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Lumped modeling of solar-evaporative ponds charged from the water of the Dead Sea
Desalination 216 (2007) 356–366
Lumped modeling of solar-evaporative ponds charged from the water of the Dead Sea A. Tamimia*, K. Rawajfehb a
Chemical Engineering Department, Jordan University of Science and Technology, Irbid, Jordan Tel. +962 (2) 7201000 ext. 22354; Fax +962 (2) 7095018; email: [email protected] b Chemical Engineering Department, the University of Jordan, Amman, Jordan
Received 20 February 2006; accepted 3 November 2006
Abstract: Solar evaporators are widely used in salt mining from seawaters or saline waters. The potash industry in Jordan and other countries utilized solar energy in the evaporation process to concentrate seawater where salt starts to deposit. In this work, the thermal performance of such evaporators was analyzed and modeled on lumped basis. The developed model indicates that the efficiency of any solar evaporator is limited by the optical absorptivity of the saline water as an upper limit. Keywords: Solar evaporation; Solar ponds; Dead Sea
1. Introduction Solar evaporation to mine valuable salts from saline water is a widely used operation in salt industries. In Jordan, the whole salt and potash industry depends on solar evaporation to concentrate the brine of the Dead Sea to high levels of salt contents before its deposition and harvesting. See reported a comprehensive work of the history and operation of salt production from saline water by solar evaporation. Salts were deposited in stages, and the process was described as a fractional crystallization one [1].
Rimawi investigated and simulated all parameters that affect the precipitation of halite and carnalite salts from the Dead Sea by fractional crystallization assuming that the evaporation pan consists of N stages. The developed model expressed a multistage, multicomponent separation problem, and was solved by Newton Raphson’s iterative technique [2]. Suhr investigated the production of anhydrous sodium sulphate in a large industrial complex utilizing solar evaporation to concentrate sodium sulphate solution in the desert of Chile where high solar irradiance levels are available [3].
*Corresponding author. 0011-9164/07/$– See front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.desal.2006.11.022
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The water of the Dead Sea, as a closed sea basin, contains high levels of dissolved salts due to natural evaporation from its surface, decrease in annual rainfall, fewer water supplies from Jordan River in recent years, and less water supply from the surrounding wadies as a result of erection of new dams. The amount of evaporated water exceeds all water supplies. The dissolved salts increased gradually with time, and include halite (NaCl), sylvite (KCl), magnesium bromide (MgBr2), bischofite (MgCl2), calcium chloride (CaCl2), and carnalite (MgCl2.KCl.6H2O). The distribution of salt content was reported by the Jordanian Potash Company as given in Table 1 [4]. The level of total dissolved salts in the Dead Sea is approximately eight times greater than that found in open seas and oceans [4,5]. 2. System description Shallow wide solar ponds, called solar pans, were filled with the brine from the Dead Sea to be evaporated by direct exposure to solar radiation. Usually, the evaporation from saline water is done in three stages:
357
Table 1 Dissolved salts in the water of the Dead Sea [4] Salt
mg/l
wt. %
ppm
NaCl MgCl2 MgBr2 CaCl2 KCl Total
93,000 181,200 7,500 46,460 15,060 34,322
7.5540 14.72 0.609 3.774 1.223 ≈27.88
75,540 147,200 6,090 37,740 12,230 278,800
2.1. First stage Saline water containing high concentration of dissolved salts is transferred from the Dead Sea to shallow large solar-evaporative ponds, called salt pans, as shown in Fig. 1. The saline water in these ponds is exposed to direct solar radiation. Experimental measurement indicated that 5–6% of solar radiation that arrives at the brine surface is reflected at the air-water interface, and about 94–95% is transmitted and absorbed into the water body as shown in Fig. 2. Part of the absorbed solar energy will be lost from the solar-evaporation pan from its bottom, its walls and its surface by conduction and con-
Fig. 1. Solar-evaporative ponds for precipitation of dissolved salts from the water of the Dead Sea.
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pans where it is subjected to further evaporation and concentration until the carnalite point is reached. The first salts to crystallize and precipitate are calcium, magnesium and iron carbonates and sulfates if the saline water contains such salts with high concentration [6]. 2.3. Third stage
Fig. 2. Reflection and transmission of solar radiation in evaporation pans during a single pass.
vection. The rest of the absorbed solar energy will cause the temperature of the saline water to rise, thus evaporation amount increased. Due to simultaneous heat and mass transfer across the saline water–air interface the evaporation-condensation operations are exchanged between the two phases. The salinity of the saline water in the salt pan is progressively being changed due to continuous evaporation. Salt will precipitate if conditions of supersaturating state are met. The imbalance between increased supersaturating state and continuous evaporating conditions during summer seasons causes continuous salt precipitation. However, low ambient temperature and surface runoff from neighboring wadies during winter seasons are important factors which reduce water salinity to a value less than supersaturating state. However, salt concentration in these solar-evaporation ponds regularly changes until it reaches a supersaturating state at the prevailing weather conditions. Most of the halite crystals (NaCl salt) start to form and precipitate in the salt pan when the brine reaches saturation conditions. Therefore, these ponds are called salt pans.
The concentrated brine is transferred by gravitational flow to a series of precipitation ponds called carnalite-precipitation pans. The remaining brine is then allowed for further evaporation and concentration under direct solar radiation. The remaining NaCl crystallizes out and precipitate in the first carnalite-precipitation pan. The precipitated NaCl salt is almost in a reasonably pure form, and is harvested mechanically later after transferring the brine to the second carnalite-precipitation pan. The brine in the second carnaliteprecipitation pan is exposed to further solar radiation and allowed to more evaporation until it reaches the saturation point of magnesium and potassium chlorides and bromides. The residence time in this pond is allowed until saturation point of these salts is reached. At this point, just before precipitation, the brine is transferred by gravitational head to the third carnalite-precipitation pan where subsequent concentration of the brine causes the dissolved salts to crystallize out and precipitate as carnalite salt (KCl. MgCl2. 6H2O) in proportion 1:1:6. When a reasonable layer thickness of carnalite salt is formed (i.e. 40–60 cm) it is harvested mechanically by floating harvesters as slurry from beneath the saline-water surface. The remaining saline water is pumped back to the Dead Sea. The crude precipitated carnalite salt is transferred for further processing to the carnalite refinery which is mainly composed of cold or hot crystallization unit [6].
