solar barometric distillation for seawater desalting part iv: analyses of one-effect and two-effect...

Solar barometric distillation for seawater desaltingPart IV: Analyses of one-effect and two-effect distillation

technologies

Mario RealiV. G.B. Angioletti 5, 20151 Milano, Italy

Tel. +39 (02) 452-1488; email: [email protected]

Received 30 April 2006; accepted 31 October 2006

Abstract

The report concerns design aspects for the recently proposed solar barometric distillation technology for seawaterdesalting (SW–SBD) via underground barometric layout. SW–SBD desalting plants applying one-effect and two-effect distillation technologies are specifically analysed. A salt seawater solution at sub-atmospheric pressure ismade to flow in vacuum solar collectors of simple design and construction to absorb solar radiation and to deliverthe water vapour which drives distillation processes at operative temperatures below 100°C. The proposed SW-SBD desalting plants have good energy efficiency and promising technico-economic features. Field research onSW-SBD prototype plants is necessary to bring SW-SBD desalting technology to its full technological development.

Keywords: Seawater desalination; Solar barometric distillation; Multi-effect distillation technology; Energy efficiency

1. Introduction

The technology of seawater desalting via so-lar barometric distillation (SW–SBD) concerns arelatively simple sun-driven distillation technol-ogy which comprises an underground barometriclayout and a field of specially designed solar col-lectors [1–3].

The present report introduces and analysesSW–SBD desalting plants applying one-effect andtwo-effect distillation technologies by means of

which a satisfactory exploitation of solar radia-tion, which is the driving force of SW–SBD tech-nology, and smooth plant operation may beachieved.

The same type of SW–SBD evacuated solarcollectors introduced in [2] has been assumed forthe present analyses. These solar collectors arecompounded with cylindrical double walled trans-parent glass tubes with closed evacuated (Dewartype) inter-space and have an operative sun irra-diated surface of ~0.90 m2.

Desalination 212 (2007) 219–237

doi:10.1016/j.desal.2006.10.0110011-9164/07/$– See front matter © 2007 Elsevier B.V. All rights reserved.

220 M. Reali / Desalination 212 (2007) 219–237

The field of SW–SBD evacuated solar collec-tors comprises a suitable number of arrays of trans-parent solar collector flow tubes affixed horizon-tally on support frames at a precise operativeheight ~1 m above ground level, inlet/outlet mani-folds, conduits, flow control valves, and sensors.

A typical array has 100 flow tubes and all ar-ray inlet (outlet) manifolds are suitably connectedamong themselves for the required fluid dynamicprocesses with treated fluids.

The following two sections concern operationand thermodynamic features of the proposed de-salting plants, and the last section concerns en-ergy efficiency and general aspects of SW–SBDdesalting technology.

References [1–3] provide several bibliographi-cal references and insights on the potential roleof SW–SBD desalting technology versus othersolar and non solar desalting technologies.

2. One-effect SW–SBD plant

2.1. Plant operation

A simplified diagram of the proposed plant isillustrated in Fig. 1 where important components,e.g., flow-control valves and temperature/pres-sure/salinity/radiation sensors, are not shown.Feed seawater preheated by waste brine and byproduced distilled water in counter-current heatexchangers is pumped from an underground tankat a depth of ~10 m through the first distillationheat exchanger placed at ground level where it isheated by absorbing the change-of-state (latent)heat of water vapour coming from the first vacuumchamber and condensing into produced distilledwater, through another counter-current heat ex-changer to be further heated by waste brine, andthrough the second distillation heat exchangerplaced at ground level where it is partiallyvaporised by absorbing the change-of-state (la-tent) heat of water vapour coming from the sec-ond vacuum chamber and condensing into pro-duced distilled water.

The brine/water vapour/air mixture producedin the second distillation heat exchanger entersinto the first vacuum chamber where it is sepa-rated into two streams: a water vapour/air streamwhich flows to the first distillation heat exchangerand a brine stream which flows through a counter-current heat exchanger, to be heated by the wastebrine released from the second vacuum chamber,and then to the solar collector field where it ab-sorbs solar radiation, is transformed into a hotterwaste brine/water vapour/air mixture, and is re-leased into the second vacuum chamber. From thelatter, the waste brine is pumped to a disposal sitewhile the hot pressurised water vapour/air mix-ture flows into the second distillation heat ex-changer where the water vapour is condensed intodistilled water while the air is vented by means ofa water-jet pump.

From the two distillation heat exchangers, theproduced distilled water streams are directed toan underground storage tank to be delivered tousers.

Plant operations are regulated by means of acustom-designed control system (not shown).Barometric water columns with suitably con-trolled water levels allow smooth plant function-ing.

2.2. Plant design parameters

The required evaluations are carried out on thebasis of the following assumption: steady-statesteady-flow production process with fixed opera-tive parameters (temperatures, pressures, salini-ties, seawater composition, mean operative solarradiation flux, mass flow rates of produced dis-tilled water, feed seawater, and waste brine).

Approximate solutions of mass balance andenergy balance equations are obtained after thetheoretical treatment developed in [2] in order toprovide basic design information for the proposedplant. All thermodynamic simplifications adoptedin [2] have been assumed, in particular, neglectof dissolved or freed air, water vapour superheat,and gravitational and kinetic energy contributions.

M. Reali / Desalination 212 (2007) 219–237 221

Fig.1. Schematic layout of a one-effect SW–SBD desalting plant with two distillation heat exchangers in which watervapour condenses into fresh water at suitable sub-atmospheric pressures and corresponding low temperatures.

The following quantities are utilized: tempera-ture, T (°C); pressure, p (kPa); salinity, σ (mass %);mass flowrate, ψ (kg/s); specific enthalpy, h(kJ/kg), mean operative solar radiation flux on ahorizontal surface, I (kW/m2). Through each heatexchanger, an overall pressure drop ∆p = ~10 kPa(for distributed and localised losses) has been as-sumed. Required thermodynamic quantities havegenerally been obtained from [4]. The enthalpiesof seawater solutions at different temperatures andsalinities have been obtained from [5].

Produced fresh water mass flowrate is assumedto have the value ψd = 1.000 kg/s (~36 m3/d for a10-h working period). The feed seawater mass

flowrate, salinity, and temperature, and the meanoperative solar radiation flux on a horizontal sur-face are assumed to have the values: ψs =10.000 kg/s; σs = 3.50; Ts = 15.0°C, and I =0.3 kW/m2.

The mass of desalted water produced in oneday is roughly proportional to the amount of so-lar radiation absorbed in the solar collector field[1], so operative flux I represents a suitable dailyaverage of the actual time dependent and site spe-cific solar radiation flux which is available at theplant site and which may be assumed to vary si-nusoidally from sunrise to sunset [6,7]. For a morerefined analysis, if all required data on equipment,


components, sensors etc. are available, operativeflux I may be represented by a histogram span-ning the whole working period (~10 h), and allcalculations may be repeated for various valuesof I on specified sub-intervals of the working pe-riod.

Saturated water vapour streams at 70 and 60°Care assumed to flow, respectively, into the secondand first distillation heat exchangers to be con-densed into produced fresh water streams at 65and 55°C. These distillation heat exchangers rep-resent critical plant components and require ac-curate designs.

