Simulation of ammonia removal from industrial wastewater streams by means of a hollow-fiber membrane contactor

Desalination 285 (2012) 383–392

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Simulation of ammonia removal from industrial wastewater streams by means of a hollow-fiber membrane contactor Mashallah Rezakazemi, Saeed Shirazian, Seyed Nezameddin Ashrafizadeh ⁎ Research Lab for Advanced Separation Processes, Department of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran

a r t i c l e

i n f o

Article history: Received 22 September 2011 Received in revised form 14 October 2011 Accepted 18 October 2011 Available online 17 November 2011 Keywords: Membrane contactor Mass transfer Wastewater treatment Ammonia removal CFD

a b s t r a c t The performance of a hollow-fiber membrane contactor in removing ammonia from aqueous solution was simulated. An unsteady state 2D mathematical model was developed to study the ammonia stripping in the hollow-fiber membrane contactor. Two sets of equations were considered for the membrane contactor and the feed tank. CFD technique was applied to solve the model equations in which concentration distribution was determined using continuity equation. Velocity field is also determined using Navier–Stokes equations for the contactor. The model was implemented in linked MATLAB–COMSOL Multiphysics. COMSOL software was applied to solve the model equations for the contactor while MATLAB software was employed to consider changes in the concentration of the feed tank. Predictions of the model were then validated against experimental data which were found to be in good agreement. The assumption of Knudsen diffusion for the transport of ammonia molecules through the membrane pores increased the accuracy of the model. The effect of different parameters including feed velocity, feed concentration and pH on the removal of ammonia was investigated. The results of simulation revealed that the developed model can be used to evaluate the effective parameters which involve in the ammonia removal by means of membrane contactors. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Ammonia (NH3) has been recognized as a major pollutant in both municipal and industrial wastewater. Dissolved ammonia exists in industrial wastewater such as coking, chemical fertilizer, coal gasification, petroleum refining, pharmaceutical and catalyst factories [1]. From the environmental point of view, a complete removal of ammonia from wastewater is desirable. This obligation is due to the extremely toxic nature of ammonia to most fish species and the fact that it becomes bio-oxidized by nitrifying microorganisms to nitrites which are undesirable to humans. The concentration of ammonia in industrial wastewater varies from 5 to 1000 mg/L [2]. The removal of dissolved ammonia from wastewater is thus mandatory to protect the environment and human health. Some conventional separation processes have been applied to remove ammonia from water and wastewater including air stripping, selective ion exchange, break-point chlorination, denitrification, and biological nitrification [3–8]. Recently, hollow-fiber membrane contactors (HFMCs) have attracted large attentions as a powerful device for the latter purpose. A major part of the interest towards HFMCs is due to their capability in setting a dispersion free contact. In addition, the velocities of both phases can be chosen independently, while neither flooding nor unloading problems may arise [9–11].

⁎ Corresponding author. Tel.: + 98 21 77240496; fax: + 98 21 77240495. E-mail address: ashrafi@iust.ac.ir (S.N. Ashrafizadeh). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.10.030

The mechanism of separation in this kind of membrane contactors is based on the mass transfer between the two phases. The ammonia evaporates from the aqueous solution, diffuses through the membrane pores, and reacts with the stripping solution. There are few studies on ammonia removal from wastewater. Hasanŏglu et al. [3] experimentally and theoretically studied the performance of the hydrophobic hollow-fiber and flat-sheet membrane contactors under various operational configurations, temperature, and hydrodynamic conditions for the ammonia removal from wastewater streams. They developed a model based on a resistance-in-series model. Tan et al. [12] developed a mass transfer model based on plug flow behavior for the ammonia removal in polyvinylidene fluoride (PVDF) hollow fibers. At any cross-section of the lumen, overall mass transfer coefficient was empirically estimated. Mandowara et al. [13] simulated the ammonia removal process in HFMCs in an unsteady state mode. They converted governing equations into a series of stiff ODEs and solved the equations using MATLAB software. Their model findings revealed that the plug-flow model over-predicts the removal of ammonia. Their numerical model which was performed with some assumptions, although considers the axial and radial diffusions it can neither investigate the effect of operating parameters nor identify the concentration variations in the contactor. Zhu et al. [14] investigated the effect of pH and viscosity of feed solution on the mass transfer in HFMCs. Based on their results, it is more accurate to use the equilibrium concentrations instead of the total concentration of ammonia to simulate the process. Semmens et al. [15] discussed the effect of pH on the mass transfer coefficients.

