Theoretical and experimental study of a seawater desalination system based on humidification-dehumidification technique

Journal Pre-proof Theoretical and Experimental Study of a Seawater Desalination System Based on Humidification-Dehumidification Technique A.S.A. Mohamed, M.Salem Ahmed, Abanob.G. Shahdy PII:

S0960-1481(20)30138-5

DOI:

https://doi.org/10.1016/j.renene.2020.01.116

Reference:

RENE 12979

To appear in:

Renewable Energy

Received Date: 3 November 2019 Revised Date:

22 January 2020

Accepted Date: 23 January 2020

Please cite this article as: A.S.A. Mohamed, M.Salem Ahmed, Abanob.G. Shahdy, Theoretical and Experimental Study of a Seawater Desalination System Based on Humidification-Dehumidification Technique, Renewable Energy (2020), doi: 10.1016/j.renene.2020.01.116 This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Published by Elsevier Ltd.

Highlights

Highlights •

Desalination by HDH process is a promising method for small capacity plants.

•

The present work presents the results of an experimental and theoretical study.

•

The theoretical and experimental values take the same trend.

•

The average productivity is 2.45 kg/hr and the cost of fresh water is 0.047 US$/L.

•

The results of present work are acceptable among those of some previous studies.

Theoretical and Experimental Study of a Seawater Desalination System Based

1

on Humidification-Dehumidification Technique

2

A. S. A. Mohamed a,b,*, M. Salem Ahmed a, Abanob G. Shahdy c

3

4 5 6

a

Mechanical Department, Faculty of Industrial Education, Sohag University, Sohag 82524, Egypt High Institute for Engineering and Technology, Sohag, Egypt c Industrial Secondary School, Sohag, Egypt b

7 8

* Corresponding author E-mail address: [email protected] (A. S. A. Mohamed).

9

Abstract

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The technique of desalination seawater by humidification dehumidification process is

11

considered a promising method for small capacity production plants. This process has many

12

advantages such as operation at low temperature, ability to use the renewable energy sources and

13

requirements of low technology level. The current work presents the results of a study on

14

humidification dehumidification desalination system using the solar energy, in addition to a

15

developed mathematical model consisting of the energy equations of each component to simulate the

16

experimental work. The results show that there is a good agreement between the theoretical and

17

experimental work. The results also reveal that there are effective values for the mass flow rate of

18

air, mass flow rate ratio, and mass flow rate of feed water. The average productivity of the

19

desalination system is 2.45 kg/hr and the estimated cost per 1 liter of fresh water is 0.047 US$.

20

Finally, the results obtained from the present work are acceptable among those of previous studies.

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Keywords: Seawater desalination; Humidification dehumidification; Productivity; Gain output ratio

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1. Introduction

24

The need for water is becoming more essential issue, for many reasons including population

25

growth, agricultural and industrial uses in light of the lack of water resources, which has created a

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strong impetus to look for other sources of water to provide us with water to meet our growing

27

needs. One of the important solutions for this problem is the desalination of seawater. Desalination is

28

a process of removing dissolved salts from seawater to produce fresh water fit for usage. 1

Nomenclature a Specific mass transfer area in humidifier, m2/m3 A Area, m2 Cp Specific heat at constant pressure, kJ/kg°C GOR Gain output ratio Air enthalpy, kJ/kg H HDH Humidification dehumidification K Overall mass transfer coefficient of water in air, kg/sm2 LMTD Logarithmic mean temperature difference Mass flow rate, kg/s m MR Mass flow rate ratio P Pressure, kPa T Temperature, °C U Overall heat transfer coefficient, J/m2s°C V Packing volume, m3 Greek symbols λ Φ ω Subscripts a amb atm av b c d db Fw h in L o S st v w wc

Latent heat of evaporation, kJ/kg Relative humidity, % Absolute humidity of air, kg vapor/kg dry air Air Ambient Atmosphere Average Brine Condenser Dehumidifier Dry bulb temperature Fresh water Humidifier Inlet Loss Outlet Solar collector Saturation condition Vapor Water Water cooling

1

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The oceans constitute the largest proportion of the world's water reserves accounting for 97.5%

20

of total amount and the remaining 2.5% freshwater is present in the atmosphere, polar ice, and

21

groundwater [1]. Therefore, the seawater desalination is the appropriate solution to the problem of 2

1

water shortage. Desalination technologies are divided into two major groups; firstly, the thermally

2

systems in which evaporation and condensation are the main processes used to separate salts from

3

water. Secondly, the membrane systems where either pressure or electric field is applied to the salty

4

water to force it through a membrane leaving salts behind [2].

5

The thermal desalination systems are the most widely used in the world and the humidification

6

dehumidification (HDH) technique is considered one of the most important methods of these

7

systems. The HDH process is similar to the rain cycle that occurs in nature, where seawater is

8

evaporated then air carries this water vapor (humidification process) and then condenses

9

(dehumidification process). So, the distillate water is obtained [3].

10

Many studies have been directed on optimizing and improving the overall performance of

11

HDH distillation systems and its components. Narayan et al. [4] worked on a comprehensive review

12

of several investigations into the HDH cycles. This review includes describing and explaining for

13

each component of these cycles such as humidifier, dehumidifier, and water heating source. They

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also painted these cycles on psychometric charts while Adewale Giwa et al. [5] discussed the

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principal HDH components, latest researches on HDH systems driven by renewable energy and

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recent innovations on HDH distillation design for sustainable fresh water production. They found

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that the HDH desalination system is a promising technique for producing fresh water to meet the

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water demand. The overall thermal energy to drive the HDH distillation system can be obtained from

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renewable sources like solar and geothermal energy.

