An empirical model for salt removal percentage in water under the effect of different current intensities of current carrying coil at different flow rates

Journal of Advanced Research (2011) 2, 351–355

Cairo University

Journal of Advanced Research

SHORT COMMUNICATION

An empirical model for salt removal percentage in
water under the effect of different current intensities
of current carrying coil at different flow rates
Rameen S. AbdelHady a,*, MohammedAdel A. Younes a, Ahmed M. Ibrahim b,
Mohammed M. AbdelAziz b
a
b

Mechanical and Electrical Institute, National Research Center, Ministry of Water Resources and Irrigation, Egypt
Electrical and Machine Power Department, Faculty of Engineering, Cairo University, Egypt

Received 26 October 2010; revised 9 December 2010; accepted 31 January 2011
Available online 12 March 2011

KEYWORDS
Magnetic field;
Water;
Flow rate;
Salt removal percentage;
Empirical model

Abstract The magnetic treatment of hard water is an alternative, simple approach by which the
hard water that needs to be treated flows through a magnetic field. This field is created by inducing

current in a coil wrapped around a pipe. Consequently some of its properties, such as total dissolved
salts (TDS), conductivity (Ec) and PH change. The primary purpose of hard water treatment is to
decrease TDS in the incoming liquid stream. Using performance data from the application of different magnetic field densities on the different flow levels of water, empirical mathematical models
were developed relating the salt removal percentage (SRP) to operating flow rate and current of the
coil. The obtained experimental results showed that the SRP increased with increasing the current at
low flow rates (up to 0.75 ml/s).
ª 2011 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

Introduction
* Corresponding author. Tel.: +20 105004402, +20 106364994, +20
2 22751997; fax: +20 2 42188948.
E-mail address: (R.S. AbdelHady).
2090-1232 ª 2011 Cairo University. Production and hosting by
Elsevier B.V. All rights reserved.
Peer review under responsibility of Cairo University.
doi:10.1016/j.jare.2011.01.009

Production and hosting by Elsevier

Hard water is water that has a high mineral content. The main
components of these minerals usually are calcium (Ca2+) and
magnesium (Mg2+) ions, in addition to dissolved metals,
bicarbonates, and sulfates. Calcium usually enters water as
either calcium carbonate (CaCO3) in the form of limestone
and chalk, or calcium sulfate (CaSO4) in the form of several
other mineral deposits. The main source of magnesium is dolomite (CaMg(CO3)2). The total water ‘hardness’ (including both
Ca2+ and Mg2+ ions) is expressed as parts per million (ppm)
or weight/volume (mg/l) of calcium carbonate (CaCO3) in
water i.e., the total dissolved salts (TDS). Due to the hardness
of water, scale is formed. The problem of scaling causes loss of

352

R.S. AbdelHady et al.

production or process time and deterioration of equipment
and equipment failure; it also increases energy consumption
and loss of turnover. The methods by which the TDS of water
can be reduced and thus scale treated can be chemical or physical. The chemical method has been shown to be very effective;
however, it can cause environmental pollution through the
disposal of treated water [1]. The physical methods such as
magnetic treatments have attracted much attention for over
100 years. Donaldson [2] suggests that the magnetic treatment
can not only reduce the scaling potential of water but can also
cause existing scale to dissolve over an extended period of time.
Hasson and Bramson [3] recorded no change in either the rate
of scale deposition or the deposit tendency after tests of
15–35 h duration and concluded that antiscale magnetic treatment (AMT) was ineffective at the very high levels of supersaturation employed. The effect of magnetic field on the scaling
rate is studied by various authors including Ellingsen and
Kristiansen [4] who studied the effect of field strength on the
scaling rate. The authors found the precipitation rate to increase with increasing magnetic flux. With only a few exceptions, the reported effects in single phase solutions have
amounted to a change of no more than a few percent in certain
fundamental solution parameters, namely light absorbance or
transmission [5–8], conductivity or pH [9], viscosity [10], and
water absorption [11]. A number of these authors have proposed mechanisms to explain the observed changes. These
have included changes in the water of hydration of the calcium
ion, alteration of the molecular rotation of water adsorbed
onto materials [11], and a localized pH shift resulting from
the electric currents generated by Lorentz forces. Here the effect of magnetic flux on TDS is studied, which was not done

by the above studies. Apart from inducing direct magnetic
flux, the application of induced magnetic flux by means of solenoid type equipment has been reported. Antiscale magnetic
treatment is a green method of TDS reduction because it does
not use chemicals and it removes the option of treatment of

