Numerical simulation of dyeing wastewater treated by a multi-stage reverse electrodialysis reactor series system

Abstract

By developing the mathematical model of a serial multi-stage reverse electrodialysis reactor (REDR) system for wastewater treatment, this paper numerically simulates the degradation process of azo dye (methyl orange) dyeing wastewater. The operation performances of the serial system with an anode and cathode synergetic degradative circulation mode are explored by numerical simulation. The influences of operation parameter variations on key performance indicators are investigated and discussed. Results indicate that the serial system can achieve excellent electricity conversion efficiency and degradative performance under an appropriate output current condition. A high initial MO concentration and electrode rinse solution (ERS) flowrate are helpful to improve the treatment performance of the system. A low concentrated solution (CS) concentration is beneficial for raising the electricity conversion efficiency and reducing the total energy consumption (TEC).

Keywords

Reverse electrodialysis reactors wastewater treatment power generation energy conversion

Introduction

Dyeing wastewaters have been an environmental water pollution source over the last few decades. During the industrial processes of textile printing and dyeing, leather tanning, papermaking, etc., amounts of wastewaters are created and discharged into natural environmental water. These wastewaters have the features of high chroma, high stability and refractory.¹ The coventional wastewater treatment technology has low efficiency in treating these wastewaters, leading to the progressive accumulation of such contaminants in the aquatic ecosystems with very negative consequences.² Nonconventional wastewater treatment such as electrochemical advanced oxidation process (EAOP) has been introduced into treating wastewater and achieves excellent treatment efficiency.³ The working principle of EAOP is to produce strong oxidants by electrochemical reactions at electrodes to oxidize and degrade various pollution in wastewater. A typical oxidant produced by electrochemical reactions is hydroxyl radical (·OH), which has a high oxidative power [E⁰(·OH/H₂O) = 2.8V/SHE]. It can incinerate almost all organic pollution in wastewater into carbon dioxide and water.⁴

EAOP includes the technologies of anodic oxidation (AO) and electro-Fenton (EF). In the refractory wastewater treatment fields, EAOP has some advantages, such as 1) mild operation conditions, 2) less land space requirement, 3) no additional requirement for auxiliary chemicals, 4) no secondary waste streams and 5) being easily combined with other treatment modes. Its disadvantage is that lots of electrical energy is consumed by EAOP devices running to incur a high treatment cost, limiting its large-scale applications in industries.

At present, a novel wastewater treatment technology of reverse electrodialysis reactor (REDR) has gained increasing attention. In this technology, the energy consumed by REDR is salinity gradient energy (SGE) from nature (sea or salt lake water and river water), the coproduct of desalination plants (concentrated seawater and natural seawater) or waste heat conversion. Figure 1 illustrates the general structure and working principle of REDR.

Figure 1.

Structure and working principle of REDR.

REDR consists of endplates, electrodes (anode and cathode), alternate arrangement of cation and anion exchange membranes (CEMs and AEMs) and woven spacers. When working fluids [Concentrated solution and diluted solution (CS and DS)] flow through their respective channels in REDR along the x-axis, cations and anions in CS will transport across the ion-exchange membranes (IEMs) towards DS in the opposite direction at the action of salinity gradient. The direction of ions transportation is perpendicular to the x-axis. A concentration difference of cation and anion on two sides of IEMs creates a membrane electrical potential [E(x)]. At the action of the potential, a redox reaction is generated on the surfuce of two electrodes. An ion current in REDR is converted to an electronic current in the external circuit. When wastewater, as electrode rinse solution (ERS), flows through the electrode channels/compartments, various strong oxidants are created in two electrode chambers by a redox reaction. These strong oxidants can oxidize and degrade various organic or inorganic pollution in wastewater.

O. scialdone et al. first proposed to treat wastewater contaminated with hexavalent chromium Cr(VI) by a reduction reaction at the cathode of REDR.⁵ Results showed that Cr(VI) in wastewater could successfully be reduced to Cr(III) when the wastewater flowed through the cathode channel. Futhermore, the authors investigated the dyeing wastewater treatment of acid orange 7 (AO7) by a REDR with 40–60 membrane pairs.⁶ Results showed that EF reaction at the cathode and electro-generated active chlorine reaction at the anode were performed. These reactions can efficiently degrade azo dye (AO7) in wastewater.

Zhou et al. researched the degradation of ammonia-nitrogen wastewater by REDR.⁷ An electro-generated active chlorine could be produced at the anode of the REDR It can efficiently remove ammonia-nitrogen from wastewater. Results showed that the maximum ammonia-nitrogen removal efficiency and output power density were 98% and 0.06 W·m⁻²_, respectively, under the given operating conditions. Ma et al. investigated the degradation of synthetic wastewater containing formic acid by REDR.⁸ A fast and high TOC removal rate (about 70% every hour) in the anode channel/compartment was achieved under optimized operating conditions.

Zhang et al. reported an electric-coagulation method to remove Cr(VI) in wastewater by a REDR with an iron anode. By redox reaction at two electrodes of REDR, a flocculant, Fe(OH)₂, was created at the anode to coagulate and remove Cr(VI) in wastewater.⁹ Results showed that the removal rate of Cr(VI) could reach 99% in 2 h, and output power density could reach 0.482 W/m².

Xu et al. first reported the influence of degradation recirculation modes by a REDR on the decolorization efficiency of AO7 simulative wastewater.¹⁰ Results showed that the decolorization efficiency in independent degradation recirculation mode was superior to synergetic degradation mode. The reason was that the redox reaction products at the anode and cathode would interact in the synergetic degradation recirculation mode. Additionally, the authors reported the decolorization efficiency of AO7 simulative wastewater by a multi-stage REDR series system.¹¹ In the series system, the independent degradation circulation mode was adopted to avoid the interaction of oxidants produced at two electrodes. The results demonstrated that a series REDR system had higher SGE utilization and decolorization efficiencies than a single-stage REDR system. Under the optimal operating conditions, the number of reactors, total decolorization rate, utilization efficiencies of SGE and membrane area, and net output power reached 19, 1.91 mg·s⁻¹, 6.92 mg·J⁻¹, 31.21 mg·m⁻²s⁻¹ and 0.68W, respectively.

