Energy efficient membrane distillation through localized heating

Energy efficient membrane distillation through localized heating

Desalination 442 (2018) 99–107 Contents lists available at ScienceDirect Desalination journal homepage: www.elsevier.com/locate/desal Energy efficien...

2MB Sizes 5 Downloads 121 Views

Desalination 442 (2018) 99–107

Contents lists available at ScienceDirect

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

Energy efficient membrane distillation through localized heating A. Alsaati, A.M. Marconnet

T

*

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Membrane distillation Desalination Porous media Evaporation Silver membranes

Membrane-based desalination technologies are crucial for generating clean water, but are energy intensive. Localizing heat generation at the liquid-membrane interface could reduce energy consumption while maintaining sufficient mass flux. Here, a locally heated membrane distillation approach is analytically and experimentally evaluated. The measured evaporated mass flux matches the analytical limits considering diffusive and advective mass transfer across a heated porous membrane into stagnant air. Experimentally, thermally-stable silver membranes demonstrate similar mass flux compared to conventional polymer based membrane at the same surface temperature. At high membrane temperatures (∼80 °C), the locally heated membrane distillation demonstrates good efficiency with up to 75% reduction of energy compared to direct contact membrane distillation and airgap membrane destination. Efficiency can be further improved with better thermal design of the supporting structure and permeate heat recovery.

1. Introduction Membrane based water purification accounts for more than 50% of installed water plant due to its simplicity and relatively low energy cost [1]. Among membrane technologies, Reverse Osmosis (RO) is the most mature technology. Nearly, 75 million liters of fresh water are produced daily using RO at a flux of 10.2 L/(m2 h) [2,1]. Despite those high-performance metrics, RO has its own challenges. Separation efficiency is affected by concentration polarization resulted from selective species transfer across membrane. Also, membrane fouling is a major challenge for production yield and reliability. A single stage RO configuration commonly operates in a range of 40–50% feed recovery rate having a water quality of 200–500 ppm [2-4]. Thus, researchers are striving to tackle those challenges. Among the promising alternative technologies is Membrane Distillation (MD), which uses a non-isothermal membrane for separation [5]. The temperature gradient provides a driving mechanism for fluid transport due to different vapor pressures at different temperatures. MD membranes only allow volatile vapor molecules to pass through hydrophobic pores while preventing feed fluid from penetrating through membrane [6]. As a result of the absence of liquid entrainment in the MD method, species such as ions, colloids, and macromolecules, which are unable to evaporate and diffuse across the membrane, are completely rejected. In contrast to conventional distillation that relies on high velocity vapor to provide ultimate vapor liquid contact, MD utilizes hydrophobic microporous media to maintain vapor-liquid contact. This allows MD to operate at low temperature without compromising the *

Corresponding author. E-mail address: [email protected] (A.M. Marconnet).

https://doi.org/10.1016/j.desal.2018.05.009 Received 16 January 2018; Received in revised form 15 May 2018; Accepted 15 May 2018 0011-9164/ © 2018 Elsevier B.V. All rights reserved.

vapor-liquid contact, which permits the use of low grade waste heat such as solar heat. Additionally, membranes in MD play a relatively small role in separation: they maintain the vapor-liquid interface, but do not filter contaminations from feed. This contrasts with filtration processes where the pores are sized smaller than contaminants. Over time, for pressure driven filtration processes, the pores get clogged affecting flux. On the other hand, membranes for MD operate with larger pores sizes compared to RO, which makes the membranes less prone to clogging [7,8]. Even though fouling could affect wetting properties of MD membranes, previous studies have reported that RO flux declines significantly more than MD flux in the presence of organic foulant and low concentration organic foulant [9]. Thus, the MD technique is particularly advantageous for high contamination concentrations. Despite the benefits, commercialization of MD technology is constrained by high energy consumption. Energy consumption for MD is affected by the membrane material and design configuration. Many configurations have been designed to optimize performance by varying the downstream phase or pressure conditions. For example, permeating the vapor into air, similar to the air gap MD configuration, improves thermal efficiency since thermal resistance to the air side of the membrane is higher [10]. Yet, the required energy consumption per permeate flux is still high at 57,600–122,400 kJ/kg [11], measured by the electrical power consumed in heating and recirculating feed. Cascade configurations have been also attempted to recover energy on the permeate side. Indeed, Multi-stage MD (MSMD) has been reported to improve thermal efficiency by recovering and reusing of vapor latent heat [8,12,13]. Nonetheless, one of the major factors for energy

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

the liquid-vapor interface at the bottom of the porous membrane. Water vapor flows through the membrane and into the air above the membrane. To predict the mass flux, we first consider the top surface of the heated membrane. At this surface, the temperature dependent evaporative mass flux is analytically calculated by analogy to natural convection above circular disk. Then, we superimpose the porous media mass resistance effect on free surface natural evaporation. Analogous to a thermal flux being proportional to a temperature gradient, the mass flux is proportional to water vapor pressure gradient. In this analytical model, we use the Boussinesq approximation: variable air density is only considered in the buoyancy terms. The flow is also assumed to be axisymmetric. Thus, the velocities in vapor phase region depend on the →. Using these assumpr + wz cylindrical coordinates (r and z): u = u→ tions and noting that gage pressure is defined as ϖ = P − Pstat where ∂P = 0 , the steady Pstat is the hydrostatic pressure such that −ρ∞ g − ∂stat z non-dimensional Navier-Stokes and mass transport equations become

(

Fig. 1. Schematic diagram of the locally heated membrane distillation configuration. The membrane is heated from the edges with an electrical heater (not shown), rather than heating the feed fluid as with conventional membrane distillation approaches. The relatively stagnant feed flow reduces the energy required for maintain the liquid-vapor surface at the desired temperature. A hydrophobic, microporous membrane helps to ensure that the liquid-vapor interface remains at membrane surface where heat is supplied. Only vapor passes through the membrane to a lower vapor pressure zone away from heated region and can be collected with a condenser.

