Organic fouling of RO membranes: Investigating the correlation of RO and UF fouling resistances for predictive purposes

Desalination 261 (2010) 272–283

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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

Organic fouling of RO membranes: Investigating the correlation of RO and UF fouling resistances for predictive purposes☆ D.C. Sioutopoulos, A.J. Karabelas ⁎, S.G. Yiantsios Department of Chemical Engineering, Aristotle University of Thessaloniki, Greece Chemical Process Engineering Research Institute, CERTH, P. O. Box 60361, GR 570 01, Thermi, Thessaloniki, Greece

a r t i c l e

i n f o

Article history: Received 14 April 2010 Received in revised form 25 June 2010 Accepted 28 June 2010 Available online 27 July 2010 Keywords: RO and UF membranes Organic fouling Humic acids Sodium alginate Mixtures

a b s t r a c t This study examines the characteristics of deposits from dead-end UF and cross-flow RO filtration of dilute mixtures of sodium alginate (SA) and humic acids (HA), which are representative of common foulants in RO and NF feed waters. The data are interpreted in terms of specific cake resistance, α. The presence of alginates in the mixed fouling layers, even in relatively small percentage, imparts characteristic properties to these deposits; i.e. a gel-like structure which is associated with reduced compressibility and permeability. With SA/ HA mixtures, high rejection of organic species and high deposition factors are obtained in UF and RO tests, respectively. The specific resistance of mixed SA and HA deposits tends to increase with increasing SA concentration in solution. The resistances α exhibit fairly strong (power law) dependence on the pressure difference across the cake, ΔΡc, for both RO and UF tests. The fairly satisfactory correlation of resistance α versus ΔΡc data, obtained from both types of tests (for the mixtures of organic species tested at small salinity) is a significant result of this work. Based on this correlation, an approach is suggested for estimating fouling index I and initial membrane fouling rate of a specific RO process, relying on limited UF tests. © 2010 Elsevier B.V. All rights reserved.

1. Introduction It has been recognized long ago (e.g. [1–3]) that the empirical Silt Density Index (SDI) and variations thereof [4], despite their wide acceptance in industry, have serious drawbacks for reliable prediction of RO/NF feed-water fouling propensity. Contrasted to the NF and RO filtration operations, carried out with very “tight” membranes under cross-flow conditions, the SDI test, employing a filter of relatively large nominal pore size (0.45 μm) in dead-end mode, has obvious limitations; in particular, the 0.45 μm filter cannot reject small colloidal particles and organic macro-molecules, and there is absence of tangential fluid shear and of concentration polarization effects (due to rejected salts) which play a significant role in RO/NF fouling. The problem of developing a more representative test, with theoretical underpinning, is still present despite significant advances made in understanding various aspects of membrane fouling over the past 20 years [5–11]. Efforts to develop a more reliable and easy to use technique, notably by Schippers and associates [12,13] rely on the fact that the dominant fouling mechanism in RO and NF processes is the formation of a layer (a

☆ This paper is respectfully dedicated to the memory of Sidney Loeb, whose pioneering work (with S. Sourirajan) laid the foundation of a new technology greatly benefiting human welfare. ⁎ Corresponding author. Chemical Process Engineering Research Institute, CERTH, P. O. Box 60361, GR 570 01, Thermi, Thessaloniki, Greece. E-mail address: [email protected] (A.J. Karabelas). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.06.071

“cake”) that can significantly degrade membrane performance. The general approach taken in recent years (e.g. in developing the modified fouling index — UF [14–16]) is to establish conditions of cake filtration in UF tests (which can be performed rather easily at low pressure) and to determine the respective fouling resistance. Then the target is to utilize the UF-derived cake resistances to deduce fouling rates in actual NF and RO plants operating at higher pressures. This “extrapolation” of UF cake resistances to the higher pressures of NF/RO is a critical issue of this approach, that has not been adequately addressed, despite significant contributions made on various aspects relating to the UF tests [9– 11,17,18]. Therefore, a new technique to determine a reliable “fouling index” for NF/RO processes has not been established yet. This publication is part of a systematic study aimed at developing a technique for making improved predictions of colloidal fouling rates in RO/NF plants, following the general methodology outlined above. Towards this goal, the novel approach taken [19] involves the experimental determination of fouling resistances (due to cake formation) from both RO and UF tests, with the same foulants and fluids, and efforts to correlate them, thus facilitating prediction of RO membrane fouling on the basis of limited UF tests. Prototype RO fouling experiments showed that there exists a linear dependence of fouling rates on foulant concentration (over the concentration range 5 to 20 mg/L) which allows extrapolation of the new results to the lower concentrations prevailing in practice. Systematic analysis of the specific cake resistances (α), determined from both RO and UF tests, shows that these resistances conform to a power-law dependence on pressure difference across the cake, although the α-values from RO

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and UF tests exhibit quantitative differences. It is, therefore, evident that the effect of pressure is quite important, and that it has to be adequately addressed in prototype tests for fouling index determination. This result suggests a direction (followed in this paper) for developing an improved tool to determine the fouling propensity of feed waters to NF and RO plants. The aforementioned tests [19] were carried out with species representative of two typical categories of foulants; i.e. inorganic (colloidal iron oxide) and organic (using separately humic acids and sodium alginate, a carbohydrate). The work reported herein is focused on mixtures of the latter two types of organic foulants, representing very significant classes of species, commonly encountered in seawater, and biologically treated effluents as well as surface waters, which are processed by RO for recycling and production of potable water, respectively [20–22]. Carbohydrates are poly-hydroxyl compounds, alternatively referred to as polysaccharides. Along with proteins and lipids, these compounds are formed in seawater through photosynthesis in living cells and micro-organisms that decompose, thus providing a significant amount of dissolved organic matter — or Dissolved Organic Carbon (DOC). Similar soluble compounds are produced in biological treatment of municipal effluents [22]. It should be noted that the amount of DOC in seawater is usually small (in the range 3 to 7 mg/L); a significant portion of that (15–30%) are the biodegradable carbohydrates [20] and another larger portion (often more than 70%) are the marine humus (humic and fulvic acids) which are chemically rather stable and refractory in nature [23]. Furthermore, there is mounting evidence [23,24] that these two classes of DOC (i.e. carbohydrates and humic acids), despite their rather small concentration in seawater, play a major role in RO membrane fouling if not adequately removed. In fact, recent work [25,26] suggests that polysaccharides tend to form quite coherent, gel-like fouling layers and to act as “binders” [6,25,40] in deposits with other foulants such as humic acids and proteins. Thus, the choice in this study to investigate mixtures of poly-saccharide and humic acids is evident. In view of the above, the scope of this paper is to employ the recently suggested [19] approach of determining the specific fouling resistances from both UF and RO tests, with the same fluids, in efforts to correlate them. In particular this paper aims: (a) to use organic foulants, i.e. dilute mixtures of sodium alginate (SA) — representative of polysaccharides — with humic acids (HAs), in proportions 25% SA– 75% HA and 50% SA–50% HA, thus extending the range of system parameter values, tested so far; b) to assess the possible correlation of experimentally determined specific resistances, α, from UF and RO tests; c) to explore the development of a technique, based on the new data, for estimating the fouling index I, as a measure of the feed-water fouling propensity for RO operations. 2. Experimental methods and materials

