Water permeability in polymeric membranes, Part II

Desalination 257 (2010) 184–194

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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

Water permeability in polymeric membranes, Part II A.A. Merdaw ⁎, A.O. Sharif, G.A.W. Derwish Centre for Osmosis Research and Applications (CORA), Chemical & Process Engineering Department, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH, UK

a r t i c l e

i n f o

Article history: Received 17 November 2009 Received in revised form 5 February 2010 Accepted 5 February 2010 Available online 19 March 2010 Keywords: Membrane separation processes Reverse osmosis Water permeability Concentration polarization

a b s t r a c t This study is a combination of experimental and theoretical works in an attempt to produce a new useful empirical model for the mass transfer in pressure-driven membrane separation processes. Following on from our previous work in Part I, this part II paper introduces three new permeability models when using aqueous solutions as feed. The Solution-Diffusion Pore-Flow Concentration-Polarization (SDPFCP) model, which is a combination between the Solution-Diffusion Pore-Flow (SDPF) model [1] and the Concentration Polarization (CP) model, is presented. The SDPFCP model examines the CP model to represent the transfer phenomena outside the membrane by merging its effect within the water permeability coefficient. A further development for this model, the SDPFCP+, is obtained by adding an additional resistance to the system in series with the membrane resistance and the CP. The second model shows fair representation of the experimental results. The Solution-Diffusion Pore-Flow Fluid-Resistance (SDPFFR) model is then proposed to provide better representation for the system. The feed solution resistance to water flux, the Fluid Resistance (FR), is suggested to replace the CP and the additional resistance. The latter model shows excellent fitting to the experimental results; it may be useful for development and design applications, when based on experimental data. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction In the pressure-driven membrane separation processes, e.g. the Reverse Osmosis (RO) and the Nano-Filtration (NF) processes, solvent permeability estimation has to cover the series of resistances to fluid flux, which include the membrane resistance and the boundary layer resistance. Many mechanistic and mathematical models have been proposed to explain the mass transfer and the hydrodynamic permeability in these processes. Some of those explanations rely on relatively simple concepts while others are far more complex and need sophisticated mathematical techniques [2]. For the mass transfer inside the membrane, the two main approaches are models based on the solution–diffusion mechanism as proposed by Lonsdale et al. [3] and models based on preferential sorption-capillary flow mechanism as proposed by Sourirajan et al. [4,5]. Although the limitations were noticed for each transport model, all have been able to predict the membrane systems to some extent of success; however, these models are still used in many cases due to their simplicity [2,6]. The main model used to describe the mass transfer outside the membrane is the Concentration Polarization (CP) model by the film theory. Estimation of CP effect requires applying numerically a suitable empirical relationship (Sherwood correlation) to calculate

⁎ Corresponding author. Tel.: +44 1483 68 6594; fax: +44 1483 686581. E-mail address: [email protected] (A.A. Merdaw).

the mass transfer coefficient through the fluid thin film. The mass transfer correlations are usually borrowed from non-porous smooth duct flow, and therefore their application in the case of membrane operation has been critisized, since neither membrane's porosity nor diffusivity due to CP are taken into consideration [7]. In the present study, we construct new semi-empirical models for the mass transfer in polymeric flexible membranes, which could be used in RO, NF, and other membrane separation processes. The proposed new models are based on a combination between two wellknown models, the Solution Diffusion (SD) and the Pore Flow (PF). By this combination a new model, the SDPF, is constructed [1], which is similar in principle to the Solution Diffusion Imperfection (SDI) model [8–10]. According the SDPF model, water flux across the membrane is jointly carried out by diffusion and pore-flow mechanisms. This model is proposed for describing the mass transfer inside the membrane only in the absence of any osmotic effect, i.e. by using pure solvent (water) as feed fluid. This model provides better representation for the pure water permeability of the polymeric membrane and considers the effects of the operational conditions, namely the hydraulic pressure and the temperature. The SDPF model equation will be regarded by the presented models as a reference upper limit for the overall water permeability of the system when using aqueous solutions as feed. The three new models, the Solution-Diffusion PoreFlow Concentration-Polarization (SDPFCP), the SDPFCP+, and the Solution-Diffusion Pore-Flow Fluid-Resistance model (SDPFFR), are intended to cover the whole membrane separation system including the membrane phase and the feed solution phase.

0011-9164/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.02.013

A.A. Merdaw et al. / Desalination 257 (2010) 184–194

2. The SDPFCP, the SDPFCP+, and the SDPFFR models The first model, the SDPFCP, combines the SDPF model with the CP model. This model is developed to examine the CP model by merging its effect within the water permeability coefficient. The second model, the SDPFCP+, is a further development for the SDPFCP model by adding an additional resistance, Ω*, in series with the membrane resistance and the CP resistance. This additional resistance is proposed to accommodate for all other resistances to water flux in the feed side of the membrane. The third model, the SDPFFR, replaces both of the CP and the additional resistance by an empirical representation, called here the Fluid Resistance (FR). Most of the known mass transfer models in membrane separation processes that use asymmetric semi-permeable membranes take into account the dense skin layer only and ignore others (the substrate and the intermediate layer), which are normally highly porous and oriented against the permeate side. For the current study, we follow this logical assumption too. However, any membrane physical properties that are mentioned in this study will refer only to the skin layer of the membrane. 2.1. Concentration polarization model Modelling concentration field in the pressure-driven membrane process is a very complex endeavour. In a membrane separation process where the solute is rejected by the membrane, there is a build up of the concentration at the membrane liquid interface, which gives rise to concentration polarization. All membrane processes experience this unavoidable phenomenon, which is caused by the unbalanced transport between bulk and membrane surface [11,12]. The solute concentration profile under the regime of concentration polarization is shown schematically in Fig. 1. The approach considered for the CP model in the present study is based on Nernst's film theory, where transport is one-dimensional and there is no turbulence within the film [7,13–17]. This well-known model is based on the following assumptions: (1) fully developed flow with no entrance effects, (2) uniform trans-membrane flux, and (3) no axial diffusion. The Nernst film model represents a somewhat oversimplified picture of the boundary layer, since the transport by eddy diffusion or