2.2. Second stage The saturated brine is transferred by difference in gravitational head to pre-carnalite precipitation
3. Lumped modeling of the evaporation process Most researchers who investigated this case
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considered fractional precipitation of various salts at subsequent separation stages [2]. However, this requires the knowledge of the exact values of their activity coefficients which are not available in most cases. Calculating their values from available thermodynamic models is an approximate effort and leads to appreciable errors due to their strong dependence on salt concentration. Thus, using the lumped approach in the evaporation pans by considering all the dissolved salts as one salt is a satisfactory straightforward substitute with almost the same level of accuracy. Open water surface in the solar-evaporative ponds is simultaneously in direct contact with air and is exposed to direct solar radiation. The water-air system is presumed to be at thermodynamic equilibrium at the prevailing weather conditions, and no air dissolves in water. Under these conditions, the water is regarded as a solvent, and its mole fraction in the air–water vapor mixture is usually calculated by modified Raoult’s law as follows: f Hv2 O = f HL2 O
(1)
Substituting for fugacity by the equivalent values, yields: yH 2 O ⋅ ϕH 2O ⋅ Ptot = γ H2 O ⋅ (1 − xsalts ) ⋅ pHsat2 O
(2)
air–water vapor mixture above the surface of the saline water of the Dead Sea. That is: yH 2 O ≈ γ H 2 O ⋅ (1 − 0.11) ⋅ 4.241/103
Thus, yH2 O ≈ 0.03665 γ H2 O
(4)
Of course, if the temperature increases above 30°C, the evaporation will increase exponentially above this level in almost the same proportion as the temperature and saturated vapor pressure of water have risen. According to Dalton’s law the total pressure is equal to the summation of the partial pressures of water vapor and the partial pressure of dry air in the atmosphere. That is: Ptot = pH2 O + pair
(5)
And according to the modified Raoult’s Law of real solutions, the total pressure above the saline water is equal to: sat Ptot = γ salts xsalts psalts + γ H 2 O xH 2O pHsat2 O + pair
(3)
where xsalts is the mole fraction of dissolved salts in the saline water of the Dead Sea , and equal to: xsalts = nsalts/nH O + nsalts ≈ 0.28 on weight basis (≈ 0.11 2 is the vapor pressure of on mole basis), and psat H2O pure water at the prevailing ambient temperature in the Dead Sea geographical zone. It equals about 4.241 kPa at T∞ ≈30oC throughout the year, and ϕH O ≈ 1 due to ideal gas behavior at low pressure. 2 Substituting into Eq. (3) with the previous values yields the mole fraction of water vapor in the
(6)
But γsalts xsalts psat ≈ 0.0 for non-volatile dissalts solved salts, thus: Ptot ≈ γ H2O xH2O pHsat2O + pair
(7)
≈ γ H2 O (1 − xsalts ) pHsat2 O + pair
Upon arrangement of Eq. (2), yields: yH 2 O = γ H 2 O ⋅ (1 − xsalts ) ⋅ pHsat2 O / ϕH2 O ⋅ Ptot
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By arrangement of Eq. (7), yields:
{
}
pHsat2 O = { Ptot − pair } / γ H2O (1 − xsalts )
(8)
The relationship between the saturated vapor pressure of saline water psat and the mole fracH2O tion of the total dissolved salts is negatively linear. Thus, the vapor pressure of saline waters is almost linearly reduced as the amount of dissolved salts increased. The vapor pressure of saline water becomes equal to the saturated vapor pressure of distilled water when xsalts = 0.0, that is:
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sat pHsat2 O = poH 2O
(9)
Therefore, the drop in the value of vapor pressure of water due to dissolved salts is estimated as follows: ∆pHsat2 O = posatH2 O − pHsat2 O =p
sat o H2O
− ( Ptot − pair ) / γ H2 O (1 − xsalts )
(10)
Eq. (10) is an inversely linear relationship between the drop of vapor pressure and the corresponding mole fraction of the dissolved salts. The amount of evaporated water at the temperature of the water–air interface can be estimated by converting the water mole fraction xH2O into water mass fraction wH O as follows: 2
wH2 O = x kg H 2 O / kg air − water mixture
(11)
The ideal gas law at standard conditions can be applied on water vapor–air mixture under atmospheric conditions. Thus, Eq. (11) yields [7]: wH 2 O ≈ pHsat2 O /1.61 Ptot − 0.61 pHsat2 O
Temperature, ºC
psatH2O, kPa
Mass concentration, wH2O = kg H2O/kg air mixture
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 100
1.227 1.704 2.337 3.167 4.243 5.623 7.378 9.585 12.339 15.745 19.925 25.014 31.167 38.554 47.365 57.809 70.112 101.325
0.0076 0.0106 0.0145 0.0198 0.0266 0.0354 0.0468 0.0614 0.0799 0.1033 0.1330 0.1705 0.2180 0.2784 0.3556 0.4554 0.5861 1.0000
(12)
The mass concentration of evaporated water in the atmosphere above the surface of the saline water of the Dead Sea varies with saturated vapor pressure of saline water which is a strong function of prevailing temperature level. Experimental data on saline water in the temperature range 10–100oC are available in the literature [7]. The results are presented in Table 2. Also, water content in the atmosphere can be expressed in terms of absolute humidity as follows: Φ = Absolute humidity = kg H 2 O/kg dry air (13)
Thus, the mass fraction wH O of water in the 2 air–water vapor mixture is expressed by:
wH2O = kg H 2 O/ ( kg H 2 O + kg dry air ) wH2O = Φ / (1 + Φ )
Table 2 Effect of temperature on saturated vapor pressure of saline water and the evaporated mass fraction
(14)
Also, wsalts = 1 − wH 2 O = 1/ (1 + Φ )
(15)
Also, lumped modeling of solar-evaporative ponds requires the following few assumptions: (a) The ponds are assumed to be shallow. Thus, one may assume one layer of homogeneous characteristics during thermal analysis. The whole pond body has one temperature and one concentration due to perfect mixing. That is, no temperature or mass stratification. (b) The prevailing wind is assumed to be quiet and steady. Thus, the rate of thermal convective losses is fixed during the day. (c) Conductive thermal losses from the bottom and side walls are small relative to evaporation and convective losses. If cancelled from the analysis it will become simpler.