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digital flow meter (Humonics 1000) connected to a PC for automatic data acquisition. Superficial cross-flow velocity in the channel is maintained constant in all tests at 19 cm/s, in order to avoid flow velocity effects on cake resistance [27,28]. Temperature is controlled at 25 ± 0.1 °C through a cooling coil submerged in the feed-water vessel. To better simulate real systems, an open loop operation is established by the continuous introduction of water and foulant into the test section and subsequent disposal of both permeate and retentate. A fresh concentrated solution of foulants in distilled water, with concentrations in the range of 360–1800 mg/L (depending on the desired concentration in the feed water), is injected into the feedwater stream at a rate of 10 mL/min, and the pH is adjusted to 7.0. The feed-water flow rate in the 27 L feed vessel is 1.8 L/min, and thus the mean residence time of water and fouling species in the system is approximately 15 min. Feed water passes through a sand filter as well as through a cartridge filter to reach an SDI close to 2 and a turbidity typically less than 0.1 NTU. The feed water employed (of potable water quality) is characterized by a conductivity of approx. 680 μS/cm and total hardness of approx. 228 mg/L CaCO3 equivalent. To obtain the desired salinity, a concentrated solution of re-crystallized natural salt is prepared with a salt concentration of 18% w/w and injected in the feed stream prior to the cartridge filter at the appropriate rate with a dosimetric pump. The system can run virtually unattended for long periods of time. A typical RO experimental run presented in this section, including membrane conditioning in the flow system, lasts approximately 3 to 4 days. The salinities selected to be tested in the RO experiments are 500 and 2000 mg/L in TDS. Regarding permeate initial flux, experiments in the range of ~19 to ~40 L/m2 h, are employed by applying the appropriate pressure. An important consideration in this study is to establish a stable membrane performance (in terms of flux and rejection) before addition of the fouling species. As reported in the literature, a certain period of time is required for membrane setting, which refers to membrane adjustment to the pressure applied and to the ionic environment of the feed water. Additionally, preservatives with which the membrane is soaked for storage should be removed through water filtration. Therefore, each RO fouling experiment was preceded by a membrane setting test period, using solution chemistry and testing conditions similar to those in the ensuing fouling experiment. Thus, the observed changes in membrane performance (i.e. permeate rate and/or salt rejection) could be attributed to the net effect of the foulant addition. In each experimental run of this study, usually 48 h are dedicated to membrane setting with clean feed water. In almost all tests, a brackish water desalination RO membrane (Osmonics AG) was employed as a model membrane; it is a polyamide thin-film composite membrane with an average salt rejection of 99.5%, as reported by the manufacturer. A limited number of tests with humic acids was carried out with a high pressure RO membrane (Osmonics SC).

2.1. RO cross-flow tests 2.2. UF dead-end tests The experimental set-up is described in sufficient detail elsewhere [19] and only a summary is provided here. The experiments are performed in a laboratory-scale unit with a stainless steel cross-flow filtration test section which employs flat sheet membrane pieces. This unit is comprised of two steel plates; in the bottom plate a porous stainless steel sheet is embedded on which the membrane rests. By means of a spacer/flange, a rectangular channel is formed of uniform 1 mm gap. The effective area is 1.30 × 10− 2 m2. A piece of standard feed spacer of thickness approx. 0.7 mm, obtained from an Osmonics AG module, is placed on top of the membrane in order to simulate the hydrodynamic conditions prevailing in actual spiral wound membrane modules. Pressure and cross-flow rate are monitored through digital sensors and controlled through two needle valves at the entrance and exit of the test section. Permeate flow is continuously monitored through a

The laboratory-scale experimental set-up, where UF fouling tests are conducted, is described in detail elsewhere [19]. It includes a 30 mL cylindrical test cell accommodating a membrane filter of diameter 2.2 cm, which corresponds to an active filtration area of 3.8 cm2. At the bottom of the test unit a porous support is fitted onto which the membrane rests. The test cell can be used in either stirred or unstirred mode, under controlled pressure provided by a nitrogen line. Permeate is collected in a beaker placed on top of an electronic balance, which is connected to a computer for automatic recording of permeate weight as a function of time. In almost all tests, a hydrophilic polyacrylonitrile (PAN) UF membrane was employed, with a reported MWCO of 100 kDa (Ultrafilic Osmonics). Limited tests were carried out with a 30 kDa (YM30 Millipore) membrane. The criteria for selecting a UF membrane for these tests were primarily its

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reduced sensitivity to compaction effects and excellent chemical stability. The PAN membrane was also recommended, for the same type of tests, in a previous investigation [14]. 2.3. Fouling species and chemical reagents All chemicals used in the fouling experiments were reagent grade. Hydrochloric acid (37% w/v) was used to adjust feed stream pH to 7.0, whereas sodium chloride solutions were added in order to examine salinity effects on membrane fouling. Commercial humic acid (Aldrich) and sodium alginate (Sigma-Aldrich, St. Louis, MO) extracted from brown algae (with reported molecular weight in the range 12–80 kDa) were employed as received for the study of organic fouling. Fresh humic acid and sodium alginate solutions were prepared for each experiment using distilled water. In this study no dialysis or other treatment was performed on humic acids, as done in other studies (e.g. [7,28]), to avoid loss of the small MW species. To obtain a test solution close to real conditions and to increase the aggregation tendency and the efficiency of humic acids attachment to the membrane, calcium concentration was increased to 2 mM by injecting a concentrated solution of CaCl2 into the feed-water line in the RO tests, or similarly adjusting the solution concentration in the UF tests. It is well known that calcium promotes intra- and intermolecular bridge formation and aggregation of humic acids [26,29]. This trend is also observed in sodium alginate solutions. More specifically, the sodium alginate aggregation phenomena taking place in the presence of calcium ions are considered to result in the formation of an egg-box-shaped network, with strong intermolecular forces [30]. In the present experiments, humic acids concentration was determined through measurements of total organic carbon (TOC) with a TOC analyzer ((Shimadzu TOC — 5000A analyzer) and of ultraviolet (UV) absorbance at wavelength of 254 nm in a UV–VIS spectrophotometer (Shimadzu UV-1700 UV–Visible spectrophotometer), whereas sodium alginate concentration was determined by TOC measurements. In order to determine the apparent molecular weight distribution (AMW) of humic acids and of sodium alginate as well as the effect of the addition of 2 mM Ca2+ on their solutions, an ultrafiltration fractionation method was employed. The ultrafiltration membrane types used for this purpose were the YM100, YM30, and YM10 (Millipore). These are made of regenerated cellulose and are widely chosen for such measurements due to their low specific binding and the associated high solute recovery characteristics. The AMW exclusion limits specified by the manufacturer for the above membranes are 100, 30, and 10 kDa, respectively. Apart from experiments with model fouling species, ultrafiltration tests using treated and untreated seawater were also performed, in order to make a preliminary assessment of a technique proposed herein for fouling rate predictions. Seawater was obtained through an open intake in an industrial plant in the Thermaikos Gulf, near Thessaloniki [31]. Samples of treated seawater were obtained from pilot seawater pre-treatment unit, comprising Poly-aluminum Chloride coagulant addition and subsequent dual-media filtration [31,32]. 3. Theoretical background 3.1. Cake formation From filtration theory [33,34] based on Darcy's law, considering resistances in series, one obtains for the liquid flux J=

