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Modelling of a hollow fibre ceramic contactor for SO2 absorption
Separation and Purification Technology 72 (2010) 174–179
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Modelling of a hollow fibre ceramic contactor for SO2 absorption P. Luis ∗ , A. Garea, A. Irabien Departamento de Ingeniería Química y Química Inorgánica, Universidad de Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
a r t i c l e
i n f o
Article history: Received 30 December 2009 Received in revised form 3 February 2010 Accepted 4 February 2010 Keywords: Process intensification Sulfur dioxide recovery Membrane contactor Mass transfer modelling
a b s t r a c t Process intensification allows significant improvements in chemical manufacturing and processing, leading to cheaper, safer and cleaner technologies. Recovery of sulfur dioxide from gas emissions using a membrane device instead of dispersive absorption (e.g. scrubbers) may intensify the process and it is in the spotlight of many investigations. This work develops the modelling of a ceramic hollow fibre membrane contactor used as membrane device in SO2 absorption. The modelling of mass transfer through the membrane is performed in order to evaluate the technical possibilities of the process. The effect of partial wetting on the mass transfer and the influence that operation conditions have on the process efficiency are evaluated. Solvent selection is an important variable to be taken into account in the technical application of the process; this variable is studied through the Henry’s law constant (H). © 2010 Elsevier B.V. All rights reserved.
1. Introduction Recovery of sulfur dioxide from gas streams is a key issue due to economic and environmental considerations. For instance, in the zinc oxide manufacture, a gas stream with around 5 vol.% of sulfur dioxide is generated during the roasting of zinc sulfide [1], which has to be recovered. Some organic solvents are widely used as absorption liquids to recover sulfur dioxide because of their high affinity and reversible reaction, leading to a regenerative process [2–4]. For example, N,Ndimethylaniline is an aromatic amine used for this application due to its high selectivity towards sulfur dioxide [5,6], allowing its separation and concentration. Gas/liquid operations are traditionally performed by means of dispersive contacts (e.g. scrubbers). However, a disadvantage of using scrubbers and other systems in which a direct contact between the gas stream and the liquid occurs is the interdependence of the fluid phases, which can produce unloading or flooding [7]. Solvent losses are also a concerning issue because they might involve serious risks due to solvent toxicity. In the case of the ASARCO process [5], solvent losses are around 0.6–0.8 kg of N,N-dimethylaniline per ton of sulfur dioxide recovered. Thus, process intensification to develop an environmentally friendly process has to be carried out. The substitution of the dispersive equipment by a membrane device intensifies the process [8–10] while increasing process efficiency and reducing solvent losses. The intensification is produced due to the compactness (high area/volume ratio) of membrane
∗ Corresponding author. Tel.: +34 942200931; fax: +34 942201591. E-mail addresses: [email protected], [email protected] (P. Luis). 1383-5866/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2010.02.003
operations, in addition to their flexibility and their modularity, since the maximization of the interfacial area (or surface-to-volume ratios) through which the mass transfer takes place is considered as one of the principles of process intensification outlined by Van Gerven and Stankiewicz (2009) [11]. Furthermore, membrane devices show a number of interesting advantages, such as controlled interfacial area and independent control of gas and liquid flow rates [7,12–14]. Membrane processes have been investigated extensively for a wide range of applications [14–17] and gas–liquid separations are reaching great interest in recent research for acid gases recovery [18–29]. Basically, it combines the conventional operation of gas absorption into solvents and a membrane contactor as a mass transfer device [14]. Suitable membrane equipment is a hollow fibre module with gas and liquid flowing on the opposite sides of the membrane and a fluid/fluid interface at the mouth of the membrane pores. Mass transfer takes place by diffusion across the interface and since the membrane itself does not lead usually to selectivity in the separation, the driving force is a concentration gradient based on solubility [19]. Thus, the selection of the absorption liquid may be a key issue in the process design. In addition, since the membrane introduces a new resistance to mass transfer, it must be considered in the equipment design [30]. In previous papers [27,29], a membrane-based gas–liquid absorption process was developed to recover sulfur dioxide leading to a zero solvent emission process. A ceramic hollow fibre membrane contactor was used as the membrane device and N,N-dimethylaniline was the absorption liquid. The mass transfer through the contactor was experimentally studied and it was observed that membrane wetting took place, increasing the mass transfer resistance according to the recent literature [31–41].
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179 Table 1 Hollow fibre membrane module.
Nomenclature A C¯ SO2 CSO2 CSO2 ,sat ∗ CSO
2
DSO2 Deff di do Gzext Gzint H Km Kmg L n P Qg r rcont re ri ro S Shm Shmg
175
membrane area, m2 dimensionless sulfur dioxide concentration sulfur dioxide concentration, mol m−3 saturation concentration of sulfur dioxide in the liquid phase, mol m−3 sulfur dioxide concentration at the membrane–liquid interface, mol m−3 diffusion coefficient, m2 s−1 effective diffusivity, m2 s−1 inside diameter of the hollow fibre, m outside diameter of the hollow fibre, m Graetz number referred to the shell side (Gzext = −1 um,g · do2 · DSO · L−1 ) 2 ,g Graetz number referred to the tube side (Gzint = −1 um,l · di2 · DSO · L−1 ) ,l
Fibre material
␣-Al2 O3
Housing material Potting material Fibre o.d. (do ), m Fibre i.d. (di ), m Fibre length (L), m Number of fibres (n) Effective membrane area, m2 Pore size of the fibre, nm Membrane porosity (ε) Tortuosity ()
316 stainless steel Epoxy 4 × 10−3 3 × 10−3 0.44 280 0.8 100 0.316 86
membrane and also the influence that operating conditions (gas and liquid flow rates) and solvent affinity (H) have on the process efficiency to fulfil a specific target of sulfur dioxide recovery according to the environmental or technical requirements.
