The Specific Behaviour of NF Membranes in the Separation

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					The Specific Behaviour of NF Membranes in the Separation of High Ionic
Strength Electrolyte Solutions
A. Schönauer and W. M. Samhaber
Institute of Process Engineering
Johannes Kepler University Linz
Welser Strasse 42, A-4060 Leonding, Austria
Tel. + 43 70 672 50 90, Fax + 43 70 672 50 95


                                             ABSTRACT

   The behaviour of NF membranes in the separation of high ionic strength electrolyte solutions
composed of different charged ions is not yet clarified in a sufficient way. In this work the
measurements were carried out with single-salt solutions containing MgCl2, NaCl and Na2SO4 and this
salts in two different combinations of NaCl-MgCl2-H2O and NaCl-Na2SO4-H2O with varying feed
concentrations and different specific permeate flux.
   On the one hand in infenitely diluted binary solutions the membrane shows salt rejection behaviour
which is typical for a negatively charged membrane. On the other the results of membrane in
concentrated solutions cannot be explained by Donnan exclusion rather then differences at the
diffusion coefficient and structure of hydrated ions.
   The rejection of chloride in the ternary ion mixtures NaCl-Na2SO4-water in comparison with the
rejection of sodium in the ternary mixtures NaCl-MgCl2-water shows similary behaviours. The
transition of monovalent ion rejection from positive to negative values with an increase in the addition
of multivalent ions in the bulk feed is observable, independently of the charge number, for both of the
solution systems.



1. INTRODUCTION

   Pressure driven membrane processes are widely used today in different industrial applications. The
fractionation of high moleculare solutes like protein can be achieved by applying ultrafiltration (UF)
membranes, for the separation of low moleculare organic components from salts nanofiltration (NF) is
used and the production e.g. of drinking water from sea water is conventionally done by reverse
osmosis (RO). NF-membranes are to be positioned between RO- and UF-membranes. In the chemical
industry there is often required a selective separation of complex high ionic strength electrolyte
solutions. One of the most important features of nanofiltration membranes is their ability to separate
ions from water. A high rejection for multivalent ions is frequently combined with a moderate
rejection for monovalent ions. So the NF-membranes exhibit an extraordinary permselectivity for
mono- and divalent ions.
   The behaviour of nanofiltration (NF) membranes in the seperation of high ionic strength electrolyte
solutions composed of different charged ions is not yet clarified in a sufficient way. Many
investigations which have been reported in the recent years were carried out in systems with low salt
content (Peeters (1998), Bowen (1996), Hagmeyer (1998), Dey (2000)) and were discussing especially
the behaviour of divalent ions like sulfates in connection with other monovalent ions like chlorides
(Wang (1997)). Possible mechanisms for the separation of electrolytes by NF-membranes are (i)
sieving, (ii) electrostatic interactions between the membrane and the ions or between the ions mutually
and (iii) differences in diffusivity and solubility or a combination of these (Peeters (1998)) and the so
called hydration mechanism probably related to the changes in the dissolving ability of water and
solute in the active layer of the membrane (Yaroshchuk (1998)).
   By adding multivalent ions (such as sodium sulfate) to a solution of constant monovalent ion
concentration ( e.g. sodium chloride), monovalent ions are forced to permeate preferentially compared
to multivalent ions together with counter ions in order to maintain electroneutrality at both sides of the
membrane. The monovalent ions rejection decreases with increasing multivalent ions concentration
and even negative rejection coefficients can be observed. This is the so-called Donnan effect. In the
literature often this specific behaviour of a sodium chloride/sodium sulfate solution will be discussed
as a result of negative fixed charges in the active layer of the membrane but these effects in NF cannot
only be shown for anions but also in the same way are active for cations.
   In this paper, experiments with single salt solutions will be described which were carried out with a
commercially available polymeric nanofiltration membrane. Also in this research work two different
solution systems will be used to compare the rejection behaviour of a NF-membrane for divalent
cations with divalent anions both in a solution matrix of sodium chloride. The separation mechanism
of NF-membranes was investigated with different ionic systems and with higher ionic strength
solutions. These experiments will be compared to theoretical calculations describing ion transport
through membranes using models based on irreversible thermodynamics.