For the purpose of reducing paper length, yetwithout sacrificing clarity, some specific abbre-viations have been adopted: E.B. (energy balance);M.B. (mass balance); B.H. (barometric height);I.M. (inlet manifolds); O.M. (outlet manifolds);↑ (top); ← (left side); ↓ (bottom); and → (rightside).

2.2.1. Second distillation heat exchanger

E.B.:

(1)

M.B.:

14 14 13b v sψ + ψ = ψ (2)

14 15v v dψ + ψ = ψ (3)

16 15d vψ = ψ (4)

14 14 1 1b b s sσ ⋅ ψ = σ ⋅ ψ (5)

B.H.:

16 2 16101.325 kPad d dg Z pρ ⋅ ⋅ = − (6)

↑(15): Water vapour/air: ψv15 = 0.500 kg/s (op-erative assumption); Tv15 = 70.0°C (opera-tive assumption); pv15 = 31.161 kPa; hv15= 2626.8 kJ/kg.

→ (13):Seawater: ψs13 = ψs1 = ψs = 10.000 kg/s;Ts13 = unknown; ps13 = unknown z pb14 +

10 kPa; σs13 = σs1 = σs = 3.50; hs13 = un-known;At inlet (13), a fluid pressure regulatingdevice (valve/throttle) keeps pressure ps13at the required sub-atmospheric value cor-responding to temperature Ts13.

← (14):Water vapour/air: ψv14 = unknown; Tv14 =60.0°C (operative assumption); pv14 =19.919 kPa; hv14 = 2609.5 kJ/kg;Brine: ψb14 = unknown; Tb14 = Tv14 =60.0°C (operative assumption); pb14 = pv14= 19.919 kPa; σb14 = unknown; hb14 = un-known.

↓ (16): Produced distilled water: ψd16 = ψv15 =0.500 kg/s; Td16 = 65.0°C (operative as-sumption); pd16 = 25.029 kPa; hd16 =267.02 kJ/kg; ρd16 = 980.48 kg/m3; Zd2 =unknown.

Solution of Eqs. (1)–(6) yields:ψv14 = 0.500 kg/s

ψb14 = 9.500 kg/s

σb14 = 3.68

hb14 = [241.18 – (241.18 – 238.00) · 0.68] kJ/kg= 239.01 kJ/kg

hs13 = (10.0)–1 · [0.5 · 267.02 + 9.5 · 239.01 + 0.5· 2609.5 – 0.5 · 2626.8] kJ/kg = 239.54 kJ/kg

Ts13 = 60°C

Zd2 = [(101.325 – 25.029) · (9.80 · 0.980)–1] m = 7.94 m

2.2.2. First vacuum chamber

E.B.:

14 14 14 14

17 17 18 18

b b v v

v v b b

h hh h

ψ ⋅ + ψ ⋅= ψ ⋅ + ψ ⋅ (7)

hv17 = hv14 (8)

hb18 = hb14 (9)


M.B.:ψv17 = ψv14 (10)

18 14b bψ = ψ (11)

18 14b bσ = σ (12)

B.H.:

18 1 18101.325 kPab b bg Z pρ ⋅ ⋅ = − (13)

↑ (17): Water vapour/air: ψv17 = ψv14 = 0.500 kg/s;Tv17 = Tv14 = 60°C; pv17 = pv14 = 19.919 kPa;hv17 = hv14 = 2609.5 kJ/kg.

→ (14):Water vapour/air: ψv14 = 0.500 kg/s; Tv14= 60°C (operative assumption); pv14 =19.919 kPa; hv14 = 2609.5 kJ/kg;Brine: ψb14 = 9.500 kg/s; Tb14 = Tv14 = 60°C(operative assumption); pb14 = pv14 =19.919 kPa; σb14 = 3.68; hb14 = 239.01 kJ/kg.

↓ (18): Brine: ψb18 = ψb14 = 9.500 kg/s; Tb18 = Tb14= 60°C; pb18 = pb14 = 19.919 kPa; σb18 =σb14 = 3.68; hb18 = hb14 = 239.01 kJ/kg; ρb18= 1020.90 kg/m3

Solution of Eq. (13) yields:

( ) ( ) 11 101.325 19.919 9.80 1.020 m

= 8.14 mbZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

2.2.3. First distillation heat exchanger

E.B.:

10 10 8 8 7 7 9 9d d s s s s v bh h h hψ ⋅ + ψ ⋅ = ψ ⋅ + ψ ⋅ (14)

M.B.:

8 7s sψ = ψ (15)

10 9d vψ = ψ (16)

8 7s sσ = σ (17)

B.H.:

10 1 10101.325 kPad d dg Z pρ ⋅ ⋅ = − (18)


→ (7): Seawater: ψs7 = ψs6 = ψs4 + ψs5 = ψs1 = ψs= 10.000 kg/s; Ts7 = unknown; ps7 = un-known z ps8 + 10 kPa; σs7 = σs1 = σs =3.50; hs7 = unknown.

← (8): Seawater: ψs8 = ψs7 =10.000 kg/s; Ts8 =50.0°C (operative assumption); ps8 = un-known; σs8 = σs7 = 3.50; hs8 = 199.50 kJ/kg;


Solution of Eqs.(14) and (18) yields:

( )7 0.050 230.16 2609.5 199.50 kJ/kg

= 100.75 kJ/kgsh = ⎡ ⋅ − + ⎤⎣ ⎦

Ts7 = 26°C

( ) ( ) 11 101.325 15.755 9.80 0.985 m

= 8.86 mdZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

2.2.4. Second vacuum chamber

E.B.:

22 22 22 22 23 23

24 24 b b v v v v

b b

h h hh

ψ ⋅ + ψ ⋅ = ψ ⋅+ ψ ⋅ (19)

22 23v vh h= (20)

22 24b bh h= (21)

M.B.:

22 23v vψ = ψ (22)

22 24b bψ = ψ (23)

22 22 18b v bψ + ψ = ψ (24)


22 22 1 1b b s sσ ⋅ ψ = σ ⋅ ψ (25)

22 24b bσ = σ (26)

B.H.:

24 2 24101.325 kPab b bg Z pρ ⋅ ⋅ = − (27)

↑ (23): Water vapour/air: ψv23 = ψv15 = 0.500 kg/s;Tv23 = Tv15 = 70.0°C (operative assump-tion); pv23 = pv15 = 31.161 kPa; hv23 = hv15 =2626.8 kJ/kg.

← (22):Water vapour/air: ψv22 = ψv23 = 0.500 kg/s;Tv22 = Tv23 = 70°C; pv22 = pv23 = 31.161 kPa;hv22 = hv23 = 2626.8 kJ/kg.Waste brine: ψb22 = unknown; Tb22 = Tv22= 70°C; pb22 = pv22 = 31.161 kPa; σb22 =unknown; hb22 = unknown.

↓ (24): Waste brine: ψb24 = unknown; Tb24 = Tb22= 70°C; pb24 = pb22 = 31.161 kPa; σb24 =unknown; hb24 = unknown; ρb24 = un-known; Zb2 = unknown.