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Applying these assumption and making an energy balance on a solar-evaporation pond during any time interval dt during the day, yields: Energy in = Energy out + Energy accumulation
I tot H Ap = Q refl + Q evap + Q conv + Q rad + M C p ( dT / dt )
(16)
The energy terms mentioned in Eq. (16) can be evaluated as follows: 3.1. Solar energy loss due to reflected solar ra diation Q refl This fraction of incident solar radiation from the surface of the saline water is a strong function in the angle of incidence θi during any time of the day. When solar radiation strikes the surface of saline water about 10% of its energy will be reflected. The reflected amount of energy is evaluated as follows: Q refl = ρ w ,θi I tot H Ap cos θi
(17)
where θi is the angle of incidence of solar radiation on the surface of the saline water, and is expressed in terms of other solar angles by: θi = sin −1 ( sin Φ l sin δ + cos Φ l cos δ cos ω) (18)
The relationship between incidence angle θi and refraction angle Ψ is given by Snell’s law as follows: nair sin θi = nw sin Ψ
(19)
where nair ≈ 1.0, and nw ≈ 1.4 for saline water. Substitution the specified values into Eq. (19) yields: Ψ = sin
−1
≈ sin
( nair sin θi / nw ) ≈ sin (1 ⋅ sin θi /1.40 ) ( 0.7143sin θi ) (20) −1
−1
The value of water-surface reflectivity at any
361
angle of incidence is expressed in terms of incidence and refractive angles, as follows (6): ρ w,θi = 1/ 2 ⎡⎣{sin 2 ( Ψ − θi ) / sin 2 ( Ψ + θi )} + {tan 2 ( Ψ − θi ) / tan 2 ( Ψ + θi )}⎤⎦
(21)
Knowing the refractive index of saline water, and substituting Eq. (20) into Eq. (21), yields the fraction of the reflected amount of solar energy from the water surface. This fraction is estimated as 5–6% from total incident insolation. Also, absorptivity of solar radiation αw,θ which i corresponds to the angle of incidence θi is expressed as follows:
α w , θi = 1 − ρ w , θi = 1 − 1/ 2 ⎡⎣{sin 2 ( Ψ − θ ) / sin 2 ( Ψ + θ )} (22)
+ {tan 2 ( Ψ − θ ) / tan 2 ( Ψ + θ )}⎤⎦
In case of normal incidence around solar noon, the reflectivity of the surface of the saline water (one reflection) is expressed by: ρn , w = {( nw − 1) / ( nw + 1)}
2
(23)
where nw is the refractive index of the saline water. In case nw = 1.4, then the optical reflectivity of its surface is equal to: ρn, w = {(1.40 − 1) / (1.40 + 1)}
2
= 0.0278 i.e. 2.78%
But, for pure distilled water n = 1.33. Thus: ρn , w = {(1.33 − 1) / (1.33 + 1)} = 0.02 i.e. 2% 2
This means that as salts content are increased in the saline water its refractive index increases, and consequently its surface reflectivity increases. Thus, its performance is almost linearly hindered with an increase in salt content. However, in case of an inclined incidence during most of the time
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Thus, the effective lumped optical absorptivity of saline water is expressed by:
α w,θ,eff = 1 − ρθ,eff
{
}
2 = 1 − ρθ ⎡1 + (1 − ρθ ) τθ2 / (1 − ρθ2 τθ2 ) ⎤ ⎣ ⎦
Fig. 3. Reflection, transmission and absorption of solar radiation in evaporation ponds during multiple diffuse reflections at its bottom.
of the day the transmitted radiation undergoes multiple reflections with longer optical paths as shown in Fig. 3. Also, the reflected radiation from the bottom of the solar-evaporative ponds is diffuse-reflection type due to the roughness of the floor of the solar-evaporative ponds. In this case, the surface effective reflectivity is almost doubled and is estimated to be 5–6%. However, all transmitted radiation is absorbed inside the saline water. Therefore, an increase of dissolved salts in the saline water increases its refractive index and increases its optical reflectivity, but increases its optical absorptivity to about 94–95%. These opposite effects may counterbalance each other. The effective lumped surface reflectivity can be evaluated by Stoke’s Law with multiple reflections:
{
}
2 ρθ,eff = ρw,θ ⎡1 + (1 − ρθ ) τθ2 / (1 − ρθ2 τθ2 ) ⎤ ⎣ ⎦
As mentioned previously, the water loss due to evaporation is due to the driving force which causes evaporation, that is, difference between water vapor pressure at the surface of the saline water and the partial pressure of water vapor in the air–water vapor mixture above its surface. The energy loss due to water evaporation was estimated by [6]:
(
)
Q evap = 9.15 ⋅ 10−7 hc′ Ap pHsat2O − pHv 2 O λ H2 O
(28)
where hc′ is the effective convective heat transfer coefficient expressed in kW/m2.K as follows:
hc′ = 0.884 ⎡⎣(Tw − Ta ) +
{( p
sat H2 O
)(
)}
1/ 3
− pHv 2O / 2016 − pHv 2O Tw ⎤ ⎦
(29)
3.3. Solar energy loss due to convection, Q conv
(25)
Solar energy is being lost from the surface of saline water in the pond by the movement of the blowing wind which moves on its surface daily. Thus, the amount of lost solar energy by convection from its surface can be estimated during the day in any time interval as follows:
ρ w,θ = 1/ 2 ⎡⎣{sin 2 ( Ψ − θ ) / sin 2 ( Ψ + θ )} + {tan 2 ( Ψ − θ ) / tan 2 ( Ψ + θ )}⎤⎦
3.2. Solar energy loss due to evaporation, Q evap
(24)
where
τθ = e − k ext ∆x
(27)
(26)
Q conv = hw Ap ( Tw − Ta )
(30)
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The relationship between solar-energy loss due to convection and solar-energy loss by evaporation is expressed by [7]: Convective heat losses to atmosphere Evaporative heat losses to atmosphere =
0.46 (Tw − Ta ) ⋅ Patm
(p
sat H2O
)
Under these assumptions, the overall thermal losses from the bottom and the side walls are expressed as follows: Q = − {k A (T − T ) / ∆x } (34) cond
(31)
− pH2 O ⋅ 101
Q rad = σ Ap (T − T
) / [1/ ε
≈ U rad Ap ( Tw − Ta )
floor
w
floor
floor
I tot H Ap = Q refl + Q evap + Q conv + Q rad + Q cond + M C p ( dT / dt ) = I tot H Ap ρ w
The surface of the solar-evaporative pond exchanges radiation with the atmosphere above it and the sky. The net radiation exchange during the day represents the fraction of absorbed solar energy that is lost by radiation to the atmosphere, assuming the saline water and the atmosphere (sky) as two parallel grey surfaces exchanging radiation to each others. Thus, at thermal equilibrium, the amount of net radiated energy from the surface of the saline water to the atmosphere is expressed as follows: 4 s
floor
Substituting the previous heat terms in Eq. (16), yields:
3.4. Solar energy loss due to radiation, Q rad
4 w
363
w
+ 1/ ε s − 1]
(
+9.15 ⋅ 10−7 hc′ Ap pHsat2 O − pHv 2 O
)
(35)
+ U conv Ap (Tw − Ta ) + U rad Ap (Tw − Ta ) +U b Ap (Tw − Ta ) + M C p ( dT / dt ) Upon arrangement and dividing by Ap , Eq. (36) yields:
I tot H (1 − ρw ) = U L (Tw − Ta ) + 9.15 ⋅ 10−7 hc′
(p
sat H2O
)
− pHv 2O + M C p ( dT / dt )
(36)
(32)
where U L is the overall heat-transfer loss coefficient and is expressed as follows:
(33)
U L = (U conv + U rad + U cond )
3.5. Solar energy loss due to conduction, Q cond The conductive thermal losses from the body of the solar-evaporative pond are due to direct heat conduction through its bottom and side walls. This depends on the nature and the structure of the soil of the bottom and side walls regarding its thickness, thermal conductivity. Also, the bottom temperature and the salt content are key parameters in determining the level of these losses. The temperature gradient across the pond is negligible due to its shallowness. Also, the nature and structure of the soil of both bottom and side walls is assumed to be similar and isotropic. Thus, the temperatures at both, bottom and side walls, are assumed equal to the surface temperature.