2. THEORY

   The transport of solutes through a membrane can be described by irreversible thermodynamics,
where the membrane is treated as a black box. For pressure driven membrane processes like RO, NF
and UF, the solute flux through the membrane can be described as the sum of a convective and a
diffusive flux. Solute transport by convection takes place because of an applied pressure gradient
across the membrane. A concentration difference on both sides of the membrane causes diffusive
transport.
   The Spiegler-Kedem equation (Spiegler (1966)) for the rejection is as follows:

                                             1−σ
                          R = 1−                                                       (1)
                                                (σ − 1)⋅ J v 
                                   1 − σ ⋅ exp               
                                                    P        

   The solute rejection R is given as a function of the water flux Jv and the solute permeability P. From
this equation it appears that the rejection increases with increasing water flux and reaches a limiting
value σ at an infinitely high water flux. As the diffusive flux of the solute transport can be neglected
at infinitely high water fluxes, the reflection coefficient σ is a characteristic of the convective transport
of the solute. A σ of 100 % indicates that the convective solute transport is totally hindered or that no
transport by convection takes place at all. This is the case for ideal RO membranes where the
membrane have a dense structure and no pores are available for convective transport. The rejection
may however be lower than 100 % because solute transport may take place by solution-diffusion. As it
has been shown that NF membranes have pores, a reflection coefficient below 100 % will be found if
the solutes are small enough to enter the membrane pores. The Spiegler-Kedem model assumes the
membrane to be uncharged. In neutral membranes salt permeability P and the reflection coefficient σ
have constant values characterizing a given salt-membrane system. Salt concentration has no effect on
P and σ so that R is not affected by solution concentration.
   For this reason Schirg and Widmer (1992) were making two major assumptions. The first
assumption was that salt permeability P varies with solution concentration, according to the power
law:

                                     β
                            P = α ⋅ c2                                                (2)

where c2 is the salt concentration at the membrane-solution interface while α and β are experimentally
determined constants. Thus in the case of single salt solution:

                                                1−σ
                             R = 1−                                                  (3)
                                                   (σ − 1)⋅ J v 
                                      1 − σ ⋅ exp               
                                                   α ⋅ c2 
                                                           β
  The second assumption was that the reflection coefficient σ appearing in Eq. (3) is independent of
solution concentration.
   Pusch (1977) derived the rejection-volume flux relationship from the Kedem-Katchalsky model
(1958) – an expression for the rejection is obtained as follows:

                   1 1  LD   2  LP ⋅ π 1           1
                        L − σ  ⋅ σ ⋅ J = A1 + A2 ⋅ J
                    = +                                                       (4)
                   R σ  P             v              v


  Plotting the experimental values of the rejection versus the inverse of the total volume flux should
confirm the linear relationship and will enable us to define the intercept (A1) and the slope A2.


3. EXPERIMENTAL

  The Trials were carried out in a laboratory scale unit and spiral wound elements from Osmonics-
Desal NF-membrane type DK with a total membrane area of about 0.5 m² have been used. A
schematic diagram of the apparatus is shown in Fig. 1.



                           M
                                          Permeate
                  TI
                                                     Retentate

                                          Water
                                                                 PI       PI

                                          M
                               1

                                          G
                                                                      4            5
                               Feed

                                      2                    3




                    Fig. 1. Schematic diagram of the test cell: 1) feed container, 2) pump,
                                3) heat exchanger, 4) separation cell, 5) valve