process water before disposal. The principle behind the technology involves using a varying electric current in a solenoid
wrapped around a pipe to create an induced electromagnetic
field inside the scale-producing solution. From the laws of
physics, electrical current flowing through a wire creates a
magnetic field around the wire. Due to both the complexity
of the phenomena involved and the lack of significant research
in this field, no satisfactory mathematical models have been
developed. SRP is influenced by many factors, such as the detailed velocity field, density and viscosity of the fluid, direction
of the magnetic field, and the effective length of the magnetic
probe on the pipe. Random environmental factors and inlet
conditions cause dramatic changes to the density and velocity
field, which in turn cause major variations in SRP. In the absence of a more valid practical approach, empirical models,
sometimes called ‘‘regression models’’, can be helpful in this
research.
Experimental
The apparatus used is shown in Fig. 1. The apparatus consists
of a coil of length L = 15 mm, inner diameter equals 10 mm,
outer diameter equals 30 mm with number of turns
N = 1100 wound with a copper wire of 1.5 degauss, maximum
voltage V = 12 V, maximum current I = 240 mA, with iron
housing, placed on a teflon pipe of 6 mm inner diameter and
8 mm outer diameter of 50 cm length. The direction of the
magnetic field is bilateral to the direction of water flow connected with a water flow system and a laboratory DC power
supply. In the flow system water passes through the tubing system ending with a syringe needle to let the water flow through
the coil as shown in Fig. 1; the input saline water with TDS

above 180 ppm, which is considered to be very hard water, is
supplied to the current-carrying coil through a tank of a capacity of 10 l; input water flow rate is controlled through valves,
each calibrated to a certain flow rate.

RAW
WATER

Conductivity
Sensor

Current
Carrying Coil

DAQ
Tubing
system

Water flow
by gravity
DC Power
Supply
0-30 volts
0-3 amp

LAP TOP connected
To DAQ card

Regulated
valve
(Syringe

needle)

PRODUCT

Fig. 1

Experimental setup schematic diagram.


An empirical model for the effect of magnetic field on water
The laboratory DC power supply type GPR-3030 of dimension 102(W) · 165(H) · 300(D) mm is used at various voltages
ranging from 0 to 30 V and 0 to 3 A applied on the coil to control the magnetic field density. The conductivity sensor, which
consists of a 9-V battery, battery snap connectors, 1 k-X resistor and two alligator clips straightened and dipped into the teflon pipe one cm apart, is connected to the DAQ card through a
USB cable that is connected to the computer system. The positive electrode of the battery is connected to the resistor and to
one of the clips and the other clip is connected to the negative
electrode [12]. The NI USB 6008 data acquisition card was
chosen for signal acquisition from the water conductivity sensor. The card has 8 analog inputs, 2 analog outputs, and 12
bidirectional digital lines and a sampling rate of up to 10 ks/
s [13]. The differential acquisition mode was chosen because
it would provide more noise immunity and accuracy of
measurement.
Magnetic field calculation [14]
H ¼ ðN Ã IÞ=L

ð1Þ

where H is the magnetic field intensity, which is the amount of
magnetizing force. It is proportional to the number of turns
per unit length of a coil and the amount of electrical current
passing through it in Amp turn/m, N is the number of turns

of current carrying coil, I is the current applied on the current
carrying coil and L is the length of the coil in meters.
B¼lÃH

ð2Þ

where B is the magnetic field density, which gives the magnetic
field’s magnitude (the number of flux lines per unit area) expressed in Tesla, l is the magnetic field permeability, which
is the measure of the ability of a material to support the formation of a magnetic field within itself in Henry/m.
l ¼ lo à lr

ð3Þ
À7

where lo is the magnetic constant equals 4 \ g \ 10 Henry/m
and lr is the relative permeability equals 1 (for air).
The samples used for the magnetic treatment experiments
were at room temperature. The SRP is determined at four different flow rates (0, 0.25, 0.5, 0.75 ml/s), with thirty different
magnetic field densities. The parameters chosen in the experiment were flow rate and current of the current-carrying coil.
The range of current used is from 5 to 200 mA with 5 mA steps
so the range of magnetic field intensity and magnetic field density becomes from 1.8 \ 10À3 T to 18.4 \ 10À3 T.