Solution of Eqs. (23)–(27) yields:ψb22 = 9.000 kg/s

ψb24 = 9.000 kg/s

σb22 = 3.88

σb24 = 3.88

( )22 281.56 281.56 277.92 0.88 kJ/kg

= 278.35 kJ/kgbh = ⎡ − − ⋅ ⎤⎣ ⎦

hb24 = hb22 = 278.35 kJ/kg

ρb24 = 1020.96 kg/m3

( ) ( ) 12 101.325 31.161 9.80 1.020 m

= 7.02 mbZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

2.2.5. Waste brine/brine heat exchanger

E.B.:

( ) ( )25 25 26 19 20 19b b b b b bh h h hψ ⋅ − = ψ ⋅ − (28)

M.B.:

20 19b bψ = ψ (29)

26 25b bψ = ψ (30)

20 19b bσ = σ (31)

26 25b bσ = σ (32)

↑ (20, 25): Brine: ψb20 = ψb18 = 9.500 kg/s; Tb20 =65°C (operative assumption); pb20 = un-known; σb20 = σb18 = 3.68; hb20 = [261.37– (261.37 – 257.94) · 0.68] kJ/kg =259.03 kJ/kg.Waste brine: ψb25 = ψb24 = 9.000 kg/s; Tb25= Tb24 = 70°C; pb25 = unknown; σb25 = σb24= 3.88; hb25 = hb24 = 278.35 kJ/kg.

↓ (19, 26): Brine: ψb19 = ψb18 = 9.500 kg/s; Tb19 =Tb18 = 60°C; pb19 = unknown; σb19 = σb18 =3.68; hb19 = hb18 = 239.01 kJ/kg;Waste brine: ψb26 = ψb25 = 9.000 kg/s; Tb26= unknown; pb26 = unknown; σb26 = σb25 =3.88; hb26 = unknown.


( ) ()

126 278.35 9.5 9.0 259.03

239.01 kJ/kg = 257.21 kJ/kg

bh −⎡= − ⋅ ⋅⎣− ⎤⎦

Tb26 = 64°C

2.2.6. Second waste brine/seawater heat ex-changer

E.B.:

( ) ( )11 12 11 11 12 11s s s b b bh h h hψ ⋅ − = ψ ⋅ − (33)

M.B.:

11 12s sψ = ψ (34)

11 12b bψ = ψ (35)

11 12s sσ = σ (36)

11 12b bσ = σ (37)


↑ (11): Seawater: ψs11 = ψs8 =10.000 kg/s; Ts11 =Ts8 = 50°C; ps11 = unknown; hs11 = hs8 =199.50 kJ/kg; σs11 = σs8 = 3.50;Waste brine: ψb11 = ψb24 = 9.000 kg/s; Tb11= unknown; pb11 = unknown; hb11 = un-known.

↓ (12): Seawater: ψs12 = ψs11 =10.000 kg/s; Ts12 =Ts13 = 60°C; ps12 = unknown; σs12 = σs11 =3.50; hs12 = hs13 = 239.54 kJ/kg.Waste brine: ψb12 = ψb24 = 9.000 kg/s; Tb12= Tb26 = 64°C; pb12 = unknown; hb12 = hb26= 257.21 kJ/kg.


( ) ()

111 257.21 9.0 10.0 239.54

199.50 kJ/kg = 212.72 kJ/kg

bh −⎡= − ⋅ ⋅⎣− ⎤⎦

Tb11 = 53°C

2.2.7. Produced fresh water/feed seawater pre-heating heat exchanger

E.B.:

( ) ( )3 5 3 3 5 3s s s d d dh h h hψ ⋅ − = ψ ⋅ − (38)

5 5 10 10 16 16d d d d d dh h hψ ⋅ = ψ ⋅ + ψ ⋅ (39)

M.B.:

5 3s sψ = ψ (40)

3 5d dψ = ψ (41)

5 10 16d d dψ = ψ + ψ (42)

5 3s sσ = σ (43)

↑ (1,3):Seawater: ψs1 = ψs = 10.000 kg/s; Ts1 = Ts= 15°C; ps1 = unknown; hs1 = 59.55 kJ/kg;σs1 = σs = 3.50.ψs3 = 2.000 kg/s (operative assumption);Ts3 = Ts1 = 15°C; ps3 = unknown; σs3 = σs1= 3.50; hs3 = hs1 = 59.55 kJ/kg.Produced distilled water: ψd3 = 1.000 kg/s;Td3 = 20°C (operative assumption); pd3 =unknown; hd3 = 83.86 kJ/kg.

↓ (5): Seawater: ψs5 = ψs3 = 2.000 kg/s; Ts5 =unknown; ps5 = unknown; σs5 = σs3 = 3.50;hs5 = unknown.Produced distilled water: ψd5 = ψd3 =1.000 kg/s; Td5 = unknown; pd5 = un-known; hd5 = unknown.

Solution of Eqs.(38) and (39) yields:

( )5 0.5 230.16 0.5 267.02 kJ/kg = 248.59 kJ/kg

dh = ⋅ + ⋅

Td5 = 59°C

( )5 59.55 0.5 248.59 83.86 kJ/kg

= 141.91 kJ/kgsh = ⎡ + ⋅ − ⎤⎣ ⎦

Ts5 = 35°C

2.2.8. Waste brine/feed seawater pre-heatingheat exchanger

E.B.:

( ) ( )2 4 2 2 4 2b b b s s sh h h hψ ⋅ − = ψ ⋅ − (44)

4 4 5 5 6 6s s s s s sh h hψ ⋅ + ψ ⋅ = ψ ⋅ (45)

M.B.:

2 3 1s s sψ + ψ = ψ (46)

4 2s sψ = ψ (47)

2 4b bψ = ψ (48)

4 2s sσ = σ (49)

2 4b bσ = σ (50)

↑ (1,2):Seawater: ψs1 = 10.000 kg/s; Ts1 = 15°C;ps1 = unknown; σs1 = 3.50; hs1 = 59.55 kJ/kg;ψs2 = unknown; Ts2 = Ts1 = 15°C; ps2 = un-known; σs2 = σs1 = 3.50; hs2 = hs1 =59.55 kJ/kg;Waste brine: ψb2 = ψb24 = 9.000 kg/s; Tb2= unknown; pb2 = unknown; σb2 = σb24 =3.88; hb2 = unknown.

↓ (4, 6):Seawater: ψs4 = unknown; Ts4 = unknown;ps4 = unknown; σs4 = σs1 = 3.50; hs4 = un-


known; ψs6 = ψs1 = 10.000 kg/s; Ts6 = Ts7 =26°C; ps6 = unknown; σs6 = σs1 = 3.50; hs6= hs7 = 100.75 kJ/kg;Waste brine: ψb4 = ψb24 = 9.000 kg/s; Tb4= Tb11 = 53°C; pb4 = unknown; σb4 = σb24 =3.88; hb4 = hb11 = 212.72 kJ/kg.

