Evaluation of oxygen transfer from bubble and free surface in bubble reactors using CFD
Accepted Manuscript Title: Evaluation of Oxygen Transfer from Bubble and Free Surface in Bubble Reactors Using CFD Author: Lee Seungjae PII: DOI: Refe...
Accepted Manuscript Title: Evaluation of Oxygen Transfer from Bubble and Free Surface in Bubble Reactors Using CFD Author: Lee Seungjae PII: DOI: Reference:
To appear in: Received date: Revised date: Accepted date:
23-5-2018 11-8-2018 11-10-2018
Please cite this article as: Lee, Seungjae, Evaluation of Oxygen Transfer from Bubble and Free Surface in Bubble Reactors Using CFD.Chemical Engineering Research and Design https://doi.org/10.1016/j.cherd.2018.10.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Evaluation of Oxygen Transfer from Bubble and Free Surface in Bubble Reactors Using CFD
Lee, Seungjae*
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Functional Manager, Environmental Process Engineering Team, Global Engineering Division, GS Engineering & Construction
Bubble and free surface mass transfer were employed by CFD model.
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Three-phase, two-domain simulation is more reliable than two-phase, one-domain.
Free surface mass transfer is nearly fixed in low gas flow rate.
For the increase of free surface mass transfer, high flow rate should be applied.
ABSTRACT This research uses the newly-developed Computational Fluid Dynamics (CFD) model which employs free surface mass transfer and bubble mass transfer using the small eddy model
(SEM), and investigates the effects of multiple factors, including SEM coefficient, airflow rate, and bubble diameter. The study reveals that (1) two-domain simulations supports experimental data better than one-domain simulations, (2) free surface mass transfer occupies a small portion of overall mass transfer, irrespective of the SEM coefficient and (3) flow rate and bubble size
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is not a critical factor on free surface mass transfer in low airflow rate condition. Thus, to enhance free surface mass transfer, high flow rate condition first of all should be applied. This
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research demonstrates a new approach for evaluating mass transfer using the CFD model, making it helpful for deriving optimal bubble reactor design and operation.
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Transfer, Small Eddy Model, Bubble Reactor Design
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Keywords; CFD (Computational Fluid Dynamics), Bubble Mass transfer, Free Surface Mass
Nomenclature
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V : velocity [m/s]
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db : bubble diameter [m]
k L : mass transfer coefficient [m/s]
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p : pressure [Pa]
g : gravity acceleration [m/s2] FL : lift force [N]
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FVM : virtual mass force [N] CVM : virtual mass force coefficient FTM : turbulent dispersion force [N] MGL,D : interphase momentum transfer due to drag Sct : turbulent Schmidt number
FD : drag force [N] CD : drag coefficient Dt : turbulent diffusivity [m2/s] Dm : molecular diffusivity [m2/s]
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C : oxygen concentration in liquids [kg/m3] c : small eddy model coefficient
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a : specific area [/m] t C : contact time [s] t slip : slip velocity [m/s]
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t : time [s]
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Greek letters
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α : volume fraction
ρ : density [kg/m3]
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μ : viscosity [Pa s]
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ε : turbulent energy dissipation rate [m2/s3]
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ν : kinematic viscosity [m2/s]
Subscripts
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b : bubble
f : free surface g : gas phase k : k (dispersed gas, continuous liquid, or continuous gas) phase l : liquid phase s : saturation
Introduction A bubble reactor is widely used in the environmental and chemical engineering fields.
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Mass transfer between a dispersed gas phase (i.e., air) and a continuous liquid phase (i.e., water) is an important mechanism for the design of a bubble reactor, as the gas dissolution into liquid
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phase greatly affects biochemical reaction rates in multiphase flows (Olle et al., 2006). In
particular, as oxygen is difficult to dissolve in water and bubble reactor operation makes up a large portion of a plant’s operational costs, an accurate mass transfer prediction is important
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for the optimal design of bubble reactors.
