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Feed water arrangements in a multi-effect desalting system
Desalination 228 (2008) 30–54
Feed water arrangements in a multi-effect desalting system M.A. Darwish*, Hassan K. Abdulrahim Mechanical Engineering Department, Kuwait University, POB 5969, Safat 13060, Kuwait Tel. +965 481-1188, ext. 5789; Fax: +965 484-7131; email: [email protected]; [email protected] Received 24 January 2007; Accepted 9 May 2007
Abstract A multi-effect boiling (MEB) desalting system with unit capacity up to 5 MIGD becomes a strong competitor to the multi-stage flash (MSF) desalting system due to its low specific energy consumption and the low temperature steam required to operate the system. A considerable number of units have been installed in the Arabian Gulf area recently. There are many flow sheet variants for the MEB desalting system. Each variant suits certain design objectives. The schemes of the feed water flow to the effects and implementation of feed water heaters and flash boxes are among the significant differences between these flow sheets that have major influences on the system performance and the adopted analysis to evaluate the system. This paper outlines the commonly used feed water arrangements in multi-effect desalting systems, e.g. forward, backward, parallel, and mixed feed. For each flow sheet arrangement, the thermodynamic analysis used is presented. These analyses determine the temperature and salinity profiles of the system, the amount of vapor generated by boiling and by flashing in each effect, the required heat transfer areas for the effects and feed heaters, the gain and recovery ratios, and cooling water to distillate ratio. The analytical results obtained in this work are compared with several practical multi-effect desalting systems of typical capacity and number of effects. This comparison illustrates the logic behind choosing each flow sheet arrangement. Keywords: MEB; Feed arrangements; Regenerative feed heating; Gain ratio
1. Introduction A multi-effect boiling (MEB) desalting system with unit capacity up to 5 MIGD is a strong competitor to the multi-stage flash (MSF) desalting system due to its low specific energy *Corresponding author.
consumption and the low temperature steam required to operate the system. A considerable number of units have been installed in the Arabian Gulf area recently (see Table 1). The first method used to desalt seawater in large quantities was the single effect desalting system consisting of an evaporator-condenser combination (Fig. 1). A heat source (steam S) heats the incoming feed
0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.05.039
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
31
Table 1 Examples of conventional multi-effect desalting units Location [ref.]
Ashdod [1]
Sidem 1 [2]
Eilat [1]
Barge unit [3]
Sidem 2 [4]
Evaporator type No. of effects Capacity (kg/s) GR Heat source
THE 6 201 5.7 Water 2778 kg/s 63–55.4EC 42 611 50 34.5 0.25 kg/s at 6.6 bar
THE 12 139 9.8 Steam 14.17 kg/s, 0.31 bar 36 45.6 64 37.5 0.7 at 8 bar
THE 12 N/A 10.1 N/A
THE-stacked 24 50 22.3 Steam
THE 16 290 12.4 Steam
N/A N/A 70 – 74 N/A N/A
33.5 N/A 99 N/A N/A
50 1502 106 46.6 N/A
2.2 9.1
2 8.14
N/A N/A
N/A N/A
N/A N/A
Polyphosphate
N/A
Polyphosphate
Anti-scale
N/A
Feed TDS (g/l) Feed (kg/s) TBT (EC) Minimum T (EC) Ejector steam, m ˙ (kg/s) P (bar) Pump energy (kWh/m3) Equivalent energy (kWh/m3) Treatment
F to the evaporator from its entering feed temperature Tf to its boiling temperature Tb, and evaporates part of it equal to D. The vapor D is directed to the condenser where it condenses and heats the cooling water Mc from seawater temperature Tc to the feed temperature Tf. Part of Mc leaving the condenser is used as feed F while the balance B (=Mc!F) is called brine blow-down and is rejected back to the sea. In the condenser of a single-effect desalting system, a small portion of the latent heat given off by condensing the vapor D is utilized to heat the feed-water F, while the balance [D.L!F.C.(Tf!Tc)]
Fig. 1. Single-effect distillation system.
is rejected back to sea. This is an inefficient utilization of thermal energy. A logical solution is to utilize the latent heat of vapor generated at one evaporator, say E1, at Tv1, and Pv1 as a heat source to a second evaporator, say E2, operating at a pressure Pv2 < Pv1 and temperature Tv2 < Tv1. The vapor formed in E2 (the second evaporator) can be used as a heating medium for a third
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
evaporator E3, and so on. The process of adding more evaporators can be continued to a final n evaporator. The vapor generated in the last evaporator n is directed to a bottom condenser where it is condensed. The heating steam (heat source) is condensed in the first effect at the highest temperature. This is called the n-effect distillation system. The use of multi-effects gives better usage of the consumed thermal energy, and thus reduces the cost of the product water. The temperature and pressure in each effect are decreased by the increase of the effect number. The choice of the number of effects is affected by the following facts: 1. The available temperature range, which is the difference between the saturation temperature Ts of the steam supplied to the first effect and the cooling water temperature in the condenser Tc, i.e. (Ts!Tc). The temperature Ts is chosen to be only few degrees (5–7EC) above the maximum allowable (top) brine temperature (TBT), T1, determined by the feed water pretreatment. Tc is the cooling seawater temperature. The brine temperature in the last effect, Tn, is usually in the range of 35–40EC to keep a reasonable specific volume of the vapor generated in the last effect. 2. The required temperature drop across the evaporator ΔT = (Ts!Tn)/n. Usually, equal temperature drop is taken between the effects. The increase of n decreases ΔT, and consequently increases the required heat transfer areas. 3. The design production rate D = ΣDi. 4. The required gain ratio (GR), which increases with the increases of n. 5. The capital cost increase by using additional effects. There are different schemes for supplying the feed water (seawater or brine) to the evaporators, mainly forward, backward, parallel, and mixed feed systems. In the forward feed arrangement, shown in Fig. 2a, the feed water F (after leaving the bottom condenser at feed temperature Tf) is supplied to the first effect of the highest tempera-
ture. Part of F equal to D1 is evaporated in the first effect and the balance brine B1 (=F!D1) enters the second effect as a feed F2, and D2 is evaporated out of it. The brine leaving the second effect B2 (=B1!D2) enters the third effect as a feed F3, and D3 is evaporated out of it, and so on to the last effect. The brine leaving the last effect is blown down to the sea. This means that the feed and vapor enter the effects and flow in the same direction. The temperature distribution for this arrangement is shown in Fig. 2b. In the backward feed arrangement, shown in Fig. 3a, the feed water F is directed from the end condenser to the last effect n, (of the lowest temperature), and Dn is evaporated out of it. The brine Bn (=F!Dn) leaving effect n is directed to the preceding effect (n!1) as a feed, and Dn-1 is generated out of it, and so on to the first effect. The brine leaving the first effect is blown down to the sea. Thus, the feed and vapor entering the effects have opposite flow directions. The temperature distribution of this arrangement is illustrated in Fig. 3b. In the parallel feed arrangement, the feed F leaving the condenser is divided and distributed almost equally to each effect. Fig. 4a shows the flow sheet of parallel feed arrangement while Fig. 4b illustrates the temperature distribution. The choice of any of these feed arrangements affects the design and performance of the MEB desalting system, e.g. the evaporator arrangements, the required heat transfer areas of the effects, the amount of vapor generated in each effect (evaporator), the amounts of vapor generated by boiling and by flashing, the pumping energy, the gain ratio (distillate to heating steam ratio), and the cooling water to distillate ratio. The analysis of the main feed water schemes are given in this paper when no feed heaters are used between the effects. Then the deficiencies appeared of the forward feed system, the most used system in desalination, are discussed. Then feed heaters are introduced between the effects to decrease these deficiencies, and the system with
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 33
Fig. 2. (a) Forward feed six-effect distillation system; (b) temperature distribution through the effects.
34 M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 3. (a) Backward feed six-effect distillation system; (b) temperature distribution through the effects.
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 35
Fig. 4. (a) Parallel feed six-effect distillation system; (b) temperature distribution through the effects.
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
feed heaters is analyzed to show the effect of using the feed heaters. In order to simplify the forthcoming analysis, some assumptions are used such as: 1. An average value for the specific heat of the distillate, feed, and brine is used and considered constant in all effects, C. 2. An average and constant value of the latent heat of steam as well as the vapor generated in each effect is used, i.e. Ls = L1 = L2 =… = Ln = L. 3. Equal temperature drops between the effects and between the heating steam and the vapor generated in the first effect, i.e.
