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Mathematical modeling and numerical simulation of ammonia removal from wastewaters using membrane contactors
G Model
JIEC-1690; No. of Pages 6 Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx
Contents lists available at ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Mathematical modeling and numerical simulation of ammonia removal from wastewaters using membrane contactors Ferial Nosratinia a,*, Mehdi Ghadiri b, Hazhir Ghahremani a a b
Department of Chemical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran RahNegar Shimi Engineers Corporation, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 22 July 2013 Accepted 30 October 2013 Available online xxx
This study investigates simulation of ammonia transport through membrane contactors. The system studied involves feed solution of NH3, a dilute solution of sulfuric acid as solvent and a membrane contactor. The model considers coupling between equations of motion and convection-diffusion. Finite element method was applied for numerical calculations. The effect of different parameters on the removal of ammonia was investigated. The simulation results revealed that increasing feed velocity decreases ammonia removal in the contactor. The modeling findings also showed that the developed model is capable to evaluate the effective parameters which involve in the ammonia removal by means of contactors. ß 2013 Published by Elsevier B.V. on behalf of The Korean Society of Industrial and Engineering Chemistry.
Keywords: Ammonia stripping Wastewater Membrane contactor Numerical simulation Mass transfer Computational fluid dynamics
1. Introduction Nowadays, wastewater treatment is of vital importance for providing drinking water and protecting environment. Finding and developing new methods and processes for wastewater treatment has been a subject of great interest. Researchers are trying to find new solutions to remove all contaminants from water and wastewaters. Among the water contaminants, ammonia (NH3) is a major contaminant which can cause adverse effects. Ammonia can be found in either municipal or industrial wastewaters. Dissolved ammonia in solutions is generated from industrial wastewaters such as coking, chemical fertilizer, coal gasification, petroleum refining, pharmaceutical and catalyst factories [1–7]. From environmental perspective, a complete removal of ammonia from wastewaters is desirable. The concentration of ammonia in industrial wastewaters varies from 5 to 1000 mg/L [8]. The removal of dissolved ammonia from wastewaters is thus mandatory to protect the environment and human health. Currently, conventional separation processes are applied to remove ammonia from water and wastewaters including selective ion exchange, air stripping, break-point chlorination, denitrification, and biological nitrification [1,9–11]. Recently, hollow-fiber membrane contactors (HFMCs) have attracted large attentions as an effective device for separation processes. A major part of the
* Corresponding author. Tel.: +98 21 33717131; fax: +98 21 33717140. E-mail address: [email protected] (F. Nosratinia).
interest toward HFMCs is due to their capability in providing a dispersion free contact between two phases. In addition, the velocities of both phases can vary independently, while neither flooding nor unloading problems may happen [12]. Membrane contactors can be considered as a promising technology for separation of ammonia from wastewaters. The mechanism of separation in membrane contactors is based on the mass transfer between the two phases. For removal of ammonia in membrane contactors, ammonia containing solution flows in the tube or shell side of the membrane contactor. The ammonia evaporates from the aqueous solution, diffuses through the membrane pores, and reacts with the stripping solution (solvent). This process could be carried out in one-through or recycling mode. Recycling mode provides high separation factor, but is difficult to simulate. One-through mode is easy to design and model. New modeling approach for ammonia removal in membrane contactors is based on solving conservation equations for ammonia in the aqueous feed and membrane phases. In this method, conservation equations including equations of motion and mass are derived and solved simultaneously by appropriate numerical methods. The computational fluid dynamics (CFD) are usually carried out to solve the governing equations. The main objective of the present study is to develop and solve a mathematical model for the simulation of ammonia removal in a membrane contactor. The type of membrane contactor is assumed to be hollow-fiber. The equations of the model are solved by numerical method based on finite element method (FEM). An
1226-086X/$ – see front matter ß 2013 Published by Elsevier B.V. on behalf of The Korean Society of Industrial and Engineering Chemistry. http://dx.doi.org/10.1016/j.jiec.2013.10.065
Please cite this article in press as: F. Nosratinia, et al., J. Ind. Eng. Chem. (2013), http://dx.doi.org/10.1016/j.jiec.2013.10.065
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ammonium ([NH4+]) and ammonia ([NH3]):
Nomenclature concentration (mol/m3) outlet concentration of ammonia in the tube side (mol/m3) inlet concentration of ammonia in the tube side Cinlet (mol/m3) Ci-tube concentration of solute in the tube side (mol/m3) Ci-membrane concentration of solute in the membrane (mol/ m 3) diffusion coefficient (m2/s) D diffusion coefficient of solute in the tube (m2/s) Di-tube Di-membrane diffusion coefficient of solute in the membrane (m2/s) Henry’s law constant (mol/(m3 kPa)) H diffusive flux of species i (mol/(m2 s)) Ji length of the fiber (m) L molecular weight (kg/mol) M number of fibers n pressure (Pa) p radial coordinate (m) r inner radius of fibers (m) rin outer radius of fibers (m) rout time (s) t temperature (K) T average velocity (m/s) u velocity in the module (m/s) V z-velocity in the tube (m/s) Vz-tube axial coordinate (m) z
C Coutlet