2
Henry’s law constant: the molar concentration in the gas divided by that in the liquid mass transfer coefficient of the membrane, m s−1 mass transfer coefficient of the non-wetted membrane, m s−1 fibre length, m number of fibres sulfur dioxide production, t yr−1 gas flow, m3 h−1 radial coordinate position radius of the membrane contactor, m free surface radius according to Happel’s model, m inner radius of the fibre, m outer radius of the fibre, m geometric factor, S = (ro − ri /ro · ln(ro /ri )) −1 Sherwood number (Shm = Km · S · ro · DSO ) 2 Sherwood number of non-wetted membrane −1 (Shmg = Kmg · S · ro · DSO )
2. Mass transfer device
effective Sherwood number (Sheff = Shm · H −1 ) velocity, m s−1 maximum velocity, m s−1 average velocity, m s−1 process efficiency axial coordinate position, m dimensionless axial coordinate position
In order to describe the mass transfer in the hollow fibre membrane contactor, a mass balance has been applied in the shell and tube sides. Mass transfer takes place through the membrane pores without mixing between phases. The fluid flow is described using the laminar flow model in the tube side and the Happel’s free surface model [47] in the shell side. This model assumes that the fibres are distributed evenly through the shell space, which allows the results obtained with a single fibre to be generalized to the entire module [14]. The coordinates of a fibre are shown in Fig. 1. The radial position of r = 0 is the center of a fibre and the radial distances ri , ro and re are the inner radius, outer radius and Happel’s free distance of the fibre. The axial distance of z = 0 means the inlet position of a fibre and the axial distance of z = L represents the outlet position of a fibre. The gas mixture with sulfur dioxide and air is fed to the shell side at z = 0 and the liquid is passed through the tube side at z = L. Sulfur dioxide is removed from the mixture by diffusing through the membrane and then, absorbing/reacting with the solvent. It is assumed that
In previous works [27,29], an experimental study was carried out using a commercially available ceramic hollow fibre membrane module (Hyflux Membranes® , The Netherlands) as the gas–liquid contactor in order to remove sulfur dioxide using N,Ndimethylaniline as the absorption liquid. This contactor is the mass transfer device in this work. Some features are shown in Table 1. The ceramic fibres are made of ␣-Al2 O3 , ensuring a total chemical compatibility with the organic solvent, and they are asymmetric with a membrane layer thickness of 20 m (pore diameter = 100 nm) and a total thickness of 500 m. A gas stream made of sulfur dioxide and air is fed through the shell side while the liquid is flowing in counter current through the tube side. Details of the experimental system are shown elsewhere [27,29,37]. 3. Model development
2
Sheff uz umax um X z z¯
Subscripts g gas l liquid in inlet of the contactor out outlet of the contactor Greek letters ı membrane thickness, m ε membrane porosity packing density of the module dimensionless radial coordinate position tortuosity
In this paper, a steady state model is developed [e.g. 12,42–46] to describe the mass transfer of sulfur dioxide in the ceramic hollow fibre membrane contactor using N,N-dimethylaniline as the absorption liquid. The model describes the mass transfer in the gas and liquid phases and the corresponding dimensionless equations for both phases have been solved simultaneously. It allows studying the effect of membrane wetting on the mass transfer through the
Fig. 1. Axial and radial coordinates of a fibre.
176
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179
um,g do2 (Graetz number in the shell side, with do = 2ro )(7c) DSO2 ,g L
local equilibrium at the fluid/fluid interface takes place and mass transfer is only produced by diffusion.
Gzext =
3.1. Outside the fibre
The resulting dimensionless mass balance and boundary conditions are:
The outside of the fibre is described according to the following assumptions: (1) steady state and isothermal condition; (2) no axial diffusion; (3) using Happel’s free surface model [47] to characterize the velocity profile at the shell side; (4) the physical properties of the fluid were constant; (5) constant shell-side pressures. Based on the Happel’s free surface model [47], only a portion of the fluid surrounding the fibre is considered, which may be approximated as a circular cross section [44]. The partial differential equation of the mass balance for cylindrical coordinates is obtained using Fick’s law of diffusion and it is given as follows:
∂C¯ SO2 ,g 1 ∂ Gzext · f (¯r ) · = 2 ∂¯z ∂
uz,g
∂CSO2 ,g ∂z
= DSO2 ,g
1 ∂ r ∂r
r
∂CSO2 ,g
r 2 o
·
re
(2) 2
=
2
(r/re ) − (ro /re ) + 2 · ln(ro /r) 4
o
·
re
∂
(8)
∂ 2
2
(¯r · ro /re ) − (ro /re ) + 2 · ln(1/r) 4
2
3 + (ro /re ) − 4 · (ro /re ) + 4 · ln(ro /re )
=0
∂ ∂C¯ SO2 ,g
∂C¯ SO2 ,g
(9)
(10a)
= Shm · (C¯ SO2 ,g − C¯ SO2 ,l )
(10b)
C¯ SO2 ,g = 1
(10c)
In addition, the sulfur dioxide removal efficiency is defined as: X = (1 − C¯ SO2 ,g,¯z=1 )
(11)
where C¯ SO2 ,g,¯z=1 is the dimensionless sulfur dioxide concentration in the gas phase at the outlet of the membrane device z¯ = 1.
