Appendix Water Properties

7/27/2019 Appendix Water Properties

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526 Appendix A Thermo dynam ic Proper t i es

A. 1. Seawater Density

The density correlation for seawater is given byp = 1 0 3 ( A i F i + A 2 F 2 + A 3 F 3 + A 4 F4 ) (A.1)wher e B = ((2)(X)/1000-150)/150G i = 0.5G2 = BG3 = 2 B2 - 1A i = 4.032219 G i + 0.115313 G2 + 3.26x10-4 G3A2 = - 0.108199 G i + 1.571x10-3 G2 - 4.23x1 0-4 G3A3 = - 0.012247 Gi + 1.74x10-3 G2 - 9x10 -6 G3A4 = 6.92x10-4 G i - 8.7x10-5 G2 - 5.3x10-5 G3A = ((2)(T) - 200 )/160F i = 0.5, F2 = A, F3 = 2 A2 - 1, F4 = 4 A3 - 3 A

In the above equat ions p is the seawater dens i ty in kg/m3, X is i s the seawatersal ini ty in ppm, an d T is the seaw ater te m pe ratu re in ^C. This correlat ion is val idover the following r an ge s: 0 < X < 160000 ppm an d 10 < T < 180 ^C. V aria tion s inthe se aw ater d ens i ty as a function of tem pe ratu re and sal ini ty are given in TableA.1 a nd Fig. A. 1.

Salinity, ppm- - 2 0 0 0 0- 4 - 30000- > ^ 40000--- 50000- - 6 0 0 0 0- ^ 7 0 0 0 0

T -40 60 80 100 120Tenperature, CFigure A. 1: Variation in density of seawater as a functionof tenperature and salinity.


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Appendix A Thermodynamic Properties 527

Table A . l : Variation in seawater density (kg/m^) as a function of temperature(oC) and salinity (ppm)

T(oC)101520253035404550556065707580859095100105110

10000100810071006100410031001999997995993990988985982979976973969966962958

20000101510141013101210101008100710041002999.9997.5994.9992.2989.3986.3983.2980976.7973.2969.6965.9

Salinity ppm30000102310221021101910181016101410121010100710051002999.5996.6993.7990.6987.4984980.6977973.3

40000103110301028102710251023102110191017101510121010100710041001997.9994.7991.4988984.4980.8

5000010381037103610341033103110291027102410221020101710141011100810051002998.8995.4991.9988.3

600001046104510441042104010381036103410321029102710241022101910161013101010061003999.3995.7

70000105410531051105010481046104410421039103710341032102910261023102010171014101010071003


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A.2. Seawater Specific Heat at Constant Pressure

The seawater specif ic heat at constant pressure is given by the followingcorrelat ionCp = (A + BT + CT2 + DT 3)xlO -3 (A.2)The var iables A, B, C and D are evaluated as a funct ion of the water sal ini ty asfollows:A = 4206.8 - 6.6197 s +1.2288x10-2 s2B = -1.1 26 2 + 5.4178x10-2 s - 2.2719x10-4 s2

C = 1.2026x10-2 - 5.3566x10-4 s + 1.8906x10-6 s2D = 6.8777xl0-'7 + 1.517x10-6 s - 4.4268x10-9 s2where Cp in kJ/kg ^C, T in ^C, and s is the water salinity in gm/kg. The abovecorrelat ion is val id over sal ini ty a nd tem pe ratu re ran ge s of 20000 < X < 160000pp m an d 20


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Appendix A Therm odynam ic Proper t i es 529

Table A.2: Variation in seawater specif ic heat (kJ/kg ^C) as a function oftemperature (^C) and salinity (ppm)

T(C)101520253035404550556065707580859095100105110

100004.144.134.134.134.134.134.134.134.134.134.134.144.144.144.154.154.154.164.174.174.18

200004.0784.0784.0784.0784.0784.0784.0794.084.0824.0834.0854.0874.094.0934.0974.1014.1054.114.1164.1224.129

Salinity p p m300004.0224.0234.0254.0264.0274.0294.034.0324.0334.0354.0384.044.0434.0464.054.0534.0584.0624.0684.0734.08

400003.9683.9713.9733.9763.9783.983.9823.9843.9863.9893.9913.9943.99744.0034.0074.0114.0154.024.0254.031

500003.9163.923.9233.9273.933.9333.9353.9383.943.9433.9453.9483.9513.9543.9573.9613.9643.9693.9733.9783.984

600003.8663.8713.8753.8793.8833.8873.893.8933.8953.8983.9013.9033.9063.9093.9123.9153.9193.9233.9273.9323.937

700003.8183.8243.8293.8343.8383.8423.8453.8493.8513.8543.8573.863.8623.8653.8683.8713.8743.8783.8823.8873.892


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A.3. Seawater Dynam ic Viscosity

The correlation for the dynamic viscosity of seawater is given by^ = ( M ( ^ R ) X 1 0 - 3 ( A . 3 )

wi t h Ln(|iw) = - 3.79418 + 604.129/(139.18+T)I ^ R = 1 + A s + B s 2A = 1.474x10-3 + 1.5x10-5 T - 3.927x10-8 T2B = 1.0734x10-5 - 8.5x10-8 T +2.23x10-10 T 2

wher e [i in kg/m s, T in ^C, and s in gm/kg. The above correlation is valid over thefollowing ra ng es 0 < s < 130 gm/kg an d 10 < T < 180 ^C. V aria tion s in th esea w ater viscos ity as a funct ion of tem pe ratu re and sa l ini ty are given in TableA.3 and Fig. A.3.

1 /^ ^1 .01.42 1.2 -1 ''-^. 0.81 0 . 6 -1 0 . 4 ^

0.2 -0.0 -

( 1 1 1 1 1) 20 40 60 80 100 i :

Salinity, ppm^ i - 2 0 0 0 0--A-30000^ ^ 4 0 0 0 0- - 50000- - -60000- h - 7 0 0 0 0

>0Tenperature, C

Figure A.3: Variation in viscosity of seawater as afunction of tenperature and salinity.


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Table A.3: V aria tion in sea w ate r viscosity (kg/m s) as a function of te m pe ra tu re(oC) and salinity (ppm)

T(oC)101520253035404550556065707580859095100105110

100001.311.151.020.910.820.740.670.610.560.520.480.440.410.390.360.340.320.30.290.270.26

200001.3381.1751.040.9280.8330.7530.6840.6250.5730.5290.4890.4550.4240.3970.3720.350.330.3130.2960.2820.268

Salinity pp300001.3651.1991.0620.9480.8510.770.70.639

0.5870.5410.5010.4660.4350.4070.3820.3590.3390.3210.3040.2890.275

400001.3951.2261.0860.9690.8710.7880.7160.6550.6010.5550.5140.4780.4460.4170.3920.3690.3480.3290.3120.2970.283

>m500001.4281.2551.1120.9930.8920.8070.7340.6710.6160.5690.5270.490.4570.4280.4020.3790.3570.3380.3210.3050.291

600001.4631.2861.141.0180.9150.8270.7530.6880.6320.5840.5410.5030.4690.4390.4130.3890.3670.3470.330.3130.298

700001.5

1.3191.1691.0440.9390.8490.7720.7060.6490.5990.5550.5160.4820.4510.4240.3990.3770.3570.3380.3220.307


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A.4. Seawater Therm al Conductivity

The seawater thermal conduct ivi ty is given byL og i o ( k ) = L og i o ( 240 + As )+0.434 2.3- 3 4 3 . 5 + B s ^^ T +2 73 .15 Y^^6 4 7.3 + C s .

(A.4)V+ 273 . 15 ,where k is the thermal conductivity in W/m ^C, s is the salinity in gm/kg, T is thete m pe ra tu re in ^C. The co nst an ts A, B, and C are eq ua l to 2x10-4, 3.7x10-2, an d

3x10-2, respectively. The above correlation valid over the following ranges, 0 < s


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Appendix A Thermo dynam ic Proper t i es 533

Table A.4: Variation in seawater thermal conductivity (kW/m^C) as atemperature (C) and salinity (gm/kg)

T(oC)101520253035404550556065707580859095100105110

100.58770.59550.6030.61

0.61680.62310.62910.63470.64010.6450.64970.6540.6580.66160.6650.66810.67080.67330.67540.67730.6789

200.58720.5950.60240.60950.61620.62260.62860.63430.63960.64460.64920.65350.65750.66120.66460.66770.67040.67290.67510.6770.6786

Salinity (gm/kg)30

0.58660.59440.60190.6090.61570.62210.62810.63380.63910.64410.64880.65310.65710.66080.66420.66730.67010.67250.67470.67660.6783

400.5860.59390.60130.60840.61520.62160.62760.63330.63860.64360.64830.65270.65670.66040.66380.66690.66970.67220.67440.67630.6779

500.58550.59330.60080.60790.61470.6210.62710.63280.63810.64320.64780.65220.65630.66

0.66340.66650.66930.67180.6740.6760.6776

600.58490.59280.60030.60740.61410.62050.62660.63230.63770.64270.64740.65180.65580.65960.6630.66610.66890.67150.67370.67560.6773

function of

700.58440.59220.59970.60680.61360.62

0.62610.63180.63720.64220.64690.65130.65540.65910.66260.66570.66860.67110.67330.67530.677


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A.5. Enthalpy of Saturated Liquid Wa ter

The correlat ion for entha lpy of sa tur ate d l iquid wa ter i s given byH = - 0.033635409 + 4.207557011 T - 6.200339x10-4 T2+ 4.459 374x 10-6 T^ (A.5)In the above equat ion, T is the saturat ion temperature in C and H is theenthalpy in kJ /kg. Values for the calculated enthalpy over a temperature range of5-200 ^C are given in Table A.5. The table also includes values extracted from thes team tables . The percentage er rors for the calculated versus the s team tablevalues are less than 0.04%. Figure A.5 show var iat ions in the calculated and thes team tables values for the l iquid water enthalpy as a funct ion of temperature .

sS.^

Entha^)yfromSteamTables (kJ/kg)Cafculated Entha^y(kJ/kg)

0 20 40 60 80 100 120 140 160 180 200 220Tenperature, CFigure A.5: Variation in entha^y of liquid water as afunction of tenperature.