(37)
At steady-state conditions and upon further arrangement, Eq. (35) yields:
(
9.15 ⋅ 10−7 hc′ pHsat2O − pHv 2O
)
= I tot H (1 − ρw ) − U L (Tw − Ta )
(38)
The left-hand side of Eq. (38) represents the useful solar energy utilized into evaporating the saline water per unit area of the solar-evaporative pond. Dividing Eq. (38) with Itot H yields:
(
9.15 ⋅ 10−7 hc′ pHsat2 O − pHv 2 O
)
I tot H =
I tot H (1 − ρ w ) − U L (Tw − Ta ) I tot H
(39)
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Now, the left-hand side of Eq. (39) represents the thermal efficiency of the solar-evaporative pond, and is denoted by ηevap. Thus: ηevap = (1 − ρ w ) − U L ( Tw − Ta ) / I tot H
(40)
ηevap = α w − U L (Tw − Ta ) / I tot H
(41)
Eq. (41) is similar to the performance equation of flat-plate solar collectors developed by Hottel–Whillier–Woertz–Bliss (HWWB). That is, the evaporative-solar ponds can be modeled as flat-plate solar collector but at stagnant conditions. Thus, Eq. (41) is called the thermal performance equation of the solar-evaporative pond, and can be represented by a linear relationship. It includes all parameters which affect their performance, as shown in Fig. 4. The intercept represents the optical efficiency of the solar-evaporative pond, and the slope represents the overall thermal losses from top, bottom, and side walls of the pond. The useful solar energy is utilized into evaporation and precipitation of salts. The performance of such ponds increases by any means which increases the absorptivity of the saline water such as adding black pigment to it, or black paint on the bottom, or black rolled paved asphalt, or rolled black tiny stones which do not hinder salt harvesting. The thermal losses from the bottom and side walls can be reduced significantly by rolling, lining, and insulating with good insulating materials.
Fig. 4. Thermal performance curve of a shallow solarevaporative pond.
4. Productivity of solar-evaporating ponds The productivity of a solar-evaporative pond is defined as the mass of deposited salts that can be obtained from the pond during certain time interval ∆t per unit of incident solar energy on the surface area of the pond during the same time duration, and it is denoted by Pprod. That is: Pprod = Mass of salt yield / Incident solar energy = ∑ m salt ∆t/ ∑ I tot H Ap ∆t = ∑ m salt / ∑ I tot H Ab
(42) Thus, the productivity of a solar-evaporative pond has units and dimensions of kg /kW.m2 on contrary of the pond-thermal efficiency in evaporation ηevap which is dimensionless and always less than unity. 5. Symbols Afloor — Area of the bottom and side walls, m2 Ap — Area of the bottom of the solar-evaporative pond, m2 Cp — Specific heat of the saline water, kJ/kg.oC L f H O — Fugacity of water, kPa 2 fHv O — Fugacity of water vapor, kPa 2 h′c — Effective convective heat-transfer coefficient, kW/m2.K hw — Convective heat-transfer coefficient, kW/m2.K Itot H — Total solar irradiance on a horizontal surface, kW/m2 kfloor — Thermal conductivity of bottom and side walls, kW/m.K M — Mass of the saline water in the solarevaporative pond, kg — Rate of salt collection from the pond, msalt kg/s nair — Refractive index of air, ≈ 1.0 nw — Refractive index of saline water, ≈ 1.4 pH O — Partial pressure of water vapor in the 2 air–water mixture, kPa
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psat — Saturated vapor pressure of saline waH2O ter, kPa psat — Saturated vapor pressure of pure water, oH2O kPa Pprod — Productivity of the solar-evaporative pond, kg of salt/kW Ptot — Barometric reading at the Dead Sea location = 103.3 kPa Qcond — Amount of lost solar energy by conduction, kW Q conv — Amount of lost solar energy by convection, kW Q evap — Amount of lost solar energy by evaporation, kW Q rad — Amount of lost solar energy by radiation, kW Q refl — Amount of lost solar energy by reflection, kW t — Time of solar energy collection, h Ta — Temperature of ambient atmosphere, K Tfloor — Temperature of the bottom and side walls, K Tw — Temperature of saline water at its surface, K Ts — Temperature of the upper atmosphere layers or ambient air, K ≈ Ta U L — Overall heat-transfer loss coefficient, kW/m2.K Ucond — Conductive-heat transfer coefficient, kW/m2.K Uconv — Convective-heat transfer coefficient, kW/m2.K Urad — Radiative-heat transfer coefficient, kW/m2.K wH O — Mass fraction of water in the air–water 2 vapor mixture above the surface of the saline water xH O — Mole fraction of water in the Dead Sea 2 xsalts — Mole fraction of dissolved salts in water of the Dead Sea ∆xfloor— Thickness of the bottom and the side walls, m yH2O — Mole fraction of water vapor in the water–air mixture
365
Greek αw δ γH O 2 εs εw Φ Φl ϕH O 2
λH O 2
ηevap θi ρw,θ
i
σ ω Ψ
— Absorptivity of solar radiation in the saline water — Earth’s inclination angle, ° — Activity coefficient of water — Emissivity of atmosphere, or upper atmosphere layers — Emissivity of the surface of saline water — Absolute humidity, kg H2O/kg dry air — Latitude angle of the Dead Sea, ° — Fugacity coefficient of water vapor in the water–air mixture — Latent heat of vaporization of water at Tb,w, kJ/kg H2O — Thermal efficiency of the solar-evaporative pond — Angle of incidence of solar radiation on top surface of saline water, ° — Reflectivity of the surface of saline water — Stefan–Boltzmann’s constant = 5.6697 ·10–11 kW/m2.K4 — Hour angle during the day of solar energy collection — Angle of refraction inside the saline water, °
References [1] D.S. See, Solar Salts. Monograph # 145, Chap. 6 in: D. W. Kaufman, ed., Sodium Chloride: The Production and Properties of Salts and Brine. American Chemistry Society, 1960. [2] M. Rimawi, Simulation of a carnalite pan fed by concentrated Dead Sea brine, M.Sc. thesis supervised by K. Rawajfeh and N. Faqir, Chemical Engineering Department, The University of Jordan, Jordan, 1994. [3] H.B. Suhr, Energy-balanced calculations on the production of anhydrous sodium sulphate with solar energy and waste heat, Paper No. 4/27 presented at the Int. Solar Energy Society Conference, Melbourne, 1970.
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[4] M.A. Saleh, The Dead Sea Chemical Complex, 3rd International Fertilizer Seminar, Amman, Jordan, 6– 10 October 1991. [5] J.A. Tallmadge, J.B. Butt and H.J. Solomon, Minerals from sea salts, Ind. Eng. Chem., 56(7) (1964) 44–65.
[6] J. Duffie and W. Beckman, Solar Engineering of Thermal Processes. Wiley, USA, 1992. [7] W.M. Kays and M.E. Crawford, Convective Heat and Mass Transfer. McGraw-Hill, USA, 1980.