20

Yamal and Solmus [6] studied theoretically the effect of different system operating conditions,

21

types of air heater, some different design parameters and weather conditions on a solar water

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desalination system performance under the climatological conditions of Ankara. The desalination

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unit consists of a double-pass flat plate solar air heater with two glass covers, humidifying tower,

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storage tank, and dehumidifying exchanger. The system used in this work is based on the idea of

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closed water, open air cycles, and air heated. They found that the system productivity is increased up

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to 8% by using a double-pass solar air heater compared to a single-pass solar air heater and

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decreased about 30% without double-pass solar air heater under the same operating conditions.

28

Mohamed and El-Minshawy [7] studied the HDH system where both water and air are heated

29

before entering to humidifier. Water is heated by geothermal energy as clean and renewable natural

30

resource of energy. The authors indicated that there is optimum water to air mass flow rate ratio in

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the range of 1.5 – 2.5, which achieved maximum water production rate. While Farsad and 3

1

Behzadmehr [8] developed a steady state thermodynamic model for HDH system. The results show

2

that there is an optimum mass flow rate ratio in the range of 1 – 1.5 that maximizes water production

3

rate and the gained output ratio (GOR) was calculated to be about 4.

4

Nafey et al. [9] presented a numerical investigation of a HDH desalination process using solar

5

energy to heat both water and air . The results show that the productivity of the unit is strongly

6

affected by the air flow rate, cooling water flow rate and total solar energy incident through the day.

7

Wind speed and ambient temperature variations show a very small effect on the system productivity.

8

In addition, the obtained results indicate that the solar water collector area strongly affects the system

9

productivity, more than the solar air collector area. In another study, Eslamimanesh and Hatamipour

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[10] designed a computer program using mass and energy balances for modeling the process

11

behavior. The results show that increasing inlet air and fresh water flow rate increases fresh water

12

production. In addition, heating the air inlet to humidification column or cooling the water inlet to

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dehumidification column increases the fresh water production rate but increasing water to air flow

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ratio in a humidifier leads to a lower production rate.

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Many experimental studies have been conducted for evaluating the performance of the HDH

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desalination. Nada et al. [11] investigated the performance of a hybrid HDH water desalination and

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air conditioning system using vapor compression refrigeration cycle. The main system components

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are air blower, air heaters, steam boiler, humidifier, and dehumidifier. The system consists of four

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loops, one closed loop for refrigerant, and the others are open loops for air, fresh water, and

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seawater. In the refrigerant loop, refrigerant R134a is used. The results show that the mass transfer

21

coefficient decreases with increasing air specific humidity and evaporator air inlet temperature.

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Gang Wu et al. [12] work on experimental investigation of a multi-stage HDH desalination

23

system heated directly by a cylindrical Fresnel lens solar concentrator. The results show that the

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maximum water productivity of the unit is about 3.4 kg/h and the maximum GOR is about 2.1, when

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the average intensity of solar radiation is about 867 W/m2.

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Guofeng Yuan et al. [13] presented an experimental study on a HDH system. The main

27

components of this system are humidifier, dehumidifier, and solar collector to heat both air and

28

water. The performance of the solar air heater field and the humidifier was investigated by

29

experimental tests and analyses. Water production tests were carried out on several typical days, and

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the results showed that water production of the system could reach 1200 L/day, when the average

31

intensity of solar radiation got to 550 W/m2. 4

1

Abdelkader et al. [14] worked on an experimental and theoretical study of a HDH desalination

2

system using solar unit. In this system, both of water and air were heated and honeycomb wood used

3

as a packing material in the humidifier while a helix-tube type condenser used in the dehumidifier.

4

The results indicate that the average productivity of the system in November, December, and January

5

ranged between 2 to 3.5 kg/m2.day while the average summer productivity was found between 6 to 8

6

kg/m2.day in June and 7.26 to 11 kg/m2.day in July and August.

7

The current work investigates the performance of HDH desalination system using the solar

8

energy as a clean and renewable natural resource of energy. The research also evaluates a

9

mathematical model to simulate the experimental work. In addition, the study introduces an

10

economic cost of the fresh water productivity and presents the results with the results obtained from

11

previous researches.

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2. Experimental work

13

2.1 Description of the HDH system

14

The seawater desalination system is established based on HDH desalination method and this

15

system is classified as an open cycle for water, close cycle for air and water heating system (CWOA-

16

WH). The HDH system consists of three main cycles: one for air, and two for water (one for hot

17

seawater and the others for feed seawater). For the first cycle (air cycle), the air is working as a

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carrier medium where it is mixed with large quantities of water vapor. In the second cycle (hot

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seawater cycle), the hot seawater is heated and sprayed on the air. Finally, in the last cycle (feed

20

water cycle), the water vapor is condensed from the air to produce the fresh water.

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The HDH system consists of three main components: humidifier (evaporator), dehumidifier

22

(condenser) and water heating source, in addition to some other components and auxiliary devices

23

such as water storage tank, water pumps, air blower, valves, pipes, and flow meter (rotameter), as

24

shown in Fig. 1.