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Table A. 5: Variat ion in l iquid water enthalpy (kJ /kg) as a funct ion of temperature(C).

T(C)5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

CalculatedEnthalpy (kJ/kg)

20.9892141.9843962.9552683.90517104.8374125.7554146.6625167.562188.4572209.3516230.2483251.1509272.0626292.9868313.9267334.8859355.8676376.8751397.9118418.9811440.0863461.2307482.4176503.6505524.9327546.2674567.6582589.1082610.6209632.1995653.8475675.5682697.3649719.241741.1998763.2446785.3788807.6058829.9289852.3514

Enthalpy from SteamTables (kJ/kg)

20.9841.9962.9883.94104.87125.77146.66167.54188.42209.31230.2251.11272.03292.96313.91334.88355.88376.9397.94419.02440.13461.27482.46503.69524.96546.29567.67589.11610.61632.18653.82675.53697.32719.2741.16763.21785.36807.61829.96852.43

PercentageError

0.0438810.0133590.0392780.0414980.0310420.0115710.0017140.0131260.0197550.0198520.0209930.0162830.0119780.0091330.0053350.0017640.003490.0066050.0070790.0092830.0099380.008530.0087830.0078390.0052050.0041280.0020830.0003050.0017820.0030910.0042120.0056570.0064410.0056990.0053650.0045340.0023990.0005170.0037470.00922


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536 Appendix A Therm odynam ic Proper t i es

A.6. Enthalpy of Saturated Water Vapor

The correlation for the water vapor enthalpy is given byH" = 2501.689 845 + 1.806916015 T + 5.087717 x10-4 T2- 1.1221x10-5 T3 (A.6)In the above equat ion, T is the saturat ion temperature in C and H" is the vaporenthalpy in kJ /kg. Values for the calculated enthalpy over a temperature range of0.01-200 ^C are given in Table A.6. The table also includes values extracted fromthe s team tables . The percentage er rors for the calculated versus the s team table

values are less than 0.017%. Figure A.6 show var iat ions in the calculated and thes tea m tab le values for the en thalp y of w ate r vapor as a function of tem pe rat ur e .

sIo>

285028002750270026502600255025002450

Calculated Entha^)y(kJ/kg) Entha^)y from SteamTables (kJ/kg)

I I I I I I I I I I0 20 40 60 80 100 120 140 160 180 200 220!

Tenperature, ^CFigure A.6 : Variation in ent ha^ y o f water vap or as afimction of tenperature.


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Table A.6: Va r iat ion in wat er vapor enth alpy (kJ/kg) as a function of tem pe rat ureCO T(C)

OOl5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

CalculatedEnthalpy (kJ/kg)

2501.7082510.7362519.7992528.872537.9422547.0052556.0522565.0742574.0622583.0092591.9052600.7422609.5132618.2072626.8182635.3372643.7542652.0632660.2532668.3182676.2482684.0362691.6722699.1482706.4562713.5882720.5352727.2882733.842740.1812746.3042752.22757.862763.2762768.442773.3442777.9782782.3352786.4062790.1822793.656

Enthalpy fromSteam Tables (kJ/kg)

2501.352510.542519.742528.912538.062547.172556.252565.282574.262583.192592.062600.862609.592618.242626.82635.282643.662651.932660.092668.132676.052683.832691.472698.962706.32713.462720.462727.262733.872740.262746.442752.392758.092763.532768.72773.582778.162782.432786.372789.962793.18

PercentageError

0.0143090.0077970.0023280.0015740.0046530.0064620.0077360.0080280.0076770.0070140.0059820.0045230.0029640.0012460.0006910.0021460.0035610.0049970.0061370.0070440.0074060.0076590.0074920.0069660.0057730.0047150.0027460.001030.0011090.0028810.0049580.0069180.0083440.009180.0093750.0085130.0065430.0034130.0012890.0079720.017047


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A. 7. Latent Heat of Water Evaporation

The correlation for latent heat of water evaporation is given byX = 2501.897149 - 2.407064037 T + 1.192217x10-3 T2- 1.5863x10-5 T3 (A.7)In the above equat ion, T is the saturat ion temperature in C an d X i s the la tentheat in kJ /kg. Values for the calculated enthalpy over a temperature range of 5-200 C are given in Table A.7. The table also includes values extracted from thes team tables . The percentage er rors for the calculated versus the s team table

values are less than 0.026%. Figure A.7 show var iat ions in the calculated and thes tea m ta ble value s for the la t en t hea t of w ate r as a function of tem pe rat ur e .


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Table A.7: Variation in latent heat of water evaporation in (kJ/kg) as a functionof temperature (^C)

T(oC)5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

Calculated LatentHeat (kJ/kg)

2489.892477.932466.0062454.1062442.2182430.332418.432406.5072394.5482382.5422370.4762358.3392346.1192333.8042321.3812308.842296.1692283.3542270.3852257.252243.9362230.4322216.7262202.8062188.662174.2762159.6432144.7482129.5792114.1252098.3732082.3132065.9312049.2162032.1572014.741996.9551978.791960.2321941.269

Latent Heat fromSteam Tables (kJ/kg)

2489.562477.752465.932454.122442.32430.482418.622406.722394.772382.752370.662358.482346.212333.842321.372308.782296.052283.192270.192257.032243.72230.22216.52202.612188.52174.172159.592144.762129.652114.262098.572082.562066.212049.52032.422014.951997.071978.761960

1940.75

PercentageError

0.0132410.0072590.0030780.0005770.0033650.0061750.0078450.0088540.0092710.0087460.0077670.0059840.003890.0015630.0004890.0026140.0051660.0071920.0086020.0097430.0105280.0104150.0102060.0089040.0073160.0048880.0024410.000580.003340.0063950.0093690.011870.0134990.0138380.012950.0104020.0057420.0014990.0118120.026741


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A.8. Entropy of Saturated Liquid Wa ter

The correlation for entropy of saturated Hquid water is given byS = - 0.00057846 + 0.015297489 T - 2.63129x10-5 T2+ 4.119 59x 10-8 T3 (A.8)In the above equat ion, T is the saturat ion temperature in C and S is the entropyof sa tur ate d l iquid wate r in kJ /k g ^C. Valu es for the ca lculated en tropy over at emper a t u r e r ange o f 5-200 ^C are given in Table A.8. The table also includesvalues extracted f rom the s team tables . The percentage er rors for the calculatedversus the s team table values are less than 0.4%. Figure A.8 show var iat ions inthe calculated and the s team table values for the saturat ion entropy of watervapor as a funct ion of temperature .

I

2.5

1.51

0.50

0

- EntropyfromSteamTables (kJ/kgK ) Cabulated Entropy(kJ/kgK)

40 2000 120 160Temprature (^C)

Figure A.8: Variation in entropy of saturated liquid wateras afimctionof tenperature

240!


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Table A.8: Var iat ion in the entropy offunction of te m pe ra tu re ("C)

saturated Hquid water (kJ /kg ^C) as aT ( o C ) Entropy fromSteam Table(kJ /kg ^C)

CalculatedEntropy (kJ/kg ^C) PercentageError101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

0.1498060.2231030.2951760.3660570.4357770.5043670.5718570.6382790.7036630.7680410.8314430.8939

0.9554431.0161031.075911.1348971.1930931.2505291.3072371.3632471.4185911.4732981.5274011.5809291.6339141.6863871.7383791.7899191.8410411.8917731.9421481.9921952.0419472.0914342.1406862.1897352.2386112.2873462.33597

0.1510.22450.29660.36730.43690.50520.57240.63860.70370.76790.83110.89340.95481.01541.07521.13421.19241.251.3068

1.36291.41841.47331.52751.58121.63431.68691.7391.79061.84171.89241.94261.99242.04182.09092.13952.18782.23582.28352.3308

0.7905060.622490.4802

0.3384460.2570640.164960.0948650.0502830.0052270.0183450.0412390.0559350.0673160.0691990.0660680.0614350.0581030.0423480.0334620.0254970.0134590.0001090.0064890.0171240.0235960.0304

0.0357350.0380090.0358020.0331270.0232810.0102670.0072030.0255190.0554250.0884310.1257320.1684250.22182


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A. 9. Entropy of Saturated Water Vapor

The correlation for entropy of saturated water vapor is given byS = 9.149505306 - 2.581012 xlO-2 T + 9.625687x10-^ T2- 1.7866 15x1 0-7 T3 (A.9)In the above equat ion, T is the saturat ion temperature in C and S is the entropyof saturated water vapor in kJ /kg K. Values for the calculated entropy over atem pe rat ur e rang e of 0 .01-200 ^C are given in Table A.9. The table a lso includesvalues extracted f rom the s team tables . The percentage er rors for the calculatedversus the s team table values are less than 0.4%. Figure A.9 show var iat ions inthe calculated and the s team table values for the saturat ion entropy of watervapor as a funct ion of temperature .