The brine leaving this effect, B1, is B1 = F!D1. Heat is gained in the second effect by the condensation of D1 and the temperature decrease of brine B1 coming from the first effect at T1 (boiling temperature at P1) to T2 (the boiling temperature at P2). Then, the heat gain to this effect is
Ts!T1 = T1!T2 = T2!T3 = T3!T4 = Ti!Ti!1 = ΔT
Q2 (energy available) = D1.L + B1.C.(T1!T2)
2. Analysis of forward feed multi-effect distillation system A simplified analysis for a four-effect forward feed arrangement is given here. The analysis can be extended to any number of effects, but it becomes more complicated. The analysis of this first case will be given with little details since the following analyses depend on the understanding of this process. Consider that the four-effect desalting system is represented by four evaporators E1, E2, E3 and E4. The amount of vapor generated in each effect is equal to D1, D2, D3 and D4 respectively. Fig. 2b illustrates the temperature distribution for a forward feed system. The vapor D1 generated in effect E1 at Tv1 is the heating vapor supplied to effect E2, and it evaporates Db2 by boiling at Tv2
directed to an end condenser. The first effect thermal load is equal to Q1 = S.L = F.C.(T1!Tf) + D.L1 = U1.A1.ΔT1 = U1.A1.(Ts!T1) = U1.A1.(Ts!Tv1!BPE)
The vapor generated in the second effect D2 consists of Df2 plus Db2, i.e. D2 = Db2 + Df2 Df2 is formed by flash evaporation from B1 as its temperature is reduced from T1 to T2 to reach equilibrium condition, thus: Df2 = B1.C.( T1!T2)/L2 = y.B1 The term y represents the fraction of the flashed vapor from the brine B1 and is equal to y = C.ΔT/L. Db2 is formed by boiling due to the latent heat liberated by condensation of D1, i.e. Db2 . L2 = D1 . L1 Db2 – D1 for L1 – L2 So, D2 = D1 + Df2 D2 = D1 + (F!D1).y D2 = D1.(1!y) + y.F
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
The heat transfer for the boiling in the second effect can be calculated from the thermal load of this effect: Db2 . L2 – D1 . L2 = U2 .A2 .(Tv1!T2) The third effect mass and energy balances give — the brine leaving the second effect B2 is the feed to the third effect, and is equal to B2 = B1!D2 = B1!(D1 + y.B1) = B1 (1! y)!D1 Vapor obtained by flashing from B2 in the third effect Df3 is equal to Df3 = B2.C.(T2!T3) /L = B2.C.ΔT/L = B2.y = (F!D1!D2).y, Vapor obtained by boiling in the third effect = Db3 = D2 and
D4 = D3 . (1! y)!y . B2, but y . B2 = Df3 = D3!Db3 = D3!D2 D4 = D3 . (2! y)! D2 A general form can be expressed by Di = Di-1 (2! y)!Di-2 for i>2 Db4 . L = U4 . A4 . (Tv3!T4) The brine leaving the fourth effect (B4) is the brine blow-down back to the sea. B4 = B3!B4 B4 = B3!(D3 + y.B3) B4 = B3.(1!y)!D3 For the end condenser, the thermal load is Qc = D4 . L = Mc . C . (Tf!Tc) = Uc . Ac . (Tf!Tc)/ln[(Tv4!Tc)/(Tv4!Tf)]
Db3.L3 = D2.L2
The condenser effectiveness is defined by
Db3 – D2 for L2 – L3
k = (Tf!Tc)/ (Tv4 –Tc)
D3 = Db3 + Df3 D3 = D2 + (F!D1!D2).y (F!D1) . y = D2! D1 D3 = D2 . (1! y) + (D2! D1) D3 = D2 . (2! y)! D1 Db3 . L = D2 . L = U3 . A3 . (Tv2!T3) Similarly for the fourth effect:
37
To utilize the above analysis in a design of an MEB system of certain capacity D, the ratio (D1/D) of vapor generated in E1 to the total distillate should be known to start the design procedure. The vapor D1 is generated from F in the first effect by boiling only; then, D2 = D1 + (F!D1) . y = D1 . (1! y) + y . F
D4 = Db4 + Df4
D3 = D2 + (F!D1!D2) . y
D4 = D3 + y.B3,
D3 = D2 . (1! y) + (D2! D1) = D2 . (2! y)! D1
Db4 = D3
D4 = D3 . (2! y)! D2
B3 = B2!D3
D = ΣDi = D1 + D2 + D3 + D4
D4 = D3 + y.B3 = D3 + y.(B2!D3)
D = D1 + D2 + [D2 . (2!y)!D1] + [D3 . (2!y)!D2]
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D = (D2 + D3) . (2! y)
X f = 42 ( g l )
D = (2! y) . [D2 + D2 . (2! y)! D1]
X b = 70 ( g l )
D = (2! y) . [D2 . (3! y)! D1]
BPE = 1.2 °C
D = (2! y) . [(3! y){D1 . (1! y) + y . F}! D1]
C = 4 ( kJ kg.° K )
D/(2! y) = [(1! y) . (3! y)– 1] . D1 + y . (3! y) . F D1/D = [{1/(2! y)}!y . (3! y) F/D]/[(1! y)
2.2. Solution
(3! y)! 1] A similar formula for D1/D can be derived for five effects, and this gives: D1/D = {1/[(2!y).(3!y)!1]!y.(2!y).F/D}/
Tv1 = T1 − BPE = 90.2 − 1.2 = 89 °C ΔT = y=
[(1!y).(2!y)!1] Also a formula for D1/D for six effects is derived, and read as: D1 = D 1 − ( F D ) y ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 3 2 4 3 2 1 − ( 2 − y ) − ( 2 − y ) + ( 2 − y ) + (1 − y ) × ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 3
2
{
}
C ΔT 4 × 10 = = 0.0172 L 2330
To get Tf:
k= 4
Tv1 − Tc 89 − 29 = = 10 °C n 6
Tv 6 − T f Tv 6 − Tc
Tv 6 = Tv1 − ( n − 1) ΔT = 89 − (6 − 1) (10) Tv 6 = 39 °C
2.1. Illustrative example 1
T f = Tv 6 − k ( Tv 6 − tc ) = 39 − 0.5 (10) T f = 34 °C
Use the formula given for D1/D for six effects to calculate the vapor generated in each effect, gain ratio, and heat transfer areas for the sixeffect desalting unit having the following data.
To get the temperature distribution:
D = 432 m 3 day , T1 = 90.2 °C , Tc = 29 °C
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tv 5 = Tv 5 − Tv 6 = Tv 6 − Tc
U e = U = 2.5 ( kW m 2 .° K ) ,
= Tv 4 − Tv 5 = Tv 5 − Tv 6 = Tv 6 − Tc Ts = 109 °C , Tv 2 = 79 °C ,
Tv 3 = 69 °C
Tv 4 = 59 °C ,
U c = 2.0 ( kW m 2 .° K )
Tv 5 = 49 °C ,
Tv 6 = 39 °C ,
Tc = 29 °C
k ( end condenser ) = 0.5
To get feed F to distillate D ratio, i.e. F/D
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Xb 70 = = 2.5 X b − X f 70 − 42
F D= D=
A1 =
432 × 1000 = 5 (m3 s ) 24 × 60 × 60
To get D1/D: D1 = D 4 3 2 1 − ( F D ) y ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 2 4 3 2 ⎡ 1 − ( 2 − y ) − ( 2 − y ) + ( 2 − y ) + (1 − y ) × 1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦
{
}
3
where y = 0.0172; and F D = 2.5 ⇒
D1 = 0.07027 D
F = 2.5 D = 2.5 × 5
=12.5
D1 = (0.07027) D = (0.07027) × 5
=0.3514 kg/s
D2 = (1!y) D1 + F y
=0.5603 kg/s
D3 = (2!y) D2 + D1
=0.7596 kg/s
D4 = (2!y) D3 + D2
=0.9458 kg/s
D5 = (2!y) D4 + D3
=1.1157 kg/s
D6 = (2!y) D5 + D4
=1.2664 kg/s
D=
6
Σ
i=1
Di = D1 + D2 + D3 + D4 + D5 + D6 = 5
kg/s
S × 2330 = 12.5 × 4 × (90.2 − 34) + 0.3514 × 2330
GR =
D 5 = = 2.69 S 1.8585
U ( Ts − Tv1 − BPE )
= 159 m 2
A2 =
D1 L = 32.84 m 2 U ( ΔT − BPE )
A3 =
D2 L = 52.28 m 2 U ( ΔT − BPE )
A4 =
D3 L = 70.82 m 2 U ( ΔT − BPE )
A5 =
D4 L = 88.14 m 2 U ( ΔT − BPE )
A6 =
D5 L = 103.9 m 2 U ( ΔT − BPE )
kg/s
S .L = F .C. (T1 − T f ) + D1 .L S = 1.8585 kg s
F . C.(T1 − T f ) + D1 . L
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3. Backward feed multi-effect distillation system
Consider a backward feed multi-effect desalting system with six evaporators E1, E2, E3, E4, E5, and E6. The feed F at Tf from the condenser enters the last effect, the sixth here. The feed F is heated to the boiling temperature T6 in this effect, and part of it equal to D6 is evaporated by utilizing the heat gained by condensing the vapor D5 coming from the preceding effect E5 and entering E6 as heating vapor. The brine leaving E6 is (F!D6), and it is pumped to E5 as feed. Similarly the brine leaving E5 is (F!D6!D5), and is pumped to the fourth effect E4 as feed and so on to the first effect. Fig. 3b gives the temperature distribution for this system. So, the feed seawater (or brine) to the effects E1, E2, E3, E4, E5, and E6 are: (F!D6! D5!D4!D3!D3!D2), (F!D6!D5!D4!D3), (F!D6 !D5!D4), (F!D6!D5), (F!D6), and F respectively. The heating steam S enters the first effect, heats the feed from T2 to T1 and evaporates D1 out
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
of it. The vapor D1 generated in effect E1 at Tv1 is the heating vapor to second effect E2. It raises the feed temperature of this effect from T3 to T2, and evaporates D2 out of it by boiling at Tv2
D2 = D3 + (F!D6 !D5!D4).C.(T2!T3)/L D2 = D3 +(F!D !D1 + D2 + D3). y D3 =[D2 (1!y) + (F!D +D1).y]/(1+y) Similarly, D4 = [D3 (1!y) + (F!D +D1+D2).y]/(1+y) D5 =[D4 (1!y) + (F!D + D1+D2+D3).y]/(1+y) Also, D5 = D6 + F.C.(T6!Tf)/L = D6
S = D1 + (F!D + D1) . y
+ F.C.(1!k)(T6!Tc)/L = D6 =D5!F(1!y).k
D1 = [S! (F!D) . y]/(1+y)
These equations show that the vapor generated in each effect is decreased as the number of effects is increased, i.e. D1 > D2 > D3>…>Dn. This is contrary to what happens in the forward feed arrangement. In addition, full analysis of the heat transfer surface areas would give more total area in the case of backward feed than the forward feed case. It is necessary here to use pumps to transfer the feed from one effect (at low pressure) to the preceding effect (which is at higher pressure) and this is another disadvantage, besides the highest salt concentration occurs in the highest temperature effect; first effect.
Q1 = U1 . A1 . ΔT1 = U1 . A1 . (Ts!T1) = U1 . A1 . (Ts!Tv1!BPE) The brine leaving the first effect, (B = F!D) is rejected back to the sea. The heat gain in the second effect E2 by condensing D1 increases the temperature of the feed to E2 from T2 (boiling temperature at P2) to T1 (the boiling temperature at P1) and evaporates D2. Then, D1.L = D2.L + (F!D6 –D5!D4!D3).C.(T2!T3) By considering constant latent heat L
3.1. Illustrative example 2
D1 = D2 + (F!D6 !D5!D4! D3).y = D2
The following are the data of the four-effect desalting unit with backward feed arrangement.
+ (F!D + D1 + D2).y D2 =[D1 (1–y)!(F!D).y]/(1+y) The vapor generated in the second effect D2 enters E3 to heat the feed from T4 to T3 and evaporate D3.
D = 432 m 3 day T1 = 90.2 °C Tc = 29 °C The temperature difference between each effect is
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
the same, and is equal to that between the heating steam and vapor generated in the first effect. This temperature difference is also equal to that between the vapor generated in the last effect and the seawater temperature entering the end condenser.
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tc
U e = U = 2.5 ( kW m .° K ) 2
U c = 2.0 ( kW m 2 .° K ) k ( end condenser ) = 0.5 X f = 42 ( g l )
T f = Tv 4 − k ( Tv 4 − Tc ) = 44 − 0.5 (15) T f = 36.5 °C To find all temperatures:
Since ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tc Ts = 104 °C , Tv 2 = 74 °C , Tv 3 = 59 °C Define F/D:
F D=
X b = 70 ( g l ) BPE = 1.2 °C C = 4 ( kJ kg.° K ) It is required to calculate its gain ratio and heat transfer area required.
