From low-pressure effusion to membrane distillation

Transcription

1 From low-pressure effusion to membrane distillation Albert S. Kim 1, Ho-Saegng Lee 2, Deock-Soo Moon 2, and Hyeon-Ju Kim 2 1 Civil and Environmental Engineering, University of Hawaii at Manoa, USA 2 Seawater Utilization Plant Research Center (SUPRC), Korea Research Institute of Ships & Ocean Engineering (KRISO), Republic of Korea Thu August 3, / 30

2 Introduction Membrane Distillation Processes Types and Specifics Feed Distillate Phase Advantages DCMD hot water cold water liquid feasible SGMD hot water sweeping 1 atm higher flux VMD hot water (low) atm highest flux AGMD hot water cold surface solid low cost 2 / 30

3 Introduction Membrane Distillation Heat Exchanger Module Structure - Flat Sheet Plate and Frame - Hollow Fiber Shell and Tube Goal of MD in HT - To maximize convenctive ( ) and minimize conductive ( ) Q. - So, if vapor flux ( ), total heat flux ( ): latent heat Thermal conductivities κ in MD processes: mw/m K Distillate Phase κ [mw/m K] AGMD Cold solid surface O ( ) DCMD Liquid water Solid membrane part SGMD Humid air Membrane (solid + gas) VMD Vacuum / 30

4 Introduction Length Scale Analysis A hollow fiber membrane module, supplied by Econity Inc. (17 cm) Length scales of HF MD: (1000) 3 = 10 9 Objects Length Order In meter HF length, L fiber m O ( 10 1) HF inter-spacing, h gap O(10 1 1) mm O ( ) HF Dims., (d o > d i > δ th ) O(10 1 ) mm Pore diameter, d pore O(10 1 ) µm O ( ) Water molecule (H 2 O) 0.1 nm O ( 10 10) 4 / 30

5 Introduction Why VMD? Basic configuration T 1 (> T 2 ) hot feed T 2 T 3 T 4 n(z) P 3 d p z = 0 membrane z = l p P 4 vacuum T 5 P 5 Example (Pros) 1 Highest production rate 2 Less wetting vulnerability 3 Less significant T effect Example (Cons) 1 High e - power req. 2 Vacuum pump req. 3 External condenser req. 5 / 30

6 Introduction Ocean Thermal Energy Conversion (OTEC) in Hawaii At the French Academy of Science in Nov. 15, 1926 Georges'Claude'(24'September'1870' ' 23'May'1960) Masayuki(Mac(Takahashi,(Deep(Ocean(Water(as(Our(Next(Natural(Resource." Retrieved"from" 2 6 / 30

7 Introduction Open Cycle OTEC: Research Motivation Open%Cycle%OTEC "Twenty thousand Leagues Under the Sea" by Jules Verne (1870). 3 Captain Nemo and his assistant discussed... OC OTEC = evaporation of 30 o C surface seawater using 5 o C deap seawater. Why don t we replace the huge evaporator by VMD modules? 1,2 Estimated footprint reduced to 10%. 1 A. S. Kim et al., Renewable Energy, 85 (2016) A. S. Kim et al., IDA J. Desal. Wat. Reuse, 7(1-4) (2015) / 30

8 Introduction Conventional Governing Equations for VMD Phenomenological equations, implicitly using ɛ, τ and κ s Q m = Q cond + Q conv [J w ] (1) J w D effective P partial (2) 1 = (Bosanquet s relationship?) (3) D effective D B D K Brownian Empirical Knudsen (for rarified gas) D B = B = k b T 3πηd w BT (4) P T (5) D K = 1 3 d pore v T 2 1 (6) 8RT v = (7) πm w 8 / 30

9 Introduction Knudsen number analysis (B vs. K) Kn = ( λw d pore ) (8) where λ w is the mean free path of vapor molecules, and d pore is the pore diameter. From continuum liquid to rare gas Flow regime Kn 1. Continuum Kn < Slip (on walls) 10 3 < Kn < Transition 10 1 < Kn < Free molecular < Kn < Table: Dominant transport mechanisms with respect to Kn. 9 / 30

10 Introduction Saturation Pressure of Water Figure: Variation of (a) water vapor pressure and (b) concentration versus temperature. P v (80 C) = atm 50 % gas concentration, Knudsen? P v (25 C) = atm vacuum pressure 10 / 30