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Generally, mass transfer in bubble reactors depends on both the static and dynamic
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properties of liquids and liquid dynamics (Merchuk and Ben-zvi, 1992). Because static
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properties such as density and surface tension are nearly uniform, dynamic properties related to flow and flow dynamics greatly affect mass transfer. Many researchers have investigated the
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relationship to express the effects of dynamic properties and flow dynamics on the mass
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transfer (Merchuk and Ben-zvi, 1992; Koynov et al., 2007; Nikov and Delmas, 1992; Murai et al., 2006; Sung et al., 1991; Shamlou et al., 1998; Contreras et al., 1999). Initial researches
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reported that mass transfer could be simply derived from global shear rate as a function of the superficial gas flow rate (Chisti et al., 1986; Kawase and Moo-Young, 1986; Merchuk and BenZvi, 1992). Other studies disclosed that additional factors such as pore size and reactor
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geometry are related to the accurate prediction of mass transfer (Deckwer and Schumpe, 1993; Contreras et al., 1999; Krishna and Van Baten, 2003; Mitani et al., 2005). Computational Fluid Dynamics (CFD) has emerged as a powerful tool for the accurate prediction of oxygen mass transfer (Van Baten and Krishna, 2004; Dhanasekharan et al., 2005; Zhang et al., 2005; Talvy et al., 2007; Fayolle et al., 2007; Kerdouss et al., 2008; Huang et al.,
2010; Li et al., 2012; McClure et al., 2015; Azargoshasb et al., 2016). In particular, in a homogeneous flow regime, defined as less than 0.034 m/s of superficial velocity, the simulated results by CFD generally have good agreement with measured data (Krishna and Van Baten, 2003). Zhang et al. (2005), Talvy et al. (2007) and Fayolle et al. (2007) developed the mass
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transfer model in gas-liquid interaction and predicted oxygen mass transfer efficiency. Huang et al. (2010) compared various mass transfer equations with experimental data and reported
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that Higbie’s Penetration Theory (1935) of bubble flow modeling was in close agreement with experimental results. Research by McClure et al. (2015) used a CFD model by employing a
measured oxygen mass transfer coefficient. Recently, CFD model has been developed for
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describing the hydrodynamics of bubbles or particles, by coupling with population balance
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model or discrete element method (Buffo et al., 2012; Renze et al., 2014; Attarakih et al., 2015;
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Ebrahimi et al., 2017). The recent technology seems to be useful to describe the interaction
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with particles and bubbles’ breakup and coalescence in the heterogeneous flow regime. These CFD models may replace time-consuming experiments and allow for simulating various
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conditions making them helpful for efficiently revealing optimal reactor design.
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Although oxygen mass transfer in bubble reactors is carried out both from free surface mass and bubble mass, to the author’s knowledge, existing research using CFD models have
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neglected the oxygen mass transfer from free surface mass (Huang et al., 2010; Fayolle et al., 2007; Talvy et al., 2007). Although these studies assumed that free surface mass transfer is not significant when compared to bubble mass transfer, DeMoyer et al. (2003) concluded that free
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surface mass transfer was 70% of bubble mass transfer in both experimental results and by mathematical model. Wilhelm and Martin (1992) reported that one-third of the total oxygen mass transfer was free surface mass transfer and the rest resulted from bubble mass transfer at a gas flow rate of 1.134 m3/h. McWhirter and Hutter (1989) also reported that the bubble mass transfer rate was five to eight times greater than the free surface mass transfer rate in a fine
bubble system, and two to three times greater in a coarse bubble system. However, Schaub and Pluschkell (2006) argued that bubble mass transfer linearly increased with the gas flow rate, while free surface mass transfer was nearly fixed irrespective of gas flow rate. The previously cited researches on the evaluation of free surface mass transfer did not include direct
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mechanisms such as surface motion and turbulence on a free surface mass and depended on using statistical methods, which may introduce statistical as well as experimental errors.