41
D=
Xb 70 = = 2.5 X b − X f 70 − 42
432 × 1000 = 5 (m3 s) 24 × 60 × 60
To find D4/D: 4
3.2. Solution To find ΔT:
Tv1 = T1 − BPE = 90.2 − 1.2 = 89°C Tv1 − Tc 89 − 29 = = 15 n 4 C ΔT 4 × 15 = = 0.0258 y= L 2330
ΔT =
To find Tf :
k=
D = ∑ Di = D1 + D2 + D3 + D4 i =1
The thermal analysis of the fourth, third, second and the first effects gives
D3 L = D4 L + F C (T4 − T f FC (T4 − T f L D2 = D3 + B4 y D3 = D4 +
Tv 4 − T f
D1 = D2 + B3 y
Tv 4 − Tc
B4 = F − D4
Tv 4 = Tv1 − ( n − 1) ΔT = 89 −(4 − 1) (15) = 44°C
B3 = F − D3 − D4 D = D1 + D2 + D3 + D4
)
)
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D = 2 D2 + B3 y + D3 + D4
To find D/S — the energy balance of the first effect gives:
D = 2 [ D3 + B4 y ] + B3 y + D3 + D4 D = D4 + 3 D3 + [ 2 B4 + B3 ] y
S .L = D1 . L + B2 . C. (T1 − T2 )
[2 B4 + B3 ] = 2 F − 2 D4 + F − D3 − D4
S = 1.6995 +
= 3 F − 3 D4 − D3
(12.5 − 1.3784 − 1.0795 − 0.8928) × 4 × 15
2330 = 1.9351 kg / s D 5 GR = = = 2.5838 S 1.9351
D = D4 + 3 D3 + [3 F − 3 D4 − D3 ] y D = (1 − 3 y ) D4 + 3 F y + ( 3 − y ) D3 D = (1 − 3 y ) D4 + 3 F y + ( 3 − y )
To find the heat transfer areas:
FC ⎡ × ⎢ D4 + (T4 − T f )⎤⎥ L ⎣ ⎦
D1 L + B2 C (T1 − T2 ) = U e A1 ( Ts − Tv1 − BPE )
D = ⎡⎣1 − 3 y + ( 3 − y ) ⎤⎦ D4 C ⎡ ⎤ + ⎢ 3 y + ( 3 − y ) (T4 − T f )⎥ × F L ⎣ ⎦ C ⎧ ⎡ ⎫ ⎤ ⎨1 − ⎢3 y + ( 3 − y ) ( T4 − T f ) ⎥ × F D ⎬ L D4 ⎩ ⎣ ⎦ ⎭, = D [4 − 4 y ] and T4 = Tv 4 + BPE = 44 + 1.2 = 45.2°C D ⇒ 4 = 0.1786 D F = 2.5 D = 2.5 × 5
=12.5
D4 = (0.1786) D = (0.1786) × 5
=0.8928 kg/s
D3 = D4 + (FC/L) (T4!Tf)
=1.9785 kg/s
D2 = D2 = D3 + (F!D4) y
=1.3784 kg/s
D1 = D1 = D2 + (F!D3!D4) y
=1.6495 kg/s
D=
6
Σ
i=1
Di = D1 + D2 + D3 + D4
=5
A1 =
= 127.3128 m 2 A2 =
D1 L = 111.401 m 2 U ( ΔT − BPE )
A3 =
D2 L = 93.09 m 2 U ( ΔT − BPE )
A4 =
D3 L = 72.905 m 2 U ( ΔT − BPE )
kg/s
kg/s
D1 L + B2 C (T1 − T2 ) U ( Ts − Tv1 − BPE )
LMTD =
(T
f
− Tc )
⎡T −T ln ⎢ v 6 c ⎢⎣ Tv 6 − T f
⎤ ⎥ ⎥⎦
and
Ac =
D6 L = 96.128 m 2 U c × LMTD
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
4. Parallel feed multi-effect distillation system
A simplified analysis for a six-effect parallel feed arrangement is given here. The analysis can be extended to any number of effects. A parallel feed multi-effect desalting system with six evaporators E1, E2, E3, E4, E5 and E6 is considered here. The feed F at Tf leaving the condenser is divided to almost equal six feeds F1, F2, F3, F4, F5 and F6, and supplied to E1, E2, E3, E4, E5 and E6 respectively. The heating steam S supplied to the first effect E1, heats F1 from Tf to T1, and evaporates D1 out of F1. The vapor D1 at Tv1 enters E2 as a heating vapor, and raises the temperature of its feed F2 from Tf to T2, and to evaporate D2b by boiling out of F2 at Tv2
43
The energy balance for the first effect gives: S.L = D1.L + F1.C.(T1!Tf) For the second effect: D1.L = D2b.L+F2.C.(T2!Tf) and Df2 = B1.C.ΔT/L = (F1!D1).y D1.L = (D2!D2f).L + (F/D).D2.C.(T2!Tf) Db2 and Df2 are the vapor generated by boiling and flashing in E2 respectively. Salt enters E2 is equal to F2.Xf should equal the salt out B2.X2, or F2..Xf = (F2! D2).X2. Since Xb1 = Xb2 = Xb, F2/D2 = Xb2/(Xb2 !Xf), then F2 = (F/D). D2, and Fi = (F/D).Di. Then, Df2 = (F1!D1).y D2 = (D1 + D2f)/[1+(F/D).C.(T2!Tf)/L]. The last two equations can be generalized to give: Df i = ∑[(F1!D1) +(F2!D2) +….+ (Fi-1!Di-1)].y Di = (Di-1 + Df i)/[1 + (F/D).C.(Ti!Tf)/L], or Df 3 = [(F1!D1) +(F2!D2)].y D3 = (D2 + Df 3)/[1 + (F/D).C.(T3!Tf)/L] Df 4 = [(F1!D1) +(F2!D2) + (F3!D3)].y D4 = (D3 + Df 4)/[1 + (F/D).C.(T4!Tf)/L] Df 5 = [(F1!D1) + (F2!D2) + (F3!D3) + (F4!D4)].y
44
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D5 = (D4 +Df 5)/[1 + (F/D).C.(T5!Tf)/L]
C = 3.9 kJ / kg . oC
Df6 = [(F1!D1) + (F2!D2) + (F3!D3) + (F4!D4)
L ( at T = 50 oC ) = 2383 kJ / kg
+….+ (F5!D5)].y D6 = (D5 + Df 6)/[1 + (F/D).C.(T6!Tf)/L] The thermal load of any effect i is given by
It is required to determine the condenser effectiveness, the vapor generated by boiling and flashing, and the temperature, and salinity distribution in each effect.
U1.Ai .(Ti!Ti-1 +BPE) = Fi .C.(Ti !Tf)+Di .L
4.2. Solution
4.1. Illustrative example 3 The following are the data of a four-effect desalting unit with parallel feed.
k=
T f − Tc Tvn − Tc
Tvn = Tn − BPE = 36 − 0.7 = 35.3 oC k = (T f − tc ) /(Tvn − Tc )
D = 4546 m 3 day
= (32.3 − 28) /(35.3 − 28) = 0.59
T1 = 64°C T f = 32.3°C
y = 3.9 × 9.3333/ 2383 = 0.01527
Tc = 28°C
T1 = 64 oC , T2 = 54.667 oC , T3
The temperature difference between each effect is the same, and equal to the temperature difference between the heating steam and vapor generated in the first effect. This temperature difference is also equal between the vapor generated in the last effect and the seawater temperature entering the end condenser.
TBT = 64 o C, Tn = 36 o C,
Db 2 = D1 −
T f = 32.3 o C
U e = 3 kW/m C, U c = 2.4 kW/m C D = 1 MIGD = 52.616 kg/s BPE = 0.7 oC
Xb F Fi 69 = = = =3 D Di X b − X f 69 − 46
D2 = Db 2 + D f 2
X b = 69 g l
2 o
F = 3 ×D S .L = D1. L + F1.C.(T1 − T f )
D = D1 + D2 + D3 + D4
= Tv 3 − Tv 4 = Tv 4 − Tc
Tc = 28 o C,
Fi / Di = 69 /(69 − 46) = 3
R=
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3
X f = 46 g l ,
= 45.334 oC , T4 = 36 oC
2 o
Df 2
F2 .C.(T2 − T f )
L = B1 . y = ( F1 − D1 ) y
D2 = D1 −
F2 .C.(T2 − T f )
+ Df 2 L C.(T2 − T f ) F = D1 + D f 2 − 2 D2 D2 L
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D2 = D1 + D f 2 − R.D2
D2 + R.D2
C.(T2 − T f ) L
C.(T2 − T f )
⎛ R.C.(T2 − t f ) ⎞ D2 ⎜ 1 + ⎟ = D1 + D f 2 L ⎝ ⎠
D2 + R.D2
C.(T2 − T f ) L
= D1 + D f 2
⎛ R.C.(T2 − T f ) ⎞ D2 ⎜ 1 + ⎟ = D1 + D f 2 L ⎝ ⎠ D2 =
D1 + D f 2 ⎛ R.C.(T2 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠
D1.(1 + ( R − 1). y ) ⎛ R.C.(T2 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ = (1 + 2 y ) × D1 /
D2 =
⎡⎣1 + 3 × 3.9 × ( 54.667 − 32.3) / 2383⎤⎦ = 0.9286 × D1 where F R= =3 D
B2 = ( F1 − D1 ) + ( F2 − D2 ) = ( R − 1) × D1 + ( R − 1) × D2 = ( R − 1) × D1 + ( R − 1)(0.9286 × D1 ) = 3.8572 × D1
D f 3 = B2 . y = 0.01527 × 3.8752 × D1
L
= D1 + D f 2
45
= 0.0589 × D1 4.3. General formula
Di −1 + D fi for i ≠ 1 ⎛ RC (Ti − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ D fi = y.Bi −1 Di =
Bi = ∑ ( R − 1) Di B1 = ( R − 1) D1 D3 =
D2 + D f 3 F3 ⎛ ⎞ C.(T3 − T f ) ⎟ ⎜ D ⎜1 + 3 ⎟ L ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
D3 = (0.9286 × D1 + 0.0589 × D1 ) / ⎡⎣1 + 3 × 3.9 × ( 45.334 − 32.3) / 2383⎤⎦ D3 = 0.9875 × D1 /1.064 = 0.9281 × D1 D3 + D f 4 ⎛ RC (T4 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ = y.B3
D4 =
Df 4
Df 4 = y. [( R − 1).D1 + ( R − 1). D2 + ( R − 1). D3 ]
D4 =
D3 + y. [( R − 1).D1 + ( R − 1).D2 + ( R − 1). D3 ] ⎛ R.C.(T4 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠
46
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Table 2 Results of illustrative example 3 Effect # T
F
Db
Df
D
Di/D
Di /D1
Fi!Di
3(F!D)
1 2 3 4 3
40.959 38.033 38.013 40.845 157.850
13.653 12.261 11.867 12.424 50.204
0.000 0.417 0.804 1.191 2.412
13.653 12.678 12.671 13.615 52.617
0.259 0.241 0.241 0.259
1.000 0.929 0.928 0.997
27.306 25.355 25.342 27.230
27.306 52.661 78.004 105.233
64.0 54.7 45.3 36.0
D4 =
0.9281 × D1 + 0.01527 × [ 2 × D1 + 2 × 0.9286 × D1 + 2 × 0.9281 × D1 ]
[1 + 3 × 3.9 × (36 − 32.3) / 2383]
= (0.9281 + 0.08724) × D1 /1.01817 = 0.9972 × D1
D = D1 + D2 + D3 + D4 D = (1 + 0.9281 + 0.9286 + 0.9972 ) × D1 = 3.8539 D1 1 = = 0.2595 D 3.85395 ∵ D = 1 MIGD = 52.616 kg / s ∴ D1 = 13.6525 5 kg / s where D1 = 13,653 kg/s; GR = 3.335, S = 15.778 kg/s and F1 = 40.959 kg/s.
