Passive aeration of wastewater treated by an anaerobic process—A design approach

Journal of Environmental Chemical Engineering 4 (2016) 4565–4573

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Passive aeration of wastewater treated by an anaerobic process—A design approach Ayman M. El-Zahabya,* , Ahmed S. El-Gendyb a b

Environmental Engineering program, The American University in Cairo (AUC), Cairo, Egypt Department of Construction Engineering, The American University in Cairo (AUC), Cairo, Egypt

A R T I C L E I N F O

Article history: Received 28 July 2016 Received in revised form 3 October 2016 Accepted 21 October 2016 Available online 22 October 2016 Keywords: Anaerobic treatment Mathematical modelling Passive aeration Tray aerator Wastewater

A B S T R A C T

Passive aeration units are units that operate without the need for electric energy. On the contrary to cascade and spray aerators, tray aerators require a much smaller area for their installation. While researching the design of tray aerators, the authors observed a shortage of literature pertaining to the topic. The research objective is to develop a model for the design of tray aerators for the purpose of increasing the dissolved oxygen in wastewater. The analysis focuses on the jetting free falling flow regime. This paper derives a set of equations that estimate the dissolved oxygen concentration in the effluent from the tray aerator system as a function of the flow rate, number of trays, tray area, spacing between trays, number and diameter of holes per tray. Results illustrate that the aeration performance is largely affected by the tray area, number of trays and flow rate while other parameters did not affect the aeration significantly. ã 2016 Elsevier Ltd. All rights reserved.

1. Introduction Anaerobic wastewater treatment gained popularity due to its relatively low investment cost, running cost and the possibility of production of biogas, instead of energy consumption in conventional aerobic treatment process. Thus anaerobic wastewater treatment units are capable of sustaining the natural energy resources [1]. One drawback of the anaerobic treatment process is that the anaerobic treatment alone cannot reach the effluent quality that is permissible for the discharge in receiving waterbody. For that reason, a post treatment unit should be installed following the anaerobic unit [2,3]. Thus, in order to promote the practical applications of anaerobic treatment units, various design arrangements that utilize an anaerobic system as a primary treatment and a post treatment aerobic system were studied. Kassab et al. [2] classified those arrangements into two categories; namely sequential anaerobic-suspended growth aerobic systems, and sequential anaerobic-attached growth aerobic systems. Several articles are published proposing the use of attached growth systems as the post treatment aerobic unit, for its low cost [4–7].

* Corresponding author. E-mail addresses: [email protected] (A.M. El-Zahaby), [email protected] (A.S. El-Gendy). http://dx.doi.org/10.1016/j.jece.2016.10.025 2213-3437/ã 2016 Elsevier Ltd. All rights reserved.

For all options of post treatment, water entering the aerobic unit must maintain high Dissolved Oxygen (DO) for the unit to operate effectively. This high DO shall either be added before the aerobic unit as in the attached growth trickling filter units, or within the unit as in the suspended growth activated sludge systems. This is due to the fact that the aerobic microorganisms need oxygen for their respiration [8]. As the effluent from the anaerobic units has zero DO [4], this effluent should be aerated to increase the water DO before entering the aerobic unit. Conventional aeration units such as mechanical aerators or diffused aerators require electrical energy input, and their mechanical parts require frequent maintenance and relatively high operating cost. Therefore, there is a need to have a more sustainable, easy to operate and economical option for aeration. These criteria can be met by using passive aeration techniques, which do not require any electrical energy, such as cascade aerators, spray aerators or tray aerators. As both cascade aerators and spray aerators need a large area footprint for their installation [7,9,10], the use of tray aerators offers a more practical option for places where land availability is a constraint. Tray aerators are aeration devices that rely on the available head in the influent water to lift water at an elevated point right above the distribution tray, from which water flows under gravitational forces over a series of horizontal perforated plates below each other as illustrated in Fig. 1. The tray aerator is generally formed of a number (N) of trays arranged vertically underneath each other at a

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Nomenclature

Water In Q

a A Aj C Cv Cd d D DL Dj g h h’ hs H HLR i KL L n n’ N Q Qhole S SP t te V

v d r s

BO We DO

Specific surface area = A/V, [m2/m3] Interfacial area, [m2] Cross section area of the water jets, [m2] Concentration, [mg/L] Coefficient of velocity for flow through nozzle, [dimensionless] Coefficient of discharge for flow through nozzle, [dimensionless] Hole diameter, [m] Falling water drop/jet diameter, [m] Diffusivity of air in water, [m2/s] Mean jet diameter, [m] Acceleration due to gravity [m/s2] (9.81 m/s2) Height of water film over tray, [m] Corrected height of water film over tray, [m] Tray side height, [m] Overall system height, [m] Hydraulic loading rate = Q/A, [m3/m2/s] Number of trays Overall liquid mass transfer coefficient, [m2] Length, [m] Number of holes per tray Corrected number of holes per tray Total number of trays in the system Flow rate, [m3/s] Flow rate per hole, [m3/s] Surface renewal rate, [1/s] Spacing between trays, [m] Time, [s] Exposure time, [s] Volume, [m3] Velocity, [m/s] Film thickness, [m] Density, [kg/m3] (997.2 kg/m3 for water at 24 ) Surface tension, [N/m] (0.073 N/m for water at 24 ) Bond number, [dimensionless] Webber number, [dimensionless] Dissolved oxygen concentration, [mg/L]