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Moreover, as measured mass transfer from experimental observation typically differs among observation points, the values may not depict the global mass transfer of the bubble reactor. So far, there is no existing research on the direct derivation of free surface mass transfer,
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and contradictory statements on its effect. For the accurate prediction and evaluation of bubble
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mass and free surface mass transfer, this research will focus on the followings:
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To develop a CFD model that includes free surface mass as well as bubble mass
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transfer;
To compare simulated local mass transfer efficiency with measured efficiency; and
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To investigate the variations of free surface and bubble mass transfer with various
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factors such as model coefficient, air flow rate and bubble size. This research is helpful for engineers to derive an optimal design and operation strategy
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of bubble reactors, by suggesting CFD techniques for the prediction of the mass transfer and indicating which one is priority for higher free surface mass transfer between the airflow rate
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and bubble size.
METHODS Reactor Geometry and Meshing The pilot scale reactor for measuring oxygen mass transfer is a transparent acryl tank with dimensions of Length × Width × Height (2 m × 0.5 m × 1 m). Diffusers are located in the
centerline of the width and they are evenly distributed with the same span of 30 cm. The diffusers are circular type with the diameter of 3 cm and placed at 5 cm from the bottom of the reactor. Water depth is fixed at 0.6 m. For the simulation of the reactor, tetrahedral and triangular type elements are used for
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volume and surface meshing, respectively. The number of volume elements ranges from 161,000 to 810,000. The meshed reactor with large number of elements is used for two-domain
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simulation. The size of elements differs from each part of the meshed reactor. As shown in
Figure 1, the small size of elements is applied to free surface for higher resolution. The number of elements on the free surface is reached to be 27,000 and it is more than 17 times of elements
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on the top side of the reactor. Average areas of unit surface element in the free surface and top
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side are 37.0 mm2 and 662.3 mm2, respectively. Air-released surface also consists of the small
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size of elements to describe their circular shape and unit element area is 7.35 mm2. In case of
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vertical direction, the size of unit element size ranges from 5 mm to 50 mm. The commercial
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software, ICEM CFD 16.0 is used for meshing.
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Details of CFD meshing
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CFD Model Development General Description
A three-phase fluid, including continuous liquid, dispersed gas, and continuous gas
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phases is used, and the Eulerian-Eulerian-Eulerian approach is applied for simulating the hydrodynamics of each phase. Bubbles are specified as the dispersed gas phase, and the continuous gas phase depicts atmosphere over free surface. In spite of higher computational loads, separating air into dispersed gas and continuous gas is inevitable to avoid an overestimation of mass transfer on a free surface. Contrary to reality, Water on a free surface in
simulations is described as high air volume fraction of 0.5. It can make bubble mass transfer on a free surface to be over-estimated when applying a two-phase (i.e., continuous water and dispersed air) approach. Because a low superficial gas velocity as applied in this study can be a homogeneous flow regime (Krishna and Van Baten, 2003), a single mean bubble diameter is
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adopted as 1.273 mm. The diameter is the volume equivalent diameter calculated from Ahn’s research data (2003), assuming that released bubbles was elliptic and the bubbles are two
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dimensionally axisymmetric. The data are acquired from an experiment used with the same diffuser. The bubble type in the simulation is assumed to be a sphere, and break-up and coalescence which affect bubble size in their ascent are not considered. Additionally, as an
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isothermal condition of 20C is applied in the developed CFD model, heat transfer between air
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and water is ignored. CFX 16.0 commercial code is used for implementing the CFD model.
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Model Setup
For each phase, the volume-averaged mass and momentum conservation in the steady
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state are shown in the following equations, respectively:
As mentioned earlier, this model was set at a temperature of 20C, and the energy
equation was not considered. In Eq. (2), the source term (SM ) represents the momentum exchange between air and water, which is generally the sum of individual components arising from independent physical effects, including virtual mass, lift force, turbulent dispersion, and drag. Azargoshasb et al. (2015) neglected force effects other than drag in the momentum
exchange. However, Delnoig et al. (1997) reported that the virtual mass and the lift force cannot be neglected in a bubble column simulation. The virtual mass and lift force are also considered in this research
FL = αg ρl CL (Vg − Vl ) × (∇ × Vl )
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(3)
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The lift force (FL ) is defined as:
The lift coefficient (CL ) is defined as 0.53 (Delnoij et al., 1997).
