Abstract
The removal of low concentration ammonia-nitrogen in industrial wastewater is necessary before discharged into the environment. In this study, vacuum plate membrane distillation (VPMD) technology was utilized and operating parameters such as pH, feed temperature, vacuum degree, feed flow and time were investigated. Based on the experimental data, the heat and mass transfer mechanism and mathematic model were studied. The experimental results show that low solution pH was significantly beneficial to ammonia-nitrogen removal but permeate flux was nearly changeless. At pH = 4, a removal rate up to 93.33% was achieved. Ammonia-nitrogen mainly exists with NH4+ ions in acidic solution, so only water molecules pass through the membrane to acquire the water product in the permeate side. Increasing the temperature of the solution was disadvantageous to the ammonia-nitrogen removal due to membrane pores expanding and the mass transfer coefficient of NH3 molecules increasing; therefore a low temperature was chosen if possible. Because vapor pressure of the feed solution increases exponentially with temperature and results in membrane surface pressure difference increases, therefore increasing the temperature enhances the permeate flux. Raising the vacuum degree enhanced ammonia removal rate and permeate flux obviously, a vacuum degree of 0.09 MPa was chosen for the experiment. The effect of feed flow rate on ammonia-nitrogen removal instead of permeate flux is weak, the reason is that the boundary layer wears thin when the feed flow rate is increased, which is conducive to permeate flux increasing. In a two-parameter model of Knudsen diffusion, Poiseuille flow was chosen to demonstrate the heat and mass transfers in the process of VPMD in the study. Based on the experimental values of permeate flux, two parameters CK and CP in the model were calculated using a nonlinear fitting method software, which indicated that the Knudsen diffusion model more than the Poiseuille flow model was suitable. The maximum values of the relative average deviation (RAD) and root mean square difference (RMSD) of experimental and calculated values with model equations of the permeate flux at the different temperature, vacuum degree and feed flow rate were no more than 8.7% and 3.20 kg · (m2 · h)−1, respectively.
HIGHLIGHTS
The affecting factors of VPMD processes on the removal of low concentration ammonia-nitrogen rate and permeate flux were studied.
An acidic solution is more beneficial to ammonia-nitrogen removal than an alkaline solution in the process of VPMD.
VPMD exhibited a high ammonia removal rate removal (93.33%).
The contribution of Knudsen diffusion to the mass transfer of VPMD is greater than that of Poiseuille flow.
Graphical Abstract
NOMENCLATURE
C0 | Initial concentration of feed | mg·L−1 |
CF | Concentration of water production | mg·L−1 |
D | Molecular diffusion coefficient, | m2·s−1 |
dh | Equivalent diameter | m |
hf | Feed side heat transfer coefficient | W·(m·K)−1 |
ΔHV | Heat of vaporization of water | J·g−1 |
Km | Total mass transfer coefficient | g·(m2·s·Pa)−1 |
Δm | Water production quality | g |
M | Water molecular weight | g·mol−1 |
Nc | Permeate flux | g·(m2·s)−1 or kg·(m2·h)−1 |
Nu | Nusselt number | |
PA | Total pressure of air and water molecules | Pa |
Pavg | Average pressure in membrane hole | Pa |
PB | Air partial pressure of cold side | Pa |
pfm | Membrane surface pressure of hot side | Pa |
Δpi | Membrane pressure difference | Pa |
ppm | Membrane surface pressure of cold side | Pa |
Pr | Prandtl number | |
R | Gas constant | J·(mol·K)−1 |
Re | Reynolds number | |
Δt | Sampling interval | s |
Ti | Feed temperature | °C |
Tfm | Film surface temperature of hot side | K |
u | Feed velocity | m·s−1 |
Greek symbols | ||
λ | Thermal conductivity of the solution | W·(m· K)−1 |
μi | Viscosity | Pa·s |
Superscripts | ||
cal | calculated value | |
exp | experimental data |
C0 | Initial concentration of feed | mg·L−1 |
CF | Concentration of water production | mg·L−1 |
D | Molecular diffusion coefficient, | m2·s−1 |
dh | Equivalent diameter | m |
hf | Feed side heat transfer coefficient | W·(m·K)−1 |
ΔHV | Heat of vaporization of water | J·g−1 |
Km | Total mass transfer coefficient | g·(m2·s·Pa)−1 |
Δm | Water production quality | g |
M | Water molecular weight | g·mol−1 |
Nc | Permeate flux | g·(m2·s)−1 or kg·(m2·h)−1 |
Nu | Nusselt number | |
PA | Total pressure of air and water molecules | Pa |
Pavg | Average pressure in membrane hole | Pa |
PB | Air partial pressure of cold side | Pa |
pfm | Membrane surface pressure of hot side | Pa |
Δpi | Membrane pressure difference | Pa |
ppm | Membrane surface pressure of cold side | Pa |
Pr | Prandtl number | |
R | Gas constant | J·(mol·K)−1 |
Re | Reynolds number | |
Δt | Sampling interval | s |
Ti | Feed temperature | °C |
Tfm | Film surface temperature of hot side | K |
u | Feed velocity | m·s−1 |
Greek symbols | ||
λ | Thermal conductivity of the solution | W·(m· K)−1 |
μi | Viscosity | Pa·s |
Superscripts | ||
cal | calculated value | |
exp | experimental data |
INTRODUCTION
As a necessary nutrient element for aquatic organisms, ammonia-nitrogen widely exists in urban sewage and industrial wastewater. If the sewage and wastewater are discharged into natural water bodies, this can lead to the explosive growth of algae, followed by a water bloom in fresh water or a red tide in the ocean, namely, water eutrophication (Chen & Wang 2020). So, it is very necessary to treat sewage and the wastewater with ammonia-nitrogen before it is discharged.
