## Abstract

The scarcity of freshwater is one of the biggest issues in the world, as a result of which more attention is given to the thermal distillation process for seawater and as well as brackish water distillation which removes almost all types of contaminants. Multiple effect distillation makes the process economical by recycling the latent heat of vaporization. In this paper a vertical tube evaporator is designed for a small scale thermal driven MED system comprising six effects and one condenser and a boiler that can produce 20–25 kg/hr of steam. VTE dimensions are calculated by estimating the outside diameter for different configurations. Heat transfer coefficient was estimated by using the developed correlations of the Bell method, Kandlikar and Kutateladze, compared with previous experiments and then used for calculating the heat transfer area for different distillate flow rates. An appropriate vertical tube evaporator is designed with the developed model to condense 25–30 kg/hr steam for producing 50–75 lt/hr freshwater. The result shows good agreement with previous work and reliability in design. The Developed model can also be used to design the vertical tube evaporator for different sizes (micro scale to large scale) MED plant.

## HIGHLIGHTS

A vertical tube evaporator was designed for six effect small scale thermal-driven multiple effect distillation.

Vertical tube evaporator dimensions were calculated by estimating outside diameter for different configurations.

The vertical tube evaporator was designed for thermal driven multiple effect distillation for different capacities with low cost and high efficiency.

## NOMENCLATURE

**Abbreviation**

**Variables**

**Greek symbols**

## INTRODUCTION

Out of two thirds of the surface of the water a very small amount is suitable for human consumption and use (Ercin & Hoekstra 2014). One fifth of the world's population is currently facing a water scarcity problem. It is estimated that by 2030, 40% of world's inhabitants will be affected by water shortages (Schewe *et al.* 2014). Furthermore, 67% of the global population lives in water scarcity conditions for 1 month a year. These statistics show that sources of water like rivers, lakes, and aquifers are not sufficient to meet human demands in water scarce areas. Potential water treatment and desalination plants are the solution to this problem and are the source of freshwater from seawater and wastewater. Countries and scientists around the world are looking for low cost, energy efficient thermal as well as membrane desalination techniques (Buros 1990). Interest in multiple-effect distillation (MED) has increased in the last three decades because of the number of new designs of plants installed in urban and rural areas working at low temperatures and reducing the scaling and corrosion problem (Buros 1990).

Hasan & Ali (2011) experimentally evaluated the heat transfer coefficient (*U*) in a vertical tube rising film evaporator with the aim to describe the variation of *U* with different process parameters: Reynolds number, temperature difference, feed temperature, and recirculation ratio. It was found from the results that all the parameters are directly proportional to heat transfer coefficient. Recirculation has a positive effect on *U* but up to a certain limit 0.8–0.85 after that, *U* starts decreasing. They also developed experimental correlation relating Nusselt number and operating parameters with laminar flow conditions. Serna-González & Jiménez-Gutiérrez (2005) developed an equation based on the Bell–Delaware method that relates pressure drop, heat exchanger area, and heat transfer coefficient with the shell side of a shell and tube heat exchanger. Prost *et al.* (2006), to understand the multiple-effect units, determined the heat transfer coefficient under different operating conditions for 240 kg/h evaporation capacity. They also simulated each evaporator effect by varying the pressure and feed concentration and then correlated the obtained value using an equation that relates the heat transfer coefficient with fluid properties, flow conditions and geometric parameters by giving the resulting correlation equation for Reynold number ranging in between and Prandtl number ranging from 2.5 to 200. Adib *et al.* (2009) considered the main process parameters like evaporating temperature and evaporating pressure (P) taking into account the boiling point elevation (BPE), the heat flux (*φ*) for describing the laws of variation of boiling heat transfer coefficient (*h*) by using falling film evaporator taking water and sugar solution at different concentrations as a Newtonian liquid food model. They concluded that increasing the concentration of a solution boiling heat transfer coefficient decreases sharply because by increasing the concentration of a solution, viscosity increases and so the heat transfer coefficient decreases in both nucleate and non-nucleate regimes. Likewise, by increasing the boiling liquid temperature, the boiling heat transfer coefficient increases because increasing the boiling temperature decreases the viscosity of the solution. Two boiling regimes are present in the vertical tube evaporator (VTE), nucleate and non-nucleate. The nucleate regime takes place when temperature increases and the non-nucleate regime takes place at low temperature difference. Heat transfer coefficient increases by increasing the temperature difference in the nucleate regime.