dVg
)
(4)
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dt
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DV
FVM = αg ρl CVM ( Dtl −
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The virtual mass force with the mass transfer is defined as:
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The virtual mass coefficient (CVM ) is generally adopted as 0.5, which is also the value
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suitable for describing a virtual mass force (Delnoij et al., 1997; Monahan, 2007). In the ANSYS CFX software, the interphase turbulent dispersion force was
∇αg
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ν
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implemented based on the Favre Averaged Drag Model, and is defined as:
FTD = MGL,D Sct,l ( α −
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t,l
g
∇αl αl
)
(5)
The interphase momentum transfer due to drag (MGL,D ) and the turbulent Schmidt
number for liquid phase (Sct,l ) typically have a value of 0.9. The drag force per volume (FD ) for spherical bubbles is written as:
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FD = 4 dD αg ρl CL (Vg − Vl )|Vg − Vl |
(6)
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The Ishii-Zuber Drag Model was used to evaluate drag coefficient (CD ) as this model is applicable to general fluid particles such as drops and bubbles (Li et al., 2012).
∇ ∙ (Vl αl ρl Cl ) = ∇ ∙ (ρl (Dm + Dt )∇Cl ) + ST
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(7)
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Oxygen transport in continuous water in a steady state is written as:
Molecular diffusivity for oxygen (Dm ) is calculated using the Wilke and Chang’s Model
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(1955) and defined in standard conditions (20C, 1 atm) as 2.42E-9 m2/s. Turbulent diffusivity
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(Dt ) may be derived by dividing the turbulent Schmidt number by the eddy viscosity (Talvy et
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al., 2007).
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The source term for mass transfer (ST ) is composed of the flux from bubbles and the
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free surface, as follows:
(8)
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𝑆𝑇 = k L,b ab × (Cs − C) + k L,f af × (𝐶s,f − C)
In this equation, the saturation concentration in liquid (Cs ) and saturation concentration
on a free surface (Cs,f ) are derived from experimental results. Details of Eq. (8) are described
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in the next section. For solving turbulence, a standard k-ε model is applied as homogeneous model in this research. In the interphase between continuous liquid and dispersed gas phase, Sato Enhanced Eddy Viscosity model is used for turbulence transfer (ANSYS, 2013).
Bubble Mass Transfer
The flux for bubble mass transfer may be presented as:
Fb = k L,b ab × (Cs − C)
(9)
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In this research, the mass transfer between bubble and water follows Higbie’s penetration theory. According to Higbie’s research (1935), the bubble mass transfer coefficient
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k L,b = 2√ tm
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(k L,b ) may be presented with contact time (t C ) and molecular diffusivity (Dm ) as follows:
(10)
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C
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Because the bubbles are assumed to be spherical, contact time (t C ) may be derived using
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the bubble diameter (db ) and slip velocity (Vslip ) as follows:
π db
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tC = V
(11)
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slip
Therefore, the mass transfer coefficient can be rewritten as per Talvy et al. (2007) as
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follows:
Dm Vslip π db
(12)
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k L,b = 2√
In the case of the specific area (ab ) for bubbles, the following equation may be written as:
ab = 𝛼𝑔
1⁄ πd3 6 b πd2b
= 𝛼𝑔
db
(13)
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π db
𝛼𝑔
db 6
× (CS − C)
(14)
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Dm Vslip
Fb = 2√
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Finally, the bubble mass transfer may be rewritten as:
Free Surface Mass Transfer
Even though the free surface mass transfer process includes molecular and turbulent
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diffusions (Nguyen et al., 2015), the turbulence near the surface largely regulates the free
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surface mass transfer (Zappa et al., 2007; Wang et al., 2015), and will be highly enhanced in
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strong turbulence. In this research, the small eddy model (SEM) developed by Lamont and
(15)
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k L,f = c (εν)1/4 Sc −1/2
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Scott (1970) is used for explaining the free surface mass transfer coefficient (k L,f ) as follows:
Because kinematic viscosity (ν) and Schmidt number (Sc = ν/Dm ) are constant under
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standard conditions, the practical application of SEM relies on the estimation of turbulent energy dissipation rate (ε) on the water side close to the free surface. Although the SEM coefficient (c) is related to turbulence in specific conditions such as a low turbulent Reynolds
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number (Wang et al., 2015), it is generally known as a constant value, although it varies with the location used for measuring the turbulent energy dissipation rate (Zappa et al., 2007; Vachon et al., 2010; Wang et al., 2015). This research, in consideration of the range of prior research findings, defines the coefficient as 0.21 (Wang et al., 2015). Specific area in free surface (af ) is calculated by dividing free surface area by water volume (Nguyen et al., 2015).