   A high cross-flow velocity was applied to minimize concentration polarisation. The measurements
were carried out with single-salt solutions containing MgCl2, NaCl and Na2SO4 and these salts in two
different combinations of NaCl-MgCl2-H2O and NaCl-Na2SO4-H2O with varying feed concentrations
and different specific permeate flux. As process parameters the temperature and the pH of the systems
were fixed, wereby the pH value was varied in the test runs between 2 and 10. Membrane performance
data were obtained in terms of permeate flux and rejection.
   Analysis of feed and permeate samples were carried out by conductance measurements in single
solute systems. Ionic concentrations of anions respectively cations in mixtures were determined with
ion chromatography columns IonPac AS9-HC 4-mm (10-32) (Fa. Dionex) respectively IC-Pac-Cation
M/D 3,9 x 150 mm (Fa. Waters).
4. RESULTS AND DISCUSSION

4.1. Single electrolyte solutions

  In Fig. 2 the rejection is plotted against the salt concentration in the feed of the solution.

                                      100




                                      80
                    Rejection R [%]




                                      60

                                                                                  Natriumchlorid
                                                                                  Magnesiumchlorid
                                      40                                          Natriumsulfat



                                      20




                                       0
                                            0,0   0,2        0,4            0,6             0,8      1,0
                                                                                    -1
                                                        Feed Concentration c [mol l ]



              Fig. 2. Rejection R of different salts as a function of the feed concentration c for a DK
                         membrane (T = 25 [°C], pH = 7, Jv = 27,3 [kg m-2 h-1])

   In infenitely diluted solutions the membrane shows the following salt rejection sequence: R (MgCl2)
< R (NaCl) << R (Na2SO4), the Donnan exclusion seemed to be the separation mechanism, which is
typical for a negatively charged membrane. The result of membrane in concentrated solutions cannot
be explained by Donnan exclusion, because both the rejection for Na2SO4 and that of MgCl2 are high.
In this case in the literature this rejection sequence is explained by two ways. One the one hand for
Peeters (1998) differences in diffusion coefficients between the different salts are responsible for the
sequence. As shown in Table 1 the diffusion coefficient decreases going from NaCl, MgCl2 to Na2SO4.
The salt with the lowest diffusion coefficient shows the highest rejection, whereas that with the highest
diffusion coefficient shows the lowest rejection. This order of diffusion coefficients is inversely
reflected in the rejection sequence. On the other hand Xu (1999) explained it with the “sieve effect”.
The sieve effect depends essentially on the steric hindrance parameter of the solute on the interface.
For a given solute, the sterice hindrance parameter of a solute depends on the chemical nature of the
solvent and the material of the membrane surface. The value of the Stokes can be used as an
approximation.

Table 1)         Comparison of Rejection with Diffusion coefficients and their Stokes radius of
different electrolytes in water

Elektrolyte      Rejection R [ - ]                                      Diffusion coefficient          Stokes radius
                 c0 = 0,4 [mol l-1], Jv = 27,3 [kg m-2 h-1 ]            D [10-9 m2 s-1]                rS [10-10 m]

NaCl             0,20                                                   1,612                          1,52
MgCl2            0,90                                                   1,254                          1,96
Na2SO4           0,98                                                   1,230                          1,99
  Figure 2 also shows the dependency of the rejection on feed concentration. The NaCl and the
Na2SO4 rejection slightly decreases with increasing salt concentration for the DK membrane. For
MgCl2 the rejection increases with with increasing salt concentration. In my opinion this is affected by
the steric hindrance behaviours of the hydrated magnesium ion.

  Experimentally determined rejections of MgCl2 solutions are shown in Figure 3 as a function of the
permeat flux for different salt concentrations


                                   100



                                    80
                 Retention R [%]




                                    60


                                                                                                                  -1
                                                                                                      c MgCl2 [mol l ]
                                    40                                                              measured calculated
                                                                                                         0,005
                                                                                                         0,015
                                    20                σ = 0,9354                                         0,05
                                                      α = 0,1639 * 10
                                                                        -06       -1
                                                                              [m s ]                     0,12
                                                      β = - 0,7439                                       0,42
                                     0
                                         0              20                40                   60          80             100
                                                                    Permeat flux Jv [kg m-2 h-1]


           Fig. 3. Measured and calculated Rejection R of MgCl2 as a function of Permeat flux Jv.
        (T = 25 [°C], pH = 7, DK membrane). Theoretical curves (lines) have been calculated by the
                           modified Spiegler-Kedem model from Schirg.