Lumped modeling of solar-evaporative ponds charged from the water of the Dead Sea A. Tamimia*, K. Rawajfehb a
Chemical Engineering Department, Jordan University of Science and Technology, Irbid, Jordan Tel. +962 (2) 7201000 ext. 22354; Fax +962 (2) 7095018; email: [email protected] b Chemical Engineering Department, the University of Jordan, Amman, Jordan
Received 20 February 2006; accepted 3 November 2006
Abstract: Solar evaporators are widely used in salt mining from seawaters or saline waters. The potash industry in Jordan and other countries utilized solar energy in the evaporation process to concentrate seawater where salt starts to deposit. In this work, the thermal performance of such evaporators was analyzed and modeled on lumped basis. The developed model indicates that the efficiency of any solar evaporator is limited by the optical absorptivity of the saline water as an upper limit. Keywords: Solar evaporation; Solar ponds; Dead Sea
1. Introduction Solar evaporation to mine valuable salts from saline water is a widely used operation in salt industries. In Jordan, the whole salt and potash industry depends on solar evaporation to concentrate the brine of the Dead Sea to high levels of salt contents before its deposition and harvesting. See reported a comprehensive work of the history and operation of salt production from saline water by solar evaporation. Salts were deposited in stages, and the process was described as a fractional crystallization one [1].
Rimawi investigated and simulated all parameters that affect the precipitation of halite and carnalite salts from the Dead Sea by fractional crystallization assuming that the evaporation pan consists of N stages. The developed model expressed a multistage, multicomponent separation problem, and was solved by Newton Raphson’s iterative technique [2]. Suhr investigated the production of anhydrous sodium sulphate in a large industrial complex utilizing solar evaporation to concentrate sodium sulphate solution in the desert of Chile where high solar irradiance levels are available [3].
*Corresponding author. 0011-9164/07/$– See front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.desal.2006.11.022
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The water of the Dead Sea, as a closed sea basin, contains high levels of dissolved salts due to natural evaporation from its surface, decrease in annual rainfall, fewer water supplies from Jordan River in recent years, and less water supply from the surrounding wadies as a result of erection of new dams. The amount of evaporated water exceeds all water supplies. The dissolved salts increased gradually with time, and include halite (NaCl), sylvite (KCl), magnesium bromide (MgBr2), bischofite (MgCl2), calcium chloride (CaCl2), and carnalite (MgCl2.KCl.6H2O). The distribution of salt content was reported by the Jordanian Potash Company as given in Table 1 [4]. The level of total dissolved salts in the Dead Sea is approximately eight times greater than that found in open seas and oceans [4,5]. 2. System description Shallow wide solar ponds, called solar pans, were filled with the brine from the Dead Sea to be evaporated by direct exposure to solar radiation. Usually, the evaporation from saline water is done in three stages:
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Table 1 Dissolved salts in the water of the Dead Sea [4] Salt
mg/l
wt. %
ppm
NaCl MgCl2 MgBr2 CaCl2 KCl Total
93,000 181,200 7,500 46,460 15,060 34,322
7.5540 14.72 0.609 3.774 1.223 ≈27.88
75,540 147,200 6,090 37,740 12,230 278,800
2.1. First stage Saline water containing high concentration of dissolved salts is transferred from the Dead Sea to shallow large solar-evaporative ponds, called salt pans, as shown in Fig. 1. The saline water in these ponds is exposed to direct solar radiation. Experimental measurement indicated that 5–6% of solar radiation that arrives at the brine surface is reflected at the air-water interface, and about 94–95% is transmitted and absorbed into the water body as shown in Fig. 2. Part of the absorbed solar energy will be lost from the solar-evaporation pan from its bottom, its walls and its surface by conduction and con-
Fig. 1. Solar-evaporative ponds for precipitation of dissolved salts from the water of the Dead Sea.
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pans where it is subjected to further evaporation and concentration until the carnalite point is reached. The first salts to crystallize and precipitate are calcium, magnesium and iron carbonates and sulfates if the saline water contains such salts with high concentration [6]. 2.3. Third stage
Fig. 2. Reflection and transmission of solar radiation in evaporation pans during a single pass.
vection. The rest of the absorbed solar energy will cause the temperature of the saline water to rise, thus evaporation amount increased. Due to simultaneous heat and mass transfer across the saline water–air interface the evaporation-condensation operations are exchanged between the two phases. The salinity of the saline water in the salt pan is progressively being changed due to continuous evaporation. Salt will precipitate if conditions of supersaturating state are met. The imbalance between increased supersaturating state and continuous evaporating conditions during summer seasons causes continuous salt precipitation. However, low ambient temperature and surface runoff from neighboring wadies during winter seasons are important factors which reduce water salinity to a value less than supersaturating state. However, salt concentration in these solar-evaporation ponds regularly changes until it reaches a supersaturating state at the prevailing weather conditions. Most of the halite crystals (NaCl salt) start to form and precipitate in the salt pan when the brine reaches saturation conditions. Therefore, these ponds are called salt pans.
The concentrated brine is transferred by gravitational flow to a series of precipitation ponds called carnalite-precipitation pans. The remaining brine is then allowed for further evaporation and concentration under direct solar radiation. The remaining NaCl crystallizes out and precipitate in the first carnalite-precipitation pan. The precipitated NaCl salt is almost in a reasonably pure form, and is harvested mechanically later after transferring the brine to the second carnalite-precipitation pan. The brine in the second carnaliteprecipitation pan is exposed to further solar radiation and allowed to more evaporation until it reaches the saturation point of magnesium and potassium chlorides and bromides. The residence time in this pond is allowed until saturation point of these salts is reached. At this point, just before precipitation, the brine is transferred by gravitational head to the third carnalite-precipitation pan where subsequent concentration of the brine causes the dissolved salts to crystallize out and precipitate as carnalite salt (KCl. MgCl2. 6H2O) in proportion 1:1:6. When a reasonable layer thickness of carnalite salt is formed (i.e. 40–60 cm) it is harvested mechanically by floating harvesters as slurry from beneath the saline-water surface. The remaining saline water is pumped back to the Dead Sea. The crude precipitated carnalite salt is transferred for further processing to the carnalite refinery which is mainly composed of cold or hot crystallization unit [6].