5. Modified forward feed multi-effect with feed heaters
Most MEB desalting system use forward feed arrangement to keep the highest brine temperature with the least salt concentration in the first effect. However as shown in illustrative example 1, less than 19% of the heat given by condensation of heating steam (1.8585 kg/s) is used to evaporate D1 (0.3514 kg/s or about 7% of the
total distillate), while the balance, 91% is used to heat the feed F to its boiling temperature. As a result, the gain ratio of this six-effect unit is 2.69. To improve the performance of the forward feed MEB system, regenerative feed heaters are usually used as shown in Fig. 5a and 5b. In this system, cooling water Mc enters an end condenser at Tc to condense Dn (last effect vapor output) and leaves at tn. Part of the leaving Mc is pre-treated and becomes feed F, and is heated successively as it flows in the feed heaters from tn to t1 before entering the first effect. The balance of the condenser cooling water (Mc!F) is rejected back to the sea. The supplied steam S to the first effect heats the feed F from t1 to boiling temperature T1, and evaporates D1 out of F (D1 is the first effect distillate). The steam condensate returns back to the steam supply source. If the steam enters the first effect as saturated vapor and leaves as saturated liquid, then:
S .L = F .C (T1 − t1 ) + D1.L Vapor D1 enters the first feed heater FH1, preheats F from t2 to t1, and then flows as heating vapor to
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 47
Fig. 5. (a) Forward feed six-effect with regenerative heating distillation system; (b) temperature distribution through the effects.
48
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
the second effect, where D2 is evaporated. Vapor D2 enters the second feed heater FH2, preheats F from t3 to t2, and then flows as heating vapor to the third effect. The process is repeated to the last effect. The vapor formed in the last effect flows to the end condenser. The condensate leaves and joins the distillate of other effects. Brine B1 from the first effect enters the second effect as feed, and brine B2 from second effect is fed to effect E3, and so on to the last effect. Brine Bn from the last effect is rejected to the sea. The feed to distillate ratio F/D is determined by the maximum allowable salinity Xb of Bn and feed salinity Xf by
Xb F = D (Xb - X f ) A simplified analysis for the MEB system is given here by assuming [5,6]: 1. Equal vapor generated by boiling in each effect, (other than first effect) = β.D. 2. Equal boiling temperature difference ΔT between effects. 3. Equal increase Δt of the feed F in feed heaters, and ΔT = Δt. 4. Equal specific heat C for the brine and feed. 5. Equal latent heat L and BPE. This analysis gives — brine
B2 = B1 (1 − y ) − β . D
B2 = (1 − y ) ( F (1 − y ) − β .D ) − β .D B2 = (1 − y ) 2 F −
β .D y
(1 −
(1 − y ) 2 )
And similarly
Bn = (1 − y ) n F −
βD y
(1 − (1 − y ) ) n
Notice that [1!(1!y)n] can be approximated by
⎡ ⎛ (n − 1) y ⎞ ⎤ ⎟⎥ ⎢ n. y ⎜ 1 − 2 ⎠⎦ ⎣ ⎝ for y n1.
F 1 β = − n D (1 − (1 − y ) ) y
β y
=
1 F − n (1 − (1 − y ) ) D
Then
β+
y. F 1 = D n (1 − ( n − 1) y 2 )
B1 = F! D1 = (1!y).F!β.D
And this is practically proportional to 1/n. The gain ratio is determined from
and
S .L = F .C.(T1 − t1 ) + D1 .L
D2 = β.D + y.B1
S .L = F .C.(T1 − t1 ) + ( y.F + β . D ).L
Then
B2 = B1 − D2 B2 = B1 − ( β . D + y.B1 )
S y. F F .C (T1 − t1 ) = β+ + D D D. L 1 F .C.(T1 − t1 ) ≅ + n D. L
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
49
Table 3 Results of illustrative example 4 Effect #
T
t
F
Db
Df
D
B
X
Ae
Af
1 2 3 4 5 6 3
50 46.9 43.8 40.7 37.6 34.5
47.5 44.4 41.3 38.2 35.1 32
611.0 577.1 543.3 509.7 476.3 443.1
33.95 30.70 30.70 30.70 30.70 30.70 187.45
0.00 3.07 2.89 2.71 2.53 2.35 13.55
33.95 33.77 33.59 33.41 33.23 33.06 201.00
577.1 543.3 509.7 476.3 443.1 410.0
44.5 47.2 50.3 53.9 57.9 62.6
11,284.5 9,474.1 9,474.1 9,474.1 9,474.1 9,474.1 58,654.9
1053.4 1053.4 1053.4 1053.4 1053.4 1053.4 6320.4
D/S is approximated by
D n = S (1 + n. F .C.(T1 − t1 ) D.L )
D6(L) = Mc(4) (32!26), Mc = 3214 kg/s, Mc/D = 16
Calculate the heat transfer specific area of the Ashdod plant. The Ashdod plant data are: n = 6, To = 50EC, Tn = 34.5EC, D = 201 kg/s, F = 611 kg/s, Xf = 42 g/kg.
Due to the low To = 50EC, the specific area is 323.26 m2/(kg/s), which is almost 75% more than that of the Sidem plant (185 m2/(kg/s) which operates with six effects at To = 65EC. Also the decrease of Tn to 34.5EC, and even Tc = 26EC, Mc/D = 16, which is very high compared to sixeffect Sidem 1 plant where Tn = 38EC. Stream flow rate, temperatures, and salinity for the Ashdod plant and effects and feed heaters calculated heat transfer surface areas are shown in Table 3.
5.2. Solution
6. Results
This shows that the gain ratio is always less than n, but close to it. 5.1. Illustrative example 4
ΔT = Δt = (50!34.5)/5 = 3.1EC; then t1 = tn + (n!1) Δt = 32.5 + 5(3.1) = 48EC F/D = 611/201 = 3.04, y = CΔT/L = 0.005322 β/y =1/[1!(1!y)n]!F/D, β = 0.1514, and βD = 30.4326 kg/s D1 = βD + yF = 34 kg/s, S = D1 + FC(T1!t1)/L = 36.09 kg/s, D/S = 5.57 To get Mc, D6 should be known (see Table 3).
The results of the derived equations for the three simple feed arrangements (forward feed FF, backward feed BF, and parallel feed PF) show the characteristics of each system when no feed heaters are used. In all system types (FF, BF, and PF), increasing the number of effects (from two to typically six effects for 1 MIGD, increases the gain ratio D/S, and the used specific heat transfer area as shown in Figs. 6 and 7. The backward feed has a favorable higher gain ratio and lower specific heat transfer areas than the forward feed. However, the BF is seldom used in desalination since the high salinity in the system occurs at the highest temperature in the first effect as shown in
50
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 6. Effect of increasing the number of effects n on the specific heat transfer area.
Fig. 7. Effect of increasing the number of effects n on the gain ratio D/S.
Fig. 8. Also in PF system the maximum salinity is reached in each effect. This increases the risk of depositing scales of inverse solubility salts like CaCO3, Mg(OH)2, and CaSO4 in the BF system than in the FF system. Another disadvantage for the BF system is the need for pumping the feed from one effect to the preceding effect (at higher pressure).
The vapor generated per effect increases with the increase of the effect number, i, in forward feed system, while decreases with the increase of i in the BF system, becoming equal to average in the PF system, as shown in Fig. 9. The use of the forward feed requires significant increase of the heat transfer area in the first effect compared to other effects when no feed heaters are used, and
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
51
Fig. 8. Salinity and temperature profiles in the different feed types.
Fig. 9. Vapor generated in each effect in a unit producing one MIGD by different feed type systems.
little fraction of D1/D of vapor is generated at this effect. High fraction of the energy supplied by the heating system is used in heating the feed rather than generating vapor, as shown in Fig. 9.
As the number of effects increase, the heat rejected by the condenser is decreased since only the magnitude of D/n needs to be condensed in the condenser as shown in Fig. 10.
52
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 10. Effect of the number of effects on the condenser capacity.
Fig. 11. Effect of adding the feed heaters on the gain ratio for different number of effects.
The use of feed heaters for a six-effect forward feed system increases the gain ratio from .033 (without feed heaters) to 5.35 (24.6%) when feed heaters are used (see Fig. 11). In addition,
the total specific heat transfer areas, including the heat transfer area of the feed heater, are less than the case of the forward feed without feed heaters (see Fig. 12).
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
53
Fig. 12. Effect of using feed heaters on the specific heat transfer area used for evaporators, feed heaters, and condenser.
7. Symbols
A B BPE C D Db Df F GR k L LMTD
— — — — — — — — — — — —
Mc n Pv Q S t
— — — — — —
Tb TBT
— —
2
Heat transfer area, m Brine flow rate, kg/s Boiling point elevation Specific heat capacity, kJ/kgEC Distillate flow rate, kg/s Distillate generated by boiling, kg/s Distillate generated by flashing, kg/s Feed flow rate, kg/s Gain ratio Condenser effectiveness Latent heat, kJ/kg Logarithmic mean temperature difference, EC Cooling water flow rate, kg/s Number of effects Vapor pressure, kPa Heat transfer load, kW Steam flow rate, kg/s Feed temperature in the feed heater, EC Brine temperature, EC Top brine temperature, EC
Tc Tf Tn Ts Tv Uc
— — — — — —
Ue
—
xb xf y ΔT
— — — —
Cooling water temperature, EC Feed temperature, EC Last effect temperature, EC Steam temperature, EC Vapor temperature, EC Overall heat transfer coefficient of the condenser, kW/m2 EC Overall heat transfer coefficient of the evaporator, kW/m2 EC Brine salinity Feed salinity Flashing fraction Temperature difference, EC
References [1] U. Fisher, A. Aviram and A. Gendel, Ashdod low temperature multi-effect desalination plant, Desalination, 55 (1985) 13–32. [2] C. Temster and J. Laborie, Dual purpose desalination plant — high efficiency multi effect evaporator operating with turbine for power produc-tion, Proc. IDA World Conference on Desalination and Water
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Science, Abu Dhabi, Vol. 3, 1995, pp. 297–308. [3] B. Ohlemann and D. Emmermann, Advanced barge mounted VTE/VC seawater desalting plant, Desalination, 45 (1983) 39–47. [4] B. Franquelin, F. Murat and C. Temstet, Application of multi-effect process at high tem-perature for large seawater, Desalination, 45 (1983) 81–92.
[5] M.A. Darwish and A.A. El-Hadik, The multi effect boiling desalting system and its comparison with the MSF, Desalination, 60 (1986) 251–265. [6] M.A. Darwish, F. Al-Juwayhel and H.K. Abdulrahim, Multi-effect boiling systems from an energy viewpoint, Desalination, 194 (2006) 22–39.
