Numerical simulation of a mechanical flocculation process with multi-chambers in series

C_A

model constant

d_p

particle diameter, m

D

diffusion coefficient

D_l

impeller diameter, m

E

breakage rate constant

G

global velocity gradient, s^–1

G_L

local velocity gradient, s^–1

H

enthalpy, m²·s^–2

[i]

molar concentration of component i

k

turbulence kinetic energy, m²·s^–2

k_λ

thermal conductivity, kg m·s^–3·K^–1

kinematic diffusivity

L

particle size, m

N

rotational speed of the impeller, rev/min

n_s

particle number density, m^–3

p

static pressure, Pa

P_ave

average power consumption

P_ij

shear turbulence production term

P_k

turbulence production due to viscous forces

P₀

impeller power number

P_εb

buoyancy production term

source term

Sc_t

Schmidt number

s_i

breakage kernel

T

temperature, K

velocity vector, m·s^–1

velocity component in kth direction, m·s^–1

Reynolds-averaged velocity in the ith and jth direction

volume fraction of flocs

the stoichiometric coefficient of component i

kth component of the position vector, m

Y

mass fraction of a component

Greek symbols

ρ

density, kg·m^–3

μ

dynamic viscosity of the fluid, kg·m^–1·s^–1

ε

turbulent dissipation rate, m²·s^–3

pressure-strain correlation

turbulent viscosity, kg·m^–1·s^–1

β(L,λ)

aggregation kernel

υ

kinematic viscosity, m²·s^–1

λ

particle size, m

σ

mechanical bonding strength, kg·m^–1·s^–2

τ

shear stress, kg·m^–1·s^–2

ω

reaction rate, mol·L^–1·s^–1

With the advantages of easy operation and low energy consumption of coagulation–flocculation, it has been widely applied to wastewater treatment as an advanced phosphorus removal technology (Teh et al. 2016). In the coagulation–flocculation process, the dissolved and suspended micro-colloids are aggregated and formed into larger flocs by the addition of chemicals (Yu et al. 2020). Then phosphorous-laden flocs could be easily separated from the water by sedimentation or flotation. Coagulation and flocculation are often used interchangeably as they simultaneously occur and are difficult to be distinguished from one another to some extent. One of the challenging problems is the complexity of scaling-up of the coagulation–flocculation process. For instance, there are various parameters in a full-scale water treatment unit process of mechanical flocculators. It is difficult to precisely control operational conditions and design geometry structures in the wastewater treatment plant. Therefore, it is necessary to investigate the phosphorus removal and overall performance of the coagulation–flocculation in industrial-scale flocculators.

Mechanical flocculation is often applied in wastewater treatment plants, where an agitator inputs the energy. Moreover, the mechanical flocculation process is arranged as a continuous system with multi-chambers in series. Bridgeman et al. (2009) investigated the inner flow states in a lab-scale flocculator with 100 mm in diameter and 127 mm in height. Ohm et al. (2020) simulated a flocculation system with a rectangular section of 1,107 × 1,107 mm and a height of 956 mm. Some studies focused on the size, strength and physical structure of flocs in the flocculation process by using electron microscopy and light scattering (Marques & Ferreira Filho 2017; Lin et al. 2020). However, most of these efforts were conducted with a lab-scale apparatus based on batch experiments. Additionally, the numerical simulation or experimental results on small systems could not be simply scalable to large systems. It is known that the hydrodynamics, flocs behavior and optimum conditions significantly vary with the scaling-up process. Therefore, the operational parameters and flocs kinetic analyzed at lab-scale are hardly extrapolated to control and design full-scale mechanical flocculation systems (Moruzzi & de Oliveira 2013). Furthermore, the performance of coagulation − flocculation not only relies on the combination of the flocculation chambers, but also on the setting of operational parameters. Thus far, there are limited published investigations on the flocculator geometry and operational conditions in the mechanical flocculation system with multi-chambers in series.