1 dV ΔP = A dt ηðRm + Rc Þ

ð1Þ

where ΔP is the applied pressure, Rm the clean membrane resistance and Rc a cake/fouling resistance to be further analyzed. Α is the

membrane area and η the dynamic viscosity. Assumptions usually made are a) that the cake resistance is proportional to the solid mass deposited on the membrane surface, and b) that the cake filtration performance under constant pressure is characterized by an average specific resistance α, so that Rc =

αCb V A

ð2Þ

where Cb is the bulk solids concentration. Substituting Eq. (2) in Eq. (1) and integrating one obtains
  ηαCb ηRm 2 V−t = 0 + V ΔP ⋅ A 2ΔP ⋅ A2




ð3Þ

To interpret experimental data, Eq. (3) is recast in the form
 t ηRm ηαCb = + V 2 V ΔP ⋅ A 2ΔP ⋅ A

ð4Þ

In a t/V versus V plot, the slope λ≡

ηαCb 2ΔP ⋅ A2

ð5Þ

of the linear region of the filtration curve is characteristic of cake filtration, for constant pressure. Schippers and Verdouw [12] have proposed the use of this quantity (λ), termed modified fouling index (MFI), as a measure of the fouling propensity of filtered water. Moreover, the quantity ð6Þ

I = α⋅Cb

usually called “fouling index,” is considered a measure of the water fouling potential. It has been recognized a long time ago (e.g. [35]) that in filtration the specific cake resistance (or the cake permeability) is affected by the applied pressure and that one may represent this effect (as a first approximation) by an empirical expression of the form α = αo ΔP

n

ð7Þ

where αo is the specific cake resistance at a reference pressure and ΔP is the pressure difference between applied pressure and reference pressure. The exponent n is referred to (e.g. [14–16]) as “compressibility coefficient” since it provides a measure of that effect. The same type of expression holds for the fouling index I, in the usual case of constant foulant bulk concentration Cb,; i.e., I = m ΔP

n

ð8Þ

Regarding pressure effects in dead-end filtration, it has been established [36,37] that the solids volume fraction and porosity may vary across the cake; i.e. the solids fraction ϕ may vary from a maximum (depending on pressure and system physico-chemical properties) at the membrane surface to a minimum at the top, ϕg, usually referred to as gelation volume fraction, which represents the transition from a ‘fluid-like’ dispersion to a ‘solid-like’ deposit. Therefore, the quantity α in Eq. (7) should be interpreted as a measure of the average specific resistance across the cake. Furthermore, filter cakes from agglomerated colloidal particles usually exhibit a readily measurable compressive yield stress (e.g. [36,37]), i.e. a critical compressive stress at which a particular cake of solids fraction ϕi will irreversibly consolidate to a new equilibrium solids fraction ϕ (Nϕi ).

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3.2. RO membrane fouling — determination of specific cake resistance α In RO membrane filtration, Eq. (1) holds, where the effective transmembrane pressure ΔPeff = [ΔP − Δπm] should be used by taking into account the osmotic pressure difference Δπm for saline waters. Concentration polarization effects, for the case of spiral wound modules with spacers can be also included in estimating Δπm [19]. The permeate flux at zero time (i.e. just before foulant addition) is a readily measurable quantity, defined in terms of ΔPeff and clean membrane resistance, Rm, Jo ≡

ΔPeff ηRm

ð9Þ

275

with very few exceptions for the smallest humic acid concentrations), 2 ηI

one obtains J o ΔP I=

eff

R′

= R d which leads to m

R′d Jo

ð13Þ

It is, therefore, possible by using Eq. (13) to determine the fouling index I for RO, directly from experimental data. Furthermore, by collecting data over a range of foulant concentrations Cb, one can determine the specific fouling resistance α (using Εq. 6), for a fixed initial flux Jo. 4. Experimental results and discussion

An analysis of the RO fouling problem at hand, which involves cake formation, is presented in detail elsewhere [19], and leads to the following expression, relating the fouling index I with the temporal variation of the normalized flux, "

#

J 2 ηI = 1− Jo ⋅t Jo ΔPeff

ð10Þ

This expression holds for the initial period of RO/NF membrane fouling, when there is a linear variation of J/Jo with t. This is, indeed, observed and of interest in practice, where the foulants concentrations are relatively small (of the order of, and smaller than, what is employed in the present study); furthermore, a flux drop of (J0 − J)/Jo ~ 10% (within this linear time period) is a broadly accepted criterion set by membrane manufacturers and plant operators to stop and clean the system. The essential difference between RO cross-flow filtration and relatively low pressure filtration (i.e. ultrafiltration) is that the additional resistance Ra due to fouling and other effects is much smaller than the membrane resistance Rm. Therefore, Eq. (1) can be modified (by multiplying nominator and denominator by [Rm − Rα]) as follows: J=

ΔPeff ΔPeff ðRm −Ra Þ ΔPeff ðRm −Ra Þ ΔPeff   ≈ = = ηðRm + Ra Þ ηRm η R2m −R2a ηR2m

 1−

Ra Rm



ð11Þ Compared to the original, this equation is accurate within 1% for [Rα/ Rm] ≤ 0.1. To proceed, the additional resistance Rα is taken to be composed of two parts, i.e. one due to membrane setting effects (Rs), and another due to the deposition of the fouling species (Rd). Considering the short duration of the fouling tests and the relatively small flux decline, prior to and after fouling species introduction, both terms can be assumed to be linear in time, i.e. Rs = Rs′ · t and Rd = Rd′ · t. Then the above equation can be written as ′