185

mixing is ignored. This approach can be used in the case when onedimensional concentration profile is assumed. However, when the diffusivity of the retained species at the membrane surface is assumed independent of the concentration, the integration of the convection– diffusion mass transfer equations in steady state leads to the following expression for the CP modulus, ϕ [17]: cm −cp ðJ = kÞ ðJ = kÞ = e v ≈e w =ϕ cb −cp

ð1Þ

where Jv is the total volumetric flux, Jw is the pure water volumetric flux, k is the mass transfer coefficient in the thin boundary layer, and c refers to the local concentration of the solute at m, the membrane surface, p, the permeate side, and b, the bulk (feed-concentrate) side. This concentration polarization increases exponentially with the trans-membrane flux and boundary layer thickness, and decreases exponentially with increasing solute diffusivity. This means that polarization is particularly severe with high solvent permeability membranes and high molecular weight solute [16]. As mentioned earlier, estimation of CP effect requires calculating the mass transfer coefficient, experimentally or by theoretical prediction. However, the accepted analogy between heat and mass transfer in conventional mass transfer processes led to the use of modified semi-empirical heat transfer correlations for membrane processes [18]. Many empirical relationships for the mass transfer coefficient estimation are available in the literature [19–24], e.g. for rectangular flat sheet cross-flow membranes, the following equation can be used [25,26]: Sh =


0:131 kdh 0:554 0:371 dh = 1:195 Re Sc Ds L

ð2Þ

where dh and L are the hydraulic diameter and the length of the filtration channel, respectively, Ds is the solute diffusivity, Re is the Reynolds number, Sc is the Schmidt number, and Sh is the Sherwood number. Many other similar empirical forms to Eq. (2) were obtained for different membrane separation systems. Even for a certain system, the value for the mass transfer coefficient may vary largely if estimated by

Fig. 1. Schematic representation of the solute concentration profile across asymmetric membrane in the pressure-driven membrane separation processes.

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two different means [27]. However, most available empirical relationships for the mass transfer coefficient estimations are to produce one constant value based on the assumption of constant fluid physical properties of the fluid alongside the membrane surface; thus introducing a critical simplification of the actual conditions. By assuming the validity of the following van't Hoff relationship [28] between the osmotic pressure, Π, and solute concentration: Π=


 iv Rg T cs Ms

ð3Þ

Eq. (6) can be simplified by expressing the exponential function for ϕ as power series: J =k

ϕ = ew

ϕ=1+

ϕ=e

cm −cp Πm −Πp ΔΠm = = = cb −cp Πb −Πp ΔΠ

ð4Þ

where iv is the van't Hoff factor, Rg is the universal gas constant, T is the temperature, Ms is the molecular weight of the solute, cs is its concentration, ΔΠm is the actual osmotic pressure difference across the membrane, and ΔΠ is the observed osmotic pressure difference between the feed side and the permeate side of the membrane. Care must be taken when applying Eq. (4), as the actual osmotic pressure relationship versus solute concentration is not linear as predicted by Eq. (3). However, for the current analysis we use this assumption, as it is reasonably valid with dilute solutions, which is the case in many of the RO and NF applications, and the curve segment between feed and permeate concentrations can be considered almost linear. 2.2. The SDPFCP model The volumetric water flux across the membrane can be represented by the following phenomenological relationship: Jw = Awm ðΔP−ΔΠm Þ

ð5Þ

where Awm is the pure water permeability coefficient as defined by the SDPF model [1], and ΔP is the hydraulic pressure difference across the membrane. The coefficient Awm is originally derived for water flux due to the driving force of the hydraulic pressure difference across the membrane. However, we assume here that the osmotic pressure of the particles dissolved within the liquid is equal to the ideal gas pressure in the gas phase, i.e., Π = P [29]. By substituting Eq. (4) in Eq. (5):   J =k Jw = Awm ΔP−ΔΠ:e w



 Jw 1 Jw 2 1 Jw 3 + + + :::: k 2! k 3! k

ð8Þ

When Jw ≪ k and the value of (Jw/k) is less than 0.1, which is the common case in most RO and NF processes, the following relationship can be used:

the effect of the CP as written in Eq. (1) can be simplified to: ðJ w = k Þ

=1+

Jw k

ð9Þ

For membranes systems with higher values of Jw, i.e. (Jw/k) is greater than 0.1 and lower than 0.4, the third term in Eq. (8) has to be used: ϕ=1+