A literature review showed the main emphasis is placed on how to improve the heat transfer coefficient and develop the correlations for different process conditions. The present work aims to design a VTE for a thermal-driven MED system whose dimensions are calculated by estimating the outside diameter of different configurations and estimating the Heat transfer coefficient by developed correlation for estimating heat transfer area. The paper presented the objective to develop a model and design the VTE for thermal driven MED and to determine the overall heat transfer coefficient (OHTC) of the evaporator with its validation. This paper is organized as follows: sections 2 and 3 are devoted to an overview of the MED concept, theoretical modeling, and design. Section 4 gives out results and discussion. The last section ends with a conclusion.

## MATERIALS AND METHODOLOGY

### MED concept

In the MED plant, the seawater entering the first effect is sprayed onto the surface of a bank of tubes inside which steam is flowing. A portion of the water is evaporated off the surface, and the rest of the seawater is collected at the bottom of the first effect. The steam condenses in the tubes and is withdrawn for recovery. The evaporated hot water vapor acts as a heat source for the second effect. It now flows into a bank of tubes on the second effect. Seawater from the first effect is pumped to the second effect and is sprayed over the tubes carrying the vapor from the first effect. Further evaporation occurs on the surface of the tube, while the rest of the water is collected at the bottom of the second effect. At the same time, the vapor condenses inside the tubes and is withdrawn as fresh water from the second effect. The vapor produced from evaporation in the second effect is likewise routed to the third effect, where it is used to separate the seawater from the second effect. Up to 8 or 16 effects can be used in this way.

According to the feedwater and heat flow direction, MED can have three configurations: parallel feed (PF), forward feed (FF), and backward feed (BF). All three configuration details are provided below.

FF: In this configuration, preheated feed water is passed through the first effect and brine is passed to the next effect where pure water is again separated by the heat released from the previous effect distillate. Hence, from the first to the last effect brine concentration increases.

PF: In this configuration, preheated feed water is distributed equally among all the effects. This configuration has a simple layout and a lower risk of scale formation.

BF: Feedwater is imported in the last effect in this configuration and for further distillation brine flow from the last effect to the first no feedwater preheater is required in this configuration. But, due to high temperature at the risk of scale formation increased.

### Plant description

### Vertical tube evaporator

The MED system consists of six effects and 1 condenser. In the first effect, feed water is heated by steam in tubes. Some of the water evaporates and this fresh steam flows into the tube of the next stage, hence for better heat transfer it is necessary to design a heat exchanger which fulfills the requirements of the MED system. VTEs which are nothing but shell and tube type heat exchangers were designed for the system by considering certain input parameters for proper heat transfer. VTE is preferred among various designs for the system since a small flow is involved in the range of 25–90 kg/h. The input parameters for VTE design are as follows:

- (i)
Input steam pressure

- (ii)
Inlet temperature of steam

- (iii)
Outlet temperature of steam

- (iv)
Inlet temperature of water

- (v)
Specific heat for steam

- (vi)
Specific heat of water

- (vii)
Mass-flow rate of steam

- (viii)
Mass-flow rate of water

- (ix)
Temperature difference between the effects

### Methodology

VTE was designed by following the iterative procedure. Firstly, the dimensions of the heat exchanger were assumed which represent the real surface area (*A*). Secondly, the OHTC is calculated by using heat transfer correlations which were generally used in literature (Bell, Kandlikar, Kutateladze). Then, we calculate the new surface which will represent the calculated surface. Calculations stop when both surfaces are equal, within a certain error to be defined. Finally, we validate the used design method, HTC with those found in previous studies.