J Rt = 1− s Jo Rm

for t b ti

J R′ t R′ ðt−ti Þ = 1− s − d for t N ti Jo Rm Rm

4.1. Molecular weight distribution of humic acids and sodium alginate The apparent molecular weight distribution of each organic foulant (i.e. humic acids and sodium alginate) are shown in Fig. 1, obtained by the ultrafiltration fractionation method from their dilute solutions, with the addition of 2 mM Ca2+. More data, shown elsewhere [29,30], show that in the absence of calcium most of the dissolved humic acids and sodium alginate are below the nominal MWCO of the UF membrane employed in the fouling tests; i.e. 100 kDa. However, with addition of Ca2+ there is an aggregation tendency leading to larger sizes. This trend is more pronounced in the case of sodium alginate, where the fraction below 10 kDa is practically zero, while that of N100 kDa is more than 85%. The significantly greater amount of large species (N100 kDa) existing in the sodium alginate solution, suggests that rejection in the UF fouling experiments would be greater than that of humic acids; this was indeed the case in the subsequently presented filtration data. Similar results have been reported by Katsoufidou et al. [30] in a systematic study of the calcium effects on fouling of UF hollow fibers. 4.2. Reverse osmosis experiments 4.2.1. Experiments with single foulants The behavior of single foulants (i.e. sodium alginate and humic acids alone), under various conditions in a concentration range of 2.5 to 20 mg/L, was examined in detail in a previous paper [19]. Some fouling data obtained with these species are given here for the

ð12aÞ

ð12bÞ

where ti is the time when fouling species are introduced in the experimental system or come in contact with the membrane. Eqs. (12a) and (12b) are employed sequentially to determine Rs′ first and then Rd′. The latter is directly measured in RO tests, and used to determine fouling parameters (I, α), as subsequently discussed. It is pointed out again, that a basic premise in this analysis is that the cake fouling resistance is much smaller compared to clean RO membrane resistance Rm, which is the case for sufficiently short experimentation times, as the present data clearly show. Finally, by comparing Eq. (10) with Eqs. (12a) and (12b), the latter applied for t N ti and R′s ≪ R′d (as is the case in the present experiments,

Fig. 1. Apparent molecular weight distribution of humic acids (Aldrich) and sodium alginate (Sigma-Aldrich) obtained by ultrafiltration fractionation. [Ca2+] = 2 mM, pH = 7, TDS = 500 mg/L.

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purpose of comparison with those of their mixtures, to be subsequently presented. Typical sets (for fixed initial flux Jo) of experimentally determined fouling indices I, in RO tests, as a function of humic acids and sodium alginate concentration are plotted in Fig. 2. A clearly linear dependence of fouling index on species concentration is observed. This linearity of index I variation with concentration, allows prediction (by extrapolation) of the fouling rate at lower concentrations with a satisfactory degree of confidence. It should be also noted that the initial membrane flux has a pronounced effect on the rate of fouling, as expected; i.e., the greater the initial flux, the more severe the fouling becomes, as shown in the data for HA at Jo = 25 and 40 L/m2 h. Finally, fouling due to SA species is significantly greater compared to HA, under the same conditions, as clearly shown in Fig. 2. Additional new data in support of this observation and discussion on the significance of SA fouling are presented in the following. 4.2.2. Experiments with mixtures of foulants Reverse osmosis membrane fouling by mixtures of sodium alginate (SA) and humic acids (HA) with proportions [SA/HA]=[1/3] and [1/1] was investigated. These ratios were selected in view of the fact that, as outlined in the introduction, they represent realistic proportions of these two species in feed water (seawater, treated effluents) to RO plants. A brackish water desalination RO membrane (Osmonics AG) was employed in these fouling experiments. The latter covered a sufficiently large range of mixture concentrations, whereas the clean membrane flux, Jo, before the introduction of the fouling species, varied in the range of 19 to 40 L/m2 h. In order to examine the effect of initial flux and ionic strength on membrane fouling, two sets of experiments were conducted with solutions of TDS 500 mg/L and 2000 mg/L. Typical raw and normalized data obtained in an experimental sequence, which included adjustment to pH=7.0, membrane setting period, and fouling species introduction under constant pressure, are presented in Figs. 3 and 4, for solutions with mixture ratios [SA/HA]=[1/3] and [SA/HA]=[1/1], respectively. The first part of the graph (i.e. until ~ 40 h; Fig. 3a) represents the flux decline attributed to membrane setting, whereas the second one (i.e. after ~ 40 h) is due to foulant addition. A similar trend is obtained in all the tests with the foulant mixtures. After foulant addition, a sharp linear decline of the permeation rate is obtained, which is similar to that in the tests with either sodium alginate or humic acids alone [19]. The data treatment procedure, described in Section 2, is applied to extract the fouling index, I, for each test. The results obtained are summarized in Tables A1 and A2. The fouling index, I, as a function of mixture concentration in the feed water for two sets of experiments, with mixture ratio [SA/HA] = [1/3], is

Fig. 3. RO fouling experiments; (a) raw experimental data of permeate flux and (b) normalized membrane flux, versus time before and after fouling species introduction. Feed-water TDS 500 mg/L. Mixture mass ratio (75% humic acid–25% sodium alginate); concentration 10 mg/L; pressure: 909 kPa (132 psi).

plotted in Fig. 5. As in the single foulant experiments (Fig. 2), a clear effect of fouling species concentration on fouling index is observed, and a linear relationship between mixture concentration and fouling index is obtained, despite the scatter due to experimental errors. Furthermore, it will be noted that the effect of feed-water ionic strength (in the range tested) appears to be relatively smaller for the SA–HA mixture compared to that of SA or HA alone as may be observed upon inspection of data reported in [19] and Tables A1 and A2 of this paper. Another observation that can be made by comparing the fouling index data of mixed foulants to those of sodium alginate alone (Fig. 2), under similar concentrations, is that there is no apparent enhancement effect as reported by Ang and Elimelech [25] for RO tests involving a mixture of sodium alginte with BSA. In fact the opposite is observed, i.e., that the overall fouling tendency due to the 25%–75% mixture is weaker than that obtained with sodium alginate alone.

Fig. 2. Fouling index, I, data from RO tests as a function of humic acid (HA) and sodium alginate (SA) concentration in the feed water.

4.2.3. Deposition factor A significant issue, especially in regard to correlation of RO with UF cake resistances, is the extent to which the cross-flow, prevailing in

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277

Fig. 5. Fouling index, I, as a function of foulant mixture (75% humic acid–25% sodium alginate) concentration, for two sets of reverse osmosis experiments.

4.3. Ultrafiltration experiments

Fig. 4. RO fouling tests; (a) raw experimental data of permeate flux and (b) normalized membrane flux, versus time before and after fouling species introduction. Feed-water TDS 2000 mg/L. Mixture mass ratio (50% humic acid–50% sodium alginate); concentration: 10 mg/L. Pressure: 1026 kPa (175 psi).