)

∼ ∂w 1 ∂ (~ r ũ) + ∼ = 0, ~ ~ ∂z r ∂r

(1)

∼ 2 2 ∼ ∂ũ ⎞ = − ∂ϖ + ⎛ ∂ ũ + 1 ∂ũ − ũ + ∂ ũ ⎞, ⎛ũ ∂ũ + w ∼ ∼ ~ ~ ~ ~ ~ ~ 2 2 2 ∂ ∂ r z r r r r r z ∂ ∂ ∂ ∂ ⎠ ⎝ ⎝ ⎠ ⎜

∼ ∼ ∼ ∼ ∂w ⎞ = − ∂ϖ + Gr ⎛ũ ∂w + w ∼ ∼ ~ ∂ ∂ ∂ r z z ⎠ ⎝

consumption is heating the entire circulating feed flow. Thus, the use of direct membrane heating has been analyzed to improve thermal efficiency [14]. This paper evaluates energy efficiency improvements of direct membrane heating method through controlled MD configuration, locally heated membrane distillation (LHMD), that accurately measures energy requirement per unit mass of distilled fluid as shown in Fig. 1. Specifically, heat is localized at the region of the fluid in close contact with the membrane using an electric heater. Compared to heating the bulk feed water, localized heating can reduce energy consumption to reach same temperature near the membrane due to the reduced effective thermal mass and elimination of the feed re-circulation power consumption. This configuration has the potential to be applied directly on naturally occurring contaminated or seawater surfaces including seawater ponds for localized clean water production. Additionally, membrane structural reliability increases due to reduction of feed circulation erosion and hydrodynamic pressure. Localized heating at the membrane interface allows this membrane distillation method to be used in miniature and modular designs to fit wide range of evaporation application beyond desalination alone. Further, the temperature gradient away from membrane could induce cool crystallization away from membrane allowing for salt collection stage in continuous operation. This work first develops an analytical model for thermal and fluid transport in the LHMD system, then demonstrates a lab-scale version of the same. In particular, we estimate analytical mass flux limits for free surface natural convection and introduce the mass flow resistance of membrane, analogous to thermal flow resistance, to account for flow through the membrane. Then, the predicted mass flux is experimentally validated including measurements of energy consumption. Ultimately, this work demonstrates a significant energy consumption reduction of MD processes. Lab scale experimental validation demonstrates that in this first prototype design, 25% of the input electrical power is used for evaporating stagnant fluid at 80 °C, and this efficiency can be significantly improved through better insulating the fixture.



(2)

∼ ∼ ∼ ∂ 2w ∂ 2w 1 ∂w ~ c + ⎛ ~ 2 + ~ ~ + ∼2 ⎞ , ∂ ∂ ∂ r r r z ⎝ ⎠ ⎜

~ ∂~ ∂ 2~ ∂~ c c c ∼ ∂c = 1 ⎡ 1 ∂ ⎛ ~ r ~ ⎞ + ∼2 ⎤ , ũ ~ +w ∼ ~ ~ ⎢ r ∂r ⎝ ∂r ⎠ ∂z ⎥ ∂r ∂z Sc ⎣ ⎦



(3)

(4)

ρ − ρ gR3 | s ρ ∞| 2 ν ∞

is the Grashof number, ρ is vapor density, ν is the where Gr = kinematic viscosity, g is acceleration due to gravity, R is the radius of the membrane, Sc = ν/D is the Schmidt number, D is mass diffusivity, ∼ = R w/v , ∼ ~ ϖ = (R2ϖ )/(ρ∞ v 2) , and nonr = r / R , ũ = Ru/ v , w c = (c − c∞)/(cs − c∞) . dimensionalized vapor concentration is ~ Subscripts s and ∞ correspond to saturation conditions and ambient conditions respectively. Here, the saturated vapor concentration at liquid vapor interface, cs, and the ambient air vapor concentration, c∞, are used as boundary conditions. Using those governing equations and Fick's law, the total mass flux is calculated from an integral over the surface of the membrane:

Q=

∫ −D ∂c (∂rz, z )

dS, z=0

(5)

where D is the diffusivity of the vapor phase into air. 2.1. Diffusion limits To estimate the lower limit of the evaporated mass flux, we consider the case of the Grashof number to be much smaller than 1. This condition means that the mass flux is purely from diffusion, with no driving buoyancy force of the vapor. In estimating diffusion limits, we also assume that vapor diffusivity, D, is constant. Consequently, uncertainties in the diffusion limits increase at high temperatures. It is important to bear in mind that these limits are developed for free surface natural evaporation in the absence on mass transport resistance caused by membrane. However, in Section 2.3, membrane effects are superimposed onto free surface natural convection limits. Hence, Eqs. (1)–(4) reduce to