GO

Io>

10

0

- EntropyfromSteamTable (k J/kgK)- Calculated Entropy(kJ/kgK)

40 2000 120 160Tenprature (^C)

Figure A.9: Variation in entropy of saturated water vaporas afimctbnof tenperature

240


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A p p e n d i x A T h e r m o d y n a m i c P r o p e r t i e s 5 4 3

T a b l e A . 9 : V a r i a t i o n i n t h e e n t r o p yf u n c ti o n of t e m p e r a t u r e (QQ)

of s a t u r a t e d w a t e r v a p o r ( k J / k g K ) a s aT (C) En tro py fromSteam Tab le (kJ /kg Ca lcu la t ed"C) En trop y (kJ/kg K) Pe r c e n t a g eE r r o r0.015101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

9.15629.02578.90078.78138.66718.55798.45338.3538.25698.16478.07627.99127.90957.83097.75527.68247.61217.54447.4797.41587.35487.29587.23867.18327.12957.07747.02696.9776.92986.88326.83786.79346.75016.70786.66636.62566.58576.54646.50786.46976.4322

9.149259.022848.900858.783418.670388.561628.457018.356418.259688.166698.077317.991407.908837.829477.753177.679827.609267.541387.476037.413087.352407.293857.237307.182627.129667.078317.028416.979856.932486.886176.840786.796196.752266.708866.665846.623096.580456.537816.495026.451956.40846

0.075940.031700.001700.024010.037800.043480.043880.040770.033630.024370.013730.002510.008450.018290.026120.033610.037250.040030.039700.036650.032630.026710.017940.008120.002280.012790.021500.040790.038610.043090.043640.041130.032060.015780.006840.037940.079690.131280.196450.274420.36903


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A.10. Saturation Pressure of Wa ter Vapor

The correlat ion for the water vapor saturat ion pressure is given by l )Ef i (0 .01(T +273.15-338 .15) )^ ' "^ )i = ll n ( P / P c ) = ( T + 273.15 (A.10)where Tc = 647.286 K and Pc = 22089 kPa and the values of f i are given in the

following tablesfl-7.419242f50.001094098

k0.29721k-0 .00439993f3-0.1155286f70.002520658

f40.008685635fs-0.000521868

w her e P is kP a a nd T is ^C. V alues for the c alcula ted vap or pre ssu re over atempera ture r ange of 5-200 ^C are given in table A.10. The table also includesvalues extracted f rom the s team tables . The percentage er rors for the calculatedversus the s team table values are less than 0.05%. Figure A.10 shows var iat ionsin the calculated and the s team table values for the vapor pressure of water as afunct ion of temperature .

Tenperature, CFigure A. 10: Variation in saturation pressure of water

vapor as a function of tenperature.


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Appendix A Therm odynam ic Proper ties 545

Table A. 10: Var iation in satu ra tio n pres sure of wa ter vapor (kPa) as a function oftemperature (C)

T (C) Calculated Pressure from PercentagePressure (kPa) Steam Tables (kPa) Error

5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

0.8721.2281.7052.3393.1694.2465.6287.3849.59312.34915.75819.94025.03331.18838.57747.38957.83370.13884.552101.348120.817143.275169.059198.529232.069270.086313.007361.287415.399475.843543.137617.825700.471791.663892.0081002.1351122.6951254.3611397.8231553.795

0.87211.22761.7052.3393.1694.2465.6287.3849.59312.3515.75819.94125.0331.1938.5847.3957.8370.1484.55101.3120.8143.3169.1198.5232.1270.1313361.3415.4475.9543.1617.8700.5791.7892

1002.21122.71254.41397.81553.8

1.04E-041.23E-033.76E-032.12E-021.61E-035.81E-048.74E-045.03E-032.26E-035.41E-038.65E-042.93E-031.05E-026.73E-037.77E-031.63E-035.57E-033.22E-032.72E-034.72E-021.40E-021.77E-022.45E-021.46E-021.32E-025.30E-032.39E-033.59E-031.34E-041.21E-026.79E-034.03E-034.08E-034.68E-038.53E-046.50E-034.07E-043.13E-031.65E-032.95E-04


22/74

546 Appendix A Thermod ynam ic Proper t i es

A.11, Saturation Temperature of Water Vapor

The correlat ion for the saturat ion temperature of water vapor is given byT = 42.6776- 3892.7 273.15 (A.11)( ln (P /1000) -9 .48654) j

w he re P is in kPa an d T is in ^C. Va lues for the c alcula ted sa tu ra tio ntemperature over a pressure range of 0 .8721-1553.8 kPa and a temperaturerange of 5-200 ^C are given in Table A .11. The tab le also includ es v alu esextracted f rom the s team tables . The percentage er rors for the calculated versusthe s team table values are less than 0.28%. Figure A.11 shows var iat ions in thecalculated and the s team table values for the vapor pressure of water as afunct ion of temperature .

250

U2^

1C/5

oO&>^

1.5010050

200 H

0

- TenperaturefromSteamTables (oC)- Calculated Tenperature (oC)500 1000 1500 2000

Saturation Pressure of Water Vapor, kPaFigure A. 11: Variation in saturation temperature of watervapor saturation tenperature as a function of saturationpressure.


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A p p e n d i x A T h e r m o d y n a m i c P r o p e r t i e s 5 4 7

T a b l e A . 11 : V a r i a t i o nof s a t u r a t i o n p r e s s u r e

i n s a t u r a t i o n t e m p e r a t u r e o f w a t e r v a p o r (^C) a s a f u n c t i o n( k P a )P (kPa) Calcu la tedTempera tu re ( C) Tempera tu re f romSteam Tables (C) Pe r c e n t a g eE r r o r

0.87211.22761.7052.3393.1694.2465.6287.3849.59312.3515.75819.94125.0331.1938.5847.3957.8370.1484.55101.3120.8143.3169.1198.5232.1270.1313361.3415.4475.9543.1617.8700.5791.78921002.21122.71254.41397.81553.8

5.0043119.97751514.9576619.9494224.9393729.9381734.9412439.9482644.9558849.9685854.9800559.9947165.0061970.0247975.0396180.0521785.0635590.0779595.08715100.0839105.1006110.1155115.1213120.1106125.1186130.1129135.1048140.0991145.0877150.0796155.0579160.0422165.0267170.0065174.9822179.962184.9349189.9109194.883199.8582

5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

0.0862230.2248470.2822490.2528870.2425020.2060980.1678990.1293380.0980350.0628490.0362680.0088190.0095230.0354120.0528140.0652120.0747650.0866120.0917390.0838970.0957970.105

0.1054740.0921290.0948930.0868680.0776510.0707570.0604510.0530850.0373460.0263440.0161660.003820.0101920.0211340.0352

0.0468960.0599820.070913


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A. 12. Specific V olume of Saturated Water Vapor

The correlation for the specif ic volume of saturated water vapor is given byV = Ve(- - l ) exp(Ef i (T + 273 .15 /^ -^^ ) (A. 12)T + 273 .15 i=i

where Tc = 647.286 K and Vg = 0.003172222 m^/kg and the values of f i are givenin the following tablesf U t U83.63213098 -0.668265339 0.002495964 5.04185E-06 5.34205E-09 -2.3279E-12w her e V is in m^/kg an d T is in ^C. Va lues for the ca lculate d s at ur at io n vap orvolumes over a temperature range of 5-200 ^C are given in Table A. 12. The tablealso includes values extracted f rom the s team tables . The percentage er rors forthe calculated versus the s team table values are less than 0.025%. Figure A. 12shows var iat ions in the calculated and the s team table values for the saturat ionvolume of w ate r vapor as a function of tem pe ratu re .

o>oP H

o>

Specific Volume fi-omSteam Tables (m3/kg)Cabulated SpecificVolume (m3/kg)

150 180 2101Ten5)erature, CFigure A. 12: Variation in water vapo r specific volume a s

a fimction of tertperature.


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Table A. 12: Variationtemperature ("C)

T(C)

5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

in water vapor specCalculated SpecificVolume (m^/kg)

147.07980106.3793377.9366457.7998243.3655732.8960125.2161919.5219815.2566012.030259.567037.669726.195915.041824.131133.407222.827742.360781.982091.673111.419531.210271.036660.891890.770590.668480.582130.508800.446270.392730.346720.307030.272680.242830.216820.194070.174120.156560.141060.12733

:ific volume (m^/kg) asSpecific Volume fromSteam Tables (m^/kg)

147.117106.37677.92557.789743.359332.893225.215819.522915.258112.03189.568357.670716.196565.042174.131233.407152.827572.360561.981861.67291.419361.210141.036580.891860.770590.66850.582170.508850.446320.392780.346760.307060.272690.242830.21680.194050.174090.156540.141050.12736

a function oPercentage

Error0.0252850.0031320.0149370.0175170.0144560.0085510.0015420.0047350.0098040.0129110.0137870.0128930.0104320.006860.0024240.0019640.0060850.0094430.0115820.0122670.0119620.0106490.0076420.0037960.0002860.0034840.0072390.0103240.0121890.0126980.0112

0.0083630.0042590.0017030.0100160.0127250.0168590.0115310.0041380.023873


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A. 13 . Specific Volum e of Saturated Liquid Wa ter

The correlation for the specif ic volume of saturated l iquid water is given by^ = ^ C ( T . S O - . ^ - ^ ) exp( i;fi(T + 273.15/i-^>) (A.13)

where Tc = 647.286 K and V^ = 0.003172222 m^/kg and the values of f i are givenin the following tables

f l-2.781015567 f20.002543267 f39.845047E-06 U3.636115E-09 fs-5.358938E-11 fe7.019341E-14In th e abo ve equ atio n V is in m^/kg and T is in ^C. V alue s for the calc ulate dsa tur a t ion vo lumes over a t em pera ture r ange of 5-200 ^C are given in Tab le A .13.The table a lso includes values extracted f rom the s team tables . The percentageerrors for the calculated versus the s team table values are less than 0.05%.Figure A.13 shows var iat ions in the calculated and the s team table values for thesaturat ion volume of l iquid water as a funct ion of temperature .

O>P H

IH-1

0.001180.001160.001140.00112

0.00110.001080.001060.001040.001020.0010.00098

- Specific Volume fi-omSteam Tables (m3/kg)- Calculated SpecificVolume (mS/kg)

0 30 60 90 120 150 180 2101Tenperature, C

Figure A. 13: Variation in liquid water specific volume as afiinction of tenperature.


