Modeling of spiral wound membrane desalination modules and plants  – review and research priorities

DES-12289; No of Pages 22 Desalination xxx (2014) xxx–xxx

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Modeling of spiral wound membrane desalination modules and plants – review and research priorities A.J. Karabelas a,⁎, M. Kostoglou a,b, C.P. Koutsou a a b

Chemical Process and Energy Resources Institute, Centre for Research and Technology - Hellas, P.O. Box 60361, 6th km Charilaou-Thermi Road, Thermi, Thessaloniki, GR 570–01, Greece Department of Chemistry, Aristotle University of Thessaloniki, Greece

H I G H L I G H T S • • • • •

Systematic review presented of SWM-module modelling requirements and approaches Module geometric parameters play dominant role in SWM desalination performance The complicated SWM modeling problem characterized by spatio-temporal variability “Separation of scales” approach to global modelling demonstrated to be effective R&D priorities outlined regarding development of a global dynamic simulator

a r t i c l e

i n f o

Article history: Received 30 August 2014 Received in revised form 1 October 2014 Accepted 3 October 2014 Available online xxxx Keywords: Spiral-wound membrane (SWM) module Desalination plants Water treatment Comprehensive model Performance simulation SWM design characteristics

a b s t r a c t Spiral Wound Membrane (SWM) modules are the basic components of modern desalination and water treatment technology. To advance this technology, a comprehensive SWM-element model and related performance simulator are indispensable tools. A flexible and efficient simulator is needed to optimize SWM modules, and to be integrated into general-purpose software for designing and monitoring/controlling entire desalination plants. Desirable features of SWM-model are outlined first, considering practical constraints. Reviewing related work, it is recognized that the complicated physico-chemical phenomena (and interactions) occurring in SWM-modules extend over several length- and time-scales, thus rendering impossible direct solution of the complete problem. Therefore, a tractable modeling-structure is needed, whereby properly correlated results of detailed studies (at small scale) on flow and mass transfer in spacer-filled channels, and sub-models representing the membrane function, are integrated into an appropriate modeling framework for a broad spatial domain, i.e. for performance simulation of entire SWM modules. Available steady-state models are reviewed and investigations toward development of dynamic simulators are outlined. Typical results are discussed of detailed twodimensional distributions of process parameters, throughout the SWM-modules in a pressure vessel, for steady-state operation. An overall assessment of simulating SWM-module performance and of designparameter effects, considering industry requirements, leads to suggestions on R&D priorities. © 2014 Elsevier B.V. All rights reserved.

1. Introduction 1.1. The Spiral Wound Membrane (SWM) module The membrane technology for water treatment has experienced tremendous growth since its inception half a century ago (e.g. [1,2]), and it is essential for achieving a sustainable global development. The Reverse Osmosis (RO) membrane process is currently the undisputed leading method, and the Spiral Wound Membrane (SWM) module the basic component for building a very broad range of water treatment facilities, for sea- and brackish-water desalination as well as purification of ⁎ Corresponding author. E-mail address: [email protected] (A.J. Karabelas).

assorted effluents for reuse. Johnson and Busch [3] have presented an illuminating account of technological developments and industrial requirements that have led to the dominance of SWM modules in desalination and water treatment applications. Other reviews on significant issues related to membrane desalination technology can be found elsewhere [4–8]. A typical SWM module is schematically shown in Fig. 1. A membrane envelope is made of two sheets, glued at the three edges, with a fabric filling the permeate channel. The open permeate-side of this envelope is fixed on a perforated inner tube where the permeate is collected. Several envelopes, separated by relatively thin net-type spacers, are tightly wrapped around the perforated inner tube. Although the SWM module was invented almost 50 years ago [2], the morphology of commercial elements, including the recently developed large 16- and 18-inch

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Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

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Fig. 1. A view of the Spiral Wound Membrane (SWM) module for desalination, showing its configuration [3].

elements, has remained essentially unchanged. Moreover, plans [9] for even larger (24-inch) modules, are apparently based on the same SWM morphology. During recent decades, very significant improvements in SWM performance were due to improved membrane surface characteristics [7]. Regarding the SWM module arrangement in plants, noteworthy improvements have been made (e.g. [10–12]), mostly to accommodate the SWM elements in series within the pressure vessels and avoid leaks, as well as to prevent module damage and to maintain its integrity (i.e., by anti-telescoping devices, special connectors and O-ring arrangement, etc). In the compact design of SWM modules, packing a large membrane surface area per unit volume leads to very narrow spacer-filled flow channels (of gap less than 1 mm), which tend to aggravate operating problems, i.e. friction losses, membrane fouling and scaling. Moreover, this design poses serious challenges to investigators aiming to study in detail SWM module performance. Specifically, despite recent progress (e.g. [13,14]) detailed/local non-invasive measurements inside real modules are almost impossible to make, thereby depriving investigators of essential information. In fact, only data on average SWM operating parameters (e.g. module-average flux, pressure drop) can be obtained as well as information from post mortem module autopsies to determine membrane condition and fouling patterns; such information has obvious limitations. Development of general-purpose SWM simulation tools has been hindered by these difficulties, which (in addition to other consequences) have had significant negative impact on the approaches followed to develop large size SWM modules. For instance, papers from industry (e.g. [15,16]) suggest that, in the development of large size elements, time-consuming “trial-and-error” approaches were taken, as apparently no reliable predictive design tools were available. Indeed, Yun et al. [15] reported that the specific flux [gal/ft2/day/ psi] of a new (under development) 16-inch element, using long-width leaves, was found in a pilot to be clearly inferior to that of shorter leaves as well as of standard 8-inch SWM elements; the longer width 16-inch element under development (1st generation) also exhibited significantly greater fouling. Lomax [16], in an interesting account of SWM industrial developments, reported similar difficulties in early efforts to develop 12-inch SWM elements. However, of particular interest to this review is the paper by Johnson and Busch [3] where a comprehensive industrial perspective on SWM module design parameters is provided, including uncertainties and areas for improvement.

1.2. The need for a comprehensive SWM model and related performance simulator The general objective of modeling SWM modules is to develop an appropriate computational tool (comprehensive, flexible, convenient to use) enabling to simulate in a reliable manner the performance of individual SWM desalination modules (within the series of modules housed in a pressure vessel) as well as of entire plants. Such a tool is most useful to industry at the equipment/module design and development stage, to run parametric studies and assess the effect of SWM design characteristics on the main process operating parameters [3,17]; plant design and performance optimization stage, helping to select the best SWM types, the optimum plant configuration (e.g. [18]) as well as optimum operating conditions for a specific water treatment task (e.g.[19,20]); plant operation stage, including plant detailed on-line monitoring and control [21]. SWM models and related tools are also valuable in systematic research activities involving comparative assessments on the importance of various equipment design and operating variables on SWM performance. These assessments facilitate prioritization of R&D activities, aimed at equipment and process development. The needs of industry in the aforementioned areas (including those of SWM module manufacturers, of engineering firms and of plant operators) are served in two ways: a) Employing commercial software available by membrane manufacturers (ROSA, IMSDesign, Q+ Projection Software, etc.). These tools use as input the SWM module geometric design and other parameters of the particular brands marketed by those companies, which render them quite inflexible for general users wishing to perform detailed parametric studies. Moreover, no information is available on the models and computer codes employed. The output of these programs provides average quantities per SWM module in a pressure vessel (i.e. pressure drop, permeate flux, salt rejection, solution properties), which seem to be adequate for basic engineering tasks and for overall system analysis in a steady-state operating mode. The performance of these codes is generally considered quite reliable for the

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particular SWM module types to which they are applicable. However, these commercial tools do not provide any information on the two-dimensional distribution (throughout the membrane sheets) of the key process parameters, such as local trans-membrane pressure (TMP), permeate flux, flow velocities and pressure distribution at the permeate side. b) Using practical experience. There is, indeed, extensive practical experience in industry on all issues related to the design, fabrication and operation of SWM modules and plants (e.g. [3,22]). This invaluable stock of information (mostly comprising plant operating data) is used to successfully design large membrane plants. Moreover, it serves the membrane industry to validate the respective commercial codes, and to make other equipment and process improvements; e.g. special arrangement of SWM modules to equalize flux distribution along the pressure vessels [23–25]. In parallel with industrial developments, rather extensive research (reviewed herein) has laid the groundwork, and has contributed directly and indirectly to improvements in SWM module and plant design. However, in the authors opinion, it is questionable whether sufficient interaction has taken place between industry and research organizations, in exploiting each other’s competencies and attributes, toward the development of much needed reliable models and advanced simulators. 1.3. Desirable features of comprehensive models – industry requirements and input The key parameters and issues in the design and operation of SWM modules and plants (to be fully accounted for by a reliable simulator) comprise: • Geometric SWM module design variables; these include mainly the membrane sheet dimensions, the detailed geometrical characteristics of feed-side spacer and of permeate side fabric. • Membrane surface physico-chemical properties, including intrinsic species rejection characteristics, surface energy, electrical charges. • Operating system parameters, including the controlled design variable (commonly the percentage permeate recovery at the pressure-vessel level), and the spatial distribution of state variables (mainly TMP, axial feed-side velocity and pressure, retentate and permeate properties). • Inherent operating problems that lead to temporal variability of SWM module and desalination plant performance; these problems include organic and colloidal membrane fouling, biofouling and scaling. Accurate results from a SWM simulator, among other uses, should facilitate meeting the main plant design and operation targets, i.e. the minimization of unit product cost and of overall environmental impact, including reduced specific energy consumption. Considering the foregoing membrane process conditions and requirements, the output of a comprehensive simulation tool should include: The spatial and temporal variation throughout the membrane plant of all key process parameters, including the local TMP and permeate flux as well as the permeate quality, under conditions of simultaneous membrane fouling. A simulation tool with such features is currently unavailable, although significant efforts to develop one have been made and are in progress. In planning and performing the SWM modeling tasks, one should take advantage of the aforementioned industrial experience and requirements. As subsequently discussed, industrial experience, in addition to assisting in practical issues and facilitating reasonable modeling simplifications, indicates that there are essential limitations on the permissible range of SWM design parameter values, mainly regarding the membrane sheet size and envelope arrangement, as well as the characteristics of feed- and permeate-spacer.