1 ∂ ⎛~ ∂~ c c ∂ 2~ r ~ ⎞ + ∼2 = 0. ~ ~ r ∂r ⎝ ∂r ⎠ ∂z

2. Theoretical limits for desalination (mass flux)

(6)

Eq. (6) can be solved by separation of variables in oblate spheroidal coordinates (k,σ) as in Ref. [15], such that the non-dimensional conc , the local diffusive mass flux, jdiff, and the total diffusive centration, ~ mass flux, Qdiff, are

In the LHMD process, the transfer of water vapor through the member involves several thermofluid phenomena. Liquid is in contact with the bottom surface of the heated membrane. Evaporation occurs at 100

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

Fig. 2. Dimensionless vapor concentration above the heated membrane considering only the diffusive component.

2 ~ c (k , σ ) = 1 − arctan(σ ), π jdiff (r ) =

2.3. Porous media mass flux

(7)

2 D (cs − c∞ ) , π R2 − r 2

The above models consider mass flux from a free liquid surface. In LHMD, a porous membrane introduces more mass transfer resistance that must be included in models of natural convection, thereby reducing the upper limit to the mass transfer estimated in Eqs. (6)–(14). The effect of porous medium can be incorporated by two methods: a modified binary diffusion coefficient or through an additional pressure drop analogous to thermal contact resistance in heat transfer. When considering the natural convection lower limit, we use the approach of modifying the binary diffusion coefficient D in Fick's law. This is more appropriate than the pressure drop approach because assuming mass transfer is purely diffusive eliminates the pressure drop across membrane due to vapor velocity. Thus, for the lower limit in natural convection, Fick's first law is modified by introduction of a porous media factor β [17]

(8)

Qdiff = 4D (cs − c∞) R.

(9)

Fig. 2 illustrates the local vapor concentration in this configuration. Note that concentration decays rapidly away from membrane surface, which influences the diffusive mass flux. High concentration gradient near membrane boundary is desirable to enhance the diffusive flux. 2.2. Convection limits For high Grashof numbers, buoyancy leads to additional vapor flow. The velocity field above a circular liquid free surface can be divided into three regions: the center, intermediate, and edge regions as illustrated in Fig. 1. Near the liquid vapor surface, the flow in intermediate zone is assumed to be mostly horizontal toward center zone where the evaporate forms an upward plume. Since we assume that most of the flow is horizontal in this region, the following rescaling should be inz, troduced to retain inertial viscous and pressure terms: z ̂ = Gr 0.2∼ ∼, and ϖ  = Gr −0.8∼ ϖ . Assuming constant diffuû = Gr −0.4ũ , ŵ = Gr −0.2w sivity, the local mass flux, jint, and the total mass flow, Qint, for the intermediate region are estimated by Dollet and Boulogne [16] to be

jint (r ) ≃ D

cs − c∞ D (cs − c∞) Gr 0.2 = , δ (r ) R0.6 (R − r )0.4

Qint ≃ 2πRD (cs − c∞) Gr 0.2 = 2π

D (cs − c∞)1.2 1.6 R . 0.2 0.4 C∞ ν

* = βDAB , DAB β = ϵSg τ ,

where τ is tortuosity, ϵ is the porosity,and Sg is the gas saturation (equal to 1 for all gas condition). We estimate tortuosity from porosity based on a numerical analysis in literature [18] that calculates the tortuosity of a membrane fabricated from solid spheres of the same radius to the porosity:

τ = 1 − 0.5 ln ϵ.

(11)

1/3

Jedge ≃ D Qedge

,

cs − c∞ , R*

c − c∞ ≃ 2πRR*D s = 2πRD (cs − c∞). R*

(16)

When considering buoyancy-driven convection through the porous media, the impact of the porous media is accounted for in mass transfer predictions as an additional pressure drop. The Dusty Gas Model (DGM) predicts the pressure drop across membrane. Then, the pressure drop is iteratively incorporated at boundary conditions of Eqs. (10)–(14) until the mass flux is balanced between flow through the porous media and the natural convection above membrane. One key feature of the DGM is that it includes both diffusion (ordinary and Knudsen) and advection. The DGM can be written in terms of total molar flux N which include diffusive and advective flux [17]

(10)

Near the edge, the edge mass flux, jedge, and mass flow rate, Qedge, are calculated with respect to characteristic scale length R* of the vapor concentration gradient [16]:

c − c∞ ν 2 ⎞ R* = ⎜⎛ s ⎟ g⎠ ⎝ c∞

(15)

(12)



(13)

j

ci Nj − cj Ni p ∇c i ⎛ B 0p ⎞ ci ∇p N ⎟ , − i = + ⎜1 + Dij* Dik Rg T D ik μ ⎠ R g T ⎝

(17)

where the subscript i indicates the transported species (water molecules) and the subscript j indicates other surrounding species. The first term of the left-hand side is the molecule-molecule interaction based on the Stefan-Maxwell equation while the second term is accounts for Knudsen molecule-particle interaction. On the right-hand side, the pressure and concentration gradients are considered as the driving forces for diffusion and advection. Effective diffusion coefficients are

(14)