2
3 + (ro /re ) − 4 · (ro /re ) + 4 · ln(ro /re )
z¯ = 0,
r 2
∂C¯ SO2 ,g
re , ro
= 1,
uz,g = umax,g · f (r) = 2um,g · f (r)
f (¯r ) = 1 −
(1)
∂r
According to the Happel’s free surface model [47], the velocity profile in the shell side may be deduced, obtaining the following equations, which have been applied by several authors [e.g. 12,42,44]:
f (r) = 1 −
(3)
3.2. Inside the fibre
where re is the free surface radius defined as: re =
1 0.5
· ro
(4)
and is the fibre packing density, calculated as: =
n · ro2
(5)
2 rcont
where n is the number of fibres and rcont is the radius of the hollow fibre contactor. The boundary conditions are the following ∂CSO2 ,g
r = re ,
∂r
= 0;
∂CSO2 ,g
(symmetry condition) ∗ = Km · S · (CSO2 ,g − CSO
r = ro ,
DSO2 ,g
z = 0,
CSO2 ,g = CSO2 ,in
∂r
2 ,g
(6a) );
Shm =
z z¯ = , L
(6c)
Km · S · ro DSO2 ,g
C¯ SO2 ,g =
CSO2 ,g CSO2 ,in
(Sherwood number)
uz,l
∂CSO2 ,l ∂z
(7a) (7b)
= DSO2 ,l
1 ∂ r ∂r
r
∂CSO2 ,l
(12)
∂r
When the velocity is fully developed in a laminar flow, the axial velocity can be written as
(6b)
where DSO2 ,g is the diffusion coefficient of sulfur dioxide in the gas ∗ phase, S is a geometric factor based on the outer radius and CSO 2 ,g is the concentration of sulfur dioxide in the gas phase in equilibrium with the liquid phase at the membrane–liquid interface. It is assumed that Henry’s law can be applied to establish a relation∗ ship between both phases. Thus, CSO = H · CSO2 ,l , where H is the 2 ,g Henry’s law constant. According to Eq. (6b), the mass transfer through the membrane is described in terms of a mass transfer coefficient (Km ) which involves the assumption of a single resistance of the membrane and linear profile of sulfur dioxide concentration through the thickness of the membrane. The differential mass balance in Eq. (1) was made dimensionless by introducing the following dimensionless variables: r = , ro
The absorption liquid flows through the lumen of the fibre and the following assumptions were utilized: (1) Steady state and isothermal condition; (2) no axial diffusion; (3) fully developed parabolic liquid velocity profile in the hollow fibre; (4) the physical properties of the fluid were constant and (5) constant tube-side pressure. Considering these assumptions, the mass conservation equation inside hollow fibres is given as [48]
uz,l = umax,l 1 −
r 2 ri
= 2um,l 1 −
Eq. (11) can be rewritten as
2um,l 1 −
r 2 ∂C
SO2 ,l
ri
∂z
= DSO2 ,l
r 2
1 ∂ r ∂r
(13)
ri
r
∂CSO2 ,l ∂r
(14)
The boundary conditions are the following r = 0,
∂CSO2 ,l ∂r
=0
∂CSO2 ,l
r = ri ,
DSO2 ,l
z = L,
CSO2 ,l = 0
∂r
(symmetry condition) = DSO2 ,g
∂CSO2 ,g ∂r
(15a) (15b) (15c)
where DSO2 ,l is the diffusion coefficient of sulfur dioxide in the liquid phase and it is assumed that the liquid does not have or have a negligible quantity of sulfur dioxide at the inlet of the liquid stream (z = L). The bulk average or ‘mixing cup’ values of the sulfur dioxide concentration in the liquid phase at z = 0 (liquid outlet) is defined
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179 Table 2 Model parameters.
as
ri 2 ri C u 2r dr r 4 0 SO2 ,l z,l CSO2 ,z=0 = r dr (16) = 2 CSO2 ,l 1 − ri 0
uz,l 2r dr
DSO2 ,DMA (m2 s−1 )a DSO2 ,g (m2 s−1 )b Hc
ri
ri
0
r¯
∂C¯ SO2 ,l
∂¯r
(17)
with the boundary conditions r¯ = 0, r¯ = 1, z¯ = 1,
Shmg =
∂C¯ SO2 ,l
=0
∂¯r ∂C¯ SO2 ,l
=
∂¯r
(18a)
∂C¯ SO2 ,g ∂¯r
·
DSO2 ,g DSO2 ,l
·H
C¯ SO2 ,l = 0
(18b) (18c)
where the dimensionless variables are defined as r¯ =
r , ri
Gzint =
z , L
z¯ =
um,l di2 DSO2 ,l L
C¯ SO2 =
CSO2 CSO2 ,sat
(19a)
(Graetz number in the tube side, with di = 2ri )(19b)
The dimensionless mixing cup may be also rewritten as
1 C¯ SO2 ,l [1 − r¯ 2 ]¯r d¯r
C¯ SO2 ,l,¯z=0 = 4
(20)
0
The numerical solutions of Eqs. (7)–(10) and (17)–(20) are obtained using the commercial software Aspen Custom Modeler (Aspen Technology Inc., Cambridge, MA). The discretization was carried out in the radial and axial directions, considering two dimensionless radial directions: r¯ and and one dimensionless axial direction: z¯ . The 4th Order Central Finite Difference (CDF4) was applied for both axial and radial directions. 4. Results and discussion Modelling of sulfur dioxide absorption in the hollow fibre membrane contactor allows the process design and selection of the most appropriate operation conditions according to the efficiency requirements. The effect that membrane wetting has on mass transfer will be considered in order to evaluate the technical viability of the studied gas–liquid membrane process for sulfur dioxide recovery. 4.1. Mass transfer through the membrane: effect of partial wetting From the experimental results obtained in previous works [27], the process efficiency, defined according to Eq. (11), was observed to be around 0.45 under the studied experimental conditions (CSO2 ,in = 0.15–4.8 vol.%; Gzext = 1.69 × 10−2 ; Gzint = 82.02). Taking into account this process efficiency and the parameters listed in Table 2 for the studied system, the Sherwood number of the membrane can be achieved from the performed model. It results in a value of Shm = 10−3 . If membrane pores were filled with gas, a theoretical value Shmg could be calculated according to the following equations: Kmg =
Deff,g ı
=
DSO2 ,g · ε ·ı
(21)
2.10 × 10−9 1.26 × 10−5 1.31 × 10−3
a Diffusion coefficient of SO2 in N,N-dimethylaniline. Estimated from the literature [48]. b Diffusion coefficient of SO2 in air. Estimated from the literature [48]. c Calculated from the industrial process for a gas stream with 5 vol.% SO2 [28].
