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Ind. Eng. Chem. Res. 2002, 41, 642-650
Evaporation Rates from Fresh and Saline Water in Moving Air Hisham T. El-Dessouky,* Hisham M. Ettouney, Imad M. Alatiqi, and Maha A. Al-Shamari† Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Measurements of the water evaporation rate in still or moving air date back to the 20th century. Unfortunately, many of these studies have provided a wide variation in the measured data. Also, several of these studies did not consider the effect of water salinity on the evaporation rate. This has motivated the current study, where three methods are used for measuring the evaporation rate. These methods include changes in the water height, water weight, and air humidity. Two evaporation modes are considered: the first is for water at ambient temperature into hot air and the second for heated water into air at ambient temperature. The air and water temperatures are varied over a range of 25-60 °C. The air velocity is varied over a range of 2-4 m/s. Also, the water salinity is changed from 26 ppm for freshwater up to 69 000 ppm for rejected brine in desalination processes. The measured data are correlated as a function of the evaporation mode, the pressure difference of the water vapor at the water surface and in the air bulk, and the air velocity. Measured rates compare favorably against a number of literature correlations. Results show a decrease in the evaporation rate upon an increase of the water salinity because of the reduction in the water vapor pressure at the water surface. Introduction Water evaporation in air occurs in natural and industrial processes. Water evaporates into ambient air from various types of water bodies, which includes oceans, seas, lakes, and rivers. The evaporation process depends on the barometric pressure, air velocity, relative humidity, water currents, temperature, and water salinity. Fundamentals of water evaporation in nature are simulated in various industries to perform specific tasks such as drying, air conditioning, air fogging in gas turbines, film cooling, thermal desalination, and production of concentrates. In addition to industrial processes, other examples for water evaporation include the following: (i) Water evaporation from indoor pools and fountains is important to determine its effects on air conditioning capacity and comfort conditions. (ii) Water evaporation rates from oceans or seas in the presence of polluting oil films are important in the devising of treatment methods and development of suitable chemical additives. In all systems, it is necessary to have good predictive models for the evaporation rate as a function of various system parameters, for example, temperatures and flow rates of the air or water streams, system geometry, the presence of dissolved or suspended material in the water, biological activity, and deviation from saturation conditions. Parts a and b of Figure 1 show psychometric charts for two modes of water evaporation. The first is for hot air flow past water at ambient temperature, and the second is for air at ambient temperature flowing past heated water. The cooling path A-B-C, shown in Figure 1a, corresponds to the case of hot air flowing over * Corresponding author. E-mail:
[email protected]. edu.kw. † Present address: Kuwait Institute for Scientific Research, Kuwait.
Figure 1. (a) Cooling path of the hot air stream moving over a water pan surface. (b) Cooling path of the air stream moving over a heated water pan.