2.2. Second stage The saturated brine is transferred by difference in gravitational head to pre-carnalite precipitation
3. Lumped modeling of the evaporation process Most researchers who investigated this case
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considered fractional precipitation of various salts at subsequent separation stages [2]. However, this requires the knowledge of the exact values of their activity coefficients which are not available in most cases. Calculating their values from available thermodynamic models is an approximate effort and leads to appreciable errors due to their strong dependence on salt concentration. Thus, using the lumped approach in the evaporation pans by considering all the dissolved salts as one salt is a satisfactory straightforward substitute with almost the same level of accuracy. Open water surface in the solar-evaporative ponds is simultaneously in direct contact with air and is exposed to direct solar radiation. The water-air system is presumed to be at thermodynamic equilibrium at the prevailing weather conditions, and no air dissolves in water. Under these conditions, the water is regarded as a solvent, and its mole fraction in the air–water vapor mixture is usually calculated by modified Raoult’s law as follows: f Hv2 O = f HL2 O
(1)
Substituting for fugacity by the equivalent values, yields: yH 2 O ⋅ ϕH 2O ⋅ Ptot = γ H2 O ⋅ (1 − xsalts ) ⋅ pHsat2 O
(2)
air–water vapor mixture above the surface of the saline water of the Dead Sea. That is: yH 2 O ≈ γ H 2 O ⋅ (1 − 0.11) ⋅ 4.241/103
Thus, yH2 O ≈ 0.03665 γ H2 O
(4)
Of course, if the temperature increases above 30°C, the evaporation will increase exponentially above this level in almost the same proportion as the temperature and saturated vapor pressure of water have risen. According to Dalton’s law the total pressure is equal to the summation of the partial pressures of water vapor and the partial pressure of dry air in the atmosphere. That is: Ptot = pH2 O + pair
(5)
And according to the modified Raoult’s Law of real solutions, the total pressure above the saline water is equal to: sat Ptot = γ salts xsalts psalts + γ H 2 O xH 2O pHsat2 O + pair
(3)
where xsalts is the mole fraction of dissolved salts in the saline water of the Dead Sea , and equal to: xsalts = nsalts/nH O + nsalts ≈ 0.28 on weight basis (≈ 0.11 2 is the vapor pressure of on mole basis), and psat H2O pure water at the prevailing ambient temperature in the Dead Sea geographical zone. It equals about 4.241 kPa at T∞ ≈30oC throughout the year, and ϕH O ≈ 1 due to ideal gas behavior at low pressure. 2 Substituting into Eq. (3) with the previous values yields the mole fraction of water vapor in the
(6)
But γsalts xsalts psat ≈ 0.0 for non-volatile dissalts solved salts, thus: Ptot ≈ γ H2O xH2O pHsat2O + pair
(7)
≈ γ H2 O (1 − xsalts ) pHsat2 O + pair
Upon arrangement of Eq. (2), yields: yH 2 O = γ H 2 O ⋅ (1 − xsalts ) ⋅ pHsat2 O / ϕH2 O ⋅ Ptot
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By arrangement of Eq. (7), yields:
{
}
pHsat2 O = { Ptot − pair } / γ H2O (1 − xsalts )
(8)
The relationship between the saturated vapor pressure of saline water psat and the mole fracH2O tion of the total dissolved salts is negatively linear. Thus, the vapor pressure of saline waters is almost linearly reduced as the amount of dissolved salts increased. The vapor pressure of saline water becomes equal to the saturated vapor pressure of distilled water when xsalts = 0.0, that is:
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sat pHsat2 O = poH 2O
(9)
Therefore, the drop in the value of vapor pressure of water due to dissolved salts is estimated as follows: ∆pHsat2 O = posatH2 O − pHsat2 O =p
sat o H2O
− ( Ptot − pair ) / γ H2 O (1 − xsalts )
(10)
Eq. (10) is an inversely linear relationship between the drop of vapor pressure and the corresponding mole fraction of the dissolved salts. The amount of evaporated water at the temperature of the water–air interface can be estimated by converting the water mole fraction xH2O into water mass fraction wH O as follows: 2
wH2 O = x kg H 2 O / kg air − water mixture
(11)
The ideal gas law at standard conditions can be applied on water vapor–air mixture under atmospheric conditions. Thus, Eq. (11) yields [7]: wH 2 O ≈ pHsat2 O /1.61 Ptot − 0.61 pHsat2 O
Temperature, ºC
psatH2O, kPa
Mass concentration, wH2O = kg H2O/kg air mixture
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 100
1.227 1.704 2.337 3.167 4.243 5.623 7.378 9.585 12.339 15.745 19.925 25.014 31.167 38.554 47.365 57.809 70.112 101.325
0.0076 0.0106 0.0145 0.0198 0.0266 0.0354 0.0468 0.0614 0.0799 0.1033 0.1330 0.1705 0.2180 0.2784 0.3556 0.4554 0.5861 1.0000
(12)
The mass concentration of evaporated water in the atmosphere above the surface of the saline water of the Dead Sea varies with saturated vapor pressure of saline water which is a strong function of prevailing temperature level. Experimental data on saline water in the temperature range 10–100oC are available in the literature [7]. The results are presented in Table 2. Also, water content in the atmosphere can be expressed in terms of absolute humidity as follows: Φ = Absolute humidity = kg H 2 O/kg dry air (13)
Thus, the mass fraction wH O of water in the 2 air–water vapor mixture is expressed by:
wH2O = kg H 2 O/ ( kg H 2 O + kg dry air ) wH2O = Φ / (1 + Φ )
Table 2 Effect of temperature on saturated vapor pressure of saline water and the evaporated mass fraction
(14)
Also, wsalts = 1 − wH 2 O = 1/ (1 + Φ )
(15)
Also, lumped modeling of solar-evaporative ponds requires the following few assumptions: (a) The ponds are assumed to be shallow. Thus, one may assume one layer of homogeneous characteristics during thermal analysis. The whole pond body has one temperature and one concentration due to perfect mixing. That is, no temperature or mass stratification. (b) The prevailing wind is assumed to be quiet and steady. Thus, the rate of thermal convective losses is fixed during the day. (c) Conductive thermal losses from the bottom and side walls are small relative to evaporation and convective losses. If cancelled from the analysis it will become simpler.