25

The humidifier is a rectangular shell of galvanized steel with overall dimensions of 400 × 500

26

mm and length of 1200 mm with thickness of 0.8 mm. Cellulose paper is used as a packing material

27

in the humidifier which insulated using thermal glass-wool in order to reduce the heat loss to the

28

surrounding. The dehumidifier is a square box made of galvanized steel with thickness of 1 mm, and

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dimension 320 × 320 mm and a height of 1000 mm. A fin-tube heat exchanger is used for 5

1

condensing the water vapor from the air. The bottom of the dehumidifier has a conical shape to easy

2

collecting the fresh water. The seawater desalination device (humidifier and dehumidifier) is

3

supported on a metal stands. Galvanized steel duct is used to connect humidifier with dehumidifier

4

from the top. As a heating source of seawater, an evacuated tube solar collector is used while the hot

5

water is sprayed on the packing material in the humidifier. To ensure the stability of water

6

temperature, an auxiliary electric heater of 5 kW is fixed inside the seawater storage tank through

7

controlling it. A silicon sealant, rubber, and screw welding are used between the different

8

components of the HDH device to prevent leakage to the surrounding.

9

Hot humid air 10 11

Dehumidifier

Humidifier

Solar collector

12 13

Outlet feed water 14 15

Condenser coil Rotameter

Inlet feed water

Hand valve

Outlet air 16

Hot water tank Fresh water

Inlet air

17

Auxiliary heater

18 19

Metal stand

Brine Hot water pump

Air blower

Metal stand

20

Fig. 1. Layout of the experimental setup. 21 22

23

2.2 Procedure

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Figure 2 shows a photo of the experimental setup. HDH process is started by forcing the air to

25

the bottom of the humidifier using 2 hp blower. The hot seawater is flowed from the insulated

26

storage tank through an insulated pipe to the top of the humidifier and is sprayed on the packing 6

1

material. The humidified air outlet from the humidifier flows to the dehumidifier where the water

2

vapor is condensed from the air (fresh water) using the cooling seawater then the dehumidified air

3

exits to the atmosphere. The brine water is collected at the bottom of the humidifier to be reheated in

4

the evacuated tube solar collector and repeat this cycle while the desalinated water is collected at the

5

bottom of the dehumidifier. In the HDH system, two pumps of 0.5 hp each are used, one for hot

6

water and the other for feed water. Hot and feed water flow rates are controlled by hand control

7

valve while the air blower controls the airflow rate.

8 9 10 11

Dehumidifier

Humidifier

12

Hot water tank Rotameter

13 14 15

Air blower 16

Data logger

Fresh water

17 18

Hot water pump

Fig. 2. Photo of the experimental setup.

19

20

2.3 Measured data

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During the experimental work, all parameters are measured and recorded to evaluate the

22

performance of the HDH desalination system. The parameters include solar radiation, dry and wet

23

bulb temperature of air inlet to and outlet from the humidifier and dehumidifier, hot water

24

temperature at inlet and outlet of the humidifier, feed water temperature at inlet and outlet of the

25

dehumidifier. In addition, the mass flow rates for both air and water are also measured.

7

1

The solar radiation is measured using solarimeter working up to 5000 W/m2. All the

2

temperatures in the HDH system are measured by thermocouples of type k connected with a data

3

logger (its error range being ±0.5 °C). The water flow rates are measured by two rotameters (0.5 - 2

4

m3/h, operating temperature 0 – 90 °C and accuracy ± 4%). The first rotameter is used to measure the

5

flow rate of hot seawater ahead the humidifier, while the other is used to measure the flow rate of

6

feed water ahead the dehumidifier. The air velocity is measured using wireless anemometer (0.4 -30

7

m/s with accuracy ±3%).

8

2.4 Experimental uncertainty analysis

9

Instruments used in the experiments with their values of accuracy and range are listed in table

10

1. It is important to make the uncertainty analysis for measuring instruments to investigate the

11

accuracy of measurements. The uncertainty is usually expressed as an interval around the estimated

12

value. There are two types of uncertainty. Type A is regarded to random errors and can be

13

determined statistically, whereas Type B is regarded to systematic errors, which is a characteristic

14

feature of the instrument itself. In this research, all measured values are supposed to be distributed

15

uniformly and so their uncertainty is of the Type B. Therefore, the standard uncertainty is expressed

16

as Eq. (1) [15, 16]. Uncertainty =

accuracy

(1)

√3

Table 1 Experimental instruments with accuracy, range and standard uncertainties Instrument

Accuracy

Range

Standard uncertainty

Solarimeter Temperature (type K)

± 1 W/m2 ± 0.5 °C

0–5000 W/m2 0-200 °C

0.58 W/m2 0.29 °C

Rotameter

± 4%

0.5-2 m3/h

2.31%

Anemometer

± 3%

0.4-30 m/s

1.73%

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3. Theoretical work

19

The mathematical model for the HDH desalination system includes energy and mass balance

20

for the components integrated with the HDH system where the air and water temperature and

21

productivity can be evaluated at various conditions. 8

1

The model assumptions include the followings:

2

•

temperature are limited to 1–2 °C during the experiment time).

3 4

• •

9

Heat losses are ignored (no energy is stored in the construction materials of each component).

7 8

The HDH device is assumed to be work at steady state condition, which is ensured by keeping the hot and feed water temperatures constant.

5 6

The air enters the humidifier at ambient conditions (variations in the ambient air

•

Pressure drop within the HDH device is neglected.