Leng et al. reported the methyl orange (MO) dyeing simulative wastewater degraded by a REDR coupled with electrochemical direct oxidation and EF processes.¹² In the report, the degradation performance of the REDR wastewater treatment system with different anodic materials was compared by experiments. Results showed that two oxidation degradation processes kept high degradation efficiency in the synergetic degradation circulation mode. Besides, the boron-doped diamond (BDD) anode presented the most excellent degradation efficiency among adopting three different anode materials.

However, only a few pieces of literature about the wastewater treated by REDR have been openly reported up to now. Relevant research on the REDR technology is insufficient. A lot of research should be done for the practical application of the technology. The purpose of this work is to theoretically explore the energy conversion efficiency of the wastewater treatment system with multi-stage serial REDRs by numerical simulation. Since the theoretical research report/literature about the REDR wastewater treatment system has never been found openly up to now, especially about a multi-stage REDR series system, the objective of this work is to theoretically research the degradation efficiency of organic wastewater by a REDR series system. The research steps are: 1) to develop a mathematical model including mass transfer and degradation processes, 2) to theoretically explore the relationships between energy conversion and degradation efficiencies, 3) to investigate the effect of operating parameter variations, such as the working fluid and ERS operating parameter variations, on the working performance of the system.

Modelling

Wastewater treatment system with multi-stage serial REDR

Figure 2 shows the scheme of a multi-stage serial REDR wastewater treatment system with synergetic degradation mode. In the system, the working fluids (CS and DS) flow through each-stage REDR in sequence, and the SGE of working fluids is consumed in stage by stage. The wastewater as ERS first flows downstream through the anode channel of each-stage REDR and then flows upstream through the cathode channel. Like a single REDR, there is an AO reaction at the anode and an EF reaction at the cathode of each-stage REDR at the action of membrane potential to degrade various organic pollutions in wastewater. The function of aeration in wastewater or ERS reservoir is to increase dissolved oxygen in the wastewater, which can improve a reduction reaction at the cathode to generate more hydrogen peroxides (H₂O₂), and then more hydroxyl radicals (•OH) can be generated by EF reaction.

Figure 2.

Flow diagram of organic wastewater treated by a multi-stage REDR series system.

Wires connect the anode and cathode of each-stage REDR to form a series of the external circuit. The external circuit is used as an electronic pathway from anode to cathode and outputs electricity. The feature of a series circuit is that the current output by each-stage REDR is equal, and the total voltage output by the system is the sum of the voltage output by each-stage REDR, or the power output by the system is the sum of power output by each-stage REDR

In this section, a mathematical model of methyl orange (MO) wastewater degraded by a multi-stage REDR series system was developed.

Assumptions

For simplifying the model, some assumptions are considered as follows:

Working fluids are sodium chloride (NaCl) aqueous solutions.

Mass transfer across IEMs along the working fluid flowing direction is one-dimensional.¹³

Parasitic currents and concentration polarization phenomenon in REDR are ignored.¹⁴

Wastewater as ERS is a perfectly mixed solution.

Energy consumed by ERS pump is ignored.¹⁵

Only the direct oxidation of the AO process and the EF process are considered in the system.

The quasi-steady-state approximation (QSSA) hypothesis is expected for the oxidation process between hydroxyl radical (·OH) and organics.^16,17

ERS volume in the reservoir is far more than that in electrode channels/compartments.¹⁸

REDR

In a REDR, the potential of membrane pair along the x-axis can be calculated by Nernst equation¹⁹:

E (x) = \frac{R T}{F} (α_{C E M} I n \frac{γ_{C S}^{+} (x) C_{C S} (x)}{γ_{D S}^{+} (x) C_{D S} (x)} + α_{A E M} I n \frac{γ_{C S}^{-} (x) C_{C S} (x)}{γ_{D S}^{-} (x) C_{D S} (x)})

(1)

Since permselectivity of IEMs (α) is affected by the concentration of working fluids,^14,20 a correction factor (β) is introduced to modify the permselectivity.

α_{C E M} = β \cdot α_{C E M}^{0}

(2)

α_{A E M} = β \cdot α_{A E M}^{0}

(3)

Where,

α_{C E M}^{0}

α_{A E M}^{0}

are a permselectivity of CEM or AEM measured at a standard condition supplied by IEM manufactory.

The ion activity coefficient (γ) of salt solution can be presented by Pitzer's virial equations²¹:

In γ = - A_{ϕ} [\frac{\sqrt{I^{'}}}{1 + b^{'} \sqrt{I^{'}}} + \frac{2}{b^{'}} In (1 + b^{'} \sqrt{I^{'}})] + m B^{γ} + m^{2} C^{γ}

(4)

Coefficients A_ϕ, B^γ and C^γ can be obtained from the relative literature.

The electrical resistance of a membrane pair consists of resistances of CS and DS compartments and resistance of IEMs.¹⁴ It is:

R (x) = R_{C S} (x) + R_{D S} (x) + R_{I E M}

(5)

Non-conductive woven spacer blocks out a partial area of IEMs, a shadow factor (f_y) is introduced to calculate the resistances of CS and DS compartments.^19,22

R_{C S} (x) = f_{y} \frac{δ_{C S}}{Λ_{C S} (x) C_{C S} (x)}

(6)

R_{D S} (x) = f_{y} \frac{δ_{D S}}{Λ_{D S} (x) C_{D S} (x)}

(7)

Where, δ and Λ respect the compartment's thickness and equivalent conductivity of solutions,²³ respectively. Similarly, an electrical resistance correction factor (f_r) is introduced to calculate the resistances of IEMs.¹⁴

R_{I E M} = f_{r} (R_{C E M} + R_{A E M})

(8)

Where,

R_{C E M}

R_{A E M}

are a resistance of CEM or AEM measured at a standardized condition, supplied by IEM manufactory.