Greek symbols e membrane porosity h dynamic viscosity (kg/(m s)) r density (kg/m3) Abbreviations FEM finite element method hollow-fiber membrane contactor HFMC 2D two-dimensional computational fluid dynamics CFD
2. Theory of ammonia removal When ammonia is dissolved in aqueous solutions, it exists in two forms. One form is ammonia (NH3) and the other form is ammonium ions (NH4+). The composition of these species depends on the pH and temperature of the solution. The compositions can be calculated from the following reaction: Kb
Ka
(2)
2.1. Mechanism of ammonia transport through membrane contactors In ammonia removal process, an aqueous solution of ammonia as feed is flown inside the tube side. The stripping solution is passed in the shell side of the membrane contactor either in cocurrent or counter-current mode. The most effective stripping solution is sulfuric acid solution because reaction rate between ammonia and sulfuric acid is high. By contacting feed and stripping phases in the membrane contactor, ammonia is transferred from the bulk toward the feed–membrane interface due to concentration gradient. At the feed–membrane interface, ammonia is volatilized into the membrane pores which are filled by gas. The membrane is microporous and provides the contact between two phases. Ammonia then diffuses across the gas-filled pores of the membrane, and is transferred into the stripping solution. At the shell–membrane interface, ammonia immediately reacts with the stripping solution. Therefore, the ammonia concentration in the stripping solution is assumed to be zero. On the other hand, water cannot diffuse through the membrane pores due to hydrophobic nature of the fibers. The principle of ammonia removal through membrane contactors is schematically shown in Fig. 1. 3. Mass transfer model A mathematical model was proposed to describe the transport of ammonia through membrane contactors. The model was based on the ‘‘non-wetted’’ mode. In this mode, it is assumed that the gas phase fills the membrane pores. The aqueous feed solution containing ammonia is fed to the tube side of the membrane contactor and the stripping solution flows in the shell side. Velocity distribution in the tube side is determined using Navier–Stokes equations. The ammonia concentration is determined using continuity equation. Axial and radial diffusions inside the tube side are considered in the mass transfer equations. Furthermore, chemical reaction between ammonia and sulfuric acid, which occurs in the shell side, is assumed to be instantaneous. Fig. 2 shows model domain for numerical simulation. 3.1. Equations of the model
algorithm is developed for the numerical simulation. Mass transfer and Navier–Stokes equations are solved simultaneously for the ammonia in the membrane contactor to obtain the concentration distribution.
NH3 þ H2 O A NH4 þ þ OH
C total ¼ ½NH4 þ þ ½NH3
(1)
where Ka and Kb values are equal to 5.6 1010 and 1.8 108, respectively [13]. The total concentration of ammonia in the solution is the summation of equilibrium concentrations of
The feed solution containing dissolved ammonia (NH3) flows with a laminar velocity inside the hollow fibers. Since the diameters of hollow fibers are very low, flow regime is assumed to be laminar in the calculations. The feed solution is flown to the tube side (at z = 0), while the stripping solution is passed through the shell side. Ammonia is removed from the feed phase by subsequent diffusion through the bulk of liquid and membrane, and becomes absorbed into the solvent. The model is built considering the following assumptions: Steady state and isothermal conditions. Laminar flow in the membrane contactor. Henry’s law is applied for feed–membrane interface. Non-wetted mode for the membrane is assumed; in which the feed aqueous solution do not fills the membrane pores. There is no reaction zone (the reaction of ammonia with the sulfuric acid is fast (instantaneous) and always occurs in excess). Velocity of both ammonia solution and sulfuric acid are constant.
The last assumption is justified by low mass transfer flux of ammonia from feed phase to solvent phase.
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Fig. 1. Mechanism of ammonia transport through membrane contactors.
3.1.1. Mass transfer equations for ammonia As it was stated earlier, membrane contactor is divided in two subdomains, i.e. tube side and membrane. The model equations are developed for these two subdomains or compartments. 3.1.1.1. Equations of tube side. The steady state continuity equation for ammonia transport in the tube side of the membrane contactor in cylindrical coordinate is obtained using Fick’s law of diffusion. Diffusive flux is estimated from Fick’s law. The continuity equation may be written as:
@C NH3 -lumen @t
solving the momentum equation. The most appropriate momentum equation here is Navier–Stokes equations. Therefore, the momentum and the continuity equations should be coupled and solved simultaneously to calculate concentration distribution of ammonia in the feed side. The Navier–Stokes equations describe flow in viscous fluids through momentum balances for each component. 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 [14]: r hðrV z-lumen þ ðrV z-lumen ÞT Þ þ rðV z-lumen rÞV z-lumen þ rp
"
þ DNH3 -lumen
@2 C NH3 -lumen 1 @C NH3 -lumen @2 C NH3 -lumen þ þ r @r @r 2 @z2
#
¼F
@C NH3 -lumen ¼ V z-lumen @z (3) The term Vz-lumen is z-velocity in the tube side of the membrane contactor. To solve Eq. (3), an equation for velocity distribution is required. Velocity distribution in the feed phase is calculated by
r V z-lumen ¼ 0
(4)
where h, V, and r denote fluid dynamic viscosity (kg/(m s)), velocity vector (m/s), and density (kg/m3), respectively; p is the pressure (Pa) and F is a body force term (N). Boundary conditions for the tube side may be written as: @z ¼ 0;
C NH3 -lumen
V z-tube ¼ V 0
ðInlet boundaryÞ
(5)
V0 is calculated from the flow rate: V0 ¼
Q 2 nprin
(6)
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
(7)
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 ;
Fig. 2. Model domain for numerical simulation.