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There are two approaches for the mass transfer modeling of ammonia removal from wastewater using HFMCs. The first one is based on the resistance-in-series model. In this model, the resistances in the aqueous feed phase, boundary layer, and the membrane phase are considered in series, while the resistance at the shell side is neglected because of instantaneous chemical reaction which occurs between ammonia and sulfuric acid. The latter approach needs mass transfer coefficients for the feed and membrane phases to be estimated. The experimental correlations are extensively used to estimate the mass transfer coefficients; which are dependent on Reynolds and Schmidt numbers. Calculation of mass transfer coefficients by this method should be thus estimated using experimental data and may be inaccurate. The second approach is based on solving conservation equations for ammonia in the aqueous feed and membrane phases. In this approach, conservation equations including continuity, energy, and momentum equations are derived and solved simultaneously by appropriate numerical methods. The applications of computational fluid dynamics (CFD) are usually carried out in three steps: preprocessing, processing, and post processing, respectively. To our knowledge, there is no CFD simulation study on mass and momentum transfers of ammonia in HFMCs. The difficulty of this process is due to the application of recycling mode of the process which needs an unsteady state simulation. For the ammonia removal, two sets of equations are required for the simulation process. The first one is for the feed tank and the second one is for the membrane contactor. These two sets of equations should be solved simultaneously to simulate the process. The main objective of the present study is to develop and solve a mathematical model for the simulation of ammonia stripping in a HFMC with recycling mode. The equations of the model are solved by numerical method based on CFD techniques. An algorithm is developed for the numerical simulation. Considering the recycling mode makes the modeling difficult, since it needs a link between the two sets of equations. Continuity and Navier–Stokes equations are solved simultaneously for the membrane contactor to obtain the concentration distribution of ammonia. Concentration of ammonia in the feed tank is obtained through a mass balance over the feed tank while considering a complete mixing. The main advantage of the developed model is that parameters which affect the contactor performance can be modified and investigated. The model is developed for recycling mode which is difficult to be built up by CFD techniques.

containing ammonia were prepared through addition of measured volumes of ammonium hydroxide to distilled water. Aqueous ammonium solutions were buffered with potassium dihydrogen phosphate and di-potassium hydrogen phosphate. The stripping solution was prepared through addition of specified volumes of sulfuric acid to distilled water. The ammonia concentration in the solution was analyzed by Nesslerization [16]. The concentration of ammonia in the samples was measured using a UV–visible Scanning Spectrophotometer, CamspecM350 model [16]. 2.2. Experimental setup A schematic representation of HFMC used for the removal of dissolved ammonia is shown in Fig. 1. The ammonia aqueous solution was passed through the lumen side whereas the stripping solution containing sulfuric acid was pumped into the shell side of the HFMC. Since the gas–liquid interface is established on the pore mouth adjacent to the shell side, passing feed solution through lumen side is more favorable because it generates higher contact area between two phases. Both solutions were recycled to their own reservoirs. Since the reaction between ammonium and sulfuric acid is exothermic, a cooling water system was used to maintain the temperature constant at 20 °C and prevent increasing the feed temperature. The characteristics of the HFMC and experimental conditions are presented in Tables 1 and 2. To calculate Reynolds number, velocity of the feed solution in the lumen side is required. The velocity of the liquid feed solution can be obtained from Eq. (1): V lumen ¼

Q nπðr in Þ2

ð1Þ

where rin, Q, and n, are inner radius of hollow fiber, volumetric flow rate, and number of fibers, respectively. Reynolds number for the feed phase is calculated through Eq. (2): Refeed ¼

2  Vlumen  r in νw

ð2Þ

where νw is kinematic viscosity of the feed phase. It is notable that the kinematic viscosity of ammonia-containing feed solution was assumed equal to that of pure water.

2. Experimental 2.3. Analytical procedure 2.1. Reagents All chemicals used were analytical grade reagents from Merck. All aqueous solutions were prepared using distilled water. Solutions

At regular time intervals, 1 mL samples were taken from the feed solution and were immediately diluted to a certain volume. The concentration of ammonia was then determined by Nesslerization tests

Fig. 1. Experimental setup used for ammonia stripping.