Subscripts c Critical f Water film over tray j Water jet from tray o Outer S Saturation 0,1,2 Initial, intermediate, final

spacing (SP) between trays. Each tray is made from a flat sheet with a number (n) of holes each with a diameter (d). When water falls over trays, a thin film of water with height (h) forms over the tray before the water exits from the holes. Trays are constructed with sides having height (hs) exceeding the thin film height to prevent overflow from the sides. Fig. 1 illustrates the main parameters of tray aerators. Subsequent sections of the current work discuss the approach of the authors to develop a model for designing and estimating the DO effluent from tray aerators. Tray aerators were studied for the stripping purpose, that is the removal of unwanted gases from water. They were investigated for the purpose of iron and manganese removal in water treatment plants [10], carbon dioxide stripping for clean water [11,12] and

C0 C1 C2

SP

SP ixSP

C3 C4 C5

Distribution tray Ød

Tray 1 Tray 2

Tray details

C2.i C2.i+1

Tray i

Water surface

hs

h' Tray Tray hole

A

A

Tray N

Sec. A-A

Water Out

Q, C2.N+1

Fig. 1. Tray aerator setup.

stripping of sulfides from ground water [13]. Few studies, if any, addressed the use of tray aerators for aeration purpose. The current work investigates the effect of different regimes of free falling flow on the performance of tray aerator. In addition, a design model for the aeration through tray aerator is developed and discussed in the current work. This model includes the potential design parameters of tray aerator. The study also investigates the effect of varying each design parameter on the aeration performance of tray aerator. 2. Materials and methods 2.1. Background on aeration process Aeration of water is a mass transfer process, with the concentration gradient acting as the driving force. Any constituent tends to transfer from the zone of high concentration to the zone of low concentration until both zones reach an equilibrium state with similar concentrations as illustrated in Fig. 2. The rate of oxygen transfer to water across an air-water interface can be described with Eq. (1) which is based on Fick’s first law of diffusion [14,15] V

@C ¼ K L AðC S  C Þ @t

ð1Þ

where (V) is the volume of water over which (C) and (A) are measured; (C) is the concentration of oxygen in water; (t) is the time; (KL) is the overall liquid mass transfer coefficient; (A) is the interface area; and (CS) is the saturation concentration of the gas in water and is equal to the partial pressure of oxygen in water divided by Henry’s law constant. The value of CS depends on the water temperature, barometric pressure and water salinity. It is obtained from published data and tables [16]. For the tray aerator system, Eq. (1) can be manipulated and integrated across the limits of time from zero to t, and the concentration from the initial concentration to the concentration at time t, to reach the form illustrated in Eq. (2). lnð

CS  Ct Þ ¼ K L at CS  C0

ð2Þ

where (Ct) is the concentration at time t; (C0) is the initial concentration; (a) is the specific area which is equal to the ratio

A.M. El-Zahaby, A.S. El-Gendy / Journal of Environmental Chemical Engineering 4 (2016) 4565–4573

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Fig. 2. Schematic illustration of Fick’s law of diffusion. a) condition before diffusion b) condition during diffusion c) condition at equilibrium.

between the interface area and the liquid volume; and t is the time and is taken to be equal to the volume of the liquid divided by the flow rate. The initial DO concentration inlet to the aeration system is generally equal to zero for wastewater effluent from an anaerobic system; hence, this parameter is uncontrollable in the design. The overall liquid mass transfer coefficient KL, is a measure of gas flux per unit concentration gradient. There are three widely used theories describing the rate of gas transfer; namely, the twofilm theory proposed by Lewis and Whitman [17], the penetration theory proposed by Higbie [18], and the surface renewal theory proposed by Danckwers [19]. The difference between the three theories lies in the physical explanation of the diffusion process, where the two film theory is based on a rigid interface between the air and liquid, and thus is more suitable for still water such as in estuaries, the penetration theory and surface renewal theory are based on a liquid displacement at the interface, such as in flowing rivers, and falling water jets or drops [20,21]. Another major difference lies in the method of estimating KL, which is a measure of gas flux per unit concentration gradient, and has the dimensions of velocity, as illustrated in Eqs. (3)–(5) for the two film theory, penetration theory, and the surface renewal theory respectively [21]. KL ¼

DL

d

sffiffiffiffiffiffiffiffi DL KL ¼ 2 pt e

KL ¼

pffiffiffiffiffiffiffiffi DL S

ð3Þ

ð4Þ

ð5Þ

where (DL) is the diffusivity of air in water; (d) is the thickness of an arbitrary thin laminar film of water through which the mass transfer occurs while the remaining of the water is assumed to be turbulently mixed (proposed in the thin film theory); (te) is the time of exposure of a thin laminar film of water to the gas considering the film is continually being replaced at a uniform rate (proposed in the penetration theory); (S) is the rate of renewal of the liquid surface which is continually being replaced at a random rate (proposed in the surface renewal theory).