Solution of Eqs. (44)–(47) yields:ψs2 = 8.000 kg/s

ψs4 = 8.000 kg/s

( ) ( )14 8.0 10.0 100.75 2.0 141.91 kJ/kg

= 90.46 kJ/kgsh −= ⋅ ⋅ − ⋅

Ts4 = 23°C

( ) ()

12 212.72 9.0 8.0 90.46

59.55 kJ/kg 185.25 kJ/kg

bh −⎡= − ⋅ ⋅⎣− ⎤⎦

Tb2 = 47°C

2.2.9. Solar collector field

E.B.:

22 22 22 22 21 21b b v v b bI A h h h⋅ = ψ ⋅ + ψ ⋅ − ψ ⋅ (51)

M.B.:

21 22 22b b vψ = ψ + ψ (52)I = 0.3 kW/m2; A = unknown

I.M. (21): Brine: ψb21 = ψb18 = 9.500 kg/s; Tb21 =Tb20 = 65°C (operative assumption); pb21 zpv22 = 31.161 kPa; σb21 = σb18 = 3.68; hb21= hb20 = 259.03 kJ/kg;At inlet (21), a fluid pressure regulatingdevice (valve/throttle) keeps pressure pb21at the required sub-atmospheric value cor-responding to the value of pv22.

O.M. (22): Water vapour/air: ψv22 = ψv23 =0.500 kg/s; Tv22 = Tv23 = 70°C (operativeassumption); pv22 = pv23 = 31.161 kPa; hv22= hv23 = 2626.8 kJ/kg;Waste brine: ψb22 = 9.000 kg/s; Tb22 = Tv22

= 70°C; pb22 = pv22 = 31.161 kPa; σb22 =3.88; hb22 = 278.35 kJ/kg


( ) ()

1

2 2

0.3 9.0 278.35 0.5 2626.8

9.5 259.03 m 4525.8 m

A −= ⋅ ⋅ + ⋅

− ⋅ =

With the chosen operative parameters, the one-effect SW–SBD desalting plant may be expectedto produce ~36 m3/d of distilled water (in ~10work hours) with some 50 arrays of solar collec-tors.

3. Two-effect SW–SBD plant

3.1. Plant operation

A simplified diagram of the proposed plant isillustrated in Fig. 2 where important components,e.g., flow-control valves and temperature/pres-sure/salinity/radiation sensors, are not shown.Feed seawater preheated by waste brine and byproduced distilled water in counter-current heatexchangers is pumped from an underground tankat a depth of ~10 m through the first distillationheat exchanger placed at ground level where it isheated by absorbing the change-of-state (latent)heat of water vapour coming from the first vacuumchamber and condensing into produced distilledwater. It is then further heated by flowing throughthe second counter-current waste brine/ seawaterheat exchanger and enters into the second distil-lation heat exchanger where it is partially vaporisedby absorbing the change-of-state (latent) heat ofwater vapour coming from the second vacuumchamber and condensing into produced distilledwater. The brine/water vapour/air mixture exit-ing from the second distillation heat exchangerenters into the first vacuum chamber where it isseparated into two streams: a water vapour/airmixture, which is directed to the first distillationheat exchanger, and a brine, which is pumpedthrough the first counter-current waste brine/brineheat exchanger and into the third distillation heat


Fig. 2. Schematic layout of a two-effect SW–SBD desalting plant with three distillation heat exchangers in which watervapour condenses into fresh water at sub-atmospheric pressures and corresponding low temperatures.

exchanger where it is partially vaporised by ab-sorbing the change-of-state (latent) heat of watervapour coming from the third vacuum chamberand condensing into produced distilled water. Thebrine/water vapour/air mixture exiting from thethird distillation heat exchanger enters into thesecond vacuum chamber where it is separated intotwo streams: a water vapour/air mixture, which isdirected to the second distillation heat exchanger,and a brine, which is pumped through the secondcounter-current waste brine/brine heat exchangerand into the solar collector field where it absorbssolar radiation to be released as a hotter wastebrine/water vapour/air mixture into the third

vacuum chamber. From the latter, the waste brineis pumped to a disposal site while the hot pres-surised water vapour/air mixture flows into thethird distillation heat exchanger where the watervapour is condensed into distilled water. From thethree distillation heat exchangers air is vented bymeans of a water-jet pump and the produced dis-tilled water streams are directed to an undergroundstorage tank to be delivered to users.

Plant operations are regulated by means of acustom-designed control system (not shown).Barometric water columns with suitably con-trolled water levels allow smooth plant function-ing.


3.2. Plant design parameters

The required evaluations have been carried outafter the treatment developed in [2] and with thesame overall assumptions and thermodynamicsimplifications. The analysis is straightforwardand provides first approximation plant designparameters for the implementation of prototypeplants.

The following quantities have been utilized:temperature, T (°C); pressure, p (kPa); salinity, σ(mass %); mass flowrate, ψ (kg/s); specific en-thalpy, h (kJ/kg), mean operative solar radiationflux on a horizontal surface, I (kW/m2). Througheach heat exchanger, and each flow control de-vice (throttle), an overall pressure drop ∆p =~10 kPa (for distributed and localised losses), hasbeen assumed. Required thermodynamic quanti-ties have generally been obtained from [4]. Theenthalpies of seawater solutions at different tem-peratures and salinities have been obtained from[5].

The produced fresh water mass flowrate, thefeed seawater mass flowrate, salinity, and tem-perature, and the mean operative solar radiationflux on a horizontal surface are assumed to havethe values: ψd = 1.000 kg/s (~36 m3/d for a tenhour working period); ψs = 10.000 kg/s; σs = 3.50(mass %); Ts = 15.0°C; and I = 0.3 kW/m2.

Saturated water vapour streams at 80, 70, and60°C are assumed to flow, respectively, into thethird, second, and first distillation heat exchang-ers to be condensed into produced fresh waterstreams at 75, 65, and 55°C. Space saving abbre-viations (the same of the previous section) areused.

3.2.1. Second distillation heat exchanger

E.B.:

16 16 14 14 14 14

13 13 15 15 d d b b v v

s s v v

h h hh h

ψ ⋅ + ψ ⋅ + ψ ⋅= ψ ⋅ + ψ ⋅ (1)

M.B.:

14 14 13b v sψ + ψ = ψ (2)

14 15 23v v v dψ + ψ + ψ = ψ (3)

23 15v vψ = ψ (4)

16 15d vψ = ψ (5)

14 14 1 1b b s sσ ⋅ ψ = σ ⋅ ψ (6)

B.H.:

16 2 16101.325 kPad d dg Z pρ ⋅ ⋅ = − (7)

↑ (15): Water vapour/air: ψv15 = 0.335 kg/s (op-erative assumption); Tv15 = 70.0°C (opera-tive assumption); pv15 = 31.161 kPa; hv15= 2626.8 kJ/kg.

→ (13):Seawater: ψs13 = ψs1 = ψs =10.000 kg/s;Ts13 = unknown; ps13 = unknown z pb14 +10 kPa; σs13 = σs1 = σs =3.50; hs13 = un-known;At inlet (13), a fluid pressure regulatingdevice (valve/throttle) keeps pressure ps13at the required sub-atmospheric value cor-responding to temperature Ts13.

← (14):Water vapour/air: ψv14 = unknown; Tv14 =60.0°C (operative assumption); pv14 =19.919 kPa; hv14 = 2609.5 kJ/kg.Brine: ψb14 = unknown; Tb14 = Tv14 =60.0°C (operative assumption); pb14 = pv14= 19.919 kPa; σb14 = unknown; hb14 = un-known.


