Prediction of spatial-temporal evolution of membrane scaling in spiral wound desalination modules by an advanced simulator

Desalination 458 (2019) 34–44

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Prediction of spatial-temporal evolution of membrane scaling in spiral wound desalination modules by an advanced simulator

T

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A.J. Karabelasa, , S.T. Mitroulia, C.P. Koutsoua, M. Kostogloub,a a b

Chemical Process and Energy Resources Institute (CPERI), Centre for Research and Technology-Hellas (CERTH), Thermi, Thessaloniki GR 570-01, Greece Division of Chemical Technology, Department of Chemistry, Aristotle University, GR 54124, Thessaloniki, Greece

A R T I C LE I N FO

A B S T R A C T

Keywords: Scaling of desalination membranes Spiral-wound modules Spatial-temporal evolution of scale Advanced simulation Rate of scale-mass deposition

There is no method available at present to determine the spatial-temporal evolution of scale throughout the membranes in desalination plants, although it would be most useful for desalination plant design and monitoring. For such tasks, various approaches are followed to estimate the scaling propensity of feed-water or concentrate, including the use of inadequate single-value indices (e.g. LSI, S&DSI). A novel method is presented herein for simulating spatial-temporal scale evolution. It is based on a comprehensive theoretical model, describing transport phenomena in the spacer-filled channel flow of spiral-wound membrane (SWM) modules, and an experimentally determined correlation (akin to a constitutive relation) of two key parameters of the scaling process; i.e. the depositing salt supersaturation ratio at the membrane surface Sw and the rate of scale-mass deposited per unit membrane area, F g/(m2·h), which represent the driving force and effect of scaling, respectively. Very good agreement is obtained by comparing experimental data from the literature on spatial scale distribution with new computational results. The challenges and priorities are discussed regarding further development of the proposed method as well as applications related to important tasks, such as the design and operation of scale-control and monitoring systems of RO/NF desalination plants.

1. Introduction - scope The problem of membrane scaling by inorganic, sparingly soluble, salts is a key issue in the design and operation of efficient and sustainable water desalination plants [1,2]. This problem is particularly acute in the case of brackish water desalination (and various effluent water-treatment) plants, as it imposes a limitation on clean water recovery [3] and necessitates consumption of environment-burdening chemicals and energy (for scaling mitigation and periodic membrane cleaning) to maintain a targeted plant productivity (e.g. [4]). In such membrane plants, failure at the design stage to correctly determine the performance characteristics of scale control schemes can have serious consequences for the plant operation. Indeed, under-predicting the dosage of scale-inhibiting chemicals/additives may impair membrane performance and plant productivity, whereas excessive use of such chemicals may cause undue environmental burden [5] and other complications, including unexpected membrane fouling of a different type (biofouling, organic fouling) (e.g. [6,7]). At present, the above issues are dealt with at the plant-design stage in a largely empirical manner (usually on a case by case basis), by companies specializing in the development of scaling control schemes/

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programs, commonly involving use of organic compounds acting as scale inhibitors (e.g. [8]). The methodology employed in such cases to determine chemicals and antiscalant dosages is not transparent and there are no broadly accepted tools available to check the optimality of dosages and of related conditions, other than the expensive and timeconsuming approach of running pilot plant tests. In parallel, a significant amount of research has been carried out in the past 20 years on the various issues related to membrane scaling; i.e. on determination of feed-fluid scaling potential, scaling control methods and monitoring techniques [1]. However, despite progress made, there is disagreement among researchers on basic aspects of incipient membrane scaling (e.g. [9–12]), that may be partly responsible for the lack of a generalized methodology to deal with the scaling issues in desalination plants. Additionally, some clearly inadequate indices (e.g. LSI, S&DSI) [1] are used to estimate the scaling propensity of feed-water or retentate. It is clear, therefore, that a reliable methodology, implemented in a comprehensive process simulator (capable of estimating the spatial-temporal evolution of membrane scaling in RO/NF plants), is highly desirable to facilitate the aforementioned tasks in practice. The development of such a methodology and a related tool of broad applicability, which is unavailable at present, motivates the work reported

Corresponding author. E-mail address: [email protected] (A.J. Karabelas).

https://doi.org/10.1016/j.desal.2019.01.027 Received 6 November 2018; Received in revised form 28 January 2019; Accepted 28 January 2019 0011-9164/ © 2019 Elsevier B.V. All rights reserved.