RO tests, may affect the particle deposition efficiency and thus cake fouling resistance characteristics. An exact determination of incomplete foulant deposition is certainly difficult to make. Nevertheless, the deposition efficiency or deposition factor in RO experiments was estimated for the present tests, by computing the ratio of the actual amount of fouling species deposited on the membrane surface over the maximum amount; the latter is the total foulant mass present in the feed stream that could be attached to the membrane. The former was estimated by soaking fouled RO membrane pieces in 200 mL of 0.1 N NaOH solution for adequate time (~1 day) and then measuring the UV254 absorbance and the TOC content for the determination of humic acid and sodium alginate deposition factor, respectively. Multiple membrane pieces were used to take into account the variability in membrane properties. The theoretical mass deposition values were calculated on the basis of the total permeate volume of each RO test. Thus, the mean deposition factor values were estimated to be 0.6, 0.9 and 0.9 for humic acids, sodium alginate and their mixtures respectively. Using these deposition factor values, revised specific cake resistances from the RO tests were finally calculated.

4.3.1. Organic species rejection by UF membrane In order to facilitate further data interpretation, it is useful to examine the organic species rejection in the UF tests for all the organic foulants tested; i.e. sodium alginate, humic acid and mixture thereof. The percentage total rejection for all the foulants, using a feed water with a 10 mg/L total concentration and 2 mM calcium, is depicted in Fig. 6. It must be noted that total rejection is determined by measuring the composite concentration, in the total permeate volume at the end of each test; therefore, this measurement is an average of the instantaneous permeate concentration, which may tend to decrease with time. Data on the temporal variation of rejection for all foulants (not presented here due to space limitations) show that this reduction from start to end of the UF test is well within ±10% of the average. The following observations are made upon inspection of the data in Fig. 6. First, the observed rejections of sodium alginate and humic acids are in accord with what would be expected on the basis of the apparent molecular weight distribution presented in Fig. 1; thus, sodium alginate rejection is approx. 80%, whereas for humic acids it is approx. 70%. Second, the rejection for

Fig. 6. Total permeate concentration of humic acids [HAs], sodium alginate [SA] and [SA/ HA] = [1/3] mixture for dead-end filtration with a UF membrane (PAN, MWCO 100 kDa). Feed concentration 10 mg/L; [Ca2+] = 2 mM.

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the [SA/HA]= [1/3] mixture appears to be greater (approx. 90%) than the rejection of either sodium alginate or humic acid. For analyzing the data from [SA/HA] =[1/1] mixture tests, the same species rejection (90%), as in the [SA/HA] =[1/3] tests, was employed. 4.3.2. Fouling resistances obtained with SA and HA mixtures Experimental work with a polyacrylonitrile (100 kDa) ultrafiltration membrane was carried out using solutions with mixtures of SA and HA in the concentration range of 6 to 20 mg/L. In order to increase the aggregation tendency of sodium alginate, a 2 mM CaCl2 was added as in the reverse osmosis experiments. Pressure effects were studied by conducting experiments at pressures, 5, 10, and 20 psi (34, 69 and 138 kPa). To interpret the experimental data, we consider again cake filtration, characterized by an average specific resistance α, and the analysis outlined in the preceding Section 2.1. Typical raw data of filtered volume of a foulant mixture solution (with 75% humic acids, 25% sodium alginate) as a function of time, as well as treated data according to the cake filtration theory (Eq. (4)) are presented in Fig. 7. It is

Fig. 7. (a) Permeate volume as a function of time for batch filtration and (b) data treatment according to cake filtration theory for batch filtration of sodium alginate with membrane UF (PAN, MWCO 100 kDa). Mixture (75% humic acids, 25% sodium alginate) and NaCl concentrations are 20 mg/L and 500 mg/L, respectively.

observed that the cake filtration model satisfactorily describes the experimental data for almost the entire filtration period, with the exception of the first minutes of experiments, over which the dominant filtration mechanisms may be different. Similar data are obtained with the 50% humic acids, 50% sodium alginate foulants mixture. The experimental data and related parameters obtained from these ultrafiltration experiments for foulant mixtures are summarized in Tables A3 and A4. It is evident that pressure has a significant effect on the obtained cake resistances. Apparently, at higher pressures more compact and less permeable cakes are created. Such an effect, which is pronounced in compressible fouling deposits, is usually modeled by considering a power-law dependence of cake resistance on applied pressure (Eq. (7)), as discussed above. Indeed, plotting the mean specific cake resistance α as a function of pressure in logarithmic coordinates, a power-law type of variation is obtained, as shown in Fig. 8 for tests with the mixture of 75% humic acids and 25% sodium alginate. Data obtained under the same conditions, but with different ionic strengths (i.e. 500 and 2000 mg/L) as well as data with a tighter UF membrane (30 kDa) are plotted in Fig. 8. The following additional observations can be made regarding these data. First, as shown elsewhere [19], the power-law type dependence of resistance α on the applied pressure can be used to present the data, provided that the cake resistance ΔPc is greater than 40–50% of the applied pressure; this may not be satisfied in some UF tests. Second, increasing ionic strength causes an increase of specific resistance α, as also observed by other researchers (e.g. [38]). Third, the tighter 30 kDa membrane appears to be associated with somewhat greater specific resistances α, possibly due to the increased foulants rejection, although this point may have to be reconsidered further on, when the data are plotted as a function of pressure difference across the cake, ΔPc. Fourth, despite their scatter the experimental data (with UF 100 kDa membrane) suggest that the specific cake resistance is almost independent of foulants concentration, for a given pressure. Fig. 9 presents similar data with a 50% humic acids–50% sodium alginate mixture, and a fixed initial foulants concentration 10 mg/L. The observation made for the preceding case (Fig. 8), regarding the effect of water ionic strength, holds for this foulants mixture as well.

Fig. 8. Specific cake resistance, α, as a function of applied pressure from the ultrafiltration experiments with a mixture 75% humic acid–25% sodium alginate. Detailed data in Table A3.

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279

Fig. 9. Specific cake resistance, α, as a function of applied pressure in the ultrafiltration experiments with mixture (50% humic acid–50% sodium alginate). Mixture concentration: 10 mg/L. Detailed data in Table A4.

Fig. 10. Specific cake resistance α, versus pressure drop across the cake for deposited mass ~ 1 g/m2, obtained from both UF and RO experiments with mixture (75% humic acid–25% sodium alginate). Plotted RO and UF cake resistance values are listed in Tables A1 and A3, respectively.

