CFD-Based Investigation of the Effects of Aeration Mode and Superficial Gas Velocity on Dissolved Oxygen Distribution and Oxygen Transfer in an Airlift Reactor

Abstract

Dissolved oxygen (DO) regulation is essential for one-stage partial nitrification–anammox (PNA), which requires oxygen supply for nitrite production while protecting anammox bacteria from excessive oxygen exposure. In this study, a computational fluid dynamics (CFD) model coupled with a population balance model, species transport model, and gas–liquid mass transfer model was developed to investigate DO regulation in an airlift reactor (ALR). The effects of aeration mode and superficial gas velocity on DO distribution, oxygen transfer, flow-field characteristics, and bubble behavior were analyzed. The results showed that annulus-rising aeration mode promoted broad oxygen dispersion, producing a relatively homogeneous DO field with a low-DO zone fraction of only 5%. In contrast, center-rising aeration mode confined oxygen transfer mainly to the riser and maintained lower DO in the downcomer, increasing the low-DO zone fraction to 52%. Under center-rising aeration, increasing superficial gas velocity from 0.5 to 3.0 cm/s enhanced gas holdup, liquid circulation, interfacial area, and k _L a. Passive-tracer analysis further showed that increasing superficial gas velocity shortened the residence times in both the riser and downcomer, while regional tracer transport was faster in the CR-ALR than in the AR-ALR at 1.5 cm/s. A superficial gas velocity of 1.5 cm/s achieved the best balance between oxygen transfer enhancement and low-DO zone preservation. This study provides guidance for constructing spatially differentiated oxygen environments in airlift reactors for one-stage PNA.

1. Introduction

Partial nitrification and anammox (PNA) is an energy-efficient biological nitrogen removal process that integrates nitrite production and anammox conversion. , Partial nitrification oxidizes part of ammonium to nitrite via ammonium-oxidizing bacteria (AOB) while suppressing nitrite-oxidizing bacteria (NOB), and anammox bacteria subsequently convert the remaining ammonium and produced nitrite to nitrogen gas under oxygen-limited or anoxic conditions. Compared with conventional nitrification–denitrification, PNA requires no organic carbon addition and can substantially reduce aeration demand, sludge production, and operational costs. ,

PNA can be operated in either two-stage or one-stage configurations. One-stage PNA integrates nitrite production and anammox conversion in a single reactor, reducing process complexity and reactor footprint. However, this integration creates a key dissolved oxygen (DO) regulation challenge: AOB require oxygen for nitrite production, whereas anammox bacteria are sensitive to excessive oxygen exposure. Therefore, an ideal one-stage PNA reactor should establish a spatially heterogeneous DO environment, where oxygen-enriched zones support partial nitrification and low-oxygen zones protect anammox activity.

ALRs are promising for constructing such oxygen environments because of their riser–downcomer structure and aeration-driven internal circulation. Oxygen transfer mainly occurs in the aerated region, whereas the downcomer or weakly aerated regions may maintain lower DO levels. In addition, ALRs have simple configuration, low mechanical energy input, favorable liquid circulation, and efficient gas–liquid contact, making them suitable for biological processes involving coupled mass transfer and reaction.

Recent studies have increasingly focused on establishing spatially differentiated DO environments in airlift reactors. Wang et al. developed a dissolved oxygen-differentiated airlift internal-circulation reactor and demonstrated that reactor configuration could establish distinct oxygen environments for different functional microorganisms. Chen et al. further introduced an airlift inner-circulation partition bioreactor with dual inner circulation and multiple spatial compartments, in which differentiated oxygen conditions were established between different reactor regions. More recently, CFD-assisted investigations of airlift inner-circulation partition bioreactors have provided detailed information on internal DO distribution and demonstrated the important role of reactor geometry in regulating spatial oxygen distribution. Oxygen-partitioned airlift reactors have also been applied to one-stage PNA systems, demonstrating the potential of spatial DO differentiation for accommodating microorganisms with contrasting oxygen requirements.

Despite these advances, previous studies have primarily emphasized reactor performance, biomass retention, sludge characteristics, microbial community evolution, and the biological responses associated with established oxygen gradients. − The hydrodynamic mechanisms governing the formation of spatial DO heterogeneity remain less systematically understood. In particular, aeration configuration determines the initial gas distribution and primary region of oxygen transfer, whereas superficial gas velocity affects gas holdup, liquid circulation, bubble transport, interfacial area, and oxygen-transfer intensity. How these hydrodynamic and mass-transfer processes collectively regulate spatial DO zonation in ALRs has not yet been sufficiently clarified. Therefore, evaluating ALRs solely on the basis of bulk DO concentration or overall oxygen-transfer capacity may overlook the spatial oxygen environments required by one-stage PNA.

CFD provides detailed spatial information on gas–liquid flow, bubble behavior, oxygen transfer, and DO distribution, and is therefore suitable for revealing the formation mechanisms of DO zonation in ALRs. ,

To address these gaps, this study developed a CFD model to investigate DO regulation in an ALR for one-stage PNA. The effects of aeration mode and superficial gas velocity on DO concentration, DO zonation, oxygen transfer, flow-field structure, and bubble behavior were systematically analyzed. Annulus-rising aeration and center-rising aeration were first compared to identify the preferred aeration mode for DO zonation, and superficial gas velocity was then optimized under the selected configuration.

2. Geometry and CFD Modeling

2.1. Geometry and Mesh Generation of the ALR

The geometric model of the ALR is shown in Figure (a). The reactor had an inner diameter of 290 mm and a working liquid height of 1500 mm. A draft tube with an outer diameter of 200 mm, a wall thickness of 5 mm, and a height of 1400 mm was coaxially installed inside the reactor. The clearances between the draft tube and the reactor top and bottom were both 50 mm.

