Proceedings of the 7th International Symposium on Fresh Water from the Sea Vol. 1, 399-406, 1980
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)
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)
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
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  and
b = 0,83 according to .
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:
Hereby an assumption has been made that jc = j 
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
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.
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;