Solution of Eqs. (1)–(6) yields:ψv14 = 0.330 kg/s

ψv23 = 0.335 kg/s

ψb14 = 9.670 kg/s


σb14 = 3.62

( )14 241.18 241.18 238.00 0.62 kJ/kg

= 239.21 kJ/kgbh = ⎡ − − ⋅ ⎤⎣ ⎦

( ) []

113 10.0 0.335 267.02 9.67 239.21

+ 0.33 2609.5 0.335 2626.8 kJ/kg = 238.37 kJ/kg

sh −= ⋅ ⋅ + ⋅

⋅ − ⋅

Ts13 = 60°C

( ) ( ) 12 101.325 25.029 9.80 0.980 m

= 7.94 mdZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.2. First vacuum chamber

E.B.:

14 14 14 14 17 17 18 18b b v v v v b bh h h hψ ⋅ + ψ ⋅ = ψ ⋅ + ψ ⋅ (8)

hv17 = hv14 (9)

hb18 = hb14 (10)

M.B.:

17 14v vψ = ψ (11)

18 14b bψ = ψ (12)

18 14b bσ = σ (13)

B.H.:

18 1 18101.325 kPab b bg Z pρ ⋅ ⋅ = − (14)

Top (17)


→ (14):Water vapour/air: ψv14 = 0.330 kg/s; Tv14= 60°C; pv14 = 19.919 kPa; hv14 =2609.5 kJ/kgBrine: ψb14 = 9.670 kg/s; Tb14 = Tv14 =60°C; pb14 = pv14 = 19.919 kPa; σb14 = 3.62;hb14 = 239.21 kJ/kg.

↓ (18): Brine: ψb18 = ψb14 = 9.670 kg/s; Tb18 = Tb14= 60°C; pb18 = pb14 = 19.919 kPa; σb18 =σb14 = 3.62; hb18 = hb14 = 239.21 kJ/kg; ρb18= 1020.43 kg/m3.


( ) ( ) 11 101.325 19.919 9.80 1.020 m

= 8.14 mbZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.3. First distillation heat exchanger

E.B.:

10 10 8 8 7 7 9 9d d s s s s v vh h h hψ ⋅ + ψ ⋅ = ψ ⋅ + ψ ⋅ (15)

M.B.:

8 7s sψ = ψ (16)

9 10v dψ = ψ (17)

8 7s sσ = σ (18)

B.H.:

10 1 10101.325 kPad d dg Z pρ ⋅ ⋅ = − (19)

↑ (9): Water vapour/air: ψv9 = ψv17 = 0.330 kg/s;Tv9 = Tv17 = 60°C (operative assumption);pv9 = pv17 = 19.919 kPa; hv9 = hv17 =2609.5 kJ/kg.

→ (7): Seawater: ψs7 = ψs6 = ψs4 + ψs5 = ψs1 = ψs= 10.000 kg/s; Ts7 = unknown; ps7 = un-known z ps8 +10 kPa; σs7 = σs1 = σs = 3.50;hs7 = unknown.

← (8): Seawater: ψs8 = ψs7 = 10.000 kg/s; Ts8 =50°C (operative assumption); ps8 = un-known; σs8 = σs7 = 3.50; hs8 = 199.50 kJ/kg.

↓ (10): Produced distilled water: ψd10 = ψv9 =0.330 kg/s; Td10 = 55°C (operative assump-tion); pd10 = 15.755 kPa; hd10 = 230.16 kJ/kg;ρd10 = 985.70 kg/m3; Zd1 = unknown.


Solution of Eqs. (15) and (19) yields:

( ) ()

7 199.50 0.33/10.0 230.16

2609.5 kJ/kg = 120.98 kJ/kgsh = ⎡ + ⋅⎣

− ⎤⎦Ts7 = 31°C

( ) ( ) 11 101.325 15.755 9.80 0.985 m

= 8.86 mdZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.4. Third distillation heat exchanger

E.B.:

24 24 22 22 22 22

21 21 23 23

d d b b v v

b b v v

h h hh h

ψ ⋅ + ψ ⋅ + ψ ⋅= ψ ⋅ + ψ ⋅ (20)

M.B.:

22 22 21b v bψ + ψ = ψ (21)

22 15v vψ = ψ (22)

24 23d vψ = ψ (23)

22 22 1 1b b s sσ ⋅ ψ = σ ⋅ ψ (24)

B.H.:

24 3 24101.325 kPad d dg Z pρ ⋅ ⋅ = − (25)

↑ (23): Water vapour/air: ψv23 = ψv15 = 0.335 kg/s(operative assumption); Tv23 = 80°C (op-erative assumption); pv23 = 47.359 kPa; hv23= 2643.8 kJ/kg.

→ (21):Brine: ψb21 = ψb18 = 9.670 kg/s; Tb21 =unknown; pb21 = unknown; σb21 = σb18 =3.62; hb21 = unknown.At inlet (21), a fluid pressure regulatingdevice (valve/throttle) keeps pressure pb21at the required sub-atmospheric value cor-responding to temperature Tb21.

← (22):Water vapour/air: ψv22 = ψv15 = 0.335 kg/s;Tv22 = 70°C (operative assumption); pv22= 31.161 kPa; hv22 = 2626.8 kJ/kg.Brine: ψb22 = unknown; Tb22 = Tv22 = 70°C

(operative assumption); pb22 = pv22 =31.161 kPa; σb22 = unknown; hb22 = un-known.

↓ (24): Produced distilled water: ψd24 = ψv23 =0.335 kg/s; Td24 = 75°C (operative assump-tion); pd24 = 38.576 kPa; hd24 = 313.93 kJ/kg;ρd24 = 974.70 kg/m3; Zd3 = unknown.

Solution of Eqs. (20), (21), (24) and (25)yields:ψb22 = 9.335 kg/s

σb22 = 3.75

( )22 281.56 281.56 277.92 0.75 kJ/kg

= 278.83 kJ/kgbh = ⎡ − − ⋅ ⎤⎣ ⎦

( ) []

121 9.67 0.335 313.93 9.335 278.83

0.335 2626.8 0.335 2643.8 kJ/kg = 279.45 kJ/kg

bh −= ⋅ ⋅ + ⋅

+ ⋅ − ⋅

Tb21 = 70°C

( ) ( ) 13 101.325 38.576 9.80 0.974 m

= 6.57 mdZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.5. Second vacuum chamber

E.B.:


hv25 = hv22 (27)

hb26 = hb22 (28)

M.B.:

25 22v vψ = ψ (29)

26 22b bψ = ψ (30)

26 22b bσ = σ (31)

B.H.:

26 2 26101.325 kPab b bg Z pρ ⋅ ⋅ = − (32)



→ (22):Water vapour/air: ψv22 = ψv15 = 0.335 kg/s;Tv22 = 70°C; pv22 = 31.161 kPa; hv22 =2626.8 kJ/kg.Brine: ψb22 = 9.335 kg/s; Tb22 = Tv22 =70°C; pb22 = pv22 = 31.161 kPa; σb22 = 3.75;hb22 = 278.83 kJ/kg.

↓ (26): Brine: ψb26 = ψb22 = 9.335 kg/s; Tb26 = Tb22= 70°C; pb26 = pb22 = 31.161 kPa; σb26 =σb22 = 3.75; hb26 = hb22 = 278.83 kJ/kg; ρb26= 1019.95 kg/m3.