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1.4. Scope of this review This paper aims to review relevant work leading to the development of comprehensive models, which was carried out mostly during the past 20 years. It is recognized at the outset that the phenomena determining the SWM performance extend over several length-scales both in space and time; i.e. from physical-chemical processes occurring at the micro-scale to the large scale of entire membrane sheets. Therefore, studies (mostly local) on modeling flow and mass transfer in spacerfilled channels are outlined first, followed by review of efforts to develop integrated models for an entire membrane sheet or SWM module. Available steady-state integrated models are reviewed, efforts to develop dynamic simulators are summarized, and indicative simulation results are provided. Finally, a critical assessment of the state of the art in modeling SWM module performance is summarized and R&D priorities are outlined.

2. The structure of an integrated membrane separation model 2.1. General model description – flow fields The aforementioned desirable features of a generalized SWM model clearly suggest that the development of a comprehensive dynamic process simulator should be pursued. However, mathematical modeling of the dynamic operation of SWM module is a very difficult task due to the complexity of the underlying physical – chemical processes and of its complicated geometric characteristics. The problem is literally speaking a multi-scale one as it includes spatial scales from the microscale (where molecular and fouling phenomena occur) to the large scale of the entire membrane element. The temporal scales also vary between short scale characterizing phenomena usually at the membrane surface (e.g. solids attachment, nucleation) to that of long term SWM operation. A general description of the integrated model, that accounts for all the phenomena occurring within SWM, is provided in the following with the aid of the information flow diagram of Fig. 2. Briefly, processes at three length scales are grouped therein; i.e. i) phenomena at the microscale mainly related to species interaction with, and deposition on, the membranes, which impart a temporal variability to the SWM module performance; ii) phenomena at a larger scale (spacer scale), commonly represented by the “unit cell” of the retentate spacer, and iii) processes at (a still larger) mesoscale, referring to the membrane sheet. The “information-flow” between the phenomena at these different scales, including the interaction between dissolved and/or dispersed species in the treated fluid, is marked in Fig. 2. It is evident that if no depositing species are present, the system is far from equilibrium (no scaling), and the intrinsic membrane properties do not change with time, then the phenomena (at the microscale) are absent and the SWM module operates at steady-state conditions. This is the (comparatively) easier case to model, where considerable progress has been made as subsequently discussed. Fig. 3 depicts the geometric domain, where the problem is defined, comprising a planar membrane sheet and (due to symmetry) half a retentate and half a permeate channel on either side of the membrane. The consideration of this representative ‘elementary’ domain is based on the realistic assumption that a SWM is comprised of a sufficiently large number of sheets, so that one can safely ignore effects at the ends of the membrane stack. However, the real structure of the commercial element introduces two complexities compared with the above simple picture. The first complexity is the curvature of the SWM sheets which may influence the flow fields in the retentate channel; it should be noted that this effect has been dealt with in the literature [26], with indications that it may not be significant. The second complexity is related to the arrangement pattern between the sheets in the element (especially near the permeate tube), which appears to be more complicated than the simple planar sheet typically considered;

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Fig. 2. Structure of integrated model of desalination membrane module performance. Information flow between sub-models simulating processes at different length scales.

this effect has not been examined in the literature, to the best of the authors knowledge. Correctly modeling the flow fields at both retentate- and permeateside is essential. For the planar geometry considered, starting point to formulate the retentate side problem are the Navier–Stokes equations that must be solved in the flow field defined by the net-type spacers and the flat membrane [27]. To formulate the permeate-side flow problem, porous media equations are considered since the size of spacer voids is much smaller than the channel gap, so that the typical homogenization procedure for porous media can be applied. The two flow fields are linked through Darcy’s law, integrated across the membrane that separates the two flow channels. The formal boundary conditions are the inlet pressure, the retentate outlet pressure and the permeate outlet pressure. The difference between the inlet and permeate outlet pressure drives the separation process whereas the difference between the inlet- and retentate outlet-pressure drives the retentate flow. The practical boundary conditions are the inlet and the permeate pressures as well as the feed flow rate. The aforementioned system of equations describes the purely hydrodynamic problem [27].

2.2. Coupling of flow and concentration fields In parallel, the species conservation equations should be considered. The concentration field of the ionic species is governed by the StefanMaxwell equations [28]. Considering the small concentration of crystallizing dissolved species (the only practical exception is NaCl) the use of the equivalent Nernst-Planck equations is much more convenient [28]. Also the conditions of electro-neutrality and zero electrical current must be taken into account [29]. The incorporation of appropriate chemical equilibria relations in the transport equations is also needed. The equilibria between the species can be determined from thermodynamic considerations [30] (for which special codes exist [31]); however, the transport dynamics can lead to deviation from equilibrium so the kinetic constants of the occurring reactions are needed, which are difficult to determine [32,33]. There is a two-way coupling between the flow and concentration fields; specifically, the concentration depends on the velocity through the convection terms and (in turn) the velocity depends on concentration through the osmotic pressure which determines the wall flux.

Retentate Channel Permeate Channel Computational Domain

Membrane z y x

Fig. 3. A view of the representative computational domain, for a stack of flat-sheet membranes, which includes half a retentate and permeate channel with a desalination membrane in-between.

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Typically, the membrane rejection of the ionic species is incomplete, thus a certain amount can pass into the permeate channel. This phenomenon is described through the so called rejection coefficient which is a local characteristic of the membrane, and it is related to the membrane physico-chemical properties (pore size distribution, charges) through lower scale theories, referred to as membrane transport models [34]; the term ‘transport’ here refers to permeation through the membrane. From the practical point of view, the water permeance and the solute rejection are the most important measures of the membrane performance. These quantities can be determined in principle from membrane transport models. There are several approaches for the computation of these quantities, ranging from empirical “black box” models to mechanistic models taking into account the structural and physicochemical properties of the membrane. In the simplest case the parameters can be assumed to be functions of temperature, pressure and concentration. In the problem considered here, there is a spatial variation of the membrane parameters due to spatial distribution of concentration and pressure; therefore, a membrane operation model is necessary to transform intrinsic membrane properties to measured quantities. A characteristic case is the one of constant rejection coefficient [35]; a distinction has to be made between the intrinsic (local) rejection coefficient which is a membrane property and the effective (observed or global) coefficient which is a measured quantity and depends on membrane operation. More complicated membrane transport models relate rejection coefficient to water flux as well, as is the extensively used Spiegler-Kedem model [34,36]; even more complex models require solution of the conservation equations inside the pores of the membrane [37]. A very recent review [34] provides a fairly thorough critical assessment on membrane transport models. In any case, such a model is employed in the boundary condition of solute on the surface of the membrane. The conservation equations must be solved for the permeate side as well, accounting for the incompletely rejected ionic species. Conservation equations for non-ionic substances must be also considered (e.g. organic macromolecules, microbial cells, colloidal particles). These substances are typically completely rejected by the RO membranes; therefore, the corresponding conservation equations can include only convection and diffusion terms. 2.3. Dealing with the complete problem The above description (considering that no species deposition occurs within the SWM module) provides a view of the pseudo-steady conditions of membrane separation. In principle, the corresponding system of equations can be solved to fully determine the flow fields in the membrane module. However, mainly the geometric complexity of the retentate side renders such direct attack on the problem practically impossible. For instance, taking into account that the ratio of the membrane sheet length to the spacer “unit cell” [38] characteristic size is of order 100, it is evident that the direct numerical simulation of the entire membrane sheet requires the discretization of too many unit cells, i.e. of order 10,000. Further, as subsequently discussed, the geometry of the unit cell is quite complicated and a fine grid is required to obtain an accurate numerical simulation; it is clear, therefore, that the direct numerical solution of the conservation equations in the entire-sheet scale is prohibitive. Consequently, efforts have focused to study in detail separately the flow field and related phenomena at reduced length scale, notably at the scale of the “unit cell” [38]. 3. Investigations in a reduced spatial domain – feed spacer scale The most important flow field in the SWM module is that formed by two neighboring membrane sheets separated by a thin net-type spacer; the latter is in contact with the active membrane surfaces, where the species separation process takes place. Therefore, the flow field detailed characteristics directly affect the physico-chemical phenomena at the

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membrane surface, which determine the effectiveness of separation. This flow field, comprising a very narrow channel with the insert, is 3dimensional and quite complicated to investigate both theoretically and experimentally. To get an improved understanding of the effect of spacer types on fluid dynamics and mass transfer, numerous studies have been performed with simplified 2-D geometries as well as with the more realistic, yet more difficult, 3-D geometries [28]. Computational and some experimental studies with such geometries will be briefly reviewed in this section. 3.1. Problem formulation 3.1.1. Geometry of spacer-filled channel in 2D and 3D simulations The flow geometry in 2D simulations is a plane channel formed by the two flat membranes (of thickness H) wherein an array of parallel filaments is inserted with their axes in a direction normal to the mean flow; the filaments are regularly spaced at a distance L. Various spacer filament geometries have been used with cross-sections usually circular (of diameter D), square, triangular, elliptical, etc. The most frequently studied spacer configurations are the so-called (e.g. [39]) i) submerged, ii) zigzag, iii) i-cavity and v) o-cavity, as shown in Fig. 4. The study of the particular geometric filament arrangements, regarding their relative position with respect to the membrane walls (e.g. whether in contact or not) provides insights into the function of real spacers. The flow geometry considered in 3D simulations is an approximation of the narrow channels with spacers which are encountered in spiral wound elements at the retentate side. The flow field geometry is determined by the net-type bi-planar filament spacer, which is formed by two layers of straight cylindrical filaments. In each layer the filaments are parallel, having different orientation, and intersect at a characteristic angle β, as shown in Fig. 5. In general, the geometric characteristics of such spacers are as follows: • • • • • •

Diameter of the top filament, D1 Diameter of the bottom filament, D2 Distance between the top cylindrical filaments, L1 Distance between the bottom cylindrical filaments, L2 Angle between crossing filaments, β Flow attack angle, α

In most studies, spacer geometrical characteristics are close to commercially available spacers. Thus, the diameters of the top and bottom cylindrical filaments are considered equal (D1 = D2 = D), and half of the channel height (H = 2D). Moreover, the distance between the parallel cylindrical filaments of the top and bottom row are commonly equal (L1 = L2 = L). Consequently, in most studies the geometrical characteristics are limited to the ratio of the filament distance over their diameter (L/D), the crossing angle (β) and the flow attack angle (α). In practice and in the majority of published works, the ratio L/D varies between 5 and 12, whereas the angles α and β are in the range 0°–90° and 30°–120°, respectively. For practical reasons, it is advantageous to have a symmetric flow field with respect to the mean flow direction [38], i.e. α = 45°. Therefore, three geometric parameters are sufficient to describe the bi-planar spacers of Fig. 5 (diameter L/D, crossing angle β, and spacer thickness commonly H = 2D). 3.1.2. Flow and mass transfer parameters in spacer-filled channels The Reynolds number (Re) for flow in spacer-filled channels is defined as Re ¼