The above model equations can be rewritten in the dimensionless form as ∂C¯ SO2 ,l Gzint 1 ∂ = [1 − r¯ 2 ] 2 r¯ ∂¯r ∂¯z
177
Kmg · S · ro DSO2 ,g
(22)
where Kmg is the theoretical mass transfer coefficient of the non-wetted membrane, Deff,g is the effective diffusivity, ε is the membrane porosity, is the tortuosity and ı is the membrane thickness (see Table 1). This theoretical Sherwood number takes a value of 12.8 × 10−3 , differing from the real one (10−3 ) by one order of magnitude. Membrane wetting may explain the differences between the experimental and expected values. According to the literature [49], the effective diffusivity is around 10−8 to 10−12 m2 s−1 when a liquid is occluded in a solid matrix. For the studied system, this value is Deff,g = 6.34 × 10−9 m2 s−1 , which is in good agreement with the membrane wetting hypothesis. A deeper study based on the experimental results is shown in a previous paper [29]. In the recent literature [29,34,36,38,39,50], the Henry’s law coefficient and the fraction of wetting are considered as the main parameters to study the membrane wetting mechanism. However, because of the lack of certainty in these considerations, in this work, the definition of a new parameter that includes the Henry’s law constant and the mass transfer coefficient of the membrane is considered. This parameter is the effective Sherwood number and it is defined as Sheff =
Shm H
(23)
Thus, the uncertainty caused for both parameters due to the membrane wetting can be grouped into one parameter. Membrane wetting involves a substantial decrease in the mass transfer flux through the membrane due to the formation of a stagnant film of liquid into the pores of the membrane which makes difficult the diffusion of sulfur dioxide through the membrane. Higher membrane resistance to mass transfer leads to a lower Sherwood number than that if a non-wetted mode is considered. Fig. 2 shows the effect that membrane wetting, expressed by different values of Sheff calculated from varying Shm (see Eq. (23)), has on the process efficiency for a specified liquid velocity (Gzint = 82.02). The dotted line refers to a hypothetical situation with membrane pores completely filled with gas, which shows the best performance (Shm,g = 12.8 × 10−3 ). If membrane wetting takes place, which means a decrease of the effective Sherwood number (Sheff ), a substantial decrease is observed in the gas treatment capacity (lower Gzext ) to achieve a specified process efficiency. 4.2. Influence of operation conditions Fig. 3 shows the process efficiency as a function of the Graetz number referred to the shell side (Gzext ), i.e. gas phase, and to the tube side (Gzint ), i.e. liquid phase. As could be expected, the higher the Gzext , the lower the process efficiency. The residence time of the gas phase in the contactor decreases when the gas flow rate increases, leading to a poorer mass transfer in the contactor. It can be also observed that the gas treatment capacity can be improved by an increase in the liquid flow rate, achieving specified process
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P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179
Fig. 2. Effect of partial wetting, expressed in terms of Sheff (- - - non-wetted mode; — membrane wetting).
efficiency; however, a limit is found: when Gzint > 1, the treatment capacity is not improved because the concentration of sulfur dioxide in the liquid phase is very far from the saturation value and it does not have any influence on the absorption process. Thus, an increase of the liquid velocity over that value will not lead to an improvement of the process efficiency. 4.3. Influence of the Henry’s law constant (solvent selection) Solvent selection is a key issue to ensure a good chemical resistance of the contactor materials and prevent the membrane wetting. However, its effect on the process efficiency in terms of its affinity (i.e. the Henry’s law constant) towards the target component is also worth noting. Fig. 4 shows different lines corresponding to different values of H. Continuous lines have been calculated under the experimental conditions for the gas phase (Gzext = 1.69 × 10−2 ) considered in previous works [27,29] and the experimental mass transfer resistance of the membrane (Shm = 10−3 ). Dotted lines have been calculated for other values of Gzext and Shm and it can be concluded that solvent affinity does not determine the maximum process efficiency that can be achieved. This is because the maximum value depends on the residence time of the gas phase in the contactor (Gzext ) and the mass transfer through the membrane (Shm ). Other combinations between Gzext and Shm when Gzint is higher enough to avoid the influence of liquid phase are shown in Table 3. The mass transfer is
Fig. 4. Influence of the solvent affinity on the process efficiency.
Table 3 Influence of Gzext and Shm on the maximum process efficiency. Gzext × 102
Shm × 103
Xmax
1.69* 0.30 1.69* 0.30
1.00* 1.00* 10.0 0.30
0.42 0.96 1.00 0.62
*
Experimental values considered in previous studies [27,29].
controlled by the membrane resistance when the concentration of sulfur dioxide in the liquid is far from the saturation [27,29], thus, although the driving force may increase, the mass transfer rate is limited. This means that only by increasing the residence time of gas through the contactor it is possible to improve the process efficiency for fixed Shm . Also, Table 3 shows an example of a possible situation where the process efficiency is equal to one. Hence, technical viability is demonstrated but an economic evaluation has to be performed to determine the real application of membrane devices as a function of technical requirements. As shown, solvent affinity does not establish the maximum process efficiency but it has an important influence on the velocity of the liquid required to fulfil the required process efficiency: the lower the liquid affinity towards sulfur dioxide (higher values of H), the higher the liquid velocity required (higher Gzint ). It involves a bigger pressure drop through the hollow fibre membrane contactor, leading to an increase in the operating costs (e.g. pumping cost).
5. Conclusions
Fig. 3. Influence of operation conditions on process efficiency (Gzext refers to gas phase; Gzint refers to liquid phase).
A mathematical model considering diffusion-controlled mass transfer has been developed for the sulfur dioxide absorption process using a hollow fibre membrane module. Previous work shows that membrane wetting may be responsible for the decrease of the mass transfer compared to the theoretical one if membrane pores would be filled with gas. Thus, the effect that membrane wetting has on the process efficiency has been studied and confirmed in the mathematical modelling. The model also allows the selection of the best operating conditions, expressed in terms of the Graetz numbers in the shell (i.e. gas phase) and tube (i.e. liquid phase) sides, according to specific requirements. The effect of the solvent affinity on the process efficiency has been described.