( ) ( ) 12 101.325 31.161 9.80 1.019 m

= 7.02 mbZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.6. Third vacuum chamber

E.B.:


hv31 = hv30 (34)

hb32 = hb30 (35)

M.B.:

31 30v vψ = ψ (36)

30 30 26b v bψ + ψ = ψ (37)

32 30b bψ = ψ (38)

30 30 1 1b b s sσ ⋅ ψ = σ ⋅ ψ (39)

32 30b bσ = σ (40)

B.H.:

32 3 32101.325 kPab b bg Z pρ ⋅ ⋅ = − (41)

↑ (31): Water vapour/air: ψv31= ψv23 = 0.335 kg/s;Tv31 = Tv23 = 80°C (operative assumption);

pv31 = pv23 = 47.359 kPa; hv31= hv23 =2643.8 kJ/kg.

← (30):Water vapour/air: ψv30 = ψv31 = 0.335 kg/s;Tv30 = Tv31 = 80°C (operative assumption);pv30 = pv31 = 47.359 kPa; hv30 = hv31 =2643.8 kJ/kg.Waste brine: ψb30 = unknown; Tb30 = Tv30= 80°C (operative assumption); pb30 = pv30= 47.359 kPa; σb30 = unknown; hb30 = un-known.

↓ (32): Waste brine: ψb32 = ψb30 = unknown; Tb32= Tb30 = 80°C; pb32 = pb30 = 47.359 kPa;σb32 = σb30 = unknown; hb32 = hb30 = un-known; ρb32 = ρb30 = unknown; Zb3 = un-known.

Solution of Eqs. (37), (39) and (41) yields:ψb30 = 9.000 kg/s

σb30 = 3.88

( )30 321.98 321.98 317.88 0.88

318.37 kJ/kgbh = ⎡ − − ⋅ ⎤⎣ ⎦

=ψb32 = ψb30 = 9.000 kg/s

σb32 = σb30 = 3.88

hb32 = hb30 = 318.37 kJ/kg

ρb32 = 1019.46 kg/m3

( ) ( ) 13 101.325 47.359 9.80 1.019 m

= 5.40 mbZ −⎡ ⎤= − ⋅ ⋅⎣ ⎦

3.2.7. Second waste brine/brine heat ex-changer

E.B.:

( ) ( )27 28 27 33 33 34b b b b b bh h h hψ ⋅ − = ψ ⋅ − (42)

M.B.:

28 27b bψ = ψ (43)

34 33b bψ = ψ (44)


28 27b bσ = σ (45)

34 33b bσ = σ (46)

↑ (28, 33): Brine: ψb28 = ψb26 = 9.335 kg/s; Tb28 =75°C (operative assumption); pb28 = un-known; σb28 = σb26 = 3.75; hb28 = [301.75– (301.75 – 297.86) · 0.75] kJ/kg =298.83 kJ/kg;Waste brine: ψb33 = ψb32 = 9.000 kg/s; Tb33= Tb32 = 80°C; pb33 = unknown; σb33 = σb32= 3.88; hb33 = hb32 = 318.37 kJ/kg.

↓ (27, 34): Brine: ψb27 = ψb26 = 9.335 kg/s; Tb27 =Tb26 = 70°C; pb27 = unknown; σb27 = σb26 =3.75; hb27 = hb26 = 278.83 kJ/kg.Waste brine: ψb34 = ψb33 = 9.000 kg/s; Tb34= unknown; pb34 = unknown; σb34 = σb33 =3.88; hb34 = unknown.


( ) ()

34 318.37 9.335 / 9.0 298.83

278.83 kJ/kg = 297.62 kJ/kgbh = ⎡ − ⋅⎣

− ⎤⎦Tb34 = 75°C

3.2.8. First waste brine/brine heat exchanger

E.B.:

( ) ( )19 20 19 35 35 36b b b b b bh h h hψ ⋅ − = ψ ⋅ − (47)

M.B.:

20 19b bψ = ψ (48)

36 35b bψ = ψ (49)

20 19b bσ = σ (50)

36 35b bσ = σ (51)

↑ (20, 35): Brine: ψb20 = ψb18 = 9.670 kg/s; Tb20 =Tb21 = 70°C; pb20 = unknown; σb20 = σb18 =3.62; hb20 = hb21 = 279.45 kJ/kg.

Waste brine: ψb35 = ψb32 = 9.000 kg/s; Tb35= Tb34 = 75°C; pb35 = unknown; σb35 = σb32= 3.88; hb35 = hb34 = 297.62 kJ/kg.

↓ (19, 36): Brine: ψb19 = ψb18 = 9.670 kg/s; Tb19 =Tb18 = 60°C; pb19 = unknown; σb19 = σb18 =3.62; hb19 = hb18 = 239.21 kJ/kg.Waste brine: ψb36 = ψb32 = 9.000 kg/s; Tb36= unknown; pb36 = unknown; σb36 = σb35 =3.88; hb36 = unknown.


[ ( ) ()

36 297.62 9.670 /9.0 279.45

239.21 kJ/kg = 254.38 kJ/kgbh = − ⋅

− ⎤⎦Tb36 = 62°C

3.2.9. Second waste brine/seawater heatexchanger

E.B.:

( ) ( )11 12 11 11 12 11s s s b b bh h h hψ ⋅ − = ψ ⋅ − (52)

M.B.:

12 11s sψ = ψ (53)

11 12b bψ = ψ (54)

12 11s sσ = σ (55)

11 12b bσ = σ (56)

↑ (11): Seawater: ψs11 = ψs8 = 10.000 kg/s; Ts11 =Ts8 = 50°C; ps11 = unknown; σs11 = σs8 =3.50; hs11 = hs8 = 199.50 kJ/kg.Waste brine: ψb11 = ψb32 = 9.000 kg/s; Tb11= unknown; pb11 = unknown; σb11 = σb32 =3.88; hb11 = unknown.

↓ (12): Seawater: ψs12 = ψs8 = 10.000 kg/s; Ts12 =Ts13 = 60°C; ps12 = unknown; σs12 = σs8 =3.50; hs12 = hs13 = 238.37 kJ/kg.Waste brine: ψb12 = ψb32 = 9.000 kg/s; Tb12= Tb36 = 62°C; pb12 = unknown; σb12 = σb32= 3.88; hb12 = hb36 = 254.38 kJ/kg.



( ) ()

11 254.38 10.0 / 9.0 238.37

199.50 kJ/kg=211.19 kJ/kgbh = ⎡ − ⋅⎣

− ⎤⎦Tb11 = 53°C

3.2.10. Produced fresh water/feed seawaterpre-heating heat exchanger

E.B.:

( ) ( )3 5 3 3 5 3s s s d d dh h h hψ ⋅ − = ψ ⋅ − (57)

5 5 10 10 16 16 24 24d d d d d d d dh h h hψ ⋅ = ψ ⋅ + ψ ⋅ + ψ ⋅ (58)

M.B.:

5 3s sψ = ψ (59)

3 5d dψ = ψ (60)

5 10 16 24d d d dψ = ψ + ψ + ψ (61)

5 3s sσ = σ (62)

↑ (1, 3):Seawater: ψs1 = 10.000 kg/s; Ts1 = Ts =15.0°C; ps1 = unknown; hs1 = 59.55 kJ/kg;σs1 = σs = 3.50; ψs3 = 3.000 kg/s (opera-tive assumption); Ts3 = Ts1 = 15.0°C; ps3 =unknown; σs3 = σs1 = 3.50; hs3 = hs1 =59.55 kJ/kg.Produced distilled water: ψd3 = 1.000 kg/s;Td3 = 20.0°C (operative assumption); pd3= unknown; hd3 = 83.86 kJ/kg.