KL can be estimated from Eq. (3), Eq. (4), or Eq. (5), depending on the hydraulic conditions of the flow regime. Other equations for estimating KL are empirical and are based on experimental or field data for a given aeration system design [20]. The literature indicates that KL has a dynamic value which is a function of the degree of turbulence of the two interacting fluids, and the chemical reactivity of gases [7,14,22]. However, most of the values reported in the literature are for KLa [23–25] and the only found value for oxygen mass transfer coefficient between air and sea water is the proposed mean value KL = 5.5  105 m/s [22] is used in the current paper. It appears in Eq. (2) that rate of aeration is directly proportional to CS, C0, KL, a, and t [10]. Therefore, as the only controllable parameters in Eq. (2) are a and t, they are the main design parameters, which shall be increased to achieve better aeration. 2.2. Mathematical model In deriving a mathematical expression for DO concentration in the effluent from tray aerators, the authors consider first a system of one aeration tray other than the distribution tray. Water entering the distribution tray shall exhibit two subsequent flow modes until it reaches the aeration tray; namely thin film formed above the distribution tray and free falling water between the distribution and aeration trays. Each mode is analyzed separately in the next sections. 2.2.1. Flow regimes Water exiting from nozzles or holes can attain several flow regimes, that are defined as dripping or jetting regimes. In dripping regime, regular spherical drops of constant mass detach from the nozzle or hole at a constant frequency (periodic dripping) or variable mass drops are formed in a random way (dripping faucet) [26]. Dripping regime occurs when Weber number (We), a dimensionless parameter is less than a critical Weber number (Wec) defined by Clanet and Lasheras [26] for any Newtonian fluid, as illustrated in Eqs. (6)–(8) We ¼

rv 1 2 D 1 s

Wec ¼ 4

 0:5 2  BOo 2 1 þ kBOo BO  ð1 þ kBOo BOÞ  1 BO

ð6Þ

ð7Þ

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" BO ¼

rgd2 2s

#0:5 ð8Þ

where We is the dimensionless Weber number, which is the ratio between the inertia force and the surface tension force; (r) is the density of the liquid; (v1) is the initial exit velocity from the nozzle, which will be defined in Section 2.2.2; (D1) is the initial water diameter exiting the hole; (s ) is the surface tension of liquid; Wec is the critical Weber number; (BOo) is the Bond Number based on the outside diameter (the wetting diameter) of the nozzle; (BO) is the Bond Number based on the inside diameter of the nozzle; (k) is a constant which is equal to 0.37 for water injected in air; (g) is the acceleration due to gravity. In the work of Clanet and Lasheras [26], the model indicated in Eqs. (6)–(8) was verified using tubes which had a small thickness, allowing for the water exiting the tube to wet the tube thickness. This was the reason the model included the outside diameter (wetting diameter) and the inside diameter. For water falling through tray aerator, the thickness of the hole is taken as the total tray area served by that hole, and thus the outside nozzle diameter is assumed to be equal to the inside nozzle diameter and both are equal to the hole diameter. Above Wec, the falling flow transits to the jetting regime. This paper focuses on the jetting regime for the practical difficulties of achieving uniform dripping regime from all the holes of a tray. Furthermore, the jetting regime can be achieved using less number of holes, and consequently smaller tray area requirements. To assure that the studied conditions include only the jetting regime, the model included a conditional loop that check We relative to the Wec, and adjusts the number of holes per tray to guarantee jetting conditions. 2.2.2. Hydraulic design For free falling water exiting from tray holes under gravitational forces, holes act as nozzles, and under steady state flow conditions, a thin water film of height h forms over the tray as illustrated in Fig. 1. The initial exit velocity from the nozzle v1 can be estimated by knowing h using nozzle equation as illustrated in Eq. (9) pffiffiffiffiffiffiffiffiffi ð9Þ v1 ¼ C v 2gh where (Cv) is the coefficient of velocity through nozzles, and is assume to be equal to 0.99. In the case of jetting regime, the water jet exiting the hole has an initial diameter D1 that is estimated as indicated in Eq. (10), and the number of holes per tray needed to achieve a desired film height is estimated as indicated in Eq. (11) sffiffiffiffiffiffi Cd ð10Þ D1 ¼ d: Cv

n¼

Q pv D 2 4 1 1

ð11Þ

where (Cd) is the coefficient of discharge through nozzles, and is assumed to be equal to 0.6 [27]; and (Q) is the total flow rate. As the number of holes should be an integer, the value obtained from Eq. (11) is rounded to the nearest integer, and then the initial water velocity, and the film height are recalculated as indicated in Eq. (12), and Eq. (13) v1 0 ¼