DUρ μ

ð1Þ

where ρ and μ are fluid density and viscosity and U is a characteristic velocity which could be either the effective velocity (Ueff), taking into account the porosity of the channel, or the superficial velocity Uo (based on empty channel). Of particular importance is the selection of an

Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

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Fig. 4. Spacer filament arrangements in a two-dimensional channel: a) zigzag, b) submerged, c) cavity in outer and inner wall [39].

appropriate characteristic length D, which (in spacer-filled channels) could be the: • hydraulic diameter, Dh • spacer filament diameter, Df • channel height, H In the case of hydraulic diameter Dh, account is taken of the channel voidage ε, which is determined by the spacer characteristics. However, as subsequently discussed, spacers of the same L/D ratio (and voidage ε) form substantially different flow fields with different behavior if the characteristic angle β is different. Therefore, merely using the hydraulic diameter Dh to develop generalized correlations for friction losses and mass transfer is inadequate, unless there is specification of the parameter value for β (and α), for which the correlations (of experimental or other data) are applicable. Unfortunately, the often quoted Schock and Michel [40] correlations, using the hydraulic diameter Dh, have this significant limitation and should not be used indiscriminately for any type of spacer arrangement. Similarly, correlations using Re based on filament diameter, Df or channel gap H are incomplete unless L/D and β parameter values are specified. Results are presented in terms of dimensionless quantities including dimensionless pressure drop, Re number as well as Schmidt (Sc) and Sherwood (Sh) numbers defined as: Sc ¼

μ ρ  Diff

ð2Þ

where k is the mass transfer coefficient and Diff a relevant diffusion coefficient. Fluid dynamics and mass transfer in spacer-filled channels, is described by the Navier–Stokes, continuity and mass balance equations, considering Newtonian incompressible fluid: ∂u 1 2 þ u:∇u ¼ −∇P þ ∇ u ; Re ∂t

kD Diff

Fig. 5. Geometrical characteristics of retentate spacers used in 3D simulations.

ð3Þ

∂C 1 2 þ u:∇C ¼ ∇ C Re  Sc ∂t

ð4Þ

For the problem at hand, permeation velocities are orders of magnitude smaller than the cross flow velocities, thus justifying the assumption (for a basic solution to the fluid flow problem) that the membrane surface is effectively impermeable where the no-slip boundary condition can be applied. Greater attention should be given to boundary conditions for the mass balance equations, where either constant wall flux or constant wall concentration can be used. As outlined in the foregoing section, a complete formulation should account for membrane permeability and species rejection, so that the retentate flow field is linked with that at permeate side. Therefore, the local fluid velocity normal to the membrane (or the local permeate flux Jv) must be related to the membrane properties. Although several membrane transport models exist of varying complexity, for the purpose of this discussion one can consider the commonly employed Spiegler-Kedem model [34] Jv ¼

Sh ¼

∇:u ¼ 0

1 ðΔP−σΔπÞ Rm μ

ð5Þ

where Rm is the membrane resistance, ΔP is the trans-membrane pressure, σ is the reflection coefficient (quantifying the rejection of ionic species) and Δπ is the osmotic pressure. Details on the boundary conditions at the membrane surfaces (Fig. 5) are provided in Fimbres-Weihs and Wiley [28] for permeable and impermeable walls. The regular pattern of the spacer geometry, i.e. a multitude of “unit cells” symmetrically arranged, suggests that it is realistic to assume a spatially periodic velocity field across the spacer-filled channel. Thus, the periodic conditions have been successfully employed to describe transport phenomena is such flow fields. This assumption leads to much reduced computational load, allowing the use of very fine grid to capture the detailed flow field and mass transfer features. In this case, the flow is assumed to be periodic, with periodicity L in the x and z directions (Fig. 5). Details on the implementation of the periodic boundary conditions in the flow problem are provided in [38,41]. The treatment of mass transfer with periodic boundary conditions (with permeable or impermeable walls) is outlined in [28]. If periodicity is not adopted, usual boundary conditions at the inlet, outlet, symmetry planes and non-permeable walls such as spacer surfaces and channel walls that are impermeable, are presented in detail elsewhere [28].

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3.2. Two-dimensional simulations The flow field is comparatively simple so that the currently available very accurate direct numerical simulation methods render feasible detailed flow description for Reynolds numbers on the order of a few thousands, and certainly within the Re range of interest to membrane processes. In early work, Karniadakis et al. [42] studied turbulence promoters for heat transfer enhancement in a plane-channel, with a periodic array of small-diameter cylinders. The latter was found to lead to flow destabilization by essentially the same mechanisms as in an empty channel (i.e. formation of Tollmien–Schlichting waves), but at greatly reduced Reynolds numbers (~150). Relevant to turbulence promotion are also the studies of Chen et al. [43] and Zovatto and Pedrizzetti [44], where flow features and stability were studied for various geometric arrangements of a single cylinder in a plane-channel. Kang and Chang [45], performed steady-state numerical simulations of mass transfer in channel containing zig-zag and cavity type spacers. The flow field was described as well as local Sherwood numbers at the channel walls. Results of flow visualization experiments were reported to be in good agreement with simulations for low Reynolds numbers. Cao et al. [46] using turbulent modeling studied two-dimensional flow in a short channel containing two cylinders at various arrangements i.e. cavity, zigzag and submerged. High shear stress regions and eddies were identified in the channel due to the cylindrical filaments whereas mass transfer enhancement on the membrane was directly related to the high shear stresses, velocity fluctuations, and eddy formation. Pressure drop and overall mass transfer coefficients were obtained for various inlet velocities. Schwinge et al. [47] visualized the flow patterns for different filament configurations involving variations in mesh length, filament diameter and for channel Reynolds numbers up to 1000. It was reported that the onset of unsteadiness occurred at much smaller Re numbers than in an empty narrow channel which depended on spacer configuration and mesh length. Indicatively, this onset was found to occur at Re numbers of 80, 300 and 400, for submerged, cavity and zigzag spacer configurations, respectively. These authors also performed direct numerical simulations of flow [48] and mass transfer [49] in channels containing five cylinders. The effect of various configurations on flow

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characteristics such as pressure drop, eddy formation, wall-shear stresses, and mass transfer was examined. Koutsou et al. [41] studied transport phenomena in a twodimensional geometry containing a periodic array of submerged cylindrical filaments. Direct Numerical Simulations (DNS) were performed over a range of Reynolds numbers typical of membrane modules, while periodic boundary conditions were applied, thus restricting the computational domain to one unit cell. The results indicate that the flow becomes unstable at a critical Reynolds number 60, and progressively tends to a chaotic state. Above a Reynolds number 78 wall eddies appear, conjugate to those shed by the cylinder. This distinct characteristic of the flow in the channel wall is due to the interaction of the vorticity shed by the cylinders with the vorticity layers created on the channel walls. Statistical characteristics were obtained such as timeaveraged velocities, Reynolds stresses, wall-shear rates and pressure drop. Li et al. [39,50] applied a two-dimensional steady-state model and various spacer configurations to study the effect of curvature of spacer-filled channel on hydrodynamics [39] and particle deposition [50]. An increase in channel curvature resulted in different profiles of shear stress between the membrane surfaces, with the difference becoming more pronounced at higher inlet velocities [39]. Particle deposition [50] was found to be strongly affected by flow distribution, decreasing in areas of high shear stress. Zigzag and submerged spacers exhibited reduced curvature effect on particle deposition whereas cavity-type spacers enhanced this effect and led to unequal deposition of the colloidal material on the inner and outer membranes, which is expected to have negative practical consequences. Typical significant results of two dimensional simulations are summarised in Table 1. 3.2.1. Concentration polarization The simpler 2D geometry facilitates studies of concentration polarization, which are summarized in the following. Contributions in understanding transport and concentration polarization phenomena in nanofiltration were made by Geraldes et al. [51–53]. Their simulations were in accord with experimental observations of fluid flow, concentration polarization and solute rejection of nanofiltration membranes. The studies relevant to spacers were limited to a 2D ladder-type

Table 1 Summary of results from numerical 2-D simulations of flow in channels with transverse filaments. Authors

Simulations

Geometry

Significant Results

Kang and Chang [45]

2D, Steady State

Cao et al. [46]

2D, Transient k-ε Turbulence model

- Flow features description - Local Sh number calculation - Pressure drop - Overall mass transfer coefficients

Schwinge et al. [46]

2D, Transient

Schwinge et al. [48,49]

2D, Steady (?)