 Jw 1 Jw 2 + : k 2 k

ð10Þ

The trend of ϕ according to Eqs. (1), (9), and (10), is shown graphically in Fig. 2 as a function of a range of (Jw/k). It can be clearly noted that using higher values of k increases the validity range of the simple relationship (9). Accordingly, the simplification for the SDPFCP model, Eq. (6), is to be divided into two classes depending on the relationship between the membrane flux and the mass transfer coefficient: 2.2.1. Low water flux membranes For the case of Jw ≪ k where the value of (Jw/k) is less than 0.1, by substituting the relationship (9) in Eq. (6), the following equation for water flux is obtained: Jw =

Awm k ðΔP−ΔΠÞ k + Awm ΔΠ

ð11Þ

from which the overall membrane water permeability (the membrane permeability, for short) for the system, Aw, can be defined as: Aw =

Awm k : k + Awm ΔΠ

ð12Þ

According to Eq. (12), Fig. 3 shows, for a system utilizing 5 b osmotic pressure difference, that Aw approaches Awm when utilizing flow regimes having high values for k. However, k cannot practically

ð6Þ

Substituting the SDPF model equation for Awm in Eq. (6) accordingly produces the principle equation of the SDPFCP model for water flux: γðΔP + 1Þλ

Jw = ln ð1 + β:ΔP Þε


η
 Jw T ΔP−ΔΠ:e k × To

"

Dw Mw ε2 d2m ε3 + ρv Rg To δm 11:25μo ð1−εÞ2 δm

# ð7Þ

where Dw, Mw, ρv, and μo, are the diffusivity, the molecular weight, the density, and the viscosity of pure water at standard conditions, respectively, ε, δm, and dm, are the membrane micro-structural parameters, namely the porosity, the skin layer thickness, and the mean pore diameter, respectively. The empirical parameters, β, γ, λ, and η, are constants, which are to be obtained after carrying out an RO experiment with pure water as feed.

Fig. 2. The concentration polarization modulus, ϕ, by different mathematical forms as a function of the ratio between water flux, Jw, and mass transfer coefficient, k.

A.A. Merdaw et al. / Desalination 257 (2010) 184–194

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2.3. The SDPFCP+ model Estimation of the feed solution effect on water permeability still needs to account for all other resistances that may occur in addition to the CP due to the interaction between the feed solution and the membrane, e.g., the electrostatic forces and the hydration properties of the solute. Furthermore, due to the original assumptions used for the CP model and the k calculation method, the obtained values for ϕ and k may differ from that of the actual process. Hence, it is suggested here that the deviation of the SDPFCP model from the actual experimental results can be corrected by adding new additional resistance in series to the system, Ω⁎, with units of m− 1. The additional resistance is to be incorporated within the total system resistance that identified by the SDPFCP model by modifying Eq. (12) to read: 1 k + Awm ΔΠ + μΩ* = Aw Awm k Fig. 3. The effect of the mass transfer coefficient, k, on the membrane permeability, Aw, at constant value of ΔΠ (5 b) as a function of the membrane's pure water permeability, Awm.

reach infinity; therefore, Aw is always lower in value than Awm and approaches or departs depending on, respectively, increasing or decreasing k. It can also be noted from Eq. (12) that as ΔΠ increases, Aw decreases. 2.2.2. High water flux membranes For the case of Jw b k and the value of (Jw/k) is less than 0.4, by substituting the relationship (10) in Eq. (12), the following equation for water flux can be obtained:

ð15Þ

where μ is the viscosity of the feed solution. The final equations for water flux and permeability according to the SDPFCP + model would then be: Jw =

Aw =

Awm k ðΔP−ΔΠÞ k + Awm ΔΠ + ΩAwm k Awm k k + Awm ΔΠ + ΩAwm k

ð16Þ

ð17Þ

where Ω is the dynamic additional resistance, i.e. Ω = μ Ω⁎ (with units of h b/m). 2.4. The SDPFFR model

2

2k Awm ðΔP−ΔΠÞ: Jw = 2k2 + 2kAwm ΔΠ + Jw Awm ΔΠ

ð13Þ

Accordingly, the membrane permeability can be defined as: Aw =

2k2 Awm 2k2 + 2kAwm ΔΠ + Jw Awm ΔΠ

ð14Þ

This model is intended to cover the whole system, as shown in Fig. 4, by adding an empirical representation for the feed solution resistance to water flux, the FR. The volumetric water flux inside the membrane (only), as represented by Eq. (5), has to be equal to water flux outside the membrane, i.e. in the feed solution side. The resistance to water transfer in the feed solution, Rf, is introduced here and suggested to be as a function of the operational conditions

Fig. 4. Schematic representation (left) and an electrical analogy (right) for the series of resistances to water flux in the pressure-driven membrane separation processes.