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2. Theoretical background

herein. Several efforts have been reported for modeling scaling of desalination membranes. A model for CaSO4 nanofiltration-membrane scaling was proposed by Lee and Lee [13]. Ignoring chemical system and flow field complexities, they considered scale development by surface deposit and bulk particles that form a “cake”. It was also assumed that the surface deposits block membrane area whereas the “cake” (comprising bulk particles) tends to increase the hydraulic membrane resistance. Simple kinetic expressions for the mass evolution of deposits were assumed, involving dependence on excess concentration, which was computed at the membrane for surface deposit and in the bulk for the cake; membrane scaling spatial evolution was not considered. This model was further developed [14] for reverse osmosis desalination. In other studies, a different approach was taken for modeling scaling of nanofiltration [15] and reverse osmosis membranes [16]; steady state was assumed and the output was the supersaturation field, which provided an indication of the local rate of deposit formation. A more recent model for reverse osmosis membranes [17] did not consider the detailed flow field (created by the spacers), accounting only for momentum and mass conservation along the module. Another similar model was proposed in [18], based on detailed chemistry combined with mass balances, predicting the supersaturation ratio. All these models [14–18] are not dynamic, predicting only steady state supersaturation but not the temporal evolution of deposits. Radu et al. [19] through a two-dimensional mechanistic model at micro-scale investigated gypsum precipitation in RO/NF spacer-filled channels, by computing the complicated flow and solute distribution, in combination with thermodynamics and kinetics of crystal formation. Very elaborate assumptions were made in modeling scale evolution, that need experimental support. The detailed theoretical results, obtained for a restricted spatial domain, suggest the importance of spacers and of operating mode on membrane-scale development. This mathematical model was also expanded [20] for combined biofouling and scaling in spacer-filled membrane channels. The present authors [21] proposed the use of the classical theory for nuclei formation and particle growth, formulated in terms of the mean field theory of population balances, for modeling incipient membrane scaling. The model was applied to CaCO3 membrane scaling in unstirred dead-end filtration cells where the particulate character of scale was evident in related experiments [21]. The transport phenomena were treated in detail (for the particular dead-end flow field) whereas the chemistry was accounted for in an approximate manner. The resulting population balance equation was solved using the so-called monodisperse approximation. The model was generalized in a subsequent work [22] considering an ideal chemical system of a sparingly soluble salt. The formation, growth and transport of particles in the liquid bulk were considered, in parallel with such phenomena for the surface particles; the latter tend to dominate the scale-evolution process. This population balance approach was incorporated in a generalized flow modeling framework to determine scale formation in a SWM module [23], as outlined in the next section. In this paper, an outline is provided first of the modeling framework, developed for steady-state flow and mass transfer simulations, that can be extended for predicting spatial-temporal scale evolution in SWM modules. Experimental work on desalination membrane scaling is revisited and correlation of appropriate scaling parameters is recommended, as an essential computational module for integration into the SWM-module simulator. Comparison is presented next of model/ simulator results with experimental data from the literature, allowing to assess the novel methodology and its prospects for future practical applications.

2.1. Modeling framework The modeling approach employed is based on results obtained from advanced Direct Numerical Simulations of transport phenomena in a periodic “unit cell” of the spacer-filled flow channels in SWM modules [24,25]. These detailed numerical data on transport phenomena allow to tackle the problem at a meso-scale [26]; i.e. at the length scale of the “unit cell”, and further to describe and predict the flow field throughout an entire membrane sheet of a SWM module. Information on friction losses and mass transfer rates at the unit cell was introduced in the modeling framework through correlations (accounting for the flowchannel and feed-spacer geometric details), which were obtained from the numerical simulation-data [24,25]. By employing a simplified chemical system and efficient mathematical solution techniques, a comprehensive simulator was developed of the entire flow field, throughout membrane sheets [27]; thus, the spatial distribution at steady state of all process parameters could be predicted. Valuable insights and realistic results of practical significance can be obtained from this simulator [27]; for instance, it is shown that the pressure at the retentate side essentially varies only in the x- (lengthwise) direction, whereas the pressure at the permeate side is only ydependent. Qualitatively, this trend is attributed to the effect of nettype spacer at the retentate side, which tends to promote fluid dispersion and eliminate lateral pressure variation. With this simulator, predictions can be readily made of the flow development along an entire multi-element pressure vessel [27]; useful results of parametric studies with this simulator have already been published [28,29]. To extend model capabilities beyond predictions of transport phenomena at steady-state, a dynamic model was recently developed [30]; the latter is structured in such a way as to permit incorporation, in a fundamental manner, of specific (constitutive-type) relationships for modeling other concurrently occurring phenomena such as membrane fouling and scaling. 2.2. Modeling scaling of desalination-membranes A population balance approach based on the fundamental theories of nucleation and particle growth has been taken by the authors [21,22] as outlined in the Introduction. This approach was incorporated in the aforementioned “meso-scale” flow modeling framework to determine scale formation in a SWM module [23]. The membrane-scaling model considers, in addition to membrane surface particles, the existence of bulk particles that may deposit on the membrane and contribute to scale formation. A parameter λ is introduced representing the fraction of particles colliding with the membrane that are attached to it. After attachment, these bulk particles are counted as surface particles. Details on the parameter λ can be found elsewhere [23]. A modification of the model [23] was proposed [31] for the case of desalination in a dead-end cell with agitation in order to better describe the respective experimental data, thus allowing the extraction of key process parameters to be introduced in the generalized SWM-module simulator. This study suggested that the classical theory of nucleation and particle growth may be inapplicable to the problem at hand. Moreover, key scaling-process parameters appeared to have a stochastic character, possibly affected by a membrane surface non-uniformity, that leads to a distribution of affinities to nucleation. Therefore, a stochastic model taking into account this distribution was considered necessary to simulate the membrane module operation. In this direction, a procedure was developed to derive the distributions of parameter-values from dead-end stirred cell experiments; however, the crucial step has not been taken yet, that involves adaptation of this information (obtained in a small-size test section) for predictions of scale evolution at the large spatial scale (i.e. the membrane sheets). While the above modeling based on fundamental theory is under 35