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Substitution of Eqs. (4) and (6) into Eq. (7) yields:

Table 1 Characteristics of Liqui-Cel HFMC and operating conditions of experiments. Parameter

Symbol

Value

Unit

Fiber inner radius Fiber outer radius Fiber porosity Fiber tortuosity Fiber length Number of fibers Pore diameter Shell side geometric void fraction Effective area Temperature

rin rout ε τ = 1/ε2 L N D – S T

110 150 40 6.25 25 6000 0.03 0.40 1.4 293

μm μm % – cm – μm – m2 K

α NH3 ¼

½OH −  Ka : ¼ ½OH−  þ K b K a þ ½Hþ 

ð9Þ

Eq. (9) indicates that the relative concentration of the two species depends on the pH of the solution. In the current modeling, concentration of ammonia ([NH3]) was calculated.

2.5. Mechanism of ammonia removal in HFMCs of the dilute solutions. Each reported experimental result is the arithmetic mean of at least two replicate experiments. The Taguchi method was used to design the experiments. More details on experiments have been mentioned elsewhere [1]. 2.4. Theory In the dissolved state, ammonia exists in two forms. One is toxic ammonia (NH3) and the other is less harmful ammonium ions (NH4+). The composition of these constituents depends on the pH and temperature of the solution from the following dissociation equilibrium: Kb

þ

−

NH 3 þ H 2 O → NH4 þ OH : ←

ð3Þ

Ka

Equilibrium constants can be defined from the following equations: Ka ¼


 ½NH3  H þ
þ NH 4

ð4Þ

Kb ¼


þ NH4 ½OH−  : ½NH 3 

ð5Þ

However, Ka and Kb values are equal to 5.6 × 10 − 10 and 1.8 × 10 − 8, respectively [17]. The total concentration of ammonia in the feed solution is the summation of equilibrium concentrations of ammonium ([NH4+]) and ammonia ([NH3]) in the feed solution: h i þ C total ¼ NH4 þ ½NH 3 

ð6Þ

Therefore, concentration of each species can be related to the total concentration. ½NH 3  C total

ð7Þ


þ NH4 ¼ C total

ð8Þ

α NH3 ¼

α

NH þ 4

Table 2 Experimental conditions for ammonia removal. Run

Ammonia feed initial concentration (ppm)

Ammonia feed velocity (m/s)

Ammonia feed (pH)

Stripping velocity (m/s)

Reynolds number of feed (Refeed)

1 2 3 4

50 200 400 800

0.053 0.213 0.106 0.160

8 10 11 9

0.02 0.20 0.05 0.10

11.66 46.86 23.32 35.20

Ammonia stripping by means of HFMCs is carried out in recycling mode. Recycling mode increases the removal of ammonia. In this process, an aqueous solution of ammonia as feed is passed inside the lumens of membrane contactor. The stripping solution, which due to the high reaction rate between ammonia and sulfuric acid can be mostly considered as a dilute sulfuric acid solution, is circulated in the shell side of the contactor. Some distinct researchers have preferred to circulate the feed solution in the lumen side [3–5]. It has been claimed that using this configuration, the formed interface between gas and liquid at the outer surface of fibers is higher than that at the inner surface. Therefore, passage of the feed solution from the lumen side is presumed to provide higher interfacial mass transfer area. In spite of this explanation, the experimental data used in the current study have been collected from a configuration in which the feed solution is passed through inside the lumens. At the same time, another research is being conducted by the current authors to examine the previously mentioned flow configuration and compare the results with the current data. By contacting two phases in the membrane contactor, ammonia is transferred by convection and diffusion mechanisms from the bulk of the feed towards the feed-membrane interface. At the fiber wall (inner radius of hollow fiber), ammonia is volatilized into the membrane pores which are filled by gas. Ammonia then diffuses across the gas-filled pores of the HFMC, and is transferred into the stripping solution. At the shell-membrane interface, ammonia immediately reacts with stripping solution and forms a nonvolatile compound. Therefore, the ammonia concentration in the stripping solution is assumed to be maintained at zero. On the other hand, water cannot diffuse through the hydrophobic fibers of HFMC. The principle of ammonia removal through HFMC is schematically shown in Fig. 2.

