Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane

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Ozone mass transfer studies in a hydrophobized ceramic membrane contactor: Experiments and analysis Stylianos K. Stylianou, Margaritis Kostoglou, and Anastasios I. Zouboulis Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01446 • Publication Date (Web): 23 Jun 2016 Downloaded from http://pubs.acs.org on June 24, 2016

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Industrial & Engineering Chemistry Research

1

Ozone mass transfer studies in a hydrophobized

2

ceramic membrane contactor:

3

Experiments and analysis

4 Stylianos K. Stylianou‡, Margaritis Kostoglou‡, Anastasios I. Zouboulis*‡

5 ‡

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Section of Chemical Technology, School of Chemistry, Aristotle University,

7

GR-54124 Thessaloniki, Greece

8 9 10

Keywords: hydrophobized a-Al2O3 membranes; bubble-less ozonation; mathematical modeling; ozone properties;

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Abstract

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Bubble-less ozone contact with water was carried out using a tubular hydrophobized a-Al2O3

14

membrane to investigate the feasibility of this process and also, to evaluate the effect of liquid

15

flow rate and the different experimental conditions on ozone transfer. Membrane contactor

16

showed increased mass transfer fluxes of ozone, ranging from 4.8·10-8 to 2.5·10-7 mol/m2·s with

17

increased liquid flow velocity. Specific ozone dosages, ranging from less than 0.1 up to 2.7

18

mg/L, were achieved by adjusting liquid flow velocity and ozone concentration in the gas phase.

19

A mathematical model recognizing all the occurring phenomena and extracting physically the

20

relevant parameters was developed. Specific ozone properties were calculated, under the tested

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experimental conditions, by properly fitting the experimental and theoretical data. This model

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also permits the further exploitation-extrapolation of data to different experimental devices and

3

conditions by adopting from literature data, or by experimentally determining the values of major

4

ozone physical parameters, such as D, s, etc., affecting the modeling results.

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1. Introduction

2 3

The intensification of water and wastewater treatment processes by modifying conventional

4

and widely implemented technologies, in order to achieve more sustainable and environmental

5

friendly results, is a major challenge for today’s environmentalists and engineers.1 The

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development of advanced equipment and the optimization of treatment processes are expected to

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offer significant improvements, such as higher energy efficiency, smaller footprint, minimum

8

environmental impact etc. Membrane processes holding the specific characteristics of high

9

selectivity, good stability and improved operational flexibility, could be among the most

10

important processes, offering innovate and efficient solutions for most water treatment

11

problems.2

12

Ozone and ozone-based advanced oxidation processes are successfully applied in several

13

applications of water/wastewater treatment field, such as in disinfection, in the oxidation of

14

refractory organic compounds, color, odor or taste removal etc.3 However, the major drawbacks

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of ozonation are the relatively high energy consumption (around 10 Kw/Kg O3)

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resulting cost increase, rather large footprint treatment unit and also certain operational problems

17

related with the dispersion of gas/ozone bubbles in water and wastewaters.5 In most large-scale

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applications, ozone transfer to water is carried out by bubble columns, injectors or gas diffusers.

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Common characteristic of all these techniques is the direct application of ozone/gas mixture to

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the water through the formation of bubbles; however, in these cases gas-liquid transport is a rate-

21

limiting process, depending mainly upon the size and distribution of ozone bubbles.6 Of

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particular important is considered the formation of even fine gas bubbles, especially in the

23

presence of surfactants, leading eventually to the creation of intensive foams and emulsions,


4

and the

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which are difficult to be controlled by the application simple mechanical measures and can create

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operational problems, such as over-flooding from the reactor tank. An alternative approach that

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can provide a solution to the aforementioned problems is the implementation of specific

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membrane contactors to optimize the gas-liquid contact and to improve the mass transfer

5

between these phases.

6

Membrane contactors, on contrary with the basic principles of separation membranes, do not

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offer any selectivity, working just as a convenient barrier between the two phases, keeping them

8

separated and allowing their contact in a large (as comparative to volume) and well-defined

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interfacial area.7 The transfer of species between the respective phases is driven only by the

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concentration gradient (i.e by diffusion) and hence, mixing and dispersion phenomena do not

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expected to influence this process. Membrane contactors are currently applied, or have been

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tested in several industrial applications of liquid-liquid extraction, or gas-liquid absorption.8,9

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Recently, certain studies have also presented the use of membranes for the bubble-less ozonation

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in various applications, such as NOM removal

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pointing out that the use of membranes contactors in these cases may offer several operational,

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such as independent gas/liquid control, optimal ozone dosage, avoidance of flooding, compact

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equipment, etc. and economical advantages, such as lower operational cost by limiting ozone

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losses, as compared with the conventional methods for ozone application.

10

, dyes destruction

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, iodide oxidation

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etc.13,

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However, the main challenge in the implementation of membrane contactors, regarding

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ozonation, is the highly reactive character of ozone, which results to the relatively fast

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deterioration of most organic and polymeric materials, commonly used for the preparation of

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most membranes in use. Shanbhag et al.14 presented the use of silicone membranes as ozone

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contactors for the destruction of organic pollutants, achieving removals up to 80%; however, a


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rapid membrane material failure was observed, confirming that only chemically inert membranes

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can be applied in such oxidative processes.

