(09)reasearches regarding the measurements of the dissolved concentration in water
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7/30/2019 (09)Reasearches Regarding the Measurements of the Dissolved Concentration in Water
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Reasearches regarding the measurements of the dissolved
concentration in water
Alexandru Ptulea1, a,Ionela Mihaela Cluaru2,b and Nicolae Bran3,c
1
Independence Splai 313, cod 060042, Bucharest, Romania2Independence Splai 313, cod 060042, Bucharest, Romania
3Independence Splai 313, cod 060042, Bucharest, Romania
aalexandru.patulea@yahoo.com,
bmihaela.calusaru@yahoo.com,
cn_baran_fimm@yahoo.com
Keywords: Water oxygenation, fine bubble generators
Abstract. The paper aims to present a procedure of measuring concentration of oxygen dissolved in
water; this procedure is based on the electrochemical method. The differential equation of the transfer
speed of the oxygen towards water is numerically integrated and theoretical results are presented. Asetup used for experimental researches regarding water oxygenation was subsequently developed;
measurements regarding the increase of the concentration of oxygen dissolved in water were
performed. Theoretical and experimental results were compared.
Introduction
The transfer of oxygen in water, denoted oxygenation or aeration in specialty literature,
constitutes a basic operation in order to assure an appropriate quality of water in water treatment and
purification processes.
Generally, the aeration is used in the following fields [1,2]: in used water treatment processes that
involve oxidation of inorganic substances present in water; for the pre-aeration of wastewaters withlow content of dissolved oxygen, before their draining into the sewage network; in aquariums,
fisheries, ponds and lakes; during separation and collection of emulsified greases from used waters;
for the biologic purification of wastewaters by the active mud process, in aerated lagoons or in
biofilters.
The aeration of used waters can be made in three ways: mechanical aeration, with mechanical
aerators; pneumatic aeration, by compressed air blowing; mixed aeration, using mechanical aerators
and compressed air blowing. The aeration system is chosen in function of the efficiency of the
aeration process and of reliability [3].
The measurement of DO concentration is performed using chemical, electric or optical methods.
A process of DO measurement using an oxygen meter endowed with a polarographic probe,
belonging to the class of electrical methods, will be presented in continuation.
The oxygen meter manufactured by Hanna Instruments, Canada, requires a water speed of
minimum 0.3 m/s in order to perform accurate measurements.
During our research, the basin water will be stationary and the probe driven by a stepping motor
will be displaced in the water with a speed of 0.39 m/s.
1. Description of the measuring instrument
The oxygen dissolved in water is measured in parts per million (ppm=mg/l) or in saturation
percentages (%). The oxygen meter is composed of a microprocessor (1) (fig.1) that, through the
connection cable (2), establishes the connection with the measurement probe (3) introduced in thewater whose DO content must be established [4]. Figures 1 and 2 present the component elements of
the oxygen meter as well as their assembling manner in order to perform DO measurements.
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A small cylinder (4) (fig.2) that contains an electrolyte solution is screwed on the threaded portion
(5) (fig.1). The cylinder base consists of an oxygen permeable Teflon membrane (5) (fig.2). The
functioning principle of the measuring instrument is the following: a d.c. battery is mounted inside the
microprocessor (1), thus an electric field where ions migrate is established between the probe
electrodes.
Fig. 1. General view of the oxygen meter.
1- microprocessor with digital display; 2connection cable; 3probe body; 4temperature
sensor; 5threaded portion of the probe body where the part 4 (fig.2) is
screwed; 6anode; 7cathode.
Fig. 2. Assembly view of the oxygen meter prepared for measurements.
1- microprocessor; 2connection cable; 3probe body; 4small cylinder
that contains an electrolyte solution; 5oxygen permeable Teflon
membrane; 6solution vail.
The intensity of the electric current between the anode and the cathode varies in function of the
concentration of dissolved O2, therefore the value of the O2 concentration displayed by the oxygen
meter also changes.
1. The equation of transfer speed of oxygen in water
For pneumatic aeration equipment, the equation that describes the transfer speed of oxygen in
water has the following shape [5,6]:
L s 3
dC kg ak ( C C )
d m s
(1)
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where:dC
d transfer speed of dissolved oxygen [kg/m3s-1]; akL volumetric mass transfer
coefficient [1/s]; Csmass concentration of the transferable component at saturation (at equilibrium)
in the liquid phase [kg/m3]; Ccurrent mass concentration of the transferable component in the liquid
phase [kg/m3].
00 LaK
s sC C C C e
(2)
where C0 represents the concentration of oxygen dissolved in water at the time moment = 0.