↓ (5): Seawater: ψs5 = ψs3 = 3.000 kg/s; Ts5 =unknown; ps5 = unknown; σs5 = σs3 = 3.50;hs5 = unknown.Produced distilled water: ψd5 = ψd3 =1.000 kg/s; Td5 = unknown; pd5 = un-known; hd5 = unknown.

Solution of Eqs. (57) and (58) yields:

()

5 0.330 230.16 0.335 267.02

0.335 313.93 kJ/kg = 270.57 kJ/kgdh = ⋅ + ⋅

+ ⋅

Td5 = 65°C

( )5 59.55 0.333 270.57 83.86 kJ/kg

= 121.78 kJ/kgsh = ⎡ + ⋅ − ⎤⎣ ⎦

Ts5 = 31°C

3.2.11. Waste brine/feed seawater pre-heatingheat exchanger

E.B.:

( ) ( )2 4 2 2 4 2s s s b b bh h h hψ ⋅ − = ψ ⋅ − (63)

4 4 5 5 6 6s s s s s sh h hψ ⋅ + ψ ⋅ = ψ ⋅ (64)M.B.:

2 3 1s s sψ + ψ = ψ (65)

4 2s sψ = ψ (66)

2 4b bψ = ψ (67)

4 2s sσ = σ (68)

2 4b bσ = σ (69)

↑ (1, 2): Seawater: ψs1 = 10.000 kg/s; Ts1 = 15.0°C;ps1 = unknown; σs1 = 3.50; hs1 = 59.55 kJ/kg;ψs2 = unknown; Ts2 = Ts1 = 15.0°C; ps2 =unknown; σs2 = σs1 = 3.50; hs2 = hs1 =59.55 kJ/kg.Waste brine: ψb2 = ψb32 = 9.000 kg/s; Tb2= unknown; pb2 = unknown; σb2 = σb32 =3.88; hb2 = unknown.

↓ (4, 6): Seawater: ψs4 = unknown; Ts4 = unknown;ps4 = unknown; σs4 = σs1 = 3.50; hs4 = un-known.ψs6 = ψs4 + ψs5 = ψs1 = ψs7 = 10.000 kg/s;Ts6 = Ts7 = 31°C; ps6 = unknown; σs6 = σs1= 3.50; hs6 = hs7 = 120.98 kJ/kg.Waste brine: ψb4 = ψb32 = 9.000 kg/s; Tb4= Tb11 = 53°C; pb4 = unknown; σb4 = σb32 =3.88; hb4 = hb11 = 211.19 kJ/kg.

Solution of Eqs. (63)–(66) yields:ψs2 = 7.000 kg/s


ψs4 = 7.000 kg/s

( ) ( )14 7.0 10.0 120.98 3.0 121.78 kJ/kg

= 120.63 kJ/kgsh −= ⋅ ⋅ − ⋅

Ts4 = 30°C

( ) ()

12 211.19 7.0 9.0 120.63

59.55 kJ/kg = 163.68 kJ/kg

bh −⎡= − ⋅ ⋅⎣− ⎤⎦

Tb2 = 41°C

3.2.12. Solar collector field

E.B.:

30 30 30 30 29 29b b v v b bI A h h h⋅ = ψ ⋅ + ψ ⋅ − ψ ⋅ (70)

M.B.:

29 30 30b b vψ = ψ + ψ (71)I = 0.3 kW/m2; A = unknown

I.M. (29): Brine: ψb29 = ψb26 = 9.335 kg/s; Tb29 =Tb28 = 75°C (operative assumption); pb29= pv30 = 47.359 kPa; σb29 = σb26 = 3.75;hb29 = hb28 = 298.83 kJ/kg;

O.M. (30): Water vapour/air: ψv30 = ψv23 =0.335 kg/s; Tv30 = Tv23 = 80°C (operativeassumption); pv30 = pv23 = 47.359 kPa; hv30= hv23 = 2643.8 kJ/kg.Waste brine: ψb30 = 9.000 kg/s; Tb30 = Tv30= 80°C; pb30 = pv30 = 47.359 kPa; σb30 =3.88; hb30 = 318.37 kJ/kg.


( ) ()

1

2 2

0.3 9.0 318.37 0.335 2643.8

9.335 298.83 m 3204.7 m

A −= ⋅ ⋅ + ⋅

− ⋅ =

With the chosen operative parameters, the two-effect SW-SBD desalting plant may be expectedto produce ~36 m3/d of distilled water (in ~10work hours) with some 36 arrays of solar collec-tors.

4. SW–SBD energy efficiency and generalaspects

SW–SBD desalting technology is driven bysolar radiation but electric power is required forpumping all fluids of interest, feed seawater, pro-duced distilled water, brine and waste brine, andfor the functioning of general services and of theelectronic system which controls all plant opera-tions.

The electric energy requirements of SW–SBDdesalting plants of various layouts are relativelysmall due to the operational advantages of under-ground barometric circuits and to the fact that allpumps are low-head circulation pumps [2].

An approximate evaluation of pumping energyefficiency ∈p, i.e., pumping electric energy re-quired for one m3 of produced fresh water (ex-cluding feed seawater pumping from sea intaketo plant site, produced fresh water pumping tousers, waste brine pumping to a disposal site, andwater jet pumping in the deaerator system), hasbeen made for the two-effect SW–SBD plant.

Pumping energy efficiency ∈p (kWh/m3) isrepresented by the expression:

( ) ( )1 h / 3600 sp P dW∈ = ⋅ Φ ⋅ (4.1)

where WP is the required SW–SBD pumping elec-tric power and Φd is the produced fresh water flowrate.

Power WP is represented by the sum:

6 18 26 32 24

16 10 P Ps Pb Pb Pb Pd

Pd Pd

W W W W W WW W

= + + + ++ + (4.2)

where specific electric powers, WPs6–WPd10, con-cern the pumps shown in Fig. 2. WP is computedon the basis of practical assumptions; specifically,for each pump, any heat exchanger, relevant pip-ing, and eventual flow control device, are assumedto provide each an overall pressure drop of 10 kPa.The solar collector field is assumed to provide anoverall pressure drop of 20 kPa and all pumps areassumed to have the same pumping efficiency


coefficient η = 0.7. Sufficiently accurate evalua-tions for SW–SBD prototype plants would bepossible if the actual components were specified.