4.4. Comparison of UF and RO specific cake resistances

affect the RO fouling rates; however, increasing salinity tends to enhance UF fouling rates [38]. Interestingly, UF data obtained with two different membranes (100 kDa and 30 kDa, Figs. 10, 12) are in substantial agreement for these gel-type deposits. Finally, it is significant to stress the same pressure dependence of both UF and RO specific fouling resistances α, which provides the basis for suggesting a technique allowing predictions of RO fouling rates from UF tests. The general trend of the UF and RO fouling data, presented in Figs. 10–13, is that with increasing percentage of polysaccharides [SA] in a mixture with humic acids [HA], the fouling resistance α, tends to increase. This is clearly shown in Fig. 14, where results from four sets of UF experiments are plotted. The conditions of these tests are the same, with the exception of the mass ratio [HA/SA] which is different; i.e., [1.0/ 0.0], [0.75/0.25], [0.5/0.5], [0.0/1.0]. The significant increase of fouling resistance α, with increasing SA percentage in the mixture is evident. Additionally, the reduced compressibility (i.e. smaller slope of data) of

In a recent paper [19], interpretation of specific cake resistance data, obtained in UF and RO tests (similar to those described here) with single foulants (i.e. HA, SA, or colloidal iron), led to the following conclusions: – The cake resistances α from RO tests, compared to those from UF, were significantly larger for colloidal iron, modestly larger for humic acids and fairly close (especially for saline solutions) in the case of sodium alginate solutions. – Main factors contributing to the above differences can be pressure (or pressure drop across the cake, ΔPc), UF membrane foulant rejection, fluid shear in RO membrane elements, and cake-enhanced concentration polarization manifested only in RO. These factors were addressed [19], through theoretical analysis and additional specific experiments. In the range of the parameters tested, the first three factors were found to be significant; moreover, cake-enhanced concentration polarization (of no significance in the present tests) could be also an important factor in the case of high salinity waters, i.e. seawater. As in the previous study [19], a consistent comparison of specific cake resistances α, obtained from RO and UF experiments under the same bulk fluid conditions, can be made by plotting α-values versus the respective pressure drop across the cake, ΔPc, but not the applied pressure in each case. However, since ΔPc varies with the deposited mass, this comparison should be made under the same deposited mass on the membrane surface (i.e. foulants surface density in g/m2) for both types of tests, within the time period of the present experiments. The deposited foulant surface density can be estimated from the mass corresponding to permeate volume, corrected for incomplete species rejection and deposition in UF and RO tests, respectively, as discussed in preceding sections. Data under these conditions are plotted in Figs. 10–13, where the pressure drop across the cake ΔPc corresponds to estimated deposit mass density 1 g/m2. These data show that, in general, the RO cake resistances tend to be higher than those from UF tests, especially for humic acids (100%). It is interesting, however, that the RO cake resistances from tests with sodium alginate (SA 100%) and mixtures of SA with HA are in fair agreement with those from UF tests (for the same fluid salinity). It should be also observed that in all these data the effect of salinity (for the cases of 500 and 2000 mg/L TDS) does not appear to significantly

Fig. 11. Specific cake resistance α, versus pressure drop across the cake for deposited mass ~ 1 g/m2, obtained from both UF and RO experiments with mixture (50% humic acid–50% sodium alginate). Plotted RO and UF cake resistance values listed in Tables A2 and A4, respectively.

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Fig. 12. Specific cake resistance α, versus pressure drop across the cake for deposited mas ~ 1 g/m2, obtained from both UF and RO experiments with sodium alginate (100%). Plotted RO cake resistance values correspond to individual experiments. Detailed data in [19].

Fig. 14. Specific UF fouling resistances versus ΔPc with foulant mixtures of sodium alginate and humic acids, in various proportions. Test conditions: total concentration of foulants 10 mg/L, TDS = 2000 mg/L, [Ca2+] = 2 mM, pH = 7.

the gel-type deposits involving sodium alginate, compared to deposits comprised of humic acids only, is also indicated in the data of Fig. 14. Finally, the similar compressibility of deposits of alginate alone and its mixtures, which is different than that of 100% humic acids deposits, lends additional support to the notion that polysaccharides in mixtures with other foulants (even in relatively small percentages) act as “binders,” thus, strongly influencing their properties such as compressibility and permeability, which are of particular interest to this study.

as the membranes after the fouling tests were left to dry at ambient temperature. Images in Fig. 15a and b show gel-like deposits, obtained in UF and RO tests, respectively; the very smooth surfaces are indicative of the uniformity of such films due to the egg-box gel network. The deposits of [SA/HA] = [25%/75%], depicted in Fig. 15c, are characterized by non-uniformity with humic acids particles apparently embedded in the alginate matrix. Of particular interest are deposits on UF membrane, from filtration of treated seawater, which are discussed in the following section. The particular seawater sample is characterised by TOC ~ 3.2 mg/L, SDI15 ~ 3.0, and appears to form a thin, gel-like, layer, with embedded assorted particulates.

4.5. Fouled membrane examination by SEM Some evidence in support of the results described above is obtained by inspecting typical SEM images of UF and RO deposits of model organic foulants (Fig. 15a to c) as well as of pre-treated seawater (Fig. 15d). All images presented in Fig. 15 correspond to experiments conducted under comparable fouling conditions, where-

5. An approach to estimate the fouling index I of feed water to a RO process As shown in the preceding section, by plotting data of specific fouling resistance versus an estimate of pressure drop across the foulant cake, ΔΡc, from both UF and RO tests, one can obtain a fair correlation, at least under some conditions of practical interest, as is the case of mixed foulants involving polysaccharides. This fact provides the basis for suggesting an approach for predicting the fouling index I, of feed water to a RO process, relying on a limited number of UF tests, as follows. The general Eq. (1), considering resistances in series, leads to ΔΡc Rc = ΔΡ Rm + Rc

ð14Þ

which is applicable to both RO and UF conditions. Here [ΔΡ = ΔΡeff, Rm = RRO] and [ΔΡ = ΔΡap, Rm = RUF] represent known parameters in RO systems and UF tests, respectively. The expression Rc =

Fig. 13. Specific cake resistance α, versus pressure drop across the cake for deposited mass ~1 g/m2, obtained from both UF and RO experiments with humic acids (100%). Plotted RO cake resistance values correspond to individual experiments. Detailed data in [19].