3.1 Humidifier modeling

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A schematic of the humidifier is shown in Fig. 3a. The air enters the humidifier from the

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bottom at operating conditions of temperature (T#,$%,& ), humidity (ωa,in,h ), enthalpy of dry air (Ha,in,h )

12 13 14 15

and mass flow rate (m# ). The air exits from the top of the humidifier at a temperature (T#,(,& ), humidity (ω#,(,& ) and enthalpy of humid air (H#,(,& ). Hot seawater with mass flow rate(m)), heat

capacity(Cp) ), temperature (Tw,in,h ) and enthalpy (H),$%,& ) is sprayed at the top of the humidifier. While the brine water exits from the bottom of the humidifier with temperature(T),(,& ), heat

16

capacity (Cp, ) and enthalpy (Hw,o,h ).

17

The energy balance in the humidifier [8, 17-20] can be written as follows: Q$%,& − Q(,& = Q/,&

18

(2)

Energy entering the humidifier is: Q$%,& = m # H#,$%,& + m)  Cp) T),$%,&

19

(3)

Energy leaving the humidifier is: Q(,& = m # H#,(,& + m)  Cp, T),(,&

20

(4)

Energy losses in the humidifier are: Q/,& = U/,& A& 4T#5,& − T#6, 7

(5)

9

1

Where: T#5,& =

2

T#,$%,& + T#,(,& 2

(6)

Then, substituting Eqs. (3) – (5) in Eq. (2), it can be obtained: m# 4H#,$%,& − H#,(,& 7 + m) Cp) 4T),$%,& − T),(,& 7 = U/,& A& 4T#5,& − T#6, 7

3

Where U/,& : is the overall heat transfer coefficient in the humidifier, A& is the external area of the

4

humidifier and T#5,& is the average temperature in the humidifier.

5

The mass transfer rate in the humidifier [8, 17, 19, 20] can be written as follows: ? C m# k. a. V >4H),$%,& − H#,(,& 7 − (H),(,& − H#,$%,& )B 4H − H#,(,& 7 = B m) #,$%,& m) >> 4H − H#,(,& 7 B ln ),$%,& (H),(,& − H#,$%,& ) = A

6 7

8

(7)

(8)

Where: k is the overall mass transfer coefficient of water in air (kg/m2s), E is the specific mass transfer area (m2/m3), and V is the packing volume (m3). 3.2 Dehumidifier modeling

9

In the dehumidifier, the hot humid air and the feed water are not in direct contact. The humid

10

air moves down through the space between the fins and tubes of condenser. During the

11

dehumidification process, the sensible and latent heat is transferred from the hot humid air stream to

12

the feed water.

13

A schematic of the dehumidifier is shown in Fig. 3b. The humid air enters the dehumidifier

14

from the top at operating conditions of temperature (T#,$%,F ), humidity ratio (ω#,$%,F ) , enthalpy of

15 16 17 18

humid air (H#,$%,F ) and the mass flow rate ( m a ). While the air exits from the bottom of the

dehumidifier at temperature (Ta,o,d ), humidity (ω#,(,F ) and enthalpy of humid air (H#,(,F ). The feed

water is introduced at temperature (T)H,$%,H ) and mass flow rate (m wc ), while it exits at temperature (T)H,(,H ).

19

10

Inlet hot water

1

Inlet humid/hot air

(T),$%,& , H),$%,& , m) , Cp) )

(T#,$%,F , ω#,$%,F , H#,$%,F , m# )

2

3

4

Outlet humid/hot air (T#,(,& , ω#,(,& , H#,(,& , m# )

Outlet feed water (T)H,(,H , m)H , Cp)H )

Humidifier

Dehumidifier

5

6

Inlet air (T#,$%,& , ω#,$%,& , H#,$%,& , m# )

Inlet feed water (T)H,$%,H , m)H , Cp)H )

7

Outlet hot water (Brine)

Outlet humid air (T#,(,F , ω#,(,F , H#,(,F , m# )

(T),(,& , H),(,& , m) , Cp, )

8

(b)

(a)

9

Fig. 3. Heat and mass balance for the humidifier and dehumidifier. 10

11

The energy balance in the dehumidifier [8, 17-20] can be written as follows: Q$%,F − Q(,F = Q /,F

12

(9)

Energy entering to dehumidifier is: Q$%,F = m # H#,$%,F + m)H  Cp)H T)H,$%,H

13

(10)

Energy leaving the dehumidifier is: Q (,F = m # H#,(,F + m)H  Cp)H T)H,(,H

14

(11)

Energy losses in dehumidifier are: Q /,F = U/,F AF 4T#5,F − T#6, 7

15

(12)

Where: T#5,F =

T#,$%,F + T#,(,F 2

(13) 11

1

Then, substituting Eqs. (10) – (12) in Eq. (9), it can be obtained: m # 4H#,$%,F − H#,(,F 7 + m)H  Cp)H 4T)H,$%,H − T )H,(,H 7 = U/,F AF 4T#5,F − T#6, 7

2

The heat transfer rate in the dehumidifier [8, 17, 19, 20] can be written as: m)H Cp)H 4T)H,(,H − T)H,$%,H 7 = UH AH LMTDH

3

(14)

(15)

Where: UH is the overall heat transfer coefficient of the condenser (J/m2s°C), AH is the condenser heat

4

transfer area (m2), and LMTDH is condenser's logarithmic mean temperature difference (°C) which is