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179
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Contents lists available at ScienceDirect
Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Modelling of a hollow fibre ceramic contactor for SO2 absorption P. Luis ∗ , A. Garea, A. Irabien Departamento de Ingeniería Química y Química Inorgánica, Universidad de Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
a r t i c l e
i n f o
Article history: Received 30 December 2009 Received in revised form 3 February 2010 Accepted 4 February 2010 Keywords: Process intensification Sulfur dioxide recovery Membrane contactor Mass transfer modelling
a b s t r a c t Process intensification allows significant improvements in chemical manufacturing and processing, leading to cheaper, safer and cleaner technologies. Recovery of sulfur dioxide from gas emissions using a membrane device instead of dispersive absorption (e.g. scrubbers) may intensify the process and it is in the spotlight of many investigations. This work develops the modelling of a ceramic hollow fibre membrane contactor used as membrane device in SO2 absorption. The modelling of mass transfer through the membrane is performed in order to evaluate the technical possibilities of the process. The effect of partial wetting on the mass transfer and the influence that operation conditions have on the process efficiency are evaluated. Solvent selection is an important variable to be taken into account in the technical application of the process; this variable is studied through the Henry’s law constant (H). © 2010 Elsevier B.V. All rights reserved.
1. Introduction Recovery of sulfur dioxide from gas streams is a key issue due to economic and environmental considerations. For instance, in the zinc oxide manufacture, a gas stream with around 5 vol.% of sulfur dioxide is generated during the roasting of zinc sulfide [1], which has to be recovered. Some organic solvents are widely used as absorption liquids to recover sulfur dioxide because of their high affinity and reversible reaction, leading to a regenerative process [2–4]. For example, N,Ndimethylaniline is an aromatic amine used for this application due to its high selectivity towards sulfur dioxide [5,6], allowing its separation and concentration. Gas/liquid operations are traditionally performed by means of dispersive contacts (e.g. scrubbers). However, a disadvantage of using scrubbers and other systems in which a direct contact between the gas stream and the liquid occurs is the interdependence of the fluid phases, which can produce unloading or flooding [7]. Solvent losses are also a concerning issue because they might involve serious risks due to solvent toxicity. In the case of the ASARCO process [5], solvent losses are around 0.6–0.8 kg of N,N-dimethylaniline per ton of sulfur dioxide recovered. Thus, process intensification to develop an environmentally friendly process has to be carried out. The substitution of the dispersive equipment by a membrane device intensifies the process [8–10] while increasing process efficiency and reducing solvent losses. The intensification is produced due to the compactness (high area/volume ratio) of membrane
∗ Corresponding author. Tel.: +34 942200931; fax: +34 942201591. E-mail addresses: [email protected], [email protected] (P. Luis). 1383-5866/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2010.02.003
operations, in addition to their flexibility and their modularity, since the maximization of the interfacial area (or surface-to-volume ratios) through which the mass transfer takes place is considered as one of the principles of process intensification outlined by Van Gerven and Stankiewicz (2009) [11]. Furthermore, membrane devices show a number of interesting advantages, such as controlled interfacial area and independent control of gas and liquid flow rates [7,12–14]. Membrane processes have been investigated extensively for a wide range of applications [14–17] and gas–liquid separations are reaching great interest in recent research for acid gases recovery [18–29]. Basically, it combines the conventional operation of gas absorption into solvents and a membrane contactor as a mass transfer device [14]. Suitable membrane equipment is a hollow fibre module with gas and liquid flowing on the opposite sides of the membrane and a fluid/fluid interface at the mouth of the membrane pores. Mass transfer takes place by diffusion across the interface and since the membrane itself does not lead usually to selectivity in the separation, the driving force is a concentration gradient based on solubility [19]. Thus, the selection of the absorption liquid may be a key issue in the process design. In addition, since the membrane introduces a new resistance to mass transfer, it must be considered in the equipment design [30]. In previous papers [27,29], a membrane-based gas–liquid absorption process was developed to recover sulfur dioxide leading to a zero solvent emission process. A ceramic hollow fibre membrane contactor was used as the membrane device and N,N-dimethylaniline was the absorption liquid. The mass transfer through the contactor was experimentally studied and it was observed that membrane wetting took place, increasing the mass transfer resistance according to the recent literature [31–41].
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179 Table 1 Hollow fibre membrane module.
Nomenclature A C¯ SO2 CSO2 CSO2 ,sat ∗ CSO
2
DSO2 Deff di do Gzext Gzint H Km Kmg L n P Qg r rcont re ri ro S Shm Shmg
175
membrane area, m2 dimensionless sulfur dioxide concentration sulfur dioxide concentration, mol m−3 saturation concentration of sulfur dioxide in the liquid phase, mol m−3 sulfur dioxide concentration at the membrane–liquid interface, mol m−3 diffusion coefficient, m2 s−1 effective diffusivity, m2 s−1 inside diameter of the hollow fibre, m outside diameter of the hollow fibre, m Graetz number referred to the shell side (Gzext = −1 um,g · do2 · DSO · L−1 ) 2 ,g Graetz number referred to the tube side (Gzint = −1 um,l · di2 · DSO · L−1 ) ,l
Fibre material
␣-Al2 O3
Housing material Potting material Fibre o.d. (do ), m Fibre i.d. (di ), m Fibre length (L), m Number of fibres (n) Effective membrane area, m2 Pore size of the fibre, nm Membrane porosity (ε) Tortuosity ()
316 stainless steel Epoxy 4 × 10−3 3 × 10−3 0.44 280 0.8 100 0.316 86
membrane and also the influence that operating conditions (gas and liquid flow rates) and solvent affinity (H) have on the process efficiency to fulfil a specific target of sulfur dioxide recovery according to the environmental or technical requirements.