For large Grashof number, the contribution of the center zone to the mass flux is negligible. Most flux from the intermediate and edge zones flows toward the center building up a static pressure at center. Hence, pressure gradient at liquid vapor interface in the center zone is much smaller than other zones. 101

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

calculated based on porous media properties and mean free path of the 2 fluid [2]: Dij0 = Kl PDij , Dik = K 0 ((8Rg T )/(πMi ))(1/2) , B 0 = (ϵrpore )/8τ , K0 = 2ϵr/(3τ), and Kl = ϵ/τ, where Rg is the gas constant, T is the temperature, μ is the dynamic viscosity, and rpore is the membrane pore radius. The DGM accounts for both continuum region and Knudsen region where pore size is smaller than mean free path of vapor. For a binary mixture of water vapor (w) in air (a) the mean free path evaluated average membrane temperature T is [19]

la / w = π

(

1

KB T σw + σa 2 p 2

)

1 + (Mw + Ma)

, (18)

where σw and σa are the collision diameter of water vapor and air, respectively, and M is the molecular weight. For an average temperature of 60 °C, a mean free path of 0.11 μm is typical [20]. Similar to approximations used for airgap membrane distillation mass transfer [2], Eq. (17) can be simplified if air is considered as stagnant film:

* J = DAB

∇pi . RT|pair |ln

Fig. 3. Analytical predictions of mass flux as a function of surface temperature for membranes of different porosities (ϕ = 0.1, 0.4, and 0.7) using the modified diffusion coefficient (D*, dashed lines) and the pressure drop (dP, dotted lines) methods. The diffusive (solid blue line) and convection (solid brown line) limits represent the maximum fluxes for free surfaces. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(19)

Accounting for Knudsen effect in small pore sizes, Eq. (19) becomes [2] −1

J=

p 1 ⎡ 1 + air ⎤ ∇pi . * ⎥ RT ⎢ D D ik AB ⎦ ⎣

(20)

Lastly, for Eqs. (17)–(20), the water vapor pressure at liquid-membrane boundary is estimated from the liquid temperature by the Antonie equation excluding the liquid surface curvature effect [2]:

B ⎤ pi0 = exp ⎡A − . C + T⎦ ⎣

min while maintaining distillate side of membrane module at 15 °C [7,8,10]). This falls within the analytical limits of the locally heated membrane configuration shown in Fig. 3. The relatively low mass flux need to be measured with high precision. Conventionally, for air gap membrane distillation, the distillation flux is measured by collecting condensate formed on a cold plate over specific period of time then dividing this by the measured membrane area to estimate flux per unit area for a given upstream temperature of the recirculating feed [10,11,23,24]. To utilize this method, large membrane areas and long times are required to reduce uncertainties due to leakage within feed circulating loop and re-evaporation of condensation collected or condensation of water vapor in air. Additionally, mass flux is correlated to feed temperature, which is not the temperature of water contacting the membrane. In this paper, the instantaneous mass loss is measured by sensitive digital balance for a pressure driven feed as shown in Fig. 4. Our design inherently eliminates the vibrations due to feed circulation allowing for sensitive flux measurements by analytical balance. However, the analytical balance can be affected by electromagnetic interference from the heater and, thus, the mass loss is also verified by observing the manometer on feed reservoir throughout the process. These accurate measurements enable the use of small membrane areas to ensure homogeneous membrane properties and instantaneous measurements of mass flux. Further, as high temperature operation is desirable to enhance the mass flux, in addition to conventional hydrophobic polymeric membranes, silver membranes with controllable pore sizes and higher temperature stability are used here and treated with self-assembled monolayers (SAMs) to enhance their hydrophobicity. Although metallic based membranes have higher thermal conductivity, overall changes in conductive losses through membrane to air are negligible since air has low thermal conductivity. In fact, higher thermal conductivity is desirable in localized heating configuration to spread heat evenly. Additionally, the thermal expansion coefficient of silver is an order of magnitude lower than the expansion coefficient of polymeric materials [25-28]. As a result, the silver pore structures are expected to be more stable at higher temperatures compared to polymer pore structures. This new MD configuration opens the possibility of measuring high temperature membranes performance simply by varying electrical power input. Operating at higher temperature improve mass flux and thermal efficiency [29].

(21)

The parameters for temperautre in Kelvin and pressure in Pascal for water vapor are A = 23.1964, B = 3816.44, and C = −46.13. Additionally, the vapor density and diffusion coefficient for water are [21,22]

ρ=

pv , 1.61p − 0.6pv

D H2 O, Air = 1.87e−10

T 2.072 . p

(22)

(23)

Fig. 3 shows the predicted mass flux as a function of temperature (below the atmospheric boiling temperature) for evaporation through membranes and from free surfaces. The surface mass flux rate increases exponentially as the temperature approaches the boiling temperature. The diffusion and convection limits are based on Eqs. (9) and (10)–(14), respectively. Vapor diffusivity and boundary conditions are estimated based on the membrane temperatures. Porosity effects take into account the impact of the membranes using the two methods described above: the modified diffusion coefficient method (D*, based on Eq. (15)) and the pressure drop model (dP, based on the dusty gas model in Eqs. (17)–(23)). Both methods of incorporating mass flux through porous media yield similar results. As membrane porosity decreases, the mass flux rate approaches the diffusive limit for a free surface. In contrast, mass flux across highly porous media closely resembles the convective limit for a free surface. Therefore, accounting for the pressure drop across membrane may be more appropriate to model the dynamic nature of vapor flow through these highly porous membranes. 3. Experimental design considerations We next experimentally evaluate the mass flux and efficiency of the new system configuration. The predicted mass flux compare well with those reported for the AGMD configuration (e.g., mass flux in the range to 5–12 kg/m2 h at feed temperature of 80 °C and flow rate of 250 mL/ 102