3. Mass transfer model A considerable amount of literature has been published on modeling of different membrane processes [18]. In this study, a comprehensive 2D mathematical model was proposed to describe the transport of ammonia through HFMC. The model was based on the “non-wetted” mode in which the gas fills the membrane pores. The stripping solution flows in the shell side, whereas the aqueous feed solution is fed to the lumen side of the HFMC. Velocity distribution in the lumen side is determined through Navier–Stokes equations. The ammonia concentration is determined using continuity equation. Axial and radial diffusions inside the lumen side and through the membrane of HFMC are considered in the model equations. Chemical reaction between ammonia and sulfuric acid, which occurs in the shell side, is assumed to be instantaneous. Recycling mode is considered in the simulation; which implies that two sets of equations must be solved to simulate the whole process. The first set of equations is obtained through a mass balance over the feed tank, and the second set of equations is for the contactor.

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Fig. 2. Mechanism of ammonia removal in HFMCs.

3.1. Equations of the model

3.2. Equations of lumen side

The ammonia flows with a laminar velocity inside the lumens. As it is indicated in Table 2, flow regime is laminar and far from turbulent flow. The ammonia aqueous solution is fed to the lumen side (at z = 0), while the stripping solution is passed through the shell side. Ammonia is removed from the aqueous solution by subsequent diffusion through the bulk of liquid and membrane, and becomes absorbed into the liquid stripper. The model is built considering the following assumptions:

The unsteady state continuity equation for ammonia in the lumen side of the HFMC in cylindrical coordinate is obtained using Fick's law of diffusion. From this equation the diffusive flux is estimated:

• Unsteady state and isothermal conditions. • Laminar flow for both streams in the HFMC. • Henry's law is applicable for feed-membrane interface (Thermodynamic equilibrium). • No pore blockage occurs. • Non-wetted mode for the membrane is assumed; in which the feed aqueous solution do not fills the membrane pores (since the HFMC is hydrophobic; it prevents passage of feed aqueous solution through the pores). • There is no reaction zone (the reaction of ammonia with the sulfuric acid is fast (instantaneous) and always occurs in excess). • Flow rates of both ammonia solution and sulfuric acid are constant. • Feed tank operates at the perfect mixing mode. 3.1.1. Mass balance over ammonia tank The first equation is obtained for the ammonia tank using a mass balance. The mass balance equation over ammonia tank considering uniform mixing can be written as follows:

V

 dC tank ¼ QC Z¼L −Q C tank dt

@ t ¼ 0;

C tank ¼ C 0

∂C NH3 −lumen ∂t

¼ V z−lumen

∂C NH3 −lumen ∂z

2

∂ C NH3 −lumen ∂r 2

þ

# 2 1 ∂C NH3 −lumen ∂ C NH3 −lumen ð12Þ þ r ∂r ∂z2

:

Velocity distribution in the lumen side is determined by solving the momentum equation, i.e. Navier–Stokes equations. Therefore, the momentum and the continuity equations should be coupled and solved simultaneously to obtain concentration distribution of ammonia in the lumen side. The Navier–Stokes equations describe flow in viscous fluids through momentum balances for each of the components. The latter also assume that density and viscosity of the fluids are constant, which yields to a continuity condition. The Navier–Stokes equations are defined as follows [19]:   −∇⋅η ∇V z−lumen þ ð∇V z−lumen ÞT þ ρðV z−lumen :∇ÞV z−lumen þ∇p ¼ F∇:V z−lumen ¼ 0

C NH3 −lumen ¼ C tank

V z−lumen ¼ V 0

ðInlet boundaryÞ: ð14Þ

ð11Þ

where Q is volumetric flow rate, m 3/s, V is volume of feed, m 3, t is time, s, and C is ammonia concentration, mol/m 3. C|Z = L is concentration of ammonia at the outlet of contactor which is inlet of the feed tank. The characteristic of inlet flow varies with time; therefore unsteady state equation of continuity for ammonia in the contactor should be solved to obtain this parameter. Important parameters and model domain are illustrated in Fig. 3. 3.1.2. Mass transfer equations for HFMC The second sets of equations are for the membrane contactor. Membrane contactor is divided in two subdomains, i.e. lumen side and membrane.

