# Air to Water Generator Integrated Systems: The Proposal of a Global Evaluation Index—GEI Formulation and Application Examples

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^{*}

## Abstract

**:**

## 1. Introduction

^{3}/h) coming from the evaporator. In this case, the innovative plant yielded a meaningful energy saving, in comparison to the existing system, while providing enough water. Savings were enough to repay the investment costs in about two-and-a-half years. This integration improvement was demonstrated by calculations based on the energy consumption measures obtained before and after the installation of the integrated AWG system.

## 2. Literature Review

- To overcome issues related to the only other existing indicator for AWGs, specific energy consumption (SEC) [21]
- To provide a standard tool, based on the same structure as COP and EER, for water production efficiency calculation from an energy point of view.

- A brief description of AWG-integrated machine technology;
- A summary of the WET indicator in order to facilitate an understanding of the genesis of the GEI index;
- The GEI index formulation, highlighting that such a formulation is suitable, not only for AWG-integrated machines, but also for HVAC-integrated machines;
- The extended version of GEI index formulation, suitable for the evaluation of combinations of integrated and non-integrated systems;
- A practical explanation of GEI formulation.

- by means of numerical examples, how GEI avoids the described issues of the overall COP and permits comparison among different systems by means of its single value;
- how to manage system powered by different energy sources, types and vectors, by means of primary energy will be described;
- a case study that takes an integrated AWG machine and other system combinations into account will be presented and discussed;
- an example of application of GEI to heterogeneous combination of plants will be finally described (with different levels of integration).

## 3. GEI Formulation

#### 3.1. Integrated AWG Systems

#### 3.2. WET Indicator

- SEC = ratio between energy consumption and produced water [kWh/dm
^{3}] - Q
_{c}= latent heat of condensation per unit mass [kJ/kg] - ρ = water density in liquid phase, assumed 1 kg/dm
^{3}

_{c}, depends on temperature, t (°C); in a range of temperatures compatible with AWG technology, it can be calculated as follows [38]:

_{c}can be assumed to be constant and equal to 2460 kJ/kg in first approximation, because for the most widespread AWG working range, the error that can occur using such a constant instead of the function is below 0.89%.

- w = hourly or daily water production [m
^{3}] - en = energy consumption required by the system to produce water [kJ]
- ρ = water density in liquid phase, assumed 1000 kg/m
^{3}

_{w}(kJ), can be expressed as follows:

#### 3.3. Global Evaluation Index (GEI) Proposal

- Id = integration degree, corresponding to the number of useful effects provided simultaneously with the same energy input;
- E
_{i}= i-th efficiency, or i-th useful effect indicator (i.e., WET, COP, EER).

_{eq}, as the sum of the GEI indices of every machine involved in the system:

- n = number of machines composing the system.

_{eq}is, the higher the global efficiency of the system.

#### 3.4. GEI Practical Explanation: Comparison between an Integrated AWG and Three Single Effect Machines

_{1}, M

_{2}, and M

_{3}.

_{1}, provides heating energy, and its energetic behavior is represented by its COP.

- COP
_{1}= Q_{h}/en = heating energy divided by consumed energy. - M
_{2}provides cooling energy, and its energetic behavior is represented by its EER. - EER
_{2}= Q_{c}/en = cooling energy divided by consumed energy. - M
_{3}provides water extraction from air by vapor condensation, and its energetic behavior is represented by its WET. - WET
_{3}= Q_{w}/en = water condensation energy divided by consumed energy.

_{h}, Q

_{c}, and Q

_{w}, consumes only one en. Its energetic behavior, thus, is:

_{eq}of the set of the three machines (called, in the formulation below, “discrete” in order to underline that the three useful effects are provided by separated single machines):

- Id = 3, because the machine provides three useful effects at the same time with the same energy consumption.

#### 3.5. GEI Application: Comparison between Two Different Machines

#### 3.5.1. Case 1—Homogenous Systems

_{1}= (30 + 20 + 20)/10 = 7

_{2}= (40 + 30 + 10)/10 = 8

_{1}= 3 (3 + 2 + 2) = 21

_{2}= 3 (4 + 3 + 1) = 24

_{S}and between GEI

_{s}are the same, thus, in this case, GEI gives the same level of information as the other index—the best machine is number 2.

#### 3.5.2. Case 2—Non-Homogenous Systems

- 1 heat pump, characterized by a COP of 6;
- 1 cooling cycle, characterized by a EER of 3.

- Heating energy with a COP of 3
- Cooling energy with a EER of 2

_{overall}= 5 > EER = 3

_{overall}= 5 < COP = 6

_{eq}

_{1}= 6 + 3 = 9

_{eq}

_{2}= GEI

_{2}= 2 (3 + 2) = 10

#### 3.6. Energy Consumption and Primary Energy: Some Notes

- GEI
_{primary}= index expressed in terms of primary energy - GEI = index calculated taking into account the energy source required by the investigated machine
- f = primary energy conversion factor.