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

heater has an outer diameter of 50 mm OD and inner diameter of 15 mm with an embedded type K thermocouple to measure the heater temperature. To improve the temperature uniformity, the heater is attached to a 3 mm aluminum heat spreader using arctic silver thermal compound that minimizes the thermal contact resistance between heater and aluminum heat spreader. All membrane samples are circular with 25.4 mm diameter and are placed on top of the heat spreader. The heater and membrane assembly is enclosed in an acrylic casing filled with Permatex high temperature red RTV silicone that acts as a sealant and thermal insulation. Temperatures are measured at various locations in the feed fluid and on the membrane using type K thermocouples. A NI USB 9162/9211 DAQ system is used to record the temperature measurements. The airside of the membrane is maintained at 21 °C and atmospheric pressure while the liquid side at 35 mm hydrostatic pressure to ensure liquid-membrane contact. Pressure and temperature differences across membranes dictate vapor saturation conditions on liquid surface, which influence permeate flux rate. The entire assembly is placed on a scale (Sartorius-ENTRIS 420) with a precision of 0.1 mg, data is recorded at 2.3 Hz. The exposed membrane area for evaporation is measured from optical images using ImageJ software. The mass flux is measured for approximately an hour, and the rate of mass change in the steady state portion of the experiment is used as a metric of performance. Steady state is reached around 0.8 h for our set up as shown in the example data in Fig. 6. We define steady sate as the region where the mass evaporation is linear with time, so from approximately 0.8 h to 1.0 h in this example. In this region, the temperatures are increasing at less than 0.01 °C/min. To quantify the baseline evaporation rate for our system, the evaporation rate is measured for a case where the heater is turned off for the same duration it takes to reach steady state condition. Fig. 7 shows the mass flux rates for various membrane materials across a range of membrane temperatures in comparison to the analytical limits calculated including the effect of the porous medium on the mass flux resistances. Experimentally, all measurements fall within the analytical predictions with no significant performance differences across membrane material and pore size. We hypothesize that because the mass transport across thin membrane (50 μm) is relatively slow and the maximum pressure drop across membrane (see Eq. (19)) is less than 5% of the vapor pressure, diffusion is the dominant transport mechanism across the membrane. Pore sizes influence diffusion rate only when sizes are comparable to mean free path of transported particles. Since investigated pore sizes are in micron range, confinement effects are not expected to be observed experimentally. Still, membrane pore size need to be controlled since it is a dominant factor in preventing liquid penetration in MD processes. On the other hand, mass flux is expected to be affected by surface energy of materials. In this study, surface energy

Fig. 4. Schematic diagram of the Locally Heated Membrane Distillation (LHMD) configuration used in this work. A U-shape manometer is used to supply fluid to the membrane and replenish the mass lost by evaporation across membrane. The entire assembly is placed on digital balance to monitor mass loss. Additionally, thermocouples are implemented at various location to measure the temperature distribution (red dots). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.1. Experimental analysis Four membrane materials are tested in this experiment: (a) GORETEX (supplied from Outdoor Wilderness Fabric), (b) ePTFE with 0.45 μm pores (Sterlitech), (c) hydrophobic PVDF with 0.1 μm pores (Sterlitech), and (d) silver membranes with 0.2, 0.45, 0.8, and 1.2 μm pores (Sterlitech). Self-assembled monolayer (SAM) coatings (1Dodecanethiol (Sigma-Aldrich)) are applied to the silver membranes to improve the surface hydrophobicity preventing liquid penetration through membrane. The SAM solution is prepared by mixing a solvent (Ethanol 200 proof (Decon labs, Inc)) with 1-Dodecanethiol maintaining a concentration of 5 mM. Then, the solution is sonicated for 10 min for proper mixing. Next, in a glove box purged with inert gas, the membrane samples are immersed and sealed in the coating solution. Then, the samples are stored for 72 h. Finally, the samples are rinsed with fresh solvent, sonicated for 3 min, and rinsed again with fresh solvent. Contact angle tests (following ASTM D5946-09) indicated that the hydrophobicity of the silver membranes after SAM coating exceeds the conventional MD membrane materials (Fig. 5). To test the effectiveness of the LHMD system, the mass flux and energy consumption are measured as shown schematically in Fig. 4. A circular ring shaped flexible silicon heater heats the membrane. The

Fig. 5. Measurement of contact angle for a silver membrane (a) before and (b) after coating with SAM. Note that the membrane is hydrophilic before coating and becomes hydrophobic with the coating. 103

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

Fig. 6. (a) Temperature and cumulative mass evaporation over time for an example membrane. The steady state evaporation rate is measured when membrane temperature increases by less than 0.01 °C/min, which is reached around 0.8 h. (b) Energy expended as a function of evaporated mass. The slope of this curve confirms that steady state is reached not only in temperature but also in energy consumption.

