# Mapping of a Novel Zero-Liquid Discharge Desalination System Based on Humidification–Dehumidification onto the Field of Existing Desalination Technologies

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}energy intensity that can be supplied completely by an electric source or in combination with heating steam. Follow-up sensitivity analysis highlights the robustness of the system in handling variations of 25% in product flowrate and 75% in feed salinity, practically without incurring any additional energy demands. The proposed system operating costs between 72 USD/m

^{3}and 96 USD/m

^{3}are comparable to those of existing brine disposal techniques. Furthermore, an operational map of existing desalination technologies suggests a niche characterized by high recovery rates and high feed salinities that are generally unfulfilled by conventional desalination methods. Overall, the proposed system shows potential for off-grid hypersaline brine treatment. This study sets the stage for future development of physics-based and data-driven predictive models as the proposed system iterates into a pilot plant deployment.

## 1. Introduction

- A mathematical model for the proposed STEWARD system used to bound operational space through physical conservation laws and to estimate the thermodynamic states at each point of the desalination process;
- A sensitivity analysis highlighting the engineering tradeoffs associated with variations in product flow rate and feed salinity;
- An evaluation of the practical implications related to deploying the STEWARD system to potentially replace existing desalination plants or complement brine processing;
- Identification of deployment opportunities for STEWARD within the current operational space of existing desalination technologies.

## 2. Methodology

#### 2.1. Overall System Description

#### 2.2. Model Description

- The partial pressure of water (${P}_{3,w})$ is defined by ${T}_{3}$ and ${\mathsf{\varphi}}_{3}$, which must be lower than ${P}_{3}$ to result in a positive humidity ratio:$${W}_{3}>0;$$
- State 4 is calculated through an iterative algorithm that finds ${T}_{4}$ such that the resulting humidity ratio ${W}_{4}$ matches that of full evaporation of the warm saline water stream (${m}_{12}/{m}_{2})$. To guarantee heat transfer and full evaporation, ${T}_{4}$ must be slightly greater than ${T}_{3}$, and thus, the checkpoint follows that:$${T}_{4}-0.5>{T}_{3};$$
- It has been determined that expansion cooling of the gas and cooling of the liquid through heat transfer are minimal during atomization processes, especially at fast discharges [27]. Therefore, the total enthalpy of the high-speed hot air and warm saline water streams before and after atomization mixing must remain equal or slightly lower due to losses in local evaporation and breaking of water droplets. The implemented checkpoint therefore ensures that ${H}_{3}$ is between 0 and 8% lower than the addition of the enthalpies in the streams preceding the atomizer such that:$$\frac{({H}_{2}+{H}_{12})-{H}_{3}}{({H}_{2}+{H}_{12})}<0.08;$$
- The superheated moist air temperature is an input to the model and must be larger than the calculated temperature at the evaporator outlet per the second law of thermodynamics. Furthermore, the temperature at the evaporator outlet must be lower than the temperature of the condensed water-and-air stream leaving the condenser. Therefore, the implemented checkpoint verifies that:

- The heat available on the condensing side of the evaporator ${Q}_{c}$ must be greater than the heat required to complete evaporation ${Q}_{e}$. This condition checks that at minimum:$${Q}_{c}>{Q}_{e}.$$

## 3. Results

#### 3.1. Baseline Operation

^{3}. The total thermal load of ~50 kWh/m

^{3}is similar to that reported in other hypersaline-brine desalination systems [51].

_{4}and CaCO

_{3}[52,53]. Although a small degree of CaCO

_{3}scaling can be beneficial by protecting equipment from corrosion [54], excessive scaling results in a lower overall heat transfer coefficient, which would prevent the achievement of full evaporation and thus decrease performance of the system through reduced product quantity and quality (defined by low salinity). This can impede continuous operation of the system and incur additional operation costs. Measures such as feed pretreatment with scaling inhibitors [8,55], periodic cleaning, and novel engineering or material science solutions could be required for sustained system operation [56].

#### 3.2. Sensitivity Analysis

## 4. Discussion

#### 4.1. Practical Operation

^{3}is impractical. Obtaining an estimate of the number of units in parallel operation and the associated energy intensities, nonetheless, can help establish operational bounds that could guide further design iterations. Table 4 shows the operational costs assuming the implementation of enough STEWARD units in parallel to fulfill existing plant production requirements or process their corresponding brine product [46].

^{3}and 174 USD/m

^{3}for surface disposal and existing deep-injection-well techniques, respectively, up to 7280 USD/m

^{3}for lined evaporative pond methods [57]. Considering electricity rates in fracking states such as Texas (0.086 USD/kWh), West Virginia (0.1066 USD/kWh), and Pennsylvania (0.0981 USD/kWh), for cost comparison with STEWARD assuming electric heating, the baseline operation cost per unit would range between 72 USD/m

^{3}and 96 USD/m

^{3}[58].

