Open-source industrial-scale module simulation: Paving the way towards the right configuration choice for membrane distillation

Desalination 464 (2019) 48–62

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Desalination journal homepage: www.elsevier.com/locate/desal

Open-source industrial-scale module simulation: Paving the way towards the right configuration choice for membrane distillation

T

Guangxi Dong , Withita Cha-Umpong, Jingwei Hou, Chao Ji, Vicki Chen ⁎

UNESCO Centre for Membrane Science and Technology, The University of New South Wales, Sydney, NSW 2052, Australia

GRAPHICAL ABSTRACT

ARTICLE INFO

ABSTRACT

Keywords: Direct contact membrane distillation Submerged vacuum membrane distillation Cross-flow vacuum membrane distillation Module scale-up simulation Seawater desalination

Understanding the impact of configuration selection of industrial-scale membrane distillation (MD) is critical for a productive and energy-efficient operation of this emerging process for desalination. However, it is rarely considered even as new high flux membranes and wider applications are developed. In this context, three opensource simulators were developed on the Matlab GUI platform for the performance prediction of industrial-size direct contact membrane distillation (DCMD), submerged vacuum membrane distillation (S-VMD), and crossflow vacuum membrane distillation (X-VMD). Using laboratory-scale experimental results as simulation inputs, the developed simulators were able to predict large-scale MD performance. Furthermore, design considerations on appropriate module scale-up for all three configurations were demonstrated. More importantly, the configuration that shows the optimal mass and heat transfer behaviour was revealed through the performance comparisons across different full-size MD configurations. In addition, these simulators are open-source allowing researchers to use these tools for the development of specific scale-up strategies of their own MD membranes — a critical step towards commercialisation.

1. Introduction Recent years have witnessed an increasing interest in membrane distillation (MD) for desalination – an innovative concept that utilises membrane to recover pure water from seawater or brackish water.

⁎

Many advantages have been identified for MD desalination, for instance it can utilise low-grade heat such as solar-thermal and geo-thermal energy. Furthermore, unlike reverse osmosis (RO) process for desalination, the capacity of MD is not limited by osmotic pressure, indicating its potential use in the area where the salinity is too high to be

Corresponding author. E-mail address: [email protected] (G. Dong).

https://doi.org/10.1016/j.desal.2019.04.018 Received 28 June 2018; Received in revised form 16 April 2019; Accepted 17 April 2019 Available online 28 April 2019 0011-9164/ © 2019 Elsevier B.V. All rights reserved.

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processed by RO [1–5]. In response to the increased industrial attention on MD process, innovative MD development has become a topical research area, with most efforts being devoted to material chemistry. Meanwhile, investigation on MD configuration and module design, particularly in industrial-scale, has received much less attention, despite the efficiency and efficacy of full-scale MD desalination processes being strongly dependent upon an appropriate choice of MD configuration and an optimal module design [6]. Typical MD configurations include direct contact membrane distillation (DCMD), air gap membrane distillation (AGMD), sweeping gas membrane distillation (SGMD), and vacuum membrane distillation (VMD), which can be further divided into cross-flow VMD (X-VMD) and submerged VMD (S-VMD). Many studies can be found in open literature on the performance evaluation and optimisation of individual configurations. However, comparison across different configurations has been barely broached, with only few publications available to date. Among the limited number of publications on comparing mass and heat transfer behaviours across different configurations, most stated that the VMD offers the highest water flux due to its negligible conductive heat loss [7–14]. However, this conclusion may only valid for certain VMD configurations with forced convection and cannot be extended to S-VMD with natural convection. S-VMD is a less well-known configuration but has some potential benefits in terms of overcoming heat pinch and solids handling by suspending the membrane in the feed tank. This aspect will be elaborated further in the following sections. Following VMD in performance is the DCMD, and its lower water flux is mainly attributed to the conductive heat loss [15–18]. At the other end of the performance spectrum are the SGMD and AGMD. The low water flux provided by these two configurations is mainly due to the extra mass transfer resistance imposed by the air film in the permeate side [19,20]. Furthermore, the stagnant air film of AGMD further amplifies the mass transfer resistance, resulting in AGMD having the lowest flux [20]. Apart from water flux as one obvious performance measure, the choice of configuration should also consider thermal efficiency. For this criterion, VMD, once again, appears to be the best due to its negligible conductive heat loss, and thus the highest thermal efficiency. Similar to VMD, AGMD and SGMD also provide good thermal efficiency as a result of the negligible conductive heat loss [21]. Whereas in the case of DCMD, the direct contact of membrane with the cold liquid leads to additional heat loss, and therefore, a lower thermal efficiency. In addition to the aforementioned factors, other issues in terms of equipment and operating complexity need to be taken into account. For instance, the design and operation of DCMD is considered the simplest, due to the fact that condensation takes place inside the membrane module [3,22]. As for VMD, which has the highest water flux and thermal efficiency, it also has improved mass transfer inside the membrane due to the removal of air in the membrane pores [23,24]. However, despite its many advantages over other configurations, the potential of undesired pore wetting for VMD is higher than other configurations due to the vacuum applied on the permeate side [25,26]. In addition, costs of vacuum systems are also a potential concern, and the need for an external condenser outside the membrane module complicates the design and operation of the VMD system but may offer additional opportunities for heat recovery and compact module configurations [3]. Although the aforementioned studies seem to provide a ranking for the selection of MD configurations, these works were only conducted in lab-scale MD settings with small membrane areas. Many conclusions drawn from these works cannot be extended to industrial-scale MD modules with membrane areas that are orders of magnitude larger. In these large modules, the driving force could diminish over module length because of the heat transfer across the membrane (heat pinch