It can be noticed from equation (1) that the transfer speed of oxygen in water depends on the
following factors:
- the specific area of interphase contact2
3
A ma
V m
;
- the coefficient of mass transferKL;
- the deficit of oxygen, namely the difference (Cs-C).
2. Method of solving the equation of transfer speed of oxygen in water
Equation (1) is an ordinary differential equation that can be solved using one of the following
methods: Euler method; Runge-Kutta method; Adams-Bashford method; Milne method; finite
differences method.
If Runge-Kutta method is used, the successive values of the dependent variable are computed
using a group of formulae expressed in function of the derivatives evaluated in predefined points. For
this purpose, the Runge-Kutta method uses a general relation of the following shape [7,8]:
1 1 1 2 2 .....i i n ny y a k a k a k (3)
where:
1
2 1 11 1
, ;
, ;
i i
i i
k h f x y
k h f x b h y c k
(4)
........................ 1 1,1 1 1,2 2 1, 1 1, ....n i n i n n n n nk h f x b h y c k c k c k (5)hstep size.
The coefficients ai, bi, cii are established using identification with the Taylor series expansion of
the function, where a certain number of terms is kept. Concurrently, the Taylor series expansion of
yi+1in the neighborhood ofxi is given by the relation:
2' "1 ...
2!i i i i
hy y hy y (6)
where 'i i iy f x y .If the first five terms of Taylor expansion are kept, the 4th order formula, the most known and used
Runge-Kutta formula, can be established [8,9,10]:
1 1 2 3 4
1 1 1 1
6 3 3 6i iy y k k k k (7)
or
1 1 2 3 41 2 26
i iy y k k k k (8)
where
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'1 1
12
23
4 3
, ;
,2 2
,2 2
,
i i i
i i
i i
i i
k h f x y k h y
khk h f x y
khk h f x y
k h f x h y k
(9)
The main advantage of the Runge-Kutta method consists in the eventuality of self-start, because
the computation of a new point of the integral curve requires the knowledge of a sole previous point.
The method has high accuracy, the approximation error of a step being of the order ofh5.
The main disadvantage of the Runge-Kutta method is the need to evaluate the function f(x,y) for
more values ofx at each step, that leads to the increase of the computing time.
For the studied case, relations (8) and (9) become:
1 1 2 3 41 2 26
i iC C k k k k (10)
11
2
23
4 3
,
,2 2
,2 2
,
i ii
ii
ii
ii
dCk f C
d
kdCk f
d
kdCk f
d
dC
k f kd
(11)
A time stepof a minute was chosen. The total computing time is equal to 120.
In order to develop a software program the following initial data has to be known:
- initial concentration of the oxygen dissolved in water for the temperature of t= 20oC;
C1= 7.72 mg/l;
- saturation concentration for the same temperature andp = 750 mmHg is Cs= 8.9 mg/l;
- duration of the oxygenation process = 120 min;
- the value aKL is established using the integral method for the first two time intervals: 0 15;
1530 using table 1:
-1s 1
L2 1 s 2
C C1
aK ln [min ]C C
(12)
where C1 and C2 denote the concentration ofO2 in water at the time moments 1 and 2.
If equation (12) is applied, it results that:
I) 1=0 2=15-1
L1 8.9 7.72
aK ln 0.0363[min ]15 0 8.9 8.30
(13)
II) 1=15 2=30 -1
L1 8.9 8.30
aK ln 0.0490[min ]30 15 8.9 8.53
(14)
Thus computations lead to a mean value of 0.0427 [min-1] for the coefficient aKL.
The graphical representation of the points of the function C=f() obtained after the computation
leads to the chart presented in figure 3.
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Fig. 3. Graphical representation of the function CO2=f()
3. The experimental setup
The setup was designed and built in the frame of the laboratory of the Department of
Thermotechnics, Engines, Thermic and Refrigeration Plants in order to research water oxygenation
processes[11,12]. The water from the public network is introduced in a tank (10) and the compressed
air spread in water using the fine bubble generator (FBG) (13) will lead to the increase of the
concentration of oxygen dissolved in water, increase conditioned by the working time of the FBG.
patm
1
mbar toC
mg/loC
220V
kWhV=24 dm3
530 500 470 400 600
240
500
2 3 4 5 6 7 8 9 11 12 10
A A
1100
1600
200
150
141315
a
bc
8
00
Fig. 4. Sketch of the experimental setup for researches regarding water oxygenation
1electro compressor with air tank; 2 - pressure reducer;3manometer; 4joint for exhausting of
air in the atmosphere; 5compressor feeder; 6rotameter; 7electric panel; 8measuring
instruments panel; 9pipe for the transport of the compressed air towards the FBG; 10water tank;
11mechanism for probe driving; 12oxygen meter probe; 13FBG; 14holder for the plant;
15control electronics (asupply unit, b- switch, c- control element).