Electrical potential loss (E_ele) of electrode system is described as²⁴:

E_{e l e} = E_{a n}^{0} - E_{c a}^{0} + | η_{a n} | + | η_{c a} |

(9)

Where, E

0 a n

and E

0 c a

are equilibrium potential difference of anode and cathode compartments. And the theoretical E_an and E_ca in the EF process and AO process are 0.698 V and 2.3 V, respectively.^25,26

| η_{a n} |

and

| η_{c a} |

are the over-potential for electrode reaction and can be calculated by the Tafel equation.²⁴

| η | = a + b \log j

(10)

Where, a and b are Tafel constants which are determined by experiments.

Current density output by REDR with N_cell pairs can be calculated as:

j (x) = \frac{N_{c e l l} E (x) - U - E_{e l e}}{N_{c e l l} R (x)}

(11)

When the working fluids flow through each-stage REDR, their concentrations will change due to a mass transfer across IEMs. The concentration of CS drops and that of DS rises because salt ions transport from CS to DS, but solvent water transports from DS to CS. Mass transfer fluxes in each-stage REDR are,

J_{t o t} (x) = \frac{j (x)}{F} + 2 \frac{D_{N a C l}}{δ_{m}} [C_{C S} (x) - C_{D S} (x)]

(12)

J_{w} (x) = - 2 L_{p} v R T [φ_{C S} C_{C S} (x) - φ_{D S} C_{D S} (x)] + n_{h} J_{t o t} (x)

(13)

The concentration variation of working fluids flowing through each-stage REDR can be presented as,

\frac{d C_{D S} (x)}{d x} = \frac{b}{Q_{D S}} J_{t o t} (x) - C_{D S} (x) \frac{b}{Q_{D S}} J_{w}^{'} (x)

(14)

\frac{d C_{C S} (x)}{d x} = - \frac{b}{Q_{C S}} J_{t o t} (x) + C_{C S} (x) \frac{b}{Q_{C S}} J_{w}^{'} (x)

(15)

Where,

J_{w}^{'}

is the volumetric flux of water across IEMs, which can be evaluated by molar flux (J_w) multiplied by the water molar density.

Volume flowrates of working fluids are,

Q_{C S} = ε v_{C S} b δ_{C S}

(16)

Q_{D S} = ε v_{D S} b δ_{D S}

(17)

Where, ε is the poriness of the woven spacer in the working fluid flowing direction, v is the velocity of solutions.

Energy consumed by working fluid pumps is,

P_{p u m p} = (Δ P_{C S} Q_{C S} + Δ P_{D S} Q_{D S}) / η_{p u m p}

(18)

Where, ΔP is a pressure drop of working fluid flowing through each-stage REDR;

η_{p u m p}

is pump efficiency set as 0.75.

A correlation equation can calculate the pressure drop of working fluids flowing through each stage REDR.²⁷ It is,

Δ P = ζ [12 μ L Q / (b δ^{3})]

(19)

Where,

ζ

is a correction factor.

From the above discussion, the current output by each-stage REDR can be evaluated by:

I = b \int_{0}^{L} j (x) d x

(20)

The gross output by a series system with N numbers of REDR (N_REDR) is,

P_{g r o s s} = I U_{s y s} = I \sum_{i = 1}^{N_{R E D R}} U_{}^{}

(21)

Oxidation processes

As mentioned above, an oxidation reaction at the anode and a reduction reaction at the cathode will be created at the action of membrane potential when wastewater as ERS flows both two electrode channels of a REDR Both reactions will produce a strong oxidant, hydroxyl radical (•OH). The reaction equations using BDD as anode and carbon felt as cathode are as follows.^28,29

There is a direct oxidation process of AO process at the anode channel,

BDD + H_{2} O \to BDD (∙ OH) + H^{+} + e^{-}

(22)

BDD (∙ OH) + Organics \to BDD + C O_{2} + H_{2} O

(23)

There is an EF process at the cathode channel,

O_{2} + 2 H^{+} + 2 e^{-} \to H_{2} O_{2}

(24)

H_{2} O_{2} + F e^{2 +} \to ∙ OH + O H^{-} + F e^{3 +}

(25)

∙ OH + Organic \to C O_{2} + H_{2} O

(26)

Limiting current density (j_lim) is introduced to the oxidation process for an AO process.³⁰ It is,

j_{lim} = 4 F k_{m} C O D (t)

(27)

A current density per unit electrode projection area (j_ele) is

j_{e l e} = I / A

(28)

The ratio of electrode current density (j_ele) to limiting current density (j_lim) at zero time is defined as α, which is,

α = j_{e l e} / j_{lim}^{0}

(29)

Literature^18,30 indicates that there are two different AO operation regimes by α value. When α < 1, the AO process is controlled by a current. Accordingly, the current efficiency of oxidative reaction on anode surface is 100%. The COD value of organic wastewater with reaction/treatment time drops linearly. When α > 1, the AO process switches to a mass transport control process. Some secondary reactions will create at the anode. Thus, the reaction rate of the AO process can be evaluated by,^18,31

r_{A O} = j_{e l e} A / (4 F V) = α j_{lim}^{0} A / (4 F V) = α A k_{m} C O D^{0} / V (α < 1)

(30)

r_{A O} = j_{i m} A / (4 F V) = A k_{m} C O D (t) / V (α > 1)

(31)

The average mass transport coefficient (k_m) of the BDD anode was determined by using the limiting-current method.³² The oxidation process of ferrocyanide ions to ferricyanide ions is used as a model reaction to detect k_m value at different ERS flowrates. Three non-dimensional groups, Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc), can be adopted to accurately predict k_m value at different operating conditions for a REDR system.³³ The details are in Appendix A.

The reaction rate (r_EF) of the EF process at the cathode channel can be considered as QSSA,²⁵ which is,

r_{E F} = k_{a b s} [\cdot O H (t)] C O D (t) = k_{E F} C O D (t)

(32)

Where, k_abs is the decay rate constant of organics; [•OH(t)] is the concentration of hydroxyl radical (•OH) at t time; k_EF is observed (apparent) decay rate constant.