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conjunction with this code, for low salinity water, a fairly complete database is used, i.e. “minteq.v4.dat” [55]. As is well known, the supersaturation ratio S is a theoretically sound parameter [53,56] characterizing the scaling tendency of all sparingly soluble salts in an aqueous solution, accounting also for ionic interactions of the species present therein. Appropriate databases are available for computing supersaturation indices of all possible solid phases for a solution of known chemical composition such as the abovementioned “minteq.v4.dat” [55] or the “pitzer.dat” for high ionic strength solutions [54]. It should be pointed out that the quantity S is considered preferable for this study, over the alternative index SI (frequently used in the literature), for practical reasons. Specifically, for a certain range of solution supersaturation of practical interest, the range of numerical S values is broader compared to that of SI (e.g., S = 1–3 corresponds to SI = 0–0.95) which facilitates the development of data correlations sensitive to relatively small S variations, as subsequently discussed. The rate of deposited scale mass F (g/m2h), or the scale-mass density M (g/m2) on the membrane, is considered as the most representative parameter of desalination membrane scaling for several reasons. Specifically: a) M can be accurately measured directly even for very small deposited mass (e.g. [9]), perhaps more so than with any other proposed technique. b) By employing scale dissolution (from membrane specimens), M can be determined; additionally, by chemical analysis of the resulting solution, in combination with SEM imaging and EDS, one can obtain almost complete characterization of the type and composition of depositing/crystallizing salts. c) M is of practical interest as it provides a measure of scale mass to be removed from SWM modules by chemical treatment and related CIP techniques (e.g. [4]). d) F or M can be correlated with S by collecting appropriate experimental data (of both S and F), through well-designed tests at small scale, as discussed in the next section. With the available steady state simulator of SWM module performance [27–29] one can compute the distribution of surface concentration Cw throughout the membrane sheets (as subsequently shown), with a spatial resolution corresponding to the “meso”-scale of spacer unit cell [26]. The aforementioned software to compute thermodynamic equilibria of ionic species (e.g. Ca2+, SO42) can be integrated in this simulator [23], thus enabling computation of the respective spatial distribution of wall supersaturation Sw using Eq. (1). Further, a correlation of Sw with mass density M or rate F, obtained from experimental data of scaling (described in the following section for gypsum), is required to predict the spatial-temporal evolution of scaling throughout the membrane sheets of SWM modules along a pressure vessel. It is noted that under conditions of incipient scaling considered here, it is assumed that pseudo-steady state flow conditions prevail, as the scale-mass deposited on membranes is relatively small and does not significantly affect transport phenomena in the spacerfilled channels of SWM elements. It may be added that independent estimates of local membrane-surface concentration Cw and of supersaturation ratio Sw can be readily obtained from the following expression, for concentration polarization, applied to each ionic species i [57]:

development, a straightforward approach is recommended in this work, for predicting membrane-scale evolution, that utilizes the simulator framework outlined in Section 2.1 and appropriate experimental data; the latter should relate the driving force (i.e. liquid supersaturation in respect of a salt) to a key membrane scaling (lumped) parameter, under specific system conditions. Considering pseudo-steady state of flow during incipient scaling, the main benefit of this approach lies in the fact that the spatial distribution of scaling-species concentration at the membrane surface Cw and the corresponding supersaturation parameter are predictable from the available simulator. In the following, this approach is demonstrated for the common case of calcium sulfate scaling. 2.3. Key scaling process parameters and computational modules To implement the aforementioned modeling approach, it is crucial to select the most appropriate parameters that quantify the driving force (as a function of system design and operating variables) and the end effect (membrane scaling). These parameters should be representative of the process, and related mathematically on a sound theoretical basis. It should be noted, parenthetically, that researchers in this field have generally disregarded this issue and inadequate attention has been paid to the selection of an appropriate parameter, truly representative of the membrane scaling process, that would facilitate reporting and correlating their data. Nevertheless, notable are the efforts of Cohen and collaborators (e.g. [16,32,33]) and few other researchers [34] who have reported membrane-surface percentage coverage by scale (usually gypsum) as an indicator of the evolution of scaling, employing optical techniques [35]. Unfortunately, no specific correlation of this quantity with a metric of the driving force (i.e. the solution supersaturation) has been presented that would allow utilization of the data, for modeling and predictive purposes. In the literature, a commonly used indicator of scaling effects is the permeate flux reduction (e.g. [12,36]), under various desalination conditions, of a scaling-prone treated fluid. However, based on detailed experiments (e.g. [37,38]), it can be argued that such measurements of flux reduction may be of value only for fairly extensively scaled membranes (i.e. when the process is well in progress), but they lack the sensitivity to quantify incipient scaling of interest here, for predictive purposes, that involves relatively small deposited scale-mass. Furthermore, numerous studies using such techniques, based on measurements of flux decline and of other bulk fluid parameters (although they have helped improve our understanding of the scaling process), have not provided data sets of archival value; i.e. data collected in terms of usable parameters and characterized by completeness of reported conditions, that would facilitate their correlation. Additionally, proposed advanced instrumental techniques such as UTDR [39–48] and EIS [49–52], even though they seem to be sensitive in identifying incipient scaling, provide data (in their present stage of development) of physical quantities that cannot be readily translated into parameters convenient for quantifying and correlating membrane scaling as outlined above. The parameters selected for the present modeling effort are the supersaturation ratio S of sparingly soluble salts prone to scaling and the rate of respective scale-mass deposited on the membrane F (in g/m2h), or the scale mass density on the membrane M (in g/m2) for various times, during the early period of membrane scaling. The supersaturation ratio S and index SI, for the case of calcium sulfate, are defined as [53]: 1