2
Henry’s law constant: the molar concentration in the gas divided by that in the liquid mass transfer coefficient of the membrane, m s−1 mass transfer coefficient of the non-wetted membrane, m s−1 fibre length, m number of fibres sulfur dioxide production, t yr−1 gas flow, m3 h−1 radial coordinate position radius of the membrane contactor, m free surface radius according to Happel’s model, m inner radius of the fibre, m outer radius of the fibre, m geometric factor, S = (ro − ri /ro · ln(ro /ri )) −1 Sherwood number (Shm = Km · S · ro · DSO ) 2 Sherwood number of non-wetted membrane −1 (Shmg = Kmg · S · ro · DSO )
2. Mass transfer device
effective Sherwood number (Sheff = Shm · H −1 ) velocity, m s−1 maximum velocity, m s−1 average velocity, m s−1 process efficiency axial coordinate position, m dimensionless axial coordinate position
In order to describe the mass transfer in the hollow fibre membrane contactor, a mass balance has been applied in the shell and tube sides. Mass transfer takes place through the membrane pores without mixing between phases. The fluid flow is described using the laminar flow model in the tube side and the Happel’s free surface model [47] in the shell side. This model assumes that the fibres are distributed evenly through the shell space, which allows the results obtained with a single fibre to be generalized to the entire module [14]. The coordinates of a fibre are shown in Fig. 1. The radial position of r = 0 is the center of a fibre and the radial distances ri , ro and re are the inner radius, outer radius and Happel’s free distance of the fibre. The axial distance of z = 0 means the inlet position of a fibre and the axial distance of z = L represents the outlet position of a fibre. The gas mixture with sulfur dioxide and air is fed to the shell side at z = 0 and the liquid is passed through the tube side at z = L. Sulfur dioxide is removed from the mixture by diffusing through the membrane and then, absorbing/reacting with the solvent. It is assumed that
In previous works [27,29], an experimental study was carried out using a commercially available ceramic hollow fibre membrane module (Hyflux Membranes® , The Netherlands) as the gas–liquid contactor in order to remove sulfur dioxide using N,Ndimethylaniline as the absorption liquid. This contactor is the mass transfer device in this work. Some features are shown in Table 1. The ceramic fibres are made of ␣-Al2 O3 , ensuring a total chemical compatibility with the organic solvent, and they are asymmetric with a membrane layer thickness of 20 m (pore diameter = 100 nm) and a total thickness of 500 m. A gas stream made of sulfur dioxide and air is fed through the shell side while the liquid is flowing in counter current through the tube side. Details of the experimental system are shown elsewhere [27,29,37]. 3. Model development
2
Sheff uz umax um X z z¯
Subscripts g gas l liquid in inlet of the contactor out outlet of the contactor Greek letters ı membrane thickness, m ε membrane porosity packing density of the module dimensionless radial coordinate position tortuosity
In this paper, a steady state model is developed [e.g. 12,42–46] to describe the mass transfer of sulfur dioxide in the ceramic hollow fibre membrane contactor using N,N-dimethylaniline as the absorption liquid. The model describes the mass transfer in the gas and liquid phases and the corresponding dimensionless equations for both phases have been solved simultaneously. It allows studying the effect of membrane wetting on the mass transfer through the
Fig. 1. Axial and radial coordinates of a fibre.
176
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179
um,g do2 (Graetz number in the shell side, with do = 2ro )(7c) DSO2 ,g L
local equilibrium at the fluid/fluid interface takes place and mass transfer is only produced by diffusion.
Gzext =
3.1. Outside the fibre
The resulting dimensionless mass balance and boundary conditions are:
The outside of the fibre is described according to the following assumptions: (1) steady state and isothermal condition; (2) no axial diffusion; (3) using Happel’s free surface model [47] to characterize the velocity profile at the shell side; (4) the physical properties of the fluid were constant; (5) constant shell-side pressures. Based on the Happel’s free surface model [47], only a portion of the fluid surrounding the fibre is considered, which may be approximated as a circular cross section [44]. The partial differential equation of the mass balance for cylindrical coordinates is obtained using Fick’s law of diffusion and it is given as follows:
∂C¯ SO2 ,g 1 ∂ Gzext · f (¯r ) · = 2 ∂¯z ∂
uz,g
∂CSO2 ,g ∂z
= DSO2 ,g
1 ∂ r ∂r
r
∂CSO2 ,g
r 2 o
·
re
(2) 2
=
2
(r/re ) − (ro /re ) + 2 · ln(ro /r) 4
o
·
re
∂
(8)
∂ 2
2
(¯r · ro /re ) − (ro /re ) + 2 · ln(1/r) 4
2
3 + (ro /re ) − 4 · (ro /re ) + 4 · ln(ro /re )
=0
∂ ∂C¯ SO2 ,g
∂C¯ SO2 ,g
(9)
(10a)
= Shm · (C¯ SO2 ,g − C¯ SO2 ,l )
(10b)
C¯ SO2 ,g = 1
(10c)
In addition, the sulfur dioxide removal efficiency is defined as: X = (1 − C¯ SO2 ,g,¯z=1 )
(11)
where C¯ SO2 ,g,¯z=1 is the dimensionless sulfur dioxide concentration in the gas phase at the outlet of the membrane device z¯ = 1.