Industrial wastewater with high concentrations of ammonia-nitrogen is usually treated by stripping technology, which can reduce the concentration of ammonia-nitrogen and produce wastewater with low concentrations of ammonia-nitrogen. If the treated wastewater is directly discharged into natural water bodies, there may be induction of eutrophication of the water bodies. If the treated wastewater is used as industrial reuse water, it not only corrodes metal devices, but also blocks pipes and equipment because of bio-fouling due to the eutrophication of water, which would seriously affect the heat transfer efficiency of the manufacturing facility (Li et al. 2018). So it is necessary to further treat wastewater with a low concentration of ammonia-nitrogen.
At present, the treatment methods for wastewater with low concentrations of ammonia-nitrogen mainly include the biological method, breakpoint chlorination method, adsorption method and membrane separation method, etc. (Ashrafizadeh & Khorasani 2010; Luo et al. 2010; Zhang et al. 2019; Khawaga et al. 2021). However, these technologies have some problems such as high cost, low rate, long reaction time and secondary pollution. Among them, the biological method has high oxygen consumption, and heavy metals in water have an inhibitory effect on microorganisms and affect the removal rate of ammonia-nitrogen (Zhang et al. 2022). The breakpoint chlorination method uses a large amount of chlorine, has a high drug cost and secondary pollution caused by by-products of chloramines and chlorinated organic compounds (Devi & Dalai 2021). The adsorption capacity of the adsorbent used in the adsorption method is low and the concentrated water after analysis is difficult to treat (Zhang & Zhang 2011).
As a new water treatment technology, membrane distillation (MD) technology has attracted wide attention in recent years. MD is a thermally driven separation process using microfiltration, and only steam or gas molecules can pass through the porous hydrophobic membranes. At present, MD technology is mainly used in the treatment of industrial wastewater, the preparation of high-purity water, the desalination of seawater or brackish water, the separation of azeotropic mixtures and the recovery of heat-sensitive substances (Drioli et al. 2015).
MD technology is also used to recover ammonia. At present, there have been dozens of academic papers published on the treatment of municipal sewage, landfill leachate, agricultural and industrial wastewater to remove ammonia-nitrogen by MD technology (Zarebska et al. 2014; Guo et al. 2019; Scheepers et al. 2020; Simoni et al. 2021; Zhou et al. 2021; Zico et al. 2021). In these studies, the concentrations of ammonia-nitrogen was were usually high; therefore, removal of ammonia-nitrogen was mainly achieved by adding alkali in the solution to volatilize ammonia gas. The relevant research on removal or the recovery of low concentrations of ammonia-nitrogen from the solution was small.
In this paper, the VMD method is used to treat low concentration ammonia-nitrogen (about 30 mg·L−1) wastewater produced in a phosphorus chemical enterprise. By the chemical method, heavy metal, phosphor, chlorine, sulfur in the wastewater are nearly removed and meet national wastewater discharge standards, except for ammonia-nitrogen (barely changing). If the treated wastewater was discharged directly into natural water, the enterprise would face a hefty fine from the Environmental Protection Department. So we concentrated on the removal rate of ammonia-nitrogen in the study.