A correlation equation of k_EF is usually achieved by a semi-empirical chemical model, artificial neural network or response surface methodology in previous research.^34,35 In this work, the correlation equation is built by fitting experimental results, and the details are in Appendix A.

Finally, the mineralizing model of organics in wastewater in the oxidation process of REDR can be written as,

d C O D (t) / d t = - (r_{E D O} + r_{E F})

(33)

Key performance indexes (KPIs)

Key performance indexes (KPIs) are used to evaluate energy conversion efficiency and treatment performance of a multi-stage serial REDR wastewater treatment system.

Net power output

P_{n e t} = P_{g r o s s} - N_{R E D R} P_{p u m p} = I \sum_{i = 1}^{N_{R E D R}} U - N_{R E D R} P_{p u m p}

(34)

Electricity conversion efficiency

η = P_{g r o s s} / S G E \times 100 %

(35)

Where, SGE is a maximum Gibbs free energy between CS and DS, which is³⁶:

S G E = 2 R T [Q_{C S} C_{C S} I n \frac{C_{C S}}{C_{M}} + Q_{D S} C_{D S} I n \frac{C_{D S}}{C_{M}}]

(36)

Where, C_M is a concentration of solution mixed by CS and DS.

COD removal efficiency

R_{C O D} = 1 - C O D (t) / C O D^{0} \times 100 %

(37)

Instantaneous current efficiency³⁷

I C E = (4 F V / I) \cdot d C O D (t) / d t

(38)

Total energy consumption (TEC) per unit mass COD removal

T E C = \frac{(G_{i n} - G_{o u t} - P_{n e t}) Δ t / 3600}{32 [C O D^{0} - C O D (t)] V}

(39)

Model validation

Figure 3 describes a full Simulink model of a multi-stage serial REDR wastewater treatment system. It shows the interactions between each ancillary in the system discussed in the previous section. In the system, the structure of each reactor remains the same, but the concentration difference of working fluids decreases in stage by stage at the inlet of each reactor. So, the output voltage of each reactor also decreases in stage by stage. When the output voltage of the last reactor closes to zero, the simulation calculation process stops. The ordinary differential equations are solved by the fourth-order Rong-Kutta method, and the step size is short enough to guarantee stability. The output power of the model was validated using the set of experimental data by reported literature.³⁸ Moreover, the treatment performance of the model was validated by an experiment with a REDR The model validation results as shown in Figure 4 and the relevant specified constant as described in Table 1. The results show that there is a good fit between the simulation results and experimental data.

Figure 3.

Simulink model of a multi-stage serial REDR wastewater treatment.

Figure 4.

Model verification results with the experimental data for (a) power density of a 5 cell pairs stack: b × L (0.1 × 0.1 m²); C_DS = 0.05M; C_CS = 0.5 M, 2.0 M, 5.0 M; v_CS = v_DS = 2 cm·s⁻¹, t = 25°C; variation of COD removal with (b) work solutions velocity (v_CS = v_DS = 0.2 cm·s⁻¹, 0.6 cm·s⁻¹, 1.0 cm·s⁻¹) and (c) ERS flow rate (Q_ERS = 200 mL·min⁻¹, 600 mL·min⁻¹, 1000 mL·min⁻¹) of a 40 cell pairs REDR: b × L (0.07 × 0.13 m²); C_DS = 0.03 mol·kg⁻¹; C_CS = 3.0 mol·kg⁻¹; initial concentration of methyl organic (MO) in wastewater: 50 mg L⁻¹. The dash lines and solid symbols are simulation results and experimental results, respectively.

Table 1.

The relevant performance and geometrical parameters of IEMs in the model.

Parameters	Notation	Unit	Value
Permselectivity of IEMs	$α_{C E M}^{0}$ , $α_{A E M}^{0}$	%	98.5, 94
Thickness of IEMs	d_m	m	1.30·10⁻⁴
Electrical resistant of IEMs	R_CEM, R_AEM	Ω·cm⁻²	1.7, 2
Salt permeability coefficient of IEMs	D_NaCl	m²·s⁻¹	1.10·10⁻¹²
Water permeability coefficient of IEMs	L_p	m·(Pa·s)⁻¹	2.22·10⁻¹⁴
Permselecitivity correction factor^a	β	-	0.9591- 0.3556C_HC - 0.043C_L_C
Resistance correction factor^a	f_r	-	2.991 + 0.2554C_HC + 0.2023C_LC

The expression of the factor is provided by this paper through fitting the experimental data shown in Figure 4.

Results and discussion

In this paper, the characteristics of a multi-stage serial REDR wastewater treatment system are theoretically investigated by the Simulink model. Specifications of REDR and the operations of working fluids and oxidation processes are listed in Table 2. An object treated by the system is methyl organic (MO) dyeing wastewater with 200 mg·L⁻¹ of 300 L.

Table 2.

Specifications of REDR and the operations of working fluids and MO wastewater (ERS).

Item	Parameters
REDR	Number of membrane pairs/cells	N_cell = 1000
	Effective area of membranes	b × L = 1.0 m × 0.1 m
	Thickness of CS & DS compartments	δ_CS = δ_DS = 350 μm
	BDD anode	b × L × δ_a = 1.0 m × 0.1 m × 2 mm
	Carbon felt cathode	b × L × δ_c = 1.0 m × 0.1 m × 5 mm
Working fluids	Volumetric flowrates of CS & DS	Q_CS = 6930 L·h⁻¹; Q_DS = 6930 L·h⁻¹
Working fluids	Concentration of CS & DS	C_CS = 4 mol·L⁻¹; C_DS = 0.05 mol·L⁻¹
ERS	Volume of MO wastewater (ERS)	V = 300 L
	Concentration of MO in ERS	C_ERS = 200 mg·L⁻¹
	Flowrate of ERS	Q_ERS = 1800 L·h⁻¹

This section will first investigate and discuss the relation between output power and degradative performance. And then, the effect of the relevant parameters, including ERS conditions, working solution velocity, and concentration ratio of CS and DS, on KPIs will be explored.