Feed water arrangements in a multi-effect desalting system M.A. Darwish*, Hassan K. Abdulrahim Mechanical Engineering Department, Kuwait University, POB 5969, Safat 13060, Kuwait Tel. +965 481-1188, ext. 5789; Fax: +965 484-7131; email: [email protected]; [email protected] Received 24 January 2007; Accepted 9 May 2007
Abstract A multi-effect boiling (MEB) desalting system with unit capacity up to 5 MIGD becomes a strong competitor to the multi-stage flash (MSF) desalting system due to its low specific energy consumption and the low temperature steam required to operate the system. A considerable number of units have been installed in the Arabian Gulf area recently. There are many flow sheet variants for the MEB desalting system. Each variant suits certain design objectives. The schemes of the feed water flow to the effects and implementation of feed water heaters and flash boxes are among the significant differences between these flow sheets that have major influences on the system performance and the adopted analysis to evaluate the system. This paper outlines the commonly used feed water arrangements in multi-effect desalting systems, e.g. forward, backward, parallel, and mixed feed. For each flow sheet arrangement, the thermodynamic analysis used is presented. These analyses determine the temperature and salinity profiles of the system, the amount of vapor generated by boiling and by flashing in each effect, the required heat transfer areas for the effects and feed heaters, the gain and recovery ratios, and cooling water to distillate ratio. The analytical results obtained in this work are compared with several practical multi-effect desalting systems of typical capacity and number of effects. This comparison illustrates the logic behind choosing each flow sheet arrangement. Keywords: MEB; Feed arrangements; Regenerative feed heating; Gain ratio
1. Introduction A multi-effect boiling (MEB) desalting system with unit capacity up to 5 MIGD is a strong competitor to the multi-stage flash (MSF) desalting system due to its low specific energy *Corresponding author.
consumption and the low temperature steam required to operate the system. A considerable number of units have been installed in the Arabian Gulf area recently (see Table 1). The first method used to desalt seawater in large quantities was the single effect desalting system consisting of an evaporator-condenser combination (Fig. 1). A heat source (steam S) heats the incoming feed
0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.05.039
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
31
Table 1 Examples of conventional multi-effect desalting units Location [ref.]
Ashdod [1]
Sidem 1 [2]
Eilat [1]
Barge unit [3]
Sidem 2 [4]
Evaporator type No. of effects Capacity (kg/s) GR Heat source
THE 6 201 5.7 Water 2778 kg/s 63–55.4EC 42 611 50 34.5 0.25 kg/s at 6.6 bar
THE 12 139 9.8 Steam 14.17 kg/s, 0.31 bar 36 45.6 64 37.5 0.7 at 8 bar
THE 12 N/A 10.1 N/A
THE-stacked 24 50 22.3 Steam
THE 16 290 12.4 Steam
N/A N/A 70 – 74 N/A N/A
33.5 N/A 99 N/A N/A
50 1502 106 46.6 N/A
2.2 9.1
2 8.14
N/A N/A
N/A N/A
N/A N/A
Polyphosphate
N/A
Polyphosphate
Anti-scale
N/A
Feed TDS (g/l) Feed (kg/s) TBT (EC) Minimum T (EC) Ejector steam, m ˙ (kg/s) P (bar) Pump energy (kWh/m3) Equivalent energy (kWh/m3) Treatment
F to the evaporator from its entering feed temperature Tf to its boiling temperature Tb, and evaporates part of it equal to D. The vapor D is directed to the condenser where it condenses and heats the cooling water Mc from seawater temperature Tc to the feed temperature Tf. Part of Mc leaving the condenser is used as feed F while the balance B (=Mc!F) is called brine blow-down and is rejected back to the sea. In the condenser of a single-effect desalting system, a small portion of the latent heat given off by condensing the vapor D is utilized to heat the feed-water F, while the balance [D.L!F.C.(Tf!Tc)]
Fig. 1. Single-effect distillation system.
is rejected back to sea. This is an inefficient utilization of thermal energy. A logical solution is to utilize the latent heat of vapor generated at one evaporator, say E1, at Tv1, and Pv1 as a heat source to a second evaporator, say E2, operating at a pressure Pv2 < Pv1 and temperature Tv2 < Tv1. The vapor formed in E2 (the second evaporator) can be used as a heating medium for a third
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
evaporator E3, and so on. The process of adding more evaporators can be continued to a final n evaporator. The vapor generated in the last evaporator n is directed to a bottom condenser where it is condensed. The heating steam (heat source) is condensed in the first effect at the highest temperature. This is called the n-effect distillation system. The use of multi-effects gives better usage of the consumed thermal energy, and thus reduces the cost of the product water. The temperature and pressure in each effect are decreased by the increase of the effect number. The choice of the number of effects is affected by the following facts: 1. The available temperature range, which is the difference between the saturation temperature Ts of the steam supplied to the first effect and the cooling water temperature in the condenser Tc, i.e. (Ts!Tc). The temperature Ts is chosen to be only few degrees (5–7EC) above the maximum allowable (top) brine temperature (TBT), T1, determined by the feed water pretreatment. Tc is the cooling seawater temperature. The brine temperature in the last effect, Tn, is usually in the range of 35–40EC to keep a reasonable specific volume of the vapor generated in the last effect. 2. The required temperature drop across the evaporator ΔT = (Ts!Tn)/n. Usually, equal temperature drop is taken between the effects. The increase of n decreases ΔT, and consequently increases the required heat transfer areas. 3. The design production rate D = ΣDi. 4. The required gain ratio (GR), which increases with the increases of n. 5. The capital cost increase by using additional effects. There are different schemes for supplying the feed water (seawater or brine) to the evaporators, mainly forward, backward, parallel, and mixed feed systems. In the forward feed arrangement, shown in Fig. 2a, the feed water F (after leaving the bottom condenser at feed temperature Tf) is supplied to the first effect of the highest tempera-
ture. Part of F equal to D1 is evaporated in the first effect and the balance brine B1 (=F!D1) enters the second effect as a feed F2, and D2 is evaporated out of it. The brine leaving the second effect B2 (=B1!D2) enters the third effect as a feed F3, and D3 is evaporated out of it, and so on to the last effect. The brine leaving the last effect is blown down to the sea. This means that the feed and vapor enter the effects and flow in the same direction. The temperature distribution for this arrangement is shown in Fig. 2b. In the backward feed arrangement, shown in Fig. 3a, the feed water F is directed from the end condenser to the last effect n, (of the lowest temperature), and Dn is evaporated out of it. The brine Bn (=F!Dn) leaving effect n is directed to the preceding effect (n!1) as a feed, and Dn-1 is generated out of it, and so on to the first effect. The brine leaving the first effect is blown down to the sea. Thus, the feed and vapor entering the effects have opposite flow directions. The temperature distribution of this arrangement is illustrated in Fig. 3b. In the parallel feed arrangement, the feed F leaving the condenser is divided and distributed almost equally to each effect. Fig. 4a shows the flow sheet of parallel feed arrangement while Fig. 4b illustrates the temperature distribution. The choice of any of these feed arrangements affects the design and performance of the MEB desalting system, e.g. the evaporator arrangements, the required heat transfer areas of the effects, the amount of vapor generated in each effect (evaporator), the amounts of vapor generated by boiling and by flashing, the pumping energy, the gain ratio (distillate to heating steam ratio), and the cooling water to distillate ratio. The analysis of the main feed water schemes are given in this paper when no feed heaters are used between the effects. Then the deficiencies appeared of the forward feed system, the most used system in desalination, are discussed. Then feed heaters are introduced between the effects to decrease these deficiencies, and the system with
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 33
Fig. 2. (a) Forward feed six-effect distillation system; (b) temperature distribution through the effects.
34 M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 3. (a) Backward feed six-effect distillation system; (b) temperature distribution through the effects.
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 35
Fig. 4. (a) Parallel feed six-effect distillation system; (b) temperature distribution through the effects.
36
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
feed heaters is analyzed to show the effect of using the feed heaters. In order to simplify the forthcoming analysis, some assumptions are used such as: 1. An average value for the specific heat of the distillate, feed, and brine is used and considered constant in all effects, C. 2. An average and constant value of the latent heat of steam as well as the vapor generated in each effect is used, i.e. Ls = L1 = L2 =… = Ln = L. 3. Equal temperature drops between the effects and between the heating steam and the vapor generated in the first effect, i.e.
