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Supercritical extraction of organic solutes from aqueous solutions by means of membrane contactors: CFD simulation
Desalination 277 (2011) 135–140
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Supercritical extraction of organic solutes from aqueous solutions by means of membrane contactors: CFD simulation Saeed Shirazian, Azam Marjani ⁎, Farzad Fadaei Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran
a r t i c l e
i n f o
Article history: Received 14 February 2011 Received in revised form 2 April 2011 Accepted 4 April 2011 Available online 22 April 2011 Keywords: Mass transfer CFD Membrane contactor Acetone Ethanol Numerical simulation
a b s t r a c t This work presents mass transfer modeling of solvent extraction by means of membrane contactors. Model was based on solving conservation equations for solutes in the membrane contactor. The system considered here was a polymeric membrane contactor, an aqueous solution of ethanol or acetone, and a dense solvent. The equations of the model were solved by numerical method using CFD techniques. The simulation results for ethanol and acetone showed an average deviation of 15.6% and 2.5% with the experimental data, respectively. Simulation results indicated that the extraction of acetone is higher than ethanol due to higher solubility of acetone in the solvent. The simulation results revealed that decreasing feed velocity and increasing solvent velocity increase solute removal. The developed mass transfer model is more accurate than other models and represents a general approach for simulation of membrane-based solvent extraction. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Separation processes using membrane contactors have been conducted in concentration or purification processes such as solvent extraction, gas absorption, ion exchange and membrane distillation. In membrane contactors, the membrane mainly operates as a physical barrier between two fluids and unlike most membrane operations, the membrane has no selectivity to the separation, i.e., it has no impact on the partition coefficients [1–4]. Among the membrane modules available as membrane contactors, hollow-fiber membrane contactors (HFMCs) have attracted many attentions. These devices provide high surface/volume ratio for mass transfer and separation. These contactors offer some advantages compared with conventional contactors such as dispersion columns [1]. In HFMCs, the interfacial mass-transfer area is much higher and better controlled, whereas the hydrophilic or hydrophobic nature of the membrane determines the position of the interface between the feed and the solvent. Meanwhile, these contactors allow the possibility to immobilize this interface at the pore's mouth by applying an adequate trans-membrane pressure gradient. Therefore, the main advantage of membrane contactors is that they allow a dispersion-free contact, so emulsions cannot be formed during the separation process. In addition,
⁎ Corresponding author. E-mail address: [email protected] (A. Marjani). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.04.011
the velocities of both phases can be chosen independently, and, as a result neither flooding nor foaming problems arise [5,6]. One of the applications of membrane contactors is supercritical extraction. This process is called porocritical extraction. Porocritical process or porocritical extraction is a commercial supercritical fluid extraction (SFE) which utilizes a HFMC to contact two phases for the purpose of separation [3]. In this process a macroporous membrane provides contact between feed and solvent. The aqueous feed solution is passed on one side, while the extraction solvent, which is a near-critical or a super-critical fluid, is flowed on the other side. The aqueous solution is also maintained at a high pressure near the dense solvent to establish interface between solvent and feed. When the membrane material is hydrophobic, i.e. the aqueous solution does not penetrate the membrane pores and the gas phase can fill the membrane pores. In this process, the driving force is concentration difference of the solute between feed and dense solvent. In porocritical extraction, there are four steps for the transfer of a solute across the membrane: transport through the boundary layer of the liquid feed solution; solubilization in the nearcritical or supercritical fluid (SCF) extraction phase; diffusion through the stagnant extraction phase within the pores; transport through the boundary layer of the extraction phase. Fig. 1 schematically shows the principles of this process [3]. The main objective of this study is to develop and solve a mass transfer model for the prediction of the porocritical process. The developed model considers both axial and radial diffusions in the tube, membrane, and shell compartments of the contactor. The developed model is then validated using experimental data obtained from literature. Effect of process parameters on the removal of solutes is then considered.
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S. Shirazian et al. / Desalination 277 (2011) 135–140
membrane, and shell side. The solvent is fed to the shell side at z = L, while the liquid phase is entered the tube side at z = 0. Following assumptions were considered in modeling: (1) Steady state and isothermal conditions; (2) Fully developed parabolic velocity profile for the liquid in the hollow fiber; (3) The aqueous feed and the dense solvent gas are considered immiscible; (4) Reynolds numbers of 2100 and 4000 were considered as the transition limits between laminar and turbulent regimes. The conservation equations for each species can be expressed as [7]: ∂ðρϕÞ → + div ρuϕ−Γ ϕ gradϕ = Sϕ ∂t
ð1Þ →
Fig. 1. Principles of mass transfer in porocritical extraction for counter-current mode [3].