The essence of mass transfer by membrane distillation is the diffusion of gas in porous media. Schofield et al. (1987, 1990) proposed that the main diffusion forms are molecular diffusion, Knudsen diffusion and Poiseuille flow based on the dust-gas model. So the mass transfer in membrane distillation can be expressed by one form or a combination of the above forms. In VMD, due to the large vacuum on the permeate side, collisions among molecules and that between molecules and pore wall will occur. The collisions between molecules can be ignored. Therefore, the mass transfer mechanism proposed by most researchers is the Knudsen model, Poiseuille flow model or a mixture of the two models without considering molecular diffusion. In this paper, the authors discuss the diffusion model of gas and establish a mass transfer model equation.
THEORY
Deamination principle
When the pH value of the wastewater is basic, ammonia-nitrogen exists as NH3 molecules (shown in Figure 2(a)). So in the VMD process, under the driving of partial pressure difference on both sides of the membrane, water vapor and ammonia molecules may pass through the air–liquid interface and enter the membrane pores. Because of the high vacuum degree on the permeate side, the gas molecules leave the membrane pores quickly and move into the condensing unit and condensate to form the solution. Then the permeability residue with less ammonia-nitrogen can be formed. Many researchers used this method to deaminate from the medium and high concentration ammonia-nitrogen wastewater and acquired high deamination rate (Choi et al. 2019; Simoni et al. 2021).
When the pH value of wastewater is acidic, ammonia-nitrogen exists as NH4+ (shown in Figure 2(b)). So in the VMD process, under the driving of the partial pressure difference, only water vapor molecules may pass through the air–liquid interface and enter the membrane pores. At the same time, under the high vacuum degree in the permeate side, the water vapor molecules leave the membrane pores quickly and move into the condensing unit and condensate to form liquid water. Then the permeability residue with more ammonia-nitrogen can be formed.
Heat transfer
In the VMD technology, the process of heat transfer includes usually three steps: firstly, heat is transferred from the feed liquid body to the membrane surface; secondly, the heat conducts in the membrane accompanying the vapor through the membrane; finally, the latent heat of vapor releases in the cold side.
Usually, it is assumed that all of the above heat transfer processes are steady-state and adiabatic, simultaneously, and the heat loss may be neglected.
Mass transfer
The emphasis of mass transfer in the VMD is on the transmembrane mass transfer of volatile components such as water vapor or NH3.
EXPERIMENTAL
Experimental materials and instruments
Ammonium chloride (analytical purity), sodium sulfate (analytical purity) and sodium carbonate (purity ≥99.0%) are used to prepare simulated low concentration ammonia-nitrogen wastewater. Ammonium chloride (analytical purity) is used to prepare standard solutions of ammonium. Potassium iodide (analytical purity), mercury iodide (analytical purity) and sodium hydroxide (purity ≥96%) are used to prepare the Nessler reagent. Sodium potassium tartrate (analytical purity) is used to prepare masking agents.
In the simulated wastewater, the content of each component was ammonium chloride 114.57 mg·L−1 (equivalently 30 mg·L−1 of ammonia-nitrogen), sodium sulfate 1,600 mg·L−1 and sodium carbonate 900 mg·L−1, respectively. The simulated wastewater's conductivity and turbidity were 3,600 mS·cm−1 and 0.2 NTU, respectively.
A ultraviolet and visible light spectrophotometer (TU-1810, Beijing Puxi General Instrument Co. Ltd) was used to measure the contents of ammonia -nitrogen in the sample; a turbidimeter (HI93703-11, Shanghai MERWAY Biotechnology Co. Ltd) was used to measure the turbidity of samples; a conductivity meter (DDS-307, Shanghai Yidian Scientific Instrument Co. Ltd) was used to measure the conductivity of the samples.
Membrane module and membrane material
Parameter . | Value . |
---|---|
Membrane pore radius (r)/μm | 0.225 |
Membrane thickness (d)/μm | 30 |
Membrane porosity (ε)/% | 85 |
Tortuosity factor of the membrane pore (τ) (Iversen et al. 1997) | 1.17 |
Membrane area (A)/m2 | 0.0015 |
Parameter . | Value . |
---|---|
Membrane pore radius (r)/μm | 0.225 |
Membrane thickness (d)/μm | 30 |
Membrane porosity (ε)/% | 85 |
Tortuosity factor of the membrane pore (τ) (Iversen et al. 1997) | 1.17 |
Membrane area (A)/m2 | 0.0015 |
Experimental device
When the feed was alkaline, the produced water was collected on the feed side; when the feed was acidic or neutral, the produced water on the permeate side was collected in the accepting bottle. The pH of the feed was adjusted with dilute NaOH and H2SO4 solutions. After the VPMD unit ran for two hours, the production water was sampled to analyze its physicochemical properties.