is quantified by contact angle shown in Tables 1 and 2. Since all materials used have a contact angle within ± 4% of 116°, we assume that there are no significant surface energy differences across samples. To evaluate the energy efficiency of this process, the specific energy consumption, defined as the ratio total input energy required per unit mass of permeate, is computed and shown in Fig. 8. The input energy consists only of the supplied electrical power and ranges from 10,000–30,000 kJ per kg of evaporate. Specific energy consumption across all the samples are up to 75% lower than other conventional MD configuration. Direct contact MD has been reported to have a consumption range of 60,000–120,000 kJ/kg [29]. On the other hand, air gap MD has energy consumption range of 57,600–122,400 kJ/kg accounting for electrical power for heating and cooling in addition to fluid circulation consumption [11]. Alternative configurations required excess energy to heat entire circulating feed with relatively larger thermal mass while proposed configuration heat is localized in smaller thermal mass. Additionally, localizing heat at the membrane interface minimizes heat losses to ambient because effective surface area that is elevated above ambient is significantly reduced. In addition to evaporating liquid, the heat generated by the heater dissipates by convection and conduction pathways, which can be minimized in a well-insulated membrane cell. The convection losses can

Table 1 Measured contact angle of conventional membrane materials. Material

Contact angle [°]

ePTFE PVDF GORE-TEX

123 ± 1.2 111 ± 1.8 111 ± 0.9

Table 2 Measured contact angle of silver membrane of different pore sizes before and after treatment with SAM. Ag pore size [μm]

Pre-SAM [°]

Post-SAM [°]

0.2 0.45 0.8 1.2

74 82 97 92

115 118 118 121

± ± ± ±

1.6 0.5 1.2 1.1

± ± ± ±

0.8 1.2 1.0 0.7

be estimated by fitting a lumped capacitance model to the heater temperature data taken after turning heater off during the cooling process. Neglecting radiation, assuming further evaporation is

Fig. 7. (a) Measured mass flux as a function of membrane temperature for the SAM-coated silver and the polymeric membranes in comparison to the analytical predictions for the diffusive and convection regimes. Note that there is little variation in the performance from membrane to membrane observable in this data. Dashed lines for the data are to guide the eye. (b) Measured mass flux for two SAM-coated silver samples compared to analytical prediction of mass flux through porous medium, shown in Fig. 3, at two volume fractions within the expected range for the commercially-obtained membranes (dotted lines). 104

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

Fig. 8. (a) Measured specific energy consumption as a function of surface temperature with various membrane materials and pore sizes in comparison to the latent heat of water (dotted line). (b) Energy consumption comparison with direct contact MD (DCMD) [29] and air gap MD (AGMD) [11] for the same operating temperature range [40–80 °C].

the effective thermal conductivity of membrane cell feed connection kAcond (including both the glass and the water) is numerically estimated using COMSOL. This enables us to estimate potential performance improved with improved fixture design. In addition to conductive and convective heat losses, some of the energy could hypothetically be recovered from the evaporative flux after condensation. Exergy is the maximum energy obtainable from the distilled fluid while bringing fluid into the environmental state. In a control volume analysis, physical exergy, e, is calculated by adding flow work to internal exergy where the chemical exergy depends on chemical potential, ψ, [30,31]

insignificant, and that the convection heat transfer coefficient is of the form hconv = C (T − T∞)n , where T∞ is the ambient temperature, C and n are constants to be determined, the energy conservation equation during cooling of the membrane cell is

− C (T − T∞)nA (T − T∞) = ρVcP

∂T , ∂t

(24)

which yields the temperature response: −1/ n

T − T∞ ncA (T − T∞)n = ⎜⎛ t + 1⎟⎞ T0 − T∞ ρVc p ⎝ ⎠

, (25)

e = (h − h*) − T0 (s − s *) +

where the unknown coefficient C, the effective system density ρ, volume V, surface area A, and heat capacity cp can be lumped into one ρVcp unknown constant . Then, a two variable least-squares fitting apCA proach is utilized to estimate this unknown lumped coefficient and unknown power dependence n. Fig. 9 shows an example cooling curve, and the results of the two-parameter parameter for several samples ρVcp enable extraction of the lumped coefficient CA = 1.5 × 106 [s K2] and the power n = 2.0 with a standard deviation of less than 5% for each parameter. Moreover, conductive heat losses are proportional to temperature ∂T gradient along feed connection (qcond = kAcond ∂t ). For losses estimation,

∑ (ψ* − ψ0),

(26)

i

where h and s are enthalpy and entropy respectively. Properties with asterisk * referring to the dead state properties. In this work, the dead state is defined as atmospheric pressure at a room temperature of 21 °C. For pure substances, the chemical exergy term (last term in Eq. (26)) disappears. Thus, we subtract potentially mitigatable thermal energy losses (conduction through the supports, convection to surroundings, and recoverable exergy from the distilled fluid) from the input electrical energy to estimate the best possible efficacy of such a LHMD system:

ηmax =

̇ fg mh V2 R



∂T kA cond ∂t

.