353
The salt removal percentage used to determine the final
desalinated product water at different magnetic field intensities
is expressed as Eq. (5):


TDSout À TDSin
SRP ¼ À

à 100
ð5Þ
TDSin
where TDSout is the outlet TDS, which is the TDS at various
currents of current-carrying coil (which represents the magnetic field applied on the pipe), and TDSin is the inlet TDS
(which is the TDS at 0 A on the pipe i.e., raw water).
Salt removal percentage was fitted to the following formula:
SRP ¼ að1 À eÀbI Þ

ð6Þ

The curve fitting parameters (a) and (b) Eq. (6) are used to
describe the relationship between SRP and the current applied
on the current-carrying coil.
Results
The obtained experimental results showed that the SRP increased with increasing the current at low flow rates (up to
0.75 ml/s). The model coefficients were derived from the combined analysis of well-correlated sets of data, thus giving a
good indication for their possible general applicability. The
analysis of experimental data also gave a relationship between
SRP and flow. The exponential equation (Eq. (6)) is applied
and the effect of flow rate on the SRP appears on the values
of the constants (a) and (b). The SRP as a function of current
applied on current-carrying coil, at various flow rates is illustrated in Figs. 2a–d. The obtained constant values (a) and
(b) at various magnetic fields from 1.1 T to 11.058 T and flow
rate from 0 mL/s to 0.75 mL/s are shown in Table 1. The analysis shows that the constant values (a) and (b) decreased as the
operating flow rate increased. It indicates that the ability to increase the SRP is more effective at lower operating flow rates.
The plot constant value (a) and (b) (as y coordinate) to the
flow rate (as x coordinate) as a linear trend followed the mathematical equation shown in Eq. (7):
y¼mÃxþc

ð7Þ

Salt Removal Percentage Fit Model at 0 ml/sec
SRP=a*(1-exp(-b*I))
a=90
b=9.034
80

Sensor calibration

Experimental Data
Fit curve

99.5% Sodium Chloride NaCl with specifications according to
British pharmacopoeia 2004 dissolved in ionized water was
used as standard to calibrate the sensor in the tubing system
by measuring TDS of this solution using a traditional calibrated portable pH/Ec/TDS/Temperature meter (Hanna with
probe HI 991300), then passing it through the tubing cell system and reading the corresponding voltage of the sensor. The
Labview program was adjusted to automatically read the TDS
in ppm. The calibration equation (Eq. (4)) is deduced by fitting
the points to a straight line using the curve fit tool in Matlab
with error 11.3588% and R2 (goodness of fit) 0.9403.
TDS ¼ À767:4V þ 6813
where V is the voltage of the sensor.

Salt Removal Percentage

70
60
50

40
30
20
10
0
0

ð4Þ
Fig. 2a

0.02

0.04

0.06

0.08
0.1
0.12
Current (A)

0.14

0.16

0.18

0.2

Effect of current applied on coil on SRP at 0 ml/s.

354

R.S. AbdelHady et al.
Salt Removal Percentage Fit Model at 0.25 ml/sec
SRP=a*(1-exp(-b*I))
a= 60
b=8.205

Salt Removal Percentage Fit Curve at 0.75 ml/sec
SRP=a*(1-exp(-b*x))
a=2.5
b=5.376
1.8

50

Experimental Data
Fit Curve

Experimental Data
Fit Curve

1.6

Salt Removal Percentage

Salt Removal Percentage

1.4
40

30

20

10

1.2
1
0.8
0.6
0.4
0.2

0

0
0

Fig. 2b

0.02

0.04

0.06

0.08

0.1
0.12
Current (A)

0.14

0.16

0.18

0.2

0

Effect of current applied on coil on SRP at 0.25 ml/s.

Fig. 2d

Salt Removal Percentage at 0.5 ml/sec
SRP=a*(1-exp(-b*I))
a=40
b=7.562
35

0.04

0.06

0.08
0.1

0.12
Current (A)

0.14

0.16

0.18

0.2

Effect of current applied on coil on SRP at 0.75 ml/s.

Value parameters (a) and (b) at various flow rates.

Flow rate of water in mL/s Value parameter a Value parameter b
0
0.25
0.5
0.75

Experimental Data
Fit Curve

30
Salt Removal Percentage

Table 1

0.02

90
60
40
2.5

9.102
8.289
7.714
5.373

25
20

Substitution of Eqs. (10) and (11) into Eq. (8) provides an
empirical model Eq. (12) that describes the SRP as a function
of current applied to the coil and flow rate.

15
10

SRP ¼ ðÀ113 à Q þ 90:5Þ Ã ð1 À expðÀð4:647 à Q þ 9:287Þ Ã IÞÞ
5

ð12Þ

0
0

Fig. 2c

0.02

0.04

0.06

0.08
0.1
0.12
Current (A)

0.14

0.16

0.18

0.2

Effect of current applied on coil on SRP at 0.5 ml/s.