2. Model development In order to validate the simulation results, experimental data reported by Bothun et al. [6] for the extraction of ethanol and acetone from aqueous solutions were used. The contactor consists of a single hollow fiber housed in a stainless steel tube. The liquid feed (aqueous solution) is flowed inside the fiber and the solvent (near-critical CO2) is passed countercurrent-wise outside the fiber. The simulations were carried out at identical conditions employed in conducting experiments. 2.1. Equations of mass transfer The conservation equations for the solute in the contactor were derived and solved to predict the performance of the contactor. The model is developed for a hollow fiber, as shown in Fig. 2. As can be seen, the feed phase flows with a fully developed laminar velocity profile in the tube side. The fiber is surrounded by the solvent which flows in the opposite direction of the feed phase. Therefore, the membrane contactor system consists of three sections: tube side,
where ρ is the density of the mixture, ϕ the dependent variable, u is the velocity vector, Γϕ is the appropriate coefficient for variable ϕ, which in the mass fraction equation is calculated as Γϕ = ρD, D is the mutual diffusion coefficient for mixture, and Sϕ is the source-sink term per unit volume for variable ρ. The continuity equation for steady state for solute (acetone or ethanol) in the three sections of membrane contactor is obtained using Fick's law of diffusion for estimation of diffusive flux: −Di ∇:ð∇Ci Þ + ∇:ðCi V Þ = 0:
ð2Þ
It is assumed that chemical reaction does not occur in the model domain. In a laminar flow, Navier–Stokes equations can be applied for the shell side [7]: ∂Vz T −∇⋅η ∇Vz + ð∇Vz Þ + ρðVz :∇ÞVz + ∇p = f ∂t ∇:Vz = 0: ρ
ð3Þ
Boundary conditions for the shell side are given as: @z = L; @r = r3 ; @r = r2 ;
Ci−shell = 0; Vz = V0 ∂Ci−shell = 0 ðinsulationÞ; no slip condition ∂r Ci−shell = Ci−membrane ; no slip condition:
ð4Þ ð5Þ ð6Þ
Boundary conditions for membrane are given as: @r = r2 ;
Ci−membrane = Ci−shell
ð7Þ
@r = r1 ;
Ci−membrane = Ci−tube × m
ð8Þ
@z = 0;
∂Ci−membrane = 0 ðinsulationÞ ∂r
ð9Þ
@z = L;
∂Ci−membrane = 0 ðinsulationÞ ∂r
ð10Þ
where m is the physical solubility of the liquid feed in the dense gas. The velocity distribution in the tube side is assumed to follow Newtonian laminar flow [7]: 2 r VZ−tube = 2u 1− r1 Fig. 2. Model domain.
where u is average velocity in the tube side.
ð11Þ
S. Shirazian et al. / Desalination 277 (2011) 135–140
Boundary conditions for the tube side are given as: @z = 0;
Ci−tube = Ci−inlet
ð12Þ
@r = r1 ;
Ci−tube = Ci−membrane = m
ð13Þ
@r = 0;
∂Ci−tube = 0 ðsymmetryÞ: ∂r
ð14Þ
Laminar flow is obtained in the module, if the Reynolds number calculated at the tube side is such that Retube b 2100 [7]. The Reynolds number is calculated from equation given by: 2r1 ρu η
137
Table 2 Experimental and simulated (this work) data for the extraction of ethanol from an aqueous solution using the single-fiber porocritical extraction system (P = 69 bar; T = 298 K; feed solution concentration = 10% w/w). F (mL/min)
S/F
Extraction (EXP) (%)
Extraction (MOD) (%)
Error (%)
0.15 0.25 0.50 1.00 0.10
3 3 3 3 10
15.2 10.4 4.7 9.9 31.9
16.04 11.01 5.53 5.21 32.55
5.5 5.9 17.6 47.3 2.0
where u is the mean fluid velocity at the tube side. The Reynolds numbers for the range of flow rates considered are between 0.05 and 20. Table 1 shows parameters of membrane module considered in this study [6].
It should be pointed out here that the higher accuracy was observed at low feed flow rates and solvent flow rates. The results show an average deviation of 15.6% and 2.5% with the experimental data for ethanol and acetone, respectively. The results also show that the developed mass transfer model is more accurate than the model developed by Estay et al. [3]. The latter model, which was based on resistances-in-series, shows an average deviation of 36.3% and 6.7% with the experimental data for ethanol and acetone, respectively.
2.2. Numerical solution of equations
3.2. Effect of configuration on the extraction
The mentioned equations were solved numerically by using COMSOL Multiphysics software, version 3.2. This software uses finite element method (FEM) for the numerical solutions of equations. The finite element analysis is combined with adaptive meshing and error control using UMFPACK solver. The applicability, robustness and accuracy of this model have been verified in previous work [8]. An IBM-PC-Pentium4 (CPU speed is 2800 MHz) was used to solve the set of equations. The computational time for solving the set of equations was about 20 min. Parameters and physical constants for numerical simulations were taken from literature [9–12].