Koutsou et al. [41]

2D, Transient, periodic boundary conditions

- Zigzag - cavity - cavity - zigzag - submerged - single cylindrical filament adjacent to a membrane wall - single cylindrical filament placed at the center of membrane channel - cavity - zigzag - submerged - single cylindrical filament adjacent to a membrane wall - single cylindrical filament placed at the center of membrane channel - cavity - zigzag - submerged Submerged

Yu-Ling Li et al. [39,50]

2D, Steady State

- submerged - zigzag - i-cavity - o-cavity

- Effect of spacer configuration on transition to unsteadiness

Effect of spacer geometry on pressure drop, eddy formation, wall-shear stresses, and mass transfer

- Temporal and spatial fluid flow description - Time-averaged local shear stress - Pressure drop correlation Effect of curvature on pressure drop, shear stress and particle deposition

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configuration [51–53] and permeation through one membrane was considered. As in previous studies, overall mass transport enhancement and concentration polarization reduction was observed for filaments attached onto the membranes, compared to the opposite side of the channel, and to an empty channel. This result was also confirmed by Ahmad et al. [54,55] who studied the effect of three 2D spacer configurations (circular, square and triangle geometries touching one wall) on concentration polarization and permeation under steady [54] and unsteady [55] hydrodynamics. A spacer performance evaluation revealed that for Re numbers prevailing in operating SWM modules (Re b 400) the cylindrical filaments are associated with smaller concentration factor. In parallel, the impact of different configurations (submerged and zigzag) and of the spacing between square obstacles/filaments was studied by Ma et al. [56,57] using the Petrov/Galerkin method for solving the conservation of momentum and mass equations. These studies suggested that the zigzag configuration tends to reduce the concentration polarization and to improve the permeation flux. Wardeh et al. [58] developed a 2D steady-state model to simulate permeation and concentration polarization for the same rectangular channel used by Fletcher and Wiley [59]. Later these authors expanded the model to investigate the effect of cylindrical submerged and zigzag spacer configurations on permeation flux and concentration polarization. It is reported that results on the pressure drop, salt mass fraction and permeate flux dependence on Re number indicate that the zigzag type is more economical and more efficient in reducing salt concentration at the membrane surface compared to the submerged one. Very recently, Amokrane et al. [60] presented an integrated modeling of the evolving (in space and time) flow and concentration fields during water desalination in membrane spacer-filled channels. Submerged and zigzag spacer filament two-dimensional configurations were employed, while permeation was considered by both membrane surfaces. Time-averaged local profiles of mass transfer coefficient and boundary layer thickness were obtained and the effect of flow structure on the aforementioned parameters was elucidated. Evaluation of spacer configurations in terms of pressure drop and mass transfer coefficient indicated that the zigzag geometry had inferior performance. However, the undesirable effect of contact lines between membrane and zigzag filaments on concentration polarization (and possibly on fouling) was evident; this is a negative feature of the zigzag arrangement, to be considered in designing real 3D spacers. 3.3. Three-dimensional simulations – proposed novel spacer Several theoretical studies have focused on three-dimensional simulations of spacer performance. Karode and Kumar [61] were apparently the first to describe the 3-D structure of several commercial spacers and the flow domain in a realistic manner. They simulated flow in a spacerfilled channel similar to the one used by Da Costa et al. [62] in their experiments; the channeling flow pattern observed before [63–65] could be reproduced by their simulations. The spacers were evaluated in terms of pressure drop and shear stress on the membrane surfaces. However, this work was limited to steady state simulations with no indication of the Reynolds number range where steady state exists. It is noted that the simulation of an extended flow field inevitably resulted in a limited spatial resolution. Santos et al. [66] performed a numerical and experimental study of pressure drop in a channel filled with various ladder-type spacers; excellent agreement is reported between results of numerical simulations and experimental data. To investigate the effect of channel hydrodynamic conditions on wall shear stress, a modified friction factor was introduced. In parallel, numerical simulation results indicated that the modified friction factor could be used for selecting the best spacer geometry in terms of mass transfer efficiency. Li et al. [67,68] presented results on flow and mass transfer, by performing three-dimensional direct numerical simulations in a geometry closely representing membrane spacers. Periodic boundary

conditions were employed, which enabled them to simulate just one unit cell of the spacer. The effect of spacer geometrical characteristics (mesh size and angles α and β) was studied in terms of Sh and power number Pn; results suggested optimum performance when the flow attack angle was 30° and the spacing between filaments (ratio L/H) was 4. Although no information regarding spatial and temporal resolution of computations was provided, experimental data of average mass transfer coefficients appeared to agree with their simulations [68,69]. Ranade et al. [70] applied a 3D transient model to study the effect of curvature on hydrodynamics of spacer filled channels. Various commercial spacers were examined, in a unit cell approach, and the results were validated with the measurements of Da Costa et al. [71]. This study results showed that pressure drop and velocity profiles of spacer-filled flat and curved channels were not significantly different, in agreement with the results of Yu-Ling Li et al. [39,50]. However, Ranade et al. [70] did not calculate the shear stress on the membrane walls for which Yu-Ling Li et al. [39,50] show that there is a difference between the two membrane surfaces with increasing curvature. Koutsou et al. [38,72] performed direct numerical simulations to study in detail the flow field development [38] and mass transfer in spacer-filled channels [72]. Realistic spacer geometries were considered in a rather broad range of geometric parameters L/D and angle β. The results clearly suggest that unsteadiness appears at relatively low Reynolds numbers (Re = 35–45) depending on spacer geometry [38]. The simulated temporal evolution of the flow field shows that the main characteristics are: a free vortex at the center of the unit cell, aligned with the direction of the men flow, and closed recirculation zones attached to the spacer filaments (Fig. 6). The effect of spacer geometry on time-averaged spatial distributions of shear stress [38] and of mass transfer coefficient [72] on the membrane surface is examined and correlations are developed of pressure drop and Sh number with Re and Sc numbers. Comparison of these numerical predictions and correlations with extensive measurements show very good agreement [38,72]. Later in an assessment of spacer performance, Koutsou and Karabelas [17] suggested that the less dense spacers (i.e. L/D = 12), with filament crossing angles β greater than 90°, may hold advantages over other commonly used spacer geometries. The correlations obtained in these studies [38,72] are employed in the general SWM modeling framework outlined in foregoing sections. Fimbres-Weihs and Wiley [73] presented a numerical study of mass transfer in 3D spacer-filled channels; a single spacer was used, with L/D = 6.67, with orientation angle α 45° and 90°. Using a typical Schmidt number (Sc = 600) and a Reynolds number range up to 200, the regions of high mass transfer were found to correlate mainly with those regions where the fluid flow is directed towards the wall; the relation between 3D flow effects, pressure drop and mass transfer was investigated. Interestingly, the exponent of Sh number dependence on Re number is reported to be 0.59. Shakaib et al. [74,75] employed a 3D, steady state model to study hydrodynamics [74] and mass transfer [75]. They investigated two types of spacer geometries; i.e. diamond and submerged with various filament spacings, thickness and flow attack angles. The critical Re number at which flow becomes unsteady was reported to be as low as 75 when filament spacing and flow attack angles are small, increasing to more than 200 for larger flow attack angles [74]. Regarding pressure drop, the effect of spacer filament thickness was found to be more pronounced compared to that of spacing [75]. The effect of spacer configuration is also evident on shear stress and mass transfer coefficient, which tend to increase for small filament spacing and flow attack angles [75]. Li et al. [76] performed a CFD analysis to study the validity and effect of periodic boundary conditions (PCB) in spacer filled channels; they calculated the pressure drop of various types of unit cells and compared the results with corresponding experimental data. It was reported that not all PBC types, presented in the literature, were suitable for analyzing the fluid flow behaviour and pressure drop predictions, although some good results by the method of PBCs were obtained, using a sufficient

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Fig. 6. A snapshot of the flow field in a unit cell of a spacer filled channel, depicting its main characteristics. Results of direct numerical simulation [38].

number of unit cells. Srivathsan et al. [77] recently studied various spacer geometric characteristics and proposed correlations of friction factor and Sh number with Re number. Although the results, regarding Sh number, do not seem to agree with other published works [67,72,73] and the data are relatively limited, the interesting feature of this work is that the ratio of spacer thickness to distance between filaments is included in the correlations. Lau et al. [78] applied the approach of Ahmad et al. [55] in a 3-D model to study the effect of filament-intersection angle β and orientation angle α on hydrodynamics and concentration polarization. Evaluation of spacers in terms of specific power consumption and concentration polarization factor indicated that a spacer with α = 120° and β = 30ο provided optimum performance. However, the fact that this spacer is placed asymmetrically with respect to the direction of mean flow (α ≠ 45°) is expected to introduce different behavior between the two membrane surfaces in terms of concentration polarization and membrane fouling, possibly negatively impacting on membrane life-time. Gurreri et al. [79] used 3D CFD to investigate concentration polarization and pressure drop in spacer filled channels for electrodialysis operations of brackish-, river- and sea-water. Various woven and crossing-filament commercial spacers were used, with thickness between 280 and 508 μm and different spacer orientation angles α.

The results suggested that woven spacers were associated with higher polarization factor at any given normalized pumping power Pn, whereas for all spacers examined, a flow attack angle α = 45° resulted in more efficient mixing compared to the 90° case. Significant results of 3D simulations are summarized in Table 2. 3.3.1. Novel spacer geometries Recently, in efforts to further optimize the flow and mass transfer conditions in feed water channels, innovative spacer configurations have been proposed [70,80–83]. These spacers are characterised by multilayer designs [80,81] or modified filaments/strands [70,81,82]. Schwinge et al. [80] proposed a multi-layer spacer which presumably leads to improved flux compared with the conventional 2-layer spacer, at both identical mesh length and identical hydraulic diameter. Although the proposed spacer leads to increased pressure drop, the authors report that an economic evaluation of that spacer performance appeared promising; however, they recognized the difficulties associated with fabrication of the proposed novel spacer. Li et al. [81], examined various innovative spacers with modified filaments, twisted tapes and multi-layer structures. The performance of these spacer configurations was tested only experimentally, due to numerical difficulties related to these fairly complicated geometries.

Table 2 Summary of results from 3-D simulations in channels with spacers. Authors

Simulations

Geometry

Significant results

Karode and Kumar [61]

3D, Steady-State

Various symmetric and asymmetric commercial spacers

Santos et al. [66]

3D, Transient

Ladder-type

Li et al. [67–69]

3D, periodic boundary conditions

Ranade et al. [70]

- 3D, Transient - Periodic BC - k-ε Turbulence model - 3D, Transient - Periodic BC

L/h = 2, 4, 6, 8,10 α = 0,15,30,45ο β = 60,120ο Various commercial and novel spacers

- Total drag as a function of Re number - Average shear rate as a function of inlet velocity - Validation with experiments - Friction factor as a function of Re and Pn numbers - Spatially averaged Sh number as a function of Pn number - Sh number as a function of Pn - Pn as a function of Re number - Validation with experiments - Contributions of viscous stress to the overall pressure drop - Drag coefficient as a function of Re number - Axial velocity profiles - Description of the temporal evolution of the flow field characteristics - Pressure drop dependence correlations on Re number - Sh number dependence correlations on Re and Sc numbers - Dependence of friction factor on Re number - Overall Sh dependence on Re number - Dependence of energy losses due to form drag on Reynolds number - Dependence of energy losses due to viscous drag on Reynolds number - Pressure drop and Sh numbers for various spacer configurations

Koutsou et al. [38,72]

L/D = 6,8,10,12 β = 90,60,120ο

Fimbres-Weihs and Wiley [73]

- 3D, Steady State - Periodic BC

L/D = 6.67 α = 45, 90ο β = 90ο

Shakaib et al. [74,75]