ð13Þ

where η ,V, and ρ denote fluid dynamic viscosity (kg/m.s), velocity vector (m/s), and density (kg/m 3), respectively; p is pressure (Pa) and F is a body force term (N). Boundary conditions for the lumen side are given as: @ z ¼ 0;

ð10Þ

" þ DNH3 −lumen

Fig. 3. Model domain for numerical simulation.

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V0 is calculated from the flow rate: V0 ¼

Q nπr2in

where rin, Q, and n are inner radius of hollow fiber, volumetric flow rate, and number of fibers. @ z ¼ L; Convective flux; p ¼ patm ðOutlet boundaryÞ

ð15Þ

The boundary condition for the convective flux assumes that the mass passing through this boundary is convection-dominated. In other words, it assumes that the mass flux due to diffusion across this boundary is zero. @ r ¼ 0; @ r ¼ r in ;

∂C NH3 −lumen

¼ 0 Axial symmetry ∂r C NH3 −lumen ¼ pNH3 −membrane =H No slip condition

ð16Þ

where rin, H, and pNH3 − membrane are inner radius of hollow fiber, Henry's law constant, and partial pressure of ammonia in the gas phase of membrane pores in equilibrium with the concentration of this compound in the aqueous solution (CNH3 − lumen). Ammonia at the liquid–membrane interfaces is in thermodynamic equilibrium with its vapor. Hence, Henry's law is applied and the partial pressures of the ammonia were estimated from the correlation for Henry's constant. The Henry's constant can be defined as follows [3]: ln H ¼ −

4200 þ 3:133 T

387

element method (FEM) for numerical solution of the equations. The finite element analysis is combined with adaptive meshing and error control using numerical solver of UMFPACK version 4.2. This solver is well suited for solving stiff and non-stiff non-linear boundary value problems. The applicability, robustness and accuracy of this method for the membrane contactors have been proved through distinct researches [11,20–23]. It should be pointed out that the COMSOL mesh generator creates triangular meshes that are isotropic in size. A large number of elements are then created with scaling. A scaling factor was employed for the contactor in the z direction due to a large difference between r and z. COMSOL automatically scales back the geometry after meshing. This generates an anisotropic mesh around 3150 elements. Adaptive mesh refinement in COMSOL, which generates the best and minimal meshes, was used to mesh the HFMC geometry. Since the ammonia concentration in the feed tank varies with time, COMSOL is linked to MATLAB to solve both equations of the feed tank and contactor. The algorithm which was developed for the numerical simulation is shown in Fig. 4. By this method, variations of both concentration and velocity can be evaluated within the contactor; on the contrary of previous models which fail to investigate variations inside the contactor. An IBM-PC-Pentium 4 (CPU speed is 2800 MHz) was used to solve the sets of equations.

Start

ð17Þ

where H is Henry's constant in atm.m 3 mol − 1, and T is in Kelvin.

Input constant

3.3. Equations of membrane Set t=0

The unsteady-state continuity equation for the transport of ammonia inside the membrane, which is considered to be due to diffusion alone, may be written as:

COMSOL

MATLAB

∂C NH3 −membrane ∂t þ DNH3 −membrane

" 2 ∂ C NH3 −membrane ∂r

2

þ

# 2 1 ∂C NH3 −membrane ∂ C NH3 −membrane þ ¼ 0: 2 r ∂r ∂z

ð18Þ Boundary conditions for the membrane are given as:

Add subdomain equations

t = t + Δt

Define geometry

Solve mass balance equation over

ammonia tank

@ r ¼ r in ; pNH3 −membrane ¼ C NH3 −lumen  H ðHenry lawÞ

ð19Þ

@ r ¼ r out ; C NH3 −lumen ¼ 0 C NH3 −lumen ¼ 0:

ð20Þ

NO Set subdomain conditions

Set boundary conditions

@ z ¼ 0 & L; Insulation

Solve coupled equations

3.4. Numerical solution of the model equations The main objective of the present study is to model HFMC with recycling mode using CFD of mass and momentum transfers. The equations of contactor related to the lumen side and the membrane with appropriate boundary conditions were solved using COMSOL Multiphysics version 3.2 software (Sweden), which uses finite

Initialize mesh

Adapt mesh

t<=t1 YES

The reaction rate between ammonia and acid sulfuric is assumed to be instantaneous; therefore the ammonia concentration in the shell side of the membrane contactor was not determined and assumed to be zero. It is also assumed that there is no mass transfer at both edges of the fibers, i.e.:

Result

Integrate from outlet concentration

End

Fig. 4. Algorithm developed for numerical simulation.