The effect of configuration on the removal of solutes was considered using mass transfer model developed in this study. Two situations were investigated, i.e. aqueous feed solution flows inside and outside of the hollow fiber. The extraction percentages of acetone and ethanol were calculated for both situations using numerical simulation. Results of these calculations are indicated in Figs. 3 and 4. As can be seen, higher extraction efficiencies are obtained when the aqueous feed solution is passed through the tube side of membrane contactor. This behavior could be attributed to the larger volume of the shell side compared to the tube side which accommodates higher volumes of the solvent in comparison with the case that solvent is passed within the tube side. As such, lower concentrations of the solute in the solvent as well as higher Reynolds numbers for the flow of solvent in the shell side would increase the extraction efficiency.
Retube =
ð15Þ
3. Results and discussion 3.1. Model validation To validate the mass transfer model, ethanol or acetone extraction percentages calculated using the mathematical model developed here, were compared with the experimental data reported by Bothun et al. [6]. The results are shown in Tables 2 and 3. Comparisons were carried out for a wide range of feed flow rate (F) and the solvent/feed molar ratio (S/F). As it can be seen, the extraction of acetone is higher than ethanol. This is mainly because of high partition coefficient for acetone between aqueous feed and the dense solvent. It is also clearly seen that the model predictions are in good agreement with the experimental data for different values of feed and solvent flow rates. Meanwhile, the simulation results are found of better accuracy for the extraction of acetone from feed phase. This could be attributed to two aspects; better prediction of transport properties for acetone and better estimation of the vapor–liquid equilibrium for the ternary acetone–CO2–water system which plays a crucial rule in the process.
3.3. Profile of the solute concentration Since the acetone has higher removal efficiency and better prediction of transport properties, we continue the simulations for acetone as a model of solute. Fig. 5 presents the distribution of acetone concentration along the tube side of the membrane contactor. The liquid feed enters from one side of the contactor (z = 0) where the concentration of acetone is the highest (C0), whereas the solvent enters from the other side (z = L) where the concentration of acetone is assumed to be zero. As the acetone flows through the tube side, it diffuses toward the membrane pores due to the concentration gradient, and then becomes extracted into the receiving phase, i.e. the moving solvent. Fig. 6 also presents contours of acetone concentration in the tube side. Fig. 6 reveals that at the regions near the membrane surface, i.e. feed–membrane interface, the concentration gradient is great. This is because of formation of concentration
Table 1 Module parameters used for numerical simulation [6]. Material
Polypropylene
Number of fibers, n Fiber length, (mm) Porosity, ε (%) Mean pore diameter, (μm) Fiber ID, (mm) Fiber OD, (mm) Shell ID, (mm) Shell OD, (mm)
1 1067 75 0.4 0.6 1.02 1.52 3.18
Table 3 Experimental and simulated (this work) data for the extraction of acetone from an aqueous solution using the single-fiber porocritical extraction system (P = 69 bar; T = 298 K; feed solution concentration = 10% w/w). F (mL/min)
S/F
Extraction (EXP) (%)
Extraction (MOD) (%)
Error (%)
0.15 0.25 0.50 1.00
3 3 3 3
96.1 89.6 68.9 67.9
98.03 87.61 67.04 65.63
2.0 2.2 2.7 3.3
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S. Shirazian et al. / Desalination 277 (2011) 135–140
Fig. 3. Extraction of acetone from an aqueous solution (10% w/w) vs. the liquid flow rate for different configurations (molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K).
boundary layer near the membrane which can be seen clearly from Fig. 6.
Fig. 5. Axial distribution of acetone concentration (C/C0) in the contactor. (Molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K; liquid flow rate = 1 mL/min; solvent flow rate = 3 mL/min).
3.4. Velocity profile in the shell side The velocity profile in the membrane contactor is shown in Fig. 7, in which the dense solvent (near-critical CO2) flows. The velocity profile in the shell side was determined by solving Navier–Stokes equations. As it can be seen from Fig. 7, the velocity profile is almost parabolic with a mean velocity which increases with the membrane length because of continuous fluid permeation. Fig. 7 also reveals that at the inlet regions in the solvent (shell) side, the velocity is not developed. After a short distance from the inlet, the velocity profile is fully developed (see Fig. 7). As observed, the model considers the entry effects on the hydrodynamics of fluid flow in the shell side.
indicates that increasing feed flow rate, decreases mass transfer of acetone to the solvent phase. This is due to reduction of feed residence time in the contactor with increasing feed velocity.
3.5. Effect of feed and solvent flow rates on the concentration distribution of solute Effect of feed and solvent flow rates on the concentration profile of solute (acetone) in the feed phase (tube side) and solvent phase (shell side) are illustrated in Figs. 8 and 9. Fig. 8 shows the radial concentration profile of acetone as a function of feed flow rate. It is seen from Fig. 8 that at the regions near the fiber center, the concentration profile of acetone is constant which can be considered as bulk (infinity) concentration of solute. At the region near the membrane surface, the concentration drop is significant. The region in the vicinity of membrane surface which the concentration gradient is significant is the concentration boundary layer [13]. Fig. 8 also
Fig. 4. Extraction of ethanol from an aqueous solution (10% w/w) vs. the liquid flow rate for different configurations (molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K).