- 3D, steady state -Periodic BC

Diamond shaped -submerged

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Additionally, the same authors proposed what they considered as novel optimal multi-layer spacer, comprising non-woven nets in the outer layers and twisted tapes in the middle-layer, which was reported to enhance Sh number by ~30% compared to an optimal conventional spacer proposed in a previous work [68,69]. Ranade and Kumar [70], using numerical simulations, analyzed the effect of several different filament profiles for two-layer spacers. The cross-section of the strands comprising those spacers was fairly complicated. As expected, they found that the shapes of spacer strands significantly affect the behavior of fluid flow around them. Furthermore, one of the cases they simulated was considered to hold notable potential for reducing pressure drop while maintaining a comparatively high level of wall shear rate. Liu et al. [83], have proposed another spacer configuration which is considered to perform as a static mixer within planar flow channels. Fluid adjacent to the top and bottom boundaries of the flow channel appears to move to the middle and be replaced by fluid from the middle of the flow channel. The authors claim that this static-mixing spacer (contrasted to conventional spacers) offers comparable or better mass transfer performance at the same power input. In general, the above studies on novel spacers offer useful insights on the effect of filament/strand shape, and of the spacer geometric arrangement in the channel, on the feed-side flow field and mass transfer. However, a criticism can be leveled against most of them in that they tend to totally disregard the important issues of a) the technical and economic feasibility of fabricating spacers with complicated filament shapes, and b) the behavior of such spacers (commonly made of relatively soft plastic material) under the significant normal stresses imposed on them during both SWM manufacturing and operation. As also subsequently discussed, one should be concerned whether the assumed nominal channel gaps in SWM modules can be achieved and whether potential damage of the membrane, in contact with possibly sharp edges of the spacer, can result due to such compressive stresses on the membrane. 3.4. Experimental studies In the foregoing sections on 2D and 3D simulations, the experimental work performed to test and/or validate the numerical results was briefly outlined. However, several additional experimental studies exist with spacer-filled channels, with or without membranes, which deal with hydrodynamics, pressure drop and mass transport [40, 63–65,84–86]. In an often quoted work, Schock and Miquel [40] studied various commercial spacers and developed dimensionless correlations for pressure drop and mass transfer coefficients. Permeate channel spacers were also taken into account in that study. Generalized correlations of the usual form f = a1Reb and Sh = a2RecScd, were obtained for the friction factor and Sherwood number, using a hydraulic diameter as the characteristic length; however, for reasons outlined in the preceding Section 1.2, care should be exercised in the application of those popular correlations because they do not take into account the spacer geometric parameter angle β, which was found in more recent studies (e.g. [38,72]) to affect the flow field. Additionally, the choice of a dependence of Sh number on Sc number to the power 0.25 was rather arbitrary, whereas more recent advance simulation and experimental results suggest that the dependence is much stronger (i.e. Sc exponent around 0.4 [72]). As expected, spacer-filled channels exhibited significantly higher mass transfer rates compared to empty channels over the same range of Reynolds numbers, but at increased pressure drop. However, significant differences could not be discerned between the various spacers used in their tests, an observation that can be disputed on the basis of other similar studies (e.g. [38,72]). Kuroda et al. [84] measured pressure drop and mass transfer coefficients (by an electrochemical technique) in channels with impermeable walls. Correlations were obtained of the form indicated above, with attempts to relate the coefficients a1 and a2, with the spacer geometrical characteristics. However, their results appear to neglect the effect of

spacer orientation with respect to the mean flow, as outlined above. The latter suggest that if spacer filaments are roughly aligned with the mean flow, lower pressure drop and mass transfer coefficients are obtained. This is born out in the experiments of Winograd et al. [85], performed in an electrochemical cell, as well as in the pressure drop measurements of Farkova [86] and of Zimmerer and Kottke [63]. Furthermore, it was shown in the latter paper that the overall flow pattern changes with orientation of the filaments between the extremes of a zig-zag (or corkscrew) and a channeling pattern, where the flow is constrained by the cell side walls. Similar behavior is exhibited in the flow experiments of Feron and Solt [64], with various idealized and realistic spacer geometries. Belfort and Guter [65] tested various commercial spacers for electrodialysis use, and evaluated them in terms of porosity, dead flow areas, stack resistance and pressure drop, proposing some optimal configurations. Their flow visualization experiments revealed interesting flow features, notably the existence of a vortex screw-like motion which is considered to reduce the thickness of concentration boundary layer. Significant work has been carried out by Fane, Wiley and coworkers [62,71,87–90], including experiments with commercial and custommade spacers to obtain pressure drop and flux [62,71,87] as well as mass transfer coefficients of UF membranes [62,71]. Studies of solute rejection and coupling between concentrate and permeate channels were also performed that took into account variable fluid properties due to concentration polarization [88,89], fouling observations with microparticles in spacer-filled channels [89], as well as economic evaluation of various spacer configurations [62,71,87]. Working with idealized geometries comprised of a set of parallel filaments, as well as with a variety of commercial spacers, Da Costa et al. [90] concluded that the presence of spacers can increase flux by a factor greater than 7. In addition, they showed that filaments attached to the membrane and transverse to the mean flow (the ladder-type spacer) are more effective in reducing concentration polarization than filaments aligned with the flow [87]. They also suggested that an optimum mesh length exists [87]. In a more recent study of membrane fouling with microparticles, Neal et al. [89] observed that fouling was more pronounced when the filaments were oriented transversely to the mean flow. These conflicting tendencies depending on feed-water properties, suggest that different fouling species (i.e. organic compounds, colloids or aggregates and microparticles) may interact differently with the spacers; therefore, a universally optimal spacer for all types of SWM modules (treating various types of feed waters) likely does not exist. Sablani et al. [91] investigated the influence of spacer thickness on permeate flux in spiral wound modules. Their results show an increase in flux with increasing spacer thickness, as one might expect. Balster et al. [92] using the limiting current technique studied standard nonwoven and multi-layer net spacers aiming at reducing concentration polarization and improving electrodialysis processes. The multi-layer spacer configurations exhibited significant mass transfer enhancement. Experimental efforts have been invested to determine the flow conditions close to membrane surface in spacer-filled channels. Gimmelshtein and Semiat [93] have employed particle image velocimetry (PIV) to measure local velocity and estimate the magnitude of a mixing index (MI) within a unit cell of spacer net. Significant flow direction changes were observed near the spacer filaments (acting as obstacles to be bypassed), which resulted in increased MI in these areas. Recently, Gao et al. [94] used Doppler optical coherence tomography (OCT) to characterize the velocity profile normal to the membrane surface by visualizing the flow patterns inside a unit cell of the spacer in an experimental module. The orientation of the spacer towards the bulk flow direction was considered. The results indicate that there are two major mechanisms inside the spacer interstices: a) tangential flows mainly driven by the bulk motion; b) development of eddies, which can generate significant flows normal to the membrane surface and create disturbances in these regions. These mechanisms and spatial flow distribution in the channel are in general accord with the detailed

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flow simulations of Koutsou et al. [38] (e.g. Fig. 6), certainly governed by spacer geometric characteristics and filament orientation in relation to mean flow direction. Rodrigues et al. [95] studied the entrance effects on Sh number across a narrow rectangular spacer-filled channel, by measuring electrochemically the overall Sh number for Re numbers up to 500. Additionally, they showed that in the transitional flow regime, above a critical Reynolds number, mass-transfer entrance effects are negligible, suggesting that periodic boundary conditions may be appropriate for flow and mass-transfer CFD computations in spacer- filled channels in the transitional regime. However, for laminar flow the periodic boundary condition should be used with care because strong mass-transfer entrance effects may prevail, depending on the spacer geometry. 4. Development of a comprehensive integrated model 4.1. Steady – state modeling Early efforts to model the flow field throughout a membrane sheet are reviewed in [96]. At present, the best (and perhaps the only) way to attack the full problem (without compromising the description of the essential physico-chemical phenomena involved) is the so-called “scale separation” approach, which is justified due to the smallness of the ratio of cell size over the sheet size. This approach is analogous to the (well known in the field of transport phenomena) homogenization procedure or to the multiple scale expansion procedure [97]. These procedures are well established for linear phenomena [97]. A discussion on their application to the non-linear intrinsically transient flows, arising due to the presence of spacers, can be found in [27]. In the range of flow rates of practical interest, the flow unsteadiness that appears due to the net-type spacers (e.g. [38]) introduces a time scale to the problem. Occasionally, this type of flow is characterized as “turbulent” (and the spacers as “turbulence promoters”) but it is preferable to retain the term unsteady (or intrinsically transient) laminar flow since turbulence is associated with disparate size ranges between the smallest eddies and the channel size. Moreover, advanced numerical simulations clearly show [38] that in the range of flow rates of practical interest (and related Reynolds numbers) an unsteady flow prevails, which is much closer to transition than to fully developed turbulent flow. A homogenization procedure can be employed that effectively “eliminates” the intrinsic time scale of flow fluctuations by considering a time scale larger than the latter, but much smaller than the time scale of the SWM module operation. Additionally, through this approach, the dependencies in the vertical direction (normal to the membrane surface) are eliminated, leaving two spatial directions for the problem which correspond to the length and the width of the membrane sheet. Before proceeding further, a brief overview will be made of simulation approaches not based on the foregoing scale separation. Attempts for direct simulation of the entire problem (including all phenomena) have been made only in two dimensions and not for the entire sheet length [98–100]. Another approach is the simulation of several three dimensional unit cells [101]; in that case the intrinsic flow dynamics is ignored by solving the steady state flow equations instead of the timedependent ones. In any case, such simulations are not expected to cover the complete sheet and they are useful only to support/validate the scale separation approach. The transfer of information from the spacer scale to the entire sheet scale can be done in two ways: (i) using a representative domain-portion, including several unit cells, to extract generalized constitutive-type expressions for key parameters (e.g. [27]) and (ii) using a single unit cell with periodic boundary conditions (e. g. [35,38]). A typical mesoscale clean-membrane model (i.e. steady-state at an appropriate intermediate time scale) consists of equations describing the solvent/water and solute conservation in retentate and permeate sides, the pressure in both sides, the membrane transport model, and a relation between the average (mixing cup) solute concentration and

