Physical water treatment using alternating variable frequency electric field device for the mitigation of limescale in industrial production.

: Electric field scale inhibition is one of the most promising methods of scale inhibition. In this study, an alternating variable frequency electric field device is presented, it able to prevent the growth of scale in industrial heat exchange equipment effectively. Conduct field test at the heat exchange station to analyze the scale inhibition performance of the device. The test results showed that after using alternating variable frequency electric field device, the scale thickness on the heat exchange surface is significantly reduced, fouling resistance reduced by more than 58%, and the anti-corrosion rate for Fe element content reaches 19.78%, The SEM image of the scale changes from a dense irregular sharp shape to a loose spherical shape. Conclusively, alternating variable frequency electric field device has grate scale inhibition performance. This is of great significance to the field of heat transfer and energy saving.


Introduction
Scale refers to the crusty chalky or soft muddy substances that gradually accumulates on the solid surface in contact with mineral ion-containing fluids [1] .
Industrial and domestic water contains excessive mineral ions. Scale species differs from depending on the treatment method and mineral content of the utilized water.
Among them, the most common mineral ions are Ca 2+ and Mg 2+ [2] . When the hard water flows through the heat transfer equipment, these ions and bicarbonate ions precipitate due to changes in pressure and solubility,, eventually forming mineral deposits(limescale) on the heat transfer surface. a process traditionally called "fouling" (Reaction (1)) [3][4] .
Ca 2+ + 2HCO3 − ⇄CaCO3(s) + H2O+CO2(g) (1) Fouling phenomena are widespread in the heat transfer process of industrial production [5][6] . Examples include thermal power, petroleum, desalination, and food industries. Scale forms on a heat exchange surface is harmful. Firstly, Once scale forms in the pipe, the water flow area gradually decreases until it is completely blocked [7] .
Secondly, since the thermal conductivity of scale deposits are much lower than that of metals, scaling not only seriously affects the heat transfer efficiency of the heat exchanger [8][9] but also lead to system operation malfunction easily [10] . Lastly, the adhesion of scale causes the metal on the heat transfer surface to corrode [11] , thereby triggering safety accidents such as pipeline perforation. Thus, it is self-evident that if one can reduce scale on heat transfer surface during production process, the saving in energy, safe and high-speed production, and maintenance of equipment will be truly significant.
At present, the common scale inhibition technology in the industry are the use of chemical reagents [12] , such as ion exchange method that using ion exchange resin to replace scaled cations (calcium ions, magnesium ions, etc.) from hard water. Or add scale inhibitor [13][14] to the hard water to inhibit the growth of scale. Even though all the above chemical scale-removing methods are effective, long-term use causes chemicals to residue in the water, affecting the environment and even human health. Furthermore, once scale on the heat transfer surface, that requires several methods to removal scale such as chemical cleaning [15] , mechanical cleaning [16] , and high-pressure jet cleaning, etc. This not only leads to economic losses caused by shutdowns, but also mechanical strength affects the service life of pipe and equipment. Therefore, an energy-saving, efficient, environmentally-friendly, and scale inhibition technology that does not affect normal production is a new research direction.
The physical method of scale inhibition is a green and pollution-free water treatment method [17] , such as solenoid coils [18][19] , catalytic materials [20] , magnetic fields [21] , electric fields [10] , ultrasonic waves and electromagnetic fields [22] . Among them, the electric field scale inhibition method is a new research hotspot, and the scale inhibition effect is more obvious. Leonard D et al. [5] used RF electric field for physical water treatment to reduce calcium carbonate scale in the cooling water, they introduced the RF electric field into the cooling water through a set of parallel graphite electrode plates, the experimental results showed that the high frequency signal with frequency of 13.56MHz and 27.12MHz has better scale inhibition effect at 2V, 5V and 13V.
Wontae Kim et al. [23] inserted dual electrodes into the pipe to inhibit mineral scale and bio-scale in the heat exchanger, and the results showed that this method can maintain the heat transfer coefficient of the heat exchanger at 90% (close to no scale).
At present, almost all such researches are configuration with artificial hard water in the laboratory, and the scale component is single, such as a single CaCO3, MgCO3, etc., and does not involve testing and application in industrial production. In real industrial production, circulating water has more complex chemical composition and the scale composition rather than a single mineral deposit. The environmental factors that affect the growth of scale are also particularly complex, such as temperature, pressure, and flow rate. Thus, the development of a device that can effectively inhibit scale in a complex industrial environment is the focus of current electric field scale inhibition research. After almost 10 years of continual research and field experimentation, an electric field inhibition scale device has been developed which, not only collects the advantages of traditional electric field scaling technology, but also make up for their shortcomings. Therefore, the objective of this paper is to introduce the working principle of the device and to conduct experiments on scale inhibition effect in industrial production. The minerals in the water are in the form of ions, thus as Ca 2+ 、Mg 2+ 、Cl -、CO3 2etc. Fig.2 is a schematic diagram of ion movement in water no applying electric field and applying electric field, in the absence of external disturbance conditions such as an electric field, ions will accumulate on the pipe wall to nucleate and crystallize, and the scaled ions in the water will adhere and deposit on the crystal surface to form scale.
However, after these ions are subjected to the electric field before nucleation, the ions quickly change the direction of motion causes the positive and negative ions to collide, nucleate, adhere , crystallize in the water, and are removed by the shear force of the water without scaling on the inner surface of the tube wall. According to Biot-Savart's law and Maxwell's theory, the electric field is finally applied to the fluid in the pipe through the magnetic ring.
In this process, the role of the coupled transducer is to complete the conversion of electric field-magnetic field-electric field, avoiding direct application of electric field to the water to damage the circulatory system equipment.
After years of trial and error and comparison of effects, a damped cosine wave whose peak-to-peak value gradually decreases from 70V to 5V is used as a periodic non-uniform electric field signal. In order to prevent the device from affecting the scale inhibition effect due to the memory of the water after long-term to use, the frequency selection varies randomly within the range of 80kHz-300kHz with grate scale inhibition effect. This process is realized by the circuit applying formula (2) underdamped attenuated oscillation signal to the coupled transducer. ω and φ randomly change according to the law within a specific range. The waveform of this signal is shown in Fig.3, when the wave reaches the output terminal, a negative sharp pulse appears, there is a long tail phenomenon.
Where A represents the basic starting phase; is the damping coefficient; is the angular frequency; is the phase. Use the oscilloscope model of Lecory354a to test the real waveform output as shown in Figure 4. The coupled transducer is an important part of introducing electric field energy into the circulating water system, it consists of an oscillator and a closed magnetic ring.
The design of the coupled transducer has an important influence on the treatment effect of the device.
According to Maxwell's equation, when the alternating current generated by the electric field source powers the oscillator, the electric field and magnetic field will establish the following relationship (3) inside the coil: Relating the electric field strength and magnetic field strength to the applied current, the above formula (4) can be expressed as: Where E represents the induced electric field vector; B is the magnetic field strength vector; ω is the angular velocity of alternating current; s is line vector along the circumference ; i is an imaginary number; r is the distance from the center line of the coil to this point.
Remove the imaginary part from the equation and replace B with Iμ_0 n to get the following equation (5): The electric field vector in equation (12) can be regarded as a concentric circle with a radius r (distance from the center line of the solenoid).
Changing the frequency and current amplitude will change ω and I respectively, at