@C NH3 -lumen ¼ 0 Axial symmetry @r C NH3 -lumen ¼
pNH3 -membrane ; H
No slip condition
(8)
(9)
where rin, H, and pNH3 -membrane are inner radius of fiber, Henry’s law constant, and partial pressure of ammonia in the gas phase of membrane pores in equilibrium with the concentration of in the aqueous solution, i.e. C NH3 -lumen . It is assumed that ammonia at the feed–membrane interface is in thermodynamic equilibrium with its vapor. 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
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be formulated as follows [1]: Sta
ln H ¼
4200 þ 3:133 T
(10)
Input constants 3
1
where H is Henry’s constant in atm m mol
, and T is in Kelvin.
Add subdomain equations
3.1.1.2. Equations of membrane. The continuity equation for the transport of ammonia inside the membrane pores, which is considered to be due to diffusion, may be written as:
@C NH3 -membrane þ DNH3 -membrane @t " 2 # @ C NH3 -membrane 1 @C NH3 -membrane @2 C NH3 -membrane þ þ r @r @r2 @z2
Define geometry
Initialize mesh
(11)
¼0
Adapt mesh
Boundary conditions for the membrane are given as: @r ¼ r in ;
pNH3 -membrane ¼ C NH3 -lumen H;
ðHenry lawÞ
Set subdomain conditions
(12)
Set boundary conditions @r ¼ r out ; ¼0
C NH3 -lumen
ðInstantaneous chemical reactionÞ
(13)
Solve coupled equations
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.:
Integrate from outlet concentration
En
@z ¼ 0&L;
Insulation
Fig. 3. Algorithm developed for numerical simulation [13].
3.2. Numerical solution of the equations
4. Results and discussion
The main objective of the present study is to simulate a membrane contactor using CFD techniques based on finite element method (FEM). The equations of ammonia transport in the contactor with the boundary conditions were solved using COMSOL Multiphysics. The latter utilizes finite element method for numerical solution of the partial differential equations. The finite element method is combined with adaptive meshing and error control using numerical solver of UMFPACK. The applicability, robustness and accuracy of this numerical method for the membrane contactors have been proved by some researches [12,15–25]. It should be pointed out that the COMSOL creates triangular meshes that are isotropic in size. A large number of elements are then created. A scaling factor was employed for the membrane contactor in the z direction due to a large difference between r and z. Adaptive mesh refinement in COMSOL, which generates the best and minimal meshes, was applied to mesh the whole geometry of membrane contactor. Further information regarding finite element method can be obtained from literature [26]. The algorithm which was developed for the numerical simulation is shown in Fig. 3. An IBM-PC-Pentium 4 (CPU speed is 2800 MHz) was used to solve the sets of equations. Parameters used for numerical simulations are listed in Table 1.
4.1. Concentration distribution of ammonia in the feed side Solving the continuity equations along with equations of motion results in determining concentration distribution in the membrane contactor. Fig. 4 illustrates the concentration distribution of ammonia in the tube side of the membrane contactor. The aqueous feed solution enters from one side of the contactor (z = 0). The stripper solution enters from the shell side counter-currently. As the aqueous feed passes through the tube side, due to the concentration gradient, ammonia is transferred from the bulk of the feed toward the feed–membrane surface. At the surface of the membrane, only ammonia evaporates into the Table 1 Parameters used in simulation. Parameter
Symbol
Value
Unit
Fiber inner radius Fiber outer radius Fiber porosity Fiber length Number of fibers Temperature Inlet ammonia concentration
rin rout
110 150 40 25 7000 293 10
mm mm
e L n T Co
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% cm – K mol/m3
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Fig. 5. Radial concentration profile of ammonia in the feed at different axial positions.
As it is seen, at the inlet of tube side, ammonia concentration is the highest (C/C0 = 1). As the feed solution flows in the tube side, concentration decreases significantly due to interphase mass transfer. Fig. 6 also reveals that at the region near the contactor entrance, concentration falls sharply [20–26]. This could be attributed to this fact that in this region, concentration gradient is high and causes significant decrease in the tube side concentration. 4.4. Concentration profile of ammonia inside the membrane
Fig. 4. Concentration distribution of ammonia in the contactor.
membrane pores and reaches the shell side. At the shell side of the membrane contactor, an instantaneous chemical reaction occurs between ammonia and acid sulfuric. Fig. 4 also shows that concentration gradient is the highest near the membrane, adjacent to the fiber wall [16].