̇ − CAconv (T − T∞)n + 1 − me

(27)

This optimal efficacy predicts a higher performance for scaled up pilot plant where membrane cell thermal losses are controlled tightly, and heat recovery unit is utilized. Likewise, Guillén-Burrieza et al. [32] reported an improvement in efficacy from 0.17 to 0.38 by recovering heat in a 3-stage AGMD pilot plant operating at 80 °C. In fact, Fig. 10 shows that further improvements in energy consumption are achievable. Because membrane area used in this study is relatively small, fairly uniform temperatures are observed. However, maintaining a uniform membrane temperature at a larger scale is an issue that needs to be considered prior scaling up LHMD configuration. This efficiency, shown in Fig. 10, increases as the temperature increases with nearly all the net input energy

(

V2 R

− kA cond

∂T ∂t

̇ − CAconv (T − T∞ )n + 1 − me

)

at

elevated temperatures is going to evaporating the liquid. The optimal efficacy trend approaches unity below atmospheric boiling temperature. This observation is likely due to reduction of local boiling temperature caused by surface curvature. Surface tension is decreased at elevated temperature increasing curvature at liquid interface [33]. Those changes affect local vapor pressure. At equilibrium,

Fig. 9. Example cooling curve for the heater thermocouple after turning off the power in comparison to the fitted temperature decay via Eq. (25). 105

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

Fig. 10. (a) Measured and (b) optimum efficiency, ηmax, of the LHMD system as a function of temperature for all membranes based on Eq. (27). Note that here to estimate the optimal efficiency, we subtract the thermal losses and available exergy of the distillate from electrical power supply. At high temperature (below the boiling point), the net input energy is nearly all used to evaporate the fluid (ηmax → 1).

consumption. The lack of unsteady effects due to fluid circulation also allows for more instantaneous mass flux measurements improving the accuracy of experimental performance validation. The proposed locally heated membrane distillation configuration, integration of new membrane materials, and analytical models open the possibility of utilizing this membrane distillation method to wider applications beyond desalination. Accurate temperature control and thermal stability makes membrane distillation applicable for organic mixture separation replacing capitally intensive distillation columns. This LHMD also can be miniaturized and decentralized as opposed to conventional distillation and integrated with alternate heat sources such as solar irradiation.

a force balance yields

2γ dP ″ − dP ′ = d ⎛ ⎞, ⎝ rcrv ⎠ ⎜



(28) ′

′′

where dP is the liquid pressure, dP is the vapor pressure, γ is the surface tension, and rcrv is the curvature radius. Since each phase is in thermal equilibrium, the Gibbs-Duhem equation can be used:

s′dT − v′dP ′ + dψ′ = 0,

(29)

and

s″dT − v″dP ″ + dψ″ = 0,

(30)

where s and v are the entropy and volume per mole respectively, ψ is the chemical potential. We can assume that external pressure is constant dP ′ = 0 . Then Eqs. (29) and (30) can be written as

Δh dT + vdP = 0, T ′

Competing interests The authors have no competing interests to declare.

(31)

Acknowledgments



where Δh = T (s − s ) is the latent heat. Substituting Eq. (28) into Eq. (31) and integrate to obtain

ln

2γ v″ Tcrv =− , T0 rcrv Δh

A.A. acknowledges the support of Saudi Arabia Cultural Mission (SACM) fellowship, sponsored by the Saudi Arabian Ministry of Education. The authors thank Prof. Ivan C. Christov for comments and discussion that greatly improved the manuscript.

(32)

where T0 is atmospheric boiling temperature of a flat plate and Tcrv is boiling temperature adjusted for surface curvature [34]. Hence, the porous heated membrane reduces the equilibrium boiling temperature due to induced curvature. As a result, optimum efficiency approaches unity at temperatures just lower than atmospheric boiling temperature.

References [1] S. Shenvi, A.M. Isloor, A.F. Ismail, A review on RO membrane technology: developments and challenges, Desalination 368 (2015) 10–26. [2] E. Driolo, A. Criscuoli, E. Curcio, Membrane Contactors: Fundamentals, Applications and Potentialities, Elsevier, Amsterdam, The Netherlands, 2006. [3] M. Elimelech, W.A. Phillip, The future of seawater desalination: energy, technology, and the environment, Science 333 (2011) 712–717. [4] R.K. McGovern, J.H. Lienhard, On the asymptotic flux of ultrapermeable seawater reverse osmosis membranes due to concentration polarisation, J. Membr. Sci. 520 (2016) 560–565. [5] P.S. Goh, T. Matsuura, A.F. Ismail, N. Hilal, Recent trends in membranes and membrane processes for desalination, Desalination 391 (2016) 43–60. [6] P. Wang, T. Chung, Recent advances in membrane distillation processes: membrane development, configuration design and application exploring, J. Membr. Sci. 474 (2015) 39–56. [7] A. Subramani, J. Jacangelo, Emerging desalination technologies for water treatment: A critical review, Water Res. 75 (2015) 164–187. [8] K.W. Lawson, D.R. Lloyd, Membrane distillation, J. Membr. Sci. 124 (1997) 1–25. [9] E.W. Tow, D.M. Warsinger, A.M. Trueworthy, J. Swaminathan, G.P. Thiel, S.M. Zubair, A.S. Myerson, J.H. Lienhard, Comparison of fouling propensity between reverse osmosis, forward osmosis, and membrane distillation, J. Membr. Sci. 556 (2018) 352–364. [10] D. Gonzalez, J. Amigo, F. Suarez, Membrane distillation: perspectives for sustainable and improved desalination, Renew. Sust. Energ. Rev. 80 (2017) 238–259. [11] A. Alkhudhiri, N. Hilal, Air gap membrane distillation: a detailed study of high saline solution, Desalination 403 (2017) 179–186. [12] H. Chung, J. Swaminathan, D. Warsinger, J.H. Lienhard, Multistage vacuum membrane distillation (MSVMD) systems for high salinity applications, J. Membr.