Fig. 6. Contours of acetone concentration (C/C0) in the feed phase (tube). (Molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K; liquid flow rate = 1 mL/min; solvent flow rate = 3 mL/min).
S. Shirazian et al. / Desalination 277 (2011) 135–140
139
Fig. 9. Axial concentration profile of acetone in the shell side. Fig. 7. Velocity profile in the shell side. Origin is in r2, r2 = 0.
3.6. Flux distribution along the membrane contactor Fig. 9 indicates the axial concentration profile of acetone in the shell side of the membrane contactor in which the solvent flows. It can be seen that at the inlet of shell, the acetone concentration is zero (pure solvent). As solvent flows along the shell side of membrane contactor, it dissolves the solute (acetone) which results enhancement of acetone concentration along the shell side. Fig. 9 also shows that increasing solvent flow rate, increases mass transfer flux of acetone. This could be attributed to this fact that increasing solvent flow rate, decreases solute concentration in the shell side (see Fig. 9) which in turn results in higher concentration gradient for transport of solute toward the shell side.
Mass transfer flux distribution of acetone in the feed phase of the membrane contactor is illustrated in Fig. 10. Both diffusive and convective fluxes for acetone mass transfer in the tube side are shown in Fig. 10 to demonstrate the contribution of axial diffusion in the simulation. As observed, contribution of convective flux in the z-direction is predominant compared to axial diffusive flux. That is due to the fact that in the axial direction, the velocity is significant and causes high convective flux for solute transport. 4. Conclusions Theoretical studies were carried out utilizing CFD techniques to study the membrane-based solvent extraction process. The latter process uses a supercritical or near-critical solvent for extraction of solutes from aqueous feeds. A mathematical model was developed
Fig. 8. Radial concentration profile of acetone in the tube side.
Fig. 10. Mass transfer flux distribution of acetone in the feed phase (tube). (P = 6.9 MPa; T = 298 K; liquid flow rate = 2 mL/min; solvent flow rate = 3 mL/min).
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S. Shirazian et al. / Desalination 277 (2011) 135–140
that can calculate the steady state concentration of the solute. Both axial and radial diffusions were considered in the model. The model findings were compared with the experimental data and showed good agreement for extraction of ethanol and acetone from aqueous solutions. The simulation results for ethanol and acetone showed an average deviation of 15.6% and 2.5% with the experimental data, respectively. It was deduced from the simulation results that higher extraction efficiencies for acetone in comparison with those for ethanol where a hydrophobic membrane is used. The results also indicated that the extraction of solute increased with decreasing the liquid velocity. The model performed superior, in comparison with similar models, in terms of accuracy as well as being independent of the experimental results. Nomenclature C concentration, mol/m3 Coutlet outlet concentration of solute in the tube side, mol/m3 Cintlet inlet concentration of solute in the tube side, mol/m3 Ci-tube concentration of solute in the tube side, mol/m3 Ci-shell concentration of solute in the shell side, mol/m3 Ci-membrane concentration of solute in the membrane, mol/m3 D diffusion coefficient, m2/s F liquid feed flow, m3/s f external force vector, N L length of the fiber, m m physical solubility P pressure, Pa r radial coordinate, m r1 inner tube radius, m r2 outer tube radius, m r3 inner shell radius, m Ri overall reaction rate of any species, mol/m3.s S solvent flow rate, m3/s Sϕ source term T temperature, K u average velocity in the tube side, m/s V velocity in the module, m/s Vz-tube z-velocity in the tube, m/s V0 inlet velocity of shell side, m/s z axial coordinate, m
Greek symbols ε membrane porosity η viscosity, kg/m.s ρ density, kg/m3
Abbreviations EXP experimental FEM finite element method HFMC hollow-fiber membrane contactor MOD modeling SCF supercritical fluid SFE supercritical fluid extraction 2D two dimensional
References [1] G. Afrane, E.H. Chimowitz, Experimental investigation of a new supercritical fluidinorganic membrane separation process, Journal of Membrane Science 116 (2) (1996) 293–299. [2] Y.W. Chiu, C.S. Tan, Regeneration of supercritical carbon dioxide by membrane at near critical conditions, Journal of Supercritical Fluids 21 (1) (2001) 81–89. [3] H. Estay, S. Bocquet, J. Romero, J. Sanchez, G.M. Rios, F. Valenzuela, Modeling and simulation of mass transfer in near-critical extraction using a hollow fiber membrane contactor, Chemical Engineering Science 62 (21) (2007) 5794–5808. [4] S. Sarrade, C. Guizard, G.M. Rios, Membrane technology and supercritical fluids: chemical engineering for coupled processes, Desalination 144 (1–3) (2002) 137–142. [5] S. Sarrade, G.M. Rios, M. Carlés, Nanofiltration membrane behavior in a supercritical medium, Journal of Membrane Science 114 (1) (1996) 81–91. [6] G.D. Bothun, B.L. Knutson, H.J. Strobel, S.E. Nokes, E.A. Brignole, S. Díaz, Compressed solvents for the extraction of fermentation products within a hollow fiber membrane contactor, Journal of Supercritical Fluids 25 (2) (2003) 119–134. [7] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edition John Wiley & Sons, New York, 2002. [8] S. Shirazian, A. Moghadassi, S. Moradi, Numerical simulation of mass transfer in gas–liquid hollow fiber membrane contactors for laminar flow conditions, Simulation Modelling Practice and Theory 17 (4) (2009) 708–718. [9] R. Reid, J. Prauznit, T. Sherwood, The Properties of Gases and Liquids, third ed McGraw-Hill Inc., New York, 1977. [10] O.J. Catchpole, M.B. King, Measurement and correlation of binary diffusion coefficients in near critical fluids, Industrial and Engineering Chemistry Research 33 (7) (1994) 1828–1837. [11] T. Funazukuri, Y. Ishiwata, N. Wakao, Predictive correlation for binary diffusion coefficients in dense carbon dioxide, AIChE Journal 38 (11) (1992) 1761–1768. [12] S. Hirohama, T. Takatsuka, S. Miyamoto, T. Muto, Measurement and correlation of phase equilibria for the carbon dioxide–ethanol–water system, Journal of Chemical Engineering of Japan 26 (4) (1993) 408–415. [13] S. Bocquet, J. Romero, J. Sanchez, G.M. Rios, Membrane contactors for the extraction process with subcritical carbon dioxide or propane: simulation of the influence of operating parameters, Journal of Supercritical Fluids 41 (2) (2007) 246–256.