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Table A. 13:temperature

T(oC)

5101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200

Variation in liquid water(C)

Calculated SpecificVolume (m^/kg)

0.0010000.0010000.0010010.0010020.0010030.0010040.0010060.0010080.0010100.0010120.0010150.0010170.0010200.0010230.0010260.0010290.0010330.0010360.0010400.0010440.0010480.0010520.0010560.0010600.0010650.0010700.0010750.0010800.0010850.0010900.0010960.0011020.0011080.0011140.0011210.0011270.0011340.0011410.0011490.001156

specific volume (m^/kg^

Specific Volume fi^omSteam Tables (m^/kg)

0.0010.001

0.0010010.0010020.0010030.0010040.0010060.0010080.001010.0010120.0010150.0010170.001020.0010230.0010260.0010290.0010320.0010360.001040.0010440.0010470.0010520.0010560.001060.0010650.001070.0010750.001080.0010850.001090.0010960.0011020.0011080.0011140.0011210.0011270.0011340.0011410.0011490.001156

) as a function oPercentage

Error0.0138680.0244330.0094360.0170428.72E-050.0405410.0035180.0124340.0084560.0144150.0433320.0147570.0089140.0164660.0085020.0144660.0520130.0071740.0230630.0389210.0549270.0280040.0012940.0396540.000990.0223610.0302030.0222940.0016490.0419440.0076010.0088340.0070620.0132030.0370270.0213950.010660.0200230.0376980.011881


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Table A. 14:t e m p e r a t u r e

Variation in l iquid water dynamic viscosity as a function ofT (oC) Calc ulate d Dy nam icViscosity (N.s/m^)xlO^ M eas u r ed Dynami cViscosity (N.s/m^)xlO^ Percen tageE r r o r11.8516.8521.8526.8531.8536.8541.8546.8551.8556.8561.8566.8571.8576.8581.8586.8591.8596.85100101.85106.85111.85

1228.6051080.795958.3665855.9817769.6022696.1335633.1779578.8578531.6884490.4848454.2936422.3411393.9953368.7358346.1318325.8241307.5116290.9404281.2965275.8956262.194249.679

12251080959855769695631577528489453420389365343324306289279274260248

0.2943070.0736430.0660610.114820.0783040.163090.3451520.3219770.6985610.303650.2855610.5574071.2841271.0235060.9130620.5629930.4939790.6714310.8231290.6918320.8438540.677015


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A. 15. Dynam ic Viscosity of Saturated Water Vapor

The correlation for the dynamic viscosity of saturated water vapor is given by|Li = exp(-3.609417664 + 275.928958/( -227.0446083-0.8960 8123 2T-0 .00229 1383 T2)) x 10-3 (A. 15)wher e |LI in kg/m s, and T in ^C. Th e above c orre latio n is valid ov er th e followinga tem pe rat ure rang e of 10-180 ^C. Va r iat ions in the sa tur ate d wa ter dyna micviscosity as a function of temperature are given in Table A. 15 and Fig. A. 15.

13 112 H1110

7 H

0

- Calculated- Measured

20 1000 60 80Tenprature (C)

Figure A. 15: Variation in dynamic viscosity of saturatedwater vapor as a function of tenperature

120


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Table A. 15 : Variat ion in the dynamic viscos i ty of saturated water vapor as afunct ion of temperature .

T(oC)iL856.8511.8516.8521.8526.8531.8536.8541.8546.8551.8556.8561.8566.8571.8576.8581.8586.8591.8596.85100

101.85106.85111.85

Calculated Dy nami cViscosity (N.s/m^)xlO^

8.1001363758.2942848928.4900835628.6873225228.8857954929.0853003919.2856398879.4866218889.6880599779.8897737910.0915893310.2933392510.4948630210.6960071410.8966252311.0965780911.2957337311.493967411.6911614711.8872054412.0100757212.0819957612.2754357712.46743551

Measured Dynami cViscosity (N.s/m^)xlO^

8.098.298.498.698.899.099.299.499.699.8910.0910.2910.4910.6910.8911.0911.2911.4911.6911.8912.0212.0912.2912.49

PercentageError

0.1252950.0516870.0009840.0308110.0472950.0517010.0469330.0355970.0200210.0022870.0157520.0324510.0463590.0561940.0608380.0593150.0507860.0345290.0099360.0235030.0825650.0662050.1185050.18066


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A.16. Surface Tension of Saturated Liquid Water

The correlation for the surface tension is given bya = 7.5798x10-2 - 1.4691x10-4 T - 2.2173xlO-'7 T2 (A.16)wher e a in N/m, and T in ^C. The above correlation is valid over the following atem pe rat ur e ran ge of 0-136 ^C. Va r iat ions in the sa tur ate d wa ter surface te ns ionas a function of temperature are given in Table A.16 and Fig. A.16.

60 90Tenperature (^C)

150

Fig ure A.16: V aria tion in surface tension of sa tu ra te d l iquid w ate r as a functionof t empe r a t u r e .


33/74

Appendix A Thermodynamic Properties 557

Table A. 16: Variation in the surface tension of saturated liquid water as afunction of temperature.T(oC)01.856.8511.8516.8521.8526.85

31.8536.8541.8546.8551.8556.8561.8566.8571.8576.8581.8586.8591.8596.85100101.85106.85111.85116.85126.85136.85

Measured7.55E-027.53E-027.48E-027.43E-027.37E-027.27E-027.17E.027.09E-027.00E-026.92E-026.83E-026.75E-026.66E-026.58E-026.49E-026.41E-026.32E-026.23E-026.14E-026.05E-025.95E-025.89E-025.86E-025.76E-025.66E-025.56E-025.36E-025.15E-02

Correlation7.58E-027.55E-027.48E-027.40E-027.33E-027.25E-027.17E-027.09E-027.01E-026.93E-026.84E-026.76E-026.67E-026.59E-026.50E-026.41E-026.32E-026.23E-026.14E-026.04E-025.95E-025.89E-025.85E-025.76E-025.66E-025.56E-025.36E-025.15E-02

error%3.95E-013.00E-012.47E-023.68E-015.97E-012.99E-018.63E-038.22E-031.19E-018.91E-021.88E-011.26E-011.95E-019.65E-021.33E-013.23E-032.36E-031.93E-025.47E-02l.lOE-011.69E-021.75E-02l . l lE-015.35E-021.39E-027.28E-03l.OlE-027.91E-02


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A.17. Enthalpy of LiBr Water Solution

The enthalpy correlat ion for saturated LiBr-H20 solut ion is given byH(X, T) = X E aiT^ + (1 - X) i biT^

(A.17)+ X ( 1 - X ) I I C i j( 2X - l) ^T J

i =O j =0where X is the mass f ract ion of LiBr and T is the solut ion temperature . Theconstants in the above relation are as follows:ao = 508.668, ai = 18.6241, a2 = 0.0985946, SL ^ = -2 .500979x10-5 ,

a4 = 4.15801x10-8, b i = 1.617155702, ba = 4.10187485, h^ = 0.000717667,Coo = - 1021.61, Cio = -5 33 .0 8, C20 = 4 83.6 28, C30 = 1155.13, C40 = 640.622,coi = 36.8773, c ^ = 40.2847, C21 = 39.9142, C31 = 33.3572, C41 = 13.1032,C02 = - 0.1 86 05 1, C12 = - 0.19 11 98, C22 = 0.1992 13, C32 = - 0.178 258 ,C42 = - 0.07 75 101 , Cos = - 7.5 12 77 E-6 , C13 = 0, C23 = 0, C33 = 0, C43 = 0

The enthalpy of the saturated LiBr solut ion are shown in Table A.17 and Fig.A.17 for a tem pe ra tu re ran ge of 10-170 ^C an d LiBr m as s fraction of 0.25-0.75.

60005000

^ 4000

J 300020001000

50 100 150Tenperature (^C)

200

Fig. A.17. Variation in the enthalpy of LiBr solution as afunction of tem pe ratu re an d mas s f ract ion


35/74

559

Table A.17: Variation in enthalpy of sa tur ated LiBr solution as a function of temLiBr mass fraction

T PC) 0.25 0.3 0.35 0.4 0.45 0.5 0.5510 113.11 127.53 142.71 159.68 180.03 205.86 239.515 176.27 198.39 221.34 246.24 274.78 309.13 351.620 240.44 270.01 300.47 333.1 369.71 412.53 463.925 305.64 342.4 380.12 420.26 464.8 516.05 576.330 371.85 415.54 460.26 507.72 560.04 619.67 688.935 439.07 489.43 540.9 595.45 655.43 723.39 801.740 507.3 564.07 622.02 683.46 750.95 827.19 914.545 576.53 639.44 703.63 771.74 846.61 931.08 1027.50 646.75 715.55 785.71 860.28 942.39 1035 1140.55 717.97 792.38 868.26 949.07 1038.3 1139.1 125460 790.17 869.94 951.27 1038.1 1134.3 1243.2 1367.65 863.36 948.22 1034.7 1127.4 1230.4 1347.3 1480.70 937.53 1027.2 1118.7 1216.9 1326.6 1451.5 1594.75 1012.7 1106.9 1203 1306.7 1422.9 1555.7 1707.80 1088.8 1187.3 1287.8 1396.7 1519.2 1659.9 1821.85 1165.9 1268.4 1373.1 1486.9 1615.7 1764.2 1935.90 1243.9 1350.3 1458.8 1577.3 1712.2 1868.5 2049.95 1323 1432.8 1544.9 1667.9 1808.8 1972.8 2162.