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and the solution properties. This resistance is joined in series to the membrane resistance, Rm, which is previously described by the SDPF model to consist of, in parallel, the resistance to diffusion and the resistance to pore flow, to give the total resistance of the system to water flux, RT: RT = Rf + Rm :

1 1 1 = + Aw Af Awm

ð19Þ

where Af is the feed solution permeability to water (the fluid permeability, for short), which is suggested here to be dependent on ΔP according to the following relationship: Af = Afo ln ð1 + ψ:ΔP Þ:


 ΔP + 1 ζðΔP ΔPo

+ 1Þθ

ð20Þ

where; ψ, ζ and θ are the model parameters (variables with feed concentration) and Afo is the nominal fluid permeability at the reference conditions, the temperature, To, and the hydraulic pressure difference, ΔPo. The value of ΔPo can be taken to have the value of one pressure unit. The first derivative for Eq. (20) would be;
 dAf ΔP + 1 θ−1 = Afo :ζðΔP + 1Þ : 1 + θ ln dΔP ΔPo 
 ΔP + 1 θ : lnð1 + ψ:ΔP Þ : exp ζðΔP + 1Þ : ln ΔPo
ζðΔP + 1Þθ Afo ψ ΔP + 1 + : 1 + ψ:ΔP ΔPo

ð21Þ


 ΔP +1 ζðΔPfmax + 1Þθ−1 : 1 + θ ln fmax ΔPo 
 ΔPfmax + 1 θ : lnð1 + ψ:ΔPfmax Þ ð22Þ : exp ζðΔPfmax + 1Þ : ln ΔPo
 θ ψ ΔPfmax + 1 ζðΔPfmax + 1Þ = 0: + 1 + ψ:ΔPfmax ΔPo However, from Eq. (19), the membrane permeability and the water flux can be obtained according to the SDPFFR model as follows: Af Awm Af + Awm

ð23Þ

Af Awm ΔP: Af + Awm

ð24Þ

The fluid permeability according to this model accounts for the effect of ΔΠ. The SDPFFR model shows excellent fitting to the experimental results. Equating the first derivative of Eq. (23) to zero can provide the ability to estimate the value of the optimum net hydraulic pressure differences across the membrane, ΔPopt, that provide the maximum membrane permeability, Aw-max: dAw 1 = dΔP Awm + Af

"

Dw Mwt ε2 d2m ε3 + ρv Rg To δm 11:25μo ð1−εÞ2 δm

#
 T η : To

ð26Þ The first derivative of Eq. (26) at the reference temperature, i.e. by eliminating the temperature effect term, is as follows:   λ dAwm β γðΔP + 1Þ λ−1 + γλ: lnðβ:ΔP + 1Þ: ln ðεÞ:ðΔP + 1Þ ð27Þ =ε β:ΔP + 1 dΔP " # 2 2 3 D M ε dm ε + : × w wt ρv Rg To δm 11:25μo ð1−εÞ2 δm

Achieving the minimum of the Specific Energy Consumption (SEC) in a pressure-driven membrane separation process is obtained by maximizing the membrane permeability [30]. This explains the importance of Eq. (25) as it provides the ability to predict Aw-max at ΔPopt for certain operational conditions bundle (feed fluid, membrane type, temperature, flow rate, flow path geometry, and osmotic pressure difference). 3. Experimental methods 3.1. Bench-scale experiments

The upper inflection point for fluid permeability curve, where the maximum fluid permeability to water, Af-max, occurs at the optimum hydraulic pressure difference, ΔPf-max, can be found by equating the first derivative to zero;

Jw =

γðΔP + 1Þλ

Awm = lnð1 + β:ΔP Þε

ð18Þ

As the resistance is the reciprocal of the permeability, hence:

Aw =

where the coefficient Awm has the following relationship according to the SDPF model:



 dA dAf Awm :Af dAwm dAf + Af wm + Awm − 2 dΔP dΔP dΔP dΔP ðAwm + Af Þ

ð25Þ

In order to examine the validity of the new models, several experiments have been carried out by using a small static RO laboratory cell supplied by Spintek Filtration Inc. (USA). The experimental rig is similar to that thoroughly described in part I and previous work [1], where the cell-setting B has been used. Two flat sheet NF membranes with known micro-structural properties were used, NF200 and NF270, manufactured by Filmtec (USA), as shown in Table 1 [31,32]. Before the initial use, each membrane has been conditioned by using pure water as feed at 25 °C and by utilizing the maximum available hydraulic pressure by the unit, which is 20 b, for 3 h in order to eliminate any irreversible changes that may occur during the experiments. The experiments investigate the obtained values of water flux and solute rejection rate at different feed hydraulic pressures. Feed solutions used are aqueous solutions of two ionic salts, NaCl and MgSO4, and an organic compound, glycerol. Both ionic salts are symmetrical electrolytes with different valences and hydration properties. All the chemicals used are of laboratory grade with high purity; their general specifications are listed in Table 2. In general, the purpose of the experiments is to observe the trend of the relationships between the controllable variables and the response parameters. The controllable variables were for the feed solution, the solute type, the temperature, and the hydraulic pressure. The experiments were carried out at different, but constant, feed flow rate and cell configuration. The observed parameters were for the Table 1 Specification of the membranes NF90, NF200, and NF270 [31,32]. Membrane type

Porosity, ε

Mean pore diametera, dm (nm)

Skin layer thickness, δm (nm)

NF90 NF200 NF270

0.171 0.155 0.117

0.5130 ± 0.019 0.2886 ± 0.017 0.6810 ± 0.016

–b 29 ± 5 15–40b

a The mean pore diameter data are given as quoted from references; the data appear to be highly accurate with very small standard deviation of individual measurement over such small length scale. b The layer thickness of NF90 and NF270 is assumed to be equal to that of the NF200.

A.A. Merdaw et al. / Desalination 257 (2010) 184–194 Table 2 Specification of the chemical materials.

Table 3 Feed solutions properties and operational conditionsa.