Concentration profile of ammonia inside the membrane is shown in Fig. 7. The concentration profile inside the membrane is calculated from the equation of diffusion (Eq. (11)). This equation only considers diffusional mass transfer inside the membrane pores. Since the membrane is tortuous, an effective diffusivity is calculated using porosity and tortuosity of the membrane. Diffusion of species through membrane contactors depends on the porosity and tortuosity of the membrane. As it is seen, concentration profile inside the membrane is linear. This is due to Fick’s law of diffusion which is applied for this subdomain of
4.2. Radial concentration profile of ammonia Variations of the radial concentration of ammonia in the tube side of the membrane contactor were also investigated. A plot of the radial concentration profile at different axial positions along the tube side of the membrane contactor is shown in Fig. 5. It is clearly shown that in the region near the axis of the hollow fiber, i.e. r = 0 the bulk concentration of ammonia slightly changes. The maximum concentration of ammonia can be observed in the center of the hollow fiber due to axial symmetry assumption. Concentration of ammonia decreases gradually in the region between the center and wall of the fiber side. Eventually, in the region adjacent the membrane–feed interface, concentration sharply decreases. This observation could be attributed to the formation of the concentration boundary layer near the fiber wall. On the other hand, at the axial positions near the tube entrance, i.e. z = 0, concentration is constant [16–20]. 4.3. Axial concentration distribution of ammonia in the feed side Axial concentration profile of ammonia along the tube side of the hollow-fiber membrane contactor (HFMC) is shown in Fig. 6.
Fig. 6. Axial concentration distribution of ammonia in the tube side.
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5. Conclusions A mathematical model was developed to study the removal of ammonia from aqueous solutions by means of hollow-fiber membrane contactors (HFMCs). The model is based on mass transfer between two phases. The model predicts the steady state concentration of ammonia in the tube and membrane side of contactor by solving the conservation equations including continuity and momentum. The Navier–Stokes equations were solved to determine velocity distribution in the tube side. The model was developed considering a hydrophobic membrane which is not wetted by the aqueous feed solution. FEM analysis was applied for numerical solution of the equations. The simulation results revealed that increasing feed velocity decreases ammonia removal in the membrane contactor. Acknowledgement Research Council of Islamic Azad University-South Tehran Branch is highly acknowledged for the financial support of this project.
Fig. 7. Radial concentration profile of ammonia in the membrane.
Outlet concentration of ammonia (mol/m3)
9
References 8 [1] [2] [3] [4] [5]
7 6
[6]
5
[7] [8]
4 3 0.0
0.2
0.4 Feedvelocity(m/s)
0.6
0.8
Fig. 8. Effect of feed velocity on the outlet concentration of ammonia.
[9] [10] [11] [12] [13] [14] [15]
membrane contactor. Fig. 7 also reveals that the concentration of ammonia reaches zero at the membrane–shell side interface [16]. 4.5. Effect of feed velocity on the ammonia removal Influence of feed velocity on the mass transfer of ammonia in the membrane contactor is shown in Fig. 8. Feed velocity corresponds to the contribution of convective mass transfer in the tube side. Fig. 8 indicates that increasing feed velocity increases ammonia outlet concentration which in turn reduces ammonia removal. Increasing feed velocity causes the residence time of feed phase in the tube side to decrease [16]. Therefore, decreasing feed velocity or feed flow rate is favorable for ammonia removal in membrane contactors.
[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
A. Hasanoglu, J. Romero, B. Pe´rez, A. Plaza, Chem. Eng. J. 160 (2010) 530. T.C. Jorgensen, L.R. Weatherley, Water Res. 37 (2003) 1723. A. Mandowara, P.K. Bhattacharya, J. Environ. Manage. 92 (2011) 121. M.J. Semmens, D.M. Foster, E.L. Cussler, J. Membr. Sci. 51 (1990) 127. Z. Milan, E. Sa´nchez, P. Weiland, C. de Las Pozas, R. Borja, R. Mayari, N. Rovirosa, Chem. Eng. J. 66 (1997) 65. B. Norddahl, V.G. Horn, M. Larsson, J.H. du Preez, K. Christensen, Desalination 199 (2006) 172. X. Tan, S.P. Tan, W.K. Teo, K. Li, J. Membr. Sci. 271 (2006) 59. R. Sedlack, Phosphorus and Nitrogen Removal from Municipal Wastewater: Principles and Practice, 2nd ed., Lewis Publisher, New York, 1991. N. Miladinovic, L.R. Weatherley, Chem. Eng. J. 135 (2008) 15. J.-H. Bae, S.