Output power and degradative performance

Figure 5 illustrates the variations of net output power (P_net) with numbers of REDR (N_REDR) at different output currents (I). It can be seen from the figure that the variation of P_net with N_REDR presents a parabola function, and the peak value of P_net is reduced with the increase of I. The reason is that the SGE of working fluids reduces in stage by stage when they flow through each-stage REDR, leading to the output power of each reactor also reducing in stage by stage. Nevertheless, the pump power rises just with the increase of N_REDR These two factors result in the variation trends of P_net increasing first and then decreasing with the increase of N_REDR The variation trends are coincident with the experimental results in our previous work.^11,39

Figure 5.

Variations of net output power (P_net) with numbers of REDR (N_REDR) at different output current (I).

Additionally, the peak values of P_net and the numbers of REDR are reduced with the increases of I. When I rises from 2.0A to 3.5A, the peak values of P_net are 1.89 kW, 1.88 kW, 1.68 kW and 1.39 kW, respectively. Moreover, the corresponding numbers of REDR are 16, 21, 26 and 32, respectively. It can be explained by the following reasons. The increase of I means the immigration rate of salt ions in working fluids across IEMs increases on the one hand. The SGE of working fluids reduces more quickly when the working fluids flow through each REDR The increase of I also means the internal energy losses caused by internal resistance and electrode system increase, on the other hand. The above reasons lead to the voltage or power output of each REDR reducing quickly.

Figure 6 illustrates COD removal quantity after treating 4 h under different output current (I) conditions when the output power reaches a peak value. It is clear from the simulation results that the series system has the largest COD removal quantity at the current of 2 A under the condition of peak output power. The COD removal quantity can reach 56.64 g after treating 4 h. Furthermore, the COD removal quantity decreases gradually with the increase of current. The degradative efficiency variations of organic pollution in wastewater by a series system with the output current are also coincident with the experimental results in our previous work.^11,39

Figure 6.

COD removal quantity at different output currents after treating 4 h under different numbers of REDR.

The result is different from that of a single REDR wastewater treatment system. For a single REDR system, it is found from experiment results that the degradative efficiency rises with the increase of current. The numerical simulation result also shows that the COD removal quantity can rise from 1.77 g to 3.14 g when the output current rises from 2 A to 3.5 A under the given operating conditions. It means that a high current is a benefit to improving the degradative performance of a serial system with a few REDRs. However, more REDRs should be adopted in a serial system by appropriately reducing output current when high organic pollution removal and output energy efficiencies are wanted to be achieved simultaneously.

Figure 7 illustrates the variations of KPIs with treating time (t) at different output currents (I) when the output power reaches a peak value. Figure 7(a) to Figure 7(c) shows the variations of COD removal rate (R_COD), instantaneous current efficiency (ICE) and TEC with treating time (t), respectively.

Figure 7.

Variations of KPIs with treating time (t) at different output current (I) when the output power reaches a peak value.

It can be seen from Figure 7(a) that the COD removal rates rise in linear almost in the first 2 h of treating time and then gradually tend to be gentle at different output current. Moreover, the higher the current is, the lower the COD removal rate is. After treating 4 h, the COD removal rate can reach 94.4% at the current of 2.0 A by a 32-stage REDR serial system. It is just 83.7% at the current of 3.5 A by a 16-stage REDR serial system. The result presents that more reactors can be connected in the system at a low output current to achieve higher total COD removal rate.

A critical time (t_cr) can be seen clearly from Figure 7(b) at different currents. It appears near he initial treating time, and the higher the current, the earlier it appears. At that time, the electrode current density (j_ele) equals limiting current density (j_lim). There is an interesting variation of ICE around t_cr. Before t_cr, ICE drops linearly with treating time increasing, but it declines rapidly after t_cr. The reason is that the degradation rate of organic pollution in wastewater is controlled by the current due to a high mass transfer rate under a condition of high COD concentration. So, in the initial periods of wastewater treatment, the j_lim is higher than the j_ele. With the decrease of COD concentration, the mass transfer rate gradually drops until it is lower than the charge transfer rate. It leads to the degradation process switching to mass transfer control, and the j_lim is lower than the j_ele.³⁷

As shown in Figure 7(b), when the current is increased from 2.0 A to 3.5 A, t_cr is 120 min, 101 min, 88 min and 81 min, respectively. The smaller the current is, the larger the t_cr is. It can be seen from Figure 7(c) that TEC rises almost linearly with the treating time before the t_cr, and the rising rate is relatively lower. However, it rises quickly after t_cr, especially for a lower current. However, the values of TEC are almost the same after treating 4 h at various currents, which are 144 kWh·kg⁻¹COD approximately. The reason is that the energy utilization efficiency in a current control process is relatively high but it in a mass transfer control process is relatively low due to some side reactions.³¹ Therefore, it is helpful for achieving low TEC to adjust output current when treating time closes to the limiting value during the oxidation process.

Effect of ERS operation conditions on KPIs

Effect of initial concentration on KPIs

Besides the output current, the variations of ERS operation conditions also affect the KPIs of the system. Figure 8 illustrates the effect of initial MO concentration in wastewater on KPIs under the conditions of 26 REDRs and 2.5A current. It can be seen from Figure 8(a), COD removal rate (R_COD) rises with the treating time increasing, but it drops with the concentration of MO in wastewater increasing. When the concentration of MO in wastewater is relatively low, the variation of R_COD appears as a quadratic curve with the treating time. However, it appears linear when the concentration is relatively high. It is because the degradation of organic pollution in wastewater is controlled by charge transfer under a high MO concentration condition during the whole wastewater treatment process. The results mentioned above also lead to the ICE drops linearly with treating time at an initial MO concentration of 500 mg·L⁻¹, as shown in Figure 8(b).

Figure 8.

Variations of KPIs with the treating time under different initial MO concentrations.