Q hole Q ¼ Aj n0 p4 D1 2

ð12Þ

0

h ¼

ðv1 0 =cv Þ2 2g

ð13Þ

where (v10 ) is the corrected initial exit velocity from the nozzle; (Qhole) is the flow rate per hole; (Aj) is the cross section area of the water jet; (n’) is the corrected number of holes per tray; and (h’) is the corrected film height. In order to avoid overflow of water from the tray sides, if the corrected film height h’ exceeds the tray side height hs the corrected number of holes is increased by one hole until h is less than hs. The iterations for n’, v10 and h’ continue till all conditions are satisfied, however the final film height shall differ from the desired film height. The jet velocity increases as the water travels downwards due to the gravitational acceleration, resulting in a decrease in the jet diameter to satisfy the continuity equation. The parameters characterizing the water jet are calculated as indicated in Eqs. (14)–(21). 0

Lj ¼ SP  h

v2 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðv1 0 Þ2 þ ð2gLj Þ

sffiffiffiffiffiffi v1 0 D2 ¼ D1 v2

ð14Þ

ð15Þ

ð16Þ

Dj ¼

D1 þ D2 2

ð17Þ

vj ¼

v1 0 þ v2 2

ð18Þ

where (Lj) is the jet length; (v2) is the jet velocity reaching the subsequent tray; (D2) is the jet diameter reaching the subsequent tray; (Dj) is the mean jet diameter; and (vj) is the mean jet velocity. 2.2.3. Thin film aeration The thin film is modelled to be uniform over the tray area, and would have a volume equal to the tray area multiplied by the film height. Since the specific area is equal to the ratio between the interface area and the liquid volume, the thin film specific area (af) is calculated as illustrated in Eq. (19) af ¼

A A 1 ¼ 0 ¼ 0 Vf Ah h

ð19Þ

where (A) is the interface area of the thin film, which is equal to the tray area; (Vf) is the liquid volume over the tray, which is equal to the tray area multiplied by the film height h’. For the aeration time, the time for water to be aerated while it travels from point (C0) to point (C1) indicated in Fig. 1, which are at distance h’ apart can be estimated as indicated in Eq. (20) tf ¼

0 0 Vf Ah h ¼ ¼ Q Q HLR

ð20Þ

where (tf) is the thin film aeration time; and (HLR) is the hydraulic loading rate (the flow rate per unit area). Using Eq. (2), and substituting a, and t by Eq. (19), and Eq. (20) respectively, the DO of water at the exit from the tray indicated as

A.M. El-Zahaby, A.S. El-Gendy / Journal of Environmental Chemical Engineering 4 (2016) 4565–4573

C1 in Fig. 1 can be calculated as illustrated in Eq. (21). h0 K L  10 HLR h

C 1 ¼ C S  ðC S  C 0 Þe

K L HLR

¼ C S  ðC S  C 0 Þe

ð21Þ

2.2.4. Water jet aeration Using the same approach of estimating the specific area and aeration time for the thin film, the specific area of water jet is estimated as indicated in Eq. (22). As indicated in Eq. (16), the jet diameter decreases as the jet travels downwards, the jet will assume an inverted cone shape rather than a perfect cylinder. However; as a simplification of the calculations, the jet is modelled as a cylinder having a diameter of Dj, and travelling with a velocity of vj. The aeration time is estimated as indicated in Eq. (23) aj ¼

Aj pDj Lj 4 ¼ ¼ V j pDj 2 Lj Dj 4

ð22Þ

tj ¼

Lj vj

ð23Þ

where (aj) is the specific area of the jet. Eq. (2) is used to calculate the dissolved oxygen concentration reaching the aeration tray by substituting a by aj from Eq. (22), and t by tj from Eq. (23), as illustrated in Eq. (24) where C1 and (C2) are the DO concentration at the exit point from the distribution tray, and the point reaching the next aeration tray respectively as illustrated in Fig. 1. C 2 ¼ C S  ðC S  C 1 ÞeK L :aj :tj

ð24Þ

2.2.5. Overall aeration through a single tray For the estimation of the overall aeration occurring over a single tray, Eq. (21), and Eq. (24) are combined to account for the two aeration regimes; namely the thin film above the tray and the water jetting from the tray, as illustrated in Eq. (25). C 2 ¼ C S  ðC S  C 0 ÞeK L ðHLRþaj :tj Þ 1