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Polyvinyl-idene-fluoride (PVDF), Polytetra-fluoro-ethylene (PTFE) 16

and ceramic membranes

17

15

, Shirasu porous glass

4

(SPG)

can be potentially applied as alternative ozone membrane

5

contactors. Additionally, ceramic membranes can offer high chemical, thermal and mechanical

6

stability and sufficient porosity structure; nevertheless, most inorganic membranes are

7

characterized by intense hydrophilic behavior, due to the presence of hydroxyl (OH–) groups on

8

their surfaces and hence, water is able to penetrate into their pores, due to capillary forces. The

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level of capillary pressure is a function of pore diameter and can reach quite high values in the

10

case of hydrophilic microporous media, therefore creating operational problems in the respective

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gas transfer through them.18 Alternatively, the use of hydrophobic membranes has been proved

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more suitable and efficient for gas-water contact, due to the lower mass transfer resistance they

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are presenting.19,20 The hydrophobicity of ceramic membranes can be relatively easy achieved,

14

through the appropriate chemical modification, or by their surface morphology modification, or

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by the combination of both methods.21

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In the present work hydrophobized (i.e. with high contact angle values of around 140°) α-

17

Al2O3 ceramic membranes were applied as contactors to study the transfer of ozone to deionized

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water. The main objectives of this study were to investigate the feasibility of utilizing ceramic

19

membranes, after appropriate surface modification, for the bubble-less ozonation and to develop

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the respective mathematical model, describing the occurring phenomena, commonly taking place

21

during ozone transfer. The influence of major parameters (i.e. liquid flow velocity, pH, ionic

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strength, temperature, and ozone concentration in the gas phase) on ozone gas transfer was

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examined.


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The essential ozone properties in water, such as diffusivity, ozone self-decomposition reaction

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order and rate, solubility etc., were determined under different experimental conditions, by

3

properly fitting the mathematical model to the specific experimental results. It is worth noting

4

that several previous studies have also estimated the aforementioned ozone properties, mostly

5

through batch or semi-batch experiments

6

attempt to determine them by properly fitting modeling and experimental data, obtained through

7

continuous-flow experiments with the use of a membrane contactor. Furthermore, the developed

8

mathematical model is expected to allow the extrapolation of data to different geometries and

9

experimental conditions and can provide the fundamental basis for the future design of bubble-

10

less ozonation processes, addressing specifically the treatment of emerging water treatment

11

problems, e.g. micro-pollutants.

22-26

; however, this study is considered to be the first

12 13

2. Material & Methods

14 15

2.1. Hydrophobized α-Al2O3 ceramic membranes

16 17

Chemically modified tubular ceramic (alumina) membranes were used for evaluating the

18

ozone (mass) transfer to deionized water through diffusion phenomena. The tubular ceramic

19

substrate consists of three subsequent α-Al2O3 layers with a pore diameters of 900 nm (base

20

support), 500 nm (intermediate layer) and 100 nm (microfiltration top layer), respectively. This

21

specimen has length of 340·10−3 m, inner diameter (ID) of 7.8·10−3 m, outer diameter (OD) of

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14·10−3 m, and surface of 8.5·10−3 m2. The hydrophobic functionalization of internal surface

23

layer of this membrane was achieved via the application of slip casting technique, using


6

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trichloro-methyl-silane (triClMS) as modifying agent. As presented in a previous study, triClMS

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showed the relevant highest hydrophobicity (i.e. water contact angles from less than 39o for the

3

original-unmodified membrane were up to a maximum of 133o-143o) among the examined four

4

different hydrophobic polymers and thus, it was selected for the development of surface

5

modified ozone membrane contactor in this case

6

summarized in Table 1.

7

(TABLE 1)

27

; the specific membrane properties are

8 9

2.2. Experiments for the bubble-less ozone transfer to water

10 11

The experimental set-up for studying the contact of ozone-water through the ceramic

12

membrane is shown in Scheme 1. Housing of the ceramic membrane was made from acrylic

13

glass and was properly designed in order to ensure air- and water-tight conditions within the

14

module. The dimensions of membrane module were 16·10−3 m inner diameter and 36·10−3 m

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length. The space formed between the ceramic membrane and the inner surface of the module

16

had the thickness of 1·10−3 m. Ozone resistant Viton O-rings were used for the sealing of

17

membrane and of the outer surface of the module, while PTFE tubing was used for the flow of

18

ozone-enriched gas mixture and of water.

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Deionized water was driven within the membrane via a peristaltic pump (Watson Marlow,

20

model 503U), while ozone gas mixture was introduced at the space formed by the outside surface

21

of the membrane and the inside of the acrylic glass module and the gas-water contact was taking

22

place through the membrane inner surface. Ozone-oxygen gas mixture was produced by an

23

ozone generator (model TOGC2A, Ozonia Triogen), feed with pure oxygen. In order to achieve


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stable ozone concentrations in the gas phase a by-pass (1 L/min) was adapted to the off-gas line

2

of the contactor. A needle valve was used to apply a low pressure difference between the two

3

phases, in the range of 1·10−3 MPa, in order to achieve the transfer of ozone without the

4

formation of bubbles (bubble-less ozonation). Practically, mix and dispersion phenomena do not

5

occur between the two phases and the transfer of ozone takes place only through diffusion. The

6

pressure difference was monitored by a digital pressure meter (WIKA, model S-10), while the

7

flow rate of ozone-oxygen gas mixture was adjusted and measured by a flow meter equipped

8

with a needle valve (Aalborg, model PMR-1).

9

Ozone concentrations in the gas phase were determined by the potassium iodide method,

10

whereas dissolved ozone concentrations in the water leaving the module were measured with the

11

Indigo method.28 The water phase circuit was entirely closed and the dissolved ozone was

12

measured immediately after the membrane module in order to avoid any ozone losses to air and

13

also, the impact of ozone self-decomposition after leaving the experimental set-up.