ðaCÞV I⋅V = A A

ð15Þ

is also applicable to both RO and UF, under the conditions discussed in Section 2. For a particular feed water (to a RO plant), of constant foulants concentration C, one may proceed as follows to determine the fouling index I. Using a membrane with known RUF, a number of UF tests (at least two) are carried out, usually in the range 0.5 to 2.0 bar, to

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281

Fig. 15. SEM images: (a) sodium alginate (100%) UF deposits; (b) sodium alginate (100%) RO deposits; (c) UF deposits of 25% sodium alginate–75% humic acids; (d) UF deposits from treated seawater (TOC ~ 3.2 mg/L, SDI15 ~ 3.0).

determine pairs of values [ΔΡap, I]. These data allow determination of the fouling index dependence on ΔPc, i.e., I = m½ΔΡap 

n

ð16Þ

which holds for ΔΡc N ~ (0.4ΔΡap) as shown elsewhere [19]. By combining Eqs. (14), (15) and (16), one obtains ΔΡc ½I =m =n 1

=

Rc = RUF + Rc

h

I

i

RUF +I V= A

ð17Þ

Regarding the fouling index for RO, Eq. (14) can be used to compute the fouling resistance, Rc, for a particular RO operation characterized by known clean membrane resistance, RRO, and ΔΡeff; i.e., ΔΡc = ΔΡeff

h

RRO V= A

iI

ð18Þ +I

It will be noted that if RRO and ΔΡeff are selected, as usual, the initially imposed permeation flux Jo is also specified. A pair of values (I, ΔΡc) is a solution satisfying Eqs. (17) and (18), which is applicable to conditions (e.g. perfect or very high retention, of foulants contained in the permeate, by both UF and RO membranes, as is the case with the mixtures of organic foulants investigated here) where there is a good correlation of I with ΔΡc from both UF and RO tests. Such a solution (I, ΔΡc) is obtained for a parameter value (V/A) ≈ (Jot), sufficiently small to correspond to the initial time period (t) of linear

flux reduction of the RO process; e.g., of order 0.1 m3/m2. Thus, one can estimate the fouling index I of the feed water to a particular RO process. The fouling index I obtained in this manner, aside from the fact that it is an indicator of the fouling propensity of RO feed water, can be also used to estimate the initial flux reduction due to fouling by employing Eq. (10). For instance, one can estimate the time period it takes for 10% reduction of relative flux J/J0, which is often employed as an indicator to decide when RO system cleaning is required. 6. Conclusions and discussion The choice to investigate the fouling characteristics of mixtures of polysaccharides and humic acids is justified by the fact that these two types of species are major foulants, ever present in common RO/NF feed waters, i.e. seawater and treated effluents. The fouling behavior of each one of these groups of compounds, separately, has been studied rather extensively; however, the fouling characteristics of their dilute mixtures has received much less attention. The substantial amount of new UF and RO fouling data, with dilute model solutions involving mixtures of sodium alginate (SA) and humic acids (HAs), in the presence of calcium ions, sheds more light to the significant problem of membrane fouling by dissolved organic matter. The main conclusions reached in this work, some of them confirming previous study results, are summarized as follows: – Dilute mixtures of SA and HA tend to form rather coherent geltype deposits in both dead-end UF and cross-flow RO experiments. The significant role of polysaccharides in the mixtures manifests itself in the reduced compressibility and permeability of these

282

–

–

–

–

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deposits, forming on the membranes, compared to deposits from humic acids alone. The specific cake resistance, α, of SA and HA foulant mixtures, tends to increase with increasing percentage of SA in the solution concentration, all other conditions being the same. The specific resistance, α, is significantly dependent on pressure difference across the cake, ΔΡc, for both UF and RO tests; this dependence can be represented by a power-law type of correlation. The fact that resistances α, from RO membrane fouling tests, conform to this type of dependence (the same as that for UF tests) is an important result of this work. For dilute humic acids (100%) solutions, the RO membrane resistances α (plotted versus ΔΡc) are noticeably higher than those from UF tests. However, this difference tends to diminish (and to disappear) with increasing percentage of SA in the concentration of foulants. The satisfactory correlation between resistances α and corresponding ΔΡc, from both RO and UF tests (using mixtures of organic species, and salinity typical of brackish water), provides the basis for suggesting a sound approach for predicting the fouling propensity of RO process feed waters from UF tests.

Regarding the correlation of UF and RO fouling resistances α, or fouling indices I, which are explored in this paper for predictive purposes, the following additional comments may be made. The satisfactory correlation obtained for deposits of alginates, and their mixtures with humic acids, is attributed to the fact that these gel-like layers are characterized by rather strong intermolecular adhesive forces [30], which are likely greater than those of humic acids alone. It appears, therefore, that the cohesiveness of alginate layers may be the dominant deposit characteristic even for layers formed under different conditions (i.e. dead-end versus cross-flow), thus leading to UF and RO “cakes” of very similar permeabilities and resistances α. In support of this hypothesis are results of other studies, carried out under conditions

similar to the present tests, showing that the effect of increasing crossflow velocity on the coherent alginate layers was insignificant [28], whereas it was quite significant for deposits of humic acids alone [41]. Furthermore, similar fouling behavior may be expected from combined organic–inorganic deposits where polysaccharides act as “binders” (e.g. [39]), imparting their properties to the mixed deposit characteristics. The fairly good correlation of fouling resistances obtained with alginate containing layers, in constant-pressure filtration, may not hold for different physico-chemical systems; such a system is the model colloidal iron dispersion [19]. Therefore, further investigation of the correlation of UF and RO fouling resistances (or lack thereof) is obviously required, as outlined elsewhere [19], to explore its limits of applicability. Other factors that need attention in future research are the feed-water salinity and foulant-membrane surface interactions (e.g. [42]), which may significantly affect fouling resistance. Feed-water chemical composition (especially high salinity, presence of other inorganic species) may significantly affect fouling layer properties and may promote cake-enhanced concentration polarization [5]. Therefore, additional experimental work is required to investigate such effects and to assess (and possibly further develop) the approach suggested here for RO fouling index predictions. Finally, it should be noted that this study has been carried out under conditions of constant filtration, as done in the commonly used tests for assessing fluid fouling propensity [4,14–16]. However, full scale RO systems usually operate in a constant-flux mode. Under such conditions, the increasing (with time) fouling thickness leads to an increasing pressure. Mainly due to cake compressibility effects, the specific cake resistance α of such layers would, in general, tent to increase with time to an extent depending on ΔP, unlike the case of constant-pressure filtration where it remains practically constant. The extent of this variability of resistance α, under constant flux, under typical conditions prevailing in membrane plants, and its relation to α-values obtained under constant pressure, are issues that require further research and they are currently under investigation in this laboratory.