ð25Þ

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2.2.7. Methodology The current research is split into two parts. The first part studies the flow regime for water falling from trays. It investigates the threshold for achieving the jetting regime at various hole diameter and flow rate. The second part investigates the effect of different design parameters on the aeration performance for a tray aerator system that is operating in the jetting regime conditions. 2.2.8. Model assumptions 1. To simplify solving the model equations, the following set of assumptions are made: 2. The flow is at steady state conditions 3. The trays are perfectly horizontal 4. All trays are square with a cross section area A. 5. All trays have the same number of holes and hole diameters, and are installed with constant spacing SP between each other 6. The maximum allowable height for the thin film hs is 25  103 m, otherwise, the tray would overflow. 7. The velocity distribution is uniform along the cross section of jets and the thin film. 8. The value for oxygen mass transfer coefficient KL between air and water is 5.5  105 m/s [22] 9. The coefficient of discharge through holes Cd is equal to 0.6, and the coefficient of velocity through holes Cv is equal to 0.99 [27] 10. The inlet dissolved oxygen concentration C0 to the system is zero

2.2.9. Model equations The authors developed two function files using MATLab R2013b (8.2.0.701); the first file aims at illustrating the threshold for the jetting regime, whereas the second file predicts the effluent DO from a tray aerator system that is installed at a distance SP above the water surface in the receiving tank. The receiving tank acts as the (Nth + 1) tray. Both codes are based on the equations derived in Mathematical model. The model was tested for the conditions indicated in Table 1. 3. Results

2.2.6. Number of trays Now considering the case where there is a number of N consecutive trays arranged beneath each other below the distribution tray, with a constant spacing between trays equal to SP as illustrated in Fig. 1. The influent DO to the (ith) tray is denoted as (C2i), where (i) = 1:N is the number of tray. Water reaching the ith tray experience i-1 thin film above the tray and i-1 falling water regimes. Thus Eq. (25) can be generalized to include the tray number as indicated in Eq. (26) C 2i ¼ C S  ðC S  C 0 ÞeK L :ði1Þ:ðHLRþaj :tj Þ 1

ð26Þ th

where (C2i) is the influent DO to the i tray including the distribution tray.

tray; and i is the number of

3.1. Flow regime The first function file solves Eqs. (6)–(8) proposed by Clanet & Lasheras [26] to get the maximum number of holes among which water is distributed in a tray before it transits from jetting to dripping for the set of tested diameters and flow rates. Results are illustrated in Fig. 3 where the maximum number of holes, among which the flow is equally distributed, increases with the increase in the total flow rate. Furthermore, the increase in the hole diameter results in a decrease in the maximum number of holes. Fig. 3 can be used as a design chart for any application involving falling water through holes or nozzles to define the threshold for

Table 1 Values of input parameters. Parameter

Unit of Measurement

Value

Flow rate Q Tray Area A Number of trays N Film height h Diameter of hole d Overall System height H Temperature Oxygen mass transfer coefficient KL

105 m3/s (m3/day) m2 Dimensionless 103 m 103 m m  C m/s

1.157(1), 1.736(1.5), 2.315(2), 2.894(2.5), 5.208(4.5) 0.15  0.15, 0.2  0.2, 0.25  0.25 1–10 2, 3, 5, 10, 15, 20 3, 4, 5, 6 1 24 5.5  105 [22]

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per tray, diameter of holes, and tray spacing on the water aeration performance over the tray aerator. Results are shown in the following sections.

70

Maximum number of holes for jetting

60

D=3mm D=4mm D=5mm D=6mm

3.2.1. Hydraulic design As illustrated earlier in the hydraulic design section, the number of holes per tray n’ for each hole diameter was estimated using a loop that optimizes the film height h’ as close as possible to the desired film height h. Table 2 shows the n’ and the corresponding h’ for each of the tested diameters and flow rates. The data show that the n’ decreases with the increase in d for the same Q and h, however; h’ is not possible to equate h and is different among different diameters. The increase in Q leads to an increase in n’. Smaller d allows more possibilities of changing n’, resulting in higher flexibility in achieving different values of h’.

50

40

30

20

10

0

1

1.5

2

2.5 3 Flow rate, (m3/day)

3.5

4

4.5

Fig. 3. Maximum number of holes for jetting flow regime at different flow rates.

the falling water regime, by using the design flow rate, and desired hole diameter. 3.2. Performance of tray aerator

3.2.2. Effect of change in hole diameter and number of holes Typical results in Fig. 4 illustrate the influent DO to the second tray from a single aeration tray system versus the change in the hole diameter and number of hole as per the values illustrated in Table 2. Presented results are for a flow rate of 1.0 m3/day of water having initial DO of zero, and the trays are placed at spacing of 0.2 m, with a tray area of 0.2  0.2 m2. The DO influent to the second tray appears to decrease with the increase in both n’ and d. However, the magnitude of that change in DO is not significant among the tested conditions of n’ or d. The values of n’ and d are important in defining the free falling flow regime.