14

The influence of different experimental parameters to ozone transfer, i.e. liquid flow velocity,

15

pH, ionic strength, temperature, ozone concentration in gas phase etc., was examined. A

16

thermostatic cabinet (Lovibond) was used to set and maintain the temperature of the liquid

17

phase. The pH of water was adjusted by adding appropriate amounts of H2SO4 or NaOH

18

solutions (0.1 N) and measured with a Jenway pH-meter (model 3540), while the ionic strength

19

was properly adjusted, when necessary, by the addition of NaCl solution (1 N).

20

Each experiment for the determination of ozone transfer to deionized water was performed in

21

triplicate and the average values are presented in the Figures. The average variation of dissolved

22

ozone concentrations measurements was approximately within 5% and the respective error bars

23

are not presented in the respective figures.


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(SCHEME 1)

2 3

3. Experimental Results

4 5

3.1 Technical feasibility of the examined process

6 7

The constructed membrane module and the modified ceramic membranes were found to

8

operate appropriately. The membrane module (from acrylic glass), the O-rings (Viton) and the

9

used tubing (PTFE) have showed excellent ozone resistance and also, it was observed that the

10

hydrophobic character of modified membrane was not influenced by its contact with relatively

11

high concentrations of ozone throughout the three months experimental period. In addition, post-

12

experiments proved that it was possible to retrieve at its initial extend, the hydrophobicity of

13

damaged hydrophobized membranes (e.g. when performed by heating at 250° C for 30 min), by

14

re-applying the same modification procedure. The ability to use ceramic membranes for long-

15

term operational periods and even to re-modify them, when the hydrophobic layer would be

16

damaged or deteriorated, can greatly increases the feasibility of this process, as it considerably

17

limits the respective maintenance costs.

18

The experiments, regarding ozone transfer via the modified ceramic membranes, also

19

revealed/confirmed the advantages of this process, when compared with the conventional

20

gas/liquid contacting methods. Besides the expected benefit of non-forming bubbles, which has

21

as a consequence the uniform distribution of ozone, other advantages were also noticed, such as

22

the independent flow adjustment for the gaseous and water phases, the easier recycle of gas

23

stream leaving the contactor (due to the complete absence of moisture, as the gas and aqueous


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streams are separate) and the optimization of ozone dosage applied to specific water needs by

2

properly adjusting liquid flow velocity and ozone concentration in the gas phase.

3

However, a difficulty was observed in achieving and maintaining the relatively low pressure

4

difference (Trans Membrane Pressure/TMP 1·10−3 MPa), required for the bubble-less ozone

5

transfer, as for higher TMPs the immediate formation of bubbles was observed, due to the

6

hydrophobic character of membranes’ surface. It is believed that this operational problem will be

7

even more intense in full-scale operations and subsequent pilot-plant experiments are planned to

8

further optimize it.

9 10

3.2 Effect of liquid flow velocity on ozone transfer rate

11 12

The influence of liquid flow velocity on ozone transfer through the α-Al2O3 ceramic membrane

13

was investigated at pH 6, temperature 15° C and stable ozone concentration in the gas phase 60

14

mg/L (± 3%). Figure 1 presents the ozone mass transfer fluxes as a function of liquid flow

15

velocity. The membrane module showed increased mass transfer fluxes, ranging from 4.8·10-8 up

16

to 2.5·10-7 mol/m2·s, with increased liquid flow velocity. The values and trend of the respective

17

molar fluxes are comparable to those calculated by previous relevant studies

18

force for ozone transfer through the membrane is the concentration difference between the two

19

phases. During the application of higher flow velocities of aqueous phase the resistance to ozone

20

transfer at the gas-water inter-phase was decreased and thus, higher ozone fluxes were able to be

21

achieved.

22

(FIGURE 1)

10,29

. The driving

23


10

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3.3. Effect of different experimental parameters on ozone transfer to water

2 3

Figures 2-4 present the dissolved ozone concentrations measured immediately after the

4

membrane contactor, as a function of liquid flow velocity for different experimental conditions.

5

Ozone concentrations ranging from less than 0.1 mg/L (at pH 9, T 25° C, velocity 0.002 m/s) up

6

to 2.7 mg/L (at pH 4, T 15° C, velocity 0.002 m/s) were determined. Furthermore, a similar trend

7

between the ozone concentration and the liquid flow velocity was observed (i.e. lower ozone

8

concentrations were determined at higher liquid velocities) for all the performed experiments,

9

except for those performed at pH 9, as subsequently explained. The influence of liquid flow

10

velocity on dissolved ozone concentration in this phase was found to be greater for lower values

11

of this parameter (i.e. for higher hydraulic retention times in the membrane), while for velocities

12

higher than 0.03 m/s the ozone concentrations remained almost constant.

13

Based on these results, pH seems to present the greatest impact on the measured dissolved

14

ozone concentrations. The increase of pH reduced the ozone concentrations, measured at the

15

outlet of membrane module. Ozone concentrations at pH 4 were around 1.5 times higher, as

16

compared to the respective values at pH 6, while the decrease of measured ozone concentration

17

was much higher at pH 9. Especially, at alkaline conditions and low liquid flow velocities the

18

dissolved ozone concentrations were almost undetectable. (FIGURE 2)

19

The addition of NaCl solution to deionized water and thus, the obtained higher ionic strength

20

values, resulted to a decrease of dissolved ozone concentrations, by around 1.25 times. The ionic

21

strength influences the equilibrium concentration of ozone between the gas and water phase, as

22

described by Henry law.24 On the other hand, an increase of ozone concentration in the gas phase


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greatly increased the dissolved ozone concentrations in the liquid phase, due to the higher

2

diffusion rate of ozone. (FIGURE 3 & 4)

3

The temperature seemed to present the relatively lower impact on the measured ozone

4

concentrations. Under similar conditions, ozone concentrations were decreased by around 1.1

5

times with every 5° C increase of temperature (Figure S1).