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Table A.17 (continued): Variation in enthalpy of saturated LiBr solution as a fmass fractionLiBr mass fraction

T (OC) 0.25 0.3 0.35 0.4 0.45 0.5 0.55100105110115120125130135140145150155160165170

1402.91483.91565.81648.61732.41817.11902.81989.52077.12165.62255

2345.42436.82529.12622.3

15161599.81684.41769.71855.61942.22029.52117.42206.12295.42385.32476

2567.32659.32751.9

1631.41718.41805.81893.61981.82070.42159.52248.92338.82429

2519.72610.72702.22794

2886.3

1758.71849.81941

2032.52124.12215.92307.92400.12492.52585

2677.82770.72863.82957

3050.5

1905.42002.12098.92195.72292.62389.52486.42583.42680.42777.52874.52971.73068.83166

3263.2

2077.12181.42285.72390

2494.32598.62702.92807.22911.43015.63119.83224

3328.13432.23536.3

227623902504261827322847

296130753189330334173532

364637603874


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A. 18. Boiling Temperature ofLiBr Wa ter Solution

The correlat ion for the boi l ing temperature of saturated LiBr-H20 solut ion isgiven by

T(P,X) = Sa ,X ^ + T ^ Sb ,X^ (A.18)i =0 i =0where T ^ i s the sa tu ra t ion t em pera ture of pure wa ter a t p res sure P , X i s themass fraction of LiBr in the solution, P is the pressure, and T is the boil ing

temperature of the LiBr-H20 solut ion. The cons tants in the above relat ion are asfollows:ao = 0, ai = 16.634856, a2 = -553.38169, ag = 11228.338, a4 = -110 283 .9,as = 621094.64, SLQ = -211 125 6.7, ay = 4385190.1, ag = -5409 811 .5,ag = 3626674.2, ai o = -10 15 30 5.9, bo = 1, b j = -0.06 82 42 82 1, b2 = 5.873619bg = -10 2.7 81 86 , b4 = 930.32374, bg = -482 2.39 4, bg = 151 89.038,hrj = -294 12.8 63, bg = 34100.528, bg = -21671.48, bio = 5799.56The boi l ing temperature of saturated LiBr solut ion is shown in Table A.18 and

Fig. A.18 for a temperature range of 10-170 ^C and LiBr mass fraction of 0.25-0.75.

50 100 150Temperature (^C) 200

Fig. A.18. Boil ing temperature of LiBr solution as a function oftempera ture and sa l t concent ra t ion


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562

Table A.18: Variation in the boiling temperature of LiBr solution as a funtemperature

LiBr mass fractionT (OC) 0.25 0.3 0.35 0.4 0.45 0.5 0.55 1015202530354045505560657075808590

13.518.723.828.934.039.244.349.454.559.764.869.975.080.285.390.495.5

15.120.225.430.635.840.946.151.356.561.666.872.077.282.487.592.797.9

17.122.327.632.838.143.348.653.859.164.369.674.880.185.390.595.8101.0

20.0 24.725.4 30.230.7 35.636.1 41.141.4 46.546.7 52.052.1 57.557.4 62.962.8 68.468.1 73.873.5 79.378.8 84.784.2 90.289.5 95.794.8 101.1100.2 106.6105.5 112.0

31.837.442.948.554.159.765.270.876.481.987.593.198.7104.2109.8115.4120.9

41.046.752.458.163.869.575.280.986.592.297.9103.6109.3115.0120.7126.4132.1


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563

Table A.18 (continued): Variation in the boiling tempera ture of LiBr solution aand temperature

LiBr mass fractionT (OC) 0.25 0.3 0.35 0.4 0.45 0.5 0.55 95 100.7 103.1 106.3 110.9 117.5 126.5 137.8100105110115120125130135140145150155160165

105.8110.9116.0121.2126.3131.4136.5141.7146.8151.9157.0162.2167.3172.4

108.2113.4118.6123.8129.0134.1139.3144.5149.7154.8160.0165.2170.4175.6

111.5116.8122.0127.3132.5137.8143.0148.3153.5158.8164.0169.3174.5179.8

116.2121.6126.9132.3137.6142.9148.3153.6159.0164.3169.7175.0180.4185.7

122.9128.4133.8139.3144.8150.2155.7161.1166.6172.0177.5183.0188.4193.9

132.1137.7143.2148.8154.4160.0165.5171.1176.7182.2187.8193.4199.0204.5

143.5149.2154.8160.5166.2171.9177.6183.3189.0194.7200.4206.1211.8217.5

170 177.5 180.7 185.0 191.0 199.3 - 210.1 223.1


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This Page Intentionally Left Blank


41/74

Appendix BThermodynamic Losses


42/74

566 Appendix B Thermodynamic Losses

B. 1 Boiling Point Elevation

wi t hThe correlation for the boil ing point elevation of seawater isB P E = A X + B X2 + C X 3 (B.l)A = (8.325x10-2 + 1.883x10-4 T + 4.02x10-6 T2)B = (- 7.625x10-4 + 9.02x10-5 T - 5.2x10-7 T 2 )C = (1.522x10-4 - 3x10-6 T - 3x10-8 T 2 )where T is the temperature in ^C and X is the sal t weight percentage. The above

equation is valid over the following ranges: 1 < X < 16%, 10 < T


43/74

Appendix B Thermodynamic Losses 567

Table B.l: Variation in seawater boiling point elevation (^C) as a function oftemperature (QQ) and salinity (wt%)

temperature C101520253035404550556065707580859095100105110

10.0850.0870.0890.0910.0930.0960.0990.1010.1040.1080.1110.1150.1180.1220.1260.1300.1350.1390.1440.1490.154

20.1710.1750.1800.1850.1900.1950.2010.2070.2130.2200.2270.2340.2410.2490.2570.2650.2740.2830.2920.3010.311

Salinity (w3

0.2580.2660.2730.2810.2900.2980.3070.3160.3260.3360.3460.3570.3680.3790.3910.4020.4150.4270.4400.4530.467

40.3480.3590.3700.3810.3930.4050.4170.4300.4430.4560.4690.4830.4970.5110.5250.5400.5550.5710.5870.6030.619

b%)5

0.4410.4560.4700.4850.5000.5160.5310.5460.5620.5780.5940.6100.6270.6430.6600.6770.6940.7110.7280.7460.764

60.5380.5560.5750.5930.6120.6300.6480.6660.6840.7030.7210.7390.7560.7740.7920.8100.8280.8450.8630.8800.898

70.6390.6620.6840.7060.7270.7480.7690.7890.8090.8290.8480.8660.8850.9030.9210.9380.9550.9710.9871.0031.018


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B.2 Non-Equilibrium Allowance in ME E

T h e c o r r e l a t i o n fo r t h e n o n - e q u i l i b r i u m a l l o w a n c e in t h e M E E p r o c e s s i sd e v e l o p e d b y M i y a t a k e e t a l . ( 1 9 7 3 ) ,(N EA )j = 3 3 (ATj)0-55/Tv. (B.2 )w h e r e , AT j = T j _ i - T j , i s t e m p e r a t u r e d i f fe r e n c e o f b o i l i n g b r i n e i n e f f ec t s j a n d j -1 , Ty- i s t he vapor t empera tu re in e f fec t j and i s g iven by Ty^ ~ 'T j ~ (BPE) j . Al lt e m p e r a t u r e s i n t h e a b o v e c o r r e l a t i o n a r e i n ^ C . R e s u l t s fo r t h e n o n - e q u i l i b r i u ma l l o w a n c e a r e s h o w n i n T a b l e B . 2 a n d F i g . B . 2 .

o

1.81.61.41.2

10.80.60.40.2

0 0 20 40 60 80 100 1201Tenperature, C

Fig. B.2 Variation in non-equilibrium alfowance in ME Eas afimctionof brine tenperature and tenperature drop

per effect for salinity of 40000 ppm


45/74


Table B.2: Variation in the non-equilibrium allowance in multiple effectevaporation as a function of effect temperature drop and temperature for asalinity of 40000 ppm.

NEA(oC) Tj AT Tyj BPE (^0)1.0420.8320.6930.5930.5190.4610.4150.3771.2210.9750.8120,6950.6080.5400.4860.4421.3801.1020.9180.7860.6870.6110.5490.4991.5571.2321.0200.8710.7610.6750.6070.551

405060708090100110405060708090100110405060708090100110405060708090100110

1.51.51.51.51.51.51.51.5222222222.52.52.52.52.52.52.52.533333333

39.649.659.569.579.589.499.4109.439.649.659.569.579.589.499.4109.439.649.659.569.579.589.499.4109.439.649.659.569.579.589.499.4109.4

0.4170.4430.4690.4970.5250.5550.5870.6190.4170.4430.4690.4970.5250.5550.5870.6190.4170.4430.4690.4970.5250.5550.5870.6190.4170.4430.4690.4970.5250.5550.5870.619


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B.3 Non-Eq uilibrium Allowance in MSF

Lior (1986) developed correlations for the non-equil ibrium allowance forthe MSF system. The following two equations give values for NEA as a functionof the br ine temperature , gate height , the br ine f low rate per uni t length of thechamber wid th , and the s t age t empera ture drop;(NE A)io = (0.9784)Ti (15.7378)H (1.3777)VbxlO-6 (B.3a)an d NEA = (NEAio/(0.5AT + NEAio)0-328lL (0.5 A T + N E A I Q ) (B.3b)Eq. B.Sa is valid for 10 ft stage length and Eq. B.Sb is applicable for stages of anyothe r leng ths . In the above equat ion, Tj i s the s tag e tem pe rat ure in ^C, H is theheight of the brine pool in m, V^ is the brine f low rate per unit length of thecha m ber w idth in kg/(m s), and AT is the s tage tem pe rat ure drop in ^C Resul tsfor the equations B.Sa and B.Sb are shown in Fig. B.S and Table B.S.

i Z

0 20 40 60 80 100 120Terrperature, C

Fig. 6.3 Variation in non-equilibriLim albwance in MSFas a function of brine temperature and brine height forbrine weir load of 180 kg^m/s and stage length = 10 ft.


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Appendix B Therm odynam ic Losses 571

Tab le B.3: V aria tion s in non -equ il ibrium allowance for M SF as a function off lashing temperature and br ine height for a weir load of 180 kg/m s and s tagelength equal to 10 f t .