Chemical material

Manufacturer

Grade

Purity

Molecular formula

Sodium Chloride Magnesium Sulphate Glycerol

Sigma

ReagentPlus™

≥99.5%

NaCl

SAFC

ACSa

N98%

MgSO4.7H2O

Sigma-Aldrich

ACS

≥99.5%

C3H8O3

a

Molecular weight 58.44

Membrane type Aqueous Concentration Feed flow k (m/h) Feed osmotic solution of of feed (ppm) rate (l/h) pressure (b) NF200

246.48 NF270 92.09

ACS: American Chemical Society. a

permeated water and for the concentrate, mainly the flow rate and the concentration, as well as the time. All experiments were preceded with preliminary tests for shorter periods to examine the repeatability of results. Acceptable repeatability has been found; the measurements were different in less than ±3 percentage between any two similar-condition experiments. The fluctuations in readings were due to the manual recording of data. However, the tolerances in the observed data reflected as error percentages in the results. For example, the permeability maximum uncertainty has been estimated as 6% according to the following equation: ð1 + 0:03ÞJw = ð1:06ÞAw : ð1−0:03ÞðΔP−ΔΠÞ

ð28Þ

Estimation of the final parameters in each model equation is done by minimizing the Sum of Squared Differences (SSD) between the experimental data and the proposed model:  2 SSD = ∑ ymod: −yexp: :

189

ð29Þ

3.2. Pilot plant experiment In order to demonstrate the validity of the SDPFFR model under the actual operational conditions by using commercial available membranes, several experiments have been carried out by using an NF module type NF90-4040, manufactured by Filmtec (USA). The module consists of two spirally wound membrane elements providing total active surface area of 15.24 m2. The micro-structural data for the membrane NF90 were quoted from literature [31] and listed in Table 1. The skin layer thickness is assumed here to be equal to that of the NF200, i.e. 29 nm.

NaCl MgSO4 glycerol NaCl MgSO4 glycerol

10100 49766 28518 10100 49517 28953

92.7 93.2 94.0 91.6 88.0 95.0

1.092 0.705 0.785 1.085 0.683 0.792

7.94 9.72 7.77 7.94 9.67 7.77

All experiments were carried out at 25 °C.

Dos , at 25 °C are 0.93 × 10− 9 m2/s for glycerol, 0.849 × 10− 9 m2/s for MgSO4, and 1.611 × 10− 9 m2/s for NaCl.

4.1.1. The SDPFCP model Table 3 summarizes the main feed solutions properties and operational conditions. Figs. 5 and 6, show the experimental overall water permeability (the membrane permeability), Aw, and as calculated by the SDPFCP model for the membranes NF200 and NF270, respectively, as a function of ΔP. The pure water permeability, Awm, curve is also shown in each figure for comparison. The Awm model parameters are quoted from our previous work on the SDPF model with similar membranes and operational conditions. Eq. (11) has been chosen to represent the SDPFCP model rather than Eq. (13) due to the low Jw/k ratio (less than 0.1). The maximum value obtained for ϕ with the NF200 at 20 b hydraulic feed pressure was 1.07, while with the NF270 the maximum value was 1.048, both for glycerol solution. It has been observed that ϕ linearly increases as ΔP, or Jw, increases, due mainly to the fixed estimated value of k. The obtained values for the SSD after applying the SDPFCP model by using Eq. (11) are listed in Table 4. The SDPFCP model shows poor representation of the experimental results with high values of SSD. This indicates that the CP model and the used method for estimation the mass transfer coefficient are far from representing the actual process. This can be explained by reviewing CP model original simplifications, viz., membranes with very high solute rejection, constant fluid film properties, and ignoring membrane's microstructural properties. The linear trend of the CP modulus, ϕ, versus ΔP, or Jw (see Fig. 2), indicates the over-simplification of the actual process. Actually, for different solutes types, the CP modulus, which represents the solute concentration gradient in the boundary layer, is expected to behave in more complex trends depending on the

4. Results and discussion 4.1. Bench-scale experiments Several RO runs have been carried out with the membranes NF200 and NF270 by using aqueous solutions of three types of solutes as feed, 1% NaCl (∼ 7.9 b osmotic pressure), 5% MgSO4 (∼ 9.7 b osmotic pressure) and 3% glycerol (∼7.8 b osmotic pressure). Another set of experiments has been carried out with the membrane NF200 by using glycerol solution at different concentrations, from one to 4%. All experiments were carried out at constant temperature of 25 °C using the cell-setting B (see part I or reference [1]), with narrow feed flow rate range. In order to estimate the SDPFCP and SDPFCP + models parameters, it was needed first to calculate the mass transfer coefficient, k, by Eq. (8). The filtration channel length and the hydraulic diameter have been estimated from the feed channel geometry. The following values were obtained: L = 581 mm and dh = 4.092 mm. The literature values [19,33–36] for the diffusivity of solutes with infinite dilution in water,

Fig. 5. Experimental permeability of the membrane NF200 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 92–94 l/h. The bold lines represent the SDPFCP model Eq. (11) in comparison with the pure water permeability curve.