-K. Kim, H.-S. Chang, Water Sci. Technol. 36 (1997) 341. M. Sarioglu, Sep. Purif. Technol. 41 (2005) 1. S. Shirazian, A. Moghadassi, S. Moradi, Simul. Model. Pract. Theory 17 (2009) 708. M. Rezakazemi, S. Shirazian, S.N. Ashrafizadeh, Desalination 285 (2012) 383. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed., Wiley, New York, 1960. M.R. Sohrabi, A. Marjani, S. Moradi, M. Davallo, S. Shirazian, Appl. Math. Model. 35 (2011) 174. S. Shirazian, M. Rezakazemi, A. Marjani, S. Moradi, Desalination 286 (2012) 290. S.A. Miramini, S.M.R. Razavi, M. Ghadiri, S.Z. Mahdavia, S. Moradi, Chem. Eng. Process. Process Intensif. 72 (2013) 130. M. Ghadiri, M. Ghasemi Darehnaei, S. Sabbaghian, S. Shirazian, Chem. Eng. Technol. 36 (2013) 507. M. Ghadiri, S. Shirazian, Chem. Eng. Process: Process Intensif. 69 (2013) 57. M. Ghadiri, S. Shirazian, S.N. Ashrafizadeh, Chem. Eng. Technol. 35 (2012) 2177. M. Ghadiri, A. Marjani, S. Shirazian, Int. J. Greenhouse Gas Control 13 (2013) 1. M. Ghadiri, S. Fakhri, S. Shirazian, Ind. Eng. Chem. Res. 52 (2013) 3098. M. Ghadiri, S. Fakhri, S. Shirazian, Polym. Eng. Sci. (2013), http://dx.doi.org/ 10.1002/pen.23601. A. Daraei, P. Aghasafari, M. Ghadiri, A. Marjani, Trans. Indian Inst. Met. (2013), http://dx.doi.org/10.1007/s12666-013-0339-6. M. Ghadiri, M. Parvini, M. Ghasemi Darehnaei, Polym. Eng. Sci. (2013), http:// dx.doi.org/10.1002/pen.23771. G.R. Liu, S.S. Quek, The Finite Element Method: Fundamentals for Finite Element Method. A Practical Course, 2nd ed., Elsevier, Burlington MA, USA, 2014p. 43.
Please cite this article in press as: F. Nosratinia, et al., J. Ind. Eng. Chem. (2013), http://dx.doi.org/10.1016/j.jiec.2013.10.065
JIEC-1690; No. of Pages 6 Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx
Contents lists available at ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Mathematical modeling and numerical simulation of ammonia removal from wastewaters using membrane contactors Ferial Nosratinia a,*, Mehdi Ghadiri b, Hazhir Ghahremani a a b
Department of Chemical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran RahNegar Shimi Engineers Corporation, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 22 July 2013 Accepted 30 October 2013 Available online xxx
This study investigates simulation of ammonia transport through membrane contactors. The system studied involves feed solution of NH3, a dilute solution of sulfuric acid as solvent and a membrane contactor. The model considers coupling between equations of motion and convection-diffusion. Finite element method was applied for numerical calculations. The effect of different parameters on the removal of ammonia was investigated. The simulation results revealed that increasing feed velocity decreases ammonia removal in the contactor. The modeling findings also showed that the developed model is capable to evaluate the effective parameters which involve in the ammonia removal by means of contactors. ß 2013 Published by Elsevier B.V. on behalf of The Korean Society of Industrial and Engineering Chemistry.
Keywords: Ammonia stripping Wastewater Membrane contactor Numerical simulation Mass transfer Computational fluid dynamics
1. Introduction Nowadays, wastewater treatment is of vital importance for providing drinking water and protecting environment. Finding and developing new methods and processes for wastewater treatment has been a subject of great interest. Researchers are trying to find new solutions to remove all contaminants from water and wastewaters. Among the water contaminants, ammonia (NH3) is a major contaminant which can cause adverse effects. Ammonia can be found in either municipal or industrial wastewaters. Dissolved ammonia in solutions is generated from industrial wastewaters such as coking, chemical fertilizer, coal gasification, petroleum refining, pharmaceutical and catalyst factories [1–7]. From environmental perspective, a complete removal of ammonia from wastewaters is desirable. The concentration of ammonia in industrial wastewaters varies from 5 to 1000 mg/L [8]. The removal of dissolved ammonia from wastewaters is thus mandatory to protect the environment and human health. Currently, conventional separation processes are applied to remove ammonia from water and wastewaters including selective ion exchange, air stripping, break-point chlorination, denitrification, and biological nitrification [1,9–11]. Recently, hollow-fiber membrane contactors (HFMCs) have attracted large attentions as an effective device for separation processes. A major part of the
* Corresponding author. Tel.: +98 21 33717131; fax: +98 21 33717140. E-mail address: [email protected] (F. Nosratinia).