The brine leaving this effect, B1, is B1 = F!D1. Heat is gained in the second effect by the condensation of D1 and the temperature decrease of brine B1 coming from the first effect at T1 (boiling temperature at P1) to T2 (the boiling temperature at P2). Then, the heat gain to this effect is
Ts!T1 = T1!T2 = T2!T3 = T3!T4 = Ti!Ti!1 = ΔT
Q2 (energy available) = D1.L + B1.C.(T1!T2)
2. Analysis of forward feed multi-effect distillation system A simplified analysis for a four-effect forward feed arrangement is given here. The analysis can be extended to any number of effects, but it becomes more complicated. The analysis of this first case will be given with little details since the following analyses depend on the understanding of this process. Consider that the four-effect desalting system is represented by four evaporators E1, E2, E3 and E4. The amount of vapor generated in each effect is equal to D1, D2, D3 and D4 respectively. Fig. 2b illustrates the temperature distribution for a forward feed system. The vapor D1 generated in effect E1 at Tv1 is the heating vapor supplied to effect E2, and it evaporates Db2 by boiling at Tv2
directed to an end condenser. The first effect thermal load is equal to Q1 = S.L = F.C.(T1!Tf) + D.L1 = U1.A1.ΔT1 = U1.A1.(Ts!T1) = U1.A1.(Ts!Tv1!BPE)
The vapor generated in the second effect D2 consists of Df2 plus Db2, i.e. D2 = Db2 + Df2 Df2 is formed by flash evaporation from B1 as its temperature is reduced from T1 to T2 to reach equilibrium condition, thus: Df2 = B1.C.( T1!T2)/L2 = y.B1 The term y represents the fraction of the flashed vapor from the brine B1 and is equal to y = C.ΔT/L. Db2 is formed by boiling due to the latent heat liberated by condensation of D1, i.e. Db2 . L2 = D1 . L1 Db2 – D1 for L1 – L2 So, D2 = D1 + Df2 D2 = D1 + (F!D1).y D2 = D1.(1!y) + y.F
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
The heat transfer for the boiling in the second effect can be calculated from the thermal load of this effect: Db2 . L2 – D1 . L2 = U2 .A2 .(Tv1!T2) The third effect mass and energy balances give — the brine leaving the second effect B2 is the feed to the third effect, and is equal to B2 = B1!D2 = B1!(D1 + y.B1) = B1 (1! y)!D1 Vapor obtained by flashing from B2 in the third effect Df3 is equal to Df3 = B2.C.(T2!T3) /L = B2.C.ΔT/L = B2.y = (F!D1!D2).y, Vapor obtained by boiling in the third effect = Db3 = D2 and
D4 = D3 . (1! y)!y . B2, but y . B2 = Df3 = D3!Db3 = D3!D2 D4 = D3 . (2! y)! D2 A general form can be expressed by Di = Di-1 (2! y)!Di-2 for i>2 Db4 . L = U4 . A4 . (Tv3!T4) The brine leaving the fourth effect (B4) is the brine blow-down back to the sea. B4 = B3!B4 B4 = B3!(D3 + y.B3) B4 = B3.(1!y)!D3 For the end condenser, the thermal load is Qc = D4 . L = Mc . C . (Tf!Tc) = Uc . Ac . (Tf!Tc)/ln[(Tv4!Tc)/(Tv4!Tf)]
Db3.L3 = D2.L2
The condenser effectiveness is defined by
Db3 – D2 for L2 – L3
k = (Tf!Tc)/ (Tv4 –Tc)
D3 = Db3 + Df3 D3 = D2 + (F!D1!D2).y (F!D1) . y = D2! D1 D3 = D2 . (1! y) + (D2! D1) D3 = D2 . (2! y)! D1 Db3 . L = D2 . L = U3 . A3 . (Tv2!T3) Similarly for the fourth effect:
37
To utilize the above analysis in a design of an MEB system of certain capacity D, the ratio (D1/D) of vapor generated in E1 to the total distillate should be known to start the design procedure. The vapor D1 is generated from F in the first effect by boiling only; then, D2 = D1 + (F!D1) . y = D1 . (1! y) + y . F
D4 = Db4 + Df4
D3 = D2 + (F!D1!D2) . y
D4 = D3 + y.B3,
D3 = D2 . (1! y) + (D2! D1) = D2 . (2! y)! D1
Db4 = D3
D4 = D3 . (2! y)! D2
B3 = B2!D3
D = ΣDi = D1 + D2 + D3 + D4
D4 = D3 + y.B3 = D3 + y.(B2!D3)
D = D1 + D2 + [D2 . (2!y)!D1] + [D3 . (2!y)!D2]
38
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D = (D2 + D3) . (2! y)
X f = 42 ( g l )
D = (2! y) . [D2 + D2 . (2! y)! D1]
X b = 70 ( g l )
D = (2! y) . [D2 . (3! y)! D1]
BPE = 1.2 °C
D = (2! y) . [(3! y){D1 . (1! y) + y . F}! D1]
C = 4 ( kJ kg.° K )
D/(2! y) = [(1! y) . (3! y)– 1] . D1 + y . (3! y) . F D1/D = [{1/(2! y)}!y . (3! y) F/D]/[(1! y)
2.2. Solution
(3! y)! 1] A similar formula for D1/D can be derived for five effects, and this gives: D1/D = {1/[(2!y).(3!y)!1]!y.(2!y).F/D}/
Tv1 = T1 − BPE = 90.2 − 1.2 = 89 °C ΔT = y=
[(1!y).(2!y)!1] Also a formula for D1/D for six effects is derived, and read as: D1 = D 1 − ( F D ) y ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 3 2 4 3 2 1 − ( 2 − y ) − ( 2 − y ) + ( 2 − y ) + (1 − y ) × ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 3
2
{
}
C ΔT 4 × 10 = = 0.0172 L 2330
To get Tf:
k= 4
Tv1 − Tc 89 − 29 = = 10 °C n 6
Tv 6 − T f Tv 6 − Tc
Tv 6 = Tv1 − ( n − 1) ΔT = 89 − (6 − 1) (10) Tv 6 = 39 °C
2.1. Illustrative example 1
T f = Tv 6 − k ( Tv 6 − tc ) = 39 − 0.5 (10) T f = 34 °C
Use the formula given for D1/D for six effects to calculate the vapor generated in each effect, gain ratio, and heat transfer areas for the sixeffect desalting unit having the following data.
To get the temperature distribution:
D = 432 m 3 day , T1 = 90.2 °C , Tc = 29 °C
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tv 5 = Tv 5 − Tv 6 = Tv 6 − Tc
U e = U = 2.5 ( kW m 2 .° K ) ,
= Tv 4 − Tv 5 = Tv 5 − Tv 6 = Tv 6 − Tc Ts = 109 °C , Tv 2 = 79 °C ,
Tv 3 = 69 °C
Tv 4 = 59 °C ,
U c = 2.0 ( kW m 2 .° K )
Tv 5 = 49 °C ,
Tv 6 = 39 °C ,
Tc = 29 °C
k ( end condenser ) = 0.5
To get feed F to distillate D ratio, i.e. F/D
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Xb 70 = = 2.5 X b − X f 70 − 42
F D= D=
A1 =
432 × 1000 = 5 (m3 s ) 24 × 60 × 60
To get D1/D: D1 = D 4 3 2 1 − ( F D ) y ⎡1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦ 2 4 3 2 ⎡ 1 − ( 2 − y ) − ( 2 − y ) + ( 2 − y ) + (1 − y ) × 1 + ( 2 − y ) + ( 2 − y ) − 2 ( 2 − y ) − ( 2 − y )⎤ ⎣ ⎦
{
}
3
where y = 0.0172; and F D = 2.5 ⇒
D1 = 0.07027 D
F = 2.5 D = 2.5 × 5
=12.5
D1 = (0.07027) D = (0.07027) × 5
=0.3514 kg/s
D2 = (1!y) D1 + F y
=0.5603 kg/s
D3 = (2!y) D2 + D1
=0.7596 kg/s
D4 = (2!y) D3 + D2
=0.9458 kg/s
D5 = (2!y) D4 + D3
=1.1157 kg/s
D6 = (2!y) D5 + D4
=1.2664 kg/s
D=
6
Σ
i=1
Di = D1 + D2 + D3 + D4 + D5 + D6 = 5
kg/s
S × 2330 = 12.5 × 4 × (90.2 − 34) + 0.3514 × 2330
GR =
D 5 = = 2.69 S 1.8585
U ( Ts − Tv1 − BPE )
= 159 m 2
A2 =
D1 L = 32.84 m 2 U ( ΔT − BPE )
A3 =
D2 L = 52.28 m 2 U ( ΔT − BPE )
A4 =
D3 L = 70.82 m 2 U ( ΔT − BPE )
A5 =
D4 L = 88.14 m 2 U ( ΔT − BPE )
A6 =
D5 L = 103.9 m 2 U ( ΔT − BPE )
kg/s
S .L = F .C. (T1 − T f ) + D1 .L S = 1.8585 kg s
F . C.(T1 − T f ) + D1 . L
39
3. Backward feed multi-effect distillation system
Consider a backward feed multi-effect desalting system with six evaporators E1, E2, E3, E4, E5, and E6. The feed F at Tf from the condenser enters the last effect, the sixth here. The feed F is heated to the boiling temperature T6 in this effect, and part of it equal to D6 is evaporated by utilizing the heat gained by condensing the vapor D5 coming from the preceding effect E5 and entering E6 as heating vapor. The brine leaving E6 is (F!D6), and it is pumped to E5 as feed. Similarly the brine leaving E5 is (F!D6!D5), and is pumped to the fourth effect E4 as feed and so on to the first effect. Fig. 3b gives the temperature distribution for this system. So, the feed seawater (or brine) to the effects E1, E2, E3, E4, E5, and E6 are: (F!D6! D5!D4!D3!D3!D2), (F!D6!D5!D4!D3), (F!D6 !D5!D4), (F!D6!D5), (F!D6), and F respectively. The heating steam S enters the first effect, heats the feed from T2 to T1 and evaporates D1 out
40
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
of it. The vapor D1 generated in effect E1 at Tv1 is the heating vapor to second effect E2. It raises the feed temperature of this effect from T3 to T2, and evaporates D2 out of it by boiling at Tv2
D2 = D3 + (F!D6 !D5!D4).C.(T2!T3)/L D2 = D3 +(F!D !D1 + D2 + D3). y D3 =[D2 (1!y) + (F!D +D1).y]/(1+y) Similarly, D4 = [D3 (1!y) + (F!D +D1+D2).y]/(1+y) D5 =[D4 (1!y) + (F!D + D1+D2+D3).y]/(1+y) Also, D5 = D6 + F.C.(T6!Tf)/L = D6
S = D1 + (F!D + D1) . y
+ F.C.(1!k)(T6!Tc)/L = D6 =D5!F(1!y).k
D1 = [S! (F!D) . y]/(1+y)
These equations show that the vapor generated in each effect is decreased as the number of effects is increased, i.e. D1 > D2 > D3>…>Dn. This is contrary to what happens in the forward feed arrangement. In addition, full analysis of the heat transfer surface areas would give more total area in the case of backward feed than the forward feed case. It is necessary here to use pumps to transfer the feed from one effect (at low pressure) to the preceding effect (which is at higher pressure) and this is another disadvantage, besides the highest salt concentration occurs in the highest temperature effect; first effect.
Q1 = U1 . A1 . ΔT1 = U1 . A1 . (Ts!T1) = U1 . A1 . (Ts!Tv1!BPE) The brine leaving the first effect, (B = F!D) is rejected back to the sea. The heat gain in the second effect E2 by condensing D1 increases the temperature of the feed to E2 from T2 (boiling temperature at P2) to T1 (the boiling temperature at P1) and evaporates D2. Then, D1.L = D2.L + (F!D6 –D5!D4!D3).C.(T2!T3) By considering constant latent heat L
3.1. Illustrative example 2
D1 = D2 + (F!D6 !D5!D4! D3).y = D2
The following are the data of the four-effect desalting unit with backward feed arrangement.
+ (F!D + D1 + D2).y D2 =[D1 (1–y)!(F!D).y]/(1+y) The vapor generated in the second effect D2 enters E3 to heat the feed from T4 to T3 and evaporate D3.
D = 432 m 3 day T1 = 90.2 °C Tc = 29 °C The temperature difference between each effect is
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
the same, and is equal to that between the heating steam and vapor generated in the first effect. This temperature difference is also equal to that between the vapor generated in the last effect and the seawater temperature entering the end condenser.
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tc
U e = U = 2.5 ( kW m .° K ) 2
U c = 2.0 ( kW m 2 .° K ) k ( end condenser ) = 0.5 X f = 42 ( g l )
T f = Tv 4 − k ( Tv 4 − Tc ) = 44 − 0.5 (15) T f = 36.5 °C To find all temperatures:
Since ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3 = Tv 3 − Tv 4 = Tv 4 − Tc Ts = 104 °C , Tv 2 = 74 °C , Tv 3 = 59 °C Define F/D:
F D=
X b = 70 ( g l ) BPE = 1.2 °C C = 4 ( kJ kg.° K ) It is required to calculate its gain ratio and heat transfer area required.