effect). Such phenomenon are difficult to observe in lab-scale settings due to the small membrane size and negligible heat loss along the module length [3]. Our previous simulation study demonstrated that, for desalination with DCMD, when scaling up two vastly different membranes from lab- to industrial-scale, the performance gap between the two membranes quickly closed as the result of this heat pinch phenomenon, with the supposedly “good” membrane only showing marginally better performance than the “bad” membrane at full industrial-size [27]. The significantly different performance between the lab- and industrial-scale DCMD modules suggests that many aforementioned conclusions based on the lab-scale configurations do not address significant heat and mass transfer issues with industrial-size modules. However, to compare the MD performances in industrial-scale for the selection of MD configurations is a task difficult to achieve in most laboratory settings. Fortunately, such a challenge can be tackled by a computer-aided simulation, which can predict mass and heat transfer behaviour inside large MD modules, and thus, providing critical information to supplement MD configuration selection. In this vein, several modelling efforts have been made in the past aiming to predict mass and heat transfer in the MD processes. However, few constraints were found in these studies: (i) most were developed for guiding membrane development in lab-scale (e.g., predicting how the thickness or porosity of a small size membrane affect lab-scale performance), and thus, unsuitable for large-scale module design; (ii) most focused on specific MD configurations and cannot be used for comparison across different configurations [3]; (iii) many were developed based on expensive commercial software such as Aspen HYSYS or ANSYS that are inaccessible to many membrane researchers, and (iv) all these simulators are unavailable to public, which has severely limited the impact of these works within membrane research. In this context, also considering that the DCMD and VMD are widely recognised as the most promising configurations for desalination [28], the current work aims to study the mass and heat transfer behaviour inside industrial-size DCMD, S-VMD, and X-VMD modules with the aid of computer simulation. These MATLAB-based simulators were developed based on an algorithm that couples finite difference method and black box method and were capable of predicting industrial-scale MD module performance using lab-scale experimental results. Using the results from these simulators, we were able to reveal the relationship between the lab-scale MD performance and industrial-scale MD module design, and therefore, bridging the gap between academic membrane research and industrial MD design. Furthermore, the comparisons across configurations allowed us to examine the effect of undesired heat pinch phenomenon on each configuration, and thus revealing the least affected configuration which should also give the highest pure water productivity. In addition, these simulators are open-source, which allows researchers to use these tools to develop specific scale-up strategies for their own MD membranes — a critical step towards commercialisation. 2. Simulator development Similar to our previous work on DCMD simulation [27], all the simulators developed in the current study take lab-scale experimental results as inputs to compute the membrane water permeation coefficient (kg·m−2·Pa−1·s−1) — an intrinsic membrane property that is only affected by the structural and thermo-physical properties of the membrane itself. Subsequently, the simulators take this coefficient as input to predict the large-scale MD performance. The following assumptions were made during the development of the simulators reported herein:

49

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• No membrane wetting takes place, and 100% salt rejection is assumed; • DCMD and X-VMD are considered to be a steady-state process; • S-VMD is considered to be a dynamic process. During the process,

• • • • • •

hot feed solution with the same temperature and salinity as the initial feed solution was continuously added from the bottom of the feed vessel to keep the liquid level unchanged. It is also assumed that the addition of hot feed solution does not cause or contribute little turbulence inside the vessel; For DCMD and X-VMD, fluid is considered fully developed, with entrance and exit effects neglected; For S-VMD and X-VMD, conductive heat transfer across the membrane is considered negligible; A linear temperature gradient is assumed inside membrane matrix, as proven valid in previous modelling work [29]; The concentration polarisation effect is assumed to be negligible, as proven valid in previous experimental work [30]; For all configurations, hollow fibre membranes are assumed to be evenly distributed inside the tubular module or cylindrical vessel; The membrane module or the feed vessel is perfectly insulated.

Fig. 2. Heat transfer resistance in MD process (depicted in the DCMD configuration).

In terms of heat transfer, as shown in Fig. 2, three regions can be identified in a typical MD process: the heat flux through the feedmembrane boundary layer (qf), the heat flux across the membrane (qm), and the heat flux through the permeate-membrane boundary layer (qp). The feed-membrane heat flux (qf) occurs as a result of convection, and can be evaluated using the equation below.

For the three simulators developed in-house, each one assumes a specific large-scale module structure. For DCMD, the large-scale module has a tubular shape with all fibres housed within. The feed solution can enter the module either from the shell- or bore-side of the hollow fibres, and the hot feed and cold permeate flows can be either co- or countercurrent. As for X-VMD, the structure of the large-scale module is identical to that of the DCMD, except that vacuum is applied on the bore-side. In the case of S-VMD, all the hollow fibres are vertically submerged in a cylindrical vessel, with mechanical agitation applied at the bottom (4-flat-blade paddle or 6-flat-blade Rushton turbine). Additional feed solution is fed into the vessel from the bottom to ensure an unchanged liquid level. The structures of the three large-scale configurations are depicted in Fig. 1.

qf = A hf (Tfb

qcond =

2.1.1. General mass and heat transfer in MD process The general form of mass transfer in the MD process can be written as follows.

J=A

sat ppm )

(2)

where hf is the heat transfer coefficient in the feed-membrane boundary layer, which is usually evaluated using a series of semi-empirical correlations depending on the nature of convection, system configuration, and flow regime. The heat flux across the membrane (qm) is the sum of two components: conductive heat flux (qcond) and latent heat of vaporisation (qv). The conductive heat flux (qcond) can be described using Eqs. (3) and (4) depending on the membrane type, whereas the latent heat of vaporisation (qv) can be calculated using Eq. (5).

2.1. Mass and heat balance mechanisms

Cm (pfmsat

Tfm)

qcond =

(1)

qv = J

The above equation clearly shows that the driving force of the MD process is the vapour pressure differences from the feed-membrane interface to the permeate-membrane interface. Depending on the configuration types, the pressure term in Eq. (1) varies.

A km

(Tfm

Tpm ) Flat sheet

n2 Lkm (Tfm ln ro/ ri

Tpm) Hollow fibre

(3) (4) (5)

H

The permeate-membrane heat flux (qp) also occurs as a result of convection, and can be assessed as follows.

qp = A hp (Tpm

Tpb )

Fig. 1. Schematic representation of the large-scale MD configurations: (a) DCMD in counter-current flow arrangement, (b) S-VMD, and (c) X-VMD.

50

(6)

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With the heat fluxes in the three regions identified, the overall heat balance in a MD module can be established, as shown below, assuming the entire MD system is perfectly insulated.

The Reynolds number (Re) in the above equations can be evaluated as follows.

qf = qcond + qv = qp

Re =

(7)

where N is the agitator speed (s , revolutions per second, rps), D is the diameter of the agitator (m). As mentioned earlier, S-VMD process was treated as a dynamic process with the additional feed solution being added continuously to counter-balance the loss of pure water in the feed vessel. By treating the process in such ways, the feed salinity will keep increasing which would affect the thermo-physical properties of the feed, and consequently the mass and heat transfer behaviour. All these factors were taken into account in the developed simulators. Furthermore, the S-VMD simulator was also designed to be able to show the saturation point of the feed solution when crystallisation can be expected — a useful information for a proper process operation.

2.1.3. S-VMD In terms of the algorithm used for S-VMD simulation, the finite difference method was adopted with the feed tank being divided into a number of horizontal tanks (each with the height of 1 cm). The transmembrane water flux in tank k was obtained by modifying the mass transfer equation used in DCMD simulation.

po )

2.1.4. X-VMD The mass and heat transfer in X-VMD was almost identical to that in S-VMD, except that (i) forced convection heat transfer correlations were used, same as those used in DCMD simulation; and (ii) a steady-state process is assumed for X-VMD.