1.

Geometry and computational mesh of the airlift reactor: (a) reactor geometry and internal circulation schematic of AR-ALR; (b) perforated annular sparger of the AR-ALR; (c) perforated central sparger of the CR-ALR; (d) overall computational mesh; (e) cross-sectional mesh near the draft-tube wall; and (f) local mesh refinement near the gas inlet.

As shown in Figure (b,c), two aeration configurations were considered: annulus-rising aeration and center-rising aeration. For the annulus-rising configuration, a perforated annular sparger was installed in the annular region at the reactor bottom. The inner and outer radii of the sparger were 120 and 130 mm, respectively, and 20 gas inlet holes, each with a diameter of 1 mm, were uniformly distributed along the circumference [Figure (b)]. This configuration was defined as the annulus-rising airlift reactor (AR-ALR). For the center-rising configuration, a smaller perforated annular sparger was concentrically positioned in the central region at the reactor bottom, with inner and outer radii of 45 and 55 mm, respectively [Figure (c)]. The same number and diameter of gas inlet holes were employed. This configuration was defined as the center-rising airlift reactor (CR-ALR). , Except for the aeration configuration, all other reactor geometries and operating conditions were kept identical between the two cases.

The three-dimensional geometry was constructed using Design Modeler and imported into Fluent Meshing for grid generation. The computational domain was discretized using an unstructured polyhedral mesh to reduce the number of cells while maintaining numerical accuracy and stability. The overall mesh configuration is shown in Figure (d). To further illustrate the mesh distribution inside the reactor, a cross-sectional view near the draft-tube wall is provided in Figure (e), showing the mesh distribution across the central region, draft-tube wall, and annular region. Local mesh refinement was additionally applied near the gas inlet, as illustrated in Figure (f), to better resolve the strong gradients in gas–liquid flow, bubble dispersion, and oxygen transfer generated in the aeration region.

2.2. Multiphase Flow Models

2.2.1. Governing Equations

In the Eulerian–Eulerian framework, the gas and liquid phases are treated as interpenetrating continua. In the absence of phase change, the continuity equation for phase q is expressed as

$$\frac{\partial ({\alpha }_q{\rho }_q)}{\partial t}+\nabla ·({\alpha }_q{\rho }_q{\mathit{u}}_q)=0$$ 1

where α _q is the volume fraction, ρ _q is the density, and u _q is the velocity vector of phase q respectively.

$$\frac{\partial ({\alpha }_q{\rho }_q{\mathit{u}}_q)}{\partial t}+\nabla ·({\alpha }_q{\rho }_q{\mathit{u}}_q{\mathit{u}}_q)=-{\alpha }_q\nabla p+\nabla ·({\alpha }_q{\mathit{\tau }}_q)+{\alpha }_q{\rho }_q\mathit{g}+{\mathit{M}}_q$$ 2

where p is the shared pressure field, τ _q is the stress tensor, g is the gravitational acceleration, and M _q represents the interphase interaction forces acting on phase q.

$${\mathit{\tau }}_q={\mu }_{\mathrm{eff},q}[\nabla {\mathit{u}}_q+{(\nabla {\mathit{u}}_q)}^T-\frac{2}{3}(\nabla ·{\mathit{u}}_q)\mathit{I}]$$ 3

$${\mu }_{\mathrm{eff},q}={\mu }_q+{\mu }_{t,q}$$ 4

Accordingly, the term ∇·(α _q τ _q ) in the momentum equation represents the divergence of the effective viscous stress and is evaluated from the local velocity gradients and the effective viscosity, which includes both molecular and turbulent contributions.

2.2.2. Interphase Force

The drag force is the primary mechanism governing momentum exchange between the gas and liquid phases. In the Eulerian–Eulerian framework, the drag force acting on the gas phase per unit volume is expressed as

$${\mathit{F}}_{\mathrm{D}}=\frac{3}{4}\frac{C_{\mathrm{D}}}{d_{\mathrm{b}}}{\rho }_{\mathrm{l}}{\alpha }_{\mathrm{l}}{\alpha }_{\mathrm{g}}|{\mathit{u}}_{\mathrm{g}}-{\mathit{u}}_{\mathrm{l}}|({\mathit{u}}_{\mathrm{l}}-{\mathit{u}}_{\mathrm{g}})$$ 5

where C _D is the drag coefficient, d _b is the equivalent bubble diameter, ρ_l is the liquid density, α_l and α_g are the liquid- and gas-phase volume fractions, respectively, and u _g and u _l are the corresponding velocity vectors. The drag force acting on the liquid phase has the same magnitude and opposite direction.

In the present simulations, drag was considered as the dominant interphase momentum-transfer force, while lift, wall-lubrication, turbulent-dispersion, turbulence-interaction, and virtual-mass forces were neglected. To account for the effect of bubble deformation on interphase momentum transfer, the Tomiyama drag model was adopted. The drag coefficient is given by

$$C_{\mathrm{D}}=\max (\frac{24}{{\mathrm{Re}}_{\mathrm{p}}}(1+0.15{\mathrm{Re}}_{\mathrm{p}}^{0.687}),\frac{8}{3}\frac{E_0}{E_0+4})$$ 6

where the bubble Reynolds number is defined as

$${\mathrm{Re}}_{\mathrm{p}}=\frac{{\rho }_{\mathrm{l}|{\mathit{u}}_{\mathrm{g}}-{\mathit{u}}_{\mathrm{l}}|d_{\mathrm{b}}}}{{\mu }_{\mathrm{l}}}$$ 7

and the Eötvös number is

$$E_0=\frac{g({\rho }_{\mathrm{l}}-{\rho }_{\mathrm{g}})d_{\mathrm{b}}^2}{\sigma }$$ 8

where μ_l is the liquid dynamic viscosity, ρ_g is the gas density, and σ is the gas–liquid surface tension.