interest toward HFMCs is due to their capability in providing a dispersion free contact between two phases. In addition, the velocities of both phases can vary independently, while neither flooding nor unloading problems may happen [12]. Membrane contactors can be considered as a promising technology for separation of ammonia from wastewaters. The mechanism of separation in membrane contactors is based on the mass transfer between the two phases. For removal of ammonia in membrane contactors, ammonia containing solution flows in the tube or shell side of the membrane contactor. The ammonia evaporates from the aqueous solution, diffuses through the membrane pores, and reacts with the stripping solution (solvent). This process could be carried out in one-through or recycling mode. Recycling mode provides high separation factor, but is difficult to simulate. One-through mode is easy to design and model. New modeling approach for ammonia removal in membrane contactors is based on solving conservation equations for ammonia in the aqueous feed and membrane phases. In this method, conservation equations including equations of motion and mass are derived and solved simultaneously by appropriate numerical methods. The computational fluid dynamics (CFD) are usually carried out to solve the governing equations. The main objective of the present study is to develop and solve a mathematical model for the simulation of ammonia removal in a membrane contactor. The type of membrane contactor is assumed to be hollow-fiber. The equations of the model are solved by numerical method based on finite element method (FEM). An
1226-086X/$ – see front matter ß 2013 Published by Elsevier B.V. on behalf of The Korean Society of Industrial and Engineering Chemistry. http://dx.doi.org/10.1016/j.jiec.2013.10.065
Please cite this article in press as: F. Nosratinia, et al., J. Ind. Eng. Chem. (2013), http://dx.doi.org/10.1016/j.jiec.2013.10.065
G Model
JIEC-1690; No. of Pages 6 2
F. Nosratinia et al. / Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx
ammonium ([NH4+]) and ammonia ([NH3]):
Nomenclature concentration (mol/m3) outlet concentration of ammonia in the tube side (mol/m3) inlet concentration of ammonia in the tube side Cinlet (mol/m3) Ci-tube concentration of solute in the tube side (mol/m3) Ci-membrane concentration of solute in the membrane (mol/ m 3) diffusion coefficient (m2/s) D diffusion coefficient of solute in the tube (m2/s) Di-tube Di-membrane diffusion coefficient of solute in the membrane (m2/s) Henry’s law constant (mol/(m3 kPa)) H diffusive flux of species i (mol/(m2 s)) Ji length of the fiber (m) L molecular weight (kg/mol) M number of fibers n pressure (Pa) p radial coordinate (m) r inner radius of fibers (m) rin outer radius of fibers (m) rout time (s) t temperature (K) T average velocity (m/s) u velocity in the module (m/s) V z-velocity in the tube (m/s) Vz-tube axial coordinate (m) z
C Coutlet
Greek symbols e membrane porosity h dynamic viscosity (kg/(m s)) r density (kg/m3) Abbreviations FEM finite element method hollow-fiber membrane contactor HFMC 2D two-dimensional computational fluid dynamics CFD
2. Theory of ammonia removal When ammonia is dissolved in aqueous solutions, it exists in two forms. One form is ammonia (NH3) and the other form is ammonium ions (NH4+). The composition of these species depends on the pH and temperature of the solution. The compositions can be calculated from the following reaction: Kb
Ka
(2)
2.1. Mechanism of ammonia transport through membrane contactors In ammonia removal process, an aqueous solution of ammonia as feed is flown inside the tube side. The stripping solution is passed in the shell side of the membrane contactor either in cocurrent or counter-current mode. The most effective stripping solution is sulfuric acid solution because reaction rate between ammonia and sulfuric acid is high. By contacting feed and stripping phases in the membrane contactor, ammonia is transferred from the bulk toward the feed–membrane interface due to concentration gradient. At the feed–membrane interface, ammonia is volatilized into the membrane pores which are filled by gas. The membrane is microporous and provides the contact between two phases. Ammonia then diffuses across the gas-filled pores of the membrane, and is transferred into the stripping solution. At the shell–membrane interface, ammonia immediately reacts with the stripping solution. Therefore, the ammonia concentration in the stripping solution is assumed to be zero. On the other hand, water cannot diffuse through the membrane pores due to hydrophobic nature of the fibers. The principle of ammonia removal through membrane contactors is schematically shown in Fig. 1. 3. Mass transfer model A mathematical model was proposed to describe the transport of ammonia through membrane contactors. The model was based on the ‘‘non-wetted’’ mode. In this mode, it is assumed that the gas phase fills the membrane pores. The aqueous feed solution containing ammonia is fed to the tube side of the membrane contactor and the stripping solution flows in the shell side. Velocity distribution in the tube side is determined using Navier–Stokes equations. The ammonia concentration is determined using continuity equation. Axial and radial diffusions inside the tube side are considered in the mass transfer equations. Furthermore, chemical reaction between ammonia and sulfuric acid, which occurs in the shell side, is assumed to be instantaneous. Fig. 2 shows model domain for numerical simulation. 3.1. Equations of the model
algorithm is developed for the numerical simulation. Mass transfer and Navier–Stokes equations are solved simultaneously for the ammonia in the membrane contactor to obtain the concentration distribution.
NH3 þ H2 O A NH4 þ þ OH
C total ¼ ½NH4 þ þ ½NH3
(1)
where Ka and Kb values are equal to 5.6 1010 and 1.8 108, respectively [13]. The total concentration of ammonia in the solution is the summation of equilibrium concentrations of
The feed solution containing dissolved ammonia (NH3) flows with a laminar velocity inside the hollow fibers. Since the diameters of hollow fibers are very low, flow regime is assumed to be laminar in the calculations. The feed solution is flown to the tube side (at z = 0), while the stripping solution is passed through the shell side. Ammonia is removed from the feed phase by subsequent diffusion through the bulk of liquid and membrane, and becomes absorbed into the solvent. The model is built considering the following assumptions: Steady state and isothermal conditions. Laminar flow in the membrane contactor. Henry’s law is applied for feed–membrane interface. Non-wetted mode for the membrane is assumed; in which the feed aqueous solution do not fills the membrane pores. There is no reaction zone (the reaction of ammonia with the sulfuric acid is fast (instantaneous) and always occurs in excess). Velocity of both ammonia solution and sulfuric acid are constant.