(8)

In terms of heat transfer, the key differences between DCMD and SVMD are: (i) the conductive heat loss across the membrane is assumed to be negligible for S-VMD, as such the convective heat flux in the feedmembrane boundary layer (qconv or qf) should be equal to the latent heat of vaporisation (qv); and (ii) the feed-membrane boundary layer convective heat transfer in S-VMD can be treated either as natural or forced convection depending on whether the agitation is applied. In the case of natural convection when the feed solution is stagnant, its heat transfer coefficient was evaluated using the Grashof number (Gr), analogous to the Reynolds number:

Gr =

g

(TS T ) L3 (µ / ) 2

2.1.5. Thermal efficiency and temperature polarisation As mentioned earlier, thermal efficiency is a critical gauge for the comparisons across different configurations. In terms of DCMD, the thermal efficiency (Π) can be expressed as:

=

13

T6

0.2814011425 10

+ 0.2250277333312 10

7

+ 0.228607033319346 10

T4 2

10

T5

0.957472904360579 10

T2

5

T3

0.290368929150213 T

=

(10)

+ 15.3259307587448

The following equations were used to evaluate the Nusselt number (Nu) for natural convection [31,32]:

Nu = 0.56 (Pr Gr )0.25 If Pr Gr < 106

(11)

Nu = 0.13 (Pr Gr )0.33 If Pr Gr

(12)

106

=

Pr range

Equation

4-flat-blade paddle

< 4000 > 4000 < 2000 > 2000

< 258,000 – 20–200 –

Nu = 1.5 ∙ Re0.37 ∙ Pr0.35 Nu = 0.34 ∙ Re0.55 ∙ Pr0.33 Nu = 0.32 ∙ Re0.67 ∙ Pr0.33 Nu = 0.49 ∙ Re0.62 ∙ Pr0.33

6-flat-blade Rushton turbine

Tfm

Tpm

Tfb

Tpb

Tfm

Tsat

Tfb

Tsat

DCMD

S

VMD and X

(19)

VMD

(20)

2.2. Thermo-physical properties of the feed solution

Table 1 Forced convective heat transfer correlations in agitated vessels. Re range

(18)

where Tsat in Eq. (20) is the equilibrium temperature of the feed that corresponds to the pressure on the permeate side. Closely examining these two equations, one would find that they both have the actual driving force as the numerator, and the theoretical driving force as the denominator. As such, a Θ value of zero indicates a poorly designed heat-transfer-limited system, and a Θ value approaching unity suggests the system is mass-transfer-limited.

In the case of S-VMD with agitation, forced convective heat transfer correlations were used [33–37]. For such systems, heat transfer correlations were evaluated using the equations in Table 1 depending on the type of the agitator and the flow regime. Note that these correlations were slightly modified by removing the dimensionless viscosity ratio term as its value is close to unity in all scenarios.

Type of agitator

qv qv + qcond

In the case of S-VMD and X-VMD, the thermal efficiency approaches unity as the conductive heat transfer across the membrane is deemed negligible. In terms of temperature polarisation — another key factor affecting MD performance, temperature polarisation coefficient (Θ) is often used to quantitatively indicate its impact on MD performance, which is defined as [2,25]:

(9)

where β is the coefficient of thermal expansion. For the feed solution at different temperatures, the following correlation was used to obtain the β value:

= 0.146288 10

(17) −1

2.1.2. DCMD The mass and heat transfer equations described above were used for DCMD simulation in both co- and counter-current flow arrangements, and the semi-empirical heat transfer correlations as well as the algorithm developed for the DCMD simulation was provided in our previous work [27].

Jk = Ak Cm (pfmsat, k

N D2 µ

Similar to our previous work, the simulators developed in the current study are capable of predicting S-VMD and X-VMD performance over a wide range of operating conditions. For an accurate simulation, the correlations describing the thermo-physical properties of the feed as functions of temperature and salinity were integrated in these simulators, and all the semi-empirical correlations used were compiled in our previous publication [27].

(13) (14) (15) (16)

51

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(a)

(b)

(c) Fig. 3. Interfaces of (a) upgraded hollow fibre DCMD, (b) S-VMD and (c) X-VMD open-source simulators. 52

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Table 2 Properties of the PP and PVDF hollow fibres membranes, and lab-scale DCMD, S-VMD, and X-VMD operating conditions, and validation results. Membrane types

PP hollow fibre membrane

MD configurations

DCMD

S-VMD [38]

X-VMD

DCMD

S-VMD

X-VMD

Effective module length/tank depth (cm) Module/tank inner diameter (cm) Number of fibres Fibre inner diameter (mm) Fibre outer diameter (mm) Membrane area (cm2) Packing density (volume occupied by membrane/module volume) Membrane porosity Polymer thermal conductivity (W/m·K) Feed inlet temperature (°C) Permeate inlet (DCMD)/outlet (VMD) temperature (°C) Feed inlet mass flow rate (kg/s) Permeate inlet mass flow rate (kg/s) Permeate pressure (Pa) Feed inlet NaCl concentration (g/kg) Process duration (s) Agitation Flow configuration Membrane water permeability (kg/m2·Pa·s) Trans-membrane water flux (kg/m2·h) — Experimental result Trans-membrane water flux (kg/m2·h) — Simulation result Error (%)

10 0.635 1 0.6 1 3.14 0.0248 0.72 0.19 60 25 0.001 0.001 N/A 35 N/A N/A Co-current shell-side feed 3.94·10−7 13.3 13.3788 0.6%

8 12 1 0.6 1 2.512 6.94 · 10−5 0.72 0.19 60 25 N/A N/A 5000 35 3600 No N/A 3.96 · 10−7 10 10.3504 3.5%

10 0.635 1 0.6 1 3.14 0.0248 0.72 0.19 60 25 0.001 N/A 5000 35 N/A N/A N/A 3.94 · 10−7 14.6 14.5986 −0.01%

10 0.635 1 1 1.24 3.8936 0.0381 0.75 0.19 60 25 0.001 0.001 N/A 35 N/A N/A Co-current shell-side feed 6.84 · 10−7 17.5 17.6299 0.7%

10 12 1 1 1.24 3.8936 1.07 · 10−4 0.75 0.19 60 25 N/A N/A 5000 35 3600 No N/A 6.85 · 10−7 13.6 14.6927 8.0%

10 0.635 1 1 1.24 3.8936 0.0381 0.75 0.19 60 25 0.001 N/A 5000 35 N/A N/A N/A 6.83 · 10−7 21.3 21.276 −0.1%

2.3. Access to the open-source simulators

PVDF hollow fibre membrane

and simulation results of two hollow fibre membranes (PP and PVDF) in three configurations (DCMD, S-VMD, and X-VMD). Note that for labscale S-VMD validation, no agitation was applied. This decision was made considering (i) the magnetic stirrer used in lab-scale set-up gives different hydrodynamic behaviour from blade paddle or Rushton turbine found in large-scale tank agitation; and (ii) stirring in lab-scale single-fibre setting caused severe fibre vibration. As shown in Table 2, excellent lab-scale accuracy of < 1% deviation was achieved, with the exception of S-VMD that reported a deviation around 8% for the PVDF hollow fibres. This may be due to the less accurate semi-empirical correlations used for the evaluation of natural convection heat transfer in the feed vessel. In terms of large-scale validation, due to the nascent stage of MD process commercialisation, only the DCMD configuration has been trialled previously in pilot- to large-scale, with the results available in public domain. As such, the full-scale validation was only done on our DCMD simulator using data provided by industry, and excellent accuracy was found as demonstrated in our previous work [27].