The simulation results indicate that after treating 4 h, R_COD is 95.4% at an initial MO concentration of 50 mg·L⁻¹ but 60.6% at an initial MO concentration of 500 mg·L⁻¹. Although a low initial MO concentration has a high COD removal efficiency, the COD removal quantity is the opposite. After treating 4 h, the COD removal quantity was 111.8 g at an initial MO concentration of 500 mg·L⁻¹, but 17.6 g at an initial MO concentration of 50 mg·L⁻¹. So, there is a higher ICE at a high initial MO concentration during the dyeing wastewater treatment process.

Figure 8(b) also shows that the critical time (t_cr) rises with the increase of initial MO concentration. It is because the limiting current density (j_lim) rises with the increase of COD concentration in ERS, as shown in Eq.(27). The increase in j_lim led to the t_cr increase. Accordingly, the value of TEC drops with the increase of initial MO concentration. The value of TEC almost keeps a constant of 88.0 kWh·kg⁻¹COD at an initial MO concentration of 500 mg·L⁻¹, which is far less than that at an initial MO concentration of 50 mg·L⁻¹. It is because the values of r_AO and r_EF rise with the increasing of COD concentration in ERS, which results in a relatively high COD removal quantity and ICE. Therefore, the REDR system is more suitable for treating high concentration organic wastewaters in light of energy consumption.

Effect of ERS flowrate on KPIs

Figure 9 shows the effect of ERS flowrate variation on KPIs. It can be seen from Figure 9(a) that the increase of ERS flowrate can enhance the COD removal efficiency (R_COD). When ERS flowrate rises from 10 L·min⁻¹ to 50 L·min⁻¹, the R_COD rises from 86.1% to 95.4% after treating 4 h. However, with the ERS flowrate rising, the growth rate of R_COD drops. The growth rate of R_COD is only 1% when ERS flowrate rises from 40 L·min⁻¹ to 50 L·min⁻¹. It can be seen from Figure 9(b) that ICE is high at a large ERS flowrate before a critical time (t_cr). The reason is that raising ERS flowrate can enhance both k_m and k_EF values. Therefore, R_COD and ICE can be raised.

Figure 9.

Variations of KPIs with the treating time under different ERS flowrates.

It can be found from Figure 9(b) that the variation of ERS flowrate hardly affects the critical time (t_cr), which is nearly around the time of 99 min. Although the dropping rate of ICE rises slightly with the increase of ERS flowrate after the t_cr, the average ICE at a large ERS flowrate is higher than that at a small ERS flowrate in 4 h treating time. That results in a lower TEC value at a large ERS flowrate, as shown in Figure 9(c). After treating 4 h, the value of TEC is minimal of 139.6 kWh·kg⁻¹COD at ERS flowrate of 50 L·min⁻¹, and it is a maximum of 154.8 kWh·kg⁻¹COD at ERS flowrate of 10 L·min⁻¹. It can be seen from Figure 9(a) and Figure 9(c) that the degradation efficiency of the system rises and the energy consumption of the system drops with ERS flowrate increasing.

Effect of Cs concentration on KPIs

The above discussions indicate that the increases of both initial MO concentration and ERS flowrate benefit promoting COD removal quantity and current efficiency and reducing the energy consumption of wastewater treatment. Besides, the concentration difference of working fluids also affects KPIs. It is well known that the SGE of working fluids depends on the concentration difference between CS and DS under the condition of fixed CS and DS flowrates. When DS concentration is fixed as 0.05M, the SGE of working fluids only relates to CS concentration. Figure 10 shows the variation of net output power (P_net) and electricity conversion efficiency (η) of a series system with the numbers of REDR under different CS concentrations (Operation conditions: C_DS = 0.05M; I = 2.5A, C_ERS = 200 mg·L⁻¹, Q_ERS = 30 L·min⁻¹, N_REDR = 26, t = 25°C).

Figure 10.

Variation of the output power and electricity conversion efficiency of a series system with the numbers of REDR under different CS concentrations.

It can be seen from Figure 10(a) that the variations of CS concentration affect the peak values of P_net. With the increase in CS concentration, the peak values of P_net rise, but the numbers of REDR in the system rise accordingly. The maximal peak value of P_net is 1.88 kW at the CS concentration of 4M and REDR numbers of 26. However, the CS concentration rises continuously to 5M, the peak value of P_net decreases. The reason is mainly that the permselectivity of IEMs drops with the CS concentration rising, which causes the membrane potential to decrease.²⁰ Figure 10(b) illustrates the variations of electricity conversion efficiency (η) with the CS concentration. They are different from the variations of P_net with CS concentration. Although the values of η rise with the increase of REDR numbers, they drop with the increase of CS concentration. That means that a low CS concentration can provide high electricity conversion efficiency. It is because more co-ions immigrate across IEMs to lead to an increase in irreversible loss of mass transfer due to CS concentration increase.

Figure 11 shows the variation of TEC with treating time under different CS concentrations (Operation conditions: C_DS = 0.05M; I = 2.5A, C_ERS = 200 mg·L⁻¹, Q_ERS = 30 L·min⁻¹, N_REDR = 26, t = 25°C). It can be seen from the figure that TEC rises with the increase of CS concentration at the same treating time. The reasons are that: With the increase of CS concentration, 1) the unused SGE of working fluids discharged from the system with determined REDR numbers will rise, and 2) an irreversible loss in energy conversion will rise due to more co-ions immigrating across IEMs. So, a relatively low CS concentration is beneficial for energy conversion of a series system with determined REDR numbers to reduce the TEC of removing unit mass COD in wastewater.

Figure 11.

Variation of the total energy consumption (TEC) with treating time under different CS concentrations.

Compared with other technologies

Compared with traditional electrochemical AO and EF wastewater treatment processes, the wastewater treatment process of a multi-stage REDR series system has excellent economic efficiency. Tsantaki et al. reported an AO process with BDD anode to treat textile effluents.⁴⁰ Results showed that the energy consumption rose from 115 kWh·kg⁻¹COD to 364 kWh·kg⁻¹COD, and the specific cost rose from 8 €·kg⁻¹COD to 25 €·kg⁻¹COD by increasing current density from 8 to 15mA·cm⁻². In the multi-stage REDR series system, the energy consumption can reach 70 kWh·kg⁻¹COD, as shown in Figure 11. Meanwhile, the energy consumed by a multi-stage REDR series wastewater treatment system is SGE which comes from nature, byproducts or waste heat conversion. Therefore, the energy cost of the system is almost negligible, leading to the specific cost of wastewater treatment being reduced greatly.