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Fig. 6. Experimental permeability of the membrane NF270 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 88–5 l/h. The bold lines represent the SDPFCP model Eq. (11) in comparison with the pure water permeability curve.

solution properties, the membrane microstructure, as well as the flow properties alongside the membrane surface, where all depend on ΔP. To eliminate the possibility of any errors that may occur due to using Eq. (2), wider range of k between 0.3 m/h (83 × 10− 4 cm/s) and 2.0 m/h (555 × 10− 4 cm/s) has also been examined. This range covers wide and different conditions of the process at 25 °C as stated by several experimental studies [27]. The extra calculations were made for the three solutions by using the membrane NF200 and show that even with this range for k the SDPFCP model is not appropriate to represent the process. It is worth noting here that with the aforementioned range of k, the condition of Jw/k b 0.1 was still valid, except with the last few points with the NaCl solution case at k = 0.3 m/h. 4.1.2. The SDPFCP+ model Figs. 7 and 8, show the experimental membrane permeability as a function of ΔP for the membranes NF200 and NF270, respectively, and as calculated by the SDPFCP + model according to Eq. (16). This model shows fair representation of the experimental results with moderate SSD values, as listed in Table 4. However, this model still does not adequately representing the process, especially in the case of the MgSO4 solution, which has high rejection properties and lower water flux. The deviation can be caused by the assumption made for k and Ω as constants. Actually, both of k and Ω are expected to be variable functions with ΔP. It is worth noting here that the values of Ω in Table 4 indicate the higher effect of the solute type and concentration, over the effect of membrane type. For example, the (50 g/l) MgSO4 solution resistance to water flux is more than 45 times higher than

Fig. 7. Experimental membrane permeability of the membrane NF200 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 92–94 l/h. The bold lines represent the SDPFCP + model Eq. (16) in comparison with the pure water permeability curve.

that of the (10 g/l) NaCl solution, or 6 times higher than that of the (30 g/l) glycerol solution, by using the membrane NF200. When the membrane NF270, which has lower porosity and higher mean pore diameter, was used, Ω rose for ionic solutes but reduced for the organic one. This difference can be attributed to the different hydration properties of the solutes and their interference with the membrane microstructure.

4.1.3. The SDPFFR model 4.1.3.1. Different feed solutions. In order to have consistent comparison with the two previous models, the calculations presented here use the (ΔP − ΔΠ), the Net Driving Pressure (NDP), instead of ΔP for the application of Eq. (24). Figs. 9 and 10, show the SDPFFR model according to Eq. (24), in bold lines, as a function of ΔP in comparison with the experimental values and their uncertainty margins by using both membranes. SDPFFR model's parameters as calculated from Eqs. (20) and (23) are listed in Table 5, in addition to the values of the maximum permeabilities, Af-max and Aw-max, as calculated from Eqs. (22) and (24). This model shows excellent representation for the experimental results with low SSD values. The instant advantage

Table 4 Estimated SDPFCP, and SDPFCP+, models parameters according to Eqs. (11) and (16), respectively. SDPFCP Membrane Solute type

NF200

NF270

SDPFCP+

Ω SSD Awm parameters by the SSD (l/m2 hb)2 (h b/m) (l/m2 hb)2 SDPF modela

NaCl 0.975 MgSO4 52.839 glycerol 13.547 NaCl 0.451 MgSO4 19.673 glycerol 0.744

10.63 469.67 70.14 14.25 489.71 33.36

0.571 1.557 0.931 0.296 1.950 0.040

β

γ

4010.1

1.3958 −0.0038

4.732 0.5650

λ

0.1397

a The parameter η of the SDPF model is not included as all experiments were carried out at 25 °C.

Fig. 8. Experimental membrane permeability of the membrane NF270 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 88–95 l/h. The bold lines represent the SDPFCP + model Eq. (16) in comparison with the pure water permeability curve.

A.A. Merdaw et al. / Desalination 257 (2010) 184–194

Fig. 9. Experimental membrane permeability of the membrane NF200 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 92–94 l/h. The bold lines represent the SDPFFR model Eq. (24) in comparison with the pure water permeability curve.

Fig. 10. Experimental membrane permeability of the membrane NF270 using different feed solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 88–95 l/h. The bold lines represent the SDPFFR model Eq. (24) in comparison with the pure water permeability curve.

obtained by applying this model was eliminating the need to calculate the CP modulus and the mass transfer coefficient. Feed fluid permeability, Af, which is a newly introduced parameter by the present study, provides better representation for the feed solution-membrane interaction. Af can be defined as the ability of water molecules to cross the bulk feed solution and the membrane interface (the boundary layer) towards the membrane surface under specific operational conditions. Fluid permeability by using the membrane

191

Fig. 11. Feed fluid permeability, Af, for different aqueous solutions at 25 °C as a function of the hydraulic pressure difference across the membrane NF200 according to the SDPFFR model.