   The dots represent the experimental values. The curves represent the rejection values calculated
from Eq. (3) using the experimentally determined rejection as an input parameter. Statistical analysis
of the data according to Eq. (3) yielded to the best values for the model parameters in Table 2:


Table 2)         Best fit values of the modified Spiegler-Kedem model parameter from Schirg by
statistical regression of the rejection data according to Eq. (3) (T = 25 [°C], pH = 7, Jv = 27,3 [kg m-2
h-1], DK membrane)

                                              σ                               α [10-6 m s-1]                 β

      NaCl                                   0.7701                            31.4902                     0.4747
      MgCl2                                  0.9354                            0.1639                      -0.7439
      Na2SO4                                 0.9920                            0,1461                      0.4496
  The theoretical linear relationship of Eq. (4) is shown to be in agreement with experimental findings
by Fig. 4 where 1/R is plotted as a function of 1/Jv for different salt concentrations.



                   4
                           c MgCl2 [mol l -1]                                                                             2
                           gemessen                                                                                      R = 0,9987

                   3           0,005
                               0,015
                               0,05                                                                                                       2
                                                                                                                                         R = 0,9984
          1/R[-]




                               0,12
                   2           0,42                                                                                            2
                                                                                                                              R = 0,9988
                                                                                                                                                             2
                                                                                                                                                        R = 0,9998
                                                                                                                                   2
                   1                                                                                                           R = 1,0000




                   0
                       0                                                     1               2                       3                        4                  5
                                                                                                          5     -1
                                                                                              1 / Jv [10 s m ]




        Fig. 4. Measured and calculated inverse Rejection 1/R of MgCl2 as a function of the inverse
    Permeat flux 1/Jv. (T = 25 [°C], pH = 7, DK membrane). Theoretical curves (lines) have been
                                   calculated by the Pusch model.


4.2. Ion rejection ternary ion mixtures

   The rejection of chloride in the ternary ion mixtures NaCl-Na2SO4-water in comparison with the
rejection of sodium in the ternary mixtures NaCl-MgCl2-water shows similary behaviours. At higher
sulphate (resp. magnesium) concentration in the feed, chloride (resp. sodium) rejection becomes
negative. With an increase in volumetric flux, chloride (resp. sodium) rejection increases. The
transition of monovalent ion rejection from positive to negative values with an increase in the addition
of multivalent ions in the bulk feed is observable, independently of the charge polarity, for both of the
solution systems (Figure 5.).


                                                                   10
                                Rejection of monovalent ions [%]




                                                                    5


                                                                    0


                                                                    -5

                                                                                 Chlorid in the NaCl-Na2SO4-solution
                                                                   -10           Sodium in the NaCl-MgCl2-solution


                                                                   -15
                                                                         0          0,1            0,2           0,3               0,4                 0,5           0,6
                                                                                                                                                  -1
                                                                                          Concentration of multivalent ions [mol l ]


              Fig. 5. Ion rejection as a function of the multivalent ion concentration of two different
            ion mixtures with high electrolyte strength (c(NaCl) = 2.5 [moll-1], ∆p = 30 [bar], T = 25
                                           [°C], DK membrane)
   It appears that the specific behaviour of NF membranes in the separation of high ionic strength
electrolyte solutions are independently from the charge number. Because of the higher permeability of
magnesium ions in opposite of sulfate ions, on account of different diffusion coefficient and ion size,
the sodium rejection in the NaCl-MgCl2-water system is higher than the chloride rejection in the
system NaCl-Na2SO4-water.