Boundary and Solving Conditions For the description of gas inflow, the mass flow rate is specified at the diffusers. In case
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of the outlet, “opening” is applied and an entrainment condition with 0 pa of relative pressure is specified. The surface, except the inlet and outlet, is specified as the wall on which a non-
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slip condition is applied. Even though the height of the geometry is 1.0 m, the water level is defined at 0.6 m. Therefore, the water volume fraction in the condition where the height is lower than 0.6 m is defined as 1, and a height higher than 0.6 m is defined as 0. Based on
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experimental results, dissolved oxygen (DO) concentration is initially specified as 0 ppm and
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0.5 ppm in four-diffuser simulation and five-diffuser simulation, respectively. There is no
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difference of the initial DO between upper and down regions.
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The developed model is solved in a steady state and the criteria for solving is 10-4 of the Root Mean Square (RMS) value, which is sufficient for an engineering application (ANSYS,
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2013). The number of maximum iterations is 5,000. All simulations were performed on a
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workstation (Operating system: Windows 7 Professional K, Memory: 32.0 GB, CPU: Intel Xeon 3.30 GHz). Twelve processors were used for the simulations in a parallel mode. Each
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simulation required approximately eight hours to complete.
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Experiment Setup
Pilot scale experiments were carried out to calculate the oxygen transfer rate. The
oxygen transfer test was conducted using tap water. For de-oxygenation, sodium sulfite (Na2SO4) and Cobalt chloride (CoCl2) were used as the reactant and the catalyst, respectively (APPA, 1996). The air pump, MP-300 (manufactured by DOOIN Tech.) was used for blowing
air. The flow meter, RMA-21-SSV, (manufactured by Dwyer) was used to control the air flow rate at 300 l/min. A glass filter of 3 cm in diameter was used as a diffuser, with the pore size of 40 μm to 60 μm. The diffuser is made by processing Funnel Buchner (manufactured by Pyrex Corning Glass). The number of diffusers used in the experiment was four or five. In each
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experiment, DO concentrations at the top and bottom sides were measured within 20 cm from the free surface and the bottom with the DO sampling points horizontally located at the middle
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of the diffusers in order to minimize the interruption of adjacent diffusers, as shown in Figure
2. The DO concentration was measured by the DO sensor, MS-DO-714 (manufactured by MicroSet) every two minute. The test was conducted until the DO concentration reached a
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saturation concentration, which took approximately 10 h.
= −k L a C
(16)
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dt
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dC
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The rate of DO is correlated with the mass transfer coefficient (k L a) as follows:
C −C
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By integrating Eq. (16), the k L a value can be derived as:
ln C s−C t = −k L a t 0
(17)
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s
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Results and Discussion Experimental Results The results of the pilot test, displayed in Figure 3, show the saturation concentrations
in the upper and lower positions recorded as 6.4 ppm and 6.2 ppm in the four-diffuser experiment, respectively, with the DO concentration in the upper position commonly higher than that in the lower position. It was concluded that k L a can be calculated as 0.0067 min-1 and 0.006 min-1 using Eq. (17) for the upper and lower positions, with the k L a for the upper
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position 10% higher than that for the lower position. This trend was obviously observed in the five-diffuser experiment, where the k L a values were derived as 0.007 min-1 and 0.006 min-1
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for the upper and lower positions. In summary, the saturation DO concentration in the upper
position was 0.2–0.4 ppm higher than DO in the lower position and the higher k L a of the
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upper position was 10% in both experiments.