4. Conclusions We report both an analytical and an experimental analysis of a local heated membrane distillation (LHMD) process including deriving limits for mass flux across the heated porous membrane and demonstrating efficient evaporation of water. The analytical models incorporating diffusive and advective mass transfer across a porous medium into stagnant air agree with the experimental measurements. In addition to conventional polymer membranes, metal-based membranes are evaluated, exhibiting similar performance to the polymer based membrane. However, metal membranes are superior in thermal stability and mechanical stability. This new membrane distillation configuration reduces energy consumption of the distillation process by confining thermally affected region of the liquid to the membrane interface where evaporation occurs reducing the mass required to be heated and also thermal losses to ambient. In addition, the proposed configuration operates with a pressure-driven stagnant fluid eliminating liquid circulation energy 106

Desalination 442 (2018) 99–107

A. Alsaati, A.M. Marconnet

of membrane, Korean J. Chem. Eng. 28 (2011) 770–777. [24] R.W. Schofield, A.G. Fane, R.M.C. Fell, Factors affecting flux in membrane distillation, Desalination 77 (1990) 279–294. [25] Y. Touloukian, R. Powell, C. Ho, P. Klemens, Thermal Conductivity Metallic Elements and Alloys, Plenum, New York, NY, 1970. [26] Y. Touloukian, R. Powell, C. Ho, P. Klemens, Thermal Conductivity Nonmetallic Solids, Plenum, New York, NY, 1970. [27] Y. Touloukian, R. Kirby, R. Taylor, P. Desel, Thermal Expansion Metallic Elements and Alloys, Plenum, New York, NY, 1975. [28] Y. Touloukian, R. Kirby, R. Taylor, T. Lee, Thermal Expansion Nonmetallic Solids, Plenum, New York, NY, 1977. [29] A. Luo, N. Lior, Study of advancement to higher temperature membrane distillation, Desalination 419 (2017) 88–100. [30] L. Fitzsimons, B. Corcoran, P. Young, G. Foley, Exergy analysis of water purification and desalination: a study of exergy model approaches, Desalination 359 (2015) 212–224. [31] M.H. Sharqawy, J.H. Lienhard, S. Zubair, On exergy calculations of seawater with applications in desalination systems, Int. J. Therm. Sci. 50 (2011) 187–196. [32] E. Guillén-Burrieza, J. Blanco, G. Zaragoza, D. Alarcón, P. Palenzuela, M. Ibarra, W. Gernjak, Experimental analysis of an air gap membrane distillation solar desalination pilot system, J. Membr. Sci. 379 (2011) 386–396. [33] N.B. Vargaftik, B.N. Volkov, L. Voljak, International tables of the surface tension of water, J. Phys. Chem. Ref. Data 12 (1983) 817–820. [34] G.Chen, Nanoscale Energy Transport and Conversion, Oxford, New York, NY, 2005.

Sci. 497 (2016) 128–141. [13] T.Y. Cath, Osmotically and thermally driven membrane processes for enhancement of water recovery in desalination processes, Desalin. Water Treat. 15 (2010) 279–286. [14] E. Summers, J.H. Lienhard, Experimental study of thermal performance in air gap membrane distillation systems, including the direct solar heating of membranes, Desalination 330 (2013) 100–111. [15] B. Marder, N.R. Keltner, Heat flow from a disk by separation of variables, Numer. Heat Transfer 4 (1981) 485–497. [16] B. Dollet, F. Boulogne, Natural convection above circular disks of evaporating liquids, Phys. Rev. Fluids 2 14 (2017) 1–10. [17] C. Ho, S. Webb, Gas Transport in Porous Media, Springer, Dordrecht, The Netherlands, 2006. [18] F.G. Ho, W. Strieder, A mean free path theory of void diffusion in a porous medium with surface diffusion. II. Numerical evaluation of the effective diffusivity for arbitrary Knudsen number, J. Chem. Phys. 76 (1982) 673–677. [19] H. Kuhn, H. Fostering, Principle of Physical Chemistry, Wiley, New York, NY, 2000. [20] J. Phattaranawik, R. Jiraratananon, Effect of pore size distribution and air flux on mass transport in direct contact membrane distillation, J. Membr. Sci 215 (2003) 75–85. [21] B. Han, G. Yun, J. Boley, S. Kim, J. Hwang, G. Chiu, K. Park, Dropwise gelationdehydration kinetics during drop-on-demand printing of hydrogel-based materials, Int. J. Heat Mass Transf. 97 (2016) 15–25. [22] T.R. Marrero, E.A. Mason, Gaseous diffusion, J. Phys. Chem (1972) 3–118. [23] K. He, H.J. Hwang, I.S. Moon, Air gap membrane distillation on the different types

107