(Ca2 +)(SO24−) ⎤ S=⎡ ⎢ ⎥ K sp ⎣ ⎦

2

1

IAP ⎤ =⎡ ⎢ K sp ⎥ ⎣ ⎦

C w,i J = (1 − Ri) + Ri∙exp ⎛ ⎞ Cb,i ⎝ ki ⎠ ⎜

(3)

if the local values are available of bulk species concentration Cb,i, permeate flux J, ion rejection Ri and mass transfer coefficient ki.. The latter can be obtained from an appropriate correlation [25].

2

(1)

SI = 2 log(S)

⎟

2.4. Correlation of scale-mass deposition rate

(2)

Experimental data obtained in the authors Laboratory with feed water weakly supersaturated in calcium sulfate [9,58], typical of incipient scaling, will be utilized to obtain a correlation of Sw with scalemass deposition rate F. Calcium sulfate dihydrate (gypsum) is a commonly encountered scale-forming compound, mostly in brackish water

2+

where the quantities in parentheses are the activities of ions Ca and SO42−, computed by an appropriate thermodynamic code (e.g. PHREEQC [54]), Ksp the thermodynamic solubility product of calcium sulfate dihydrate (gypsum) and IAP the ion activity product. In 36

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Fig. 1. Correlation of rate of calcium sulfate dihydrate (gypsum) mass deposition (F) with the respective wall supersaturation ratio Sw. Experimental data from [9,58].

real plants); thus, it may be considered as a “local fit”, to the complicated real form of the function f(Sw), not necessarily applicable outside of the Sw range of the data employed. d) Correlations similar to Eq. (4) should be developed for each particular scaling compound (crystalline phase), and their validity should be checked for co-precipitating salts.

desalination plants (e.g. [8]). It has been, therefore, extensively studied in many R&D laboratories (e.g. [12,32,59,60]); unfortunately, most of these data are inappropriate for developing correlations of the type pursued in this work, as outlined above. Nevertheless, some fairly detailed scale distribution data from laboratory pilot testing are available [41] for comparison with simulation results, that are presented in the following section. Fig. 1, depicts membrane-scaling experimental data, taken in smallscale cross-flow spacer-filled test-section [9] and dead-end pressure cell with agitation [58] under conditions representative of those prevailing in real systems. These data correspond to incipient scaling at small supersaturation ratio, taken (after membrane compaction) over the initial period of desalination of a specific membrane. For data taken at a fixed filtration/desalination time, the following correlation (with a coefficient of determination R2 = 0.8) is obtained of the rate of gypsum scalemass deposition, F [g/(m2·h)], with the respective supersaturation ratio at the membrane surface Sw:

F = 6.4·10−3 (S w )8 for S w > 1.0

3. Comparison of model predictions with experimental data 3.1. Data on membrane-scaling distribution Chai et al. [41] have obtained valuable local membrane-scaling data (through an autopsy, in terms of local scale mass density M, g/m2); a SWM module was employed in a laboratory pilot, for desalination of a mildly supersaturated CaSO4 solution. Fig. 2 depicts qualitatively the measured (by a gravimetric technique) local scale-mass density distribution in various locations on one leaf of a Koch 2521 SWM module. Table 1 includes the design characteristics of this module as well as the conditions of the pilot tests, which correspond to the data depicted in Fig. 2 and listed in Table 2; the latter are reported by Chai et al. [41] (their Table 1). An et al. [62] also reported data of interest on the axial distribution of gypsum in a SWM module, obtained in laboratory pilot experiments, which are depicted in Fig. 3. The supersaturation prevailing in these tests (in respect of gypsum) was significant and somewhat greater, compared to conditions commonly encountered in desalination plants; therefore, quite high scale-mass deposit densities were obtained (by a gravimetric technique) for the relatively short test period of 90 h. In the next section, a comparison will be made with predictions based on the novel approach demonstrated in this paper. Table 3 lists the conditions of the pilot test [62] corresponding to the data in Fig. 3. These data show a roughly linear variation of scale-mass density M deposited along the SWM module, although (unfortunately) inadequate information is provided on the exact location of the specimens used, in respect of the 1.17 m width of the membrane sheet. Very recently Benecke et al. [34] reported interesting gypsum membrane-scaling data taken in a test section 100 cm long, 4 cm wide with 0.4 cm gap, employing no spacers and a brackish-water desalination membrane (Dow, Filmtech BW30). For the cross flow velocity