NF200 as estimated from Eq. (20) is shown as a function of ΔP in Fig. 11, while Fig. 12 shows the same but by using the membrane NF270. It is worth noting here that the experimental values for the fluid permeability can also be easily obtained by using Eq. (19). As shown in Fig. 11 for the membrane NF200, Af of the NaCl solution starts with small value at low ΔP. As the ΔP increases, Af also increases until reaching an inflection point. After this inflection point, the permeability of the feed solution continuously decreases due to the expected increase of the solute concentration at the membrane surface. In Fig. 12 for the membrane NF270, similar behaviour can be observed for glycerol and MgSO4 solutions, although no inflection point was detected, while NaCl solution behaves differently. This difference in NaCl behaviour can be explained by considering the mean pore diameter, dm, for both membranes (dm is 0.2886 nm in NF200 and 0.6810 nm in NF270) and the molecular properties of the solutes, e.g. the molecular diameters and the hydration numbers. This can also be related to the observed solute rejection, Ro, in both membranes. NaCl and glycerol solutions have lower rejection properties than the MgSO4 solution, i.e. have higher solute passage across the membrane. With the NF200, at 20 b feed hydraulic pressure, Ro was about 90% for MgSO4, and 48–49% for both NaCl and glycerol, while with the NF270, at the same hydraulic pressure, Ro was about 80% for MgSO4, 27% for NaCl, and 37% for glycerol. The solution permeability to water increases as the solute passage increases, as both of the solute and the solvent are combined to each other in a dynamic state. Although NaCl and glycerol solutions have similar rejection properties by using the NF200, the fluid permeability of NaCl solution was higher due to the lower solute concentration. Increasing the solute concentration reduces the fraction of the free water molecules in solution.

Table 5 Estimated SDPFFR model parameters for different feed solutions. Solute A) NF200 NaCl MgSO4 Glycerol B) NF270 NaCl MgSO4 Glycerol

Afo 0.000002 0.000024 0.000803 500.001 0.150 3.082

ψ

ζ

θ

SSD

ΔPf-max

Af-max

ΔPopt

NDPopt

24.641 0.001 28631

20.835 11.479 8.274

− 0.472 − 0.267 − 0.411

0.246 0.190 0.046

7.83 123.07 No inflection point 11.23 16.72

15.53 11.9 No inflection point 16.30 12.6

282.60 8.713 852.58

− 2.443 0.008 1908.7

− 0.131 1.483 − 6.845

0.197 0.090 0.031

No inflection point No inflection point No inflection pointa

9.11 8.0 No inflection point 16.12 13.7

Units: Af and Aw in l/m2 h b, SSD in (l/m2 h b)2, ΔP and NDP in b. a Only low inflection point is detected with Af-min = 26.15 l/m2 h b at ΔPf-min = 4.65 b.

Aw-max 4.311 3.565 2.701 2.603

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Fig. 13. The membrane permeability of the membrane NF200 using glycerol aqueous solutions as a function of ΔP at constant temperature of 25 °C and feed flow rate of 100 l/h.

parameters according to the SDPFFR have been found constants, Afo, and Ψ, or relative to feed concentration, ζ, and θ, as follows: ζ = 1 × 10 Fig. 12. Feed fluid permeability, Af, for different aqueous solutions at 25 °C as a function of the hydraulic pressure difference across the membrane NF270 according to the SDPFFR model.

Although the high values for NaCl fluid permeabilities with the membrane NF270 (compare Figs. 11 and 12), the final membrane permeability, Aw, of NF200 is higher (compare Figs. 9 and 10). This indicates the effect of Awm, which depends on the mean pore diameter of the membrane (as quoted above), and on the membrane porosity (ε is 0.155 for NF200 and 0.117 for NF270). It can be noted here that the porosity effect is higher than the mean pore diameter effect on the membrane permeability. From a comparison between the obtained values for Af and Awm in each case, the dominant resistance to water transfer can be determined. For example, NaCl solution with the membrane NF200 has higher Af than Awm, which indicates that the membrane phase is the controlling phase, while with MgSO4 solution by using the same membrane the Af was lower than the Awm, which shows that the fluid phase is the controlling one. Hence, membrane separation processes can be improved to increase the membrane permeability, Aw, in view of Eq. (19); the efforts can be focused on the controlling phase to increase its permeability. 4.1.3.2. Different feed concentrations. Several experiments have been carried out by utilizing similar cell-setting with the membrane NF200 by using four different concentrations of glycerol aqueous solution as feed. All tests were carried out at 25 °C with 100 l/h feed flow rate. These RO experiments were referenced to a new pure water permeability test carried out at similar conditions, but differ slightly due to adding two extra filter papers above the membrane on the permeate side; we call this cell-setting B1. The change in the set-up was to indicate the change in the permeability results. Fig. 13 shows the membrane permeability as a function of the hydraulic pressure difference across the membrane, while Fig. 14 shows the same but for the predicted fluid permeability. Reduction in the pure water permeability can be noticed from a comparison between the Awm curves in Figs. 9 and 13 due to the extra resistance of the additional filter papers. Table 6 shows the obtained model parameters for this set of experiments. The fluid permeability

−9 2 cf −1

θ = 8 × 10

−4

× 10

−11 2 cf −3

× 10

  2 cf + 4:9034 R = 0:9950

ð30Þ

  2 cf −0:4541 R = 0:9465

ð31Þ

−8

where cf is the concentration of glycerol in feed (ppm), and R2 is the coefficient of determination (A number from 0 to 1 that reveals how closely the estimated values for the trend-line correspond to the actual data). The obtained Af-max and Aw-max as functions of the feed concentration, as well as the corresponding ΔPf-max and ΔPopt, were as follows: −0:9286

Afmax = 141861 cf

−0:1528

Awmax = 12:482 cf

  2 R = 0:9979 

0:00005 cf

ΔPfmax = 5:1692e

0:00005 cf

ΔPopt = 9:6205 e

ð32Þ

 2 R = 0:9987

ð33Þ

  2 R = 0:8814

ð34Þ

  2 R = 0:9696 :

ð35Þ

Fig. 14. Feed fluid permeability of glycerol aqueous solutions as a function of ΔP across the membrane NF200 at constant temperature of 25 °C according to the SDPFFR model.