6 7

4. Model Development

8 9

The process under examination is typically described in the literature through the global mass

10

transfer coefficients.16 However, the resulting coefficients are rather empirical parameters and

11

have the disadvantage that they cannot be scaled-up to different devices or experimental

12

conditions. A different methodology, based on the application of first principles, was followed in

13

this study, recognizing all the occurring phenomena and extracting physically the relevant

14

parameters, allowing the extrapolation of data to different situations. The model will be derived

15

at two stages: (1) Initially, a single mass transfer model will be developed, by admitting a closed

16

form solution. This model is needed in order to check, whether the experimental data can be

17

efficiently described, by considering only the case of mass transfer. (2) In the 2nd stage the initial

18

model will be further enhanced, by considering also the ozone decomposition reaction. In the

19

later case the model will be solved numerically.

20 21

4.1. Mass transfer model

22


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1

The driving force for the dissolution of ozone in water is the concentration difference between

2

gas and liquid phases. However, a major complication arising in this case is that the ozone

3

concentration in both gas and liquid phases can vary along the flow, requiring the detailed

4

solution of the corresponding mass balances. Fortunately, ozone excess in the gas phase during

5

the present experiments ensures its constant concentration in the gas phase, rendering much

6

simpler the model development task. The solubility of ozone in the liquid Ceq is related to the

7

partial ozone pressure Pf in the gas phase through the Henry’s Law equation: Ceq= H Pf, where H

8

is the Henry coefficient. The gas transfer to a liquid via a microporous wall is considered as a

9

multi-phase system and takes place during three subsequent steps: (a) diffusion in gas phase, (b)

10

transfer thought the pores to the inner surface of the membrane, and (c) diffusion to water.

11

The contribution of gas diffusion step is negligible, since the diffusion coefficient in gas is

12

generally around four orders of magnitude less, than the diffusion coefficient in water.23,30

13

However, the liquid phase pore diffusion step has to be specifically considered. The pores are

14

hydrophobic, but this does not mean that there is no even a partial penetration of water phase

15

inside the pores. When δ is the average liquid penetration length, which of course is smaller than

16

the porous wall thickness, then the mass transfer coefficient for the pore diffusion step is simply

17

given as hp= D/δ (noting that the liquid is motionless in the pores), where D is the diffusivity of

18

ozone in water.

19

The ozone is released to the main liquid flow through the edge of inner surface of membrane

20

pores. The concentration field in this case is considered locally as 2-dimensional, but the

21

characteristic pore size (e.g. diameter) and the intra-pore distance are in the order of 1 µm,

22

allowing the homogenization of mathematical problem at axial and azimuthal directions and

23

assuming the variation of ozone concentration only for the radial direction. The mass transfer of


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ozone in the flowing liquid is regarded to be performed through a convection-diffusion

2

mechanism. Considering also the respective Reynolds number, it was shown that the velocity

3

profile of liquid within the membrane (in this case: tubular) corresponds to laminar flow for all

4

experiments.

5

In principle, the steady state partial differential ozone conservation equation, including

6

convection and diffusion terms, must be solved to evaluate the respective mass transfer extent.

7

Nevertheless, it can be shown that under the particular experimental conditions, the so-called

8

Leveque solution for the mass transfer, regarding a laminar flowing liquid in a tube, can be

9

employed. Denoting as d the internal diameter of the tube, then R=d/2 is the corresponding

10

radius, U the average fluid velocity, z the distance from the entrance of the tube and L the total

11

tube length and then, according to the Leveque solution the corresponding average Sherwood

12

number is given as 31:

13 14

Sht= α (R/L)1/3 Pe1/3

(1)

15 16

Several values for the constant α can be found in the literature, but this simply has to do with

17

the respective definition, used for Peclet number (i.e. based on the radius, or on the diameter) and

18

by the specifically applied boundary condition (i.e. considering constant flux, or constant

19

concentration) on the tube wall.32 In the present work Pe is defined as (2 R U/D) and the constant

20

concentration boundary condition is employed, as being more relevant to the problem. The

21

condition for validity of Equation (1) is that L/R< Pe/50, i.e. that the ozone profile has not reach

22

the center of the tube, which can be shown to be true for all the experiments of present work. The

23

pore diffusion and the tube diffusion-convection resistances to mass transfer are acting in series;

24

therefore, the total Sherwood number is given as:


14

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1 2

Sh= (1/Sht + 1/Shp)-1

(2)

3 4

Where: Shp= d/δ, i.e. the ratio of the tube radius to the pore length penetrated by liquid. A

5

simple mass balance of the solute along the tube leads after appropriate calculations to the

6

following expression for the determination of solute concentration Cf at the tube outlet:

7 8

Cf = Ceq + (C0 − Ceq ) exp(−

4LDSh ) Ud 2

(3)

9 10

Where: C0 is the feed ozone concentration. The above solution is accurate at both limits of

11

domination, i.e. at the pore and tube mass transfer, and it is expected to be exact also in any other

12

intermediate case.