_{s}are expressed in terms of primary energy, also GEI

_{eq}will be expressed in the same way:

## 4. GEI Application to a Case-Study

- Cooling circuit, equipped with a screw compressor, with a nominal cooling capacity of 100 kW;
- Air treatment unit, equipped by evaporation coil for direct evaporation of the coolant (R134a) and water from air condensation. The air treatment unit is equipped also with a heat recovery system;
- Coolant condensation heat recovery provided by a plate fin heat exchanger linked to a domestic water circuit, nominal heating capacity: 120 kW;
- Condensed water treatment system.

- A cooling effect, under the form of a dry cooled air flux released by the evaporator after the water extraction, that can be quantified into the cooling energy Q
_{c}; - A heating effect, that is the thermal energy released by the condenser, which can be quantified into heating energy Q
_{h}; - Condensed water, which can be quantified into the water condensation energy Q
_{w}.

- Actual hotel LPG boiler, with a nominal heating power of 820 kW and an efficiency (η) of 0.7;
- Actual hotel air conditioning system, with a yearly average EER of 3.5;
- Simple AWG machine, with a yearly WET average of 2.23.

_{eq primary}result is reported.

- Revamped air conditioning, able to provide cooling and heating, characterized by yearly average COP and EER, respectively, of 4.5 and 3.5;
- Simple AWG machine, with a yearly average WET of 2.23;

## 5. Observations on GEI Application to Heterogeneous Combination of Plants

_{s}, composing the GEI

_{eq}, must be evaluated weighing the influence of each component of the plant on the global amount of useful effects provided by it. Such a weighting can be easily done taking the fraction between the energy, consumed by each component of the plant system configuration and the whole energy consumption into account. The expression of the equivalent GEI becomes:

_{eq}calculation can be useful to show how the index can be easily determined also in those cases where integrated and non-integrated machines work together in order to cover the all useful effect demands.

_{eq}, the energy absorbed by each machine must be evaluated.

_{eq}, equal to 16.34, is obviously less than the previous GEI, which was 26.97, calculated in the case of maximum integration, with a single machine covering the needs of the entire building.

## 6. Conclusions

- A first equation suitable for comparison among homogenous integrated machines;
- An extended equation, which can be used to compare different combinations of HVAC and AWG systems, also comprising conventional plants;
- A further expression, involving primary energy, that permits to take into account different plant configurations, using various energy sources, types, and vectors

- (a)
- The first calculation example, applied to two cases are highlighted:
- How the index can take into account the integration level and the overall efficiency, deriving from the real use of each useful effect of a reverse cycle, combining them in a simple but meaningful way to produce existing efficiency indicators, such as COP, EER, WET, etc.;
- In which way the index overcomes the possible ambiguity related to the overall COP calculation and provides an intuitive metrics for comparisons.

- (b)
- In the case study, three different plant configurations, providing cooling, heating, and water, were described, each one of them characterized by a different degree of integration and different efficiencies. In this case, GEI allowed to carry out an immediate comparison and the results permitted to determine the most efficient solution, avoiding the in depth analysis normally required for integration plant evaluation. For example, the configuration with the maximum plant integration achieved a GEI of 26.97 and a GEI
_{primary}value of 14.98, almost four times higher than that achieved by the one characterized by the minimum integration. The result reflects the real efficiency difference of the two configurations. - (c)
- In the final practical example, the useful effects of an integrated machine covered only a part of the required energy of a building and the rest was given by a non- integrated machine. Results showed again how the index is able to highlight and weigh the role of the integration in order to provide a more accurate estimation of the real overall efficiency of the plant. In this case, the GEI
_{eq}value was equal to 16.34, lower than that of the configuration characterized by the maximum integration.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronyms | |

ATU | air treatment unit |

AWG | air-to-water generator |

COP | coefficient of performance |

EER | energy efficiency ratio |

GEI | global evaluation index |

GEI_{ei} | index calculated taking into account the ith energy source e required by the investigated machine |

GEI_{eq} | equivalent GEI: the sum of the GEI indices of every machine involved in the system |

GEI _{primary} | index expressed in terms of primary energy |

HVAC | heating ventilation air conditioning |

MOF | metal organic framework |

Overall COP | ratio between the sum of the useful effect powers divided by the power required to obtain them |

SEC | ratio between energy consumption and produced water [kWh/L] or [kWh/dm^{3}] |

WET | Water Energy Transformation |

Symbols | |

Id | integration degree, corresponding to the number of useful effects provided with the same energy input |

E_{i} | i-th efficiency, or i-th useful effect indicator |

en | energy consumption [kJ] |

en_{j} | energy consumption required by the j-th system [kJ] |

f_{i} | i-th primary energy conversion factor |

M_{1}…_{3} | conventional machines, each one of them providing a single useful effect |

n | number of useful effects provided by a machine or number machines composing the system |