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Supercritical extraction of organic solutes from aqueous solutions by means of membrane contactors: CFD simulation Saeed Shirazian, Azam Marjani ⁎, Farzad Fadaei Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran
a r t i c l e
i n f o
Article history: Received 14 February 2011 Received in revised form 2 April 2011 Accepted 4 April 2011 Available online 22 April 2011 Keywords: Mass transfer CFD Membrane contactor Acetone Ethanol Numerical simulation
a b s t r a c t This work presents mass transfer modeling of solvent extraction by means of membrane contactors. Model was based on solving conservation equations for solutes in the membrane contactor. The system considered here was a polymeric membrane contactor, an aqueous solution of ethanol or acetone, and a dense solvent. The equations of the model were solved by numerical method using CFD techniques. The simulation results for ethanol and acetone showed an average deviation of 15.6% and 2.5% with the experimental data, respectively. Simulation results indicated that the extraction of acetone is higher than ethanol due to higher solubility of acetone in the solvent. The simulation results revealed that decreasing feed velocity and increasing solvent velocity increase solute removal. The developed mass transfer model is more accurate than other models and represents a general approach for simulation of membrane-based solvent extraction. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Separation processes using membrane contactors have been conducted in concentration or purification processes such as solvent extraction, gas absorption, ion exchange and membrane distillation. In membrane contactors, the membrane mainly operates as a physical barrier between two fluids and unlike most membrane operations, the membrane has no selectivity to the separation, i.e., it has no impact on the partition coefficients [1–4]. Among the membrane modules available as membrane contactors, hollow-fiber membrane contactors (HFMCs) have attracted many attentions. These devices provide high surface/volume ratio for mass transfer and separation. These contactors offer some advantages compared with conventional contactors such as dispersion columns [1]. In HFMCs, the interfacial mass-transfer area is much higher and better controlled, whereas the hydrophilic or hydrophobic nature of the membrane determines the position of the interface between the feed and the solvent. Meanwhile, these contactors allow the possibility to immobilize this interface at the pore's mouth by applying an adequate trans-membrane pressure gradient. Therefore, the main advantage of membrane contactors is that they allow a dispersion-free contact, so emulsions cannot be formed during the separation process. In addition,
⁎ Corresponding author. E-mail address: [email protected] (A. Marjani). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.04.011
the velocities of both phases can be chosen independently, and, as a result neither flooding nor foaming problems arise [5,6]. One of the applications of membrane contactors is supercritical extraction. This process is called porocritical extraction. Porocritical process or porocritical extraction is a commercial supercritical fluid extraction (SFE) which utilizes a HFMC to contact two phases for the purpose of separation [3]. In this process a macroporous membrane provides contact between feed and solvent. The aqueous feed solution is passed on one side, while the extraction solvent, which is a near-critical or a super-critical fluid, is flowed on the other side. The aqueous solution is also maintained at a high pressure near the dense solvent to establish interface between solvent and feed. When the membrane material is hydrophobic, i.e. the aqueous solution does not penetrate the membrane pores and the gas phase can fill the membrane pores. In this process, the driving force is concentration difference of the solute between feed and dense solvent. In porocritical extraction, there are four steps for the transfer of a solute across the membrane: transport through the boundary layer of the liquid feed solution; solubilization in the nearcritical or supercritical fluid (SCF) extraction phase; diffusion through the stagnant extraction phase within the pores; transport through the boundary layer of the extraction phase. Fig. 1 schematically shows the principles of this process [3]. The main objective of this study is to develop and solve a mass transfer model for the prediction of the porocritical process. The developed model considers both axial and radial diffusions in the tube, membrane, and shell compartments of the contactor. The developed model is then validated using experimental data obtained from literature. Effect of process parameters on the removal of solutes is then considered.