13 14

4.2. Mass transfer and reaction model

15 16

In principle, the partial differential equation of solute conservation, including diffusion,

17

convection and reaction terms, must be solved, noting that this solution can be performed only

18

numerically. In order to simplify this complex approach, a perimeter averaged 1-dimensional

19

approximate model will be further developed. The key of this model is the assumption of

20

additivity, regarding transfer and reaction phenomena, occurring simultaneously. Transfer is

21

assumed to follow the aforementioned Leveque relation, whereas the reaction rate is assumed to

22

be a function of the cross-sectional averaged solute concentration. Considering also that this

23

approach of independently handling mass transfer and reaction rate, is regarded as a common


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Page 16 of 40

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approach in chemical engineering practice. Assuming a reaction of order n, then the governing

2

equation for the perimeter averaged ozone concentration C is:

3 4

U

dC 4DSh = (Ceq − C) − KCn dz d2

(4)

5 6

Where: K is the reaction rate constant. The above ordinary differential equation must be solved

7

with the initial condition C= C0 at z= 0 in order to obtain the required value Cf, as C= Cf at z= L.

8

In the particular case of 1st order reaction, the Equation (4) was solved analytically to obtain the

9

following expression for the prediction of outlet ozone concentration:

10 11

Cf = C0 e − BL +

A Ceq (1 − e − BL ) B

(5)

12 13

where: A =

4DSh 4DSh K and B = + 2 Ud Ud 2 U

14 15

An analytical solution is also possible for n= 0 (zero order reaction), but this case is irrelevant

16

to the particular reaction studied here. For any other value of n the Equation (4) must be solved

17

numerically. This can be done quite easily by employing the Euler explicit numerical

18

discretization scheme with a fine mesh, and programmize it directly on a spreadsheet. In

19

particular, the discretization at N points with step δt= L/N the following set of differential

20

equations results for i= 0 to N-1 to equation (6):

21 22

C(i +1) = C(i) + δ t

4DSh K (Ceq − C(i) ) − δ t C(i)n 2 Ud U


(6)

16

Page 17 of 40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 2

with C(0)= Co and Cf= C(N).

3 4

It is noted that this model is a reduced order model; thus, it conveys all the parametric

5

dependence of the original problem, by admitting extraction of parameters from the experimental

6

data and by using them for different conditions. The only simplification refers to the accuracy of

7

solution of mathematical problem and leads to a final model of an order of magnitude simpler,

8

than the original one, based on partial differential equations.

9 10

5. Data analysis & discussion

11 12

5.1. Influence of ozone self-decomposition on dissolved ozone concentration

13 14

Initially, the influence of ozone self-decomposition on the measured ozone concentrations in

15

the liquid phase was investigated, by considering also the necessity for including this parameter

16

or not in the respective mathematical description. This was performed, by comparing three

17

different fittings between the theoretical and the experimental data (i.e. for pH 6, T 20° C, zero

18

ionic strength), where the mass transfer model, or the mass transfer and reaction model (1st and

19

2nd reaction order) were applied (Figure 5). In case that only diffusion (Equation 3) was taken

20

into consideration during ozone transfer, the model was unable to predict correctly the resulting

21

ozone concentrations. This holds for all the experiments of present work, i.e. the final ozone

22

concentration - flow rate dependence does not correspond to those predicted by the mass transfer

23

model of Equation 3.


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 40

1

However, the theoretical and experimental results were comparable at relatively high liquid

2

velocities, while for velocities lower than 0.001 m/s the concentrations calculated by the

3

mathematical model were found twice as high, when compared with the respective experimental

4

values. The computations were performed for a liquid penetration (in the membrane) of 100 µm.

5

Increasing this value in order to make significant the contribution of intra-pore diffusion leads to

6

even worse fitting of the data. Therefore, a different source of model deviation from the

7

experiments must be found. (FIGURE 5)

8

The appreciable impact of ozone decomposition on resulting ozone concentrations in the

9

membrane module, especially for higher hydraulic retention times (i.e. for lower liquid

10

velocities) led to the conclusion that this cannot be excluded from the mathematical description

11

of the process. In this case, the use of mass transfer and reaction model, following a 1st order

12

reaction (Equation 5) for the decomposition of ozone, was found to improve the correlation

13

between theoretical and experimental data, but yet not to an accepted level. Only when a 2nd

14

order reaction (Equation 6) was used, the obtained results presented a satisfactory fit. To

15

summarize, the rate and order of ozone decomposition greatly affects the dissolved ozone

16

concentrations, especially for low liquid velocities; therefore, it is necessary to be also

17

considered in the mathematical description for the correct prediction of dissolved ozone

18

concentrations.

19

Figure 6 displays ozone concentrations as calculated by the mathematical model, i.e. the

20

diffusion and self-decomposition rate in respect to dimensionless membrane length. As described

21

by Equation 6, the ozone diffusion rate depends on the concentration difference between the gas

22

and liquid phases. During the water transfer across the membrane length, ozone concentration in

23

the liquid phase is expected to increase, reaching values close to the equilibrium concentration


18

Page 19 of 40

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1

and thus, the concentration difference: Ceq - C(i) (i.e. the moving force in this case) is getting

2

smaller, reducing the mass transfer rate of ozone. On the other hand, the increase of dissolved

3

ozone concentration across the membrane length increases the decomposition rate of ozone, as

4

described by the 2nd term of Equation 6. Therefore, the ozone concentration at each point of the

5

membrane length is resulting by the subtraction of decomposed ozone from the ozone

6

transferred, due to diffusion.