2.2.3. Turbulence Model

In the ALR, bubble rise, liquid circulation, and gas–liquid slip generate complex turbulent flow. In this study, the dispersed standard k–ε model was employed, in which turbulence of the continuous liquid phase was described by transport equations for the turbulent kinetic energy and its dissipation rate ε. The corresponding equations are expressed as

$$\frac{{{\partial (\alpha }_{\mathrm{l}}\rho }_{\mathrm{l}}{k}_{\mathrm{l}})}{\partial t}+\nabla ·({{\alpha }_{\mathrm{l}}\rho }_{\mathrm{l}}{k}_{\mathrm{l}}{\mathit{u}}_{\mathrm{l}})=\nabla ·({\alpha }_{\mathrm{l}}({\mu }_{\mathrm{l}}+\frac{{\mu }_{t,\mathrm{l}}}{{\sigma }_k})\nabla k_{\mathrm{l}})+{\alpha }_{\mathrm{l}}{G}_{k.\mathrm{l}}-{{\alpha }_{\mathrm{l}}\rho }_{\mathrm{l}}{\epsilon }_{\mathrm{l}}$$ 9

$$\nabla ·({\alpha }_{\mathrm{l}}({\mu }_{\mathrm{l}}+\frac{{\mu }_{t,\mathrm{l}}}{{\sigma }_{\epsilon }})\nabla {\epsilon }_{\mathrm{l}})+{\alpha }_{\mathrm{l}}{C}_{1\epsilon }{G}_{k,\mathrm{l}}\frac{{\epsilon }_{\mathrm{l}}}{k_{\mathrm{l}}}-{\alpha }_{\mathrm{l}}{C}_{2\epsilon }{\rho }_{\mathrm{l}}\frac{{{\epsilon }_{\mathrm{l}}}^2}{k_{\mathrm{l}}}$$ 10

The turbulent viscosity is calculated as

$${\mu }_{t,\mathrm{l}}={\rho }_{\mathrm{l}}{C}_{\mu }\frac{k_{\mathrm{l}}^2}{{\epsilon }_{\mathrm{l}}}$$ 11

and the production of turbulent kinetic energy due to the mean velocity gradients is expressed as

$$G_{k,\mathrm{l}}=2{\mu }_{t,\mathrm{l}}{S}_{\mathit{ij}}{S}_{\mathit{ij}}$$ 12

where S _ij is the mean strain-rate tensor. The model constants were C _μ = 0.09, C _1ε = 1.44, C _2ε = 1.92, σ _k = 1.0, σ_ε = 1.3.

2.3. Population Balance Model (PBM)

Conventional multiphase flow models often assume a constant bubble size or a single equivalent diameter, which fails to capture the dynamic evolution of bubble size caused by breakup and coalescence during the rising process. This limitation reduces the accuracy in describing gas–liquid flow and mass transfer behavior. To overcome these limitations, the Population Balance Model (PBM) was introduced to describe the bubble size distribution. The governing equation is expressed as a transport equation of the bubble number density function

$$\frac{\partial }{\partial t}[n(v,\mathbf{x},t)]+\nabla ·[\mathbf{u}(v)n(v,\mathbf{x},t)]=B_{\mathrm{break}}-D_{\mathrm{break}}+B_{\mathrm{coag}}-D_{\mathrm{coag}}+S$$ 13

where n(v, x, t) is the number density function of bubbles with size v, representing the number of bubbles per unit volume. B _break and D _break denote the birth and death terms due to breakup, while B _coag and D _coag represent the birth and death terms due to coalescence. S is a source term accounting for phase change or bubble growth. The detailed expressions of these terms are given as

$$B_{\mathrm{break}}(v)={\int }_v^{\infty }a(v^{\prime })\beta ({v|v}^{\prime })n(v^{\prime }){\mathrm{d}v}^{\prime }$$ 14

$$D_{\mathrm{break}}(v)=a(v)n(v)$$ 15

$$B_{\mathrm{coag}}(v)=\frac{1}{2}{\int }_0^v\omega (u,v-u)n(u)n(v-u)\mathrm{d}u$$ 16

$$D_{\mathrm{coag}}(v)=n(v){\int }_0^{\infty }\omega (v,u)n(u)\mathrm{d}u$$ 17

where a(v) is the breakup frequency, β­(v|v′) is the daughter size distribution function, and ω­(u,v) is the coalescence kernel. These terms collectively determine the evolution of bubble size distribution under breakup and coalescence processes.

In the population balance framework, the evolution of the bubble-size distribution is governed by the combined effects of bubble breakup and coalescence. Both breakup and coalescence were described using the Luo model. The discrete method was employed to solve the population balance equation, and the bubble-size distribution was divided into 10 discrete size classes. A geometric-ratio discretization with a ratio exponent of 1.3 was adopted. The minimum bubble diameter was set to 1 mm, and the resulting maximum diameter calculated from the discretization was approximately 14.93 mm. These discretization parameters provided a bubble-size range sufficiently broad to represent the size variation associated with breakup and coalescence under the investigated conditions. Ten size classes were adopted as a compromise between particle-size resolution and computational cost.

2.4. Gas–Liquid Mass Transfer Model

In this study, the gas–liquid mass transfer process was modeled based on the two-film theory, and the volumetric mass transfer coefficient k _L a was used to characterize the overall mass transfer performance.

$$R=k_{\mathrm{L}}a(C^{*}-C)$$ 18

where R is the oxygen mass transfer rate, k _L is the liquid-side mass transfer coefficient, a is the interfacial area, C* is the saturation DO concentration, and C is the actual DO concentration in the liquid phase.