The laboratory setup used for experimental researches (fig. 4) includes an electro compressor
with a 24dm
3
tank that supplies constant pressure compressed air towards a plexiglass tank containingwater from the public network. The setup is endowed with modern devices for the measurement of
pressure, temperature and flow rate of the air introduced in the FBG.
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4. Methodology of measurements, obtained experimental results
For a constructive version of FBG of rectangular shape with =0.5 mm nozzles, the measurements
are performed in eight stages. At the beginning of the first stage, fig. 4, the height of the water layer
over the FBG is hH2O = 500 mm, the probe is situated at hprobe = 250 mm with respect to the nozzle
plate, the initial O2 concentration being C0 =7.72 mg/l, the indication of the electric counter
E0 = 0.0325 kWh and water temperature t= 20.5oC. Pressure and flow rate of air that enters the FBG
are measured: p1=583.44 mmH2O; V
= 600 dm3/h, values that are kept constant during
measurements. After a functioning of the FBG for 1=15, it is stopped and O2 concentration is
measured by rotating the probe in water. The FBG is put in functioning again and air is blasted in
water during 15, the total time being 2=30; O2 concentration is measured.
Similarly, the time values of3=45, 4=60, 5=75, 6=90, 7=105, 8=120 are
reached. Finally, the concentration of O2 dissolved in water after two hours of FBG functioning is
measured. The measured values are presented in table 1.
Table 1.Variation of the O2 concentration in function of the functioning time of the FBGValues of the concentration of O2 dissolved in water[mg/l]
=0 1=15 2=30 3=45 4=60 5=75 6=90 7=105 8=120
7.72 8.30 8.53 8.72 8.78 8.84 8.85 8.85 8.85
The chart CO2=f(), curve no.3 from figure 5, is traced based on data presented in table 1.
Fig. 5. Variation of the concentration of oxygen dissolved in water
1-chart based on theoretical results; 2- chart based on experimental data.
Figure 5 proves good coincidence between theoretical models and obtained experimental results.
5. Conclusions
1. It can be noticed that theoretical results regarding the variation of the concentration of oxygendissolved in water obtained by Runge-Kutta method are more accurate compared with experimental
results.
2. The deviation between the two theoretical methods, Euler and Runge-Kutta, is of only 0.1%because the computation step is small enough to guarantee good results in both situations.
3. The deviation between theoretical and experimental values is of 0.3% in the case ofRunge-Kutta method and 0.4% in the case of Euler method, fact that confirms the correctness of
experimental measurements.
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4. Unconventional technology was used in order to manufacture the nozzle plate, namely thenozzles were manufactured by electro erosion, fact that brings certain advantages.
5. A rectangular shape FBG with 37 0.5 nozzles was used; the flow rate of the air blown in thewater mass is thus better controlled and the pressure loss on the FBG is less than in the case of porous
diffusers.
Acknowledgements
The work has been funded by the Sectoral Operational Programme Human Resources
Development 2007-2013 of the Romanian Ministry of Labour, Family and Social Protection through
the Financial Agreement POSDRU/88/1.5/S/60203 and POSDRU/107/1.5/S/76903.
References
[1] G. Oprina, I. Pincovschi, Gh. Bran, Hydro-gas-dynamics of aeration systems equipped with fine
bubble generators (in Romanian), Politehnica Press Publishing House, Bucharest, 2009.
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Politehnica University of Bucharest, Faculty of Power Engineering, 1999.
[3] D. Robescu a.o., Reliability of processes and plants for water treatment and purification (in
Romanian), Technical Publishing House, Bucharest, 2002.
[4] Instruction manual of the oxygen meter manufactured by HANNA Instruments, Canada, 2010.
[5] G. Mateescu, Hydro-gas-dynamics of fine bubble generators (in Romanian), PhD Thesis,
Politehnica University of Bucharest, Faculty of Mechanical Engineering and Mechatronics,
Bucharest, 2011.
[6] G. Oprina, Contributions of the hydro-gas-dynamics of porous diffusers (in Romanian), PhDThesis, Politehnica University of Bucharest, Faculty of Power Engineering, 2007.
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Value Problem, W.H. Freeman Press, San Francisco, 1975.
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[10] G. Palmer, Technical Java: Applications for Science and Engineering, Editura Prentice Hall,
ISBN 10: 0131018159/0-13-101815-9, Upper Saddle River, New Jersey 07458, 2003.
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[12] N. Bran, Gh. Bran, G. Mateescu, Al. Ptulea, Water oxigenation, Bulletin of th e Polytechnic
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