The phosphorus removal process in coagulation–flocculation is rather complex, as it involves chemical reactions, transport phenomena, and particle dynamics. In the coagulation stage, the particles become unstable due to the influence of multiple factors, e.g., double-layer compression, physical enmeshment of colloids within coagulant precipitates, chemical reaction or physical/chemical adsorption (Jarvis et al. 2005). In the subsequent flocculation stage, flocs size increases by gentle mixing to improve the removal efficiency of very small particles, colloids and micropollutants. The detailed mechanism of phosphorus ions reactions in coagulation–flocculation is primarily concerned by researchers (Prazeres et al. 2019; Shrestha et al. 2021). For instance, the commonly used coagulants are Al³⁺ or Fe³⁺ salts. After dosing these chemical coagulants in wastewater, a series of chemical coagulation/flocculation reactions occur (Liu & Zhou 2021). The metal ions and ions undergo settling reactions to generate AlPO₄ (s) and FePO₄ (s). Furthermore, the Fe³⁺ ions or Al³⁺ ions and OH⁻ ions also take part in precipitation reactions to produce Al(OH)₃ (s) and Fe(OH)₃ (s). Gels like Al(OH)₃ and Fe(OH)₃ and insoluble compound FePO₄ have strong adsorption properties which enhance phosphorus removal. In addition, coagulation–flocculation relies heavily on the conditions of particle transport and dynamics. From the point of view of particle dynamics, the coagulation–flocculation rate depends on the mechanisms of particle collisions, particle size distribution, the structural features of particle aggregates, as well as the mixing intensity (Li & Zhang 2003). Many experiments have demonstrated that the coagulation–flocculation performance is significantly affected by the initial pH, coagulant or flocculant dosage, residence time, temperature and mixing conditions (Mao et al. 2021; Zhang et al. 2021). Despite being useful, these physical experiments could barely be used to illustrate the interactions between the chemical reactions and particle transport in coagulation–flocculation processes.

Mathematical modeling and numerical simulation overcome the limitations associated with experimental studies. There are two kinds of modeling strategies for coagulation–flocculation simulation. The first one is a single-phase flow model which focuses on the flow characteristics in flocculators (Bridgeman et al. 2010; Vadasarukkai et al. 2011; Llano-Serna et al. 2019). Oliveira et al. (Oliveira & Donadel 2019) conducted a computational fluid dynamics (CFD) simulation to investigate the influences of several hydraulic and geometric parameters on the flocculation efficiency in wastewater treatment plants. Cho et al. (2010) explored how the paddle shape affects the hydrodynamic behavior with a CFD model. The global or local velocity gradient, turbulent kinetic energy and residence time are used as criteria to indirectly evaluate the flocculation processes. Therefore, these studies lack the quantitative indicators for the evaluation of the flocculation performance and comprehensive description of flocs behavior. The second one is a multiphase flow model which involves flow, transport and flocs dynamics. Population Balance Model (PBM) is supplemented to describe the aggregation and growth of colloids and predict the floc size distribution in flocculation (Nopens et al. 2015; Wang et al. 2022). Marchisio et al. (2003) developed a CFD–PBM model based on the Eulerian–Eulerian approach to simulate the flocs aggregation-breakage dynamics in a lab-scale mechanical flocculation device. Prat and Ducoste (Prat & Ducoste 2007) demonstrated that the CFD–PBM model based on the Eulerian–Lagrangian approach was more effective to quantify the flocculation process. However, most of the simulations mentioned above focused on the relatively small-scale mechanical flocculation system. In addition, few studies involved the chemical reactions of phosphorus removal in the coagulation–flocculation modeling. There is still a lack of quantitative analysis in the phosphorus removal. Therefore, the simulation results could not directly guide the design and operation of the full-scale mechanical flocculation system in wastewater treatment plants.

To fulfill the gaps identified above, a CFD model is developed to comprehensively describe the complex behavior of the fluid flow, chemical reactions and flocs dynamics in coagulation–flocculation. Compared to our previous model (Zhan et al. 2021), the current work considers the chemical reaction kinetics to simulate the phosphorus removal efficiency. The effects of the mechanical flocculator geometry and operational conditions are investigated in terms of the number of flocculation chambers, locations and sizes of the flocculation chamber connection as well as operational combinations of impeller speeds. It will provide a deeper understanding of the inner states and corresponding performance in a full-scale mechanical flocculator with multi-chambers in series, which is critical to structure design and process optimization.

Wastewater is a multiphase and multicomponent mixture in nature. The coagulation–flocculation is a complex multiphase reacting flow process, where small initial floc seeds gradually grow under the physicochemical process in the three flocculators in series. In order to simplify the phosphorus ions reactions and relief computational efforts, the reaction of Al³⁺ salt and ions is considered as the main phosphorus removal reaction and the generated AlPO₄ as the main composition of flocs (Liu & Zhou 2021). The present work is based on our recently developed CFD model to simulate the flow and physicochemical in a single-chamber mechanical flocculation process (Zhan et al. 2021). The model is developed and solved on a commercial software package – ANSYS-CFX, and its details are described in the following.