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S. Shirazian et al. / Desalination 277 (2011) 135–140
membrane, and shell side. The solvent is fed to the shell side at z = L, while the liquid phase is entered the tube side at z = 0. Following assumptions were considered in modeling: (1) Steady state and isothermal conditions; (2) Fully developed parabolic velocity profile for the liquid in the hollow fiber; (3) The aqueous feed and the dense solvent gas are considered immiscible; (4) Reynolds numbers of 2100 and 4000 were considered as the transition limits between laminar and turbulent regimes. The conservation equations for each species can be expressed as [7]: ∂ðρϕÞ → + div ρuϕ−Γ ϕ gradϕ = Sϕ ∂t
ð1Þ →
Fig. 1. Principles of mass transfer in porocritical extraction for counter-current mode [3].
2. Model development In order to validate the simulation results, experimental data reported by Bothun et al. [6] for the extraction of ethanol and acetone from aqueous solutions were used. The contactor consists of a single hollow fiber housed in a stainless steel tube. The liquid feed (aqueous solution) is flowed inside the fiber and the solvent (near-critical CO2) is passed countercurrent-wise outside the fiber. The simulations were carried out at identical conditions employed in conducting experiments. 2.1. Equations of mass transfer The conservation equations for the solute in the contactor were derived and solved to predict the performance of the contactor. The model is developed for a hollow fiber, as shown in Fig. 2. As can be seen, the feed phase flows with a fully developed laminar velocity profile in the tube side. The fiber is surrounded by the solvent which flows in the opposite direction of the feed phase. Therefore, the membrane contactor system consists of three sections: tube side,
where ρ is the density of the mixture, ϕ the dependent variable, u is the velocity vector, Γϕ is the appropriate coefficient for variable ϕ, which in the mass fraction equation is calculated as Γϕ = ρD, D is the mutual diffusion coefficient for mixture, and Sϕ is the source-sink term per unit volume for variable ρ. The continuity equation for steady state for solute (acetone or ethanol) in the three sections of membrane contactor is obtained using Fick's law of diffusion for estimation of diffusive flux: −Di ∇:ð∇Ci Þ + ∇:ðCi V Þ = 0:
ð2Þ
It is assumed that chemical reaction does not occur in the model domain. In a laminar flow, Navier–Stokes equations can be applied for the shell side [7]: ∂Vz T −∇⋅η ∇Vz + ð∇Vz Þ + ρðVz :∇ÞVz + ∇p = f ∂t ∇:Vz = 0: ρ
ð3Þ
Boundary conditions for the shell side are given as: @z = L; @r = r3 ; @r = r2 ;
Ci−shell = 0; Vz = V0 ∂Ci−shell = 0 ðinsulationÞ; no slip condition ∂r Ci−shell = Ci−membrane ; no slip condition:
ð4Þ ð5Þ ð6Þ
Boundary conditions for membrane are given as: @r = r2 ;
Ci−membrane = Ci−shell
ð7Þ
@r = r1 ;
Ci−membrane = Ci−tube × m
ð8Þ
@z = 0;
∂Ci−membrane = 0 ðinsulationÞ ∂r
ð9Þ
@z = L;
∂Ci−membrane = 0 ðinsulationÞ ∂r
ð10Þ
where m is the physical solubility of the liquid feed in the dense gas. The velocity distribution in the tube side is assumed to follow Newtonian laminar flow [7]: 2 r VZ−tube = 2u 1− r1 Fig. 2. Model domain.
where u is average velocity in the tube side.
ð11Þ
S. Shirazian et al. / Desalination 277 (2011) 135–140
Boundary conditions for the tube side are given as: @z = 0;
Ci−tube = Ci−inlet
ð12Þ
@r = r1 ;
Ci−tube = Ci−membrane = m
ð13Þ
@r = 0;
∂Ci−tube = 0 ðsymmetryÞ: ∂r
ð14Þ
Laminar flow is obtained in the module, if the Reynolds number calculated at the tube side is such that Retube b 2100 [7]. The Reynolds number is calculated from equation given by: 2r1 ρu η
137
Table 2 Experimental and simulated (this work) data for the extraction of ethanol from an aqueous solution using the single-fiber porocritical extraction system (P = 69 bar; T = 298 K; feed solution concentration = 10% w/w). F (mL/min)
S/F
Extraction (EXP) (%)
Extraction (MOD) (%)
Error (%)
0.15 0.25 0.50 1.00 0.10
3 3 3 3 10
15.2 10.4 4.7 9.9 31.9
16.04 11.01 5.53 5.21 32.55
5.5 5.9 17.6 47.3 2.0
where u is the mean fluid velocity at the tube side. The Reynolds numbers for the range of flow rates considered are between 0.05 and 20. Table 1 shows parameters of membrane module considered in this study [6].