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Applying these assumption and making an energy balance on a solar-evaporation pond during any time interval dt during the day, yields: Energy in = Energy out + Energy accumulation
I tot H Ap = Q refl + Q evap + Q conv + Q rad + M C p ( dT / dt )
(16)
The energy terms mentioned in Eq. (16) can be evaluated as follows: 3.1. Solar energy loss due to reflected solar ra diation Q refl This fraction of incident solar radiation from the surface of the saline water is a strong function in the angle of incidence θi during any time of the day. When solar radiation strikes the surface of saline water about 10% of its energy will be reflected. The reflected amount of energy is evaluated as follows: Q refl = ρ w ,θi I tot H Ap cos θi
(17)
where θi is the angle of incidence of solar radiation on the surface of the saline water, and is expressed in terms of other solar angles by: θi = sin −1 ( sin Φ l sin δ + cos Φ l cos δ cos ω) (18)
The relationship between incidence angle θi and refraction angle Ψ is given by Snell’s law as follows: nair sin θi = nw sin Ψ
(19)
where nair ≈ 1.0, and nw ≈ 1.4 for saline water. Substitution the specified values into Eq. (19) yields: Ψ = sin
−1
≈ sin
( nair sin θi / nw ) ≈ sin (1 ⋅ sin θi /1.40 ) ( 0.7143sin θi ) (20) −1
−1
The value of water-surface reflectivity at any
361
angle of incidence is expressed in terms of incidence and refractive angles, as follows (6): ρ w,θi = 1/ 2 ⎡⎣{sin 2 ( Ψ − θi ) / sin 2 ( Ψ + θi )} + {tan 2 ( Ψ − θi ) / tan 2 ( Ψ + θi )}⎤⎦
(21)
Knowing the refractive index of saline water, and substituting Eq. (20) into Eq. (21), yields the fraction of the reflected amount of solar energy from the water surface. This fraction is estimated as 5–6% from total incident insolation. Also, absorptivity of solar radiation αw,θ which i corresponds to the angle of incidence θi is expressed as follows:
α w , θi = 1 − ρ w , θi = 1 − 1/ 2 ⎡⎣{sin 2 ( Ψ − θ ) / sin 2 ( Ψ + θ )} (22)
+ {tan 2 ( Ψ − θ ) / tan 2 ( Ψ + θ )}⎤⎦
In case of normal incidence around solar noon, the reflectivity of the surface of the saline water (one reflection) is expressed by: ρn , w = {( nw − 1) / ( nw + 1)}
2
(23)
where nw is the refractive index of the saline water. In case nw = 1.4, then the optical reflectivity of its surface is equal to: ρn, w = {(1.40 − 1) / (1.40 + 1)}
2
= 0.0278 i.e. 2.78%
But, for pure distilled water n = 1.33. Thus: ρn , w = {(1.33 − 1) / (1.33 + 1)} = 0.02 i.e. 2% 2
This means that as salts content are increased in the saline water its refractive index increases, and consequently its surface reflectivity increases. Thus, its performance is almost linearly hindered with an increase in salt content. However, in case of an inclined incidence during most of the time
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Thus, the effective lumped optical absorptivity of saline water is expressed by:
α w,θ,eff = 1 − ρθ,eff
{
}
2 = 1 − ρθ ⎡1 + (1 − ρθ ) τθ2 / (1 − ρθ2 τθ2 ) ⎤ ⎣ ⎦
Fig. 3. Reflection, transmission and absorption of solar radiation in evaporation ponds during multiple diffuse reflections at its bottom.
of the day the transmitted radiation undergoes multiple reflections with longer optical paths as shown in Fig. 3. Also, the reflected radiation from the bottom of the solar-evaporative ponds is diffuse-reflection type due to the roughness of the floor of the solar-evaporative ponds. In this case, the surface effective reflectivity is almost doubled and is estimated to be 5–6%. However, all transmitted radiation is absorbed inside the saline water. Therefore, an increase of dissolved salts in the saline water increases its refractive index and increases its optical reflectivity, but increases its optical absorptivity to about 94–95%. These opposite effects may counterbalance each other. The effective lumped surface reflectivity can be evaluated by Stoke’s Law with multiple reflections:
{
}
2 ρθ,eff = ρw,θ ⎡1 + (1 − ρθ ) τθ2 / (1 − ρθ2 τθ2 ) ⎤ ⎣ ⎦
As mentioned previously, the water loss due to evaporation is due to the driving force which causes evaporation, that is, difference between water vapor pressure at the surface of the saline water and the partial pressure of water vapor in the air–water vapor mixture above its surface. The energy loss due to water evaporation was estimated by [6]:
(
)
Q evap = 9.15 ⋅ 10−7 hc′ Ap pHsat2O − pHv 2 O λ H2 O
(28)
where hc′ is the effective convective heat transfer coefficient expressed in kW/m2.K as follows:
hc′ = 0.884 ⎡⎣(Tw − Ta ) +
{( p
sat H2 O
)(
)}
1/ 3
− pHv 2O / 2016 − pHv 2O Tw ⎤ ⎦
(29)
3.3. Solar energy loss due to convection, Q conv
(25)
Solar energy is being lost from the surface of saline water in the pond by the movement of the blowing wind which moves on its surface daily. Thus, the amount of lost solar energy by convection from its surface can be estimated during the day in any time interval as follows:
ρ w,θ = 1/ 2 ⎡⎣{sin 2 ( Ψ − θ ) / sin 2 ( Ψ + θ )} + {tan 2 ( Ψ − θ ) / tan 2 ( Ψ + θ )}⎤⎦
3.2. Solar energy loss due to evaporation, Q evap
(24)
where
τθ = e − k ext ∆x
(27)
(26)
Q conv = hw Ap ( Tw − Ta )
(30)
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The relationship between solar-energy loss due to convection and solar-energy loss by evaporation is expressed by [7]: Convective heat losses to atmosphere Evaporative heat losses to atmosphere =
0.46 (Tw − Ta ) ⋅ Patm
(p
sat H2O
)
Under these assumptions, the overall thermal losses from the bottom and the side walls are expressed as follows: Q = − {k A (T − T ) / ∆x } (34) cond
(31)
− pH2 O ⋅ 101
Q rad = σ Ap (T − T
) / [1/ ε
≈ U rad Ap ( Tw − Ta )
floor
w
floor
floor
I tot H Ap = Q refl + Q evap + Q conv + Q rad + Q cond + M C p ( dT / dt ) = I tot H Ap ρ w
The surface of the solar-evaporative pond exchanges radiation with the atmosphere above it and the sky. The net radiation exchange during the day represents the fraction of absorbed solar energy that is lost by radiation to the atmosphere, assuming the saline water and the atmosphere (sky) as two parallel grey surfaces exchanging radiation to each others. Thus, at thermal equilibrium, the amount of net radiated energy from the surface of the saline water to the atmosphere is expressed as follows: 4 s
floor
Substituting the previous heat terms in Eq. (16), yields:
3.4. Solar energy loss due to radiation, Q rad
4 w
363
w
+ 1/ ε s − 1]
(
+9.15 ⋅ 10−7 hc′ Ap pHsat2 O − pHv 2 O
)
(35)
+ U conv Ap (Tw − Ta ) + U rad Ap (Tw − Ta ) +U b Ap (Tw − Ta ) + M C p ( dT / dt ) Upon arrangement and dividing by Ap , Eq. (36) yields:
I tot H (1 − ρw ) = U L (Tw − Ta ) + 9.15 ⋅ 10−7 hc′
(p
sat H2O
)
− pHv 2O + M C p ( dT / dt )
(36)
(32)
where U L is the overall heat-transfer loss coefficient and is expressed as follows:
(33)
U L = (U conv + U rad + U cond )
3.5. Solar energy loss due to conduction, Q cond The conductive thermal losses from the body of the solar-evaporative pond are due to direct heat conduction through its bottom and side walls. This depends on the nature and the structure of the soil of the bottom and side walls regarding its thickness, thermal conductivity. Also, the bottom temperature and the salt content are key parameters in determining the level of these losses. The temperature gradient across the pond is negligible due to its shallowness. Also, the nature and structure of the soil of both bottom and side walls is assumed to be similar and isotropic. Thus, the temperatures at both, bottom and side walls, are assumed equal to the surface temperature.