5

described by LMTDH =

6

4T#,$%,F − T)H,(,H 7 − 4T#,(,F − T)H,$%,H 7

(16)

4 T#,$%,F − T)H,(,H 7 ln 4 T#,(,F − T)H,$%,H 7

3.3 Water heating source modeling

7

The seawater is heated in HDH desalination system using an evacuated tube solar collector so

8

that it is important to estimate the energy input to the system, QM is added between the inlet and

9

outlet of the humidifier as expressed by the following equation [21]: QM = m) Cp) 4T),$%,& − T),(,& 7

(17)

10

One of the aims of this research is to calculate the amount of the fresh water which obtained

11

from the HDH desalination system so that it is needed to estimate the difference of air water content

12

between the air inlet to and outlet from the dehumidifier, as expressed by the next equation: mN) = m# 4ω#,$%,F − ω#,(,F 7

13

3.4 Model correlations The physical properties for the air and water streams are needed and defined as follows:

14

15

(18)

-

Absolute humidity of air is given by the following relation [17,18]:

ω# = 0.62198

PF, P#P6 − PF,

(19) 12

1

2

Where: PF, is the water vapor pressure at the dry bulb temperature (kPa). -

The water vapor pressure at the dry bulb temperature [17,18]:

PF, = ϕ PRP 3

4

(20)

Where: ϕ is the air relative humidity and PRP is the air saturation pressure at Ta . -

The saturation pressure for water vapor at dry bulb temperature [22]:

PRP = Exp U

−6096.938 + 21.240964 − 2.71119 × 10WX T# + 1.67395 × 10WY T#X T# + 2.4335 ln(T# )Z

5

-

(21)

The air enthalpy as given in [18]:

H# = ( Cp# + Cp5 ω# )T# + λ ω# 6 7

8

(22)

Where: H# is the enthalpy of dry air (kJ/kg), Cp# is the heat capacity of air (kJ/kg°C), Cp5 is the heat capacity of vapor (kJ/kg°C), and λ is the latent heat of water evaporation (kJ/kg). -

The latent heat of water evaporation is given by [17]:

λ = 2501.897149 − 2.407064037T) + 1.192217 × 10WX T)X − 1.5863 × 10WY T)[ 9

10

(23)

Where: T) is the water temperature (°C). 3.5 Method of solution

11

To solve the mathematical model, the parameters are considered as known: flow rates;

12

(m) ,m)H and m# ), properties; ( Cp# , Cp5 , Cp) , Cp)H , λ, P#P6 ), external geometry; ( A& , AF ), internal

13

geometry; ( V, a, AH ), and temperatures; (T)H,$%,H , T),$%,& , T#,$%,& = T#6, ,T#,(,& = T#,$%,F )

14

The mathematical model consists of two steps. Firstly, these parameters are used to calculate

15

the mean values of heat and mass transfer, U/,& , U/,F , UH, and k coefficients. Secondly, the mean

16

values are used to study the different conditions and to predict the temperatures of air and water, and

17

the productivity as described in flow chart shown in Fig. 4. 13

1

Start 2

3

4

Read input data m) , m# , m)H T),$%,& , T)H,$%,H , (T#,$%,& = T#6, , T#,(,& = T#,$%,F ) Cp# , Cp5 , Cp) , Cp)H , λ, P#P6 A& , AF ,V, a, AH

5

Calculate (U/,& , U/,F , UH , and k)

6

7

Calculate mean values of (U/,& , U/,F , UH , and k)

8

Using mean values to calculate

9

(T#,$%,F , T#,(,F , T)H,(,H , mN) )

10

End

11

Fig. 4. Flow chart of theoretical modeling.

12

The mathematical model given by the above equations is solved by using Engineering

13

Equation Solver (EES) which uses a numerical iterative procedure to solve the set of equations. The

14

convergence of the numerical solution is achieved when the relative equation residuals are less than

15

10-6 or if the change in variables is less than 10-9. It has a data base of reliable correlations for the

16

properties of humid air and seawater. EES evaluates seawater properties using the correlations

17

provided by Sharqawy et al. [23]. While humid air properties are evaluated using the formulations

18

presented by Hyland and Wexler [24].

19

4. Results and discussion

20

The measured temperatures at steady state are used as known values in the procedure

21

mentioned above, and the next parameters can be calculated to calibrate the mathematical model:

22

U/,& , U/,F , UH , k. Appendix A shows some of experimental results. Mean values obtained from this

23

procedure are: U/,& = 34.98 J/m2sk, U/,F = 36.96 J/m2sk, UH = 28.09 J/m2sk and k= 0.00114 kg/m2s.

24

The thermal performance of the HDH desalination system was evaluated by the GOR. GOR is

14

1

defined as the ratio of the latent heat of evaporation of the fresh water produced to the total energy

2

input into the HDH desalination system [25], as given by Eq. (24). GOR =

λ × m N) QM

(24)

3

A lot of experiments were conducted and compared with the simulation results to validate the

4

developed models. Figure 5 illustrates the effect of air mass flow rate on the fresh water productivity

5

and the GOR of the HDH desalination system. It is shown that increasing the mass flow rate of air

6

increases the production of fresh water and GOR up to its maximum value, then these values

7

decrease because the increase of the air flow rate decreases the contact time between air and water in

8

the humidifier that makes the air exit without reach to saturation state. In this work a 0.81 kg/min

9

was selected as the best mass flow rate of air although it does not achieve the maximum productivity

10

but it gives the maximum GOR.