It should be pointed out here that the higher accuracy was observed at low feed flow rates and solvent flow rates. The results show an average deviation of 15.6% and 2.5% with the experimental data for ethanol and acetone, respectively. The results also show that the developed mass transfer model is more accurate than the model developed by Estay et al. [3]. The latter model, which was based on resistances-in-series, shows an average deviation of 36.3% and 6.7% with the experimental data for ethanol and acetone, respectively.
2.2. Numerical solution of equations
3.2. Effect of configuration on the extraction
The mentioned equations were solved numerically by using COMSOL Multiphysics software, version 3.2. This software uses finite element method (FEM) for the numerical solutions of equations. The finite element analysis is combined with adaptive meshing and error control using UMFPACK solver. The applicability, robustness and accuracy of this model have been verified in previous work [8]. An IBM-PC-Pentium4 (CPU speed is 2800 MHz) was used to solve the set of equations. The computational time for solving the set of equations was about 20 min. Parameters and physical constants for numerical simulations were taken from literature [9–12].
The effect of configuration on the removal of solutes was considered using mass transfer model developed in this study. Two situations were investigated, i.e. aqueous feed solution flows inside and outside of the hollow fiber. The extraction percentages of acetone and ethanol were calculated for both situations using numerical simulation. Results of these calculations are indicated in Figs. 3 and 4. As can be seen, higher extraction efficiencies are obtained when the aqueous feed solution is passed through the tube side of membrane contactor. This behavior could be attributed to the larger volume of the shell side compared to the tube side which accommodates higher volumes of the solvent in comparison with the case that solvent is passed within the tube side. As such, lower concentrations of the solute in the solvent as well as higher Reynolds numbers for the flow of solvent in the shell side would increase the extraction efficiency.
Retube =
ð15Þ
3. Results and discussion 3.1. Model validation To validate the mass transfer model, ethanol or acetone extraction percentages calculated using the mathematical model developed here, were compared with the experimental data reported by Bothun et al. [6]. The results are shown in Tables 2 and 3. Comparisons were carried out for a wide range of feed flow rate (F) and the solvent/feed molar ratio (S/F). As it can be seen, the extraction of acetone is higher than ethanol. This is mainly because of high partition coefficient for acetone between aqueous feed and the dense solvent. It is also clearly seen that the model predictions are in good agreement with the experimental data for different values of feed and solvent flow rates. Meanwhile, the simulation results are found of better accuracy for the extraction of acetone from feed phase. This could be attributed to two aspects; better prediction of transport properties for acetone and better estimation of the vapor–liquid equilibrium for the ternary acetone–CO2–water system which plays a crucial rule in the process.
3.3. Profile of the solute concentration Since the acetone has higher removal efficiency and better prediction of transport properties, we continue the simulations for acetone as a model of solute. Fig. 5 presents the distribution of acetone concentration along the tube side of the membrane contactor. The liquid feed enters from one side of the contactor (z = 0) where the concentration of acetone is the highest (C0), whereas the solvent enters from the other side (z = L) where the concentration of acetone is assumed to be zero. As the acetone flows through the tube side, it diffuses toward the membrane pores due to the concentration gradient, and then becomes extracted into the receiving phase, i.e. the moving solvent. Fig. 6 also presents contours of acetone concentration in the tube side. Fig. 6 reveals that at the regions near the membrane surface, i.e. feed–membrane interface, the concentration gradient is great. This is because of formation of concentration
Table 1 Module parameters used for numerical simulation [6]. Material
Polypropylene
Number of fibers, n Fiber length, (mm) Porosity, ε (%) Mean pore diameter, (μm) Fiber ID, (mm) Fiber OD, (mm) Shell ID, (mm) Shell OD, (mm)
1 1067 75 0.4 0.6 1.02 1.52 3.18
Table 3 Experimental and simulated (this work) data for the extraction of acetone from an aqueous solution using the single-fiber porocritical extraction system (P = 69 bar; T = 298 K; feed solution concentration = 10% w/w). F (mL/min)
S/F
Extraction (EXP) (%)
Extraction (MOD) (%)
Error (%)
0.15 0.25 0.50 1.00
3 3 3 3
96.1 89.6 68.9 67.9
98.03 87.61 67.04 65.63
2.0 2.2 2.7 3.3
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Fig. 3. Extraction of acetone from an aqueous solution (10% w/w) vs. the liquid flow rate for different configurations (molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K).
boundary layer near the membrane which can be seen clearly from Fig. 6.
Fig. 5. Axial distribution of acetone concentration (C/C0) in the contactor. (Molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K; liquid flow rate = 1 mL/min; solvent flow rate = 3 mL/min).