11 Theoretical Problem Statement Thermodynamic dilemma in a (straight) pore 1 Mass transport: Saturation pressure or Ideal gas law? J w = D eff C = B eff (P v or P sat ) 2 If Browniand diffusion 3 only and T = 0: (? dpv = B eff dt ) T(9)? = B eff (RTC) (10) Questions 4 1 What is the true driving force? J w = D B C D B (CT) (11) T 2 How do we deal with the effective (combined) diffusion? 3 Isn t there any analogous phenomenon in statistical physics? 3 A. Efros, Soviet Physics J. Exp. Theor. Phys., 1966, 23, A. S. Kim et al. Research Perspective of Membrane Distillation, Desalination & Water Treatment, 58 (2017) / 30

12 Theoretical Standard Effusion ( ν) in both T & P along a tube l p = 2h p n 1 = P1 RT 1 T 1 T 2 d p P 1 P 2 n 2 = P2 RT 2 x = h p x = 0 x = +h p The true driving force for VMD may be the gradient of the incidence rate ν: ν = 1 4 n v = P 2πMw RT P (12) T Governing euqations for MT and HT (using enthalpy H v ) can be J w = 4 ( 3 d p ν P/ ) T (13) Q conv = 4 3 d p (H v ν) = H v J w (14) 12 / 30

13 Theoretical Combined transport through a straight pore may be calculated using Molecular Kinetics and Statistical Mechanics. Example (Straight pore) Top: pore inlet Number of vapor molecules colliding with a pore wall Knudsen dl = adφ z = h dn m = dω db νe ρ/λ (15) dz db β ρ s z α an adjacent molecule Brownian dn g = dτ dψsds cos α πρ 2 ν λ e ρ/λ (16) rp p ψ s r da φ θ z = 0 and the total dn total = dn m + dn g (17) Bottom: middle cross-section before passing through the bottom middle cross-section. 13 / 30

14 Theoretical Flux contributions Knudsen flux: J m = N m 1 4 πd2 p = 1 π 2 2π 0 ( dν dz ) + ĥ p + π 2 dφ dζ ĥp π 2 [ 0 ] ζ 2 ω 2 cos 4 ψ e ρ/λ (cos 2 ψω 2 + ζ 2 ) 2 1 dψ 0 dω (18) Brownian flux: J g = N g 1 4 πd2 p = 8 πd 2 p ( dν dz +π/2 smax π s csc α dψ sds dα dρ ( ρ ) cos 2 α sin α e ρ/λ (19) 0 λ π/2 ) Total flux: J w = J m + J g 14 / 30

15 Theoretical Regional Governing Equations for a HF membane Lumen region 1 Momentum Transport: NS eq. constant u 2 HT: Thermal diffusion = Thermal convection (κ lmn T inr ) = ( ) ρw c pw ut inr z (20) Shell region 1 Continuity equation: ρv = 0 2 Energy balance equation: ρc v v T + p v = 0 3 Euler s equation: ρv v + p = 0 4 State equation (ideal gas law): p = nk B T = CRT Membrane region 1 Continuous T and P 2 J w = v of gas 15 / 30

16 Results and Discussions Efffects of T Gradient Mean molecular speed under T gradient, v From the new general definition of vapor flux: J w = 1 3 d p (n v) (21) Effective mean molecular speed v from (n v): proportional to the linear momentum density: (n v) = v n (22) v = ( 8RT πm w ) ( 1 + ln T ) 1/T 2 ln n 1 /n 2 (23) 16 / 30

17 Results and Discussions Efffects of T Gradient Example: v in DCMD Figure: Ratio of the effective and mean molecular speed, v / v, with respect to the feed T ranging from 26 C to 90 C at cold distillate T at 25 C. The minimal influence of the temperature graident on v because so that v v even if = 0. ln T 1 /T 2 ln n 1 /n 2 1 (24) 17 / 30

18 From low-pressure effusion to membrane distillation Results and Discussions Experimental verifications Experimental setup Figure: Schematic of vacuum membrane distillation operation using cold deepsea water. 18 / 30

19 Results and Discussions Experimental verifications Experimental parameters Table: Characteristics of hollow fiber membranes. 19 / 30