11

The mass flow rate ratio (MR) is defined as the inlet seawater mass flow rate to the inlet dry air

12

mass flow rate circulated in the HDH device. Figure 6 shows the MR versus the productivity of the

13

HDH device at different seawater temperatures. It is clear that the fresh water productivity increases

14

with increasing the MR. The seawater temperature has a significant effect on the fresh water

15

productivity. The productivity increases slightly with low seawater temperature while it increases

16

rapidly with high temperature. In this work, 4.5 was chosen as the value of MR during performing

17

the experiments.

18

Figure 7 shows the effect of the feed water flow rate on the fresh water productivity at different

19

values of hot seawater temperature entering the humidifier. Increasing the feed water flow rate

20

decreases the surface temperature of the condenser. As a result, the condensation rate and the fresh

21

water productivity are increased. As shown in Fig. 7, the optimum mass flow rate of feed water is 4

22

kg/min.

23

The effect of seawater temperature inlet to the humidifier on the productivity and GOR is

24

shown in Fig. 8. The productivity and GOR are increased significantly with increasing the seawater

25

temperature inlet to the humidifier, especially after 50 °C. It is noted also that there is a good

26

agreement between the experimental and theoretical work.

27

15

1

4

5

6

Productivity (kg/min)

3

Gain output ratio, GOR. (-)

2

7

8

Mass flow of air (kg/min)

9

Fig. 5. Influence of air mass flow rate on productivity and GOR of HDH system. 10

11

13

14

15

Productivity (kg/min)

12

_ ` = 0.81 kg/min

 = 4 kg/min _ab

16

17

Mass flow rate ratio, MR. (-)

18

19

Fig. 6. Effect of mass flow rate ratio (MR) on the productivity of the HDH system. 20

16

1

3

4 5

Productivity (kg/min)

2

_ ` = 0.81 kg/min MR = 4.5

6 7

Mass flow rate of feed water (kg/min)

8 9 10

Fig. 7. Effect of feed water flow rate on productivity of the HDH system. 11 12

Gain output ratio, GOR. (-)

_ ` = 0.81 kg/min

13

15 16 17

Productivity (kg/min)

MR = 4.5 14

18 19 20 21

Seawater temperature inlet to humidifier, ca,de,f (°C)

22

Fig. 8. Effect of seawater temperature inlet to humidifier on productivity and GOR.

17

The performance of humidifier (as a cooling tower) is generally determined by the ratio of

1 g.#.h

2

(

3

can be calculated using Eq. (8). As shown in Fig. 9, increasing the mass flow rate ratio in humidifier

4

reduces the characteristic parameter of the humidifier at all values of seawater temperature. In

5

addition, the dimensionless parameter (

6

humidifier, as shown in Fig. 10, where the dimensionless characteristic parameter increases with

7

increasing the seawater temperature.

6i

). This ratio is named the dimensionless characteristic parameter of the humidifier [26], and

g.#.h 6i

) was affected by the seawater temperature inlet to the

8 9 10

_ ` = 0.81 kg/min

11

 = l kg/min _ab

13

j. `. k _a

12

14 15 16 17 18

Mass flow rate ratio, MR. (-)

19 20

Fig. 9. The Effect of mass flow rate ratio on the humidifier characteristics.

21 22 23 24 25 18

1

 = l kg/min, MR = 4.5 _ ` = 0.81 kg/min, _ab

2 3

5

j. `. k _a

4

6 7 8 9 10

Seawater temperature inlet to humidifier, ca,de,f (°C)

11

Fig. 10. Effect of seawater temperature inlet to humidifier on humidifier characteristics.

12

13

4.1. Model validation

14

It is necessary to validate the accuracy of simulation results against the experimental values

15

obtained from HDH desalination system. The accuracy of simulation results is achieved by its

16

comparison with the experimental results. The absolute relative error is defined as follows equations

17

(24) [27]. u

q Trst (i) − TR$6 (i)q 100 Ԑ#n (%) = p k Trst (i)

(24)

$vw

18

Where: Trst denotes the experimental data, TR$6 the theoretical prediction, and k is the number of

19

experimental measurement.

20

The comparison between the calculated results by the model and the experimental values is

21

represented in Fig. 11. The average relative absolute difference is 5.25%, 5.47% and 2.7% for

22

temperature of air inlet to dehumidifier, air outlet from dehumidifier and water cooling outlet from

19

1

condenser, respectively. According to the comparison results, the calculated results accord well with

2

the experimental values.

3

The comparison between the calculated productivity and the experimental values is shown in

4

Fig. 12, generally with the average relative absolute difference of 19.89%. The present work

5

performed at air flow rate of 0.81 kg/min, MR = 4.5 and water temperature inlet to humidifier of 40,

6

50, 60, 70 °C. At these parameters, the average relative absolute difference of productivity is 8.78%.

7

According to the comparison results, the theoretical and experimental values take the same trend.

8

The maximum, minimum and average relative absolute difference of the air and water temperatures

9

and the productivity shown in Figs. 11 and 12 is presented in table 2.

10

11

13 14 15 16 17

Calculated temperature (ºC)

12

_a = 4.864 kg/min  = l kg/min _ab

18 19 20 21

Measured temperature (ºC) Fig. 11. Comparison between calculated and measured temperatures at three points in HDH system.