The interfacial area is determined by the gas holdup and bubble diameter, where the bubble diameter is dynamically obtained from the PBM.

$$a=\frac{6{\alpha }_{\mathrm{g}}}{d_{\mathrm{b}}(1-{\alpha }_{\mathrm{g}})}$$ 19

The consumption of dissolved oxygen by biochemical reactions was not considered, and the analysis focused solely on gas–liquid mass transfer. To describe the dissolution and diffusion of oxygen in the liquid phase, a species transport model was employed to simulate dissolved oxygen. The governing equation is expressed as

$$\frac{\partial {\alpha }_{\mathrm{l}}{c}_{\mathrm{l}}}{\partial t}+\nabla ·({\alpha }_{\mathrm{l}}{c}_{\mathrm{l}}{v}_{\mathrm{l}})=-\nabla ·({\alpha }_{\mathrm{l}}(J_{\mathrm{l}}+c_{\mathrm{l}}^{\prime }{v}_{\mathrm{l}}^{\prime }))+S_{\mathrm{c},\mathrm{l}}$$ 20

where α_l is the liquid volume fraction, c _l is the dissolved oxygen concentration, v_l is the liquid velocity, c _l′ and v_l′ denote the fluctuating components of dissolved oxygen concentration and liquid velocity, respectively. J is the diffusive flux of oxygen in the liquid phase, and S _c,l is the interphase mass transfer source term.

The gas–liquid mass transfer process involves the coupling of bubble size, gas holdup, and local hydrodynamic conditions. To consistently couple the local bubble characteristics and hydrodynamic conditions with the oxygen-transfer calculation, a user-defined function (UDF) was developed to implement the interphase mass-transfer source term. In the UDF, the interfacial area a is first calculated based on the local gas volume fraction and bubble diameter. The liquid-side mass transfer coefficient k _L is determined using the Higbie penetration theory, which assumes that mass transfer is governed by unsteady diffusion during short contact timesNE.Cms_Insert. − The Higbie model effectively captures the enhancement of mass transfer due to rapid interfacial renewal under turbulent conditions. It can be expressed as

$$k_{\mathrm{L}}=2\sqrt{\frac{D_{\mathrm{L}}{v}_{\mathrm{r}}}{\pi d_{\mathrm{b}}}}$$ 21

where D _L is the molecular diffusivity of oxygen in the liquid phase and v_r is the gas–liquid relative velocity.

By combining k _L with interfacial area a, the volumetric mass transfer coefficient k _L a is obtained and incorporated into the source term of the dissolved oxygen transport equation, thereby enabling numerical coupling of the gas–liquid mass transfer process

$$S_{c,\mathrm{l}}=k_{\mathrm{L}}a(c_{\mathrm{l}}^{*}-c_{\mathrm{l}})$$ 22

The coupling principle is shown in Figure .

2.

Coupled Framework.

2.5. Boundary and Initialization Conditions

The liquid phase was defined as water at ambient temperature, and the gas phase was defined as air with an oxygen volume fraction of 21%. Initially, the computational domain was filled with stationary liquid water, and the dissolved oxygen concentration was set to zero. Standard initialization was used, and the initial turbulent kinetic energy and turbulent dissipation rate were estimated based on the inlet hydraulic diameter and turbulence intensity. To reduce start-up fluctuations, a preliminary transient calculation with a small fixed time step was conducted, and the stabilized flow field was used as the initial condition for subsequent oxygen transfer simulations.

A mass-flow inlet boundary condition was applied at the gas inlet, and the gas flow rate was determined according to the specified superficial gas velocity. The reactor outlet was set as a pressure outlet, with the operating pressure fixed at 101,325 Pa. All solid boundaries were treated as no-slip walls for both liquid and gas phases, and standard wall functions were used for near-wall turbulence treatment. For species transport, the dissolved oxygen flux at the walls was set to zero, indicating that the walls did not participate in oxygen transfer or reaction.

2.6. Numerical Solution Strategy

A pressure-based solver was used to simulate the transient incompressible gas–liquid flow in the ALR. The pressure–velocity coupling was handled using the Phase-Coupled SIMPLE algorithm. The momentum, turbulence, species transport, and population balance model (PBM) equations were discretized using a second-order upwind scheme to improve numerical accuracy. A fixed time step was adopted to resolve the transient evolution of gas–liquid flow, bubble behavior, oxygen transfer, and DO distribution.

Convergence was evaluated using both residual reduction and the stability of key physical variables. The residual convergence criterion was set to 10^–4. Meanwhile, reactor-scale variables, including average DO concentration, gas holdup, liquid velocity, and interfacial area were monitored during the simulation. When the residuals satisfied the convergence criterion and the monitored variables reached a stable fluctuating state, the system was considered statistically steady. The quasi-steady values obtained after this stage were used for subsequent analysis.

2.7. Passive-Tracer Analysis

To further characterize the circulation of suspended microorganisms between regions with different oxygen levels, a passive-tracer analysis was performed based on the statistically stabilized liquid-phase flow field. Massless passive tracers were released from a fixed rake surface near the lower part of the riser and were assumed to follow the motion of the continuous liquid phase without influencing the calculated flow field. Identical tracer-release positions and tracking settings were used for all superficial gas velocities to ensure consistency among the different operating conditions.