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4. Results and discussions

Table 3 Comparison between experimental and calculated mass transfer coefficients.

4.1. Model validation The main objective of the present study is to simulate ammonia removal in a HFMC considering recycling mode using CFD techniques. By recycling mode ammonia can be almost completely removed. Variation of ammonia concentration in the feed tank is a vital parameter which should be accurately calculated. The experimental results along with the predictions of the model for the concentrations of ammonia in the feed tank versus time are presented in Fig. 5. As it can be seen from Fig. 5, the concentration of ammonia is exponentially decreased with time, i.e. ammonia concentration sharply drops at the initial durations while slightly decreases at advanced time intervals. This observation could be attributed to the fact that at the beginning of the operation, the driving force of ammonia transfer between lumen and shell sides of the contactor is high due to a relatively high concentration gradient across the membrane. Apparently, as ammonia is transferred to the shell side, its concentration in the feed decreases and that would result in a lower driving force. The predictions of the model presented in Fig. 5 also confirm the validity of the simulation against experimental data. As it is shown, there is a good agreement among the simulated and experimental results. It is notable that the model overestimates the mass transfer flux. The reason is that the fiber length used in numerical calculations is the nominal length which is reported by the manufacturer. However, the effective length of fibers is smaller than the nominal one. Therefore, the predicted mass transfer area and consequently the predicted mass transfer flux are slightly higher than the experimental values. To further validate the mass transfer model developed here, mass transfer coefficients calculated using simulations were compared with the experimental ones. The mass transfer coefficient is of vital importance for design and optimization of ammonia removal process. The overall mass transfer coefficient for ammonia transport was determined as follows: K¼

V C0 ln At C t

Run

Reynolds number of feed (Refeed)

KExp.(× 105) (m/s)

KCal. .(× 105) (m/s)

1 2 3 4

11.66 46.86 23.32 35.20

0.12 1.32 1.31 0.69

0.13 1.39 1.42 0.72

membrane length was considered in the simulation whereas the actual length of membrane is lower than simulated length. 4.2. Validation of the model using Knudsen diffusion On the basis of the membrane pore diameter and the mean free path of NH3 molecules, it is possible to consider NH3 diffusion across the membrane pores as mainly controlled by a combined bulkKnudsen diffusion mechanism. Knudsen mode of ammonia transport through the membrane is important when the mean free path of the ammonia molecules is much greater than the pore size of the membrane, i.e. (rp/λ ≤ 0.05) [24]. In such situations, the collisions of the molecules with the pore walls are more frequent than the collisions among molecules. This mechanism which is often predominant in macroporous and mesoporous membranes [25] is described by Knudsen equation for the diffusive flow of molecules in a capillary tube: J k ¼ −Dk

ð22Þ

where Dk is the Knudsen diffusion coefficient. This coefficient is dependent on the mean molecular speed, u, and pore radius, rp, and is given by: Dk ¼

ð21Þ

where K, V, A, C0 and C are the overall mass transfer coefficient, total volume of feed solution, membrane surface area, concentration of ammonia at initial and time t in the bulk feed solution, respectively. Table 3 shows these comparisons. As can be seen, modeling predictions are in good agreement with the experimental ones. It is notable that the calculated mass transfer coefficients are higher than the experimental ones. This could be attributed to this fact that whole

  dC dz

2 ur : 3 p

ð23Þ

An expression for the mean molecular speed can be obtained from the kinetic theory of gases [26]: u¼

rffiffiffiffiffiffiffiffiffi 8RT πM

ð24Þ

where M is the molecular weight of permeant (kg/mol). Both of the diffusion coefficients were corrected for the effect of membrane porosity, ε = 0.4 (Table 1), and tortuosity, τ, using the following relations: Dk;ef f ¼

εDNH3 εDk and DNH3 ;ef f ¼ : τ τ

ð25Þ

The effective diffusion coefficient can be obtained using the Bonsaquet equation [27]: 1 1 1 ¼ þ : Deff Dk;ef f DNH3 ;ef f

Fig. 5. Experimental and simulated concentrations of ammonia in the feed tank vs. time.