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diffuser experiment>
Comparison between One-Domain and Two-Domain Simulations and Model Verification
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As discussed, earlier CFD researchers neglected to consider the free surface mass
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transfer. The previous CFD simulation was generally adopted as a single domain and the outlet condition was specified as a degassing condition. Both gas and liquid domains were applied in
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the present study, with the oxygen mass transfer limited within the liquid domain. Figure 4 shows the difference of k L a values between the one-domain and two-domain simulations. High k L a values in both simulations are illustrated in the bubble plume, with the two-domain
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simulation showing a wider distribution of k L a than the one-domain simulation. As height is adjacent to the free surface, the k L a value seems to be horizontally more diffusive in the twodomain simulation. The results indicated that a higher k L a value in the two-domain simulation was observed at the upper regions between diffusers, which may be due to a difference in gas outlet conditions. While the free surface in the one-domain simulation is fixed and bubbles
disperse with the degassing condition, the free surface in the two-domain simulation was determined by the density difference between water and air and bubbles moving with the density difference. As a result, bubbles may be more easily transported horizontally in the twodomain simulation.
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Table 1 shows local k L a values of the simulations and experiments in each sampling point. In the four-diffuser case, although the one-domain simulation showed no difference
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between upper and lower sampling points, the two-domain simulation and experiments show that the upper sampling points are higher at 0.00732 min-1 and 0.00673 min-1, respectively.
Similar trend was also observed in the five-diffuser case. The difference between the k L a
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values of the upper and lower sampling was 0.00024 min-1 in the one-domain simulation, but
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values reached 0.00101 min-1 and 0.00113 min-1, in the experiment and two-domain simulation,
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respectively.
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(b) Two-domain simulation>
The results were statistically analyzed to investigate which simulation was more robust,
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as shown in Table 1. The mean absolute percentage error (MAPE) statistical tool was used for measuring prediction accuracy, with a value inversely proportional to the accuracy of the prediction data (Lee et al., 2016). The two-domain simulation was more accurate with MAPE
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values of 4.82% and 1.30%, making the simulation generally acceptable (Lee et al., 2016). Therefore, the two-domain simulation was chosen for its greater accuracy in the oxygen transfer modeling.
For more robust verification, previous experimental data (Vandu and Krishna, 2004) are compared. The experiments were carried out in clean water and ten cases experiments in bubble columns with diameter of 0.1m and 0.15m were chosen for the verification of the developed CFD simulation. All cases are affiliated to the homogenous flow regime. The results
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show that determination coefficient (R2) is reached to be 0.95, as shown in Figure 5. MAPE
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value is also calculated to be 5.0% and thus, the simulation is reasonable and acceptable.
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Effect of SEM Coefficient on Free Surface Mass Transfer
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Although the SEM coefficient is defined as 0.21 in this research, it generally varies
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from 0.15 to 0.7 (Zappa et al., 2007; Vachon et al., 2010). Because the coefficient has a wide
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variation and directly relate to the effect on free surface mass transfer, many readers may wonder whether it is one of main effect factors on free surface mass transfer due to the
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uncertainty. Thus, it should be revealed how much the coefficient affects free surface mass transfer with the variation. To investigate the effect, the coefficient of 0 to 0.6 was applied to
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the CFD simulation. In that the coefficient cannot affect mass transfer from bubbles, the k L a
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in the coefficient of 0 means only oxygen mass transfer occurs from bubbles. Therefore, the difference between the k L a value in the coefficient of 0 and the k L a value in another
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coefficient shows the mass transfer from the free surface in the specific SEM coefficient. Figure 6 shows that global and free surface mass transfers linearly increase with the
SEM coefficient in four-diffuser and five-diffuser simulations. In the coefficient of 0, mass transfers were recorded as 0.02513 min-1 and 0.02414 min-1 in both simulations. However, if the coefficient is changed to 0.4, the values increased to 0.02788 min-1 and 0.02659 min-1, respectively. Finally, the free surface mass transfer linearly increased with the coefficient by
the slope of 0.000688 min-1 and 0.000613 min-1, respectively. This trend corresponds to our expectations because the free surface mass transfer is linearly proportional to the SEM coefficient as demonstrated in Eq. (15). Even if the SEM coefficient is high value as 0.6, the free surface mass transfer is just 12 - 13 % of the global mass transfer. It means that free surface
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occupies a small portion of global mass transfer, irrespective of the magnitude of the SEM
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coefficient.