Test procedure
In order to test the scale inhibition performance of the device in industrial production, field test was carried out. Field test at Sunshine Heat Exchange Station in Shuangliao City, Jilin Province. A diagram of the scale inhibition test flowloop is presented in Fig.6. The flowloop consists of a water circulation loop, an alternating variable frequency electric field device, a RTD temperature sensor, heat exchanger A and B, pressure sensor, water supply tank, water pump and Programmable primary network water supply pipeline of heat exchanger B, and the device is not installed on heat exchanger A. A diagram of the field test installation is presented in Fig.7. 7A is the installation diagram of the alternating variable frequency electric field device, and 7B is the working voltage, current and power of the device.
The circulating water used in the test is municipal tap water. Two sets of plate heat exchangers A and B of the same batch and model are selected in the test. Table 1 lists the parameters of plate heat exchanger. Before the test, the two heat exchangers were thoroughly cleaned. After 750 hours, the test system runs stably, at this time, install the device at the water inlet of the primary network of heat exchanger B. The system records the primary network supply and return water temperature, the secondary network supply and return water temperature, t the primary network supply and return water pressure, the secondary network supply and return water pressure through the programmable controller (PLC) monitoring system of the heat exchange station. Table   2 lists the parameters of experimental system operating.
Where v represents the scale inhibition rate; 1 , 2 is the scale thickness of heat exchanger A and scale thickness of heat exchanger B, respectively. Fouling resistance R f (m 2 KW -1 )on the surface of the plate heat exchanger, which can be defined as formula (7) [24][25] : Where U f represents the total heat transfer coefficient of scale;U I is the total heat transfer coefficient of clean surface.
The total heat transfer coefficien U f can be expressed as formula (8): Where Q represents the heat transfer between the fluid and the heat exchange surface; A is the total heat transfer area; ΔT LMTD is the log mean temperature difference; In the test, the primary network and the secondary network are parallel flow. ΔT LMTD can be expressed as formula (9): Where ΔT hi represents the temperature difference between cold and hot fluid inlet; ΔT ho is the temperature difference between cold and hot fluid outlet; As an observation point every 100 hours, calculate the average fouling resistance.
The fouling resistance of heat exchanger A and B is shown in Fig. 9 and Table 3. From Where v represents the reduction rate of the fouling resistance; 1 is the fouling resistance of heat exchanger A; 2 is the fouling resistance of heat exchanger B. The SEM image of scale on the surface of heat exchanger shows in Fig.10. In   Fig.10A, the morphology of the scale sample of heat exchanger A is mainly irregular and sharp, dense clusters, and sharp edges. In Fig.10B, the scale sample morphology of heat exchanger B is mainly spherical, with loose clusters and small particles. The scale crystals of heat exchanger A conform to the characteristics of calcite, which the growth rate of the long axis of the crystal is faster than the short axis. it is easy to produce adhesion between crystals, which gradually aggravates the scaling phenomenon. The scale crystals of heat exchanger B belong to the orthorhombic system, its growth rate in each axis is the same and forms spherical crystals and conform to the characteristics of aragonite, which the adhesion between the crystals is weakened and it is easy to leave the heat exchanger surface with the fluid flow.  Table 4. In Fig,11A, the scale of heat exchanger A contains more Fe element, combining with the scale on the surface of heat exchanger A, it is inferred that the possible cause is that the scale is completely dense during growth and the resulting alkali corrosion. The circulating water is alkaline, which causes the heat exchange wall metal, scale and circulating water to form a chemical battery, causing oxygen-consuming corrosion (the scale is the anode and the metal is the cathode).
In Fig,11B  (2) The analysis of heat exchanger scale thickness and fouling resistance change shows that the scale inhibition rate of this device is 58% and 68% respectively; ( 3) The SEM analysis shows that the scale treated by the device has a spherical shape and an orthorhombic crystal structure. Besides, the adhesion between the crystals is weakened, and it is easy to leave the surface of the heat exchanger with the flow of water, so as to achieve the effect of scale inhibition and corrosion protection;