The specific electric powers of interest are thusrepresented by the approximate expressions:

( )( )( )( )( )( )( )

6 6 6

18 18 18

26 26 26

32 32 32

24 24 24

16 16 16

10 10 10

1/

1/

1/

1/

1/

1/

1/

Ps s s

Pb b b

Pb b b

Pb b b

Pd d d

Pd d d

Pd d d

W p

W p

W p

W p

W p

W p

W p

= η ⋅Φ ⋅ ∆

= η ⋅Φ ⋅ ∆

= η ⋅ Φ ⋅ ∆

= η ⋅ Φ ⋅ ∆

= η ⋅ Φ ⋅ ∆

= η ⋅ Φ ⋅ ∆

= η ⋅ Φ ⋅ ∆

(4.3)

With:Φs6 =

ψs6 /ρs6 = (10.000/1021) m3/s = 9.794 · 10–3 m3/s;∆ps6 = 50 kPa (1 pipe, 3 heat exchangers, 1 throttle);Φb18 = ψb18 /ρb18 = (9.670/1020) m3/s = 9.480·10–3m3/s;∆pb18 = 40 kPa (1 pipe, 2 heat exchangers, 1 throttle);Φb26 = ψb26 /ρb26 = (9.335/1019) m3/s = 9.160·10–3 m3/s;∆pb26 = 50 kPa (1 pipe, 1 heat exchanger, 1 throttle, solar collector drop);Φb32 = ψb32 /ρb32 = (9.000/1019) m3/s = 8.832 · 10–3 m3/s;∆pb32 = 50 kPa + ~101.325 kPa z 151.325 kPa (1 pipe, 4 heat exchangers);Φd24 = ψd24 /ρd24 = (0.335/974) m3/s = 3.439 · 10–4 m3/s;∆pd24 = 20 kPa (1 pipe, 1 heat exchanger);Φd16 = ψd16 /ρd16 = (0.335/980) m3/s = 3.418 · 10–4 m3/s;∆pd16 = 20 kPa (1 pipe, 1 heat exchanger);Φd10 = ψd10 /ρd10 = (0.330/985) m3/s = 3.350 ·10–4 m3/s;∆pd10 = 20 kPa (1 pipe, 1 heat exchanger);

With these values, one obtains:

( ) ( ) ( )( ) ( )( ) ( )( ) ( )

1 3 3

3 3

4 4

14

0.7 9.794 10 50 9.480 10 40

9.160 10 50 8.832 10 151.325

3.439 10 20 3.418 10 20

3.350 10 20 0.7 2.68 kW

= 3.82 kW

PW− − −

− −

− −

−−

=

⎡⋅ ⋅ ⋅ + ⋅ ⋅⎣

+ ⋅ ⋅ + ⋅ ⋅

+ ⋅ ⋅ + ⋅ ⋅

⎤+ ⋅ ⋅ = ⋅⎦

Thus, the expected pumping energy efficiencyis:

∈p = (3.82/3.6) kWh/m3 = 1.06 kWh/m3

Waste brine disposal is a potentially criticalenvironment issue for which adequate solutionswill have to be found to achieve satisfactory fieldimplementations of SW–SBD prototype plants.

The overall good energy efficiency of SW–SBD plants suggests useful couplings with anyavailable renewable energy sources so that SW–SBD desalting technology may be utilized also atcoast sites lacking an electric grid.

The performance ratio (defined as the ratiobetween the mass flow rate of product fresh wa-ter and the mass flow rate of heating vapour [8,9])is an important feature of desalting plants in whichseawater distillation is driven by heating steam.The performance ratios of the present one-effectand two-effect SW–SBD desalting plants are, re-spectively, (1.000/0.500) = 2.0 and (1.000/0.335)= 2.9: quite promising values considering themuch lower values of conventional (non solar)plants.

Without a working SW–SBD prototype plant,no direct quantitative evaluation of SW–SBDdesalting technology can be made. The Abu Dhabiplant [10] would be an important reference plantfor useful technology checks. Its 18-effect evapo-rator is designed for a rated distillate output of120 m3/d and a heat accumulator allows continu-


ous (day and night) operation. The actual plantproductivity shows large fluctuation, the yearlyaverage distillate production being some 80 m3/d.SW–SBD desalting technology appears to have asimpler design (without a heat accumulator sys-tem) and a larger energy efficiency. SW–SBDdistillate production would depend on the num-ber of effects which a SW–SBD plant design couldsuitably incorporate.

SW–SBD underground layout entails impor-tant operational and constructional advantageswhich compensate the burdens of excavationworks. Also, as mentioned in [2], undergroundshaded spaces may be very useful in sunny andarid sites.

In the design of SW–SBD plants, plastic com-ponents (in particular, pipes, pumps, and heat ex-changers) should be assumed as far as possible inview of avoiding (or greatly reducing) corrosionproblems and of achieving economic benefits.

Important technological features of SW–SBDplants concern their electronic control systemswhich must regulate plant productivity parameterson available solar radiation flux via inputs fromseveral specific sensors located at suitable posi-tions. Clearly, field research on prototype plantsis required to clarify all technological issues ofinterest.

5. Symbols and abbreviationsB.H. — Barometric heightE.B. — Energy balanceI.M. — Inlet manifoldsM.B. — Mass balanceO.M. — Outlet manifoldsA — Operative area of solar collector field,

m2

g — Gravitational acceleration, m s–2

h — Specific enthalpy, kJ/kgI — Mean operative solar radiation flux on

a horizontal surface, W/m2

p — Pressure, kPa

∆p — Fluid pressure drop, kPaT — Temperature, °CW — Electric power, WZ — Barometric height, m↑ — Top← — Left side↓ — Bottom→ — Right side

Greekη — Pumping efficiency coefficient∈ — Energy efficiency, kWh/m3 of produced

fresh waterρ — Density, kg/m3

σ — Salinity, mass %Φ — Flow rate, m3/sψ — Mass flow rate, kg/s

Subscriptsb — Brined — Fresh (distilled) waterp — Pumpings — Seawaterv — Vapour

References[1] M. Reali, G. Modica, A.M. El-Nashar and P. Marri,

Solar barometric distillation for seawater desaltingPart I: Basic layout and operational/technical fea-tures, Desalination, 161 (2004) 235–250.

[2] M. Reali, Solar barometric distillation for seawaterdesalting Part II: Analyses of one-stage and two-stage distillation technologies, Desalination, 190(2006) 29–42.

[3] M. Reali, Solar barometric distillation for seawaterdesalting Part III: Analyses of one-stage and two-stage solar vapour thermo-compression distillationtechnologies, Desalination, 207 (2007) 304–323.

[4] N.B. Vargaftic, Tables on the Thermophysical Prop-erties of Liquids and Gases in Normal and Dissoci-ated States. Hemisphere Publishing Corporation,London, 1975.

[5] L.A. Bromley, A.E. Diamond, E. Salami and D.G.Wilkins, Heat capacities and enthalpies of sea salt


solutions to 200°C, J. Chem. Eng. Data, 15(2) (1970)246–253.

[6] E.D. Howe, Distillation of seawater, in Solar En-ergy Technology Handbook, Part B, W.C. Dickinsonand P.N. Cheremisinoff, eds., Marcel Dekker, NewYork, 1980.

[7] D.J. Close, A design approach for solar processes,Solar Energy, 7 (1967) 112–122.

[8] K.S. Spiegler, Salt-Water Purification. 2nd ed., Ple-

num Press, New York, 1977.[9] H.T. El-Dessouky and M.H. Ettouney, Fundamen-

tals of Salt Water Desalination. Elsevier, Oxford,2002.

[10] A.M. El-Nashar and M. Samad, A solar asssistedseawater multiple effect distillation plant- 10 yearsof operating performance, Proc. IDA World Con-ference on Desalination and Water Sciences, AbuDhabi, 5 (1995) 451–473.

solar barometric distillation for seawater desalting part iv: analyses of one-effect and two-effect...

Documents