Like our previous DCMD simulator, the S-VMD and X-VMD simulators also came with user-friendly interfaces (Fig. 3) that only require users to provide lab-scale experimental results and large-scale operating conditions as simulation inputs. In addition, the previously published hollow fibre DCMD simulator was upgraded with more functionality. The link to access these simulators are provided in the Appendix A. 3. Experimental The experiments carried out in this study were to validate the two in-house developed simulators (S-VMD and X-VMD). Note that the validation of DCMD simulator was reported in our previous work [27]. To study the performance response of different membrane types on module scale-up, two types of hollow fibre membranes were used to provide lab-scale simulation inputs, and they are: polypropylene (PP) and polyvinylidene fluoride (PVDF) hydrophobic hollow fibre membranes. The structural and thermo-physical properties of these two membrane types are summarised in Table 2, along with the experimental conditions and the trans-membrane water flux results. As mentioned in previous sections, the algorithm behind all three simulators started with taking lab-scale experimental results as inputs to compute intrinsic membrane water permeation coefficient (Cm). In this part of simulation, black-box algorithm was adopted, meaning the heat loss along the lab-scale module length was not considered. As such, when setting up lab-scale testing facilities to obtain the simulation inputs, it is recommended to choose shorter fibre length and wider module inner diameter when possible. In this way, the three opensource simulators will be able to provide more accurate Cm value for the subsequent large-scale simulation where the finite difference algorithm was adopted in order to predict the heat transfer behaviour as a function of large-scale module length.

4.2. Effects of MD operating variables on water flux — general trends The effects of MD operating variables on trans-membrane vapour flux have been thoroughly investigated in previous studies. Table 3 summarises the trends agreed in most studies on how increasing the value of operating variables would change the trans-membrane vapour flux. It should be noted that most of the reported trends were observed on lab-scale settings. Using our in-housed developed DCMD, S-VMD, and X-VMD simulators, the predicted large-scale MD performance showed identical trends as those summarised in Table 3. All the enhanced performance can be rationalised as the result of improved mass transfer driving force. For instance, in terms of operating temperatures, increasing the feed temperature or decreasing the permeate temperature would certainly improve the driving force according to the Antoine equation. In addition, elevating the feed temperature also enhances the diffusivity of water vapour [49,50] and mitigates temperature polarisation [29,51]. As for the feed salinity, increasing feed salt concentration leads to a reduced driving force based on the Raoult's law. For feed and permeate flow rates, an increase in these variables will see an improved mass

4. Results and discussions 4.1. Simulator validation The lab-scale validation was done by comparing the experimental 53

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Table 3 Effects of MD operating variables on trans-membrane water vapour flux. Operating variables

Feed

Permeate

Increasing temp.

Increasing salinity

Increasing flow rate/Velocity

Increasing stirring rate

Increasing temp.

Increasing flow rate/Velocity

Increasing vacuum level

DCMD water flux S-VMD water flux X-VMD water flux

Increase Increase

Decrease Decrease

Increase N/A

N/A Increase

Decrease Decrease

Increase N/A

N/A Increase

[2,27,39–41] [42,43]

Increase

Decrease

Increase

N/A

Decrease

N/A

Increase

[14,41,44–48]

transfer due to the mitigated temperature and concentration polarisation [3,52]. Considering all the observations mentioned above are well-documented, no detailed discussion will be offered in this work. Instead, the following sections will focus on (i) the response of different membrane types to the change of operating conditions when scaled up to full-size MD modules, and (ii) the selection of appropriate full-size configuration and the corresponded operating conditions for MD desalination.

References

membrane type. Closely examining the modelled vapour flux profiles, it was also discovered that increasing membrane area by increasing the module length led to a sharper water flux decline than by increasing the packing density. This was mainly due to the fact that, when increasing the packing density, the cross-flow velocity was accelerated which led to a higher heat transfer coefficient, less contribution of convective heat transfer to the overall heat transfer, and a slower decline in water flux with increased packing density. On the other hand, when increasing the module length with a fixed packing density, the cross-flow velocity remained unchanged, and so did the undesired convective heat transfer, which eventually led to a sharper drop in driving force and water vapour flux. Fig. 4b shows the profiles of temperature polarisation coefficient as a function of membrane area. Comparing the two membrane types, in general, more permeable membrane (i.e., PVDF) offered lower Θ value than the less permeable one (i.e., PP). This observation can be ascribed to the greater overall heat loss of the PVDF membrane. In terms of the scale-up strategy, increasing packing density led to an enhanced Θ value, whereas increasing module length showed negligible impact on the Θ value. Furthermore, excellent Θ values higher than 0.7 were found for all cases, indicating a mass-transfer-limited system. This was largely attributed to the rather high feed flow rate (1 kg/s) chosen for the full-scale simulation. According to Eq. (2), the choice of higher feed flow rate led to a greater convective heat transfer coefficient (hf), a higher feed-membrane boundary layer temperature (Tfm), and thus a Θ value closer to unity. Comparing Fig. 4a and Fig. 4b, one can also discover that, in terms of the trans-membrane vapour flux in the X-VMD configuration, a proper choice of membrane types is the key. With the same membrane area, the performance gap between the membrane types was much greater than the gap between the two scale-up strategies. In contrast, when enhancing the Θ value in the X-VMD configuration becomes critical, choosing a proper scale-up strategy will have greater impact on temperature polarisation than choosing different membrane types.