P | input power [kW] |

P_{c} | cooling power [kW] |

P_{h} | heating power [kW] |

P_{j} | input power of the j-th machine [kW] |

P_{w} | water condensation power [kW] |

Q_{c} | latent heat for condensation per unit mass [kJ/kg] |

w | hourly or daily water production [m^{3}] |

Greek letters | |

ρ | water density in liquid phase, assumed 1 kg/dm^{3} or 1000 kg/m^{3} |

η | boiler energy efficiency |

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P_{h} [kW] | P_{c} [kW] | P_{w} [kW] | P [kW] | COP | EER | WET | |
---|---|---|---|---|---|---|---|

Machine 1 | 30 | 20 | 20 | 10 | 3 | 2 | 2 |

Machine 2 | 40 | 30 | 10 | 10 | 4 | 3 | 1 |

_{h}= heating power [kW]; P

_{c}= cooling power [kW]; P

_{w}= water condensation power [kW]; P = input power [kW].

**Table 2.**AWG-integrated machine hourly behaviour averaged over the year, expressed as water production, heating, cooling energy and energy consumption.

Water Production | Heating Energy | Cooling Energy | Energy Consumption |
---|---|---|---|

[dm^{3}/h] or [L/h] | [kWh] | [kWh] | [kWh] |

94.6 | 109.2 | 86.6 | 29 |

Efficiency Indicator | Formulation | Calculations | Results |
---|---|---|---|

WET | $\frac{{Q}_{w}}{en}$ | ${Q}_{w}=0.00946{\mathrm{m}}^{3}\xb71000\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}\xb72460\frac{\mathrm{kJ}}{\mathrm{kg}}=\mathrm{232,761}\mathrm{kJ}$ $en=29\text{}\mathrm{kWh}\text{}\xb73600\mathrm{s}=\mathrm{104,400}\mathrm{kJ}$ | 2.23 |

COP | $\frac{{Q}_{h}}{en}$ | ${Q}_{h}=109.2\mathrm{kWh}\xb73600\mathrm{s}=\mathrm{393,120}\mathrm{kJ}$ | 3.77 |

EER | $\frac{{Q}_{c}}{en}$ | ${Q}_{c}=86.6\mathrm{kWh}\xb73600\mathrm{s}=\mathrm{311,760}$ | 2.99 |

Index | Formulation | Calculations | Results |

GEI | $Id\xb7{\displaystyle \sum _{i=1}^{Id}}{E}_{i}$ | $Id=\mathrm{heating}+\mathrm{cooling}+\mathrm{water}=3$ | 26.97 |

GEI_{primary} | $\frac{{\mathrm{GEI}}_{el}}{f}$ | $f=1.8$ | 14.98 |

Efficiency Indicator | Value | Energy Input | f | Id | GEI_{i} _{primary} | Results |
---|---|---|---|---|---|---|

WET | 2.23 | Electricity | 1.8 | 1 | $1\xb7\frac{2.23}{1.8}$ | 1.24 |

η | 0.7 | LPG | 1.1 | 1 | $1\xb7\frac{0.7}{1.1}$ | 0.64 |

EER | 3.5 | Electricity | 1.8 | 1 | $1\xb7\frac{3.5}{1.8}$ | 1.94 |

Index | Formulation | Results |
---|---|---|

GEI_{eq} _{primary} | $\sum _{i=1}^{Id}}{\mathrm{GEI}}_{i\mathrm{primary}$ | 3.81 |

Indicator | Value | Energy Input | f | Id | GEI_{i primary} | Results |
---|---|---|---|---|---|---|

WET | 2.23 | Electricity | 1.8 | 1 | $1\xb7\frac{2.23}{1.8}$ | 1.24 |

COP | 4.5 | Electricity | 1.8 | 2 | $2\xb7\left(\frac{3.5}{1.8}+\frac{4.5}{1.8}\right)$ | 8.89 |

EER | 3.5 | Electricity | 1.8 |

Index | Formulation | Results |
---|---|---|

GEI_{eq primary} | $\sum _{i=1}^{Id}}{\mathrm{GEI}}_{i\mathrm{primary}$ | 10.13 |

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**MDPI and ACS Style**

Cattani, L.; Cattani, P.; Magrini, A.
Air to Water Generator Integrated Systems: The Proposal of a Global Evaluation Index—GEI Formulation and Application Examples. *Energies* **2021**, *14*, 8528.
https://doi.org/10.3390/en14248528

**AMA Style**

Cattani L, Cattani P, Magrini A.
Air to Water Generator Integrated Systems: The Proposal of a Global Evaluation Index—GEI Formulation and Application Examples. *Energies*. 2021; 14(24):8528.
https://doi.org/10.3390/en14248528

**Chicago/Turabian Style**

Cattani, Lucia, Paolo Cattani, and Anna Magrini.
2021. "Air to Water Generator Integrated Systems: The Proposal of a Global Evaluation Index—GEI Formulation and Application Examples" *Energies* 14, no. 24: 8528.
https://doi.org/10.3390/en14248528