Conclusions

A degradation process of dyeing wastewater was simulated numerically by developing the mathematical model of a multi-stage REDR series system for wastewater treatment. Some conclusions can be drawn as follows：(1) The system can not only degrade organic pollution in wastewater but also output net power. When the current output by the system is low within a research scope, the peak value of net power output by the system is high and the number of REDR employed in the system is more. At that condition, high COD removal efficiency can be achieved. (2)Under the conditions of determining numbers of REDR and output current, the COD removal efficiency drops with the increase of initial MO concentration but the current efficiency and the COD removal quantity rise, leading to the decrease of TEC of the system. (3)Under the conditions of a constant initial MO concentration, raising ERS flowrate can enhance both COD removal and current efficiencies of the system, leading to the decrease of TEC of the system. (4)Under the conditions of a constant DS concentration, raising CS concentration can enhance the net power output by the system, but it is not beneficial for the electricity conversion efficiency and energy consumption for treatment.

This work provides a new simulation method to combine the organic wastewater oxidation degradation with the reverse electrodialysis processes of the multi-stage serial REDR wastewater treatment system. And the degradation and energy efficiencies of the system are evaluated by numerical simulation. Although there is still a long way to realize the practical application of reverse electrodialysis technology in the wastewater treatment fields, the work achieved the first step for REDR wastewater treatment technology in theoretical research fields.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China, (grant number 51776029, 52076026) and the Fundamental Research Funds for the Central Universities, (grant number DUT22JC25).

ORCID iD

Qiang Leng

Nomenclature

Greek letters

Superscripts and subscripts

Acronyms

Appendix A

Sherwood number (Sh), Reynolds number (Re) and Schmidt number (Sc) are generally used to accurately predict the values of average mass transport coefficient (k_m) under different operation conditions of the REDR wastewater treatment system. They are³³: (A1)

S h = k_{m} d_{h} / D

(A2)

R e = v_{E R S} d_{h} / μ_{E R S}

(A3)

S c = μ_{E R S} / D

(A4)

S h = 5.61 R e^{0.185} S c^{0.24}

Where, d_h is equivalent hydraulic diameter, m; D is diffusivity, m² s⁻¹; v is the fluid velocity, m s⁻¹; µ is kinematic viscosity m² s⁻¹. Subscript: ERS is an electrode rinse solution (wastewater).

A correlation equation of k_EF can be built by fitting experimental results. The correlation equation can be written as follows, in which a pore-phase velocity, v_ca, is introduced.⁴¹ (A5)

k_{E F} = 1.38 \times 10^{- 8} j_{c a} + 2.644 \times 10^{- 6} v_{c a} - 5 \times 10^{- 10} C_{0} - 2.3 \times 10^{- 7}

Where, j_ca is current density, A·m⁻²; v_ca is pore-phase velocity, m·s⁻¹, C₀ is initial MO concentration, mg·L⁻¹. (A6)

j_{c a} = I / (L_{c a} H_{c a})

(A7)

v_{c a} = Q_{E R S} / (L_{ca} W_{c a} β)

Where, L_ca, H_ca_, and W_ca are length, height, and width of carbon felt, m, respectively; β is porosity of carbon felt (Set as 75%).

The correlation coefficients (R²) between calculated and experimental results are listed in Tab. A1 and they are higher than 0.95.

References

Brillas

Martínez-Huitle

. Decontamination of wastewaters containing synthetic organic dyes by electrochemical methods. An updated review. Appl Catal, B 2015; 166–167: 603–643.

Sires

Brillas

. Upgrading and expanding the electro-Fenton and related processes. Curr Opin Electrochem 2021; 27, DOI: 10.1016/j.coelec.2020.100686.

Rodriguez-Narvaez

Picos

Bravo-Yumi

, et al. Electrochemical oxidation technology to treat textile wastewaters. Curr Opin Electrochem 2021; 29, DOI: 10.1016/j.coelec.2021.100806.

Moreira

Boaventura

RAR

Brillas

, et al. Electrochemical advanced oxidation processes: a review on their application to synthetic and real wastewaters. Appl Catal, B 2017; 202: 217–261.

Scialdone

D'Angelo

De Lume

, et al. Cathodic reduction of hexavalent chromium coupled with electricity generation achieved by reverse-electrodialysis processes using salinity gradients. Electrochim Acta 2014; 137: 258–265.

Scialdone

D'Angelo

Galia

. Energy generation and abatement of Acid Orange 7 in reverse electrodialysis cells using salinity gradients. J Electroanal Chem 2015; 738: 61–68.

Zhou

Zhao

, et al. Electrochemical oxidation of ammonia accompanied with electricity generation based on reverse electrodialysis. Electrochim Acta 2018; 269: 128–135.

Hao

Galia

, et al. Development of a process for the treatment of synthetic wastewater without energy inputs using the salinity gradient of wastewaters and a reverse electrodialysis stack. Chemosphere 2020; 248: 125994. Article 2020/02/09.

Zhang

Zhou

, et al. Electricity generation from salinity gradient to remove chromium using reverse electrodialysis coupled with electrocoagulation. Electrochim Acta 2021; 379, DOI: 10.1016/j.electacta.2021.138153.

10.

Leng

Jin

, et al. Experimental investigation on dye wastewater treatment with reverse electrodialysis reactor powered by salinity gradient energy. Desalination 2020; 495, DOI: 10.1016/j.desal.2020.114541.

11.

Leng

, et al. Influence of output current on decolorization efficiency of azo dye wastewater by a series system with multi-stage reverse electrodialysis reactors. Energy Convers Manage 2021; 228, DOI: 10.1016/j.enconman.2020.113639.

12.

Leng

, et al. Degrade methyl orange by a reverse electrodialysis reactor coupled with electrochemical direct oxidation and electro-Fenton processes. Electrocatalysis 2022; 13: 242–254, DOI: 10.1007/s12678-022-00712-y

13.