4.3. Scaling up X-VMD system For X-VMD, scaling up from lab-size to industrial-size module can be achieved by increasing the module length (fixed module inner diameter and packing density) or by increasing the packing density (fixed module inner diameter and length). These two scenarios were simulated using the lab-scale results from the PP and PVDF hollow fibre membranes. In terms of simulation inputs, the lab-scale experimental conditions can be found in Table 2, whilst the large-scale simulation inputs are summarised in Table 4. These numbers were chosen to represent typical industrial-scale membrane modules, which gave membrane areas ranging from 1 to 20 m2 per module. Note that in this study packing density is defined as the ratio of the cross-sectional area of all hollow fibre membranes to the cross-sectional area of the tubular module. Fig. 4a compares the performances of two membrane types to the increased membrane area. Similar to what was observed in our previous DCMD scale-up study, increasing membrane area led to a decreased trans-membrane vapour flux regardless of the scale-up strategies, a clear result of the heat loss along the module length and subsequently the loss in driving force [27]. More importantly, it was found that despite the higher membrane water permeation coefficient offered by the PVDF membrane than the PP membrane, when scaling up to a full-size X-VMD module, the performance gap between the two quickly closed, echoed our previous discovery on the large-scale DCMD module. Such trends highlighted that, when dealing with industrial-scale X-VMD modules, choosing an appropriate module dimension and heat management scheme is equally important as choosing a more permeable Table 4 Large-scale modelling conditions for the X-VMD simulation. Scale-up strategy

Increasing module length (fixed module ID and packing density)

Increasing packing density (fixed module ID and length)

Membrane types

PP

PP

Effective module length (cm) Module inner diameter (cm) Number of fibres Packing density Feed inlet temperature (°C) Permeate outlet temperature (°C) Feed inlet mass flow rate (kg/s) Permeate pressure (Pa) Feed inlet NaCl concentration (g/kg)

10–200 10 3184 0.32 60 25 1 5000 35

PVDF

100 10 300–7000 0.03–0.7 60 25 1 5000 35

2568 0.39

54

PVDF

250–5000 0.04–0.77

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(a)

(b) Fig. 4. Effect of X-VMD module scale-up strategies on (a) trans-membrane water vapour flux, and (b) temperature polarisation coefficient.

4.4. Scaling up S-VMD system

flat-blade paddle and 6-flat-blade Rushton turbine, illustrated in Fig. 1) on full-size S-VMD performance were studied. As shown in Fig. 5a, regardless of the type of membrane materials and agitators, increasing agitator rotation speed led to a sharp increase in trans-membrane vapour flux within the low speed region (below 10 rpm), followed by a stabilised vapour flux at the high speed region (above 10 rpm). This suggested that an optimal rotation speed existed where the hot feed solution was well mixed, and further increasing rotation speed resulted

For S-VMD, increasing membrane area led to similar trend as observed in X-VMD, and therefore will not be discussed in detail. The focus of this section was on the effects of agitation, process duration, and feed vessel size on large-scale S-VMD performance. Simulation conditions are summarised in Table 5. The effects of agitator rotation speed and the choice of agitators (455

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Table 5 Large-scale modelling conditions for the S-VMD simulation. Effect of agitation Membrane types Effective hollow fibre length (cm) Cylindrical feed vessel inner diameter (cm) Number of fibres Feed temp. (°C) Permeate outlet temp. (°C) Permeate pressure (Pa) Feed initial NaCl concentration (g/kg) Type of agitator Agitator diameter (cm) Agitator rotation speed (rpm) Process duration (min)

Effect of process duration

PP & PVDF 100 50 20,000 60 25 5000 35 4-flat-blade paddle & 6-flat-blade Rushton turbine 25 0 (stagnant), 0.5, 1, 3, 5, 10, 15, 20, 30, 40, 50, 60 30

in marginal improvement at the expense of energy cost. Furthermore, as expected, 6-flat-blade Rushton turbine was found to offer better mixing than the 4-flat-blade paddle. In order to compare the performance response of different membrane types to agitator speed, vapour fluxes at different rotation speeds were normalised with the flux obtained under stagnant condition for an easy comparison. As shown in Fig. 5a, increasing rotation speed benefited more for the highly permeable membrane (i.e., PVDF) than its less permeable counterpart (i.e., PP). When increasing the rotation speed from 0 to 60 rpm, the vapour flux of PVDF membrane was almost doubled, whereas the PP membrane only showed a flux jump of 64%. In terms of the temperature polarisation coefficient (Θ), as shown in Fig. 5b, increasing rotation speed also led to an initial sharp increase in Θ, which was then stabilised at a very high level when the rotation speed exceeded 10 rpm, suggesting a well-designed mass-transfer-limited system. When reducing the rotation speed to near-zero, a relatively low Θ value of 0.6 was found. This was a clear result of natural convection with no agitation inside the feed vessel. Natural convection always gives a much lower heat transfer coefficient (hf) than the forced convection, which leads to greater difference between the bulk and boundary layer temperatures, and thus a lower Θ value and less water vapour flux. The most important message delivered from Fig. 5 was that, for full-size S-VMD, sufficient agitation is critical to ensure an optimal MD performance. For the industrial-scale S-VMD module design proposed in this study (Fig. 1b), hot feed solution is continuously fed into the bottom of the feed vessel to counter-balance the loss of water vapour, so that the liquid level remains unchanged. Such a design inevitably leads to an increased feed salinity over time, which in turn not only affects the thermo-physical properties of the feed solution but also the vapour pressure at the feed-membrane boundary layer. Considering these, the in-house developed S-VMD simulator treated the S-VMD process as a dynamic one, and the effect of process duration on MD performance was evaluated. As seen in Fig. 6, the trans-membrane vapour flux reduced over time, with the more permeable PVDF membrane showing larger degree of decrement than the less permeable PP membrane. The performance gap between the two membranes became much narrower towards the end of 2 h operation, suggesting the more permeable membrane lost it competitiveness over its less permeable counterpart when operating over an extended period of time. This was mainly due to the increased salinity which caused a reduced vapour pressure driving force. For highly permeable membranes, their greater vapour permeability amplifies the aforementioned phenomenon, and thus a greater loss in driving force. These results suggested that, for full-size SVMD operation, especially when highly permeable membranes are used, it is necessary to remove salt from the feed vessel in order to limit the loss of vapour pressure driving force. In terms of the temperature polarisation coefficient, both membranes showed slightly increased Θ value over time as a result of the increased salinity. Closely examining the equations used for the evaluation of thermo-physical properties of