Analysis and calculation method
The permeate flux and the removal rate of the ammonia-nitrogen are important parameters for evaluating the performance of membrane distillation. In this experiment, the concentration of ammonia- nitrogen was measured using Nessler's reagent spectrophotometry (Cui 2008). The standard ammonium solution was prepared using analytic purity ammonium chloride and deionized water (it was self-made, of which resistivity was 18.25 MΩ·cm−1). A spectrophotometer was used to measure the absorbance of the sample at a wavelength of 420 nm for linear correlation of the standard curve was 0.9996.
RESULTS AND DISCUSSION
Factors affecting ammonia-nitrogen removal and permeate flex
Effect of the feed pH
It is obvious that the removal rate of ammonia-nitrogen increases slightly with the increase in pH when the raw material is alkaline and the highest removal rate is 42.5%. Relative to the wastewater with high concentrations of ammonia-nitrogen, the effect of pH on that with a low concentration of ammonia-nitrogen is more weaker (EL-Bourawi et al. 2007; He et al. 2018). NH3 molecules and NH4+ ions coexisted when the solution is basic. It was supposed that NH3 molecules can transfer membrane instead of NH4+ ions, so either the penetrating fluid or permeability residue had a certain concentration of ammonia-nitrogen, which resulted in the low removal rate of ammonia-nitrogen. When the raw material was acidic, it is obvious that the removal rate of ammonia-nitrogen is higher than 80% and then up to 93.33% at pH = 4 within 2 h. At this moment, ammonia-nitrogen mainly exists with the form of NH4+ ions, hence only water molecules pass across the membrane and the produced water on the permeate side has few NH4+ ions.
As shown in Figure 5, the experimental values of permeate flex of acidic solution were slightly higher than that of the alkali solution. According to Equation (10), the dominant factors of permeate flux include membrane surface pressure difference and mass transfer coefficient. At a certain vacuum degree and temperature, the membrane surface pressure difference changed little with pH value. So the mass transfer coefficient had more influence on the permeate flux. As above described, ammonia-nitrogen exists with NH3 molecules in alkali solution but with NH4+ in basic solution. It is supposed that intermolecular hydrogen bond action of NH3–H2O in alkali solution hindered the membrane transfer of NH3 gas and H2O vapor and resulted in the permeate flux reducing.
Effect of the temperature
As seen from Figure 6, when the pH of the solution is 5, the ammonia-nitrogen removal rate drops from 95.92% to 85.32% with the temperature increasing from 50 °C to 75 °C at the operating time of 2 h; however, when the pH of the solution is 12, the ammonia-nitrogen rate rises from 20.14% to 42.56% at the same experimental temperature and time.
When the solution is acidic with the temperature increasing, the membrane pore will expand; simultaneously, the diffusivity of NH4+ ions increases; so the content of NH4+ ions in the produced water on the permeate side increases and the ammonia-nitrogen removal rate drops. This result is consistent with most literature reports (Choi et al. 2019; Simoni et al. 2021).
By contast, when the solution is basic, with the temperature increase, the membrane hole will expand; simultaneously, there are more NH3 molecules passing through the membrane; so the content of NH3 in the permeability residue reduces and ammonia-nitrogen removal rate rises.
As observed, the experimental value of permeate flux at pH of 4 increased rapidly from 11.23 kg·(m2·h)−1 to 47.36 kg·(m2·h)−1 with the feed temperature increasing from 50 °C to 75 °C. Slightly changed temperature has weak influence on the mass transfer coefficient, so it is the dominating cause that the vapor pressure of the feed solution increases exponentially with temperature.
Effect of vacuum degree on the permeate side
As shown in Figure 7, with a vacuum degree increase from 0.07 MPa to 0.09 MPa, when the pH of the feed solution is 5, the removal rate of ammonia-nitrogen increases from 77.58% to 85.32%. When pH = 12, the removal rate of ammonia-nitrogen decreased from 57.80% to 42.56%.