A.A. Merdaw et al. / Desalination 257 (2010) 184–194

193

Table 6 The SDPFFR model parameters for different concentration of glycerol aqueous solutions in RO experiments at 25 °C with 100 l/h feed flow rate. Pure water permeability (Awm) parameters β 4010.06 γ 1.482345 λ 0.013217 Concentration, ppm 10000

by the SDPF model 16404 b ΔPm-max 4.25 l/m2 h b Awm-max SSD 0.044 (l/m2 h b)2 20000 30000 40695

Fluid permeability (Af) parameters by the SDPFFR model: Afo, l/m2 h b 0.10 0.10 ψ 28631.0 28631.0 ζ 3.720 2.883 θ − 0.441 − 0.437 8.98 11.05 ΔPf-max, b 2 27.755 14.175 Af-max, l/m h b

0.10 28631.0 1.982 − 0.366 20.47 9.606

0.10 28631.0 1.526 − 0.324 34.30 7.656

Membrane permeability (Aw) model: 17.44 ΔPopt, b Aw-max, l/m2 h b 3.048 0.013 SSD, (l/m2 h b)2

28.49a 2.577 0.020

76.22a 2.463 0.032

a

22.78a 2.761 0.012

Curve extrapolations.

4.2. Pilot plant experiment Two experiments have been carried out by using the module NF90-4040 at 25 °C by utilizing seawater salt (NaCl) solution as feed. Both experiments were carried out with feed concentration of ∼ 10000 ppm, which provides ∼ 7.8 b osmotic pressure at 25 °C. The first experiment was done with feed flow rate of 1503 l/h, which is similar to that used in an SDPF model experiment by using pure water as feed [1]. The second experiment was carried out by utilizing higher feed flow rate of 1715 l/h. Applying the SDPFFR model to any RO experiment should be referenced to an SDPF model experiment by using pure water as feed with similar operational conditions. However, both of these different flow rate experiments are referenced to a single SDPF experiment; this is provided by the low effect of flow rate change on membrane's pure water permeability. Effect of the change in feed flow rate can be more clearly observed on the permeability when utilizing aqueous solutions. Fig. 15 shows NF90 membrane permeability as a function of ΔP. The SDPFFR model shows good agreement with experimental results.

Fig. 16. Fluid permeability by using ∼10000-ppm seawater at 25 °C as a function of ΔP across the membrane NF90 according to the SDPFFR model.

Fig. 16 shows the fluid permeability as calculated from this model as a function of ΔP. Model parameters and SSD values are listed in Table 7. 5. Conclusions Most of the currently known models for pressure-driven membrane separation processes, e.g. the RO process, separate the membrane phase from the fluid phase, i.e., by dealing with only one part of the problem, although it has been experimentally found that the interaction between these two phases is far from being simple. Modelling the strong interaction between the membrane and the fluid requires a better view for the whole system. Hence, the SDPFCP model for water transfer across the semi-permeable membrane has been presented to examine this process. This model is based on a combination between the empirical SDPF model, which describes the mass transfer inside the membrane, and the CP model, which is proposed to describe the mass transfer outside the membrane. It has been experimentally shown that the SDPFCP model is poorly representing the system due to the weakness of the film theory based CP model. The CP model failed to be adequately representing the transfer phenomena in the feed side of the membrane. However, the SDPFCP + model shows better fitting to the behaviour of the actual process due to adding the dynamic resistance, Ω, to represent, with the CP, the feed solution resistance. The obtained values of Ω point to a much higher resistance to water flux in the feed side of the membrane than that predicted by the CP model alone. The SDPFFR model is then introduced to evaluate the new definition for the feed solution resistance, and permeability, as a function of the feed hydraulic pressure. The feed solution permeability is empirically suggested here to fit with the actual process behaviour. This model offers better representation, as well as understanding, for water transfer towards the membrane surface. The model shows good agreement with the experimental results and may provide a solid basis for further process development and design applications. Acknowledgements

Fig. 15. The membrane permeability of NF90 at 25 °C as a function of ΔP by using two different feed flow rates of 1503 and 1715 l/h. Feed fluid composed of ∼ 10000 ppm seawater salt solution providing ∼7.8 b osmotic pressure.

The authors would like to convey thanks to Modern Water Plc and the Faculty of Engineering and Physical Sciences at the University of Surrey for providing the financial means and laboratory facilities. The authors would also like to acknowledge the useful comments and the kind assistance of Prof. U. Tuzun, Dr. A. Tate, Mr. D. Hawkins, and Mr. C. Crossley.

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Table 7 Estimated SDPFFR model parameters in pilot plant experiment. Membrane type

Solute

Concentration of feed (ppm)

Feed flow rate (l/h)

Aof (l/m2 h b)

ψ

ζ

θ

SSDa (l/m2 h b)2

NF90-4040 NF90-4040

Seawater salt Seawater salt

10000 10000

1503 1715

24.991 22.823

0.0223 0.0329

− 0.00049 − 0.00394

1.7986 1.2682

0.030 0.032

a

SSD values for the membrane permeability curves in Fig. 15.

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