The last assumption is justified by low mass transfer flux of ammonia from feed phase to solvent phase.
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Fig. 1. Mechanism of ammonia transport through membrane contactors.
3.1.1. Mass transfer equations for ammonia As it was stated earlier, membrane contactor is divided in two subdomains, i.e. tube side and membrane. The model equations are developed for these two subdomains or compartments. 3.1.1.1. Equations of tube side. The steady state continuity equation for ammonia transport in the tube side of the membrane contactor in cylindrical coordinate is obtained using Fick’s law of diffusion. Diffusive flux is estimated from Fick’s law. The continuity equation may be written as:
@C NH3 -lumen @t
solving the momentum equation. The most appropriate momentum equation here is Navier–Stokes equations. Therefore, the momentum and the continuity equations should be coupled and solved simultaneously to calculate concentration distribution of ammonia in the feed side. The Navier–Stokes equations describe flow in viscous fluids through momentum balances for each component. 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 [14]: r hðrV z-lumen þ ðrV z-lumen ÞT Þ þ rðV z-lumen rÞV z-lumen þ rp
"
þ DNH3 -lumen
@2 C NH3 -lumen 1 @C NH3 -lumen @2 C NH3 -lumen þ þ r @r @r 2 @z2
#
¼F
@C NH3 -lumen ¼ V z-lumen @z (3) The term Vz-lumen is z-velocity in the tube side of the membrane contactor. To solve Eq. (3), an equation for velocity distribution is required. Velocity distribution in the feed phase is calculated by
r V z-lumen ¼ 0
(4)
where h, V, and r denote fluid dynamic viscosity (kg/(m s)), velocity vector (m/s), and density (kg/m3), respectively; p is the pressure (Pa) and F is a body force term (N). Boundary conditions for the tube side may be written as: @z ¼ 0;
C NH3 -lumen
V z-tube ¼ V 0
ðInlet boundaryÞ
(5)
V0 is calculated from the flow rate: V0 ¼
Q 2 nprin
(6)
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
(7)
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 ;
Fig. 2. Model domain for numerical simulation.
@C NH3 -lumen ¼ 0 Axial symmetry @r C NH3 -lumen ¼
pNH3 -membrane ; H
No slip condition
(8)
(9)
where rin, H, and pNH3 -membrane are inner radius of fiber, Henry’s law constant, and partial pressure of ammonia in the gas phase of membrane pores in equilibrium with the concentration of in the aqueous solution, i.e. C NH3 -lumen . It is assumed that ammonia at the feed–membrane interface is in thermodynamic equilibrium with its vapor. 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
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be formulated as follows [1]: Sta
ln H ¼
4200 þ 3:133 T
(10)
Input constants 3
1
where H is Henry’s constant in atm m mol
, and T is in Kelvin.
Add subdomain equations
3.1.1.2. Equations of membrane. The continuity equation for the transport of ammonia inside the membrane pores, which is considered to be due to diffusion, may be written as:
@C NH3 -membrane þ DNH3 -membrane @t " 2 # @ C NH3 -membrane 1 @C NH3 -membrane @2 C NH3 -membrane þ þ r @r @r2 @z2
Define geometry
Initialize mesh
(11)
¼0
Adapt mesh
Boundary conditions for the membrane are given as: @r ¼ r in ;
pNH3 -membrane ¼ C NH3 -lumen H;
ðHenry lawÞ
Set subdomain conditions
(12)
Set boundary conditions @r ¼ r out ; ¼0
C NH3 -lumen
ðInstantaneous chemical reactionÞ
(13)
Solve coupled equations
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.:
Integrate from outlet concentration
En
@z ¼ 0&L;
Insulation
Fig. 3. Algorithm developed for numerical simulation [13].
3.2. Numerical solution of the equations
4. Results and discussion
The main objective of the present study is to simulate a membrane contactor using CFD techniques based on finite element method (FEM). The equations of ammonia transport in the contactor with the boundary conditions were solved using COMSOL Multiphysics. The latter utilizes finite element method for numerical solution of the partial differential equations. The finite element method is combined with adaptive meshing and error control using numerical solver of UMFPACK. The applicability, robustness and accuracy of this numerical method for the membrane contactors have been proved by some researches [12,15–25]. It should be pointed out that the COMSOL creates triangular meshes that are isotropic in size. A large number of elements are then created. A scaling factor was employed for the membrane contactor in the z direction due to a large difference between r and z. Adaptive mesh refinement in COMSOL, which generates the best and minimal meshes, was applied to mesh the whole geometry of membrane contactor. Further information regarding finite element method can be obtained from literature [26]. The algorithm which was developed for the numerical simulation is shown in Fig. 3. An IBM-PC-Pentium 4 (CPU speed is 2800 MHz) was used to solve the sets of equations. Parameters used for numerical simulations are listed in Table 1.