an unheated pan of water. Point A gives the inlet airdry bulb temperature, point B gives the outlet air-dry bulb temperature, and point C gives the wet bulb temperature for the inlet or outlet air. Point C represents the minimum possible outlet dry bulb temperature for the air stream. Achieving this condition implies that
10.1021/ie010327o CCC: $22.00 © 2002 American Chemical Society Published on Web 01/03/2002
Ind. Eng. Chem. Res., Vol. 41, No. 3, 2002 643 Table 1. Summary of Literature Studies on Water Evaporation Rates air velocity (m/s)
ref
air relative humidity (%)
air temp range (°C)
water temp range (°C)
Hinchley and Himus5 Haji and Chow7
20-70 150-260
20-70
Yoshida and Hyodo8
50-400
50-400
measuring method
configuration
weight level
0.023-0.07 m2 pan 5.08 cm width, 30.48 length, 2.54 cm depth
flow rate
wetted-wall column
flow rate
6 cm width, 40 cm length, 6.5 cm depth 6 cm width, 40 cm length, 6.5 cm depth 0.5 m width, 8 m length, 0.3 m depth
Katto and Aoki9
3-40
30-175
Katto et al.10
0-20
50-110 30
25 50
flow rate
Liss et al.11
0.36-9.2
60.4-89.9
6.8-31.9
13.8-16.3
air humidity
Pauken et al.12
0
50-70
20
20
weight
Pauken et al.13
1.45
50-70
20
20
weight
3-4 22-4
weight
Petri dish
flow rate
porous media of 3 kg wet hog fuel 1.18 m diameter, 0.3 m depth, pan Petri dish
Brekhovskikh et al.14 Sheikholeslami and Watkinson15 Pauken3 Kozak and Majchrzycka16
44-55 1.35 0.33-1.45
20-260 50
20
40-80
30-36
Lee17
50
25-50
weight weight
25
the process effectiveness is 100%. The system effectiveness depends on several factors, which include the air/ water contact area, residence time, extent of turbulence, and water salinity. The A-B-C cooling path indicates that as the air flows over the water surface a small amount of water vapor evaporates per unit mass of the air stream. The second evaporation mode is shown in Figure 1b, where points A and B correspond to the dry bulb temperature of the inlet and outlet air streamflowing over a heated water pan. This indicates that the air temperature increases as it flows over the surface of the hot water pan. Also, water evaporation from the pan increases the absolute humidity of the air stream. Dalton developed the first equation for water evaporation in 1834, which is given by
J ) C(Pw - Pa) where J is the water evaporation flux, C is the evaporation coefficient, Pw is the vapor pressure of the water surface, and Pa is the partial pressure of the water vapor in the air (kPa). Since the early 1990s, water evaporation is investigated in several configurations that include water evaporation in air and superheated steam, evaporation from flat pans, wetted-wall columns, and water droplets. The main features for several of these studies are shown in Table 1. The following is a summary for the main findings in these studies: (i) Measurements of the water evaporation rates are very sensitive to various effects within the system, which includes the following:
weight
1.2 m diameter, 0.25 m depth 1.2 m diameter, 0.25 m depth
wetted nonhygroscopic porous media in a dish
remarks large deviations in the literature measurements and analytical results measure inversion temp measure turbulent effects on evaporation rate measure turbulent effects on evaporation rate evaporation and condensation effects on oxygen transfer from water measure evaporation rates in still air measure evaporation rates in low velocity air measure inversion temp at 170 °C measure free convection effects at low air velocities evaporation rates as a function of temp, and gas type salt lowers the evaporation rate by 20%
(a) Heat loss to surroundings would result in nonuniform air and water temperatures. This makes it difficult to determine the evaporation rate by performing an energy balance on the system. (b) Contamination of the water surface is caused by precipitation of dust and small particles carried in the air stream. A thin fouling film over the water surface would strongly retard the water evaporation rates.1 (c) Measurement of the water surface temperature requires the use of accurate and sensitive thermocouple wires. This effect becomes more apparent for small temperature differences between the water and the air stream. Also, inaccurate positioning of the thermocouple wire might yield the temperature of the water bulk or the air stream.1 (ii) Compiling available literature correlations shows wide deviations among a large number of these correlations. However, a number of the older and newer correlations provide compatible results. (iii) Investigators reported an inversion temperature of 250 °C, below which the water evaporation rate is highest in dry air, followed by humid air, and then superheated steam. The opposite trend is found above the inversion temperature. (iv) The presence of thin oil films on the water surface reduces the evaporation rates, especially at temperatures below 15 °C. However, temperature increase and reduction in the oil film thickness increase the water evaporation rates because of oil degradation by increased microbial activity.