The tracer trajectories were obtained by integrating the liquid-phase velocity field. The progressive development of the trajectories was visualized using increasing tracking steps, whereas the quantitative residence-time analysis was based on the particle time recorded along each trajectory rather than on the number of tracking steps. The reactor was divided into the riser and downcomer according to the physical flow regions, and the residence time of each tracer in the corresponding region was determined from its particle-time history and regional location. The mean residence time and its standard deviation were subsequently calculated from the ensemble of released tracers to characterize the transport behavior of suspended biomass under different superficial gas velocities.

For comparison between the two aeration configurations, equivalent tracer-release surfaces were positioned near the lower part of the physical riser in the AR-ALR and CR-ALR, and identical tracking settings were applied at 1.5 cm/s.

3. Results and Discussion

3.1. Mesh Independence

To ensure numerical reliability, a mesh independence test was conducted using average gas holdup as the evaluation parameter. As shown in Figure , the predicted gas holdup gradually stabilized with increasing mesh number. When the mesh number reached approximately 4 × 10⁵, further refinement produced negligible changes, indicating mesh-independent results. Therefore, a mesh with approximately 4 × 10⁵ cells was selected for subsequent simulations considering both accuracy and computational cost.

3.

Mesh independence test.

3.2. Model Validation

To validate the developed numerical model, the simulated gas holdup and k _L a were compared with experimental and numerical data from the literature, as shown in Figure , gas holdup increased monotonically with superficial gas velocity and agreed well with the data reported by Zheng et al. and Chen et al., increasing from approximately 0.0007 to 0.0032 as the superficial gas velocity increased from 0.5 to 3.0 mm/s. Similarly, k _L a increased from approximately 0.0004 to 0.0024 s^–1, showing comparable trends and magnitudes to the results of Luo et al., , Zhang et al. and Chen et al. The agreement of both hydrodynamic and oxygen transfer parameters indicates that the PBM–CFD model can reliably predict gas–liquid flow and mass transfer behavior in the airlift reactor.

4.

Comparison of the present simulations with previous experimental and numerical results.

3.3. Effect of Aeration Mode on Dissolved Oxygen Distribution and Oxygen Transfer

It should be noted that the riser and downcomer are defined according to the direction of the main liquid circulation rather than by fixed geometric regions. In the AR-ALR, aeration in the annular region drives upward liquid flow in the annulus; therefore, the annular region acts as the riser, whereas the central region inside the draft tube acts as the downcomer. In contrast, in the CR-ALR, aeration is concentrated in the central region, resulting in upward flow inside the draft tube and downward return flow through the annular region. Accordingly, the central region serves as the riser and the annular region as the downcomer in the CR-ALR. The definitions of riser and downcomer used throughout Section follow these configuration-specific circulation directions.

For the comparison of the two aeration configurations in Section , the superficial gas velocity was fixed at 1.5 cm/s, while all other operating conditions were kept identical.

3.3.1. Dissolved Oxygen Concentration and Spatial Distribution

The aeration mode significantly affected the DO distribution in the ALR. As shown in Figure (a,c), AR-ALR produced a relatively uniform DO field, with an average DO concentration of 1.32 mg/L. The DO concentrations in the riser and downcomer were 1.45 and 1.23 mg/L, respectively, indicating that oxygen was rapidly transported throughout the reactor by internal circulation. The small DO difference between the riser and downcomer suggests that annular-riser aeration enhanced radial oxygen dispersion and weakened the spatial DO gradient. In contrast, CR-ALR generated a more heterogeneous DO distribution. As shown in Figure (b,c), oxygen transfer was mainly concentrated in the central riser, while the downcomer maintained a much lower DO level. The average DO concentration in CR-ALR was 0.60 mg/L, with 0.86 mg/L in the riser and 0.39 mg/L in the downcomer. Compared with AR-ALR, CR-ALR reduced the overall DO level but increased the DO difference between the riser and downcomer, indicating stronger spatial separation between oxygen-enriched and oxygen-limited regions.

5.

Dissolved oxygen distribution under different aeration modes: (a) AR-ALR; (b) CR-ALR; (c) regional DO concentration; (d) volume fractions of low-, transition-, and high-DO zones.

Based on previous studies on DO regulation in one-stage PNA systems, the reactor volume was divided into low-DO (<0.5 mg/L), transition-DO (0.5–1.0 mg/L), and high-DO (>1.0 mg/L) zones to evaluate the spatial oxygen environment. , The DO zoning results further confirmed this difference. As shown in Figure (d), AR-ALR was dominated by the high-DO zone, and the low-DO zone accounted for only 5% of the reactor volume. In contrast, CR-ALR increased the low-DO zone fraction to 52%, while transition- and high-DO zones were still retained near the aerated riser. Therefore, central-riser aeration was more suitable for constructing DO zonation because it maintained oxygen supply in the riser while preserving a low-oxygen environment in the downcomer.

3.3.2. Oxygen Transfer Characteristics

The temporal variations of k _L, a, and k _L a under different aeration modes are shown in Figure . All oxygen transfer parameters increased rapidly at the initial stage and then gradually reached a quasi-steady state, indicating the establishment of gas–liquid circulation and oxygen transfer. However, the two aeration modes showed distinct spatial differences in oxygen transfer behavior.

6.

Oxygen transfer characteristics in the riser and downcomer under different aeration modes: (a, c, e) riser; (b, d, f) downcomer.

In the riser, CR-ALR showed higher oxygen transfer capacity than AR-ALR. As shown in Figure (a,c,e), the k _L, a, and k _L a values of CR-ALR were generally higher after the initial development stage. The steady-state k _L a of CR-ALR was approximately 0.022 s^–1, compared with 0.015 s^–1 for AR-ALR. This indicates that central-riser aeration enhanced local oxygen transfer in the riser by concentrating the gas phase, increasing local gas holdup, and strengthening gas–liquid interaction.