7

(FIGURE 6)

8 9

5.2. Determination of ozone properties

10 11

After the completion of ozone transfer experiments and the selection of parameters that would

12

be included to the mathematical model, the optimal fitting between theoretical and experimental

13

data was investigated in order to determine specific ozone properties. Data fitting was selected to

14

be accomplished rather manually, than applying the most commonly used method of least

15

squares. Least squares method provides the best fit by minimizing the sum of squared

16

differences, between measured and fitted values

17

concentration of ozone is depended on several (independent) variables, the satisfactory data

18

fitting is possible with many different combinations, although without presenting any physical

19

meaning. As illustrated in Equation 6, the major parameters affecting ozone concentrations,

20

provided by the mathematical model, are: (1) diffusion coefficient, (2) equilibrium concentration

21

(which depends on ozone solubility), and (3) ozone self-decomposition order and rate. The

22

physical correctness of modeling results was secured, by finding out the best fit in a specific

23

range of aforementioned parameters. A wide range of parametric values were selected, based on

33

; however, in our case, where the


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 40

1

the results presented by several previous relevant studies.24,26,30,34-37 Figure 7 presents examples

2

of successful fittings between theoretical and experimental data for different experimental

3

conditions, noting that the developed mathematical model was able to predict satisfactorily the

4

dissolved ozone concentrations in all examined cases. More examples of relevant successful

5

fittings are included in the Supporting Information section (Figure S2).

6

(FIGURE 7)

7

Ozone properties, as calculated by the mathematical model, are provided in the Supporting

8

Information (Table S1): diffusivity 1.55 – 2.2·10-9 m2/s, ozone equilibrium concentration 5.5 - 26

9

mg/L, dimensionless coefficient factor 2 - 4.3, ozone self-decomposition reaction order 1 - 2 and

10

rate 9·10-4 - 8·10-1 (1/s·(L/mg)(n-1)). The further analysis of obtained data demonstrates the effect

11

of each particular experimental condition to the parameters obtained by the mathematical model.

12

The pH of deionized water was found to influence mainly the decomposition of ozone (Table 2).

13

For all the examined temperatures the decomposition of ozone followed a 2nd order reaction

14

kinetics at pH 4 and 6 (except for the experiments performed at pH 6 and T 15o C, where the

15

reaction order was found 1.5), while at pH 9 the decomposition of ozone was found to follow 1st

16

order kinetics. (TABLE 2)

17

The reaction rate constant at acidic and neutral conditions was in the range of 10-4 s-1·(L/mg)-1

18

and it was approximately 3 times higher at pH 6, as compared to pH 4, while for pH 9 was

19

dramatically increased (around 10-1 s-1). The stability of ozone in water depends strongly on the

20

pH value of water, because the presence of hydroxide ions act as initiators (or promoters) for the

21

ozone decomposition process 38. The ionic strength and the ozone concentration in the gas phase

22

practically affecting only the equilibrium concentration of ozone (Table 3). The equilibrium

23

concentration of ozone at the gas/liquid interphase can be described by Henry’s law in respect


20

Page 21 of 40

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1

with the ozone concentration in the gas phase, i.e. Ceq = CO3_gas /s, where s is the dimensionless

2

partition coefficient for ozone. Therefore, an increase of ozone concentration in the gas phase

3

can increase also the equilibrium concentration of ozone in the liquid phase. On the other hand,

4

an increase of ionic strength decreases the solubility of ozone (leading to higher partition

5

coefficient) and thus, reduces the equilibrium concentration of ozone. (TABLE 3)

6

Temperature is affecting ozone diffusivity, decomposition rate constant and ozone solubility in

7

water (Table 4). The increase of temperature increases also the diffusivity of water, due to the

8

greater mobility of water molecules and also, increases the ozone decomposition rate, due to

9

lower energy required for the reaction of ozone with hydroxyl ions. The diffusivity of ozone was

10

increased by around 1.2 times, the decomposition rate constant increased by around 1.5 times,

11

while the ozone equilibrium concentration was decreased by around 1.15 times with every 5° C

12

increase of temperature. These trends are physically relevant (i.e. diffusion coefficient and

13

reaction constant increases and gas solubility decreases with the increase of temperature),

14

confirming the validity of this methodology for obtaining the respective values of these

15

parameters. (TABLE 4)

16 17

5.2. Comparison of the ceramic membrane contactor with other ozone transfer systems

18

According to the respective literature, a hypothetical scenario was examined to compare the

19

necessary volumes required to dose an equivalent amount of ozone in the same water matrix

20

between the ceramic membrane contactor examined in the present study, a conventional ozone

21

transfer system (in this case: a bubble column) and a PVDF hollow fiber contactor. Pines et. al39

22

showed that a bubble column with 12 m3 volume, 2 m2 footprint and 6 m height, using ozone

23

gaseous concentration 87.6 mg/L, 80% mass transfer efficiency, water flux 85 m3/h/m2 and


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 40

1

without chemical reaction, is required to achieve an ozone dose of 2 mg/L for a flow rate of 4000

2

m3/d, whereas only a 0.15 m3 hollow fiber membrane contactor, using PVDF fibers with 1.8 10−3

3

m inner diameter and 20 cm-1 interfacial area at 2000 Reynolds number, is required to dose the

4

same amount of ozone. Similar experimental conditions, with 61.3 mg/L mean ozone

5

concentration in the gaseous phase (i.e. 87.6 mg/L ozone concentration in the gaseous phase and

6

40% mass transfer efficiency40), were considered for the mathematical model developed in the

7

present study. A multi-channel typical ceramic membrane with 1.2 m length, 51·10−3 m outer

8

diameter, 3.3·10−3 m channel diameter, 85 channels per membrane and 1·10−3 space between the

9

membrane and the inner surface of the housing module was used for the design of ozonation

10

process in this study and the respective modeling results are presented in Figure 8, showing that

11

a scale-up of this process is feasible in the examined case. A liquid flow velocity of 0.085 m/s,

12

corresponding to 283 Reynolds number, is required to achieve 2 mg/L ozone concentration at the

13

outlet of the contactor module and thus, a ceramic membrane contactor with around 1.9 m3

14

volume is needed. Therefore, the designed ceramic membrane contactor is approximately six

15

times smaller, when compared to the bubble column; however, one order of magnitude higher,

16

when compared with the hollow fiber contactor, as presented by Pines et. al. This is because the

17

bigger inner diameter of ceramic membranes reduces the respective ozone mass transfer rate and

18

thus, larger contactor volume is required in this case to achieve the same ozone dose. This

19

conclusion points out that the difficulty to produce ceramic membranes with smaller inner

20

diameter is considered as the major drawback for the implementation of ceramic membrane

21

contactors, when compared to polymeric hollow fibers.