22 23 24 25

20

1

Calculated productivity (kg/min)

2 3 4 5 6 7

_ a = 4.864 kg/min  = 4 kg/min _ab

8 9

Measured productivity (kg/min) 10

Fig. 12. Comparison between the calculated and measured productivity of the HDH system. 11 12

Table 2 13 14 15 16 17

The accuracy of the theoretical results. Average relative

Maximum relative

Minimum relative

error Ԑar (%)

error Ԑmax (%)

error Ԑmin (%)

5.25

15.40

0.44

5.47

13.08

0.09

T)H,(,H

2.70

7.90

0.49

Productivity

19.89

29.44

0.19

Parameter T#,$%,F T#,(,F

18

19

20

5. Economic study

21

Another aim of this research is the economic analysis of the HDH system. The economic

22

analysis depends on some important parameters such as, the expected lifetime of the system (n), the

23

variable cost (V) and the total cost of the fresh water product (C) [18,28]. The total cost of the fresh

24

water product is determined by summing the total cost of the HDH device (F), (which determined by

25

summing the cost of each components of this device) and the variable cost (maintenance cost) (V), 21

1

where (C = F + V). The total cost of the HDH device is estimated to be 1042 US$, as given in Table

2

3. Assume that the maintenance cost equals to 20% of the total cost of the HDH device per year [29].

3

The lifetime for the HDH system was assumed to be 10 years, where (V = 20% × 1042 × 10 =

4

2084 US$) and the total cost of the fresh water product (C = 1042 + 2084 = 3126 US$). The average

5

number of fresh water liters produced per day (the operation period of the HDH system is 8 hours per

6

day; starts at 9 am and ends at 17 pm) equals 2.45 kg/hr × 8 = 19.6 kg/day. Assuming that HDH

7

device operates 340 days per year as the sun rises along the year in Egypt [18].

8

The number of fresh water liters that would be produced = production per day × production period ×

9

life time = 19.6 liters/day × 340 day/year × 10 years = 66640 liters

10

Cost of fresh water per liter =

the total cost of the water product 3126 = = 0.047 US$ the number of liters that would be produced 66640

11

12

Table 3 Approximate cost of the HDH device s.

13

14

15

16

17

18

19

20

Components

Cost (US$)

System cover ( humidifier, dehumidifier )

92

Duct connection and elbows

61

Water tank

62

Frame of the HDH device (metal stands)

60

Condensers

65

Pipelines and accessories

60

Packing materials

62

Pumps

120

Air blower

125

Insulation

35

Solar collector

300

Total fixed cost (F)

1042

21

22

22

1

The current results and those obtained from some previous researches are illustrated in table 4.

2

The table shows some available parameters and results such as packing material, air and water flow

3

rate, type of flow, feed water temperature, productivity, GOR and cost per liter. Based on the

4

available data, the productivity and cost per liter of the current desalination unit is acceptable among

5

those studied in some previous researches.

6

6. Conclusions

7

A seawater desalination system working under the air HDH method using solar energy is

8

presented. Developed mathematical model has been tested to simulate the heat and mass exchange

9

and calculate the temperatures and the productivity of the HDH system at steady state conditions and

10

comparing it with the experimental results. In addition, the developed model is simulated to study the

11

effect of operating conditions on the thermal performance of the HDH system and the dimensionless

12

characteristic parameter of the humidifier. The results show that the calculated results accord well

13

with the experimental values. There are effective values for the mass flow rate of air, mass flow rate

14

ratio and the flow rate of feed water, which are 0.81 kg/min, 4.5 and 4 kg/min, respectively. The

15

average productivity of the HDH system is 2.45 kg/hr and the estimated cost per 1 liter of fresh water

16

is 0.047 US$.

17

18 19 20 21 22 23 24 25

23

Table 4 The current results and those obtained from some previous researches. Classification

Packing material

_` (kg/s)

_a (kg/s)

Type of flow

ca,de,f (°C)

Productivity

GOR

Cost/liter (US$)

Reference

CWOA – WH

Cellulose paper

0.0135

0.06075

Counter flow

40 - 70

0.76 - 4.9 kg/hr

0.35 - 0.55

0.047

Current study

OWCA – WH

Cellulose paper

0.016 - 0.02067

0.033333

Cross flow

43 - 87

5.5 kg/hr

1.8 - 2.2

0.0578

Ref [18]

OWCA – WH

Cellulose paper

0.040 - 0.043

0.012 - 0.023

Cross flow

44.6 - 68.9

0.77 - 1.45 kg/hr

0.91

---

Ref [19]

OWCA – WH

A metal packing

0.0264 - 0.0363

0.001 - 0.045

Counter flow

40 - 70

1.2 - 3.2 kg/hr

Not given

---

Ref [20]

CWOA - WH,AH

Aluminum sheets

0.15

0.53

Counter flow

49

5 kg/hr

Not given

0.01

Ref [25]

OWCA - WH,AH

Textile packing

0.01

0.04

Cross flow

44.69

21.75 kg/day

Not given

0.08

Ref [28]

OWCA – WH

Structured-type

0.044

0.089

Counter flow 50 - 70

10 kg/hr

OWCA- AH

packing-material

0.137

0.091

Counter flow

1 2 3 4 5 6 7

24

1.93 2.19

---

Ref [30]

Appendix A: some of experimental results. Measured data c`,de,f

c`,de,z

c`,{,z

ca,de,f

ca,{,f

cab,de,b cab,{,b

Calculated data _`

_a

_ab

_|a

(kw)