Effect of vessel size

6, 8, 10, 15, 20, 25, 30, 40, 50 1500

4-flat-blade paddle 6 1, 5, 10, 20, 30, 60, 90, 120

No agitation No agitation No agitation 30

NaCl aqueous solution (Table 2 in our previous publication [27]), it was found that the specific heat capacity was the most affected parameter among all when increasing the solution salinity, with a steep decline over increased salinity. Such drops in specific heat capacities caused a reduced heat transfer which led to a lower temperature difference between the bulk and boundary layer, and eventually an increased Θ value, according to Eq. (15) in our previous publication [27]. Unlike DCMD or X-VMD, where a bundle of hollow fibres are usually closely packed inside a tubular module with a rather small tube diameter, the diameter of cylindrical feed vessel for S-VMD can be significantly larger. Considering this, the effect of vessel diameter on SVMD performance was studied. As shown in Fig. 7, with a fixed number of hollow fibre membranes, increasing vessel diameter led to an initial sharp increase in trans-membrane vapour flux, followed by a stabilised flux when further increasing the vessel diameter. The increase in vapour flux with enlarged vessel diameter, especially in the low diameter range (< 10 cm), can be ascribed to the increased total heat stored in the vessel due to the larger volume of hot feed solution. As a result, the drop in bulk feed temperature along the axial direction was much less than that in a smaller vessel, which eventually led to an improved flux. Based on these simulation results, it was concluded that when choosing module dimensions, a low aspect ratio (i.e., ratio of length to diameter) is preferred over high aspect ratio (e.g., with the same membrane area, a short but wide cylindrical feed vessel gives better performance than a long but thin tubular module). 4.5. Performance comparisons across configurations For the commercialisation of MD process in desalination, one most critical question to be answered is that, for industrial-scale implementation, which configuration and corresponded operating schemes should be chosen for an optimal performance with a maximum trans-membrane water vapour flux. To address this, we compared the performance of four full-size MD configurations (DCMD, X-VMD, SVMD without agitation, and S-VMD with agitation) on a relatively comparable basis. Fig. 8 demonstrates the effect of increasing module length on transmembrane water vapour flux. As shown in Fig. 8a and b, within the low membrane area region (around 1 m2), the trans-membrane water flux followed the order of X-VMD ≥ S-VMD with agitation > DCMD > SVMD without agitation. However due to the much faster decline of water flux in X-VMD and DCMD with increased membrane area, the water flux order became S-VMD with agitation > S-VMD without agitation > X-VMD > DCMD in the high membrane area region (> 7 m2). The normalised water flux profiles shown in Fig. 8c and d clearly indicated that the two S-VMD configurations showed negligible decline in water flux within the assessed range, whilst X-VMD and DCMD displayed significant drop in water flux, with the DCMD being the worst. The change of order for the four configurations with increased 56

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(a)

(b) Fig. 5. Effect of agitation rotation speed in S-VMD vessel on (a) trans-membrane water vapour flux, and (b) temperature polarisation coefficient.

membrane area can be rationalised as the result of the loss in driving force in different directions. The heat loss in a full-size MD module occurs in two directions: (i) heat loss in radial direction, reflected on the differences in bulk and membrane-liquid interface temperatures; and (ii) heat loss in axial direction along the module, reflected on the temperature drop over the module length (heat pinch effect). The two most extreme cases on loss in driving force are the DCMD and S-VMD without agitation. Therefore, the bulk and boundary layer temperature profiles of these two full-size configurations were simulated (Fig. 9) to demonstrate the impact of heat loss in different directions on MD

performance. Note that the unrealistic 5 m module length was only chosen to highlight the differences in two configurations. In terms of DCMD, the flowing liquids in feed and permeate sides provided sufficient local mixing, so that the radial direction temperature drop from the bulk to the liquid-membrane boundary layer (black and red arrows) were moderate to low, which led to a moderate to high driving force (blue arrow). This is particularly true in the entrance region of the fullsize DCMD module. However, due to the high module aspect ratio and the conductive heat transfer across the membrane, the heat loss in axial direction appeared to be enormous for the full-size DCMD, which led to 57

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Fig. 6. Effect of S-VMD process duration on trans-membrane water vapour flux and temperature polarisation coefficient.

a negligible driving force near the exit of the DCMD module as the result of the heat pinch effect. Entirely opposite heat loss behaviour was found on the S-VMD without agitation, the extremely low heat transfer coefficient (hf) of this particular configuration indicated that a large temperature drop in radial direction from the bulk to the boundary layer is required to compensate the low hf value (black and red arrows). This inevitably led to a lower driving force near the entrance region (blue arrow) than that of the DCMD. However, the heat loss in axial direction for the S-VMD was much milder than that of DCMD, resulting in its exit driving force being greater than the DCMD. As a result of the different heat transfer behaviours in two directions, DCMD outperformed S-VMD without agitation when shorter module length was chosen. However, a threshold length existed, above which the S-VMD

without agitation delivered better performance than the DCMD. The concerns over low heat transfer coefficient (hf) for S-VMD no longer exist once agitation is applied. With an optimal agitation speed, a heat transfer coefficient comparable to that in DCMD can be achieved. In this way, the S-VMD with agitation can offer the best performance over all four configurations as shown in Fig. 8. In terms of X-VMD, its performance was better than the DCMD because of the absence of conductive heat loss. On the other hand, its module inner diameter is usually smaller than the inner diameter of the S-VMD feed tank. As a result, the total heat stored in its module is less than that in the S-VMD feed tank, and thus leading to its lower performance than S-VMD. When comparing the different membrane types, the less permeable PP membrane appeared to follow the similar trends that were found in

Fig. 7. Effect of S-VMD feed vessel diameter on trans-membrane water vapour flux and temperature polarisation coefficient.

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Fig. 8. Effect of increasing module length of four MD configurations on trans-membrane water vapour flux: (a, b) trans-membrane water vapour flux profiles as a function of membrane area, and (c, d) normalised trans-membrane water vapour flux profiles as a function of membrane area.

Fig. 9. Bulk and boundary layer temperature profiles in the feed and permeate streams for (a) DCMD and (b) S-VMD without agitation configurations (for SVMD without agitation, the permeate boundary layer temperature of 33 °C corresponds to the temperature that gives 5000 Pa vapour pressure — the vacuum pressure chosen for this set of simulation).

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the more permeable PVDF membrane. More importantly, the performance gap between the two membranes only appeared to be narrowed with increased membrane area for the X-VMD and DCMD, whilst the two S-VMD configurations showed negligible reduction in performance when scaled up. Such observations suggested that, for the DCMD and XVMD configurations, membrane type is no longer a significant factor to be considered for full-size modules. Whilst for the S-VMD, the choice of membrane types still matters. Another critical factor to be considered when choosing full-scale MD configuration is the energy consumption, which is usually gauged by the amount of energy consumed to produce 1 kg of pure water. Rather scattered energy usage data were reported in open literature, ranging from 3.55 kWh/kg for lab-scale DCMD [12], 1.1 kWh/kg for lab-scale XVMD [12], 0.2 kWh/kg for full-scale spiral wound DCMD [53], and to 0.09 kWh/kg for pilot-scale AGMD [54]. The drastically different results from these studies highlighted the fact that the energy consumption is highly susceptible to configuration choice and module size. Furthermore, most previous studies only considered heating/cooling energy in their assessment, disregarding the energy consumption from pumping, or furthermore, potential heat integration/recovery in MD systems. The open-source simulators developed in this work enable the evaluation of energy consumption in full-scale MD modules across different configurations, and will be assessed in our future work.