In the downcomer, a different pattern was observed. Although k _L remained slightly higher in the CR-ALR, the AR-ALR exhibited substantially larger a and k _L a. As shown in Figure (d,f), AR-ALR exhibited much higher a and k _L a than CR-ALR. The interfacial area of AR-ALR stabilized at approximately 32 m²/m³, whereas that of CR-ALR remained below 10 m²/m³. Correspondingly, the downcomer k _L a of AR-ALR was about three times that of CR-ALR. Since the difference in k _L was relatively small, the higher k _L a in the AR-ALR downcomer was mainly attributed to the larger gas–liquid interfacial area.

These oxygen transfer characteristics explain the DO distribution patterns discussed in Section . In AR-ALR, oxygen transfer occurred strongly in both the riser and downcomer, promoting oxygen dispersion throughout the reactor and producing a more homogeneous DO field. In contrast, CR-ALR confined oxygen transfer mainly to the riser and greatly reduced oxygen transfer in the downcomer. This spatially selective oxygen transfer pattern allowed CR-ALR to maintain oxygen-enriched conditions in the riser while preserving a low-oxygen environment in the downcomer.

3.3.3. Flow-Field Mechanism and Bubble Behavior

The flow-field characteristics and bubble size distribution under different aeration modes are shown in Figures and . Under AR-ALR, the gas phase was distributed over a wider annular region, allowing more gas to enter both the riser and downcomer, thereby promoting gas entrainment and spatial gas dispersion. In contrast, under CR-ALR, the gas phase was mainly concentrated in the central riser, while gas dispersion into the downcomer was restricted.

7.

Flow-field characteristics under different aeration modes: (a), (b) liquid velocity distribution; (c), (d) gas velocity distribution; (e), (f) gas holdup distribution; (g) gas holdup in the riser; (h) gas holdup in the downcomer.

8.

Bubble size characteristics under different aeration modes: (a) bubble size distribution and cumulative frequency in the AR-ALR; (b) bubble size distribution and cumulative frequency in the CR-ALR; (c) comparison of bubble volume fractions between the AR-ALR and CR-ALR.

The difference in gas distribution explains the DO patterns observed in Figure . In AR-ALR, broader gas dispersion enhanced radial mixing and promoted oxygen transport throughout the reactor, thereby reducing the DO difference between the riser and downcomer and producing a more homogeneous DO field. However, this also weakened the formation of low-DO zones. By contrast, CR-ALR confined gas–liquid interaction mainly to the riser, reducing oxygen transfer in the downcomer and maintaining a clear DO gradient.

The bubble size distribution further supported the regional differences in gas–liquid mass transfer. As shown in Figure , the two configurations exhibited different bubble-size distributions due to differences in gas dispersion, breakup, and coalescence. However, the interfacial area is determined not only by bubble size but also by the local gas holdup. In the CR-ALR, the gas phase was concentrated mainly in the riser, where the combination of relatively small bubbles and higher local gas holdup resulted in a comparatively large interfacial area. In contrast, only a limited amount of gas entered the downcomer, leading to a much smaller interfacial area in this region. For the AR-ALR, broader gas dispersion promoted gas entrainment into the downcomer; consequently, despite the occurrence of relatively larger bubbles, the higher local gas holdup produced a larger interfacial area in the downcomer. Therefore, the regional differences in a shown in Figure result from the combined effects of bubble size and local gas holdup rather than from bubble size alone.

Overall, AR-ALR favored gas dispersion, liquid mixing, and DO homogenization, whereas CR-ALR favored spatially selective oxygen transfer. This flow-field and bubble behavior mechanism explains why CR-ALR was more suitable for constructing DO zonation in the ALR.

3.4. Effect of Superficial Gas Velocity under CR-ALR

3.4.1. Dissolved Oxygen Concentration and Spatial Distribution

The DO distribution under different superficial gas velocities is shown in Figure . As the superficial gas velocity increased from 0.5 to 3.0 cm/s, the DO concentration continuously increased, and the oxygen-enriched region gradually expanded from the bottom aeration zone to the upper riser and downcomer. At 0.5 cm/s, the reactor was dominated by low-DO regions, indicating insufficient oxygen supply. When the gas velocity increased to 1.0–1.5 cm/s, DO increased markedly in the riser, while the downcomer still maintained a relatively low DO level. Further increasing the gas velocity to 2.0–3.0 cm/s promoted oxygen transport into the downcomer, resulting in a broader oxygen-enriched region and a weaker spatial DO gradient.

9.

Dissolved oxygen distribution under different superficial gas velocities: (a–f) DO contours at 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 cm/s; (g) regional DO concentration; (h) volume fractions of low-, transition-, and high-DO zones.

The regional average DO concentrations further confirmed this trend. As shown in Figure (g), DO concentrations in the whole reactor, riser, and downcomer all increased with superficial gas velocity. When the gas velocity increased from 0.5 to 3.0 cm/s, the average DO concentration increased from 0.20 to 0.90 mg/L. The riser DO increased from 0.22 to 1.14 mg/L, while the downcomer DO increased from 0.18 to 0.60 mg/L. The riser always maintained a higher DO level than the downcomer, indicating that oxygen transfer was mainly concentrated in the aerated riser.

As shown in Figure (h), the low-DO fraction decreased continuously with increasing superficial gas velocity, while the transition- and high-DO fractions increased. At 1.5 cm/s, the low-, transition-, and high-DO zones accounted for 52%, 28%, and 20% of the reactor volume, respectively, indicating a balanced oxygen environment. When the gas velocity exceeded 1.5 cm/s, the low-DO zone decreased rapidly, reaching 30% at 2.0 cm/s and 14% at 2.5 cm/s. At 3.0 cm/s, the low-DO zone almost disappeared, indicating excessive oxygen dispersion. Therefore, 1.5 cm/s was identified as the preferred superficial gas velocity because it provided sufficient oxygen enrichment in the riser while preserving a considerable low-DO region in the downcomer.