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its concentration on the membrane surface (both at retentate side). The difference between these two concentrations is due to the socalled concentration polarization phenomenon. The “communication” of information between the spacers scale and the mesoscale is implemented through relations for the friction factor and mass transfer coefficient in the retentate channel. The former expressions are used in the mesoscale model for pressure drop determination and the latter to account for concentration polarization. Typically, the membrane operation models used in the literature deal with the analysis of experimental data so they focus on particular aspects of the process depending on the particular experimental design considered. The consideration of spacers at the mesoscale varies; i.e. in some cases the presence of spacers is completely ignored as an approximation [102,103]. Another approximation is that of using an empirical velocity profile to account for the presence of spacers. Unfortunately, the particular approach overestimates concentration polarization as it is not representative of the real effect of spacers on mass transfer [104,105]. In the general case, the constitutive relations discussed above are used to adequately account for the effect of spacers. In case of insignificant pressure drop in the permeate side, the retentate problem is purely onedimensional [106]. However, if there is significant permeate-side pressure drop, the wall flux is two-dimensional and the model is two dimensional as well. The majority of mesoscale models consider the “1 + 1 direction” approximation, that is, the retentate side exhibits variations only along the main flow direction and the permeate side displays variations only transverse to the main flow direction [107–111]. A formal proof for the validity of such an approach for the pure hydrodynamic problem is given in [112]. The linearization of the concentration polarization relation (a quite valid assumption due to the spacer-induced enhanced mass transfer) allows analytical manipulation of the governing equations, leading to simplified models [113,114]. It is worth noting that in most of the two-dimensional models of the membrane operation in the literature, no spatial distribution of quantities is presented since the focus is on integral quantities for parameter extraction from experimental quantities and global optimization [107,108,110,111]. A fully two-dimensional semiformal modeling framework for membrane operation has been presented in [35], where several results for spatial distribution of variables in steady-state (i.e. clean membrane) operation are presented. 4.2. Dynamic model development The preceding discussion refers to the absence of any type of material accumulation in the membrane element. However, material accumulation can occur through four different mechanisms and introduces new time scales to the problem; a classification of fouling mechanisms can be made on the basis of the type of the depositing species. The first accumulation/fouling mechanism is the so-called organic fouling, whereby a gel-type layer is created from organic macromolecules transferred with the flow onto the membrane. The local fouling layer growth rate is usually taken simply proportional to the local wall flux [115,116]. The properties of this layer depend on the trans-membrane pressure (TMP) as well as on the instantaneous flux and they determine the wall flow. The relevant studies are usually focused on the organic fouling layer main properties (i.e. the specific cake resistance or permeability) accounting also for cake compressibility, and disregarding any possible small scale non-uniformities [117]. Such a representative local organic-layer thickness is non-uniform throughout the membrane sheet but appears to have the tendency to become spatially more uniform as time proceeds (auto-regulation tendency) [118]. Moreover, the growth of the fouling layer naturally tends to modify the flow and concentration fields in the retentate channel and the phenomenon of cakeenhanced concentration polarization is considered to emerge [119]. The second accumulation/fouling mechanism, which is more complicated (at least from the geometric point of view), is referred to as scaling i.e. the formation of solid deposits on the membrane due to

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local supersaturation of sparingly soluble inorganic salts. This is brought about by the rejection of species by the membrane, leading to local concentration increase of dissolved compounds and thus to local supersaturation, which triggers the well-known precipitation sequence of nucleation and particle growth [120]. Initially, scaling occurs in a completely localized pattern (i.e. in the form of distinct particles), contrary to organic fouling where the accumulated mass is rather uniformly distributed on the membrane from the outset. Several complexities exist regarding scaling. The major one is that additional nucleation and growth of particles can concurrently take place in the bulk of the liquid (typically close to the wall due to higher concentration [32]). In that case, the new particles can either stick to the membrane surface, where they can be considered as part of developing scale, or they can remain detached and free to move [32]. The latter case is more difficult to be treated since such particles grow in the flow by consuming ionic species and reducing supersaturation. The reported scaling modeling studies vary from simple super-saturation computation [121,122] to detailed nucleation-growth models [123]. The chemistry considered is more complicated for simple scaling models [124,125] and simpler for more complex ones [126]. An attempt to use benchmark dead-end filtration experiments in order to extract scaling model parameters and to use them in modeling spiral wound module encountered difficulties [123]; specifically, supersaturation values appeared to be much larger in dead-end experiments than in cross flow spiral wound experiments [33]. The dead end scaling data appear to be compatible with the classical nucleation-growth approach [123] but this is not the case for the low supersaturation cross flow data [33]. There are several possible reasons for the incapability of the classical nucleation theory to describe these results. To name a few, one may attribute such differences to the nonuniform distribution of surface energies on the membrane and to modern ideas such as the concept of pre-nucleation clusters for homogeneous and heterogeneous nucleation [127,128]. It will be added that the nucleation- growth model has been used in spacer scale model [129] and in mesoscale model [32]. However, clearly the improvement of modeling scaling (especially incipient) is an open research subject. Another mass accumulation mechanism, detrimental to the membrane operation, is biofouling, i.e. growth of microbial colonies on the membrane and spacer surfaces. It is by far the most complicated fouling mechanism to be modeled. A very detailed spatially distributed biomass growth model has been considered both in two [130] and three dimensions [131] of spacer geometry (for representative sheet portions), which have led to very interesting results of biofilm profiles in the retentate channel [131]. Such results have not been incorporated to mesoscale membrane-operation models yet, a difficult task of high priority nevertheless. Finally, the fourth mechanism is the so-called colloidal fouling which has been extensively studied in the literature [132]. It is noted that this type of fouling involves particles (mostly inorganic), entering the membrane module with the feed-flow. These particles are generally considered inert, with respect to the existing ionic species, although (depending on their type) they may contribute to heterogeneous nucleation of sparingly soluble salts, if other conditions also favor it [33,120]. As these colloidal particles are seldom encountered alone in operating plants [22], they tend to interact with the aforementioned foulants in still unclear ways that are a significant topic of investigation. Commonly such inorganic particles, of colloidal size or larger, are identified in membrane autopsies together with other foulants (e.g. [133]), generating uncertainty on their true origin and true contribution to the overall fouling process. The majority of the modeling work is restricted to the case of a single solute or multiple solutes behaving independently of each other. Nevertheless, recent work on multi-component systems has shown that interactions between solutes may be significant and can even lead to negative rejection; it appears, therefore, necessary to account for interaction between solutes [134,135]. There is also interdependence between the aforementioned four mechanisms of mass accumulation on the membrane that must be considered in a comprehensive modeling

attempt. For instance, it has been found that the composition of dissolved inorganic salts in the feedwater (e.g. Ca ions) tends to modify significantly the organic layer properties [117] whereas conversely the presence of the fouling layer tends to modify the surface properties and correspondingly the nucleation and crystal growth phenomena related to scaling (e.g.[136]). Sub-models for these interdependencies should be eventually derived and incorporated in the mesoscale model in order to better understand and assess their effect on the membrane operation. 5. Desalination plant modeling – performance simulations 5.1. Outline of SWM module steady-state simulator An advanced simulator for SWM-module steady-state operation has been developed, based on the modeling framework described in preceding sections, and details on the theoretical background have been reported elsewhere [35]; here the main features are summarized. It is reiterated that several simplifications and approximations are employed in order to develop a robust and efficient mathematical model appropriate for realistic design and optimization applications. However, these simplifications are of a mathematical type and not physical [27,112], so that the final “model” retains all the parametric dependency of the original detailed model. The rectangular computational domain of Fig. 3 is employed, ignoring the effect of the leaf curvature. The periodic flow structure considered at the “unit cell” scale is exploited and detailed results are obtained for the flow and mass transfer problem using advanced CFD codes [38,72]. These computational results are codified in the form of correlations for friction factor and mass transfer coefficients [38,72] which are incorporated in the integrated meso-scale model; separate correlations are introduced for different feed-spacer characteristics, i.e. L/D and angle β. Provided that the definition of spacer geometric parameters and of dimensionless quantities (Re, Sh, Sc, ΔP/ΔL) are the same, one can introduce in the software the particular correlations applicable (at spacer scale) to any type of spacer including novel designs; the latter can be obtained through advanced simulations. Therefore, no empirical correlations or parameter values are used. The leaf-scale (meso-scale) equations have as state variables quantities averaged over the channel thickness/gap to render them compatible with the correlations obtained from sub-grid modeling at unit cell scale. The sub-grid constitutive correlations serve to connect pressure with flow and wall- with bulk-concentration in the retentate channel. The local wall flux depends on TMP and on wall concentration at both retentate and permeate sides. The boundary conditions are the inlet pressure and concentration and the outlet (retentate and permeate) pressures. The smooth variation of the state variables permits high accuracy using second order finite differences even in a coarse grid. To ensure convergence, some highly non-linear equations arising from the discretization (e.g. wall concentration equations) are treated separately from the rest of the system using one-dimensional root capturing techniques [35]. In the code, the inlet flow is an input (as in practice) and not the outlet retentate flow. It is provided in the algorithm to first estimate/assign for each element an initial outlet retentate pressure (using an approximate solution) and then, guessing iteratively outlet pressures, to converge to the required inlet flow rate [35]. To simulate an entire pressure vessel, the output of each element is taken as input to the next one. The entire procedure is completely automated, having the basic single membrane-leaf algorithm coded in Visual basic and all the input and output data in Excel sheets communicating with the code. Therefore, computations involving several SWM elements in series are readily performed to simulate the performance of a pressure vessel; moreover, incorporation of this simulator into a general-purpose software can be implemented for performance predictions of an entire SWM-module train of a desalination plant, or other similar processing unit.

Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

A.J. Karabelas et al. / Desalination xxx (2014) xxx–xxx Table 3 Range of parameter values employed in parametric study of SWM module performance [137]. Feed water characteristics

Brackish

Seawater

Salinity Operating parameters Feed flow rate, Q Recovery, R Module design parameters Membrane resistance, Rm

2000 ppm Brackish 10 m3/h 70%

40,000 ppm Seawater 9.8 m3/h 50%

Membrane area, A Number of envelopes, N Membrane sheet length, L Membrane sheet width, W Retentate spacer geometry Retentate channel gap, hr Permeate channel gap, hp Permeate spacer lateral permeability, k

Brackish Seawater 0.9×1014 m−1 3.04×1014 m−1 37 m2 15, 20, 30 0.96 m A/(2×N×L) m G-1: L/D = 8, β = 90ο G-2: L/D = 12, β = 105ο 0.71 mm (28 mil) 0.86 mm (34 mil) 0.23 mm 2.0, 3.5, 5.0×10−10 m2

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intermediate parameter values (N = 20, 34 mil, L/D = 12, β = 105°, kp = 3.5×10−10 m2). Fig. 7 shows axial profiles of productivity per module along the pressure vessel for brackish- and sea-water desalination, under constant permeate recovery 70% and 50%, respectively. Comparison is also made with predictions using commercial software (“ROSA” by Dow [140]), corresponding to Dow commercial elements BW30-400 and SW30HRLE-400i for brackish and sea-water, respectively. It is interesting that these profiles are very close, for all cases, for the operating mode of constant recovery. The flux level in the case of brackish water (Fig. 7a) is maintained at rather high level, along the vessel, due to the much smaller (compared to seawater) retentate osmotic pressure; this type of concave profile is expected [138]. On the contrary, for seawater desalination the productivity is reduced very significantly along the vessel due to the much higher osmotic pressure, and the wellknown [138] convex profile is observed. The effect of SWM design parameters is evident in Fig. 8, where the one-dimensional profiles of pressure drop per module, the cross flow velocity at module inlet and the mean permeate concentration per

5.2. Indicative results of parametric studies Typical results are included herein (presented in detail elsewhere [138,139]), regarding the performance of a pressure vessel, with seven 8-inch RO-membrane modules, in order to demonstrate, and comment on, the capabilities of the current state of the art steady-state simulator. The input data for the parametric studies are summarized in Table 3. Three sets of SWM module design parameter values are considered: The “reference case” with small number of envelopes (N = 15), relatively thin and dense feed-spacer (28 mil, L/D = 8), conventional angle β = 90° and permeate-fabric permeability kp = 2.0× 10− 10 m2; the “best case” with large envelope number N = 30, a relatively thick and less-dense feed-spacer (34 mil, L/D = 12), angle β = 105° and higher permeate-fabric permeability kp = 5.0 × 10− 10 m2; a set with

Fig. 7. Axial profiles of productivity per module along a pressure vessel comprising seven SWM modules. (a) Brackish water desalination. (b) Seawater desalination.

Fig. 8. Brackish water desalination. Average performance characteristics of each SWM element in a 7-element pressure vessel. a) Pressure drop, b) cross flow velocity at element inlet and c) mean permeate concentration. Input data in Table 3.

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module are plotted. As discussed in detail elsewhere [138,139] the effect of envelope number and of feed-spacer thickness are very significant, especially with regard to pressure drop (Fig. 8a). The new finding from the recent parametric studies [138,139] was the quite strong effect of permeate-fabric permeability, especially for the case of brackish water desalination, which requires additional attention in optimization studies. Fig. 8b shows that, as expected, the thicker feed-spacer (associated with smaller pressure drop) leads to smaller cross-flow velocities; however, the benefits from reduced energy consumption may be off-set by an inferior performance of these spacers if fouling takes place, which is considered to be mitigated by increased velocities. Interestingly, Fig. 8c indicates that the permeate quality, under the conditions examined, is not significantly affected by the SWM module design parameters, which is apparently due to the counter-acting effects of particular spacer design parameters, as explained elsewhere [139]. Fig. 9 depicts the pressure profiles at the retentate side for the cases of brackish and sea-water desalination, which correspond to the same conditions as those of Figs. 7 and 8. It is interesting that, under these conditions, the pressure drop in the pressure vessel, which is directly proportional to the energy expenditure for the desalination process, is so much dependent on SWM design parameters; indeed, there is an approximately 50% reduction in pressure drop between “reference” and “best” case. Of course, as subsequently discussed, in simulations to optimize SWM module, these results will be somewhat modified, because the real modules with the “best” set of design parameters, will have somewhat smaller total active membrane area due to thicker feedspacer and more “glue-lines”. The preceding computational results provide the “one-dimensional” profiles, as is the case with commonly used commercial programs. However, of particular interest are the spatial distributions of all the process parameters throughout the pressure vessel, helpful in better understanding the function of SWM modules and in optimizing their performance. Such typical distributions for the “reference” and an “intermediate” case are included in Figs. 10, 11 and 12, for the

trans-membrane pressure (TMP), the permeate-channel pressure, and the membrane -surface concentration at the retentate side, respectively. These distributions, for the 1st, 4th and 7th element in the pressure vessel, clearly exhibit the influence of the SWM module design parameters on the desalination process. These results are discussed at greater length elsewhere [139], and only brief comments on the salient features of distributions are made: The TMP for the shorter envelopes with thicker feed-spacer (34 mil, N = 20, Fig. 10) is much more uniform. TMP uniformity leads to uniform flux distribution (not shown here to economize space) with no high local flux values. Since high local fluxes cause high rates of fouling [132,142,143], the SWM-modules with design-parameter values leading to flux uniformity hold definite advantages. Noteworthy is the greater TMP non-uniformity of the leading elements, which are known in practice to suffer from fouling more than the rest. The significantly different pressure distributions in the permeate channels (Fig. 11) is clearly due to the effect of the lateral permeability kp of the permeate-fabric and of envelope width; i.e. fewer (and larger) envelopes with smaller fabric permeability kp are associated with greater pressure drop in the permeate channel than envelopes of smaller width and higher permeability kp. It is also interesting to observe that the pressure distributions exhibit insignificant variability in the axial (x) direction, varying only in the lateral flow direction. The distribution of membrane surface concentration (Fig. 12) is indicative of the magnitude and variation of concentration polarization throughout the vessel. One would expect [139] the trend of uniform wall concentration in the leading elements, and the non-uniformity at the tail elements. Moreover, for the two sets of parameters compared, the differences in the SWM geometry do not appear to significantly affect concentration polarization. 6. Discussion – R & D priorities 6.1. Development of global model of SWM module performance Overall the model (and related simulator) for predictions of SWM performance at steady state is considered quite satisfactory, linking the detailed geometric features of SWM modules (spacers, sheet dimensions, etc.) and operating variables to SWM module performance. The same modeling framework can be used to develop a dynamic simulator. Some areas that need attention are outlined:

Fig. 9. Retentate pressure profiles along a 7-SWM element pressure vessel for (a) brackish water and (b) sea water desalination. Input data in Table 3.

• A more elaborate sub-model to account in more detail for interactions (at the membrane surface) and rejection of all ionic species in the treated water. Such sub-models may have to be developed for particular types of membranes, based on complete characterization of their intrinsic ionic species rejection. These surface characterizations should preferably be comprehensive (including other physicalchemical surface properties, relevant to fouling and scaling phenomena) to facilitate the development of a dynamic simulator. • A sub-model to account for non-uniformities of the channel gap of the spiral-wound membrane envelopes. Such non-uniformities tend to develop during fabrication, i.e. wrapping the envelopes around the permeate tube, and could be tackled by a modified state-steady model. Another type of channel non-uniformity (more difficult to tackle) tends to develop even at low level of fouling. There is a subtle point regarding this problem in that the channel gap is reduced due to fouling, while the size of the spacer remains unchanged, thus preventing to invoke geometric similarity and use existing constitutive relations for the transport phenomena in the modified channel. In line with the general SWM modeling (“separation of scales”) approach outlined in this paper, it appears that computational fluid dynamics unit cell calculations, for the channel geometric patterns arising from the aforementioned effects, are necessary; subsequently, these results can be incorporated into the overall modeling framework.

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a

b

c

Fig. 10. Brackish water desalination. Spatial distributions of trans-membrane pressure. Comparison of SWM module performance for two sets of design parameters; i.e. “reference” and “intermediate”. a) 1st element, b) 4th element, c) 7th element, in a pressure vessel operating under constant water recovery 70%.

Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

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A.J. Karabelas et al. / Desalination xxx (2014) xxx–xxx

a

b

c

Fig. 11. Brackish water desalination. Spatial distributions of pressure in the permeate side channels. Comparison of SWM module performance for two sets of design parameters; i.e. “reference” and “intermediate”. a) 1st element, b) 4th element, c) 7th element, in a pressure vessel operating under constant recovery 70%.

Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

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a

b

c

Fig. 12. Brackish water desalination. Spatial distributions of salt concentration at the membrane surface, in retentate channel. Comparison of SWM module performance for two sets of design parameters; i.e. “reference” and “intermediate”. a) 1st element, b) 4th element, c) 7th element, in a pressure vessel operating under constant recovery 70%.

Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002

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• Appropriate level sub-models for all the fouling mechanisms should be further developed based on constitutive relations to be incorporated to the mesoscale model, thus, allowing simulation of the dynamic membrane operation. It should be stressed that such a dynamic model is of crucial importance for practical as well as theoretical applications. Regarding the latter, a global dynamic model can reveal interactions between the aforementioned complicated phenomena in the real module geometry which are not obvious by considering their interaction at a local level. 6.2. Comments on specific SWM design parameters and related research needs The influence on module performance of all SWM geometrical design parameters is very significant, clearly suggesting that in developing optimum SWM elements for particular separation tasks, all these parameters should be taken into account in addition to the practical constraints imposed by the SWM overall size and fabrication. In recent papers [138, 139], a discussion is presented on the ranges of these geometric design parameters and on their desirable and possible extension for SWM optimization. In the following, additional remarks are made from the perspective of simulating SWM module performance. 6.2.1. Membrane envelope number Theoretically, for a constant total module membrane area, the SWM performance tends to improve with increasing number of envelopes. However, the upper limit of the envelope number N (akin to a “constrained optimum”) is imposed by a combination of practical limitations, including the external SWM element diameter, the thickness of materials used (i.e. of the membrane and both spacers), and the increased loss of active membrane area by the glue lines (in the case of large envelope number N). Another factor (seldom discussed – if ever – in literature) is related to difficulties (and possible local membranechannel non-uniformities) in adapting numerous envelopes around the, relatively small-diameter, permeate tube. Detailed parametric studies, with a reliable simulator discussed herein, can be most helpful in assessing the impact of the aforementioned factors in maximizing the envelope number. 6.2.2. Retentate-side spacer In addition to the reviewed detailed studies, use of integrated SWMmodule simulators has provided improved overall understanding on the impact of thickness and morphology of feed-spacers on SWM element performance [138], clearly suggesting that the issue of retentate spacer improvements is still open, as also recognized by industry experts [3]. At present, the prevailing approach to optimize spacer thickness (for fixed feed flow) is based on balancing energy benefits (achieved with thicker spacer and greater gap) against reduction of cross-flow, of shear stresses and mass transfer rates (related to thick spacers); the latter can lead to increased concentration polarization effects and inferior fouling performance. Regarding the other retentate spacer geometrical parameters (i.e. L/D and angle β), theoretical predictions supported by experiments [38,72] suggest that relatively less dense spacers (e.g. L/D N 8 and β N 90°) are advantageous. However, as Johnson and Busch [3] report, in practice the less dense spacers (with a reduced number of contact points of spacer per unit membrane surface area) tend to cause an undesirable reduction of permeate size gap (called “nesting”) due to normal stresses during the tight wrapping of envelopes. Using the criterion of “minimum contact points” points in the direction of denser spacers with reduced ratio L/D. Another spacer characteristic worth exploring is the spacer filament cross-section (whether circular, oval, other) and its arrangement/orientation with respect to the mean flow direction, which appear to affect the retentateside flow field [99]. Nevertheless, for assessing the performance of any type of novel spacer design, the approach suggested in the context of global SWM modeling is straightforward; i.e. one should perform