22 23

(FIGURE 8)


22

Page 23 of 40

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1


6. Conclusions

2 3

The ozone transfer to water through a hydrophobized ceramic membrane contactor was

4

investigated in this study. The technical feasibly of the process was confirmed by achieving the

5

bubble-less ozone transfer to water and also, by the ability to use the modified membrane for

6

long-term operational periods and even re-modified it, when the surface lost its specific

7

properties. The influence of liquid flow and the different experimental conditions on ozone mass

8

transfer was studied. Increased ozone molar fluxes were observed with increased liquid phase

9

velocities. The pH and ozone concentration values in the gas phase had the greatest impact on

10

dissolved ozone concentration, while the increase of temperature slightly decreased the measured

11

ozone.

12

A mathematical model considering all the simultaneously occurring phenomena during ozone

13

transfer was developed. The model was able to describe/predict with good agreement with the

14

experimental results (average deviation around 5%), the dissolved ozone concentrations at the

15

outlet of (ceramic membrane) contactor module. The presented model permits the further

16

exploitation-extrapolation of data for different devices (scale-up) and experimental conditions by

17

adopting the values of major physical parameters, affecting the developed model (i.e. D, s, K’

18

etc.) from the literature, or from the experimental determination of them. Furthermore, essential

19

ozone physical properties and decomposition reaction parameters were calculated, under the

20

tested experimental conditions, by properly fitting this model with the experimental data,

21

applying different experimental conditions. The range of (estimated) major ozone properties

22

were: diffusivity 1.55 – 2.2·10-9 m2/s, ozone equilibrium concentration 5.5 - 26 mg/L,


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 40

1

dimensionless coefficient factor 2 - 4.3, ozone self-decomposition reaction order 1 - 2 and rate

2

9·10-4 - 8·10-1 (1/s·(L/mg)(n-1)).

3 4


24

Page 25 of 40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1


Table 1. Major properties of hydrophobically modified α-Al2O3 ceramic membrane. Membrane material Nominal pore size (nm) MWCO (kDa) Membrane porosity (ε) Internal interface area (m2) Internal specific area (m2/m3) Contact angle (deg)

Hydrophobized a-alumina 100 1000 0.5 0.0085 500 133o-143o 27

*Unmodified membranes purchased from A-Τech.

2 3 4

Table 2. Influence of pH on reaction order and rate constant of ozone decomposition at 20° C. Experimental Conditions

Calculated ozone properties

Experiment

pH

n

8 9 10

4 6 9

2 2 1

K’ (1/s· (L/mg)^(n-1) (±5%) 0.0017 0.0049 0.624

5 6 7

Table 3. Influence of ionic strength and ozone concentration in gas phase on ozone equilibrium

8

concentration at 20° C.

Experimental Conditions Experiment 11 12 13 14

I (M) 0.2 0.4 0 0

CO3_gas (mg/L) (±3%) 60 60 40 20

Calculated ozone properties Ceq (mg/L) (±5%) 20 19 16 8

s 3 3.2 2.5 2.5

* I = 0 M correspond to deionized water without the addition of NaCl

9


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 40

1 2

Table 4. Influence of temperature on ozone equilibrium concentration, diffusivity and reaction

3

rate constant at pH 4. Experimental Conditions

Calculated ozone properties

Experiment

θ (° C)

Ceq (mg/L) (±5%)

s (±5%)

D (m2/s) (±5%)

1 8 15 22

15 20 25 30

26 22.5 20 17

2.3 2.7 3 3.5

1.55·10-9 1.75·10-9 2·10-9 2.2·10-9

K’ (1/s· (L/mg)^(n-1) (±5%) 0.0009 0.0017 0.0029 0.0039

4 5 6


26

Page 27 of 40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


2. Ozone generator

7. 4. 3.

1.

PI 5.

12. 4. 6. 11.

8.

pH

9.

13.

10.

Scheme 1. Flow-chart of the experimental set-up used for ozone mass transfer experiments: (1) O2 Tank, (2) Ozone generator, (3) Ozone flow meter, (4) Pressure transducer, (5) Ceramic membrane module (acrylic glass), (6) Needle valve, (7) Air hood, (8) Water tank, (9) pH meter, (10) Thermostatic Cabinet, (11) Water flow meter, (12) Peristaltic pump, (13) Indigo solution trap.


27


3,00E-007

2,50E-007

2

Mass Transfer Flux (mol/m s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 40

2,00E-007

1,50E-007

1,00E-007

5,00E-008 0,00

0,01

0,02

0,03

0,04

0,05

Velocity (m/s)

Figure 1. Ozone molar transfer flux as a function of liquid flow velocities at pH 6, T = 15° C and CO3_gas = 60 mg/L (±3%).


