(09)Reasearches Regarding the Measurements of the Dissolved Concentration in Water

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

[email protected],

[email protected],

[email protected]

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.

[2] I. Pincovschi, Hydrodynamics of disperse gas-liquid systems (in Romanian), PhD Thesis,

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.

[7] L. F. Shampine, M. K. Gordon, Computer Solution of Ordinary Differential Equations: The Initial

Value Problem, W.H. Freeman Press, San Francisco, 1975.

[8] I. Dancea, Computer programming for solving technical and scientific research problems (in

Romanian), Dacia Publishing House, Cluj, 1973.

[9] N. Bakhvalov, Methodes numeriques, Edition de Moscou, Traduction francaise Edition Mir,

1976.

[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.

[11] N. Bran, Gh.Bran, G. Mateescu, Research Regarding a New Type of Fine Bubble Generator,

Romanian Review of Chemistry, vol. 61, no.2, 2010, pp. 196-199, ISSN 0034-7752.

[12] N. Bran, Gh. Bran, G. Mateescu, Al. Ptulea, Water oxigenation, Bulletin of th e Polytechnic

Institute of Jassy, tome LVI (LX) fasc.3b, POLITEHNIUM Publishing House 2010, pp.78-83.

(09)Reasearches Regarding the Measurements of the Dissolved Concentration in Water

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