•

List of symbols A Membrane area Cm Membrane water permeation coefficient cp Specific heat capacity d Diameter of the agitator h Heat transfer coefficient J Water flux across the membrane k Thermal conductivity L Effective fibre length N Agitator speed n Number of fibres in one module p Vapour pressure po Vacuum pressure Conductive heat transfer rate qc qv Vaporisation latent heat r Hollow fibre radius T/t Temperature Greek letters β Thermal expansion coefficient δ Flat sheet membrane thickness ε Membrane porosity μ Dynamic viscosity ρ Density Superscripts sat Saturation Subscripts f Feed fb Bulk feed fi Feed inlet fm Feed and membrane boundary layer fo Feed outlet k Tank number p Permeate pb Bulk permeate pi Permeate inlet pm Permeate and membrane boundary layer po Permeate outlet Dimensionless parameters Gr Grashof number Nu Nusselt number Pr Prandtl number Re Reynolds number

5. Conclusions Three open-source simulators were developed on the Matlab GUI platform for the performance prediction of industrial-scale DCMD, SVMD, and X-VMD. The developed simulators were subsequently used to demonstrate selection considerations for the appropriate configurations for industrial-scale MD desalination. By means of a thorough assessment including a wide range of criteria, the following conclusions were drawn.

• Significant heat loss in radial direction is a key concern for in-

•

•

size modules for DCMD and X-VMD, whilst for S-VMD, the choice of materials still show great influence over industrial-scale performance; All the statements above only remain true under certain prerequisites. Providing general guidelines for the large-scale MD desalination process is impossible due to the interconnected heat and mass transfer as well as the large number of intricate operating parameters involved. Nevertheless, with the aid of the three simulators developed and made publicly available herein, researchers will be able to investigate specific MD unit scale-up strategies of their own membranes and further consideration of heat integration scenarios available for the various configurations.

dustrial-scale S-VMD, which can be limited by sufficient agitation. On the other hand, substantial heat loss in axial direction as a result of heat pinch effect is a main issue for industrial-scale DCMD and XVMD, due to the large aspect ratio of full-size DCMD and X-VMD modules as well as the presence of conductive heat loss in DCMD; When scaled up to industrial-size MD unit, with sufficient agitation, S-VMD not only offers the highest trans-membrane water flux, but also appears to be the configuration that is the least sensitive to module scale-up. This is mainly due to (i) the much lower aspect ratio of cylindrical feed vessel (tank height to tank diameter) than that of the tubular modules used in DCMD and X-VMD (module length to module diameter); and (ii) the absence of conductive heat loss in S-VMD; Purely from a theoretical heat and mass transfer viewpoint, the influences of membrane materials and properties upon pure water productivity become less significant when scaled up to industrial-

Appendix A Access to the open-source simulators Software requirement: Matlab® 2007 or above (Windows® only). Download all Matlab® files via the link below: https://www.dropbox.com/sh/tx1lbq28vqmkjlk/AACOK-r28Qng37Bk_Q09RUa2a?dl=0

•

Upgraded hollow fibre DCMD simulator ➢ MD_simulation_hollow_fibre.m ➢ MD_simulation_hollow_fibre.fig Submerged hollow fibre VMD simulator ➢ S_VMD_N.m

•

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m2 kg·m−2·Pa−1·s−1 J·kg−1·K−1 m W·m−2·K−1 kg·s−1 W·m−1·K−1 m s−1 Pa Pa W W m K/°C m Pa·s kg·m−3

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➢ S_VMD_N.fig Cross-flow hollow fibre VMD simulator ➢ X_VMD.m ➢ X_VMD.fig

•

Simulation algorithm

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References [1] A.M. Alklaibi, N. Lior, Membrane-distillation desalination: status and potential, Desalination 171 (2005) 111–131. [2] K.W. Lawson, D.R. Lloyd, Membrane distillation, J. Membr. Sci. 124 (1997) 1–25. [3] M.S. El-Bourawi, Z. Ding, R. Ma, M. Khayet, A framework for better understanding membrane distillation separation process, J. Membr. Sci. 285 (2006) 4–29. [4] A. Alkhudhiri, N. Darwish, N. Hilal, Membrane distillation: a comprehensive review, Desalination 287 (2012) 2–18. [5] E. Mathioulakis, V. Belessiotis, E. Delyannis, Desalination by using alternative energy: review and state-of-the-art, Desalination 203 (2007) 346–365. [6] M. Khayet, T. Matsuura, Membrane Distillation: Principles and Applications, Elsevier Publication Great Britain, 2011. [7] Z. Ding, L. Liu, Z. Li, R. Ma, Z. Yang, Experimental study of ammonia removal from water by membrane distillation (MD): the comparison of three configurations, J. Membr. Sci. 286 (2006) 93–103. [8] G.A. Mannella, V. La Carrubba, V. Brucato, Evaluation of vapor mass transfer in various membrane distillation configurations: an experimental study, Heat Mass Transf. 48 (2012) 945–952. [9] E. Drioli, A. Ali, S. Simone, F. Macedonio, S.A. Al-Jlil, F.S. Al Shabonah, H.S. AlRomaih, O. Al-Harbi, A. Figoli, A. Criscuoli, Novel PVDF hollow fiber membranes for vacuum and direct contact membrane distillation applications, Sep. Purif. Technol. 115 (2013) 27–38. [10] S. Cerneaux, I. Strużyńska, W.M. Kujawski, M. Persin, A. Larbot, Comparison of various membrane distillation methods for desalination using hydrophobic ceramic membranes, J. Membr. Sci. 337 (2009) 55–60. [11] J.-M. Li, Z.-K. Xu, Z.-M. Liu, W.-F. Yuan, H. Xiang, S.-Y. Wang, Y.-Y. Xu, Microporous polypropylene and polyethylene hollow fiber membranes. Part 3. Experimental studies on membrane distillation for desalination, Desalination 155 (2003) 153–156. [12] A. Criscuoli, M.C. Carnevale, E. Drioli, Evaluation of energy requirements in membrane distillation, Chem. Eng. Process. Process Intensif. 47 (2008) 1098–1105. [13] S. Bandini, C. Gostoli, G.C. Sarti, Separation efficiency in vacuum membrane distillation, J. Membr. Sci. 73 (1992) 217–229. [14] J.I. Mengual, M. Khayet, M.P. Godino, Heat and mass transfer in vacuum membrane distillation, Int. J. Heat Mass Transf. 47 (2004) 865–875. [15] L. Eykens, T. Reyns, K. De Sitter, C. Dotremont, L. Pinoy, B. Van der Bruggen, How to select a membrane distillation configuration? Process conditions and membrane influence unraveled, Desalination 399 (2016) 105–115. [16] L. Song, B. Li, K.K. Sirkar, J.L. Gilron, Direct contact membrane distillation-based desalination: novel membranes, devices, larger-scale studies, and a model, Ind. Eng. Chem. Res. 46 (2007) 2307–2323. [17] M. Essalhi, M. Khayet, Surface segregation of fluorinated modifying macromolecule for hydrophobic/hydrophilic membrane preparation and application in air gap and direct contact membrane distillation, J. Membr. Sci. 417 (2012) 163–173. [18] A.M. Alklaibi, N. Lior, Comparative study of direct-contact and air-gap membrane distillation processes, Ind. Eng. Chem. Res. 46 (2007) 584–590. [19] F.A. Banat, J. Simandl, Theoretical and experimental study in membrane distillation, Desalination 95 (1994) 39–52. [20] G.L. Liu, C. Zhu, C.S. Cheung, C.W. Leung, Theoretical and experimental studies on air gap membrane distillation, Heat Mass Transf. 34 (1998) 329–335. [21] A. Cipollina, M.G. Di Sparti, A. Tamburini, G. Micale, Development of a membrane distillation module for solar energy seawater desalination, Chem. Eng. Res. Des. 90 (2012) 2101–2121. [22] S. Yarlagadda, V.G. Gude, L.M. Camacho, S. Pinappu, S. Deng, Potable water recovery from As, U, and F contaminated ground waters by direct contact membrane distillation process, J. Hazard. Mater. 192 (2011) 1388–1394. [23] M. Khayet, P. Godino, J.I. Mengual, Theory and experiments on sweeping gas membrane distillation, J. Membr. Sci. 165 (2000) 261–272. [24] S. Bandini, G.C. Sarti, Heat and mass transport resistances in vacuum membrane distillation per drop, AICHE J. 45 (1999) 1422–1433. [25] M.A.E.-R. Abu-Zeid, Y. Zhang, H. Dong, L. Zhang, H.-L. Chen, L. Hou, A comprehensive review of vacuum membrane distillation technique, Desalination 356 (2015) 1–14. [26] G.C. Sarti, C. Gostoli, S. Bandini, Extraction of organic components from aqueous streams by vacuum membrane distillation, J. Membr. Sci. 80 (1993) 21–33. [27] G. Dong, J.F. Kim, J.H. Kim, E. Drioli, Y.M. Lee, Open-source predictive simulators

