# Theoretical Analysis of an Integrated, CPVT Membrane Distillation System for Cooling, Heating, Power and Seawater Desalination

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

^{3}/year; the lowest month was 3.8 m

^{3}in November.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. System Description

#### 2.2. Governing Equations

#### 2.2.1. Concentration Photovoltaic/Thermal

#### Energy Equations

_{C}cells, Equation (2) is used, in which the special thermal coefficient of the concentrator is equal to 6% [10]:

_{bT}is the direct solar radiation. The ideal electrical energy produced by each multi-junction solar cell can be calculated using Equation (3) [10]:

_{2}O

_{3}nanofluids.)

_{aperture}is the area of the opening. By combining Equations (1)–(6), the electrical energy produced by each cell is obtained as follows [11]:

#### Exergy Equations

#### 2.3. Rankine Cycle

#### Energy Equations

#### 2.4. Absorption Cooling Cycle

#### 2.4.1. Energy Equations

_{1}is the mass ratio of lithium bromide in a dilute solution (a solution with a lower amount of water). Using relations (25) and (26), the temperatures of points 3 and 5 are obtained.

#### 2.4.2. Exergy Equations

#### 2.5. Distillation System

#### 2.5.1. Energy Equations

_{f,g}is the enthalpy of water evaporation and k

_{m}, ${\mathsf{\delta}}_{\mathrm{M}}$ are the conductivity coefficient and membrane thickness, respectively. J

_{P}is the mass transfer rate of permeated water (freshwater passing through the membrane) per unit area of the membrane. Also, T

_{mp}is the temperature of the membrane surface in the distance of the infiltration flow. The rate of heat transfer in the distance of the infiltration flow is obtained using Equation (34):

_{M}is the area of the membrane. ${\mathrm{S}}_{\mathrm{Eo}}$, and ${\mathrm{S}}_{\mathrm{Ei}}$ are the water salinity at the inlet and outlet of the evaporator channel, respectively.

#### 2.5.2. Exergy Equations

## 3. Results

#### 3.1. Concentration Photovoltaic/Thermal System

#### 3.2. Organic Rankine Cycle

#### 3.3. Desalination System

^{3}/year; the lowest was 3.8 m

^{3}in November. Obviously, in the months when high solar radiation is available, higher thermal energy can be fed into the desalination unit to produce freshwater.

## 4. Conclusions

^{3}, the output ratio is 41.3 and the recovery ratio is 57.2. In general, for the combined system, thermal efficiency and exergy efficiency has been obtained, 75% and 93.72%, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | Area (m^{2}) |

a | Temperature coefficient |

C | Concentration ratio |

EX | Exergy rate (kW) |

e | Specific exergy |

F | Fill factor |

h | Specific enthalpy (kJ/kg) |

I_{bT} | Direct solar radiation (W/m^{2}) |

J_{P} | Mass transfer rate |

k_{m} | Conductivity coefficient |

$\dot{\mathrm{m}}$ | Mass flow rate (kg/s) |

n | Cells number |

P | Power (kW) |

$\dot{\mathrm{Q}}$ | Heat transfer rate (kW) |

s | Specific entropy (kJ/kg·K) |

T | Temperature (°C) |

$\dot{\mathrm{W}}$ | Work (kW) |

X | Solution concentration ratio |

Greek symbols | |

δ_{m} | Membrane thickness |

η | Thermal efficiency (%) |

ψ | Exergy efficiency (%) |

Subscripts | |

a | ambient |

abs | absorber |

c | cell |

coll | collector |

con | condenser |

ev | evaporator |

gen | generator |

id | ideal |

in | inlet |

opt | optical |

out | outlet |

par | parasitic loss |

sol | solar |

T | turbine |

Abbreviations | |

ARS | Absorption refrigeration system |

COP | Coefficient of performance |

CPV/T | Concentrator photovoltaic/thermal |

EES | Engineering equation solver |

MD | Membrane desalination |

ORC | Organic Rankine cycle |

PTC | Parabolic trough collector |

SF | Solar fraction |

TF | Thermal factor |

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**Figure 6.**The amount of electricity produced, the amount of electricity consumed and the amount of monthly useful electrical energy in the city of Kerman.