2
3 + (ro /re ) − 4 · (ro /re ) + 4 · ln(ro /re )
z¯ = 0,
r 2
∂C¯ SO2 ,g
re , ro
= 1,
uz,g = umax,g · f (r) = 2um,g · f (r)
f (¯r ) = 1 −
(1)
∂r
According to the Happel’s free surface model [47], the velocity profile in the shell side may be deduced, obtaining the following equations, which have been applied by several authors [e.g. 12,42,44]:
f (r) = 1 −
(3)
3.2. Inside the fibre
where re is the free surface radius defined as: re =
1 0.5
· ro
(4)
and is the fibre packing density, calculated as: =
n · ro2
(5)
2 rcont
where n is the number of fibres and rcont is the radius of the hollow fibre contactor. The boundary conditions are the following ∂CSO2 ,g
r = re ,
∂r
= 0;
∂CSO2 ,g
(symmetry condition) ∗ = Km · S · (CSO2 ,g − CSO
r = ro ,
DSO2 ,g
z = 0,
CSO2 ,g = CSO2 ,in
∂r
2 ,g
(6a) );
Shm =
z z¯ = , L
(6c)
Km · S · ro DSO2 ,g
C¯ SO2 ,g =
CSO2 ,g CSO2 ,in
(Sherwood number)
uz,l
∂CSO2 ,l ∂z
(7a) (7b)
= DSO2 ,l
1 ∂ r ∂r
r
∂CSO2 ,l
(12)
∂r
When the velocity is fully developed in a laminar flow, the axial velocity can be written as
(6b)
where DSO2 ,g is the diffusion coefficient of sulfur dioxide in the gas ∗ phase, S is a geometric factor based on the outer radius and CSO 2 ,g is the concentration of sulfur dioxide in the gas phase in equilibrium with the liquid phase at the membrane–liquid interface. It is assumed that Henry’s law can be applied to establish a relation∗ ship between both phases. Thus, CSO = H · CSO2 ,l , where H is the 2 ,g Henry’s law constant. According to Eq. (6b), the mass transfer through the membrane is described in terms of a mass transfer coefficient (Km ) which involves the assumption of a single resistance of the membrane and linear profile of sulfur dioxide concentration through the thickness of the membrane. The differential mass balance in Eq. (1) was made dimensionless by introducing the following dimensionless variables: r = , ro
The absorption liquid flows through the lumen of the fibre and the following assumptions were utilized: (1) Steady state and isothermal condition; (2) no axial diffusion; (3) fully developed parabolic liquid velocity profile in the hollow fibre; (4) the physical properties of the fluid were constant and (5) constant tube-side pressure. Considering these assumptions, the mass conservation equation inside hollow fibres is given as [48]
uz,l = umax,l 1 −
r 2 ri
= 2um,l 1 −
Eq. (11) can be rewritten as
2um,l 1 −
r 2 ∂C
SO2 ,l
ri
∂z
= DSO2 ,l
r 2
1 ∂ r ∂r
(13)
ri
r
∂CSO2 ,l ∂r
(14)
The boundary conditions are the following r = 0,
∂CSO2 ,l ∂r
=0
∂CSO2 ,l
r = ri ,
DSO2 ,l
z = L,
CSO2 ,l = 0
∂r
(symmetry condition) = DSO2 ,g
∂CSO2 ,g ∂r
(15a) (15b) (15c)
where DSO2 ,l is the diffusion coefficient of sulfur dioxide in the liquid phase and it is assumed that the liquid does not have or have a negligible quantity of sulfur dioxide at the inlet of the liquid stream (z = L). The bulk average or ‘mixing cup’ values of the sulfur dioxide concentration in the liquid phase at z = 0 (liquid outlet) is defined
P. Luis et al. / Separation and Purification Technology 72 (2010) 174–179 Table 2 Model parameters.
as
ri 2 ri C u 2r dr r 4 0 SO2 ,l z,l CSO2 ,z=0 = r dr (16) = 2 CSO2 ,l 1 − ri 0
uz,l 2r dr
DSO2 ,DMA (m2 s−1 )a DSO2 ,g (m2 s−1 )b Hc
ri
ri
0
r¯
∂C¯ SO2 ,l
∂¯r
(17)
with the boundary conditions r¯ = 0, r¯ = 1, z¯ = 1,
Shmg =
∂C¯ SO2 ,l
=0
∂¯r ∂C¯ SO2 ,l
=
∂¯r
(18a)
∂C¯ SO2 ,g ∂¯r
·
DSO2 ,g DSO2 ,l
·H
C¯ SO2 ,l = 0
(18b) (18c)
where the dimensionless variables are defined as r¯ =
r , ri
Gzint =
z , L
z¯ =
um,l di2 DSO2 ,l L
C¯ SO2 =
CSO2 CSO2 ,sat
(19a)
(Graetz number in the tube side, with di = 2ri )(19b)
The dimensionless mixing cup may be also rewritten as
1 C¯ SO2 ,l [1 − r¯ 2 ]¯r d¯r
C¯ SO2 ,l,¯z=0 = 4
(20)
0
The numerical solutions of Eqs. (7)–(10) and (17)–(20) are obtained using the commercial software Aspen Custom Modeler (Aspen Technology Inc., Cambridge, MA). The discretization was carried out in the radial and axial directions, considering two dimensionless radial directions: r¯ and and one dimensionless axial direction: z¯ . The 4th Order Central Finite Difference (CDF4) was applied for both axial and radial directions. 4. Results and discussion Modelling of sulfur dioxide absorption in the hollow fibre membrane contactor allows the process design and selection of the most appropriate operation conditions according to the efficiency requirements. The effect that membrane wetting has on mass transfer will be considered in order to evaluate the technical viability of the studied gas–liquid membrane process for sulfur dioxide recovery. 4.1. Mass transfer through the membrane: effect of partial wetting From the experimental results obtained in previous works [27], the process efficiency, defined according to Eq. (11), was observed to be around 0.45 under the studied experimental conditions (CSO2 ,in = 0.15–4.8 vol.%; Gzext = 1.69 × 10−2 ; Gzint = 82.02). Taking into account this process efficiency and the parameters listed in Table 2 for the studied system, the Sherwood number of the membrane can be achieved from the performed model. It results in a value of Shm = 10−3 . If membrane pores were filled with gas, a theoretical value Shmg could be calculated according to the following equations: Kmg =
Deff,g ı
=
DSO2 ,g · ε ·ı
(21)
2.10 × 10−9 1.26 × 10−5 1.31 × 10−3
a Diffusion coefficient of SO2 in N,N-dimethylaniline. Estimated from the literature [48]. b Diffusion coefficient of SO2 in air. Estimated from the literature [48]. c Calculated from the industrial process for a gas stream with 5 vol.% SO2 [28].