The aeration model was run to investigate the effect of the change in the flow rate, tray area, number of trays, number of holes Table 2 Test conditions for fixing the jet area. Q  105 (m3/s)

h (mm)

d 3 (mm)

4 (mm)

d 5 (mm)

6 (mm)

3 (mm)

4 (mm)

n’

5 (mm) h’ (mm)

6 (mm)

1.157

2 3 5 10 15 20

14 11 9 6 5 4

8 6 5 3 3 3

5 4 3 2 2 2

3 3 2 1 1 1

1.94 3.14 4.67 10.54 15.18 23.72

1.88 3.34 4.80 13.34 13.34 13.34

1.97 3.07 5.47 12.30 12.30 12.30

2.64 2.64 5.93 23.72 23.72 23.72

1.736

2 3 5 10 15 20

21 17 13 9 8 7

12 10 7 5 5 4

8 6 4 3 3 3

6 4 3 2 2 2

1.94 2.96 5.05 10.54 13.34 17.43

1.88 2.70 5.51 10.81 10.81 16.89

1.73 3.07 6.92 12.30 12.30 12.30

1.48 3.33 5.93 13.34 13.34 13.34

2.315

2 3 5 10 15 20

28 22 17 12 10 9

16 12 10 7 6 5

10 8 6 4 4 3

7 6 4 3 3 2

1.94 3.14 5.25 10.54 15.18 18.74

1.88 3.34 4.80 9.80 13.34 19.22

1.97 3.07 5.45 12.30 12.30 21.86

1.94 2.64 5.93 10.54 10.54 23.72

2.894

2 3 5 10 15 20

34 28 22 15 13 11

19 16 12 8 7 6

12 10 8 5 4 4

8 7 6 3 3 3

2.05 3.03 4.90 10.54 14.03 19.60

2.08 2.93 5.21 11.73 15.32 20.85

2.13 3.07 4.80 12.30 19.21 19.21

2.32 3.03 4.12 16.47 16.47 16.47

5.208

2 3 5 10 15 20

62 51 39 28 23 20

35 29 22 16 13 11

22 19 14 10 8 7

15 13 10 7 6 5

2.00 2.95 5.05 9.80 14.53 19.21

1.98 2.89 5.02 9.5 14.39 20.10

2.06 2.76 5.08 9.96 15.57 20.33

2.13 2.84 4.80 9.80 13.34 19.21

A.M. El-Zahaby, A.S. El-Gendy / Journal of Environmental Chemical Engineering 4 (2016) 4565–4573

1.6

8

1.58

DO effluent from the system, (mg/L)

d=3mm d=4mm d=5mm d=6mm

DO influent to second tray, (mg/L)

1.56 1.54 1.52 1.5 1.48 1.46

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d=3mm d=4mm d=5mm d=6mm

7 6 5 4 3 2 1

1.44

0

2

3

0.5

0.33

1.42 1.4

0

2

4

6 8 Number of holes per tray

10

12

14

4

5 6 Number of trays

7

0.25 0.2 0.17 0.14 Spacing between trays, (m)

8

9

10

0.13

0.11

0.1

Fig. 4. Typical change in DO resulting from changing the number of holes per tray and diameter of holes. Results are for a single tray at Q = 1.157 m3/s of water, DO0 = zero, SP = 0.2 m, A = 0.2  0.2 m2.

Fig. 6. Typical change in DO from the system resulting in change in tray spacing and number of trays at different hole diameters. Results are for Q = 1.157 m3/s of water, DO0 = zero, SP = 0.2 m, A = 0.2  0.2 m2.

3.2.3. Effect of changing the spacing between trays Through running the model while varying the tray spacing, it is illustrated in Fig. 5 that the aeration through a single tray increases with the increase in the spacing between trays. This increase is mainly due to the increase in the jet length, which leads to more aeration time over the water jets. Furthermore, with the increase of the jet length, the volume of water jet increases, resulting in a decrease in the aj as the jet area is constant. Regarding the sensitivity of the DO to the change of SP, it can be concluded that the change in SP has limited impact on the DO.

where the overall height is calculated as illustrated in Eq. (27)

3.2.4. Effect of increasing the number of trays In the design of tray aerators, the available height for the installation acts as a constraint on the maximum number of trays that can be installed. Thus, Fig. 6 illustrates a typical change in the DO resulting from the simultaneous change in the number of trays and tray spacing to adopt the system for an overall height of 1m,

H ¼ SP  N

where (H) is the overall system height. It appears from Fig. 6 that the increase in the number of trays highly increases the DO. This is due to the formation of more thin films, which increases the aeration. 3.2.5. Effect of changing the tray area and flow rate Increasing the tray area results in a decrease in the hydraulic loading rate, and thus an increase in the specific area for the thin film, which is reflected in higher DO. The effect of increasing the tray area is illustrated in Fig. 7, in which the increase in tray area results in offsetting the curve towards higher DO. Fig. 7 also illustrates that the increase in the flow rate for the same tray area results in a decrease in the DO. This decrease results mainly from the increase in the hydraulic loading rate.