41
D=
Xb 70 = = 2.5 X b − X f 70 − 42
432 × 1000 = 5 (m3 s) 24 × 60 × 60
To find D4/D: 4
3.2. Solution To find ΔT:
Tv1 = T1 − BPE = 90.2 − 1.2 = 89°C Tv1 − Tc 89 − 29 = = 15 n 4 C ΔT 4 × 15 = = 0.0258 y= L 2330
ΔT =
To find Tf :
k=
D = ∑ Di = D1 + D2 + D3 + D4 i =1
The thermal analysis of the fourth, third, second and the first effects gives
D3 L = D4 L + F C (T4 − T f FC (T4 − T f L D2 = D3 + B4 y D3 = D4 +
Tv 4 − T f
D1 = D2 + B3 y
Tv 4 − Tc
B4 = F − D4
Tv 4 = Tv1 − ( n − 1) ΔT = 89 −(4 − 1) (15) = 44°C
B3 = F − D3 − D4 D = D1 + D2 + D3 + D4
)
)
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D = 2 D2 + B3 y + D3 + D4
To find D/S — the energy balance of the first effect gives:
D = 2 [ D3 + B4 y ] + B3 y + D3 + D4 D = D4 + 3 D3 + [ 2 B4 + B3 ] y
S .L = D1 . L + B2 . C. (T1 − T2 )
[2 B4 + B3 ] = 2 F − 2 D4 + F − D3 − D4
S = 1.6995 +
= 3 F − 3 D4 − D3
(12.5 − 1.3784 − 1.0795 − 0.8928) × 4 × 15
2330 = 1.9351 kg / s D 5 GR = = = 2.5838 S 1.9351
D = D4 + 3 D3 + [3 F − 3 D4 − D3 ] y D = (1 − 3 y ) D4 + 3 F y + ( 3 − y ) D3 D = (1 − 3 y ) D4 + 3 F y + ( 3 − y )
To find the heat transfer areas:
FC ⎡ × ⎢ D4 + (T4 − T f )⎤⎥ L ⎣ ⎦
D1 L + B2 C (T1 − T2 ) = U e A1 ( Ts − Tv1 − BPE )
D = ⎡⎣1 − 3 y + ( 3 − y ) ⎤⎦ D4 C ⎡ ⎤ + ⎢ 3 y + ( 3 − y ) (T4 − T f )⎥ × F L ⎣ ⎦ C ⎧ ⎡ ⎫ ⎤ ⎨1 − ⎢3 y + ( 3 − y ) ( T4 − T f ) ⎥ × F D ⎬ L D4 ⎩ ⎣ ⎦ ⎭, = D [4 − 4 y ] and T4 = Tv 4 + BPE = 44 + 1.2 = 45.2°C D ⇒ 4 = 0.1786 D F = 2.5 D = 2.5 × 5
=12.5
D4 = (0.1786) D = (0.1786) × 5
=0.8928 kg/s
D3 = D4 + (FC/L) (T4!Tf)
=1.9785 kg/s
D2 = D2 = D3 + (F!D4) y
=1.3784 kg/s
D1 = D1 = D2 + (F!D3!D4) y
=1.6495 kg/s
D=
6
Σ
i=1
Di = D1 + D2 + D3 + D4
=5
A1 =
= 127.3128 m 2 A2 =
D1 L = 111.401 m 2 U ( ΔT − BPE )
A3 =
D2 L = 93.09 m 2 U ( ΔT − BPE )
A4 =
D3 L = 72.905 m 2 U ( ΔT − BPE )
kg/s
kg/s
D1 L + B2 C (T1 − T2 ) U ( Ts − Tv1 − BPE )
LMTD =
(T
f
− Tc )
⎡T −T ln ⎢ v 6 c ⎢⎣ Tv 6 − T f
⎤ ⎥ ⎥⎦
and
Ac =
D6 L = 96.128 m 2 U c × LMTD
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
4. Parallel feed multi-effect distillation system
A simplified analysis for a six-effect parallel feed arrangement is given here. The analysis can be extended to any number of effects. A parallel feed multi-effect desalting system with six evaporators E1, E2, E3, E4, E5 and E6 is considered here. The feed F at Tf leaving the condenser is divided to almost equal six feeds F1, F2, F3, F4, F5 and F6, and supplied to E1, E2, E3, E4, E5 and E6 respectively. The heating steam S supplied to the first effect E1, heats F1 from Tf to T1, and evaporates D1 out of F1. The vapor D1 at Tv1 enters E2 as a heating vapor, and raises the temperature of its feed F2 from Tf to T2, and to evaporate D2b by boiling out of F2 at Tv2
43
The energy balance for the first effect gives: S.L = D1.L + F1.C.(T1!Tf) For the second effect: D1.L = D2b.L+F2.C.(T2!Tf) and Df2 = B1.C.ΔT/L = (F1!D1).y D1.L = (D2!D2f).L + (F/D).D2.C.(T2!Tf) Db2 and Df2 are the vapor generated by boiling and flashing in E2 respectively. Salt enters E2 is equal to F2.Xf should equal the salt out B2.X2, or F2..Xf = (F2! D2).X2. Since Xb1 = Xb2 = Xb, F2/D2 = Xb2/(Xb2 !Xf), then F2 = (F/D). D2, and Fi = (F/D).Di. Then, Df2 = (F1!D1).y D2 = (D1 + D2f)/[1+(F/D).C.(T2!Tf)/L]. The last two equations can be generalized to give: Df i = ∑[(F1!D1) +(F2!D2) +….+ (Fi-1!Di-1)].y Di = (Di-1 + Df i)/[1 + (F/D).C.(Ti!Tf)/L], or Df 3 = [(F1!D1) +(F2!D2)].y D3 = (D2 + Df 3)/[1 + (F/D).C.(T3!Tf)/L] Df 4 = [(F1!D1) +(F2!D2) + (F3!D3)].y D4 = (D3 + Df 4)/[1 + (F/D).C.(T4!Tf)/L] Df 5 = [(F1!D1) + (F2!D2) + (F3!D3) + (F4!D4)].y
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M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D5 = (D4 +Df 5)/[1 + (F/D).C.(T5!Tf)/L]
C = 3.9 kJ / kg . oC
Df6 = [(F1!D1) + (F2!D2) + (F3!D3) + (F4!D4)
L ( at T = 50 oC ) = 2383 kJ / kg
+….+ (F5!D5)].y D6 = (D5 + Df 6)/[1 + (F/D).C.(T6!Tf)/L] The thermal load of any effect i is given by
It is required to determine the condenser effectiveness, the vapor generated by boiling and flashing, and the temperature, and salinity distribution in each effect.
U1.Ai .(Ti!Ti-1 +BPE) = Fi .C.(Ti !Tf)+Di .L
4.2. Solution
4.1. Illustrative example 3 The following are the data of a four-effect desalting unit with parallel feed.
k=
T f − Tc Tvn − Tc
Tvn = Tn − BPE = 36 − 0.7 = 35.3 oC k = (T f − tc ) /(Tvn − Tc )
D = 4546 m 3 day
= (32.3 − 28) /(35.3 − 28) = 0.59
T1 = 64°C T f = 32.3°C
y = 3.9 × 9.3333/ 2383 = 0.01527
Tc = 28°C
T1 = 64 oC , T2 = 54.667 oC , T3
The temperature difference between each effect is the same, and equal to the temperature difference between the heating steam and vapor generated in the first effect. This temperature difference is also equal between the vapor generated in the last effect and the seawater temperature entering the end condenser.
TBT = 64 o C, Tn = 36 o C,
Db 2 = D1 −
T f = 32.3 o C
U e = 3 kW/m C, U c = 2.4 kW/m C D = 1 MIGD = 52.616 kg/s BPE = 0.7 oC
Xb F Fi 69 = = = =3 D Di X b − X f 69 − 46
D2 = Db 2 + D f 2
X b = 69 g l
2 o
F = 3 ×D S .L = D1. L + F1.C.(T1 − T f )
D = D1 + D2 + D3 + D4
= Tv 3 − Tv 4 = Tv 4 − Tc
Tc = 28 o C,
Fi / Di = 69 /(69 − 46) = 3
R=
ΔT = Ts − Tv1 = Tv1 − Tv 2 = Tv 2 − Tv 3
X f = 46 g l ,
= 45.334 oC , T4 = 36 oC
2 o
Df 2
F2 .C.(T2 − T f )
L = B1 . y = ( F1 − D1 ) y
D2 = D1 −
F2 .C.(T2 − T f )
+ Df 2 L C.(T2 − T f ) F = D1 + D f 2 − 2 D2 D2 L
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
D2 = D1 + D f 2 − R.D2
D2 + R.D2
C.(T2 − T f ) L
C.(T2 − T f )
⎛ R.C.(T2 − t f ) ⎞ D2 ⎜ 1 + ⎟ = D1 + D f 2 L ⎝ ⎠
D2 + R.D2
C.(T2 − T f ) L
= D1 + D f 2
⎛ R.C.(T2 − T f ) ⎞ D2 ⎜ 1 + ⎟ = D1 + D f 2 L ⎝ ⎠ D2 =
D1 + D f 2 ⎛ R.C.(T2 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠
D1.(1 + ( R − 1). y ) ⎛ R.C.(T2 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ = (1 + 2 y ) × D1 /
D2 =
⎡⎣1 + 3 × 3.9 × ( 54.667 − 32.3) / 2383⎤⎦ = 0.9286 × D1 where F R= =3 D
B2 = ( F1 − D1 ) + ( F2 − D2 ) = ( R − 1) × D1 + ( R − 1) × D2 = ( R − 1) × D1 + ( R − 1)(0.9286 × D1 ) = 3.8572 × D1
D f 3 = B2 . y = 0.01527 × 3.8752 × D1
L
= D1 + D f 2
45
= 0.0589 × D1 4.3. General formula
Di −1 + D fi for i ≠ 1 ⎛ RC (Ti − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ D fi = y.Bi −1 Di =
Bi = ∑ ( R − 1) Di B1 = ( R − 1) D1 D3 =
D2 + D f 3 F3 ⎛ ⎞ C.(T3 − T f ) ⎟ ⎜ D ⎜1 + 3 ⎟ L ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
D3 = (0.9286 × D1 + 0.0589 × D1 ) / ⎡⎣1 + 3 × 3.9 × ( 45.334 − 32.3) / 2383⎤⎦ D3 = 0.9875 × D1 /1.064 = 0.9281 × D1 D3 + D f 4 ⎛ RC (T4 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠ = y.B3
D4 =
Df 4
Df 4 = y. [( R − 1).D1 + ( R − 1). D2 + ( R − 1). D3 ]
D4 =
D3 + y. [( R − 1).D1 + ( R − 1).D2 + ( R − 1). D3 ] ⎛ R.C.(T4 − T f ) ⎞ ⎜1 + ⎟ L ⎝ ⎠
46
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Table 2 Results of illustrative example 3 Effect # T
F
Db
Df
D
Di/D
Di /D1
Fi!Di
3(F!D)
1 2 3 4 3
40.959 38.033 38.013 40.845 157.850
13.653 12.261 11.867 12.424 50.204
0.000 0.417 0.804 1.191 2.412
13.653 12.678 12.671 13.615 52.617
0.259 0.241 0.241 0.259
1.000 0.929 0.928 0.997
27.306 25.355 25.342 27.230
27.306 52.661 78.004 105.233
64.0 54.7 45.3 36.0
D4 =
0.9281 × D1 + 0.01527 × [ 2 × D1 + 2 × 0.9286 × D1 + 2 × 0.9281 × D1 ]
[1 + 3 × 3.9 × (36 − 32.3) / 2383]
= (0.9281 + 0.08724) × D1 /1.01817 = 0.9972 × D1
D = D1 + D2 + D3 + D4 D = (1 + 0.9281 + 0.9286 + 0.9972 ) × D1 = 3.8539 D1 1 = = 0.2595 D 3.85395 ∵ D = 1 MIGD = 52.616 kg / s ∴ D1 = 13.6525 5 kg / s where D1 = 13,653 kg/s; GR = 3.335, S = 15.778 kg/s and F1 = 40.959 kg/s.