28

o

Dissolved Ozone Concentration (mg/L)

3,0

pH = 4 pH =6 pH = 9

T = 15 C

2,5

2,0

1,5

1,0

0,5

0,0 0,00

0,01

0,02

0,03

0,04

o

3,0

2,5

2,0

1,5

1,0

0,5

0,0 0,00

0,05

0,01

pH = 4 pH =6 pH = 9

2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,03

0,04

0,04

0,05

o

3,0

0,05

pH = 4 pH =6

T = 30 C

2,8


T = 25 C

2,8

0,02

Velocity (m/s)

o

3,0

pH = 4 pH =6 pH = 9

T = 20 C

Velocity (m/s)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 29 of 40

2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

Velocity (m/s)

0,02

0,03

0,04

0,05

Velocity (m/s)

Figure 2. Dissolved ozone concentrations as a function of liquid flow velocities at different pH values.


29



I=0M I = 0,2 M I = 0,4 M

T = 15 C

2,8 2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,04

o

3,0 2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,05

0,01

Velocity (m/s)

2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,03

0,04

0,04

0,05

o

3,0

0,05

I=0M I = 0,2 M I = 0,4 M

T = 30 C

2,8


I=0M I = 0,2 M I = 0,4 M

T = 25 C

2,8

0,02

Velocity (m/s)

o

3,0

I=0M I = 0,2 M I = 0,4 M

T = 20 C

2,8


o

3,0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 40

2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,04

0,05

Velocity (m/s)

Velocity (m/s)

Figure 3. Dissolved ozone concentrations as a function of liquid flow velocities at different ionic strength values.


30

Page 31 of 40

o

3,0

2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,04



CO3_gas = 60 mg/L CO3_gas = 40 mg/L CO3_gas = 20 mg/L

2,2

T = 20 C

2,8

2,6 2,4

o

3,0

T = 15 C

2,8

2,6 2,4 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,05


2,2

0,01

Velocity (m/s)

2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

0,02

0,03

0,04

0,05


CO3_gas = 60 mg/L CO3_gas =40 mg/L CO3_gas = 20 mg/L

2,2

0,04

0,05

T = 30 C

2,8

2,6 2,4

0,03

o

3,0

T = 25 C

2,8

0,02

Velocity (m/s)

o

3,0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2,6


2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,00

0,01

Velocity (m/s)

0,02

0,03

0,04

0,05

Velocity (m/s)

Figure 4. Dissolved ozone concentrations as a function of liquid flow velocities at different ozone concentrations in the gas phase.


31


Experimental Model

4,0

(a )

3,5

Only Diffusion

3,0 2,5 2,0 1,5 1,0

0,0 0,00

0,01

0,02

0,03

0,04

0,05

0,04

0,05

0,04

0,05

Velocity (m/s)

4,0 3,5

(b)

3,0 2,5 2,0 1,5 1,0 0,5 0,00

0,01

0,02

0,03

Velocity (m/s)

4,0

2nd order decomposition


0,5

1st order decomposition

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 40

(c )

3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,00

0,01

0,02

0,03

Velocity (m/s)

Figure 5. Different fittings between model data and experimental results at pH 6, T 20° C, zero ionic strength by: (a) only diffusion, (b) 1st order, and (c) 2nd order ozone self-decomposition.


32

Page 33 of 40

Ozone Measured

Ozone diffusion rate

Predicted Ozone Concentration

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ozone decomposition rate

0,0

0,2

0,4

0,6

0,8

1,0

Dimensionless Membrane Length

Figure 6. Predicted ozone concentrations, diffusion and decomposition rate in respect to membrane length.


33


(a)

2,5

0,10

0,08

0,06

Experimental Model

0,04

0,02

0,00 0,00

0,01

0,02

0,03

0,04



0,12

2,0

Experimental Model

1,5

1,0

0,5

0,0 0,00

0,05

(b)

0,01

Velocity (m/s)

1,0 0,8 0,6 0,4 0,2

0,03

0,04

0,05


Experimental Model

0,02

0,04

0,05

(d)

1,2

0,01

0,03

0,9

1,4

0,0 0,00

0,02

Velocity (m/s)

(c)

1,6


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 40

0,8

Experimental Model

0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0,00

0,01

Velocity (m/s)

0,02

0,03

0,04

0,05

Velocity (m/s)

Figure 7. Examples of fitting between experimental and model data: (a) pH 9, T 15° C, zero ionic strength (I), ozone CO3_gas 60 mg/L (±3%), (b) pH 4, T 25° C, zero ionic strength, ozone CO3_gas 60 mg/L (±3%), (c) pH 6, T 15° C, ozone CO3_gas 60 mg/L (±3%), I 0.4 M, (d) pH 6, T 15° C, zero ionic strength, ozone CO3_gas 20 mg/L (±3%).


34

Page 35 of 40

4,0

Predicted ozone concentration (mg/L)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 0,00

0,01

0,02

0,03

0,04

0,05

Velocity (m/s)

Figure 8. Predicted ozone concentrations for a multi-channel ceramic membrane (1.2 m length, 51·10−3 m outer diameter, 3.3·10−3 m channel diameter and 85 channels per membrane) as a function of liquid velocity.


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Page 36 of 40

Supporting Information Table of calculated ozone properties, influence of temperature on ozone transfer, examples of fittings between modeling and experimental data.

AUTHOR INFORMATION

Corresponding Author *Email: [email protected], tel.:+30-2310997794

Acknowledgements Thanks are due also to EKETA - Laboratory of Inorganic Materials (Prof. V. Zaspalis, Dr. S. Sklari and Dr. A. Pagana) for the provision and hydrophobic modification of inorganic membrane used in this study.


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TOC (Table of Contents)


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Ozone Mass Transfer Studies in a Hydrophobized Ceramic Membrane

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