ð26Þ

Therefore, in the current simulation, diffusion through the membrane pores is considered to be governed by the combined bulkKnudsen mechanism. Comparison among experimental and simulated results considering Knudsen diffusion is presented in Fig. 6. As it is seen, considering Knudsen diffusion slightly increases the accuracy of the model predictions. This implies that although the Knudsen diffusion is not predominant, but has a partial contribution in the overall diffusion across the membrane pores. Furthermore, Fig. 6 confirms

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Fig. 6. Concentration of ammonia in the feed tank vs. time: comparison among experimental results with simulated values considering Knudsen diffusion.

the superiority of the developed model for predicting unsteady state concentration of ammonia. Therefore, the rest of the reported simulations were investigated with considering Knudsen diffusion.

4.3. Unsteady state concentration distribution of ammonia in the contactor The simulation was carried out for run 1 of experiments. Fig. 7 illustrates the concentration distribution of ammonia in the lumen side of the membrane contactor for different time intervals. The aqueous feed enters from one side of the contactor (z = 0), whereas the stripper solution enters from the opposite side. As the aqueous feed passes through the lumen side, due to the concentration gradient, ammonia diffuses from the bulk of the feed towards the membrane surface. At the surface of the membrane, only ammonia evaporates into the membrane pores and reaches the shell side. At the shell side of the membrane surface, an instantaneous chemical reaction occurs between ammonia and acid sulfuric. Fig. 7 also illustrates the variations of ammonia concentration during the stripping process. As it is seen, at the beginning of the process, the driving force is higher and thus causes a higher mass transfer rate of ammonia towards the shell side. This also confirms the trend which was observed in at initial periods (Fig. 5). At the end of the process,

Fig. 8. Dimensionless concentration distribution of ammonia (C/Ctank) in the contactor (t = 1 min).

Fig. 7. Unsteady state concentration distribution of ammonia in the contactor.

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concentration gradient is vanished, which in turn causes a very low rate of transfer for ammonia. To investigate the concentration distributions of ammonia in the lumen side of the membrane contactor in more details, Fig. 8 is drawn which represents local concentrations. This figure shows dimensionless concentration of ammonia at the mesh points used for numerical simulation. This figure represents the concentrations 1 min after the beginning of the contact. From Fig. 7, it can be seen that concentration variations in the contactor are significant after 1 min. Therefore, this moment was chosen to further investigate the contactor performance parameters. As it is seen, the meshes are more compact in the regions that concentration gradient is large. Fig. 8 indicates that in the regions near the membrane surface at the inlet of the lumen side, meshes are very small. In this region, the largest mass transfer flux of ammonia exists. As the feed flows along the lumen side, concentration gradient decreases, i.e. more uniform distribution and larger meshes. 4.4. Radial concentration distribution of ammonia in the contactor Variations of the radial concentration of ammonia in the lumen side of the membrane contactor were also investigated. In order to obtain the radial concentration profile in the lumen side, a moment at which the ammonia removal is significant, was identified. The contact time of 1 min was chosen (see Fig. 6). A plot of the radial concentration profile at t = 1 min and different axial positions along the lumen side of the membrane contactor is shown in Fig. 9. As it is seen, in the region near the axis of the fiber (r = 0), the bulk concentration of ammonia only slightly changes. Apparently, the maximum concentration of ammonia is located in the center of the lumen due to axial symmetry. Concentration of ammonia reduces gradually in the region between the center and wall of the lumen side. Eventually, in the region adjacent the membrane surface, concentration sharply decreases. This observation could be attributed to the formation of the concentration boundary layer near the fiber wall. Furthermore, the ammonia concentration is slightly distributed at Z/L = 1, i.e. at the lumen exit. On the other hand, at the axial positions near the lumen entrance, i.e. Z/L = 0.25, concentration changes is more significant. 4.5. Velocity field in the contactor The velocity field in the lumen side of membrane contactor was simulated by solving the Navier–Stokes equations. Fig. 10 shows the velocity field in the lumen side, within which the aqueous feed flows. The velocity profile is a parabolic with a mean velocity

Fig. 10. Velocity field in the lumen side of membrane contactor.