20 Results and Discussions Experimental verifications Experimental conditions Table: Experimental factors using low-temperature feed stream. 1 P vac = bar equivalent to T dist 25 C in DCMD. 2 T feed 26 C about sea surface temperature in tropical areas. 20 / 30

21 Results and Discussions Experimental verifications Saturation pressure of seawater: P v (C, T)/P v (0, T) Empirical correlations reported: ML 5, EJ 6, and WP 7. In Weiss and Price s work, P v ln C. 5 Millero & Leung, American Journal of Science, 276 (1976) Emerson and Jamieson, Desalination, 3 (1967), Weiss and Price, Marine Chemistry, 8 (1980) / 30

22 Results and Discussions Experimental verifications Diffusive Tortuosity 1 Maxwell 8 originally used the concept of tortuosity to compare the electric conductivity of a medium with and without non-conducting spheres (for high ɛ): τ = (1 ɛ) 2 Mota et al. 9 conducted an empirical study on the tortuosity of binary mixtures with β = 0.4: τ = 1 e β 3 Iversen and Jørgensen 10 provided a similar correlation to Maxwell s theoretical expression with q = 2: τ = 1 + q(1 ɛ). 4 Beekman 11 developed an analytical approach to model the nature of highly interconnected pores: τ = ɛ/[1 (1 ɛ) 1/3 ] 5 For a various arrangement of cylinders 12 (P = 1) and spheres 13 (P = 2): τ = 1 P ln ɛ 8 A Treatise on Electricity and Magnetism, Clarendon Press, Oxford, Transactions of Filtration Society 1 (2001) Geochim. Cosmochim. Acta 57 (3) (1993) Chem. Eng. Sci. 45 (8) (1990) Tsai, D.S., and W. Strieder. Chem. Eng. Commun. 40 (1986) Geochimica et Cosmochimica Acta, 60, (16) (1996) / 30

23 Results and Discussions Experimental verifications VMD experiment using cold deepsea water Figure: Comparison with experimental observation and theoretical prediction for salinity 0.0, 32.0, and 64.0 g/kg using HF VMD module consisting of N fiber = 180 fibers. (d p = 0.10µm, ɛ = 0.70, κ = 0.10 W/m K, a f = 0.35 mm, b f = 0.6 mm, and l f = 0.17 m, P v = bar, T vacum = 4.5 ± 0.5 C, and u = 0.24 m/s). 23 / 30

24 Results and Discussions Experimental verifications Heat flux insensitive to salt concentrations Figure: Heat transfer rate simulations using the same parameters of Fig / 30

25 Results and Discussions Experimental verifications Effects of T vac on mass and heat fluxes: (P/ T) Figure: As T vac ( ), J w ( ) and Q( ) 25 / 30

26 Concluding Remarks On-going work: module-scale CFD simulations MD as pseudo-conductive heat transport: Q total = Q conductive + Q convective (25) = κ m (κ s, ɛ) T 4 3 d p (νh w ) (26) = κ m (κ s, ɛ, H w, T) T (27) 1 Q conductive : CFD using an impermeable membrane 2 Q total : CFD using pseudo-thermal conductivity κ m 3 Q convective = Total Conductive 26 / 30

27 Concluding Remarks Undergraudate students posters: VMD & DCMD Flat sheet module: 20 cm 10 cm cm CFD package: OpenFOAM (customized) 27 / 30

28 Concluding Remarks Conclusions 1 The fundamental transport quantity primarily controlling the mass and heat fluxes is the incidence rate: ν. 2 In VMD, both vacuum-side P vac as well as T vac can be controlling factors. 3 Saline concentration does not significantly influence the vapor flux: P v (C, T) P v (0, T). 4 Mass transport in VMD must be in the transition region between Browniand and Knudsen diffusion (in review): 0.1 < Kn < / 30

29 Concluding Remarks Acknowledgements Albert S. Kim and Hyeon-Ju Kim, Chapter Membrane Thermodynamics for Osmotic Phenomena in Desalination (book title) edited by T. Yonar, InTechOpen, in press (2017), open to download. 29 / 30

30 Concluding Remarks Thanks for enough(?) FoodEnergyWater. Thanks You! 30 / 30