The above model equations can be rewritten in the dimensionless form as ∂C¯ SO2 ,l Gzint 1 ∂ = [1 − r¯ 2 ] 2 r¯ ∂¯r ∂¯z
177
Kmg · S · ro DSO2 ,g
(22)
where Kmg is the theoretical mass transfer coefficient of the non-wetted membrane, Deff,g is the effective diffusivity, ε is the membrane porosity, is the tortuosity and ı is the membrane thickness (see Table 1). This theoretical Sherwood number takes a value of 12.8 × 10−3 , differing from the real one (10−3 ) by one order of magnitude. Membrane wetting may explain the differences between the experimental and expected values. According to the literature [49], the effective diffusivity is around 10−8 to 10−12 m2 s−1 when a liquid is occluded in a solid matrix. For the studied system, this value is Deff,g = 6.34 × 10−9 m2 s−1 , which is in good agreement with the membrane wetting hypothesis. A deeper study based on the experimental results is shown in a previous paper [29]. In the recent literature [29,34,36,38,39,50], the Henry’s law coefficient and the fraction of wetting are considered as the main parameters to study the membrane wetting mechanism. However, because of the lack of certainty in these considerations, in this work, the definition of a new parameter that includes the Henry’s law constant and the mass transfer coefficient of the membrane is considered. This parameter is the effective Sherwood number and it is defined as Sheff =
Shm H
(23)
Thus, the uncertainty caused for both parameters due to the membrane wetting can be grouped into one parameter. Membrane wetting involves a substantial decrease in the mass transfer flux through the membrane due to the formation of a stagnant film of liquid into the pores of the membrane which makes difficult the diffusion of sulfur dioxide through the membrane. Higher membrane resistance to mass transfer leads to a lower Sherwood number than that if a non-wetted mode is considered. Fig. 2 shows the effect that membrane wetting, expressed by different values of Sheff calculated from varying Shm (see Eq. (23)), has on the process efficiency for a specified liquid velocity (Gzint = 82.02). The dotted line refers to a hypothetical situation with membrane pores completely filled with gas, which shows the best performance (Shm,g = 12.8 × 10−3 ). If membrane wetting takes place, which means a decrease of the effective Sherwood number (Sheff ), a substantial decrease is observed in the gas treatment capacity (lower Gzext ) to achieve a specified process efficiency. 4.2. Influence of operation conditions Fig. 3 shows the process efficiency as a function of the Graetz number referred to the shell side (Gzext ), i.e. gas phase, and to the tube side (Gzint ), i.e. liquid phase. As could be expected, the higher the Gzext , the lower the process efficiency. The residence time of the gas phase in the contactor decreases when the gas flow rate increases, leading to a poorer mass transfer in the contactor. It can be also observed that the gas treatment capacity can be improved by an increase in the liquid flow rate, achieving specified process
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Fig. 2. Effect of partial wetting, expressed in terms of Sheff (- - - non-wetted mode; — membrane wetting).
efficiency; however, a limit is found: when Gzint > 1, the treatment capacity is not improved because the concentration of sulfur dioxide in the liquid phase is very far from the saturation value and it does not have any influence on the absorption process. Thus, an increase of the liquid velocity over that value will not lead to an improvement of the process efficiency. 4.3. Influence of the Henry’s law constant (solvent selection) Solvent selection is a key issue to ensure a good chemical resistance of the contactor materials and prevent the membrane wetting. However, its effect on the process efficiency in terms of its affinity (i.e. the Henry’s law constant) towards the target component is also worth noting. Fig. 4 shows different lines corresponding to different values of H. Continuous lines have been calculated under the experimental conditions for the gas phase (Gzext = 1.69 × 10−2 ) considered in previous works [27,29] and the experimental mass transfer resistance of the membrane (Shm = 10−3 ). Dotted lines have been calculated for other values of Gzext and Shm and it can be concluded that solvent affinity does not determine the maximum process efficiency that can be achieved. This is because the maximum value depends on the residence time of the gas phase in the contactor (Gzext ) and the mass transfer through the membrane (Shm ). Other combinations between Gzext and Shm when Gzint is higher enough to avoid the influence of liquid phase are shown in Table 3. The mass transfer is
Fig. 4. Influence of the solvent affinity on the process efficiency.
Table 3 Influence of Gzext and Shm on the maximum process efficiency. Gzext × 102
Shm × 103
Xmax
1.69* 0.30 1.69* 0.30
1.00* 1.00* 10.0 0.30
0.42 0.96 1.00 0.62
*
Experimental values considered in previous studies [27,29].
controlled by the membrane resistance when the concentration of sulfur dioxide in the liquid is far from the saturation [27,29], thus, although the driving force may increase, the mass transfer rate is limited. This means that only by increasing the residence time of gas through the contactor it is possible to improve the process efficiency for fixed Shm . Also, Table 3 shows an example of a possible situation where the process efficiency is equal to one. Hence, technical viability is demonstrated but an economic evaluation has to be performed to determine the real application of membrane devices as a function of technical requirements. As shown, solvent affinity does not establish the maximum process efficiency but it has an important influence on the velocity of the liquid required to fulfil the required process efficiency: the lower the liquid affinity towards sulfur dioxide (higher values of H), the higher the liquid velocity required (higher Gzint ). It involves a bigger pressure drop through the hollow fibre membrane contactor, leading to an increase in the operating costs (e.g. pumping cost).
5. Conclusions
Fig. 3. Influence of operation conditions on process efficiency (Gzext refers to gas phase; Gzint refers to liquid phase).
A mathematical model considering diffusion-controlled mass transfer has been developed for the sulfur dioxide absorption process using a hollow fibre membrane module. Previous work shows that membrane wetting may be responsible for the decrease of the mass transfer compared to the theoretical one if membrane pores would be filled with gas. Thus, the effect that membrane wetting has on the process efficiency has been studied and confirmed in the mathematical modelling. The model also allows the selection of the best operating conditions, expressed in terms of the Graetz numbers in the shell (i.e. gas phase) and tube (i.e. liquid phase) sides, according to specific requirements. The effect of the solvent affinity on the process efficiency has been described.
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