In the following section, correlations are presented for each mechanism and author. These correlations are selected because they give stability over a wide range of conditions.

here is the convective boiling term; ; ; constants to be determined; Convection number; Boiling number; Single phase heat transfer coefficient.

*h*

_{TP}for tube geometry from the following expression

Kutateladze (1963) developed correlation on a vertical surface for calculating the condensation heat transfer coefficient with the following expression:

*φ*is the window correction factor and is the leakage correction. This method is described in detail (Bell 1963).

OHTC usually requires iterative calculations, and fouling resistance (*R*_{f}) for water at moderate temperature is 0.00009 (Bell 1963).

S.no . | Case . | Number of tubes . | Length of tubes L (mm)
. | Outer diameter (mm) . |
---|---|---|---|---|

1 | 1 | 7 | 1,000 | 14.08 |

2 | 2 | 5 | 1,000 | 18.21 |

3 | 3 | 7 | 920 | 18 |

4 | 4 | 7 | 500 | 28.16 |

5 | 5 | 5 | 500 | 39.42 |

6 | 6 | 5 | 750 | 26.28 |

7 | 7 | 7 | 750 | 18.77 |

8 | 8 | 115 | 1,200 | 9.3 |

9 | 9 | 118 | 2,400 | 9.50 |

10 | 10 | 128 | 2,500 | 9.55 |

11 | 11 | 140 | 2,560 | 9.60 |

S.no . | Case . | Number of tubes . | Length of tubes L (mm)
. | Outer diameter (mm) . |
---|---|---|---|---|

1 | 1 | 7 | 1,000 | 14.08 |

2 | 2 | 5 | 1,000 | 18.21 |

3 | 3 | 7 | 920 | 18 |

4 | 4 | 7 | 500 | 28.16 |

5 | 5 | 5 | 500 | 39.42 |

6 | 6 | 5 | 750 | 26.28 |

7 | 7 | 7 | 750 | 18.77 |

8 | 8 | 115 | 1,200 | 9.3 |

9 | 9 | 118 | 2,400 | 9.50 |

10 | 10 | 128 | 2,500 | 9.55 |

11 | 11 | 140 | 2,560 | 9.60 |

## THEORETICAL MODELING AND DESIGN

### MED process modeling

- Salt balance in effect
*i*:where*M*_{d}is the effect distillate from the effect,*M*_{b}is the flow rate of brine from the effect,*X*is salt concentration and*M*_{f}is the feed flow rate into the effect. The left-hand side of Equation (25) represents the heat added to the effect condensing the previous effect vapor.

### Heat transfer area

For required distillate flow rate taken the value of OHTC (*U*) from the correlation heat transfer area can be calculated assuming *λ* to be 2,257 kJ/kg and Δ*T* of 4 °C (Sen *et al.* 2011a).

## RESULTS AND DISCUSSION

In this part, the heat transfer coefficient and design of the VTE presented are based on the TEMA standard (N. Edition 2007) for the selection of dimensions for desired production. Thus, an iterative procedure has been followed in the theoretical modeling and design part and the design method can be validated by comparing the heat transfer coefficient found in the literature (Sen *et al.* 2011c). Appropriate dimensions of VTE designed for thermal driven MED systems to condense 25–30 kg/h steam by determining the OHTC using theoretical modeling and developed correlations and compared with previous work are shown in Table 2. The OHTC was found to be 13,000 W/m^{2}K which is in the range of OHTC assumed by Sen *et al.* (2011b). Hence correlations can be validated for the range (25–30 kg/h). Therefore, developed correlations can also be used to estimate the dimension of VTEs for MED systems of different production sizes and input sources; for example it can be used for micro-scale production using low powered steam even by using solar energy in the range (3–5 kg/h), and also for large-scale production in the range of (120–150 kg/h). Due to agronomic conditions tubes of a very large diameter are not selected and the smallest diameter is not selected because it is not practically feasible. The dimension selected for the designed VTE is shown in bold in Table 2.