The mathematical model is based on the following assumptions: (1) The raw water and micro-flocs are well-mixed and assumed to be a miscible mixture, while the velocities of the raw water and flocs are identical with no slip. (2) The raw water-flocs mixture flow is turbulent. (3) The chemical reaction of phosphorus removal is treated as an irreversible and single-step global reaction, while the chemical/physical adsorption is neglected. (4) The flocs are assumed to be spherical particles. (5) The particle aggregation, growth and breakage are considered in the flocs dynamics, while the local nucleation is neglected. (6) The particle size is assumed to be uniform in the control volume to relieve computational efforts.

The coagulation–flocculation process model considers the turbulent flow, chemical reaction, species transport, and particle dynamics. The raw water-flocs mixture is treated as a continuum. Therefore, a multicomponent, single-phase and steady-state numerical model is developed. The raw water-flocs mixture is described by a set of mass, momentum, enthalpy and species conservation equations. All the steady-state governing equations are listed in Supplementary material, Appendix A. The flocculation system has a strong turbulent flow due to the agitation of impellers. Thus, the Reynolds stress model (RSM) is chosen to describe the mixture turbulent flow. To take into account the flocs growth without the local nucleation, the particle size spatial distribution could be obtained by solving an additional equation describing the population balance. The number density of flocs is defined as an additional scalar, which is solved by the so-called population balance equation (PBE). Thus, the particle diameter of flocs is determined by solving the PBE. The aggregation and breakage are considered in the model, since they have a significant effect on the flocs dynamics. Correspondingly, the formulas are summarized in Supplementary material, Appendix A. Their details can be found in the literature of our previous study (Zhan et al. 2021).

For simplicity, the reaction between Al³⁺ ions and ions is represented by a single-step global irreversible reaction in liquid phase solution: reagents AlCl₃ and KH₂PO₄, as well as the product AlPO₄, are treated as liquid phase solution. Besides, the other products also remain in the solution.

Supplementary material, Appendix C lists the boundary conditions in the simulation. A velocity inlet boundary is defined for the raw water-flocs mixture inlet with a flow rate of 20,000 m³/day, mass concentrations of AlCl₃ 20 mg/L and KH₂PO₄ 50 mg/L, and an initial floc particle size of 20 μm. An outlet boundary condition with a static pressure of 0 Pa is defined for the mechanical flocculation system. The top surface of flocculators is set up as a free slip wall condition, while the other walls and impellers surface are considered as a no-slip boundary. The impeller rotates clockwise at different speeds. The flocs volume fraction is specified to be 0.05 based on experiments.

The phosphorus removal efficiency is first validated against the measurements in terms of industrial-scale flocculation experiments. Then, the current work focuses on the effects of mechanical flocculators geometry and operational conditions on phosphorus removal and flocculation performance. To characterize the performance of the flocculation process, the phosphorus removal efficiency η and the average floc size d_p at the outlet are considered as the key performance indicators. In addition, the corresponding transport phenomena of mechanical flocculators with multi-chambers in series are discussed in terms of flow, chemical and particle behavior. For comprehensive visualization of the inner states in the flocculation system, the slice and volume rendering illustrations of variables are presented.

The validity of the flow field characteristics and floc growth process has been verified elsewhere (Zhan et al. 2021). The current model validation focuses on the chemical reaction process. The overall performance of an industrial flocculator in BXWWTP under various operating conditions is examined. A sample tube is inserted at the center of the flocculation system inlet. Accordingly, the inlet concentration is measured by the on-line PHOSPHAX sc ANLZR (HACH, USA). Similarly, a sample tube is also inserted at the outlet center of the flocculation system to detect the outlet concentration. The pH and inlet flow rate are measured by pH meter and flowmeter, respectively.