(4)

Noteworthy is the large exponent in this power function, expressing the dependence of scaling rate F on wall supersaturation Sw, at small supersaturation ratios; i.e. for Sw < 2. However, such an exponent should not be surprising, considering that the function F comprises contributions from both heterogeneous nucleation and growth of surface particles on the membrane [22]; for instance, it is well-known that the nucleation rate is extremely sensitive to crystallizing species supersaturation ratio [61], which is also reflected in the above highly sensitive F-dependence on Sw. Some additional comments are in order regarding the above correlation (Eq. (4)): a) On the basis of the available data, no clear dependence of the rate F on time can be established; thus, it is considered here that the incipient scaling rate F is time independent (and the deposited mass M increases linearly with time) – a point to be clarified in the future. Therefore, in functional form, one obtains F = (dM/ dt) = C[Sw]a and M = C[Sw]at. b) Eq. (4) represents a tentative correlation, based on fairly limited measurements, that should be improved by collecting additional data; obviously, F = 0 for Sw < 1. c) The power function F = C[Sw]a was derived for a relatively narrow range of supersaturations (nonetheless representative of those encountered in 37

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Fig. 2. Schematic diagram indicating the distribution of scale deposits on 18 subsections of the membrane sheet, cut from sections B (near feed entry) and E (near retentate exit). The degree of shading of these subsections indicates the scalemass density determined gravimetrically, which is listed in Table 2. This figure is copied from Chai et al. [41] (Fig. 6); copyright Elsevier.

Table 1 SWM module basic characteristics and operating conditions of pilot desalination tests as reported by Chai et al. [41].

Table 3 Basic characteristics of SWM module and operating conditions of brackishwater desalination tests by An et al. [62].

Module type (KOCH 2521 [41]) Envelope length, m Membrane width, m

0.47 1.5

Module type (CSM-RE4021-TL [63]) Feed-spacer thickness, mm Membrane active area, m2

0.71 1.2

Envelope length, m Membrane width, m

Operating conditions Feed flow rate, L/min Pressure, MPa Duration of test

9 (outermost) 8 7 6 5 4 3 2 1 (innermost) Total

Feed-spacer thickness, mm Membrane area, m2

0.71 3.3

Operating conditions 0.1–2.0 0–2.8 90 days

Calcium sulfate concentration, g/L Temperature, °C

Feed flow rate, L/min Pressure, MPa

0–1.6 10–30

Mass density on membrane subsection, M, mg/cm2 Section B (near feed entry)

Section E (near retentate exit)

0.14 0.14 0.45 0.54 0.54 0.56 0.95 0.99 3.78 8.09

1.32 4.69 5.86 6.71 7.89 9.70 10.2 11.2 21.6 79.2

1 1

Feed-water CaSO4 concentration, g/L Temperature, °C

2.0 25

0.19 m/s used, laminar flow prevailed in these desalination tests, whereas the flux was maintained constant at 30 L/m2 h. The reported data in Fig. 4 of this study [34] also show an almost linear axial variation of scale mass density M, as in the data of An et al. study [62]. It should be added that these data, corresponding to a rather short desalination test-period of 270 min, exhibit no evidence of significant induction period of membrane scale formation, as also observed in other similar detailed studies of gypsum scaling (e.g. [9,10,58]).

Table 2 Data reported by Chai et al. [41] on calcium sulfate (gypsum) mass density M, obtained from subsections cut from SWM module after pilot tests; section designation as in Fig. 2. Subsection number

0.47 1.17

3.2. Computational results – comparisons with experimental data 3.2.1. Determination of flow field characteristics The simulator outlined in the preceding Section 2 was employed for the predictions and comparisons with the literature data outlined in Section 3.1. The constitutive expression (Eq. (4)) as well as supporting computational modules for speciation calculations and Sw determination were incorporated in the basic simulator [27–29]. Regarding the Chai et al. [41] study, input data for the computer simulations were Fig. 3. Gypsum mass density variation in the axial, feedflow direction, obtained gravimetrically from membrane subsections, after 90 h of desalination-scaling experiments. The points marked by full circles (at M = 1.03 and 49.41 g/m2, corresponding to SWM module entry and exit, respectively) represent predictions based on the novel approach. This figure is copied from An et al. [62]; copyright Elsevier.