8

1.6 Sp=0.5 m Sp=0.33 m Sp=0.25 m Sp=0.2 m Sp=0.17 m Sp=0.14 m Sp=0.13 m Sp=0.11 m Sp=0.1 m

1.56 1.54

7

DO effluent from the system, (mg/L)

1.58

DO influent to second tray, (mg/L)

ð27Þ

1.52 1.5 1.48 1.46

6

5

4

3

2 1.44

1 1.42

A=0.0225 m2 A=0.04 m2 A=0.0625 m2

1.4

3

3.5

4

4.5 Hole Diameter (mm)

5

5.5

6

Fig. 5. Typical change in DO resulting from changing the spacing between trays and diameter of holes. Results are for a single tray at Q = 1.157 m3/s of water, DO0 = zero, h = 2 mm, A = 0.2  0.2 m2.

0 10

15

20

25

30 35 Flow rate, (x10−6 m3/sec)

40

45

50

55

Fig. 7. Typical change in DO from the system resulting from change in flow rate and tray area. Results are for N = 10 trays, DO0 = zero, SP = 0.1 m, h = 2 mm, A = 0.2  0.2 m2.

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4. Discussion

5. Conclusion

The first part of the analysis illustrates different flow regimes that can be achieved for the water falling from trays; most commonly dripping and jetting regimes. Even though the dripping regime is thought to have higher mass transfer than the jetting regime for the larger specific area of drops over jets, it is difficult to achieve dripping regime with uniform water distribution among tray holes. Moreover, jetting regime can be achieved using less number of holes per tray, resulting in smaller area requirements. Hence the analysis deals only with the jetting regime. The threshold for achieving the jetting regime is dependent on the hole diameter, number of holes and the flow rate as per Eq. (6), and Eq. (7) proposed by Clanet and Lasheras [26]. Their equation was applied to the water setup from tray aerators, and design charts were obtained for any application involving falling water through holes or nozzles to define the threshold for the falling water regime, by using the design flow rate, and desired hole diameter. In the second part of the study, the authors analyzed the hydraulic design of the tray aerators and the parameters that might affect the aeration performance of tray aerators. The model investigated in the current work addressed only the aeration due to the molecular diffusion, where other possible aeration forms such as the aeration due to the water splashing over the thin film, or air entrainment from the falling water jet were not addressed, and are out of the scope of the current study. The analysis addressed the estimation of a, and t which are the design parameters for Eq. (2). Those two parameters are dependent on d, Q, N, n, SP, and A. The impact of each parameter on the effluent DO was investigated separately. Changing d defines the flow regime into jetting or dripping, with minor effect on the effluent DO. This slight impact of d on the DO is seen from Eq. (22), where the value of aj is inversely proportional to Dj, which is a function of d, SP, Q, and n. However, in order to limit the flow regime to the jetting regime for a given Q, n changed accordingly, to assure that We is greater than Wec to satisfy Eqs. (6)–(8), mitigating the impact of changing d. Changing Q is inversely proportional with the DO, and as a result has a high impact on its value. Increasing Q results in an increase in HLR, which in turn results in a decrease in tf (Eq. (20)). Similarly, increasing A results in an increase in DO due to the decrease in HLR. La Motta realized the same conclusion but for CO2 stripping, where the model equations he developed illustrated that the CO2 stripping is inversely proportional with the HLR [11,12]. Similarly, Duranceau and Faborode reported that the sulfide stripping from tray aerators is inversely proportional with the HLR [13]. The DO increased slightly with the increase in SP, which was interpreted to be due to the increase in Lj (Eq. (14)), which led to the increase in v2 and vj, and a decrease in D2 and Dj according to Eqs. (15)–(18). As a result, aj decreased (Eq. (22)) and tj increased (Eq. (23)) resulting in higher mass of oxygen diffusing into the falling water. This conclusion is contradicting with the conclusion for CO2 stripping developed by La Motta. CO2 stripping is proportional with SP [11,12]. Whereas Duranceau and Faborode did not address SP in their analysis for sulfide stripping [13]. Increasing N results in an increase in the number of thin films and water jets within the tray aerator system, leading to an increase in DO. The exponential trend of increase in DO with the increase in N (Fig. 6) is the result of the decrease in the concentration gradient with the increase of the DO, resulting in a decrease in the rate of mass transfer, according to Fick’s law indicated in Eq. (1). Similar dependence was observed for the tray aerators studied for CO2 stripping [10–12] as well as for sulfide stripping [13].