NEA(oC) Tj(oC) H (m ) NEA (QQ) TJ (QQ) H (m)0.630.510.410.330.260.210.170.140.720.580.470.380.300.240.200.16

405060708090100110405060708090100110

0.150.150.150.150.150.150.150.150.20.20.20.20.20.20.20.2

0.830.670.540.430.350.280.220.180.950.770.620.500.400.320.260.21

405060708090100110405060708090100110

0.250.250.250.250.250.250.250.250.30.30.30.30.30.30.30.3


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572 Appen dix B The rmo dyna mic Losses

B.4 Dem ister Pressure Drop

The correlation for pressure drop in the demister , APp, is developed by El-Dessouky et al . (2000) for industr ial type wire pads. The ranges of theexperimental variables were V (0.98-7.5 m/s) , pp (80.317-208.16 kg/m^), L (100-200 mm ), 6^ (0.2- .32 mm ), an d d^ (1-5 mm ). Th is correlation is given by

APp = 3.8 81 78 (pp)0.375798(v)0.81317(g^)-1.56114147 ^g ^^where APp is the demis ter pressure drop in Pa/m, 5^ is the wire diameter in mm,d( j i s the diameter of entrained droplets in mm, L is the mesh pad thickness inmm, V is the vapor velocity in the demister in m/s, and p is the demister densityin kg/m^. In Eq. B.4 the subscript p denotes the demister . Results for thedemis ter pressure drop is shown in Table B.4. Figures i l lus t rat ing the demis terpressure are given in Chapter 9 .


49/74

Appen dix B The rmo dyn am ic Losses 573

Table B.4: Variations in the demister pressure drop as a function of the vaporvelocity , pack ing dens i ty , and wire diam eter .Ap (Pa /m ) V (m/s) Pp (kg/ni3) ^w (m) Ap (Pa /m ) V (m/s) Pp (kg/m3) ^w (m)190.1495299.9815370.3531419.028456.3063594.874689.6065527.0877631.9565352.5772441.4914520.6471590.3651673.5824751.298804.1878327.6714434.2842517.1443644.0559720.3196799.4394829.6542333.4171452.1815543.5242676.3193761.546772.7173848.1905935.0569965.0183

1.372.43.113.624.025.576.684.862.262.983.654.265.015.736.231.862.633.264.274.95.575.831.762.563.214.24.862.83.143.543.68

80.31780.31780.31780.31780.31780.31780.31780.31780.317140.6140.6140.6140.6140.6140.6140.6176.35176.35176.35176.35176.35176.35176.35208.16208.16208.16208.16208.16176.35176.35176.35176.35

0.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.280.20.20.20.2

799.5571832.1666429.5316597.2926656.1643342.3253434.9566581.3096672.578769.0008839.5147931.4795885.7715383.9096480.7253566.9154642.8291733.4416818.0635875.6535243.6977301.5393374.2175471.4877546.6402601.2238659.4141761.510472i:0738809.5738687.5985790.6104

5.165.421.362.042.291.461.962.83.353.954.454.72.262.983.654.265.015.736.231.672.172.833.764.515.075.686.786.347.315.987.1

208.16208.16176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35176.35

0.280.280.20.20.20.240.240.240.240.240.240.240.240.280.280.280.280.280.280.280.320.320.320.320.320.320.320.320.320.320.320.32


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B,5 Pressure D rop in Conn ecting Lines

The pressure drop in the l ines connecting the vapor space in effect i andthe evaporator tubes of the next effect is calculated from the Unwin formula,ORNL (1967),A P :

0.0001306 M 2 L ( 1 + )^P v^

(B.5)where M is the mass f low rate of the vapor s tream (kg/s) , L is the tube length (m),5i is the tube inner diameter (m), py is the vapor density (kg/m^), and AP is thepressure drop (Pa/m). Results for the pressure drop in connecting l ines are givenin Table B.5 and Fig. B.5.

0 20 40 60 80 100 120Temperature, C

Fig. B.5 Variation in connection line pressure drop as aftinction offlowrate and and temperature

(5i =0.2 m, L = 1 m)


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Appen dix B The rmo dyn am ic Losses 575

Table B.5: Va r iat ion in connect ing l inetem pe rat ur e an d flow rate for L = 1 m and b{

pressure drop as a function of= 0.2 m.

T ^ C )405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

AP (Pa/m)151.380793.2870459.4738939.0961926.4208418.306412.973899.384879605.5229373.1482237.8956156.3848105.683473.2255851.8955437.539512422.0921492.593951.5823625.5391422.7334292.9023207.5822150.15815449.7063358.3342141.061407.463951.1502659.0303467.0599337.85569688.3665970.3713806.3292502.1561690.9341171.609830.3287600.6322

M (kg/s)

22222222444444446666666688888888

Pv (kg/m3)0.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.826262685


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Table B.5 (Cont inued) : Var iat iontemperature and f low rate for L =

in connecting l ine pressure drop as a function of1 m and Sj = 0.2 m.

T(oC)405060708090100110405060708090100110405060708090100110

AP (Pa/m)15138.079328.7045947.3893909.6192642.0841830.641297.389938.487921798.8213433.338564.2415629.8523804.6012636.1211868.2391351.42329670.6218284.2611656.887662.8545178.4843588.0542542.8821839.436

M (kg/s)101010101010101012121212121212121414141414141414

Pv (kg/m3)0.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.8262626850.0512243240.0831238160.130382840.1983409130.2934946670.4235882910.5976910430.826262685


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B.6 Gravitational Pressure Drop

The gravi ta t ional pressure drop dur ing condensat ion ins ide the evaporatortubes is given byA P = ( p v a + ( l - a ) p ^ ) g L s i n ( G ) (B.6)where AP is the pressure drop in Pa, g is the gravitat ional acceleration (m/s^), Lis len gth of the eva po rator tu be s (m), an d G is th e inclin ation ang le. Theexpression for a is given by Zivi (1964), a = -y ^^-^ , where % is the

1 + 1 - X Pi JxO.5

vapor mass fraction, which is greater than zero and less than 1. In Eq. B.6, pyand p are the dens i ty of vapor an d l iquid s t rea m s at satu rat ion cond i t ions an dare given in (kg/m^). Results for the above losses are given in Table B.6 and Fig.B.6.

2 5 j

3 H2 H

-0.01-0.2-0.4-0.6-0.8-1

20 40 60Tenperature, C

80 100 120

Fig. B.6 Variations in the gravitational pressure drop as afimction of the vapor tenperature and the vapor massfractioa (6 = 5^ and L = 10 m)


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Table B.6: Var iat ion inand vapor mass f ract ion

gravi ta t ional pressure drop as a funct ion of temperaturefor 6 = 5 and L = 10 m.

AP (Pa) T (oQ JL P (kg/m3) Pv (kg/m3)3522.7974016.4684473.9814886.445249.6865563.2165829.0146050.516237.1867299.3431370.8429451.7166541.7984640.7363748.0056862.927890.79624115.2305143.686176.336213.3048254.669300.4589350.6601

405060708090100110405060708090100110405060708090100110

0.010.010.010.010.010.010.010.010.20.20.20.20.20.20.20.20.40.40.40.40.40.40.40.4

992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84

0.0512240.0831240.1303830.1983410.2934950.4235880.5976910.8262630.0512240.0831240.1303830.1983410.2934950.4235880.5976910.8262630.0512240.0831240.1303830.1983410.2934950.4235880.5976910.826263


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Table B.6 (Cont inued) : Var iat ion in gravi ta t ional pressure drop as a funct ion oftem pe ratu re and va por m ass f raction for 9 = 5" and L = 10 m.AP (Pa) T(oC) P (kg/m3) Pv (kg/m3)

40.83051.98765.07680.22297.539117.127139.076163.46615.63020.01225.21431.31638.40146.55355.86466.4261.0521.4922.0902.8953.9635.3617.1689.473

405060708090100110405060708090100110405060708090100110

0.60.60.60.60.60.60.60.60.80.80.80.80.80.80.80.80.990.990.990.990.990.990.990.99

992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84

0.0512240.0831240.1303830.1983410.2934950.4235880.5976910.8262630.0512240.0831240.1303830.1983410.2934950.4235880.5976910.8262630.0512240.0831240.1303830.1983410.2934950.4235880.5976910.826263


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B. 7 Acceleration Pressure Drop

The accelerat ion pressure drop dur ing condensat ion ins ide the evaporatortubes is calculated from the following relationAP = M ' x! ( i -x i r x i (i-x2r (B.7)where AP is the pressure drop in Pa, M is the mass f low rate in kg/s , A is thecross section area in m^, p^ is the vapor density in kg/m^, p is the l iquid density

1in kg/m^, % is the va por ph ase m ass fraction, a is a =1 + 1 -XX

P ^Pi

0.5 T he

sub scrip ts 1 an d 2 refer to the in let an d outlet con dit ions. Re sults for the abovecorrelation are shown in Table B.7 and Fig. B.7.

35003000

d 2500S'S 20001 1500

10005000 ^

\ \ - ^ 2\\ " ^ " ^\ v \ -^m - '^ ^ ^ ^ "0 50 100

Tenperature, CFig. B.7. Variation in the acceleration pressuredrop as a fimction of temperature and flow rate.

(A = l m ' , XI =0.99,^2 = 0.01)

150


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Table B.7: Va r iat ion s in the accelerat ionflow rate and temperature for a crossfractions of 0.01 and 0.99.

pre ssu re drop as a function of th e m as ssection area of 1 m2 a nd vapor m ass

T(C)405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

AP (Pa)19.1311.797.524.943.342.311.641.1976.5247.1530.0619.7613.359.256.554.74

306.09188.62120.2579.0453.4137.0026.2218.96688.70424.39270.55177.84120.1783.2558.9942.661224.36754.47480.98316.16213.64148.01104.8775.85

M (kg/s)

22222222444444446666666688888888

p (kg/m^)992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84

Pv (kg/m3)0.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.83

ai0.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.9890

^20.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.0091


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582 Appendix B Thermo dynamic Losses

Table B.7 (continued): Variations in the acceleration pressure drop as a functionof the mass flow rate and temperature for a cross section area of 1 m^ and vapormass fractions of 0.01 and 0.99.