€,f

€,z

b



2

(j/m s k )

2

(j/m s k )

2

(j/m s k )

(kg/m2s )

(°C)

(°C)

(°C)

(°C)

(°C)

(°C)

(°C)

(kg/s)

(kg/s)

(kg/s)

24.19

38.1

31.37

41.83

32.35

28.76

31.39

0.0225

0.081

0.06667

1.296

3.212

89.36

0.8017

25.49

0.00046

23.1

38.16

32.01

41.41

31.01

27.12

31.62

0.03083

0.081

0.06667

1.032

3.521

37.19

8.103

33.38

0.00069

24.77

41

32.94

44.53

31.01

29.16

32.7

0.035

0.081

0.06667

0.696

4.578

54.86

46.64

25.94

0.00122

24.88

39.31

33.24

44.78

31.12

29.22

32.96

0.03917

0.081

0.06667

0.618

4.625

47.96

51.49

30.86

0.00148

24.73

41.52

34.02

44.8

29.1

29.36

33.23

0.04333

0.081

0.06667

0.384

5.318

50.26

57.59

25.83

0.00235

23.91

48.88

33.84

50.67

42.86

29.02

32.51

0.0135

0.081

0.06667

1.644

2.645

5.751

27.57

15.52

0.0001

23.79

47.16

35.26

50.7

39.81

29.01

33.62

0.018

0.081

0.06667

1.896

3.689

23.23

20.61

20.56

0.00023

23.83

46.06

35.41

50.85

38.22

29.03

34.04

0.02233

0.081

0.06667

1.596

4.277

29.1

22.47

23.63

0.00037

23.79

44.68

35.49

50.91

36.79

29.05

34.32

0.0265

0.081

0.06667

1.536

4.782

30.98

28.6

26.87

0.00055

24.73

47.23

36.95

53.17

36.88

29.36

35.56

0.03083

0.081

0.06667

1.62

5.516

32.89

25.71

27.48

0.00081

24.53

46

37.01

53.44

35.31

29.4

35.59

0.03517

0.081

0.06667

1.296

6.14

35

40.17

29.14

0.00118

24.56

46.43

37.25

53.18

33.92

29.4

35.12

0.03883

0.081

0.06667

1.092

6.187

15.25

63.78

25.42

0.0014

24.49

44.26

37.85

50.9

32.09

29.35

34.63

0.04283

0.081

0.06667

0.888

6.37

0.6518

94.87

24.57

0.00177

22.88

53.99

39.59

59.96

42.01

27.87

36.78

0.018

0.081

0.06667

3.48

6.081

50.65

0.5482

26.22

0.00034

23.38

55.5

39.96

62.28

40.02

27.94

37.02

0.02233

0.081

0.06667

3.372

7.543

17.57

67.49

25.45

0.00052

23.8

56.15

40.25

61.42

39.42

29.39

37.22

0.0265

0.081

0.06667

3.144

7.454

6.464

68.33

22.68

0.00067

23.59

51.94

40.75

60.71

37.83

27.92

37.12

0.03083

0.081

0.06667

2.97

7.753

36.64

22.91

28.4

0.00095

23.83

52.29

41.02

60.44

35.01

28.5

37.75

0.03517

0.081

0.06667

2.928

8.614

43.41

29.34

28.83

0.00146

24.28

52.67

41.01

61.56

35.4

28.6

37.97

0.03883

0.081

0.06667

2.298

8.864

30.94

39.63

29.17

0.00172

24.43

50.79

41.22

60.74

33.58

28.99

38.02

0.04283

0.081

0.06667

2.112

9.203

63.1

28.48

30.42

0.00281

23.01

61.56

45

70.51

44.04

27.64

41.25

0.018

0.081

0.06667

5.868

8.977

23.68

33.05

30.48

0.0004

23.18

59.65

45.88

71.45

39.95

27.98

41.81

0.02233

0.081

0.06667

5.52

10.68

43.22

42.4

32.56

0.0007

23.25

58.22

46.25

70.14

39.75

27.95

41.93

0.0265

0.081

0.06667

5.388

10.31

25.13

42.89

34.05

0.00086

24.58

56.93

46.3

70.2

39.32

28.76

42.01

0.03083

0.081

0.06667

4.488

10.47

35.65

31.99

34.43

0.00113

25

(kg/hr)

}~

24.62

57.83

47.54

71.4

38.59

28.9

42.12

0.03517

0.081

0.06667

4.302

11.13

31.76

36.01

32.47

0.001521

24.91

58.58

47.46

70.71

35.54

29.02

42.51

0.03883

0.081

0.06667

4.212

11.93

39.04

39.4

32.96

0.00219

24.94

56.1

47.85

68.58

34.9

29.11

42.65

0.04283

0.081

0.06667

3.924

11.42

44.81

27.04

35.73

0.00282

Mean value

34.98

36.96

28.09

0.00114 3

4 5 6 7 8 9 10 11 12

26

2

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Credit Author Statement M. Salem Ahmed: Conceptualization, Methodology, Resources, Writing - Review & Editing, and Project administration A. S. A. Mohamed: Conceptualization, Methodology, Validation, Formal analysis, Writing Review & Editing, and Supervision Abanob G. Shahdy: Software, Validation, Formal analysis, Investigation, and Writing - Review & Editing

Declaration of interests ☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.