                                                40
                                                                                    +          -1
                                                                            c (Na ) [mol l ]
                                                                               0,05        0,5
                                                20                             1,0         2,5
                       Rejection R (Na +) [%]




                                                 0




                                                -20




                                                -40
                                                      0,0    0,2                        0,4         0,6
                                                                               2+         -1
                                                            Concentration c(Mg ) [mol l ]




                Fig. 6. Sodium rejection as a function of the magnesium concentration in the
        system NaCl-MgCl2-water (T = 25 [°C], pH ~ 5.7, Jv = 27,3 [kgm-2h-1], DK membrane)

   Negative rejections of sodium ions in the mixture of NaCl-MgCl2 were also observed
experimentally for the Desal-5 DK membrane for low mole fractions of NaCl (Figure 6.). The negative
rejection of more permeable sodium ions in binary mixed systems arises from the near total rejection
of magnesium by the membrane and the diffusive mobility of chloride ions through the membrane.
Since the driving force for the diffusive mobility of chloride is higher, diffusive flux of chloride is
increased. To maintain the electroneutrality criteria, sodium ion mobility is also increased resulting in
negative rejection. The lower sodium rejection with increase in magnesium concentration also
supports this. The transition from negative to positive rejection at higher volume flux arises due to
dillution of the product which is as well indicated in the data for single solute systems.
   Also it can be observed a linear dependence between the sodium rejection and the magnesium
concentration at constant permeat flux. Using data from the Eq. (3) enables to predicted magnitudes
for the sodium rejection at constant permeate flux with a modified equation for the ternary solute
mixture:

                                             
                                             
               
                          1−σ                 
                                                     1 c1, Mg 2 + 
                                                                    
     RNa +   = 1 −                            ⋅ 1 −   ⋅                                         (5)
                             (σ − 1)⋅ J    K 3 c1, Na + 
                1 − σ ⋅ exp  α ⋅ c β
                                           v
                                                                 
               
                            
                                   1, Na +  
                                             


  Figure 6 compares experimental results for the rejection with magnitudes predicted by Eq. (5). The
value of the empirical constante at invariable permeate flux is shown in Table 3:
Table 3)         Values of Eq. (5) for the ternary solute mixture NaCl-MgCl2-water (T = 25 [°C], pH ~
5.7, Jv = 27,3 [kgm-2h-1], DK membrane)

Value of Constants in the binary mixed system          Value of Constant in the ternary mixed system
NaCl-water                                             NaCl-MgCl2-water

σ = 0,7701                                             K3 = 0,4064 [l mol-1]
α = 31,4902 * 10 –6 [m s-1]
β = 0,4747




5. CONCLUSIONS

   For the membrane high retention were found for Na2SO4 and for MgCl2 in concentrated solutions.
This result of the membrane rejection in concentrated solutions cannot be explained by Donnan
exclusion rather than differences at the diffusion coefficient and the hydrated ion radii. Also the
rejection of chloride in the ternary ion mixtures NaCl-Na2SO4-water in comparison with the rejection
of sodium in the ternary mixtures NaCl-MgCl2-water shows similar behaviours. The transition of
monovalent ion rejection from positive to negative values with an increase in the addition of
multivalent ions in the bulk feed is observable, independently of the charge polarity, for both of the
solution systems.


6. SYMBOLS

A1                coefficient in Pusch´s Eq. (4)                            [-]
A2                coefficient in Pusch´s Eq. (4)                            [ m s-1 ]
c                 concentration                                             [ mol m-3 ]
D                 diffusion coefficient                                     [ m2 s-1 ]
Jv                permeate flux                                             [ m s-1 ]
K3                coefficient in ternary solute mixtures Eq. (5)            [-]
LD, Lπ            osmotic permeability coefficient                          [ m s-1 bar-1 ]
LP                hydraulic permeability coefficient                        [ m s-1 bar-1 ]
P                 local solute permeability                                 [ m s-1 ]
R, RS             rejection                                                 [-]
α                 coefficient in Schirg´s Eq. (3)                           [ m s-1 ]
β                 coefficient in Schirg´s Eq. (3)                           [-]
π                 osmotic pressure                                          [ bar ]
σ                 reflection coefficient                                    [-]



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