**Figure 8.**Amount of exergy of the incoming flow, exergy of the outgoing flow and destroyed exergy for the months of the year.

**Figure 9.**The exergy level of the Sigel single-effect lithium-bromide absorption cooling components for the months of the year.

**Figure 10.**The amount of freshwater produced and the heat taken by the desalination plant for the months of the year.

Components | Equations |
---|---|

Generator | ${\mathrm{EX}}_{\mathrm{dGe}}={\dot{\mathrm{E}}\mathrm{X}}_{3}+{\dot{\mathrm{E}}\mathrm{X}}_{13}-{\dot{\mathrm{E}}\mathrm{X}}_{4}-{\dot{\mathrm{E}}\mathrm{X}}_{7}-{\dot{\mathrm{E}}\mathrm{X}}_{14}$ |

Evaporator | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{Eva}}}={\dot{\mathrm{E}}\mathrm{X}}_{9}+{\dot{\mathrm{E}}\mathrm{X}}_{11}-{\dot{\mathrm{E}}\mathrm{X}}_{10}-{\dot{\mathrm{E}}\mathrm{X}}_{12}$ |

Condenser | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{Con}}}={\dot{\mathrm{E}}\mathrm{X}}_{7}+{\dot{\mathrm{E}}\mathrm{X}}_{8}-{\mathrm{Q}}_{\mathrm{con}}\left(1-\frac{{\mathrm{T}}_{\mathrm{o}}}{{\mathrm{T}}_{\mathrm{amb}}}\right)$ |

Absorber | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{Abs}}}={\dot{\mathrm{E}}\mathrm{X}}_{6}+{\dot{\mathrm{E}}\mathrm{X}}_{10}-{\dot{\mathrm{E}}\mathrm{X}}_{8}-{\mathrm{Q}}_{\mathrm{Abs}}\left(1-\frac{{\mathrm{T}}_{\mathrm{o}}}{{\mathrm{T}}_{\mathrm{amb}}}\right)$ |

Heat exchanger | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{Shx}}}={\dot{\mathrm{E}}\mathrm{X}}_{4}+{\dot{\mathrm{E}}\mathrm{X}}_{2}-{\dot{\mathrm{E}}\mathrm{X}}_{5}-{\dot{\mathrm{E}}\mathrm{X}}_{3}$ |

Pump | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{Shx}}}={\dot{\mathrm{E}}\mathrm{X}}_{1}+{\dot{\mathrm{E}}\mathrm{X}}_{2}-{\mathrm{W}}_{\mathrm{pump}}$ |

Cooling system expansion valve | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{rev},\mathrm{v}}}={\dot{\mathrm{E}}\mathrm{X}}_{8}+{\dot{\mathrm{E}}\mathrm{X}}_{9}$ |

Pressure relief valve | ${\mathrm{EX}}_{{\mathrm{d}}_{\mathrm{sev},\mathrm{v}}}={\dot{\mathrm{E}}\mathrm{X}}_{5}+{\dot{\mathrm{E}}\mathrm{X}}_{6}$ |

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## Share and Cite

**MDPI and ACS Style**

Anazi, A.A.A.; Alghamdi, M.I.; Chammam, A.; Kadhm, M.S.; Al-Kharsan, I.H.; Alayi, R. Theoretical Analysis of an Integrated, CPVT Membrane Distillation System for Cooling, Heating, Power and Seawater Desalination. *Water* **2023**, *15*, 1345.
https://doi.org/10.3390/w15071345

**AMA Style**

Anazi AAA, Alghamdi MI, Chammam A, Kadhm MS, Al-Kharsan IH, Alayi R. Theoretical Analysis of an Integrated, CPVT Membrane Distillation System for Cooling, Heating, Power and Seawater Desalination. *Water*. 2023; 15(7):1345.
https://doi.org/10.3390/w15071345

**Chicago/Turabian Style**

Anazi, Abeer Abdullah Al, Mohammed I. Alghamdi, Abdeljelil Chammam, Mustafa Salam Kadhm, Ibrahim H. Al-Kharsan, and Reza Alayi. 2023. "Theoretical Analysis of an Integrated, CPVT Membrane Distillation System for Cooling, Heating, Power and Seawater Desalination" *Water* 15, no. 7: 1345.
https://doi.org/10.3390/w15071345