5. Modified forward feed multi-effect with feed heaters
Most MEB desalting system use forward feed arrangement to keep the highest brine temperature with the least salt concentration in the first effect. However as shown in illustrative example 1, less than 19% of the heat given by condensation of heating steam (1.8585 kg/s) is used to evaporate D1 (0.3514 kg/s or about 7% of the
total distillate), while the balance, 91% is used to heat the feed F to its boiling temperature. As a result, the gain ratio of this six-effect unit is 2.69. To improve the performance of the forward feed MEB system, regenerative feed heaters are usually used as shown in Fig. 5a and 5b. In this system, cooling water Mc enters an end condenser at Tc to condense Dn (last effect vapor output) and leaves at tn. Part of the leaving Mc is pre-treated and becomes feed F, and is heated successively as it flows in the feed heaters from tn to t1 before entering the first effect. The balance of the condenser cooling water (Mc!F) is rejected back to the sea. The supplied steam S to the first effect heats the feed F from t1 to boiling temperature T1, and evaporates D1 out of F (D1 is the first effect distillate). The steam condensate returns back to the steam supply source. If the steam enters the first effect as saturated vapor and leaves as saturated liquid, then:
S .L = F .C (T1 − t1 ) + D1.L Vapor D1 enters the first feed heater FH1, preheats F from t2 to t1, and then flows as heating vapor to
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54 47
Fig. 5. (a) Forward feed six-effect with regenerative heating distillation system; (b) temperature distribution through the effects.
48
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
the second effect, where D2 is evaporated. Vapor D2 enters the second feed heater FH2, preheats F from t3 to t2, and then flows as heating vapor to the third effect. The process is repeated to the last effect. The vapor formed in the last effect flows to the end condenser. The condensate leaves and joins the distillate of other effects. Brine B1 from the first effect enters the second effect as feed, and brine B2 from second effect is fed to effect E3, and so on to the last effect. Brine Bn from the last effect is rejected to the sea. The feed to distillate ratio F/D is determined by the maximum allowable salinity Xb of Bn and feed salinity Xf by
Xb F = D (Xb - X f ) A simplified analysis for the MEB system is given here by assuming [5,6]: 1. Equal vapor generated by boiling in each effect, (other than first effect) = β.D. 2. Equal boiling temperature difference ΔT between effects. 3. Equal increase Δt of the feed F in feed heaters, and ΔT = Δt. 4. Equal specific heat C for the brine and feed. 5. Equal latent heat L and BPE. This analysis gives — brine
B2 = B1 (1 − y ) − β . D
B2 = (1 − y ) ( F (1 − y ) − β .D ) − β .D B2 = (1 − y ) 2 F −
β .D y
(1 −
(1 − y ) 2 )
And similarly
Bn = (1 − y ) n F −
βD y
(1 − (1 − y ) ) n
Notice that [1!(1!y)n] can be approximated by
⎡ ⎛ (n − 1) y ⎞ ⎤ ⎟⎥ ⎢ n. y ⎜ 1 − 2 ⎠⎦ ⎣ ⎝ for y n1.
F 1 β = − n D (1 − (1 − y ) ) y
β y
=
1 F − n (1 − (1 − y ) ) D
Then
β+
y. F 1 = D n (1 − ( n − 1) y 2 )
B1 = F! D1 = (1!y).F!β.D
And this is practically proportional to 1/n. The gain ratio is determined from
and
S .L = F .C.(T1 − t1 ) + D1 .L
D2 = β.D + y.B1
S .L = F .C.(T1 − t1 ) + ( y.F + β . D ).L
Then
B2 = B1 − D2 B2 = B1 − ( β . D + y.B1 )
S y. F F .C (T1 − t1 ) = β+ + D D D. L 1 F .C.(T1 − t1 ) ≅ + n D. L
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
49
Table 3 Results of illustrative example 4 Effect #
T
t
F
Db
Df
D
B
X
Ae
Af
1 2 3 4 5 6 3
50 46.9 43.8 40.7 37.6 34.5
47.5 44.4 41.3 38.2 35.1 32
611.0 577.1 543.3 509.7 476.3 443.1
33.95 30.70 30.70 30.70 30.70 30.70 187.45
0.00 3.07 2.89 2.71 2.53 2.35 13.55
33.95 33.77 33.59 33.41 33.23 33.06 201.00
577.1 543.3 509.7 476.3 443.1 410.0
44.5 47.2 50.3 53.9 57.9 62.6
11,284.5 9,474.1 9,474.1 9,474.1 9,474.1 9,474.1 58,654.9
1053.4 1053.4 1053.4 1053.4 1053.4 1053.4 6320.4
D/S is approximated by
D n = S (1 + n. F .C.(T1 − t1 ) D.L )
D6(L) = Mc(4) (32!26), Mc = 3214 kg/s, Mc/D = 16
Calculate the heat transfer specific area of the Ashdod plant. The Ashdod plant data are: n = 6, To = 50EC, Tn = 34.5EC, D = 201 kg/s, F = 611 kg/s, Xf = 42 g/kg.
Due to the low To = 50EC, the specific area is 323.26 m2/(kg/s), which is almost 75% more than that of the Sidem plant (185 m2/(kg/s) which operates with six effects at To = 65EC. Also the decrease of Tn to 34.5EC, and even Tc = 26EC, Mc/D = 16, which is very high compared to sixeffect Sidem 1 plant where Tn = 38EC. Stream flow rate, temperatures, and salinity for the Ashdod plant and effects and feed heaters calculated heat transfer surface areas are shown in Table 3.
5.2. Solution
6. Results
This shows that the gain ratio is always less than n, but close to it. 5.1. Illustrative example 4
ΔT = Δt = (50!34.5)/5 = 3.1EC; then t1 = tn + (n!1) Δt = 32.5 + 5(3.1) = 48EC F/D = 611/201 = 3.04, y = CΔT/L = 0.005322 β/y =1/[1!(1!y)n]!F/D, β = 0.1514, and βD = 30.4326 kg/s D1 = βD + yF = 34 kg/s, S = D1 + FC(T1!t1)/L = 36.09 kg/s, D/S = 5.57 To get Mc, D6 should be known (see Table 3).
The results of the derived equations for the three simple feed arrangements (forward feed FF, backward feed BF, and parallel feed PF) show the characteristics of each system when no feed heaters are used. In all system types (FF, BF, and PF), increasing the number of effects (from two to typically six effects for 1 MIGD, increases the gain ratio D/S, and the used specific heat transfer area as shown in Figs. 6 and 7. The backward feed has a favorable higher gain ratio and lower specific heat transfer areas than the forward feed. However, the BF is seldom used in desalination since the high salinity in the system occurs at the highest temperature in the first effect as shown in
50
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 6. Effect of increasing the number of effects n on the specific heat transfer area.
Fig. 7. Effect of increasing the number of effects n on the gain ratio D/S.
Fig. 8. Also in PF system the maximum salinity is reached in each effect. This increases the risk of depositing scales of inverse solubility salts like CaCO3, Mg(OH)2, and CaSO4 in the BF system than in the FF system. Another disadvantage for the BF system is the need for pumping the feed from one effect to the preceding effect (at higher pressure).
The vapor generated per effect increases with the increase of the effect number, i, in forward feed system, while decreases with the increase of i in the BF system, becoming equal to average in the PF system, as shown in Fig. 9. The use of the forward feed requires significant increase of the heat transfer area in the first effect compared to other effects when no feed heaters are used, and
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
51
Fig. 8. Salinity and temperature profiles in the different feed types.
Fig. 9. Vapor generated in each effect in a unit producing one MIGD by different feed type systems.
little fraction of D1/D of vapor is generated at this effect. High fraction of the energy supplied by the heating system is used in heating the feed rather than generating vapor, as shown in Fig. 9.
As the number of effects increase, the heat rejected by the condenser is decreased since only the magnitude of D/n needs to be condensed in the condenser as shown in Fig. 10.
52
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
Fig. 10. Effect of the number of effects on the condenser capacity.
Fig. 11. Effect of adding the feed heaters on the gain ratio for different number of effects.
The use of feed heaters for a six-effect forward feed system increases the gain ratio from .033 (without feed heaters) to 5.35 (24.6%) when feed heaters are used (see Fig. 11). In addition,
the total specific heat transfer areas, including the heat transfer area of the feed heater, are less than the case of the forward feed without feed heaters (see Fig. 12).
M.A. Darwish, H.K. Abdulrahim / Desalination 228 (2008) 30–54
53
Fig. 12. Effect of using feed heaters on the specific heat transfer area used for evaporators, feed heaters, and condenser.
7. Symbols
A B BPE C D Db Df F GR k L LMTD
— — — — — — — — — — — —
Mc n Pv Q S t
— — — — — —
Tb TBT
— —
2
Heat transfer area, m Brine flow rate, kg/s Boiling point elevation Specific heat capacity, kJ/kgEC Distillate flow rate, kg/s Distillate generated by boiling, kg/s Distillate generated by flashing, kg/s Feed flow rate, kg/s Gain ratio Condenser effectiveness Latent heat, kJ/kg Logarithmic mean temperature difference, EC Cooling water flow rate, kg/s Number of effects Vapor pressure, kPa Heat transfer load, kW Steam flow rate, kg/s Feed temperature in the feed heater, EC Brine temperature, EC Top brine temperature, EC
Tc Tf Tn Ts Tv Uc
— — — — — —
Ue
—
xb xf y ΔT
— — — —
Cooling water temperature, EC Feed temperature, EC Last effect temperature, EC Steam temperature, EC Vapor temperature, EC Overall heat transfer coefficient of the condenser, kW/m2 EC Overall heat transfer coefficient of the evaporator, kW/m2 EC Brine salinity Feed salinity Flashing fraction Temperature difference, EC
References [1] U. Fisher, A. Aviram and A. Gendel, Ashdod low temperature multi-effect desalination plant, Desalination, 55 (1985) 13–32. [2] C. Temster and J. Laborie, Dual purpose desalination plant — high efficiency multi effect evaporator operating with turbine for power produc-tion, Proc. IDA World Conference on Desalination and Water
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Science, Abu Dhabi, Vol. 3, 1995, pp. 297–308. [3] B. Ohlemann and D. Emmermann, Advanced barge mounted VTE/VC seawater desalting plant, Desalination, 45 (1983) 39–47. [4] B. Franquelin, F. Murat and C. Temstet, Application of multi-effect process at high tem-perature for large seawater, Desalination, 45 (1983) 81–92.
[5] M.A. Darwish and A.A. El-Hadik, The multi effect boiling desalting system and its comparison with the MSF, Desalination, 60 (1986) 251–265. [6] M.A. Darwish, F. Al-Juwayhel and H.K. Abdulrahim, Multi-effect boiling systems from an energy viewpoint, Desalination, 194 (2006) 22–39.