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(v) The presence of dissolved salts in the evaporating water reduces the water evaporation by as much as 20% because of salt effects on the evaporation layer and reduction of the water vapor pressure at the water surface. (vi) Although experimental measurements and analysis of water evaporation are close to two centuries old, newer experiments, measurements, and analysis remain to be conducted to address the need for more accurate correlations and a better understanding of the various facets of this interesting phenomenon. The above has motivated execution of this research study, which focuses on measurement of the effect of water salinity on the evaporation rate of water in moving air. To ensure accuracy, three methods for measuring the water evaporation rate are used simultaneously. The experiments are performed for two evaporation modes: the first is for water evaporation from heated water in air at ambient temperature, and the second is for water at ambient temperature into heated air. Water Evaporation Rate Three methods are used for measuring the water evaporation rate, which include changes in the air humidity, water weight, and water level. The results for various measuring methods are only accepted if the deviations among the different measuring techniques are below 5%. Calculations of the change in the water absolute humidity require measurement of the dry and wet bulb temperatures for the inlet and outlet air. The two temperatures are used to calculate the absolute humidity at the inlet and outlet conditions. Therefore, the water evaporation flux is defined by
R ) Md(Wo - Wi)/A
(1)
Evaluation of the evaporation rate by eq 1 involves the following calculations: (i) Determine the saturation pressure at the wet bulb temperature, Pw. (ii) Calculate the water vapor pressure at the dry bulb temperature.2
(Pt - Pw)(Td - Tw) Pd ) Pw 1546.62 - 1.44Tw
(2)
(iii) Calculate the air humidity at the inlet and outlet points.2
Pd W ) 0.62198 Pt - Pd
(3)
(4)
(v) Calculate the air density.
F)
1+W v
(vi) Calculate the mass flow rate of moist air.
(5)
(6)
(vii) Calculate the mass flow rate of dry air.
Md )
Mw 1+W
(7)
Measuring the change in the water level is shown in Figure 2a. As is shown, the measuring system includes an electric circuit, a sharp end needle, a lever arm, and a length scale. Because variations in the height of the water level in the water pan are very small, then the length of the lever arm is adjusted to reduce the measuring error. Therefore, the ratio of L1 and L2 is adjusted at a value of 50. For a ratio of 50, lowering the needle a distance of 0.02 mm would correspond to 1 mm on the length scale. Initially, the lever is adjusted to a horizontal position, where the needle tip is touching the water surface and the light bulb will be on. After a specified period of time and as the water level drops, the electric circuit becomes open and the light bulb is no longer on. To determine the drop in the water level, the needle is lowered by using the ball-bearing mechanism. This is until the needle tip touches the water surface, where the electric circuit is closed and the light bulb is turned on. The reading on the length scale is recorded, and the above procedure is repeated throughout the experimental measurements. The following equation is used to calculate the evaporation rate from the water level measurements:
R)
F∆h(A1 + A2) A2∆t
(8)
where h is the water level, A1 is the surface area of the small pan, A2 is the surface area of the large pan, F is the water density, and ∆t is the time interval. The weight change measuring system is shown in Figure 2b. The system is constituted of the water pan used for evaporation, a small water pan with covered surface or zero evaporation, a weighing balance, and a connection between the two pans. The masses of the small and large pans are given by
m1 ) FA1h
(9)
m2 ) FA2h
(10)
where m1 and m2 are water masses in the small and large pans. It should be noted that, because the two pans are connected, then the water height and density in both pans are equal. Therefore, dividing eqs 9 and 10 gives
m1/m2 ) A1/A2
(iv) Calculate the air specific volume.2
(Td + 273.15)(1 + 1.6078W) v ) 0.2869 Pt
Mw ) VAF
(11)
Because the cross-sectional area for both pans as well as the water weight in the small pan can be measured accurately, then eq 11 can be used to calculate the mass of the large pan. As a result, the water evaporation flux from the large pan can be determined by subtracting the total mass of water in both pans (m1 + m2) over a period of time (∆t) and dividing by the evaporation area (A2), or
R ) [(m1 + m2)t - (m1 + m2)t+∆t]/A2∆t
(12)
Ind. Eng. Chem. Res., Vol. 41, No. 3, 2002 645
Figure 2. (a) Schematic of the water level measurement method. (b) Schematic of the experimental system.