3.4.2. Oxygen Transfer Characteristics

The temporal variations of the k _L, a, and k _L a under different superficial gas velocities are shown in Figure . All oxygen transfer parameters increased rapidly during the initial stage, reached a peak at approximately 5–6 s, and then gradually approached a quasi-steady state. Increasing superficial gas velocity enhanced oxygen transfer, but the response of a and k _L a was more pronounced than that of k _L.

10.

Oxygen transfer characteristics under different superficial gas velocities: (a–c) liquid-side mass transfer coefficient, k _L; (d–f) interfacial area, a; (g–i) volumetric mass transfer coefficient, k _L a. The columns represent the whole reactor, riser, and downcomer, respectively.

As shown in Figure (a–c), k _L increased slightly with superficial gas velocity, and the differences among gas velocities became less pronounced after flow stabilization. In contrast, a increased markedly with gas velocity, as shown in Figure (d–f). In the whole reactor, the quasi-steady interfacial area increased from approximately 8 m²/m³ at 0.5 cm/s to 38 m²/m³ at 3.0 cm/s. In the riser, a reached approximately 70 m²/m³ at 3.0 cm/s, mainly due to the increased gas holdup and bubble number. The downcomer was more sensitive to superficial gas velocity. At 0.5 cm/s, the interfacial area in the downcomer was close to zero, indicating that few bubbles entered the downflow region. At 1.5 cm/s, bubbles began to be transported into the downcomer, and a increased to approximately 6–8 m²/m³. When the gas velocity further increased to 2.5–3.0 cm/s, the downcomer a rose sharply to 17–24 m²/m³, indicating enhanced bubble entrainment and oxygen transfer in the downcomer.

The variation in k _L a was generally consistent with that of a. As shown in Figure (g–i), k _L a increased continuously with superficial gas velocity in the whole reactor, riser, and downcomer. In the whole reactor, the steady-state k _L a increased from approximately 0.004 s^–1 at 0.5 cm/s to 0.017 s^–1 at 3.0 cm/s. In the riser, k _L a reached approximately 0.034 s^–1 at 3.0 cm/s. These results indicate that the increase in k _L a was mainly governed by the enlargement of gas–liquid interfacial area rather than by k _L alone.

However, higher oxygen transfer capacity did not necessarily lead to better DO zonation. Although 2.0–3.0 cm/s produced higher a and k _L a, these conditions also enhanced bubble transport and oxygen transfer in the downcomer, leading to the expansion of transition- and high-DO zones. In contrast, 1.5 cm/s maintained sufficient oxygen transfer in the riser while keeping downcomer a and k _L a relatively low. Therefore, 1.5 cm/s provided a better balance between oxygen transfer enhancement and low-DO zone preservation.

3.4.3. Flow-Field Mechanism and Bubble Behavior

The flow-field characteristics and bubble behavior under different superficial gas velocities are shown in Figures and . Increasing superficial gas velocity strengthened the gas–liquid flow structure in the ALR. The gas plume in the riser became wider and more continuous, and the high-gas-holdup region expanded upward. Meanwhile, liquid circulation was enhanced, indicating that higher gas input increased the driving force for internal circulation between the riser and downcomer.

11.

Flow-field characteristics under different superficial gas velocities: (a) gas holdup contours; (b) gas holdup in the riser; (c) gas holdup in the downcomer; (d) liquid velocity contours; (e) liquid velocity in the riser; (f) liquid velocity in the downcomer.

12.

Bubble behavior under different superficial gas velocities: (a) bubble number; (b) bubble size distribution.

As shown in Figure (a–c), gas holdup increased continuously with superficial gas velocity. In the riser, the steady gas holdup increased from approximately 0.01 at 0.5 cm/s to 0.034 at 3.0 cm/s, directly enlarging the gas–liquid interfacial area. The downcomer was more sensitive to gas velocity. Almost no gas entered the downcomer at 0.5 cm/s, whereas gas entrainment became evident at 2.0–3.0 cm/s. This enhanced oxygen transfer in the downcomer but also promoted oxygen dispersion, thereby weakening low-DO zone preservation.

The liquid velocity distribution further confirmed the enhancement of internal circulation. As shown in Figure (d–f), the steady liquid velocity increased from approximately 0.28 to 0.44 m/s in the riser and from 0.22 to 0.32 m/s in the downcomer as the superficial gas velocity increased from 0.5 to 3.0 cm/s. The intensified circulation promoted liquid-film renewal around bubbles and enhanced oxygen transfer. However, excessive circulation also accelerated DO transport from the riser to the downcomer, leading to a more homogeneous DO field.

Bubble behavior also changed markedly with superficial gas velocity. As shown in Figure (a), the bubble number increased almost linearly from approximately 5 × 10⁵ at 0.5 cm/s to approximately 45 × 10⁵ at 3.0 cm/s, providing more gas–liquid contact sites and increasing interfacial area. As shown in Figure (b), the bubble size distribution shifted toward medium and large bubbles at higher gas velocities, which was attributed to enhanced bubble collision and coalescence under higher gas holdup and stronger turbulence. Although the increase in bubble number enlarged the total interfacial area, the formation of larger bubbles partly reduced the specific interfacial area per unit gas volume.