Appendix A Table A1 Analysis of data from reverse osmosis experiments with a mixture of 75% humic acids and 25% sodium alginate. Values of specific cake resistance, α, are determined from Fig. 5 for each set of experiments. Rs′ (m− 1 s− 1)

Rd′ (m− 1 s− 1)

I (m− 2)

High flux experiments; TDS = 500 mg/L; α = 2.7 × 10+ 15 or a⁎ = 3.0 × 10+ 15 m kg− 1 2 41.8 132 (909) 7.7 × 10+ 13 6 40.1 132 (909) 8.1 × 10+ 13 10 42.0 132 (909) 7.7 × 10+ 13

3.2 × 10+ 6 7.0 × 10+ 6 1.3 × 10+ 7

6.6 × 10+ 7 1.7 × 10+ 8 3.2 × 10+ 8

5.7 × 10+ 12 1.5 × 10+ 13 2.8 × 10+ 13

Low flux experiments; TDS = 2000 mg/L; α = 3.1 × 10+ 15 or a⁎ = 3.4 × 10+ 15 m kg− 1 2 26.3 108 (774) 1.0 × 10+ 14 5 26.0 103 (710) 9.7 × 10+ 13 8 26.8 132 (909) 1.2 × 10+ 14 10 24.8 132 (909) 1.3 × 10+ 14

1.6 × 10+ 7 2.0 × 10+ 7 1.3 × 10+ 7 2.1 × 10+ 7

7.6 × 10+ 7 1.4 × 10+ 8 1.5 × 10+ 8 2.1 × 10+ 8

1.0 × 10+ 13 2.0 × 10+ 13 2.1 × 10+ 13 3.1 × 10+ 13

C (mg L− 1)

ΔP psi (kPa)

J0 (Lm− 2 h− 1)

Rm (m− 1)

⁎ Corrected for incomplete deposition onto the membrane surface. Table A2 Analysis of data from reverse osmosis experiments with a mixture of 50% sodium alginate and 50% humic acids. C (mg L− 1)

J0 (Lm− 2 h− 1)

ΔP psi (kPa)

Rm (m− 1)

Rs′ (m− 1 s− 1)

Rd′ (m− 1 s− 1)

I (m− 2)

α⁎ (m kg− 1)

TDS = 500 mg L/L 10 10 10 10

19.3 25.7 32.1 37.8

90 (620) 125 (861) 150 (1034) 170 (1171)

1.08 × 10+ 14 1.15 × 10+ 14 1.11 × 10+ 14 1.08 × 10+ 14

8.1 × 10+ 7 6.5 × 10+ 7 3.3 × 10+ 7 3.5 × 10+ 7

1.8 × 10+ 8 2.4 × 10+ 8 5.2 × 10+ 8 6.2 × 10+ 8

3.4 × 10+ 13 4.1 × 10+ 13 5.9 × 10+ 13 5.9 × 10+ 13

3.8 × 10+ 15 4.6 × 10+ 15 6.5 × 10+ 15 6.6 × 10+ 15

TDS = 2000 mg/L 10 10 10

21.0 25.6 30.7

105 (723) 135 (930) 175 (1206)

1.15 × 10+ 14 1.09 × 10+ 14 1.23 × 10+ 14

1.9 × 10+ 7 7.7 × 10+ 7 2.0 × 10+ 7

2.3 × 10+ 8 4.3 × 10+ 8 6.2 × 10+ 8

4.0 × 10+ 13 6.0 × 10+ 13 7.3 × 10+ 13

4.5 × 10+ 15 6.7 × 10+ 15 8.1 × 10+ 15

⁎ Corrected for incomplete deposition onto the membrane surface.

D.C. Sioutopoulos et al. / Desalination 261 (2010) 272–283 Table A3 Analysis of data from Ultrafiltration experiments with a mixture of 75% humic acid and 25% sodium alginate. α (m kg− 1)

α⁎ (m kg− 1)

TDS = 500 mg/L Membrane type: Osmonics Ultrafilic, MWCO 100 kDa; 5 (34.5) 6 4.6 × 10+ 12 10 7.7 × 10+ 12 16 1.0 × 10+ 13 20 1.1 × 10+ 13 10 (68.9) 6 5.4 × 10+ 12 10 8.0 × 10+ 12 16 1.3 × 10+ 13 20 1.5 × 10+ 13 15 (103.4) 6 6.6 × 10+ 12 10 8.9 × 10+ 12 16 1.6 × 10+ 13 20 1.6 × 10+ 13 20 (137.8) 6 6.0 × 10+ 12 10 1.0 × 10+ 13 16 1.6 × 10+ 13 20 1.8 × 10+ 13

7.7 × 10+ 14 7.7 × 10+ 14 6.7 × 10+ 14 5.7 × 10+ 14 9.0 × 10+ 14 8.0 × 10+ 14 8.1 × 10+ 14 7.7 × 10+ 14 1.1 × 10+ 15 8.9 × 10+ 14 1.0 × 10+ 15 8.2 × 10+ 14 1.0 × 10+ 15 1.0 × 10+ 15 1.0 × 10+ 15 9.0 × 10+ 14

8.5 × 10+ 14 8.5 × 10+ 14 7.4 × 10+ 14 6.3 × 10+ 14 1.0 × 10+ 15 8.9 × 10+ 14 9.0 × 10+ 14 8.5 × 10+ 14 1.2 × 10+ 15 9.9 × 10+ 14 1.1 × 10+ 15 9.1 × 10+ 14 1.1 × 10+ 15 1.1 × 10+ 15 1.1 × 10+ 15 1.0 × 10+ 15

Membrane type: 10 (68.9) 15 (103.3) 20 (137.8) 30 (206.7)

Millipore YM30, MWCO 30 kDa 10 6.6 × 10+ 12 10 2.6 × 10+ 13 10 3.2 × 10+ 13 10 5.7 × 10+ 13

6.6 × 10+ 14 2.6 × 10+ 15 3.2 × 10+ 15 5.7 × 10+ 15

7.3 × 10+ 14 2.9 × 10+ 15 3.5 × 10+ 15 6.3 × 10+ 15

TDS = 2000 mg/L 10 (68.9) 20 (137.8) 30 (206.7)

membrane type: Osmonics Ultrafilic, MWCO 100 kDa 10 1.7 × 10+ 13 1.7 × 10+ 15 10 2.3 × 10+ 13 2.3 × 10+ 15 10 3.5 × 10+ 13 3.5 × 10+ 15

P psi (kPa)

Cb (mg L− 1)

I (m− 2)

1.9 × 10+ 15 2.5 × 10+ 15 3.9 × 10+ 15

⁎ Corrected with the mixture rejection coefficient of 0.9.

Table A4 Analysis of data from Ultrafiltration experiments with a mixture of 50% humic acids and 50% sodium alginate. Membrane type: PAN, MWCO 100 kDa. I (m− 2)

α (m kg− 1)

α⁎ (m kg− 1)

TDS = 500 mg/L 10 5 (34.5) 10 10 (68.9) 10 20 (137.8)

1.2 × 10+ 13 1.7 × 10+ 13 3.1 × 10+ 13

1.2 × 10+ 15 1.7 × 10+ 15 3.1 × 10+ 15

1.5 × 10+ 15 2.2 × 10+ 15 3.9 × 10+ 15

TDS = 2000 mg/L 10 5 (34.5) 10 10 (68.9) 10 20 (137.8)

2.2 × 10+ 13 3.3 × 10+ 13 4.3 × 101 + 3

2.2 × 10+ 15 3.3 × 10+ 15 4.3 × 10+ 15

2.8 × 10+ 15 4.2 × 10+ 15 5.4 × 10+ 15

Cb (mg L− 1)

P psi (kPa)

⁎ Corrected with the mixture rejection coefficient of 0.9.

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