With the vacuum degree increased, the driving power across the membrane increases, so that, whether in acidic or basic medium, more NH4+ ions and NH3 molecules can pass through the membrane. Therefore, when the feed solution is acidic, the content of ammonia-nitrogen in the produced water on the permeate side increases, so the removal rate of ammonia-nitrogen decreases with the vacuum degree increase. When the feed solution is basic, the content of ammonia-nitrogen in the produced water (namely the permeability residue) increases, so the removal rate of ammonia-nitrogen increases with the vacuum degree increase.
It was observed that the value of permeate flux increased with vacuum degree on the permeate side. At a certain temperature, the vapor pressure of the solution is constant; so that the membrane surface pressure difference will increase with vacuum degree. As shown in Equation (10), permeate flux is in direct proportion to the membrane surface pressure difference. Therefore, increasing the vacuum degree enhances the mass transfer driving power and permeate flux.
Effect of feed flow rate
In general, with the feed flow increase, the heat transfer efficiency increases and the residence time of the material liquid on the membrane surface reduces, so that both water flux and ammonia-nitrogen flux increase.
Therefore, similar to the effects of vacuum degree on the permeate side and the feed temperature mentioned above, when the feed solution is acidic, the removal rate of ammonia-nitrogen in the produced water on the permeate side decreases with the feed flow rate increase. When the feed solution is basic, the removal rate of ammonia- nitrogen in the permeability residue increases with the feed flow rate increase.
On the whole, the effect of feed flow rate on ammonia -nitrogen removal is weak; conversely, the effect on permeate flux is strong. Permeate flux increases with feed flow rate up to 50 L·h−1. With the feed flow rate increase, the boundary layer wears thin, and then the transmembrane driving force and heat transfer effect are enhanced, so the permeate flux is increased.
Effect of the time
As shown in the Figure 9, when the raw material liquid is acidic, the removal rate of ammonia-nitrogen in the produced water on the permeate side gradually decreases; when the raw material liquid is basic, the removal rate of ammonia-nitrogen in the permeability residue gradually increases. With time increasing, water vapor or volatile NH3 in the membrane holes tend to balance with the feed liquid, so the content of ammonia-nitrogen in the produced water tends to be constant.
As observed in the experiments, membrane fouling was increasingly seriously with time extending due to the crystallization of ions in the solution on the membrane surface and/or in the membrane pores (Lu et al. 2017), so that the permeate flux obviously decreased (Figure 10). Hence, it was necessary to back flush the polluted membrane at intervals.
Optimal experimental conditions
Based on the above experiments, the optimal operating conditions of VPMD in the research can be achieved: pH of the feed solution was 4, the temperature of feed liquid was 75 °C, vacuum degree was 0.09 MPa, the feed flow rate was 40 L·h−1 and the operation time was 2 h. The water quality of the treated water is shown in Table 2. From Table 2, the ammonia-nitrogen content in the water meets the national standard of sewage discharge (<15 mg·L−1) (GB 8987-1996 in China).
Project . | Ammonia -nitrogen content/ . | Conductivity/ . | Turbidity/ . |
---|---|---|---|
mg·L−1 . | μs·cm−1 . | NTU . | |
Inlet | 30.00 | 3,600 | 0.20 |
Outlet | 2.00 | 3.21 | 0.12 |
Removal rate/% | 93.33 | 99.91 | 40.00 |
Project . | Ammonia -nitrogen content/ . | Conductivity/ . | Turbidity/ . |
---|---|---|---|
mg·L−1 . | μs·cm−1 . | NTU . | |
Inlet | 30.00 | 3,600 | 0.20 |
Outlet | 2.00 | 3.21 | 0.12 |
Removal rate/% | 93.33 | 99.91 | 40.00 |
Establishment of the model equation
Based on the VMD experimental values above and the calculated process shown in Equations (1)–(14), we tried to choose the Knudsen diffusion-Poiseuille flow two-parameter model (Equation (14)) (Ding et al. 2001), used the experimental data of permeate flux to fit CK and CP in the two-parameter model, and studied the contribution of Knudsen diffusion and Poiseuille flow to mass transfer. The nonlinear fitting results by the Levenberg–Marquardt + general global optimization method offered by the 1-stOpt software are shown in Table 3.
From Table 3, Cp is far less than CK, if plugging in Cp and CK into the formula(14) under the optimal experimental conditions (the pH is 4, the temperature is 75 °C, the vacuum degree is 0.09 MPa and the feed flow rate is 40 L·h−1), the values of the first item and the second item on the right-hand side can be calculated as 46.66 kg·(m2·h)−1 and 6.09 × 10−15 kg·(m2·h)−1 respectively, which indicated that the contribution of the Poiseuille flow model to the mass transfer of the VPMD process of the wastewater with low ammonium-nitrogen concentration can be negligible and may take into account the Kunden diffusion model.