T(oC)405060708090100110405060708090100110405060708090100110

AP (Pa)1913.061178.87751.53494.00333.81231.26163.87118.512754.801697.571082.21711.36480.69333.01235.97170.653749.592310.581473.01968.24654.27453.27321.18232.28

M (kg/s)101010101010101012121212121212121414141414141414

p (kg/m3)992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84992.19988.00983.14977.68971.68965.18958.23950.84

Pv (kg/m3)0.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.830.050.080.130.200.290.420.600.83

^10.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.98900.95730.96620.97280.97780.98170.98470.98710.9890

a20.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.00910.00230.00290.00360.00450.00540.00650.00770.0091


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Append ix B The rmo dyn am ic Losses 583

References

El-Dessouk y, H .T. , Ala tiqi , I .M., E t t o un e y , H .M ., and Al-Deffeeri, N.S.,Performance of wire m esh m is t e l iminator , Ch em. Eng. & P ro c, 39(2000)129-139.Lior, N., Fo rm ulas for calculat ing the ap proach to equi l ibr ium in open ch ann elf lash evaporators for saline water , Desalination, 60(1986)223.Miya take , O., M urak am i , K., Kaw ata , Y., and Fuj ii , Fun da m en ta l Exp er imen ts

with Flash Evaporat ion, Heat Transfer Jpn. Res . , 2(1973)89-100.Oak Ridge Nat ional Laboratory (ORNL), Uni ted States Depar tment of theInter ior , Research and Development Progress Repor t No. 315, December 1967.Zivi, S.M., Estimation of steady-state steam void fraction by means of the principle ofminimum entropy production, Trans. ASM E, J. of Heat Transfer, 86(1964), 247-252.


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This Page Intentionally Left Blank


61/74

A p p e n d i x CH eat Tran sfer C oeff ic ients


62/74

586 Appendix C Heat Transfer Coefficients

C.l Falling Film on the Tube Outside Surface

The heat transfer coefficient of boiUng thin film of water flowing over theouts ide surface of smooth hor izontal tubes was developed by Han and Fletcher(1985),h = 0.00 04 (p2 g k3/^2)l/3 ReO.2 PrO.65 qO.4 ( d )The re latio nsh ip is valid over the following par am et er ran ge ; 770 < Re < 7000, 1.3< Pr < 3.6, 30 < q < 80 kW/m2, and 49 < T < 127 C. In th e above e qu atio n R e an dP r are R eynolds an d Pr an dt l nu m be rs respectively, q, is the h ea t f lux, |.i is theviscosity, p is the density and k is the thermal conductivity of the f luid. Table C.land Fig. C.l show variations in the heat transfer coefficient as a function of thesys tem tempera ture and the hea t f lux .

n 1 r40 60 80Tenperature, C

120

Fig. C.l . Variation in the heat transfer coefficient forboiling falling film


63/74

Ap pend ix C H ea t Tra nsfe r Coefficients 587

Ta ble C. l: Th e he a t tra ns fe r coefficient for boiling falling film for 5o = 0.03 m, 5^:0.025 m, q ^ 80 kW/m^, and X = 40000 ppm .T(-C)405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

h(kW/m^ oC)

0.890.920.960.991.021.041.061.080.961.001.041.071.101.131.151.181.021.061.101.141.171.201.221.251.101.151.191.231.271.301.331.351.171.221.261.301.341.371.401.43

V(m/s)i~11111111.51.51.51.51.51.51.51.5222222223333333344444444

Re42784.2450750.4059113.5667786.8476688.3985742.4694879.95104038.6564176.3676125.6188670.34101680.26115032.59128613.69142319.92156057.9785568.48101500.81118227.11135573.68153376.79171484.92189759.90208077.30128352.72152251.21177340.67203360.52230065.18257227.37284639.85312115.95171136.95203001.62236454.23271147.36306753.57342969.83379519.80416154.60

Pr4.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.68

k(kW/m C)6.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-04

1(kg/m s)7.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-04

Cp(kJ/kg oC)lis3.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.03

P(kg/m3)1021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.79


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C.2 Vapor Condensation Inside Tubes

The heat transfer coefficient for vapor condensation inside horizontal tubes wasdeveloped by Shah (1978).h/h u = 1 + 3.8 / ZO-95 (C.2)w here Z = ((1/x) - l)^-^ PrO-4, h ^ = h^ (1 - x)^"^, ^ = 0.023 ReO-8 PrO.4 (k^/g.)^ ^ igthe vapor phase mass f ract ion and the subscr ipts i , , and u denotes the tubeinside, the l iquid phase, and the local superficial value. The above correlation isva lid over t he following ra ng es : 2.8 < 5i < 40 m m , 2 1 < T < 355 ^C, 0 < x < 1, 0.158< q < 16000 kW /m2, 11 < G < 400 0 kg/m2 s, 0.7 < P < 1 ba r, 0.0019 < P r < 0.82, 3 50< Re < 100000. Table C.2 and Fig. C.2 show variations in the heat transfercoefficient a s a function of th e system te m pe ra tu re a nd vapor fraction.

1.aOU

cd

40 60 80Tenperature, C 120Fig. C.2. Variation in the heat transfer coefficient forvapor condensat ion ins ide the tubes


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Ap pend ix C H ea t Tra nsfe r Coefficients 589

Table C.2: The heat transfer coefficient for vapor condensation inside the tubes,for 5o = 0.03 m, 5i = 0.025 m, an d X = 40000 ppm .T

(oC)405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

h(kW/m^ o Q

0.150.160.170.180.190.200.210.221.341.451.551.651.741.831.911.982.883.113.333.543.743.924.094.258.499.189.8310.4511.0311.5712.0812.5516.8218.1819.4720.6921.8422.9223.9324.86

X0.010.010.010.010.010.010.010.010.10.10.10.10.10.10.10.10.20.20.20.20.20.20.20.20.50.50.50.50.50.50.50.50.990.990.990.990.990.990.990.99

Re427.84507.50591.14677.87766.88857.42948.801040.394278.425075.045911.366778.687668.848574.259487.9910403.868556.8510150.0811822.7113557.3715337.6817148.4918975.9920807.7321392.1225375.2029556.7833893.4238344.2042871.2347439.9752019.3242356.4050242.9058522.4267108.9775921.5184885.0393931.15102998.26

Pr4.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.68

k(kW/m C)6.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-046.28E-046.39E-046.48E-046.57E-046.64E-046.70E-046.74E-046.78E-04

^(kg/m s)7.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-047.16E-046.01E-045.14E-044.46E-043.92E-043.48E-043.12E-042.83E-04

Cp(kJ/kg oC)

3^983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.033.983.993.994.004.004.014.024.03

P(kg/m3)1021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.791021.371017.071012.241006.891001.06994.75987.99980.79


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C.3 Seawater Flowing Inside T ubes

The heat transfer coefficient for seawater inside the tubes was developedfor desal inat ion pla nts by Wangnick (1995).h = (3293.5+T(84.24-0.1714 T)- X (8.471+0.1161 X + 0.2716 T))/((5i/0.017272)0-2)((0.656 V)0.8)(5i/5o) (C.3)

w here x is the sa l t concentrat ion in we ight percent , T is the te m pe rat ure , an d b{an d 0 ^^^ t^^ inside an d the outside tub e dia m ete r respectively. Table C.3 andFig. C.3 show variations in the heat transfer coefficient as a function of thesys tem temperature and the veloci ty . Table C.3 includes also values of the heattransfer coefficient as predicted by the Dittus-Bolter equation. I t should be notedthat values for Reynolds number , Prandt l number , and other phys ical proper t iesare the same as those given in Table C. l .

20 40 60 80Tenperature, ^C

100 120

Fig. C.3. V aria tion in the he at tra nsfe r coefficient forseawater f lowing ins ide the tubes


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Appendix C Heat Transfer Coefficients 591

Tab le C.3: The h ea t tran sfer coefficient for sea w ate r f lowing inside the tu be s, for5o = 0.03 m , 5i = 0.025 m, an d X = 40000 ppm.T e O h (Eg. c.3) (kW/m2 oC) h (Dittus-Bolter) (kW/m^ oQ) V (m/sT

40506070809010011040506070809010011 040506070809010 011 040506070809010 0110405060708090100110

3.493.864.214.554.875.175.455.714.825.345.836.296.737.157.537.896.076.727.347.928.489.009.489.948.399.2910.1510.9611.7212.4413.1113.7410.5711.7012.7813.8014.7615.6616.5117.30

4.194.584.975.335.686.016.326.625.796.346.877.387.868.328.759.157.297.988.659.299.8910.4711.0111.5210.0911.0411.9612.8413.6814.4815.2315.9312.7013.9015.0616.1717.2318.2319.1720.05

1.51.51.51.51.51.51.51.5222222223333333344444444


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C.4 Vapor Condensation on the Outside Surface of Tubes

The correlation for the heat transfer coefficient during vapor condensationouts ide the preheater /condenser tubes was developed by Henning and Wangnick(1995),h = 0 . 725 ( k? p^ ( p^ - P v )g?^ v / 6o ^ A T ) ^ - ^ ^ C i C 2

w ith Ci = 1.23795 + 0.353808Ni - 0.0017035Nf,C2 = l -34 .313Xnc +1226.8X^c -14923X^c^

(C.4)

N i = 0 . 5 6 4 . ^ , an d N t = 4 M f7i5. pfVfVariations in the heat transfer coefficient are shown in Table C.4 and Fig. C.4.