This study investigates analytically the design parameters of passive aeration technique. This technique is suitable as an intermediate stage after anaerobic treatment to enhance the performance of the subsequent aerobic unit. A key benefit from tray aerators lies in the fact that they do not require energy input for aeration in its operation, and hence sustains the natural resources and is suitable for installation in rural areas. The design equations for the tray aerator are introduced in this research, and were tested analytically to evaluate the sensitivity of the performance to the change in the design parameters. Based on the current work, the aeration performance of the system for water falling under jetting flow regime is mainly controlled by the thin film aeration, which is controlled by the hydraulic loading rate. the number of holes, and hole diameters controls the flow regime to fall within the jetting or dripping regime. they further control the height of the thin film to assure that no overflow would occur from the tray sides. Achieved results need to be verified by experimental work to confirm on the values of KL, Cd and Cv, which were assumed in the current work from published papers. Funding This work was supported by the American University in Cairo (AUC), Egypt through a Graduate Research Grant. References [1] I. Urban, D. Weichgrebe, K.-H. Rosenwinkel, Anaerobic treatment of municipal wastewater using the UASB-technology, Water Sci. Technol. 56 (2007) 37, doi: http://dx.doi.org/10.2166/wst.2007.732. [2] G. Kassab, M. Halalsheh, A. Klapwijk, M. Fayyad, J.B. van Lier, Sequential anaerobic-aerobic treatment for domestic wastewater—a review, Bioresour. Technol. 101 (2010) 3299–3310, doi:http://dx.doi.org/10.1016/j. biortech.2009.12.039. [3] E.J. La Motta, E. Silva, A. Bustillos, H. Padrón, J. Luque, H. Padron, J. Luque, Combined anaerobic/aerobic secondary municipal wastewater treatment: Pilot-plant demonstration of the UASB/aerobic solids contact system, J. Environ. Eng. 133 (2007) 397–403, doi:http://dx.doi.org/10.1061/(ASCE)07339372(2007)133:4(397). [4] A.S. El-Gendy, T.I. Sabry, F.A. El-Gohary, The use of AN aerobic biological filter for improving the effluent quality of a two-stage anaerobic system, Int. Water Technol. J. 2 (2012) 298–308. [5] T.I., Sabry, A.S., El-Gendy, F.A, El-Gohary, An Integrated Anaerobic—Aerobic System for Wastewater Treatment In Rural Areas, in: An Integr. Anaerob.— Aerob. Syst. Wastewater Treat. Rural Areas, IWA Conferences (2011). [6] A. Tawfik, F. El-Gohary, A. Ohashi, H. Harada, Optimization of the performance of an integrated anaerobic-aerobic system for domestic wastewater treatment, Water Sci. Technol. 58 (2008) 185, doi:http://dx.doi.org/10.2166/ wst.2008.320. [7] G. Tchobanoglous, F.L. Burton, H.D. Stensel, Metcalf, Eddy, Wastewater Engineering: Treatment and Reuse, McGraw-Hill, 2004. [8] F. Garcia-Ochoa, E. Gomez, V.E. Santos, J.C. Merchuk, Oxygen uptake rate in microbial processes: an overview, Biochem. Eng. J. 49 (2010) 289–307, doi: http://dx.doi.org/10.1016/j.bej.2010.01.011. [9] D.A. Lytle, M.R. Schock, J.A. Clement, C.M. Spencer, Using aeration for corrosion control, Am. Water Work. Assoc. 90 (1998) 74–88. [10] G.R. Scott, Q.B. Graves, P.D. Haney, L. Haynes, J.E. McKee, M. Pirnie, G.J. Rettig, J. H. Svore, Aeration of water: revision of water quality and treatment, chapter 6, J. Am. Water Works Assoc. 47 (1955) 873–885. (accessed 02.06.16) http:// www.jstor.org/stable/41254169. [11] E.J. La Motta, Chemical analysis of CO2 removal in tray aerators, J. Am. Water Resour. Assoc. 31 (1995) 207–216, doi:http://dx.doi.org/10.1111/j.17521688.1995.tb03374.x. [12] E.J. La Motta, S. Chinthakuntla, Corrosion control of drinking water using tray aerators, J. Environ. Eng. 122 (1996) 640–648, doi:http://dx.doi.org/10.1061/ (ASCE)0733-9372(1996)122:7(640). [13] S.J. Duranceau, J.O. Faborode, Predictive modeling of sulfide removal in tray aerators, Am. Water Work. Assoc. J. 104 (2012). [14] P. Wójtowicz, M. Szlachta, Aeration performance of hydrodynamic flow regulators, Water Sci. Technol. 67 (2013) 2692–2698, doi:http://dx.doi.org/ 10.2166/wst.2013.181. [15] J.S. Gulliver, A.J. Rindels, Measurement of air-water oxygen transfer at hydraulic structures, J. Hydraul. Eng. 119 (1993) 327–349, doi:http://dx.doi. org/10.1061/(ASCE)0733-9429(1993)119:3(327).

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