numerical simulations at the spacer (or “unit cell”) scale and derive correlations (preferably validated with experiments), at least for pressure drop and mass transfer coefficient, within a sufficiently broad design parameter range, to be incorporated in the SWM modeling framework for simulations at full scale. 6.2.3. Permeate-side fabric Parametric studies [138,139] suggest that the characteristics of the permeate fabric (i.e. its thickness and lateral permeability kp) play a very significant role in overall SWM performance, by directly influencing the TMP distribution throughout the membrane sheets. This effect is much more pronounced in the case of low pressure SWM modules (compared to high pressure desalination elements), where somewhat higher fluxes are employed, leading to greater flow rates and pressure drop in the permeate channels. The range of aforementioned permeate-fabric parameters has been very inadequately studied so far [141], especially under the conditions prevailing in real SWM modules. Two issues require particular attention: a) The permeate spacer effective thickness during SWM element operation, when normal stresses are exerted on the spacer by both neighboring high-pressure retentate channels, appears to be significantly smaller [141] than that under no pressure; therefore, more work is needed to clarify this issue and to examine under what conditions (feed pressure, material properties) there may be undesirable spacer–membrane interaction (i.e. compaction/ compression) causing permeate channel reduction/modification, which would have a negative impact on permeate flow and SWM performance. b) The weaving pattern of the currently used fabric (e.g. that examined in [141]), characterized by a kind of small parallel “channels” in one direction, suggests that there may be a significant difference of the lateral permeability kp in directions parallel and normal to the channels direction, with impact on module performance [139]. Both issues warrant detailed R&D study, which can be greatly facilitated by employing a reliable SWM simulator. 7. Conclusions The development of a reliable performance simulator of a membrane train, or of an entire water treatment RO/NF plant, is relatively straightforward provided an appropriate software tool is available for dynamic simulation of an individual SWM module. Such a SWM simulator (with sound theoretical underpinning) should be accurate, flexible (accounting for all important design and operating parameters) and computationally convenient, i.e. not particularly demanding and readily adaptable to general computational frameworks for various purposes (e.g. [18–20,137]). The length scale of SWM (of order 1 m) is referred to as meso-scale, compared to the large scale of a membrane plant, or part thereof. The SWM module performance (to be simulated) largely depends on mechanisms and phenomena occurring at the molecular scale and nano-scale; i.e. ionic species rejection by the membrane, interaction of organic macromolecules with (and deposition on) the membrane, localized nucleation/crystallization of salts on the membrane, etc. However, these phenomena are strongly affected by processes at larger length scales, notably those related to the flow field at the feed-side channels of the SWM module; this intermediate scale is determined by the retentate-side spacer (which is commonly of regular, net-type, morphology), thus termed spacer scale. Therefore, the problem at hand is a multi-scale one and its complete formulation should fully account for phenomena at the smaller scales. The SWM performance, aside from the controlled process variables (mainly feed pressure and flow rate), depends on two classes of parameters: a) Those representing the detailed geometric characteristics and membrane properties of the module, and b) the feed-water composition (physical, chemical, biological) and temperature. The interaction of these two classes of parameters and of other process parameters at spacer-scale (related to transport phenomena), renders the general

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mathematical modeling problem extremely complicated; in addition to other complications, the deposition of species on the membrane surface introduces time scales and temporal variability to the SWM module and plant performance (well known in practice and undesirable). Therefore, an adequately formulated comprehensive model of SWM-module operation is impossible to solve directly by present-day means. This paper suggests that a very good strategy to attack the full problem (perhaps the only one available) is to implement the technique of “separation of scales”, which is rather well known in science and engineering. This approach entails a) detailed studies of phenomena at small scales (locally) and development of constitutive type expressions, relating appropriate “process parameters” (species mass transfer rates, deposition rates, friction losses, etc.) with parameters describing the “process environment” (pressure, local flow velocities, shear stresses, etc.); b) an appropriate mathematical modeling framework at the meso-scale, allowing integration of the sub-models accurately describing the phenomena occurring at the smaller scales. It is noted that this strategy can be employed to develop the relatively easier simulator of steady-state operation (i.e. with no material accumulation in the SWM module and with constant membrane intrinsic properties) as well as a dynamic simulator adequately accounting for the aforementioned complicated interactions of species and mechanisms. In reviewing the state of the art, the effectiveness of the above type of steady-state modeling framework is demonstrated, where phenomena at the spacer scale are incorporated through accurate correlations (akin to constitutive expressions) developed by performing detailed studies at the spacer “unit cell” level. Even though mathematical simplifications are made, the important attribute of this modeling approach is that the physically correct parametric inter-dependencies are retained and that no arbitrarily fixed empirical parameter of any type is used. Very satisfactory results obtained recently from realistic parametric studies [138,139] are encouraging even though additional research work is needed. The SWM module morphology and its detailed geometric design parameters essentially determine the performance of the module itself and of the entire membrane plants. Comments follow on these important parameters. - The number N of envelopes per SWM element, for fixed module O.D. directly affects the performance, so that short envelopes (large N) are preferable and N should be increased to the maximum possible extent. However, practical type limitations related to the fabrication of the SWM module (e.g. accommodation of the envelopes at/ around the small diameter permeate tube, “glue-lines”) place constraints on maximization of N. - Retentate spacers play a well-known dominant role. Despite the fact that a great deal of useful work has been carried out, mostly using advanced numerical methods, there is scope for further pursuing detailed (well designed) studies at both theoretical and experimental level, to better understand the spacer morphology effects on the flow field and related transport phenomena. Such investigations should be done both with clean feed-fluids, and under concurrent deposition of foulants on the membrane and on the spacers. These studies, especially with well-characterized foulant species, can offer improved understanding of mechanisms involved as well as the much needed constitutive expressions to facilitate the development of a SWM-module dynamic simulator. - The permeate fabric and its impact on SWM performance (with few exceptions [40,141]) have been essentially neglected in relevant literature, even though its importance is apparently appreciated by the module manufacturers ([3,10]). Recent parametric studies confirm empirically known trends, additionally showing that the permeatefabric lateral permeability and thickness have a comparatively greater effect on low pressure membrane operations (i.e. in brackish water desalination). In optimizing permeate fabric properties, it is desirable to maximize its lateral permeability and thickness for

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pressure drop reduction; however, in doing so, there is negative impact on cost and indirectly on total membrane area. The permeability is generally increased with increasing the fabric porosity, which (on the contrary) negatively affects fabric stiffness and its capability to support the membrane against the imposed significant compressive forces. Research is needed to investigate these counteracting effects and to correctly account for them in a reliable SWM simulator. In reviewing research work performed on SWM geometric parameters, to set priorities for future R&D, one should not fail to observe that there is often a significant discrepancy between the real conditions (of SWM module fabrication and operation) and those employed in research studies. During fabrication (involving envelope wrapping around the permeate tube), the imposed normal stresses on the net-type plastic spacers are fairly high, and can potentially deform them and/or damage the flexible membrane (in particular the sensitive active surface layer). This review reveals that in studies on novel feed-spacer designs, efforts made to optimize the fluid mechanical aspects of the process have often led to suggested spacer morphologies (with complicated cross-sections of strands, also involving sharp edges) which in practice would be either highly deformable (resulting in a drastic reduction of the nominal channel gap), or (if made of rigid material) would damage the membrane at the contact areas between spacer/membrane. Somewhat similar considerations are applicable to the case of permeate fabric which has to support the membrane against the rather large operating pressure. The above factors, aside from their great practical significance, have a significant impact on the realistic simulation of SWM module performance, as shown in this paper. Indeed, specifying the correct geometric parameters (e.g. channel gaps at both sides of the membrane, feedspacer deformability, fabric permeability) is of the utmost importance in SWM module and overall plant optimization studies. In taking an overall view of the factors determining the membrane module and plant performance, it is very likely that there is no single set of “optimum” SWM design parameter values, and that particular “near optimum” SWM modules should be determined for particular classes of water treatment tasks; i.e. specific types of feed-waters and permeate characteristics (quality, degree of recovery, etc.). Industry has already taken such steps by offering SWM modules with different design characteristics for different applications. Nevertheless, a reliable dynamic SWM module simulator (unavailable at present) would be of great help in realistic optimization studies. Current R&D activities to develop very large SWM modules as well as high permeability membranes render such a tool indispensable. There are significant challenges faced by researchers aiming to develop a reliable SWM dynamic simulator, with features described in this paper. Although systematic steps have been taken toward that goal (e.g. [118]), there is a need for a great deal of additional work. The general approach and modeling framework outlined herein appears to be very appropriate as a basis. However, particular emphasis should be placed on work mainly at small scale a) to improve understanding of mechanisms and of their interaction, and b) to develop constitutive type expressions accurately representing those mechanisms and relating properties of membrane and foulants’ with the other process and controlled parameters (essentially the local flow field properties). It is hoped that the quite extensive ongoing research work carried out in the areas of organic and colloidal fouling, biofouling, and scaling (as well as in related areas) will be properly focused to provide the input needed to develop reliable simulation tools.

Acknowledgement The authors wish to acknowledge the contribution by Professor S.G. Yiantsios, Dept. of Chemical Engineering, Aristotle Univ. of Thessaloniki, to some aspects of work presented herein, particularly in the area of advanced numerical simulations.

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Please cite this article as: A.J. Karabelas, et al., Modeling of spiral wound membrane desalination modules and plants – review and research priorities, Desalination (2014), http://dx.doi.org/10.1016/j.desal.2014.10.002