Fig. 9. Radial concentration distribution of ammonia in the contactor at different axial positions and t = 1 min.

increasing along the membrane length. The contours of velocity are also shown in Fig. 11. At the regions near the membrane surface, velocity reduces because of no-slip condition at the fiber walls. The effect of viscous forces can be found in this region which causes the formation of concentration and velocity boundary layers near the membrane surface. Furthermore, Fig. 11 reveals that the velocity varies in the axial direction. It implies that at the regions close to the lumen entrance, velocity is not fully developed. This is one of the advantages of the developed model that considers the entrance effects which in turn can increase the accuracy of the developed model. In the middle of the lumen side, the flow tends to be fully developed.

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4.6. Effect of feed velocity on the concentration distribution of ammonia in the contactor Effect of feed velocity on the concentration distribution of ammonia in the contactor is shown in Fig. 12. All provided images are at t = 1 min for different feed velocities. The values of feed velocities are in accordance with the experimental data (see Table 2). Obviously, feed velocity changes the concentration distribution of ammonia in the lumen side of membrane contactor. Increasing feed velocity results in a more uniform concentration distribution in both r and z directions. For instance, for the case of Vf = 0.213 m/s, concentration of ammonia does not reduce significantly along the contactor, i.e. an almost uniform distribution is formed except for the regions near the membrane surface. Increasing feed velocity is not favorable for the stripping of ammonia; increasing feed velocity reduces the feed residence time in the contactor which in turn results in a lower mass transfer rate of ammonia. 5. Conclusions An unsteady-state, 2D mathematical model was developed to study the removal of ammonia from aqueous solutions by means of a hollow-fiber membrane contactor (HFMC). The model predicts the unsteady state concentration of ammonia in the membrane contactor as well as the feed tank by solving the conservation equations including continuity and momentum. The model was developed considering a hydrophobic membrane which is not wetted by the aqueous feed solution. Both axial and radial diffusions within the lumen and membrane of the contactor were considered. Two sets of equations were solved simultaneously. The predictions of the mass transfer model were validated by comparing the results of ammonia stripping with the experimental data. The simulation results well predict the unsteady state concentration of ammonia in the feed tank. Furthermore, it was assumed that Knudsen diffusion is responsible for the ammonia transfer across the membrane pores. The assumption of combined bulk-Knudsen diffusion increased the accuracy of the model.

Fig. 11. Contour of velocity in the lumen side of membrane contactor.

Nomenclature A cross section of tube, m 2 C concentration, mol/m 3 Coutlet outlet concentration of solute in the tube side, mol/m 3 Cintlet inlet concentration of solute in the tube side, mol/m 3 Ci-tube concentration of solute in the tube side, mol/m 3

Fig. 12. Effect of feed velocity on the concentration distribution of ammonia in the contactor (t = 1 min).

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Ci-shell concentration of solute in the shell side, mol/m 3 Ci-membrane concentration of solute in the membrane, mol/m 3 D diffusion coefficient, m 2/s Di-shell diffusion coefficient of solute in the shell, m 2/s Di-tube diffusion coefficient of solute in the tube, m 2/s Di-membrane diffusion coefficient of solute in the membrane, m 2/s H Henry's law constant, mol/m 3 kPa Ji diffusive flux of species i, mol/m 2s K overall mass transfer coefficient, m/s L length of the fiber, m M molecular weight (kg/mol) N number of fibers P pressure, Pa R radial coordinate, m rin inner radius of fibers, m rout outer radius of fibers, m t time, s T temperature, K U average velocity, m/s V velocity in the module, m/s Vz-tube z-velocity in the tube, m/s Z axial coordinate, m

Greek symbols ε membrane porosity η dynamic viscosity (kg/m.s) ρ density (kg/m 3) νw kinematic viscosity of the feed phase (m 2/s)

Abbreviations FEM finite element method HFMC hollow-fiber membrane contactor 2D two dimensional ODE ordinary differential equation PVDF polyvinylidene fluoride CFD computational fluid dynamics

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