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five-diffuser simulation>
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The four-diffuser simulation had a slightly higher mass transfer coefficient than the
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five-diffuser simulation, as depicted in Figure 6. Because superficial velocity in a larger
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diffusion area is actually less in fixed air flow rate condition, slip velocity between the bubble and the interfacing water may be less in a five-diffuser simulation, resulting in a higher mass
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transfer rate in the four-diffuser simulation. However, the trend that a smaller diffusing area
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may result in a higher mass transfer rate cannot be generalized because bubble diameter may be larger in a higher superficial velocity condition in the same diffuser, and smaller bubble size
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enhances higher mass transfer rate. Therefore, in the author’s opinion, the optimal diffusing area may be derived for the highest mass transfer rate. The research will be done in a future
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study.
Effect of Airflow Rate on Bubble and Free Surface Mass Transfer Table 2 shows the variance in the mass transfer coefficient with an increasing airflow rate. As total flow rate increases from 300 ml/min to 1,000 ml/min, the global mass transfer rate also increases from 0.0261 min-1 to 0.1106 min-1 in the four-diffuser simulation, although
the free surface mass transfer rate is nearly fixed at 0.00124 min-1, irrespective of airflow rate. The same condition was also observed in the five-diffuser simulation. The free surface mass transfer rate is nearly fixed as 0.00128 min-1 while the bubble mass transfer rate increases from 0.0241 min-1 to 0.0754 min-1 in the five-diffuser simulation, in agreement with the study
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findings by Schaub and Pluschkell (2006) which showed that the bubble transfer rate linearly increased with the flow rate while the free surface rate was nearly uniform. Considering the
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ratio of free surface mass transfer rate to global mass transfer value, shown in Figure 7, free surface mass transfer has a small portion of the global mass transfer, decreasing from 5% to 1%
with increasing airflow rate in both simulations, as free surface mass transfer rate is nearly
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constant. Finally, the increase of oxygen mass transfer with high flow rate results from the
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dissolution of oxygen in bubbles, not by re-aeration from the free surface mass.
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Previous research has not shown common conclusions on the free surface mass transfer
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rate. McWhirter and Hutter (1989) evaluated bubble and free surface mass transfer rates by
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obtaining a best-fit regression curve from experimental data. DeMoyer et al. (2003) applied the same framework as that of McWhirter and Hutter using nitrogen dissolution. These studies
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commonly concluded that surface mass transfer rate increased with high air flow rate. In particular, DeMoyer et al. (2003) reported that the free surface mass transfer rate reached 85% of the bubble mass transfer rate in high flow rate conditions. These studies considered high
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flow rate conditions, in the range of 51 – 76 m3/h in the DeMoyer et al. study, and in the range of 125.4 – 683.4 m3/h in the McWhirter and Hutter study. Schaub and Pluschkell (2006) reported on an experiment conducted in a relatively low flow rate of 2.41 – 53.16 ×10-5 m3/h. The present study applied low flow rate range, with results similar to those found by Schaub and Plushckell (2006), leading the author to conclude that the free surface mass transfer rate
can sharply increase only at a high flow rate. That is, airflow in a high flow rate condition has a critical effect on the turbulence of the free surface and free surface mass transfer rate.