4.1. Concentration distribution of ammonia in the feed side Solving the continuity equations along with equations of motion results in determining concentration distribution in the membrane contactor. Fig. 4 illustrates the concentration distribution of ammonia in the tube side of the membrane contactor. The aqueous feed solution enters from one side of the contactor (z = 0). The stripper solution enters from the shell side counter-currently. As the aqueous feed passes through the tube side, due to the concentration gradient, ammonia is transferred from the bulk of the feed toward the feed–membrane surface. At the surface of the membrane, only ammonia evaporates into the Table 1 Parameters used in simulation. Parameter
Symbol
Value
Unit
Fiber inner radius Fiber outer radius Fiber porosity Fiber length Number of fibers Temperature Inlet ammonia concentration
rin rout
110 150 40 25 7000 293 10
mm mm
e L n T Co
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% cm – K mol/m3
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Fig. 5. Radial concentration profile of ammonia in the feed at different axial positions.
As it is seen, at the inlet of tube side, ammonia concentration is the highest (C/C0 = 1). As the feed solution flows in the tube side, concentration decreases significantly due to interphase mass transfer. Fig. 6 also reveals that at the region near the contactor entrance, concentration falls sharply [20–26]. This could be attributed to this fact that in this region, concentration gradient is high and causes significant decrease in the tube side concentration. 4.4. Concentration profile of ammonia inside the membrane
Fig. 4. Concentration distribution of ammonia in the contactor.
membrane pores and reaches the shell side. At the shell side of the membrane contactor, an instantaneous chemical reaction occurs between ammonia and acid sulfuric. Fig. 4 also shows that concentration gradient is the highest near the membrane, adjacent to the fiber wall [16].
Concentration profile of ammonia inside the membrane is shown in Fig. 7. The concentration profile inside the membrane is calculated from the equation of diffusion (Eq. (11)). This equation only considers diffusional mass transfer inside the membrane pores. Since the membrane is tortuous, an effective diffusivity is calculated using porosity and tortuosity of the membrane. Diffusion of species through membrane contactors depends on the porosity and tortuosity of the membrane. As it is seen, concentration profile inside the membrane is linear. This is due to Fick’s law of diffusion which is applied for this subdomain of
4.2. Radial concentration profile of ammonia Variations of the radial concentration of ammonia in the tube side of the membrane contactor were also investigated. A plot of the radial concentration profile at different axial positions along the tube side of the membrane contactor is shown in Fig. 5. It is clearly shown that in the region near the axis of the hollow fiber, i.e. r = 0 the bulk concentration of ammonia slightly changes. The maximum concentration of ammonia can be observed in the center of the hollow fiber due to axial symmetry assumption. Concentration of ammonia decreases gradually in the region between the center and wall of the fiber side. Eventually, in the region adjacent the membrane–feed interface, concentration sharply decreases. This observation could be attributed to the formation of the concentration boundary layer near the fiber wall. On the other hand, at the axial positions near the tube entrance, i.e. z = 0, concentration is constant [16–20]. 4.3. Axial concentration distribution of ammonia in the feed side Axial concentration profile of ammonia along the tube side of the hollow-fiber membrane contactor (HFMC) is shown in Fig. 6.
Fig. 6. Axial concentration distribution of ammonia in the tube side.
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5. Conclusions A mathematical model was developed to study the removal of ammonia from aqueous solutions by means of hollow-fiber membrane contactors (HFMCs). The model is based on mass transfer between two phases. The model predicts the steady state concentration of ammonia in the tube and membrane side of contactor by solving the conservation equations including continuity and momentum. The Navier–Stokes equations were solved to determine velocity distribution in the tube side. The model was developed considering a hydrophobic membrane which is not wetted by the aqueous feed solution. FEM analysis was applied for numerical solution of the equations. The simulation results revealed that increasing feed velocity decreases ammonia removal in the membrane contactor. Acknowledgement Research Council of Islamic Azad University-South Tehran Branch is highly acknowledged for the financial support of this project.
Fig. 7. Radial concentration profile of ammonia in the membrane.
Outlet concentration of ammonia (mol/m3)
9
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7 6
[6]
5
[7] [8]
4 3 0.0
0.2
0.4 Feedvelocity(m/s)
0.6
0.8
Fig. 8. Effect of feed velocity on the outlet concentration of ammonia.
[9] [10] [11] [12] [13] [14] [15]
membrane contactor. Fig. 7 also reveals that the concentration of ammonia reaches zero at the membrane–shell side interface [16]. 4.5. Effect of feed velocity on the ammonia removal Influence of feed velocity on the mass transfer of ammonia in the membrane contactor is shown in Fig. 8. Feed velocity corresponds to the contribution of convective mass transfer in the tube side. Fig. 8 indicates that increasing feed velocity increases ammonia outlet concentration which in turn reduces ammonia removal. Increasing feed velocity causes the residence time of feed phase in the tube side to decrease [16]. Therefore, decreasing feed velocity or feed flow rate is favorable for ammonia removal in membrane contactors.
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