Assuming that the sedimentation is not observed in the flocculator and neglecting the adsorption of phosphorus by flocs. The phosphorus removal represents the ions concentration loss due to the reaction between Al³⁺ ions and ions. Accordingly, the efficiency of phosphorus removal is calculated by the variation of ions concentration. Typical plant operational parameters and conditions for model validations are summarized in Table 1. The inlet ions concentration varies from 2 to 3 mg/L as biologically treated. The inlet flow rate and pH slightly fluctuate from 18,000 to 21,000 m³/day and 7 to 8, respectively. The different PAC dosages ranging from 20 to 60 mg/L are tested for the model validation. Table 1 compares the predicted and the measured ions concentration at the outlet. It shows that the predicted ions concentrations agree with the measured ones with a discrepancy of 2%, for low PAC dosages. It should be noted that a discrepancy of 15% between the measured and predicted ions concentration is observed for the PAC dosages from 40 to 60 mg/L. It might be the influences of the significant reaction of Al³⁺ ions and OH⁻ ions or strong physical/chemical adsorption properties of AlPO₄/Al(OH)₃, for high PAC dosages case. However, the results are all acceptable for predicting industrial-scale wastewater treatment. In brief, these agreements confirm the validity of the model, at least quantitatively, in describing the chemical reactions of phosphorus in the coagulation–flocculation process.

Table 1

Model validations and their experimental conditions

Cases .	Inlet flow rate, m3/day .	pH .	Temperature, °C .	Inlet concentration, mg/L .	PAC concentration, mg/L .	Velocity gradient, s−1 .	Contact time, s .	Outlet concentration, mg/L .
								Measured .	Predicted .	Error .
1	20,000	7.35	21.2	2.3	20	36.44	1,575	1.75	1.72	−1.7%
2	18,500	7.57	25.5	2.22	30	15.65	1,702	1.25	1.27	1.6%
3	19,600	7.28	22.3	2.51	40	30.39	1,607	0.96	1.11	15.6%
4	20,860	7.66	18.7	2.75	40	42.99	1,510	1.06	1.21	14.7%
5	19,200	7.19	19.7	2.29	60	22.13	1,640	0.66	0.58	−12%

Cases .	Inlet flow rate, m3/day .	pH .	Temperature, °C .	Inlet concentration, mg/L .	PAC concentration, mg/L .	Velocity gradient, s−1 .	Contact time, s .	Outlet concentration, mg/L .
								Measured .	Predicted .	Error .
1	20,000	7.35	21.2	2.3	20	36.44	1,575	1.75	1.72	−1.7%
2	18,500	7.57	25.5	2.22	30	15.65	1,702	1.25	1.27	1.6%
3	19,600	7.28	22.3	2.51	40	30.39	1,607	0.96	1.11	15.6%
4	20,860	7.66	18.7	2.75	40	42.99	1,510	1.06	1.21	14.7%
5	19,200	7.19	19.7	2.29	60	22.13	1,640	0.66	0.58	−12%

Note: Other conditions for these cases include (a) PAC (AlCl₃ content is up to 90%) and (b) rotational speed is 3.82 rev/min.

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For the effectiveness of the flocculation system, on the one hand, the phosphorus removal efficiency used here is not the effluent quality of the BXWWTP. The treatment process configuration of BXWWTP contains following stages: pre-treatment, biological treatment, flocculation and sedimentation, cloth filtration, and UV. The phosphorus removal efficiency is detected at the outlet of the flocculation system by the on-line PHOSPHAX sc ANLZR (HACH, USA). The wastewater would be subsequently treated by a cloth filter system. On the other hand, in order to validate our CFD model, a relatively wide distribution of the phosphorus removal efficiency is deliberately selected. The phosphorus removal efficiency also includes the data of the process examination.

Figure 5(b) presents the mass concentration contour rendered over the working volume. A similar -rich zone is found at the inlet of all the flocculation systems. However, the decrease in mass concentration varies with the number of flocculation chambers. In the base case of A ∪ B ∪ C, the mass concentration decreases gradually through the three chambers. In the case of A ∪ BC, the distribution of mass concentration in flocculator A is qualitatively similar to that of A ∪ B ∪ C. The reaction rate highly depends on the flow pattern and turbulent features when using the eddy dissipation model. The same impeller speed and flocculation chamber geometry correspond to the identical reaction rate, thus yielding a similar reactant distribution. Therefore, a similar distribution of mass concentration in flocculator A is also observed in A ∪ BC and A ∪ B ∪ C. In the case of A ∪ BC, it should be noted that the mass concentration about 1.138 mg/L is observed at the bottom of chamber BC, which is lower than that in the base case. Relatively, higher mass concentration about 1.353 mg/L is observed in the upper part. Due to the chamber BC without inside wall between impellers, the main vortexes are affected each other as the same clockwise rotation. A relative waken turbulent flow is created in the bottom of chamber BC, which reduces chemical reaction and flocs growth. Therefore, an irregular low mass concentration is formed in chamber BC in A ∪ BC. In addition, a sharp decrease in mass concentration is observed in one flocculation chamber of ABC. Correspondingly, the lower limit value of mass concentration is about 1.377 mg/L. In contrast, the corresponding value is about 1.205 mg/L in A ∪ B ∪ C. This is because a relatively sufficient residence time in three flocculation chambers in series of A ∪ B ∪ C is obtained, which promotes the chemical reaction of phosphorus removal. It is demonstrated that the phosphorus removal weakens as the number of flocculation chambers decreases.