Veerman

Saakes

Metz

, et al. Reverse electrodialysis: a validated process model for design and optimization. Chem Eng J 2011; 166: 256–268.

14.

Tedesco

Cipollina

Tamburini

, et al. A simulation tool for analysis and design of reverse electrodialysis using concentrated brines. Chem Eng Res Des 2015; 93: 441–456.

15.

Tedesco

Brauns

Cipollina

, et al. Reverse electrodialysis with saline waters and concentrated brines: a laboratory investigation towards technology scale-up. J Membr Sci 2015; 492: 9–20.

16.

Mousset

Oturan

. An unprecedented route of center dot OH radical reactivity evidenced by an electrocatalytical process: ipso-substitution with perhalogenocarbon compounds. Appl Catal, B 2018; 226: 135–146.

17.

Sopaj

Rodrigo

Oturan

, et al. Influence of the anode materials on the electrochemical oxidation efficiency. Application to oxidative degradation of the pharmaceutical amoxicillin. Chem Eng J 2015; 262: 286–294.

18.

Kapalka

Foti

Comninellis

. Kinetic modelling of the electrochemical mineralization of organic pollutants for wastewater treatment. J Appl Electrochem 2008; 38: 7–16. Article.

19.

Tedesco

Cipollina

Tamburini

, et al. Modelling the reverse ElectroDialysis process with seawater and concentrated brines. Desalin Water Treat 2012; 49: 404–424.

20.

Zlotorowicz

Strand

Burheim

, et al. The permselectivity and water transference number of ion exchange membranes in reverse electrodialysis. J Membr Sci 2017; 523: 402–408.

21.

Pitzer

Peiper

Busey

. Thermodynamic properties of aqueous sodium-chloride solutions. J Phys Chem Ref Data 1984; 13: 1–102.

22.

Giacalone

Catrini

Tamburini

, et al. Exergy analysis of reverse electrodialysis. Energy Convers Manage 2018; 164: 588–602.

23.

Islam

Gupta

Ismail

. Extension of the Falkenhagen-Leist-Kelbg equation to the electrical conductance of concentrated aqueous-electrolytes. J Chem Eng Data 1991; 36: 102–104.

24.

Chen

Jiang

Zhang

, et al. Storable hydrogen production by reverse electro-electrodialysis (REED). J Membr Sci 2017; 544: 397–405. Article.

25.

Brillas

Sires

Oturan

. Electro-Fenton process and related electrochemical technologies based on Fenton's reaction chemistry. Chem Rev 2009; 109: 6570–6631. 2009/10/21.

26.

Iniesta

Michaud

Panizza

, et al. Electrochemical oxidation of phenol at boron-doped diamond electrode. Electrochim Acta 2001; 46: 3573–3578.

27.

Vermaas

Saakes

Nijmeijer

. Doubled power density from salinity gradients at reduced intermembrane distance. Environ Sci Technol 2011; 45: 7089–7095. 2011/07/09.

28.

Cavalcanti

Garcia-Segura

Centellas

, et al. Electrochemical incineration of omeprazole in neutral aqueous medium using a platinum or boron-doped diamond anode: degradation kinetics and oxidation products. Water Res 2013; 47: 1803–1815. 2013/01/29.

29.

Zhou

. Electro-Fenton process for water and wastewater treatment. Crit Rev Environ Sci Technol 2017; 47: 2100–2131. Review.

30.

Panizza

Michaud

Cerisola

, et al. Anodic oxidation of 2-naphthol at boron-doped diamond electrodes. J Electroanal Chem 2001; 507: 206–214. Article.

31.

Urtiaga

Ortiz

Anglada

, et al. Kinetic modeling of the electrochemical removal of ammonium and COD from landfill leachates. J Appl Electrochem 2012; 42: 779–786. Article.

32.

Cañizares

García-Gómez

de Marcos I

, et al. Measurement of mass-transfer coefficients by an electrochemical technique. J Chem Educ 2006; 83: 1204–1207. Article.

33.

Anglada

Urtiaga

Ortiz

. Laboratory and pilot plant scale study on the electrochemical oxidation of landfill leachate. J Hazard Mater 2010; 181: 729–735. Article 2010/06/15.

34.

Akkaya

Erkan

Sekman

, et al. Modeling and optimizing Fenton and electro-Fenton processes for dairy wastewater treatment using response surface methodology. Int J Environ Sci Technol 2018; 16: 2343–2358.

35.

Ramirez

Rondan

Ortiz-Hernandez

, et al. Semi-empirical chemical model for indirect advanced oxidation of acid orange 7 using an unmodified carbon fabric cathode for H2O2 production in an electrochemical reactor. J Environ Manage 2016; 171: 29–34. Article 2016/02/14.

36.

Veerman

Saakes

Metz

, et al. Reverse electrodialysis: performance of a stack with 50 cells on the mixing of sea and river water. J Membr Sci 2009; 327: 136–144.

37.

Mousset

Pechaud

Oturan

, et al. Charge transfer/mass transport competition in advanced hybrid electrocatalytic wastewater treatment: development of a new current efficiency relation. Appl Catal, B 2019; 240: 102–111.

38.

Micari

Bevacqua

Cipollina

, et al. Effect of different aqueous solutions of pure salts and salt mixtures in reverse electrodialysis systems for closed-loop applications. J Membr Sci 2018; 551: 315–325.

39.

, et al. Multi-stage reverse electrodialysis: strategies to harvest salinity gradient energy. Energy Convers Manage 2019; 183: 803–815. Article.

40.

Tsantaki

Velegraki

Katsaounis

, et al. Anodic oxidation of textile dyehouse effluents on boron-doped diamond electrode. J Hazard Mater 2012; 207–208: 91–96. 2011/05/03.

41.

You

Cheng

. The dependence of mass transfer coefficient on the electrolyte velocity in carbon felt electrodes: determination and validation. J Electrochem Soc 2017; 164: E3386–E3394. Article; Proceedings Paper.