3.4. Velocity profile in the shell side The velocity profile in the membrane contactor is shown in Fig. 7, in which the dense solvent (near-critical CO2) flows. The velocity profile in the shell side was determined by solving Navier–Stokes equations. As it can be seen from Fig. 7, the velocity profile is almost parabolic with a mean velocity which increases with the membrane length because of continuous fluid permeation. Fig. 7 also reveals that at the inlet regions in the solvent (shell) side, the velocity is not developed. After a short distance from the inlet, the velocity profile is fully developed (see Fig. 7). As observed, the model considers the entry effects on the hydrodynamics of fluid flow in the shell side.
indicates that increasing feed flow rate, decreases mass transfer of acetone to the solvent phase. This is due to reduction of feed residence time in the contactor with increasing feed velocity.
3.5. Effect of feed and solvent flow rates on the concentration distribution of solute Effect of feed and solvent flow rates on the concentration profile of solute (acetone) in the feed phase (tube side) and solvent phase (shell side) are illustrated in Figs. 8 and 9. Fig. 8 shows the radial concentration profile of acetone as a function of feed flow rate. It is seen from Fig. 8 that at the regions near the fiber center, the concentration profile of acetone is constant which can be considered as bulk (infinity) concentration of solute. At the region near the membrane surface, the concentration drop is significant. The region in the vicinity of membrane surface which the concentration gradient is significant is the concentration boundary layer [13]. Fig. 8 also
Fig. 4. Extraction of ethanol from an aqueous solution (10% w/w) vs. the liquid flow rate for different configurations (molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K).
Fig. 6. Contours of acetone concentration (C/C0) in the feed phase (tube). (Molar flow ratio S/F = 3; P = 6.9 MPa; T = 298 K; liquid flow rate = 1 mL/min; solvent flow rate = 3 mL/min).
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Fig. 9. Axial concentration profile of acetone in the shell side. Fig. 7. Velocity profile in the shell side. Origin is in r2, r2 = 0.
3.6. Flux distribution along the membrane contactor Fig. 9 indicates the axial concentration profile of acetone in the shell side of the membrane contactor in which the solvent flows. It can be seen that at the inlet of shell, the acetone concentration is zero (pure solvent). As solvent flows along the shell side of membrane contactor, it dissolves the solute (acetone) which results enhancement of acetone concentration along the shell side. Fig. 9 also shows that increasing solvent flow rate, increases mass transfer flux of acetone. This could be attributed to this fact that increasing solvent flow rate, decreases solute concentration in the shell side (see Fig. 9) which in turn results in higher concentration gradient for transport of solute toward the shell side.
Mass transfer flux distribution of acetone in the feed phase of the membrane contactor is illustrated in Fig. 10. Both diffusive and convective fluxes for acetone mass transfer in the tube side are shown in Fig. 10 to demonstrate the contribution of axial diffusion in the simulation. As observed, contribution of convective flux in the z-direction is predominant compared to axial diffusive flux. That is due to the fact that in the axial direction, the velocity is significant and causes high convective flux for solute transport. 4. Conclusions Theoretical studies were carried out utilizing CFD techniques to study the membrane-based solvent extraction process. The latter process uses a supercritical or near-critical solvent for extraction of solutes from aqueous feeds. A mathematical model was developed
Fig. 8. Radial concentration profile of acetone in the tube side.
Fig. 10. Mass transfer flux distribution of acetone in the feed phase (tube). (P = 6.9 MPa; T = 298 K; liquid flow rate = 2 mL/min; solvent flow rate = 3 mL/min).
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that can calculate the steady state concentration of the solute. Both axial and radial diffusions were considered in the model. The model findings were compared with the experimental data and showed good agreement for extraction of ethanol and acetone from aqueous solutions. The simulation results for ethanol and acetone showed an average deviation of 15.6% and 2.5% with the experimental data, respectively. It was deduced from the simulation results that higher extraction efficiencies for acetone in comparison with those for ethanol where a hydrophobic membrane is used. The results also indicated that the extraction of solute increased with decreasing the liquid velocity. The model performed superior, in comparison with similar models, in terms of accuracy as well as being independent of the experimental results. Nomenclature C concentration, mol/m3 Coutlet outlet concentration of solute in the tube side, mol/m3 Cintlet inlet concentration of solute in the tube side, mol/m3 Ci-tube concentration of solute in the tube side, mol/m3 Ci-shell concentration of solute in the shell side, mol/m3 Ci-membrane concentration of solute in the membrane, mol/m3 D diffusion coefficient, m2/s F liquid feed flow, m3/s f external force vector, N L length of the fiber, m m physical solubility P pressure, Pa r radial coordinate, m r1 inner tube radius, m r2 outer tube radius, m r3 inner shell radius, m Ri overall reaction rate of any species, mol/m3.s S solvent flow rate, m3/s Sϕ source term T temperature, K u average velocity in the tube side, m/s V velocity in the module, m/s Vz-tube z-velocity in the tube, m/s V0 inlet velocity of shell side, m/s z axial coordinate, m
Greek symbols ε membrane porosity η viscosity, kg/m.s ρ density, kg/m3
Abbreviations EXP experimental FEM finite element method HFMC hollow-fiber membrane contactor MOD modeling SCF supercritical fluid SFE supercritical fluid extraction 2D two dimensional
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