Equations 11 and 12 are combined to yield the following relation:
R)
∆m1(A1 + A2) A1A2∆t
(13)
(v) The conductivity meter for measuring the water salinity has an accuracy of (0.01 µS/m. Temperature and relative humidity measurements are stored in a data logger. Data logging is made at intervals of 10 min. The logger allows for automatic calibration of the thermocouples and relative humidity probes.
Experimental Apparatus and Instrumentation The experimental system for water evaporation in air is shown in Figure 2a. The system includes an air fan, water pan, air and water heaters, and air duct. The air intake is obtained through a low-pressure compressor unit, which is equipped with a filtration system to remove dust and suspended particles in air. The system specifications include the following: (i) The air duct and water holding tank are made of Plexiglas and reinforced with an aluminum frame. (ii) The water tank dimensions are 0.575 × 0.195 × 0.1 m in length, width, and depth. (iii) The air duct dimensions are 1.583 × 0.2 × 0.3 m in length, height, and width. (iv) The air fan is of axial flow type with a power rating of 0.9 kW. (v) The air heaters have a power rating of 1 kW. (vi) The water heaters have a power rating of 1 kW. The system instrumentation includes the following: (i) An anometer is used to measure the air velocity with an accuracy of 0.1 m/s. (ii) Ten thermocouple probes are used to measure the temperature at various points within the system. The accuracy of the thermocouples is (0.01 °C. (iii) Two humidity probes are used to measure the relative humidity of the intake ambient air and the outlet air. The accuracy of the humidity probes is rated at 0.1%. (iv) The weight balance has a measuring accuracy of 0.01 g.
Experimental Procedure System operation and measurements are conducted according to the following procedure: (i) Prior to system operation and calibration of instruments, all power and thermocouple wiring as well as fitting of the fan, the air duct, and the water pan is visually inspected. (ii) A water sample is prepared which includes deionized tap water, seawater, rejected brine water from the desalination plant, and their mixtures. (iii) All instrumentations are calibrated, which include the thermocouples, velocity probe, relative humidity probes, level meter, conductivity meter, and weight balance. (iv) The water pan is filled with water to a specified level, and the beaker placed on the balance is also filled with the same water to have a constant density. (v) Operation starts with switching the air fan and adjusting to the desired velocity. Also, the air or water heaters are switched to the desired power rate. (vi) Automatic data logging commences for various system temperatures, humidity, and weight or level. (vii) Each power setting experiment is conducted for a period of 3 h with measurements at 10 min intervals. Error Analysis Error analysis in calculating the evaporation rates is performed using the Kline-McClintock procedure. The
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uncertainty in the measurements is defined as the root sum square of the fixed error by the instrumentation and the random error observed during different measurements. The error analysis depends on the method of measurement of the amount of water evaporated. The following is the estimated errors in calculating the evaporation rates, which depends on the method for measurement of the amount of water evaporated: (i) Change in the inlet/outlet absolute humidity of the air stream: The measured errors in the temperature, air velocity, time, surface area of the water pan, and air relative humidity are 1.5%, 0.5%, 0.1%, 0.1%, and 1%, respectively. These errors give an error of 1.3% in the calculated evaporation rate. (ii) Change in water mass: The measured errors in the water mass, time, and surface area are 0.5%, 0.1%, and 0.1%, respectively. These errors give an error of 0.47% in the calculated evaporation rate. (iii) Change in the water level: The measured errors in the water level, time, and surface area are 3%, 0.1%, and 0.1%, respectively. These errors give an error of 2.75% in the calculated evaporation rate. Results and Discussion Two experimental sets are obtained in this study: the first is for hot air flowing over the surface of unheated water and the second is for air at room temperature flowing over the surface of heated water. The experimental parameters include the following: (i) air velocity of 2, 3, and 4 m/s; (ii) air temperatures of 20, 30, 40, and 50 °C; (iii) water temperatures of 25, 30, 40, 50, and 60 °C; (iv) water salinity of 26, 34 000, 56 000, and 69 000 ppm. The measured evaporation rate for the mode of heated water as a function of the water salinity and air velocity is shown in Figure 3. As is shown, the evaporation rate increases upon increasing the air velocity and decreasing the water salinity. Increasing the air velocity results in an increase of mixing, turbulence, and reduction in the boundary layer resistance. All of these effects enhance the water evaporation rate. Increasing the water salinity increases the boiling point elevation, which reduces the temperature of the evaporated water and its vapor pressure. The following equation relates the water vapor temperature to the water temperature:
(14)
Figure 3. Variation in the evaporation rate for hot water in ambient air.