A statistical treatment known as linear regression can be
applied to the data and these constants can be determined,
where m is the slope of the line and c is the y-intercept.
Given a set of data with n data points, the slope and yintercept can be determined using the following equations:
P
P
P
n ni¼1 ðxyÞ À ni¼1 x ni¼1 y

m¼
ð8Þ
P
P
n ni¼1 ðxÞ2 À ð ni¼1 xÞ2
Hence Eq. (8) is used to determine the slope of the line.
Pn
P
y À m ni¼1 x
c ¼ i¼1
n

ð9Þ

Eq. (9) is used to determine the y-intercept.
Using the data in Table 1 and applying Eqs. (8) and (9) to
deduce the slope and y-intercept, the Eqs. (10) and (11) of constant values (a) and (b) become:
a ¼ À113Q þ 90:5

ð10Þ

b ¼ À4:647Q þ 9:287

ð11Þ

where in Eq. (12) Q is the flow in ml/s and I is the current applied on the coil in Ampere.
Validation of the general equation
The flow rate was adjusted to 10 ml/min (1 min = 60 s; 10 ml/
min = 1/6 ml/s = 0.167 ml/s, which is in the range of the flow

Table 2 Salt removal percentage at different current intensities and 10 ml/min (0.167 ml/s) flow rate.
Current of coil Experimental Empirical salt Accuracy
SRPexp ÀSRPemp
j à 100
in ampere
salt removal removal
j
SRPexp
percentage
percentage
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2

9.2980
16.8503
32.2795
42.3386
47.7833
54.1806
58.8217
60.4449
64.8784

68.7636

13.0631
23.7451
32.4800
39.6228
45.4636
50.2398
54.1454
57.3391
59.9507
62.0862

40.4935
40.9179
0.6212
6.4145
4.8546
7.2735
7.9500
5.1382
7.5953
9.7107


An empirical model for the effect of magnetic field on water

properties. Among those physical properties are conductivity
and thus TDS and pH. Analyses of the performance data from
the lab show that a simple empirical relationship in the form

SRP ¼ að1 À eÀbI Þ can satisfactorily describe the salt removal
percentage in terms of the operating flow rate. The coefficients
(a) and (b) were found to be flow rate-dependent according to
a ¼ À113Q þ 90:5 and b ¼ À4:647Q þ 9:287, valid for operating flow rate 0–0.75 ml/s.

Emperical and Experimental Salt Removal Percentage at 10ml/min
70
Experimental SRP
SRP deduced from Model

Salt Removal Percentage

60

355

50

40

30

Acknowledgments

20

I would like to thank all the people of the Mechanical & Electrical Research Institute for their wonderful support.

10

0
0.02

0.04

0.06

0.08

0.1

0.12 0.14
Current (A)

0.16

0.18

0.2

0.22

Fig. 3 Experimental and empirical salt removal percentage at
different applied magnetic fields at 10 ml/min flow.

rates at which the model was utilized) and the current of the
coil ranged from 0 to 200 mA. The salt removal percentage
experimentally reached 68% at 200 mA as shown in Table 2.
By applying Eq. (9) putting I = 0.02–0.2 with 0.02 steps and
Q = 0.1667 mL/s to deduce the SRP empirical gives results

that are also shown in Table 2.
As seen in Table 2 and Fig. 3, the difference between the
experimental SRP and the SRP deduced from Eq. (12) gives results that are satisfactory; the model can predict the SRP
approximately although the accuracy was higher than 10%
at lower current intensities. Due to the low values of the
SRP at these intensities, however, the model gives only a rough
value; also it has been observed that at high current values the
model-predicted values are less than the experimental values
due to the approximation of the constant value (a); the parameter (a) represents the length on the y scale between the function’s height at x = 0 and the asymptote approached by the
function as x approaches infinity and it can be seen in
Fig. 2a–d that the created model values are less than the experimental values.
Discussion and conclusion
The experimental work in determining the effect of operating
flow rate allows us to conclude that flow rate influences salt removal percentage. The results reveal that the removal percentage decreases as the flow rate increases. Increased flow rate
increases the drag force; therefore, particles are not easily
aggregated or accumulated under high flow velocity [15].
Increasing the current, i.e., increasing the magnetic field density, leads to an increase in the salt removal percentage because
water molecules are electrically charged and have a small dipole and thus a small dielectric constant. This dipole may be
susceptible to the effects of exogenous electric and magnetic
fields. It is well known that the subjection of water to a small
magnetic field can change its dielectric constant. The change in
the electric dipole of water can result in change of the physical

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