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Fig. 4. Computed permeate flux distribution throughout the membrane sheet of SWM module, for the pilot tests of Chai et al. [41]. The main flow is in the x (length) direction. Space average flux J = 30 L/m2 h.

3.2.2. Comparisons with experimental data Fig. 8 shows a comparison of predicted local values of scale mass density M with corresponding experimental measurements reported by Chai et al. [41] and listed in Table 2. The local values (obtained from small specimens) extend across the width (y-direction) of the membrane sheet, for two axial locations (i.e. x ≈ 0.08 m and x ≈ 0.4 m). The agreement obtained is gratifying, taking into account that no adjustable parameter is employed in these simulations, which are based on a theoretically sound model, and a correlation of scale-mass deposition rate obtained from laboratory tests. Such detailed predictions of membranescale distribution, and comparisons with relevant experimental data, are presented here for the first time, to the authors' best knowledge. It should be noted that beyond an axial location x ≈ 0.2 m both experimental data and predictions show that scale development covers the entire membrane widthwise, due to permeate removal and supersaturation. However, near the feed entry (x ≈ 0.08 m) the model predicts Sw values > 1 (and, thus, membrane scaling) only relatively close to the permeate tube, which is located at y = 0. In that region (i.e. for y < ~0.2 m) Sw > 1 and there is fair agreement with the measured scale local density M. At the entry (x ≈ 0.08 m), for lateral locations further from the permeate tube (where it is computed that Sw < 1, and the model predicts no scaling) there is small, yet measurable, scale-mass density M. One should consider, however, that this deposit density values are quite small (after 3 months of desalination/filtration) and represent possibly unstable conditions at the limits of supersaturation. Furthermore, regarding predictions, it should be recalled that within the spatial scale of a “unit cell” created by the feed-spacer [24,25] there is considerable variability of wall conditions. Indeed, locations exist of low shear particularly near spacer filaments [24] and it is expected that the local concentration polarization is greater there compared to the average “unit cell” value considered in the present model. Therefore, greater scale-mass deposition may occur in these small regions near spacers, even though the average concentration polarization value of the “unit-cell” would not exhibit supersaturation. It should be noted that increased scale deposition/growth at the crossing of spacer filaments has been reported (e.g. [8]), although such evidence has not been clearly observed in authors' experiments for incipient scaling and small experimentation times [38]. Attention should be paid to another feature of the experimental data near the permeate tube, plotted in Fig. 8; i.e. it is observed that the first data points near y = 0 (at both axial locations) exhibit a rather unexpected high value, in comparison to the relatively smooth lateral variation of scale density M further away from the permeate tube. One

obtained from Table 1. Other related input data are listed in the Supplement (Table S1), where the detailed simulator output is also provided (Tables S2–S4) on the SWM module performance in terms of the key parameters (J, Cw, Sw, M). Fig. 4 clearly shows the very uneven spatial distribution of permeate flux J, of the Chai et al. [41] study. For the long membrane sheet width of this SWM module [39], such uneven distribution is expected on the basis of previous studies [28,29]; as is well known, it is caused by the similarly uneven distribution of trans-membrane pressure (TMP). The latter is the net-result of the interaction of the two flow fields, i.e. the high-pressure flow field at the retentate channel and the low-pressure one at the permeate side. The high fluxes prevailing near the permeate tube are of interest as they are responsible for the similarly greater concentration polarization in that region, and further for the increased membrane surface concentration Cw and supersaturation ratio Sw there. In Fig. 4 and subsequent similar figures, the coordinate system x (length) – y (width) is employed, which corresponds to a flat membrane sheet of a SWM module; thus, the y coordinate (with y = 0 at the permeate tube) is equivalent to the circumferential direction of a SWM module. Figs. 5 and 6 depict the computed spatial distributions of membrane-surface concentration and supersaturation ratio Cw and Sw, respectively, which correspond to the flux distribution of Fig. 4, for the conditions of the Chai et al. [41] pilot tests. It is interesting that the distribution pattern in these Figures (with greater variability in the axial x direction compared to y-direction) is significantly different than that of Fig. 4. This is largely due to the cumulative effect of permeate removal that tends to cause a significant increase of Cw and Sw in the axial direction. In Fig. 6 the membrane area, over which there is potential for scaling (i.e. Sw > 1.0), is marked by a different color. It is noted that the predicted Sw values for this case (Fig. 6) are within the range of data F vs. Sw (plotted in Fig. 1) on which the respective correlation (Eq. (4)) is based. The final result of the simulations is shown in Fig. 7, where the spatial distribution of scale-mass density on the membrane M (g/m2) is presented. The very significant unevenness of scale mass density within a single SWM module (of relatively short length x = 0.4 m) is very interesting and somewhat surprising. Nevertheless, it can be certainly explained on the basis of the high sensitivity of scale mass deposition rate F to modest variations of supersaturation ratio Sw, as shown in the respective correlation, Eq. (4).