[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54]

62

for scale-up of direct contact membrane distillation modules for seawater desalination, Desalination 402 (2017) 72–87. E. Curcio, E. Drioli, Membrane distillation and related operations—a review, Separation & Purification Reviews 34 (2005) 35–86. J. Phattaranawik, R. Jiraratananon, A.G. Fane, Heat transport and membrane distillation coefficients in direct contact membrane distillation, J. Membr. Sci. 212 (2003) 177–193. L. Martínez-Díez, M.I. Vázquez-González, Temperature and concentration polarization in membrane distillation of aqueous salt solutions, J. Membr. Sci. 156 (1999) 265–273. J.P. Holman, Heat Transfer, 10th ed., McGraw-Hill, New York, 2010. S.K.S. Boetcher, Natural convection heat transfer from horizontal cylinders, Natural Convection from Circular Cylinders, Springer International Publishing, Cham, 2014, pp. 3–22. R.K. Sinnott, CHAPTER 12 - heat-transfer equipment, Coulson and Richardson's Chemical Engineering, Pergamon, Amsterdam, 2005, pp. 565–702. P. Mohan, A. Nicholas Emery, T. Al-Hassan, Review heat transfer to Newtonian fluids in mechanically agitated vessels, Exp. Thermal Fluid Sci. 5 (1992) 861–883. T.H. Chilton, T.B. Drew, R.H. Jebens, Heat transfer coefficients in agitated vessels, Industrial & Engineering Chemistry 36 (1944) 510–516. V.W. Uhl, Heat Transfer to Viscous Materials in Jacketed Agitated Kettles, 6 ed., Lehigh University, 1955. G. Brooks, G.J. Su, Heat transfer in agitated kettles, Chem. Eng. Prog. 55 (1959) 54–57. W. Zhong, J. Hou, H.-C. Yang, V. Chen, Superhydrophobic membranes via facile bio-inspired mineralization for vacuum membrane distillation, J. Membr. Sci. 540 (2017) 98–107. F. Laganà, G. Barbieri, E. Drioli, Direct contact membrane distillation: modelling and concentration experiments, J. Membr. Sci. 166 (2000) 1–11. M. Khayet, J.I. Mengual, T. Matsuura, Porous hydrophobic/hydrophilic composite membranes: application in desalination using direct contact membrane distillation, J. Membr. Sci. 252 (2005) 101–113. F. Banat, F.A. Al-Rub, K. Bani-Melhem, Desalination by vacuum membrane distillation: sensitivity analysis, Sep. Purif. Technol. 33 (2003) 75–87. H. Julian, S. Meng, H. Li, Y. Ye, V. Chen, Effect of operation parameters on the mass transfer and fouling in submerged vacuum membrane distillation crystallization (VMDC) for inland brine water treatment, J. Membr. Sci. 520 (2016) 679–692. S. Meng, Y.-C. Hsu, Y. Ye, V. Chen, Submerged membrane distillation for inland desalination applications, Desalination 361 (2015) 72–80. K.W. Lawson, D.R. Lloyd, Membrane distillation. I. Module design and performance evaluation using vacuum membrane distillation, J. Membr. Sci. 120 (1996) 111–121. C. Cabassud, D. Wirth, Membrane distillation for water desalination: how to chose an appropriate membrane? Desalination 157 (2003) 307–314. S. Bandini, A. Saavedra, G.C. Sarti, Vacuum membrane distillation: experiments and modeling, AICHE J. 43 (1997) 398–408. F.A. Banat, J. Simandl, Removal of benzene traces from contaminated water by vacuum membrane distillation, Chem. Eng. Sci. 51 (1996) 1257–1265. F. Banat, S. Al-Asheh, M. Qtaishat, Treatment of waters colored with methylene blue dye by vacuum membrane distillation, Desalination 174 (2005) 87–96. T.-C. Chen, C.-D. Ho, H.-M. Yeh, Theoretical modeling and experimental analysis of direct contact membrane distillation, J. Membr. Sci. 330 (2009) 279–287. S. Srisurichan, R. Jiraratananon, A.G. Fane, Mass transfer mechanisms and transport resistances in direct contact membrane distillation process, J. Membr. Sci. 277 (2006) 186–194. J. Phattaranawik, R. Jiraratananon, Direct contact membrane distillation: effect of mass transfer on heat transfer, J. Membr. Sci. 188 (2001) 137–143. P. Termpiyakul, R. Jiraratananon, S. Srisurichan, Heat and mass transfer characteristics of a direct contact membrane distillation process for desalination, Desalination 177 (2005) 133–141. D. Winter, J. Koschikowski, M. Wieghaus, Desalination using membrane distillation: experimental studies on full scale spiral wound modules, J. Membr. Sci. 375 (2011) 104–112. H.C. Duong, P. Cooper, B. Nelemans, T.Y. Cath, L.D. Nghiem, Evaluating energy consumption of air gap membrane distillation for seawater desalination at pilot scale level, Sep. Purif. Technol. 166 (2016) 55–62.