Here, Nc is the permeate flux calculated from the initial value of the hypothesis. Nc+1 is permeate flux iterated by secant method. The calculation process applied iterative approach to calculate the Nc.
Theoretical calculation of the effect of the VPMD operating parameters
The RAD and RMSD of the theoretical calculation values and experimental data of effects of parameters on the permeate flux are calculated and listed in the Table 4. The maximum values of RAD and RMSD was no more than 8.7% and 3.20 kg·(m2·h)−1, which indicated again that the Knudsen diffusion model is suitable for the heat transfer and mass transfer mechanisms of the VPMD process of the wastewater with low concentrations of ammonium-nitrogen.
Operating conditions . | Temperature . | Vacuum degree . | Flow rate . |
---|---|---|---|
RAD/% | 8.70 | 4.22 | 6.52 |
RMSD/kg·(m2·h)−1 | 1.95 | 1.73 | 3.20 |
Operating conditions . | Temperature . | Vacuum degree . | Flow rate . |
---|---|---|---|
RAD/% | 8.70 | 4.22 | 6.52 |
RMSD/kg·(m2·h)−1 | 1.95 | 1.73 | 3.20 |
CONCLUSIONS
As a kind of important pollutant leading to water eutrophication, removal of low concentration ammonia-nitrogen in the industrial wastewater before discharged into environment is very necessary, but is also difficult. In this paper, VPMD technology as a novel technology was utilized to treat low concentration ammonia-nitrogen wastewater from a phosphorous chemical enterprise. The operating parameters such as pH, feed temperature, vacuum degree, feed flow and time were investigated. Based on the experimental data, the heat and mass transfer mechanism and mathematic model were studied.
The experimental results showed that low solution pH was significantly beneficial to ammonia-nitrogen removal but permeate flux was nearly changeless. The main reasons is that ammonia-nitrogen mainly exists as NH4+ ions in the acidic solution, instead of NH3 molecules in the alkali solution; so material transferring membranes and the quality of the water product were different in the process of VPMD.
Increasing the temperature of the solution was disadvantageous to ammonia-nitrogen removal due to membrane pores expanding and vapor pressure of NH3 molecules rising. Increase in vapor pressure resulted in membrane surface pressure difference increases, and then permeate flux increased with temperature; therefore a low temperature was chose when possible.
As the important factor to drive vapor or gas to transfer membrane, raising vacuum degree enhanced permeate flux obviously, so the vacuum degree of 0.09 MPa was chosen in the experiment. The effect of feed flow rate on ammonia-nitrogen removal instead of permeate flux is weak. Due to the boundary layer wearing thin, it was easier for vapor or gas to transfer across membrane, which resulted in permeate flux increasing.
Membrane fouling causing permeate flux obviously decreasing is seemly inevitable with time extending, it was supposed that ions in the solution crystallized on the membrane surface and/or in the membrane pores in the process of VPMD although the wastewater was pretreated by other methods such as chemical precipitation, physical absorption, etc. Hence, it was necessary to back flush the polluted membrane at intervals.
In the experimental investigation, the optimal operating factors of the process of VPMD were that pH and temperature of feed liquid were 4 and 75 °C, respectively; the vacuum degree on the permeate side was 0.09 MPa, the feed flow was 40 L·h−1 and the time was 2 h. The concentration and the removal rate of ammonia-nitrogen in the treated effluent was 2 mg·L−1 and 93.33%, respectively.
The models of VMD mainly included the Knudsen diffusion model, Poiseuille flow model and the combination model of the two. So two-parameter model of the Knudsen diffusion–Poiseuille flow was chosen to demonstrate the heat and mass transfer in the process of VPMD in the study. Based on the experimental values of permeate flux, two parameters CK and CP in the model were met. The calculated results indicated that the Knudsen diffusion model was suitable to demonstrate the membrane transfer mechanism in the process of VPMD. The maximum values of RAD and RMSD of experimental and calculated values of the permeate flux at different temperatures, vacuum degree and feed flow rate was no more than 8.7% and 3.20 kg·(m2·h)−1, respectively.
ACKNOWLEDGEMENTS
The authors are very grateful for the support of the National Natural Science Foundation of China (21868010) and the Open Foundation of State Key Laboratory of Efficient Utilization of Medium and Low Grade Phosphate Ore and Its Associated Resources (WFKF2018-02).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.