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Fig. 5. Computed spatial distribution of scaling species concentration at the membrane surface (Cw) of SWM module prevailing in the pilot tests of Chai et al. [41].

The data in Fig. 3, obtained by An et al. [62] after a 90 h test, show a roughly linear variation of scale-mass density M deposited along the SWM module; a noticeable difference of M values was obtained between the two membrane faces of an envelope, which is a matter for further investigation. As there is inadequate information on the exact size and location of the specimens (in respect of the width of the membrane sheet), used to measure scale-mass density M, comparison is made with model predictions at the feed entry and the concentrate exit of the SWM module. Table S5 in the Supplement lists specific conditions, obtained from the paper [62], which were used in the

may hypothesize that the local conditions of membrane-sheet/envelope rolling and attachment to the permeate tube may create local flow and membrane permeation conditions significantly different than those in the rest of the spacer-filled channel. It should be also recalled in this respect that in modeling the flow in spacer-filled channels a flat geometry is commonly considered [24,64] and possible local variability due to SWM module fabrication is not taken into account. A related issue of membrane channel geometry, significantly modified by the normal stresses imposed during envelope rolling/winding [65], might also contribute to such non-uniformities.

Fig. 6. Predicted spatial distribution of calcium sulfate supersaturation ratio at the membrane surface Sw, corresponding to conditions of pilot tests by Chai et al. [41]. 40

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Fig. 7. Predicted spatial distribution of gypsum scale-mass density M (g/m2) on the membrane surface of SWM module, corresponding to conditions of Chai et al. [41] pilot tests.

Fig. 8. Comparison of predictions, based on the novel approach, with experimental data by Chai et al. [41], on the local variation of scale-mass density M on the membrane. Plotted M variation in the membrane sheet-width direction, at two axial locations/distances from feed; i.e. x = 0.08 m and x = 0.4 m.

4 mm gap with no spacers, under laminar flow conditions, quite different than those prevailing in the narrow spacer-filled channels. Therefore, concentration polarization during desalination in that channel [34] is significantly greater than in the latter case. However, these data are interesting, clearly showing that heterogeneous nucleation (leading to membrane-surface particle growth) dominates the scaling evolution process, with insignificant induction period. Additionally, the

computations. The predicted mean concentration of scaling species at feed entry and retentate exit are Cw = 2.43 kg/m3 and 5.33 kg/m3, respectively, whereas the corresponding scale-mass densities are M = 1.03 g/m2 and 49.41 g/m2. As shown in Fig. 3, these predicted M values are in very good agreement with the reported measurements, thus providing added support to the recommended modeling approach. The data of Benecke et al. [34] have been obtained in a channel of 41

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constitutive relations, if either or both types of membrane-fouling dominate. The parallel on-going work on spatial-temporal evolution of organic fouling (e.g. [30]) would provide insights helpful to deal with this more complicated issue.

observed nearly linear distribution of membrane scaling in the axial direction in these rather short duration tests (4.5 h) is similar to that observed in the data by An et al. [62] of much longer duration (90 h) obtained with a SWM module. It should be also noted that the feed-fluid in these tests [34] was at the limit of supersaturation, characterized by supersaturation index SI = log (IAP/Ksp) ≈ 0. For comparison with predictions based on the present modeling approach, reported [34] data are used; i.e. values of mean supersaturation index at the membrane surface for gypsum, SIG,W = 0.51 and 0.53, with corresponding mean scale-mass density M = (443 mg/ 400 cm2) = 1.11 mg/cm2 and M = (392 mg/400 cm2) = 0.98 mg/ cm2, averaged over the entire test section. The reported SIGW values are based on these authors' [34] estimates of an average concentration polarization in their test channel. Using the aforementioned correlation (Eq. (4)), one obtains corresponding predictions of scale-mass density M = 0.33 mg/cm2 and 0.39 mg/cm2, for SW = 1.8 and 1.84. Regardless of experimental errors and uncertainties involved, this rough (order of magnitude) agreement of data with predictions is considered satisfactory, taking into account that the employed M-S correlation (Eq. (4)) was obtained under quite different flow–field conditions (with significantly smaller concentration polarization).

