hc*(1- exp(-T*Q1/V))*Q/Q1 (12)
and antiscaling efficiency of magnetic treatment
of water in re-circulation systems can be expressed by
h=1-exp(-6,9*10-6*Re(b-1)*Sc-2/3*[L*P*Hc*Q*r/Dc*Q1*rc]*(1-exp(-T*Q1/V))) (13)
Conclusions
1) Antiscaling magnetic treatment of water can be considered as a complex
of simultaneously proceeding, technological water treatment processes:
2) Estimation of anti-scale magnetic treatment of water in re-circulation
systems (equn.13) shows that antiscaling efficiency can reach considerable
values. This specific peculiarity of water magnetic treatment is connected with
the ability to concentrate the rather small solid phase quantity formed during
one passage of the water through the magnetic apparatus per water mass unit;
this is relative only to recirculating heat exchange systems.
3) Explanations of some observations were found, such as: external dependence
of magnetic treatment efficiency from water velocity in the gap; the role of
magnetic induction gradient; the high efficiency of multipolar magnetic
apparatuses, etc.
4) One of the possible mechanisms of magnetic treatment of water on gaseous
impurities is found.
Nomenclature;
a –
parameter, characterizing the antiscaling magnetic apparatus as a magnetic
filter, kg/T;
B – magnetic induction in the gap, T;
C –
scaleable dissolved components' concentration in the water, kg/kg;
Cc – seed crystals' concentration in
the water, kg/kg
Cin
– intel scaleable dissolving components' concentration in the water, kg/kg;
D –
diameter of heat exchanger's tubes, m;
Dc – seed crystals' effective
diameter, m;
Fm
– surface area of the suspended magnetite layer in the magnetic gap, m2;
Gm – mass of the suspended magnetite layer in the gap, kg;
Gm max – maximal mass of the
suspended magnetite layer in the gap, kg;
Hc
– carbonate hardness of the water, mg-equ/kg;
J – volumetric bicarbonate thermal decomposition
rate, kg/(m3 s)
Jc
– volumetric rate scale precipitation on the seed crystals' surface, kg/(m3
s);
j –
mass flow rate of the scaleable dissolved components in the water, kg/(m2
s);
jm
– calcium carbonate scale precipitation's intensity on the surface of magnetite
particles suspended in the magnetic gap, kg/(m2 s);
js – scale formation's rate, kg/(m2
s) ;
jc – mass flow rate of the scaleable
dissolved components to the seed crystal’s surface, kg/(m2 s);
k – ratio of the seed crystal’s surface area in
the water and the heat exchange's surface area, m2 /m2 ;
L – length of the heat exchanger's tube, m;
P –
part of the carbonate hardness of the water precipitated in the magnetic gap;
Q – flow rate of the water through the heat
exchange system, m3/h;
Qf – flow rate of the teed water
entering the beat exchange system, m3/h;
Qm – flow rate of the water through
the magnetic gap, m3 /h;
Q1 – flow rate of the lost water out of
the heat exchange sys-tem, m3/h;
S –
solubility of the scaleable dissolved components in the water, kg/kg;
t – temperature of the water, °C;
V – water volume in the heat exchange system, m3;
w – flow velocity in the heat exchanger, m/s;
wm – flow velocity in the magnetic gap,
m/s;
w m lim – limited flow velocity in
the magnetic gap, m/s;
b – mass
transfer coefficient to the beat exchange's surface, m/s;
h – antiscaling efficiency of the water magnetic treatment;
r –
water density, kg/m3;
rc – seed crystals density, kg/m3;
T – time non-stopping work of the magnetic
apparatus, h.