S.no . | d_{o} (mm)
. | d_{i} (mm)
. | L_{T} (mm)
. | N_{T}
. | OHTC (W/m^{2}K)
. | Previous work (Sen et al. 2011c; United Nations World Water Assessment Programme 2014)
. | Remarks . |
---|---|---|---|---|---|---|---|

1 | 9.3 | 200 | 1,200 | 115 | 3,870 | 3,000–14,000 W/m^{2}K | Large-scale production |

2 | 9.50 | 210 | 2,400 | 118 | 2,790 | ||

3 | 9.55 | 223 | 2,500 | 128 | 2,630 | ||

4 | 9.60 | 235 | 2,560 | 140 | 2,634 | ||

5 | 23.7 | 20.5 | 1,000 | 7 | 9,500 | Small-scale production | |

6 | 18 | 12 | 9,200 | 7 | 13,000 | ||

7 | 23.7 | 20.5 | 1,000 | 1 | 9,000 | Micro-scale production |

S.no . | d_{o} (mm)
. | d_{i} (mm)
. | L_{T} (mm)
. | N_{T}
. | OHTC (W/m^{2}K)
. | Previous work (Sen et al. 2011c; United Nations World Water Assessment Programme 2014)
. | Remarks . |
---|---|---|---|---|---|---|---|

1 | 9.3 | 200 | 1,200 | 115 | 3,870 | 3,000–14,000 W/m^{2}K | Large-scale production |

2 | 9.50 | 210 | 2,400 | 118 | 2,790 | ||

3 | 9.55 | 223 | 2,500 | 128 | 2,630 | ||

4 | 9.60 | 235 | 2,560 | 140 | 2,634 | ||

5 | 23.7 | 20.5 | 1,000 | 7 | 9,500 | Small-scale production | |

6 | 18 | 12 | 9,200 | 7 | 13,000 | ||

7 | 23.7 | 20.5 | 1,000 | 1 | 9,000 | Micro-scale production |

Present Model was used to design the VTE for small scale thermal driven system to condense 25–30 Kg/h, After iterative procedure has been followed in theoretical modeling and design part , the best dimension for for VTE design for present model is indicate by bold.

*M*

_{d}using Equation (13). Figure 2 shows the

*M*

_{d}of 3–50 kg/h area increases significantly as M

_{d}increases above 50 kg/h the area changes abruptly due to change in OHTC. Thus, developed correlations provide high stability for determining the dimension of VTE for different capacities of (micro to large-scale) MED systems.

## CONCLUSION

A model for designing the VTE for the MED system has been developed. The design procedure follows the Bell, Kandlikar, and Kutateladze correlation which provides good projection and steadiness for shell side heat transfer coefficient and is considered the best possibility to incorporate correlations in the design model of the MED plant. Thus, the present model was used to design the VTE for small scale thermal driven MED systems to condense 25–30 kg/h with the appropriate dimensions given as:

number of tubes *N*_{t} = 7, length of tubes = 920 mm, shell length = 750 mm, outside diameter = 18 mm; latent heat transfer area = 0.3 m^{2}.

The present model can also be used to design the VTE for MED systems of different capacities with low cost and high efficiency and can also be used to assess MEDs integrated with solar power like Fresnel mirror collector, flat plate collector, or evacuated tube collector for freshwater production at an economic price.

## ACKNOWLEDGEMENTS

We are grateful to Moradabad Institute of Technology, Moradabad for providing infrastructure facilities for research work. We are also thankful to staff members of the mechanical engineering department for their support.

## DATA AVAILABILITY STATEMENT

All relevant data are available from https://data.mendeley.com/datasets/8bbyy5k69s/1.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Final Report of the Cooperative Research Programe on Shell and Tube Heat Exchanger*. Univ. Delaware Eng. Exp. Station. Newark, Delaware Title, Bulletin N