The floc size distribution rendered over the working volume is significantly affected by the number of flocculation chambers, as shown in Figure 5(c). In the base case of A ∪ B ∪ C, the floc size grows gradually through the three chambers, and large flocs of 42.8 μm are formed in flocculation chamber C. In the case of A ∪ BC, large flocs of 42.2 μm are formed in the lower part of the flocculation chamber BC. Although the same number of flocculation chambers, the floc size distribution in AB ∪ C is different from that of A ∪ BC. Furthermore, the maximum floc size of 34.8 μm is formed in one flocculation chamber of ABC. For the ABC arrangement, it means that there is only one flocculation tank without the connection walls among impellers. Due to the difference of rotating speeds, three main vortexes with different strengths are formed. Thus, the reaction rate and flocs growth will be influenced, leading to the inhomogeneous distribution of particle diameters. Moreover, flocs flow into the three vortexes regions in sequence and larger flocs will be gradually generated.

Generally, the connection between flocculation chambers determines the flow pattern in the flocculation system, thus influencing the phosphorus removal and flocculation performance. Therefore, the location of the connection and inlet in three flocculation chambers in series are investigated in Group II. Besides, to evaluate the role of each flocculation chamber in the whole system, the phosphorus removal efficiency and the average floc size at each connection are collected as additional performance indicators.

The key performance indicators are determined by the distribution of mass concentration and the average particle size. It demonstrates that the variation of the connection location of flocculation chambers A–B weakens the main vortexes. The turbulent flow and chemical reactions are weakened in G5. Therefore, the significant difference in inner states leads to a relatively remarkable difference in key performance indicators.

The impeller speed directly determines the turbulent flow. Thus, the reaction and flocs dynamics are also affected significantly. Moreover, the reactants concentration declines and flocs grow as the reaction and flocculation progress in the series system. Therefore, three schemes of impeller speeds are considered in terms of a decrease speed combination of 3.82–1.9–0.95 rev/min, a same speed combination of 3.82–3.82–3.82 rev/min and an increase speed combination of 3.82–5.73–8.595 rev/min.

Coagulation–flocculation is a major advanced phosphorus removal technology for wastewater treatment. For the industrial-scale mechanical flocculation system with multi-chambers in series, its performance not only relies on the combination of the flocculation chambers, but also comes from the matching sets of operational parameters. The inner flow, physicochemical behavior and overall performance of mechanical flocculators in series have been studied using our previously developed CFD model. The effects of the number of flocculation chambers, locations and sizes of the flocculation chamber connection as well as operational combinations of impeller speeds are numerically investigated. The major findings are summarized as follows.

With decreasing number of flocculation chambers, the main vortexes and phosphorus removal are weakened, while the small flocs are formed. Both the phosphorus removal efficiency η and the average floc size d_p reduce as the number of flocculation chambers decreases. The connection location of flocculation chambers directly determines the turbulent flow, thus influencing the key performance indicators. However, the phosphorus removal efficiency and average particle size are little affected by the size of the flocculation chamber connection as evidenced by the slight variation of the flow pattern in the flocculation system. The combination of impeller speeds significantly affects the inner states and overall performance. The higher the impeller speed is applied, the greater the main vortexes in size are observed. As the impeller speeds in series gradually increase, the gradient of the floc size distribution in each chamber is enlarged and the chemical reaction is enhanced over the working volume. Finally, a higher efficiency η of 72.59% and larger average floc size d_p of 119.98 μm are formed in the increased speed combination of impellers.

The authors acknowledge the financial support by Important Projects in the Scientific Innovation of CECEP (Grant No. cecep-zdkj-2020-005).

J.Z. investigated and wrote the draft; F.Y. acquired funds, visualized the study. M.Z. conceptualized the study; prepared the methodology, wrote and supervised the study; W.X. acquired funds. G.C. collected resources and validated the study. A.Y. designed the concept, revised and supervised the article.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.