where Tv is the vapor temperature, Tb is the water temperature, and BPE is the boiling point elevation. BPE is calculated from the empirical formula given in the appendix. The effect of the water salinity is more evident for water evaporation from a solution with a salinity of 68 720 ppm. It should be noted that evaporation from the water surface would result in an increase of the local salt concentration in the surface layer. This would reduce further the water vapor pressure at the water surface or the driving force for evaporation. As is shown in Figure 3, the evaporation rate from the distilled water with a salinity of 26 ppm varies over a range of 2000-6000 g/h‚m2 as the air velocity is increased from 2 to 4 m/s. On the other hand and at the same conditions, the evaporation rates for the brine
solution with a salinity of 68 720 ppm varies over a range of 500-1700 g/h‚m2. Results for water evaporation into a hot air stream are shown in Figure 4. The effect of the air velocity is similar to those discussed in the previous section, where an increase in the air velocity increases the evaporation rate. As is shown in Figure 4, the evaporation rates can increase by as much as 100% upon an increase in the air velocity at the same vapor pressure difference. The salinity effect in these experiments is very evident. As is shown, the evaporation rates for freshwater have a maximum value of 1000 g/h‚m2, while the evaporation rates from seawater and brine solutions have maximum values below 500 g/h‚m2. As is shown, similar evaporation rates are obtained for the seawater and the two brine solutions.
Tv ) Tb - BPE
Ind. Eng. Chem. Res., Vol. 41, No. 3, 2002 647
Figure 4. Variation in the evaporation rate for water at ambient temperature in hot air.
Figure 5. Measured and calculated dimensional evaporation rates.
Fitting Correlations
The coefficient of determination for the above correlation is 0.94. A display of the correlation predictions against the measured evaporation rate is shown in Figure 5b. The dimensionless correlation for the above correlations include three dimensionless groups, which include the Reynolds number, Re ) FVD/µ, the dimensionless evaporation rate, R h ) R/FV, and the dimensionless difference of the water vapor pressure, ∆P h ) ∆P/FV2. The dimensionless correlation for the case of water evaporation from hot water into unheated ambient air is given by
Literature review shows that the fitting correlations of the evaporation rate are performed in dimensional form rather than dimensionless form. In this section both forms of regression are performed. The correlations are made as a function of the vapor pressure difference at the water surface and air bulk, air velocity, and water salinity. The dimensional correlation for the case of water evaporation from hot water into unheated ambient air is given by
R ) 169.02V1.478X-0.103∆P0.654
(15)
R h ) 1.103 × 10-7∆P h 1.78X-0.103Re0.65
(17)
which is valid over the following parameter range: 2 < V < 4 m/s; 26 < X < 68 720 ppm; 0.29 < ∆P < 12.37 kPa; 25 < T for the hot water < 60 °C; T for the air stream ) 25 °C. The coefficient of determination for the above correlation is 0.84. A display of the correlation predictions versus the measured evaporation rate is shown in Figure 5a. The dimensional correlation for the case of water evaporation from unheated water into heated air is given by
which is valid over the following parameter range: 36