Overall, superficial gas velocity regulated DO distribution through the coupled effects of gas holdup, liquid circulation, bubble number, and bubble size distribution. At low gas velocity, insufficient gas holdup, bubble number, and circulation limited oxygen transfer. At high gas velocity, stronger bubble entrainment and liquid circulation enhanced oxygen transfer in the downcomer, causing excessive oxygen dispersion and reducing the low-DO fraction. Therefore, 1.5 cm/s represented a suitable operating condition because it provided sufficient oxygen transfer in the riser while avoiding excessive oxygen dispersion into the downcomer.

3.5. Passive-Tracer Transport and Regional Residence-Time Characteristics

Because the low-, transition-, and high-DO zones do not correspond to fixed independent hydrodynamic compartments, the reported regional residence times should not be interpreted as exact residence times within these three DO classes.

The aeration configuration markedly affected passive-tracer transport within the ALR. As shown in Figure (a,b), the AR-ALR exhibited comparatively streamlined tracer trajectories along the circulation loop, whereas the CR-ALR produced a more concentrated and tortuous transport pattern, particularly within the central riser. At the same superficial gas velocity of 1.5 cm/s, the mean residence times of passive tracers in the riser and downcomer of the AR-ALR were approximately 9.39 and 6.03 s, respectively, compared with 5.7 and 3.8 s in the CR-ALR. Thus, tracers required longer times to pass through both circulation regions in the AR-ALR, whereas regional tracer transport was faster in the CR-ALR. This difference is consistent with the liquid-velocity fields shown in Figure , where the CR-ALR exhibited a more concentrated high-velocity liquid flow in the central riser.

13.

Passive-tracer transport and residence-time characteristics in ALR: (a) tracer trajectories in the AR-ALR at 1.5 cm/s; (b) tracer trajectories in the CR-ALR at = 1.5 cm/s; and (c) residence times of passive tracers in the riser and downcomer of the CR-ALR at different superficial gas velocities.

The effect of superficial gas velocity on regional residence time was further examined under the CR-ALR configuration. As shown in Figure (c), the residence times in both the riser and downcomer decreased progressively with increasing superficial gas velocity. When increased from 0.5 to 3.0 cm/s, the mean residence time decreased from approximately 6.6 to 3.6 s in the riser and from 4.9 to 2.4 s in the downcomer. This reduction indicates that increasing gas input accelerated tracer transport and increased the exchange frequency between the two circulation regions. The trend agrees with the increase in liquid velocity shown in Figure , confirming the important role of superficial gas velocity in regulating liquid-phase transport. ,

These residence-time characteristics should be interpreted together with the spatial DO distribution rather than considered independently. In the CR-ALR, the aerated riser represented the relatively oxygen-rich region, whereas the downcomer remained comparatively oxygen-limited because gas–liquid oxygen transfer was strongly suppressed in this region. Therefore, the regional residence times provide a hydrodynamic indication of the duration of alternating exposure to these contrasting oxygen environments. At low superficial gas velocity, the longer regional residence times were accompanied by insufficient oxygen supply and weak liquid transport. In contrast, at high superficial gas velocity, the shorter residence times and more frequent regional exchange were accompanied by enhanced bubble entrainment and oxygen transport into the downcomer, which progressively weakened DO zonation. At 1.5 cm/s, the CR-ALR retained a low-DO fraction of approximately 52% while maintaining sufficient oxygen transfer in the riser and intermediate residence times in both circulation regions. By comparison, although the AR-ALR exhibited longer regional residence times, its broadly distributed oxygen transfer produced a nearly homogeneous DO field, with only approximately 5% of the reactor remaining in the low-DO range. These results indicate that residence time alone does not determine the preferred configuration; rather, CR-ALR operated at 1.5 cm/s provides a more appropriate balance among liquid-phase transport, oxygen transfer, and preservation of an oxygen-limited region for one-stage PNA.

4. Conclusion

In this study, CFD simulation was used to investigate the effects of aeration mode and superficial gas velocity on DO regulation in an airlift reactor. The results showed that aeration mode determined the spatial pattern of oxygen transfer, whereas superficial gas velocity controlled the balance between oxygen supply and low-DO zone preservation.

Compared with AR-ALR, CR-ALR was more suitable for constructing DO zonation. AR-ALR promoted oxygen dispersion throughout the reactor, resulting in a relatively homogeneous DO field and a low-DO zone fraction of only 5%. In contrast, CR-ALR confined oxygen transfer mainly to the riser and maintained lower DO in the downcomer, increasing the low-DO zone fraction to 52%. This spatially selective oxygen transfer was mainly associated with lower gas holdup, interfacial area, and k _L a in the downcomer.

Under CR-ALR, increasing superficial gas velocity from 0.5 to 3.0 cm/s enhanced DO concentration, gas holdup, liquid velocity, interfacial area, and k _L a. However, excessive gas velocity promoted bubble entrainment and oxygen transport into the downcomer, causing rapid shrinkage of the low-DO zone. When the superficial gas velocity exceeded 1.5 cm/s, transition- and high-DO zones expanded markedly, indicating weakened DO zonation. Passive-tracer analysis further showed that increasing superficial gas velocity shortened the residence times in both the riser and downcomer, consistent with the enhancement of liquid-phase transport. At 1.5 cm/s, the CR-ALR also exhibited shorter regional tracer residence times than the AR-ALR.

Among the tested conditions, center-rising aeration combined with a superficial gas velocity of 1.5 cm/s achieved the best balance between oxygen transfer enhancement and low-DO zone preservation. This condition maintained sufficient oxygen transfer in the riser while preserving a considerable low-DO region in the downcomer, making it a suitable operating condition for constructing DO zonation in the ALR.

J.Q.: Conceptualization, methodology, investigation, data curation, writing original draft. X.A.: Methodology, investigation, data curation. W.W.: Formal analysis, funding acquisition, resources, supervision.

The authors declare no competing financial interest.