Effect of Bubble Diameter on Bubble and Free Surface Mass Transfer
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Bubble size may also affect mass transfer. Coarse bubbles decrease the interfacial area between the water and the bubble and helps the bubble mass transfer rate to be reduced.
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However, because coarse bubbles can generate stronger turbulence in the water body (Yoon,
2015), they may theoretically result in a higher free surface mass transfer rate. Figure 8 shows the variance of bubble and free surface mass transfer rates according to bubble diameter in the
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four-diffuser simulation. As the bubble diameter increases from 1.273 mm to 3.310 mm, the
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global mass transfer rate is linearly reduced from 0.0486 min-1 to 0.0133 min-1, caused by the
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expected decrease of the bubble mass transfer rate. The interfacial area sharply decreased to
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38% with increasing bubble diameter, and the bubble mass transfer reduced to 42%. As the bubble mass transfer rate makes up a significant portion of the global mass transfer rate, it
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directly resulted in the decrease of the global mass transfer rate. In the case of the free surface
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mass transfer rate, significant changes with bubble diameter changes were not observed. As shown in Figure 9, the turbulent energy dissipation rate on the free surface is nearly fixed,
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indicating that the turbulence generated on free surface by bubbles is not great, irrespective of bubble size. The author concluded that the effect of bubble size on the free surface mass transfer rate is not critical in a low airflow rate condition. Therefore, the free surface mass transfer rate
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may be greatly determined by air flow rate.
In this research, to investigate the effect of bubble size, various bubble sizes were applied at a fixed flow rate and the bubble breakup and coalescence were ignored. In practical terms, a bigger bubble may be diffused at a high flow rate and bubble size can be changed
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according to the flow path. In a future study considering these bubble size variables, the CFD model should be revised for practical use, and a general relationship for calculating the mass
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transfer coefficient should be derived.
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Conclusion
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In bubble reactors, oxygen mass transfer occurs from two interfacial surfaces: bubble
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and free surface. Although many researchers have statistically compared and quantified the
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bubble and free surface mass transfer, how free surface transfer influences global mass transfer
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has remained in question. In this research, free surface mass transfer was evaluated using the CFD model, and a new CFD model was developed for the estimation of bubble and free surface
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mass transfer.
The following conclusions were established:
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The experimental results show that the mass transfer rate in the upper position is 10% higher than that found in the lower position. This condition was obviously present in
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the two-domain simulation and not the one-domain simulation as bubbles in the twodomain simulation may be easily transported horizontally due to the unlimited boundary condition. Thus, two-domain simulation with three phases is recommended for more accurate simulation of free surface mass transfer.
The free surface mass transfer is calculated using SEM and the coefficient in the SEM has a wide variation. Evaluation of mass transfer with varying the SEM coefficient
shows, as expected, the free surface mass transfer is linearly increases with the SEM coefficient. However, the free surface mass transfer has a small portion of overall mass transfer, irrespective of the SEM coefficient. As airflow rate increases from 300 ml/min to 1,000 ml/min, the global mass transfer
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rate is enhanced but the free surface mass transfer remains nearly fixed, indicating that the airflow rate affects only the bubble mass transfer. Based on a review of previous
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research, the author concludes that the flow rate is less important to free surface mass transfer in homogeneous flow regime.
In considering the effect of bubble size, there is also no visible change of free surface
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mass transfer in large bubble simulation. The effect of bubble size does not appear to
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be critical in low airflow rate and the increase of airflow rate is inevitable for higher
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free surface mass transfer, rather than the increase of bubble size.
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Biotechnology and Applied Biochemistry 41(1) 1–8
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Details of CFD meshing
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experiment>
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6
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4
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DO (ppm)
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200
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100
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4EA_Lower 4EA_Upper
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Time (min)
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(b) Two-Domain simulation>
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(a) One-Domain simulation
(b) Two-Domain simulation
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Simulated Volumetric Mass Transfer Coefficient [1/min]
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Observed Volumetric Mass Transfer Coefficient [1/min]