Regarding the duration of the above incipient scaling tests, to determine S – M correlations, one should take into account the results of recent studies (e.g. [9,34,38,58,66]) showing that heterogeneous nucleation, with growth of surface-particles on the SWM-module membranes, dominate the scaling process, and that an induction period is insignificant. Under such conditions, tests of relatively short duration of a few hours (e.g. 4–5 h) appear to be sufficient for collecting representative data under constant supersaturation. This suggestion is supported by the comparison of literature data with the new simulation results included in Section 3. Indeed, although these results/predictions were based on a correlation (Eq. (4)) developed from short-time tests, satisfactory agreement was obtained with literature data spanning a very broad range of experimentation times; i.e. 4.5 h [34], 90 h [62] and ~2160 h [41]. In view of the above issues, it is considered necessary to develop a data-base, comprised of complete data-sets of the key parameters (S, M), and their correlation, over a sufficiently broad range of experimental conditions; additional detailed supporting data on the scaling process would be useful. Such a data-base, enhanced by contributions from various literature studies, would be valuable in the establishment of constitutive expressions as well as in minimizing and/or facilitating experimental work for their determination in practice. Two general areas of practical applications of the proposed methodology can be considered; i.e., at the RO process and plant design stage and for monitoring RO process/plant operation. In the former case, as outlined above, an appropriate S – M correlation would be obtained through experiments, and with possible aid from the “data-base”, for the particular feed-fluid. Then, projections would be made of membrane scaling evolution as a function of SWM module and system design and operating conditions. A similar approach would be taken for RO plant monitoring, except that the S – M correlation should be obtained from tests with 3–4 slip-streams toward the rear-end of a multi-element pressure vessel. For the common operating mode of constant permeate recovery, each of these slip-streams would be characterized by nearly constant retentate-fluid composition and degree of supersaturation of scaling prone compounds. The modeling effort reported herein is focused on incipient membrane scaling and relies on a simplified (yet realistic) approach; i.e. pseudosteady state is assumed to prevail at this early stage, when scaling does not cause significant flux reduction, as shown elsewhere [37,38]. However, at longer time, with increased (locally uneven) membrane coverage and mass-deposition, significant (spatially uneven) flux reduction can take place. Under such conditions, a variable local resistance (due to membrane fouling/scaling) will develop, and flux (as well as deposit mass M) redistribution on the membrane sheets is expected to occur. In future model development, the simulation of these more complicated scaling-dynamics trends should be pursued; it is noted that such fouling-redistribution trends have already been modeled for the case of organic fouling [30]. It should be added that the simulator code, developed in the authors' Laboratory [27–29], and employed in this paper for determining the spatial distribution of scalants concentration Cw (throughout the membrane sheets of a SWM module) can be used by interested readers (through an internet link) upon request from the authors.

4. Discussion The proposed methodology to simulate the spatio-temporal evolution of desalination-membrane scaling (by certain inorganic species) relies on a correlation (akin to a constitutive expression) relating parameters representative of the driving force (supersaturation ratio S for the particular species) and of the main effect, i.e. the scale-mass density on the membrane, M. The rationale and advantages of selecting the latter are outlined in the preceding Section 2. It should be stressed, however, that little information exists in the literature on such M-S correlations; in fact, in the foregoing demonstration of the methodology, for the case of calcium sulfate membrane-scaling, the relatively limited available data have been used, obtained in previous studies by the authors. Therefore, for practical applications of this methodology, significant additional work will be required and the following main issues should be addressed, regarding the determination of the abovementioned correlation: i) Test conditions for S, M data acquisition. These conditions should be representative of the flow field prevailing in desalination modules, considering also the geometric details of the feed-spacers. No particular problems are foreseen in dealing with this issue in well-designed experiments. ii) Multiple depositing inorganic salts. Given the fluid composition, available software for dissolved species equilibria calculations [54] can account for ionic species interactions and yield reliable predictions of supersaturation index for various inorganic salts. In parallel, scaling experiments, at constant supersaturation ratio S, can provide the total scale-mass density M; additionally, analysis of scale from membrane specimens by appropriate techniques (i.e. elemental analysis, SEM – EDS, XRD, etc.), would allow the characterization of various deposited salts. It is considered that systematic work along these lines would be fruitful in determining S – M correlations for a specific set or range of conditions. iii) Combined scaling – fouling. The interaction of organic matter and of other foulants present in the feed-fluid, with inorganic ions and particles (at incipient scaling), is a complicated issue, inadequately researched so far (e.g. [58]). One might include in this general category the action of scale inhibitors on nuclei and growing particles. Despite obvious complications and the need for more basic research, it is envisioned that the proposed methodology, properly extended, could be employed to deal with combined scaling-fouling of desalination membranes. The aforementioned well-designed tests (i) are considered necessary for determining appropriate

5. Conclusions The novel methodology demonstrated herein, for simulating incipient membrane-scaling evolution, comprises a constitutive expression, involving appropriate scaling process parameters, that is incorporated in a generalized modeling framework of the SWM module 42

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operation. Comparison of predictions of spatial-temporal membrane scaling evolution, based on this method, with literature data shows very satisfactory agreement. There is no comprehensive method available in the literature, of the type presented here. However, a significant amount of work lies ahead to further develop this method. Priority issues to deal with, for practical applications of this method, include the development of reliable constitutive expressions for the various types of feed-waters currently treated in RO plants, and the selection of experimental conditions (for measuring scaling parameters) representative of those prevailing in the SWM modules and systems of interest. Practical applications and establishment of this methodology would be greatly facilitated by the development of a data-base that would include systematically collected, complete data-sets of scalingprocess parameters and their correlations.

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