(37)
At steady-state conditions and upon further arrangement, Eq. (35) yields:
(
9.15 ⋅ 10−7 hc′ pHsat2O − pHv 2O
)
= I tot H (1 − ρw ) − U L (Tw − Ta )
(38)
The left-hand side of Eq. (38) represents the useful solar energy utilized into evaporating the saline water per unit area of the solar-evaporative pond. Dividing Eq. (38) with Itot H yields:
(
9.15 ⋅ 10−7 hc′ pHsat2 O − pHv 2 O
)
I tot H =
I tot H (1 − ρ w ) − U L (Tw − Ta ) I tot H
(39)
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Now, the left-hand side of Eq. (39) represents the thermal efficiency of the solar-evaporative pond, and is denoted by ηevap. Thus: ηevap = (1 − ρ w ) − U L ( Tw − Ta ) / I tot H
(40)
ηevap = α w − U L (Tw − Ta ) / I tot H
(41)
Eq. (41) is similar to the performance equation of flat-plate solar collectors developed by Hottel–Whillier–Woertz–Bliss (HWWB). That is, the evaporative-solar ponds can be modeled as flat-plate solar collector but at stagnant conditions. Thus, Eq. (41) is called the thermal performance equation of the solar-evaporative pond, and can be represented by a linear relationship. It includes all parameters which affect their performance, as shown in Fig. 4. The intercept represents the optical efficiency of the solar-evaporative pond, and the slope represents the overall thermal losses from top, bottom, and side walls of the pond. The useful solar energy is utilized into evaporation and precipitation of salts. The performance of such ponds increases by any means which increases the absorptivity of the saline water such as adding black pigment to it, or black paint on the bottom, or black rolled paved asphalt, or rolled black tiny stones which do not hinder salt harvesting. The thermal losses from the bottom and side walls can be reduced significantly by rolling, lining, and insulating with good insulating materials.
Fig. 4. Thermal performance curve of a shallow solarevaporative pond.
4. Productivity of solar-evaporating ponds The productivity of a solar-evaporative pond is defined as the mass of deposited salts that can be obtained from the pond during certain time interval ∆t per unit of incident solar energy on the surface area of the pond during the same time duration, and it is denoted by Pprod. That is: Pprod = Mass of salt yield / Incident solar energy = ∑ m salt ∆t/ ∑ I tot H Ap ∆t = ∑ m salt / ∑ I tot H Ab
(42) Thus, the productivity of a solar-evaporative pond has units and dimensions of kg /kW.m2 on contrary of the pond-thermal efficiency in evaporation ηevap which is dimensionless and always less than unity. 5. Symbols Afloor — Area of the bottom and side walls, m2 Ap — Area of the bottom of the solar-evaporative pond, m2 Cp — Specific heat of the saline water, kJ/kg.oC L f H O — Fugacity of water, kPa 2 fHv O — Fugacity of water vapor, kPa 2 h′c — Effective convective heat-transfer coefficient, kW/m2.K hw — Convective heat-transfer coefficient, kW/m2.K Itot H — Total solar irradiance on a horizontal surface, kW/m2 kfloor — Thermal conductivity of bottom and side walls, kW/m.K M — Mass of the saline water in the solarevaporative pond, kg — Rate of salt collection from the pond, msalt kg/s nair — Refractive index of air, ≈ 1.0 nw — Refractive index of saline water, ≈ 1.4 pH O — Partial pressure of water vapor in the 2 air–water mixture, kPa
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psat — Saturated vapor pressure of saline waH2O ter, kPa psat — Saturated vapor pressure of pure water, oH2O kPa Pprod — Productivity of the solar-evaporative pond, kg of salt/kW Ptot — Barometric reading at the Dead Sea location = 103.3 kPa Qcond — Amount of lost solar energy by conduction, kW Q conv — Amount of lost solar energy by convection, kW Q evap — Amount of lost solar energy by evaporation, kW Q rad — Amount of lost solar energy by radiation, kW Q refl — Amount of lost solar energy by reflection, kW t — Time of solar energy collection, h Ta — Temperature of ambient atmosphere, K Tfloor — Temperature of the bottom and side walls, K Tw — Temperature of saline water at its surface, K Ts — Temperature of the upper atmosphere layers or ambient air, K ≈ Ta U L — Overall heat-transfer loss coefficient, kW/m2.K Ucond — Conductive-heat transfer coefficient, kW/m2.K Uconv — Convective-heat transfer coefficient, kW/m2.K Urad — Radiative-heat transfer coefficient, kW/m2.K wH O — Mass fraction of water in the air–water 2 vapor mixture above the surface of the saline water xH O — Mole fraction of water in the Dead Sea 2 xsalts — Mole fraction of dissolved salts in water of the Dead Sea ∆xfloor— Thickness of the bottom and the side walls, m yH2O — Mole fraction of water vapor in the water–air mixture
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Greek αw δ γH O 2 εs εw Φ Φl ϕH O 2
λH O 2
ηevap θi ρw,θ
i
σ ω Ψ
— Absorptivity of solar radiation in the saline water — Earth’s inclination angle, ° — Activity coefficient of water — Emissivity of atmosphere, or upper atmosphere layers — Emissivity of the surface of saline water — Absolute humidity, kg H2O/kg dry air — Latitude angle of the Dead Sea, ° — Fugacity coefficient of water vapor in the water–air mixture — Latent heat of vaporization of water at Tb,w, kJ/kg H2O — Thermal efficiency of the solar-evaporative pond — Angle of incidence of solar radiation on top surface of saline water, ° — Reflectivity of the surface of saline water — Stefan–Boltzmann’s constant = 5.6697 ·10–11 kW/m2.K4 — Hour angle during the day of solar energy collection — Angle of refraction inside the saline water, °
References [1] D.S. See, Solar Salts. Monograph # 145, Chap. 6 in: D. W. Kaufman, ed., Sodium Chloride: The Production and Properties of Salts and Brine. American Chemistry Society, 1960. [2] M. Rimawi, Simulation of a carnalite pan fed by concentrated Dead Sea brine, M.Sc. thesis supervised by K. Rawajfeh and N. Faqir, Chemical Engineering Department, The University of Jordan, Jordan, 1994. [3] H.B. Suhr, Energy-balanced calculations on the production of anhydrous sodium sulphate with solar energy and waste heat, Paper No. 4/27 presented at the Int. Solar Energy Society Conference, Melbourne, 1970.
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[4] M.A. Saleh, The Dead Sea Chemical Complex, 3rd International Fertilizer Seminar, Amman, Jordan, 6– 10 October 1991. [5] J.A. Tallmadge, J.B. Butt and H.J. Solomon, Minerals from sea salts, Ind. Eng. Chem., 56(7) (1964) 44–65.
[6] J. Duffie and W. Beckman, Solar Engineering of Thermal Processes. Wiley, USA, 1992. [7] W.M. Kays and M.E. Crawford, Convective Heat and Mass Transfer. McGraw-Hill, USA, 1980.