Fig. C.4. Variation in the heat transfer coefficient on theoutside surface of tubes


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Table C.4: Variation inoutside surface of tubes.Vf = 1.5 m/s, 5i = 0.0251.47, C2 = 0. 71 .

the heat transfer coefficient during condensation on theP a ra m e te rs inclu de Xj ^ ~ 0.015 , S^ = 0.03 m, Mf = 1 kg/s,m. Calculated values include Nt = 1.37, N^ = 0.66, Ci =

T(C)405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

h(kW/m2 oC)

31.4133.1234.6836.1137.4138.5639.5840.4721.0122.1523.1924.1525.0225.7926.4727.0717,6618.6219.5020.3121.0421.6922.2622.7614.8515.6616.4017.0817.6918.2418.7219.1412.4913.1713.7914.3614.8715.3315.7416.09

AT(C)0.10.10.10.10.10.10.10.10.50.50.50.50.50.50.50.5

2222222244444444

Pv(kg/m3)0.0510.0830.1300.1980.2930.4240.5980.8260.0510.0830.1300.1980.2930.4240.5980.8260.0510.0830.1300.1980.2930.4240.5980.8260.0510.0830.1300.1980.2930.4240.5980.8260.0510.0830.1300.1980.2930.4240.5980.826

Pi(kg/m3)991.861987.683982.924977.602971.734965.339958.434951.037991.861987.683982.924977.602971.734965.339958.434951.037991.861987.683982.924977.602971.734965.339958.434951.037991.861987.683982.924977.602971.734965.339958.434951.037991.861987.683982.924977.602971.734965.339958.434951.037

k(kW/m oQ)6.30E-046.41E-046.50E-046.58E-046.65E-046.71E-046.76E-046.79E-046.30E-046.41E-046.50E-046.58E-046.65E-046.71E-046.76E-046.79E-046.30E-046.41E-046.50E-046.58E-046.65E-046.71E-046.76E-046.79E-046.30E-046.41E-046.50E-046.58E-046.65E-046.71E-046.76E-046.79E-046.30E-046.41E-046.50E-046.58E-046.65E-046.71E-046.76E-046.79E-04

Ay(kJ/kg)2406.502382.522358.312333.762308.772283.252257.112230.252406.502382.522358.312333.762308.772283.252257.112230.252406.502382.522358.312333.762308.772283.252257.112230.252406.502382.522358.312333.762308.772283.252257.112230.252406.502382.522358.312333.762308.772283.252257.112230.25

^(kg/m s)6.55E-045.48E-044.67E-044.04E-043.54E-043.14E-042.81E-042.54E-046.55E-045.48E-044.67E-044.04E-043.54E-043.14E-042.81E-042.54E-046.55E-045.48E-044.67E-044.04E-043.54E-043.14E-042.81E-042.54E-046.55E-045.48E-044.67E-044.04E-043.54E-043.14E-042.81E-042.54E-046.55E-045.48E-044.67E-044.04E-043.54E-043.14E-042.81E-042.54E-04


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C.5 Wa ter Flow in Plate Heat Exchanger

The heat transfer coefficient in plate heat exchangers is developed byBuon opane et a l . (1974) and is given in term s of var ia t ions in the N ussel t nu m beras a function of the Reynolds and Prandtl numbers of the f luid; this ish = 0.2 53 6 ReO-65 PrO.4 (k ^/ D e) (C.5)Where Re is the Reynolds number, which is defined in terms of the effectivediameter (Re = De pv/ | i ) , Pr i s the Prandt l number , and De is the equivalentdiameter , which is defined by De = 4 (wd)/(2(w+d)). In the above equations, p isdens i ty , [i is viscosity, k is th er m al c onductivity, Cp is he at c apacity, v is velocity,w is pla te width , and d is pla te spacing . V aria tion s in th e hea t transf er coefficientare shown in Table C.5 and Fig. C.5 as a function of temperature and velocity.Va lues for phys ical prope r t ies , which includes |LI, k, Cp, and p are given Table C.l .

Fig. C.5. V aria tion in th e he at tra nsfe r coefficient forseawater f lowing in plate heat exchanger


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Table C.5: The heat transfer coefficient in plate heat exchanger for w = 0.2 m, d '0.02 m , De = 0.036 m, X = 40,000 pp m .

T(oC)405060708090100110405060708090100110405060708090100110405060708090100110405060708090100110

h (kW/m^ "O9.319.8010.2610.6811.0711.4211.7512.0412.1112.7613.3513.9014.4114.8715.2915.6614.6015.3816.1016.7617.3717.9318.4318.8919.0120.0220.9621.8222.6123.3323.9924.5822.9124.1425.2626.3027.2628.1328.9229.63

V (m/s)

1.51.51.51.51.51.51.51.5222222223333333344444444

Re51859.6861515.6471652.8082165.8792955.63103930.25115006.00126107.4577789.5292273.46107479.19123248.80139433.44155895.38172509.00189161.18103719.37123031.28143305.59164331.73185911.26207860.50230012.00252214.91155579.05184546.93214958.39246497.60278866.88311790.76345018.00378322.36207438.73246062.57286611.19328663.46371822.51415721.01460023.99504429.82

PrZ543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.684.543.753.162.712.362.081.861.68


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596 App endix C H ea t Tra nsfer Coefficients

C.6 Condensers and Evaporators OverallHeat Transfer Coefficient

Sev eral correlation s are availab le for the overall hea t tran sfe r coefficient.Pre dicte d va lue s by the se s correlatio ns vary be twe en lows of 2 kW/m^ oQ up tohig hs of 4 kW/m2 oQ. V aria tion s dep end on the fouling resis tan ce an d the surfacecondit ions. Results for these correlations are shown in Fig. C.6. The following is al is t of these correlations:- Fouled cond enser, El-Dessou ky et al . (1998)

Uc =1x10 -3 (1617.5+ 0.1537 T + 0.1825 T2 - 0.00 008 02 6 T^) (C.6)- Fouled eva pora tor , El-Dessou ky et al . (1998)

Ue =1x10-3 (1939.4+ 1.40562 T - 0.0207 525 T2 + 0.0023 186 T3) (C.7)- Fouled cond enser, Ta ka da et al . (1983)

Uc =0 .8 (3+0 .05 (T - 60)) (C.8)- Clea n drop wise cond enser, Brom ly et al . (1970)

Uc =1x10 -3 (5186 - 90.82 T + 0.5566 T2 - 0.0009 159 T3)/0.17612 (C.9)- Cle an film wise con den ser, Brom ly et al. (1970)

Uc = 1x10 -3 (_ 316.2 + 6.62 T)/0.17612 (C IO )- Oxidize d film wise con den ser, Brom ly et al. (1970)

Uc = 1x10-3 (- 64.37+4.625 T)/0.17612 (C .l l)In the above equa tion s, Uc is the co nden ser overall he at tran sfe r coefficient(with vapor condensing on the outside surface and seawater f low on the tubeside), Ue is the evaporator overall heat transfer coefficient (with water forming a

fall ing f i lm on a horizontal tube bundle and vapor is condensing inside the tubes) ,and T is the evaporat ion/condensat ion temperature . As is shown in Fig. C.6 theunits of (U) and (T) are kW/m^ ^C and ^C, respectively. I t should be noted thatFig. C.6 includes addi t ional data points by other inves t igator ; however , theseinvestigators did not provide a correlation. In addit ion, the clean overall heat


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transfer coefficient by El-Dessouky et al. (1998) is the same as Eqs. (C.6) andC.7), where it uses a fouling resistance of 0.08 m^ oC/kW.

- El-Dessouky, et al.,1998, Uc, fouled- El-Dessouky, et aL,1998, Ue, fouled- El-Dessouky, et al.,1998, Uc, clean- El-Dessouky, et al.,1998, Ue, cleanBromfy, etaL, 1970,film wise, cleanBromly, etal.,1970,film wise, oxidizedEl-Nasher, et al.,1995Weinberg, et aL,1997, industrialTakada, etaL, 1983Reddy, etaL, 1993

Figu re 4: V aria tion s in the overall hea t tran sfer coefficient pre dicte d byvar ious correlat ions and as a funct ion of temperature .References

Bromley, L.A., and Read, S.M., Multiple effect flash (MEF) evaporator,Desal inat ion, 70(1970)3413-391.Buonopane, R.A. , Troupe, R.A. , and Morgan, J .C, Heat t ransfer des ign methodfor plate h ea t exc hang ers , Chem . Eng. Progress , 59(7)(1963)57-61.El-Dessouky, H. , Alatiqi , I . , Bingulac, S. , and Ettouney, H. , Steady-state analysisof the multiple effect evaporation desalination process, Chem. Eng. TechnoL,21(1998)15-29.


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598 App endix C H ea t Tran sfer Coefficients

El-N asha r , A.M. , and Q am hiyeh, A.A., Sim ulat ion of the s tea dy-s tage opera t ionof a mulit-effect s tack seawater dist i l lat ion plant, Desalination, 101(1995)231-243 .

Han, J . and Fletcher, L. , Fall ing f i lm evaporation and boil ing in circumferentialand axial grooves on horizontal tubes, Ind. Eng. Chem. Process Des. Dev. ,24(1985)570-597.Henning, S, and Wangnick, K. , Comparison of different equations for thecalcu lation of he at trans fer coefficients in M SF multi-s tage f lash ev ap ora tors .Proceedings of the IDA World Congress on Desal inat ion and W ater Sciences,Abu Dhabi, November, 1995, Vol. I l l , pp. 515-524.Reddy, G.P. , Husain, A. , and Al-Gobaisi , D.M.K., Modell ing and optimization ofmuliple effect horizontal tube fall ing f i lm evaporators . Proceeding of the IDAWorld Congress on De sal inat ion and W ater Sciences , Ma dr id, Spain, October,1997, Vol. I, pp 131-14 9.Shah, M.M. , Heat t ransfer , pressure drop, visual observat ions , tes t data foram mo nia ev apo rat ing ins ide tubes , ASHRA E Tran s . , Vol. 84, Pa r t 2 , 1978.Takada, M. , and Drake, J .C, Appl icat ion of improved high performanceevaporator . Desal inat ion, 45(1983)3-12.Wangnick, K. , How incorrect ly determined phys ical and cons truct ional proper t iesin the seawater and br ine regimes inf luence the des ign and s ize of an MSFdesa l inat ion p lan t - s t im ulu s for fur ther tho ugh ts . Proceedings of the IDAWorld Congress on Desal inat ion and Water Science, Abu Dhabi , November ,1995, Vol. II, pp. 201-218.W einberg, J ., an d O phir , A., Ashdod exper ience and o ther d ual purposedesal inat ion plants based on mul t i ef fect desal inat ion wi th aluminum tubes .Symposium on Desal inat ion of Seawater wi th Nuclear Energy, Taejon,Repu blic of Korea, M ay, 1997.

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