#### 4.2. Operational Map

^{3}corresponds to thermal energy input to the superheater, which matches the midrange point of the thermal energy intensity of MED desalination and lies at the lower ranges of TVC and HDH desalination. This implies that most energy is required in atomization (about 95%), which facilitates and integrates ZLD within the desalination process, in contrast with the energy intensity associated with the conventional desalination methods presented in Figure 6, which represents the desalination process alone at lower feed salinities. The energy loss in atomization is reflected in the pressure drop across the component; therefore, the competitiveness of the STEWARD system in the marketplace is contingent upon efficient atomizer design and performance. The presence of the compressor implies that the current STEWARD concept must depend on electricity alone or electricity and heat to operate. This could potentially be an important factor when considering locations for deployment. From an operational perspective, adoption of the STEWARD system would ultimately be associated with the costs of energy available and brine management at the desalination site.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Component | Equation | Variables | ||
---|---|---|---|---|

Compressor | ${W}_{isen}={m}_{1}\left(\frac{{\gamma}_{1}}{{\gamma}_{1}-1}\right){P}_{1}\left(\frac{1}{{\rho}_{1}}\right)\left[{\left(\frac{{P}_{2}}{{P}_{1}}\right)}^{\left(\frac{{\gamma}_{1}-1}{{\gamma}_{1}}\right)}-1\right]$ | (7) | ${W}_{isen}$ | Compressor power, isentropic |

${m}_{1}$ | Slow-moving dry-air mass flow rate | |||

${\gamma}_{1}$ | Isentropic ratio | |||

${P}_{1}$ | Inlet pressure | |||

${W}_{comp}=\frac{{W}_{isen}}{{\eta}_{c,isen}}$ | (8) | ${P}_{2}$ | Outlet pressure | |

${W}_{comp}$ | Actual compressor power | |||

${\eta}_{c,isen}$ | Compressor isentropic efficiency | |||

Evaporator | ${Q}_{e}={m}_{3,sw}{\lambda}_{3,sw}+\left({m}_{3,w}+{m}_{3,a}\right){c}_{p,ma}\left({T}_{4}-{T}_{3}\right)$ | (9) | ${Q}_{e}$ | Heat required for full evaporation |

${m}_{3,sw}$ | Saltwater flow rate | |||

${\lambda}_{3,sw}$ | Saltwater latent heat of vaporization | |||

${m}_{3,w}$ | Water-vapor flow rate | |||

${m}_{3,a}$ | Air flow rate | |||

${c}_{p,ma}$ | Specific heat capacity of moist air | |||

${T}_{4}$ | Outlet temperature | |||

${T}_{3}$ | Inlet temperature | |||

Superheater | $d{H}_{sup}={m}_{w}\left({h}_{7,w}-{h}_{6,w}\right)+{m}_{a}\left({h}_{7,a}-{h}_{6,a}\right)+{m}_{s}\left({c}_{{p}_{7s}}{T}_{7}-{c}_{{p}_{6s}}{T}_{6}\right)$ | (10) | $d{H}_{sup}$ | Superheat enthalpy difference |

${m}_{w}$ | Water-vapor mass flow rate | |||

${h}_{7,w}$ | Water-vapor enthalpy at superheat temp. | |||

${h}_{6,w}$ | Water-vapor enthalpy at vapor saturation | |||

${m}_{7,a}$ | Dry-air mass flow rate | |||

${h}_{7,a}$ | Air enthalpy at superheat temp. | |||

${h}_{6,a}$ | Air enthalpy at saturation temp. | |||

${m}_{7,s}$ | Solid-salt mass flow rate | |||

${c}_{{p}_{s}}$ | Specific heat capacity of solid salt | |||

${T}_{7}$ | Superheat temp. | |||

${T}_{6}$ | Saturation temp. | |||

Condenser | $d{H}_{sat}={m}_{w}\left({h}_{6,w}-{h}_{8,w}\right)+{m}_{a}\left({h}_{6,a}-{h}_{8,a}\right)$ | (11) | $d{H}_{sat}$ | Condensation enthalpy difference |

${h}_{8,w}$ | Water-vapor enthalpy at liquid saturation | |||

${h}_{8,a}$ | Air enthalpy at saturation temp. | |||

${Q}_{c}=d{H}_{sup}+d{H}_{sat}$ | (12) | ${Q}_{c}$ | Condensation heat | |

Cyclone | ${P}_{6}={P}_{5}-d{P}_{cy}$ | (13) | ${P}_{6}$ | Outlet pressure |

${P}_{5}$ | Inlet pressure | |||

$d{P}_{cy}$ | Cyclone pressure drop | |||

${m}_{s}={m}_{5,s}{\eta}_{cy}$ | (14) | ${m}_{s}$ | System-salt flow rate | |

${m}_{5,s}$ | Inlet-salt flow rate | |||

${\eta}_{cy}$ | Collection efficiency |

General Inputs | |
---|---|

Product flow rate, ${M}_{d}$ (kg/s) | 0.0027 |

Intake salinity, ${C}_{f}$ (g/kg) | 100 |

Intake temp., ${T}_{in}$ (°C) | 18 |

Family Inputs | |

Motive steam pressure, ${P}_{s}$ (kPa) | 200 |

Specific Inputs | |

Superheat temp., ${T}_{sup}$ (°C) | 120 |

Slow-moving dry-air pressure, ${P}_{1}$ (kPa) | 48 |

Slow-moving dry-air temp., ${T}_{1}$ (°C) | 20 |

Slow-moving dry-air rel. hum., ${\mathsf{\varphi}}_{1}$ (−) | 0.63 |

Air flow rate, ${m}_{1}$ (kg/s) | 0.0054 |

High-speed hot-air pressure, ${P}_{2}$ (kPa) | 150 |

Warm saline-water temperature, ${T}_{12}$ (°C) | 20 |

General Outputs | |
---|---|

Product flow rate, ${M}_{d}$ (kg/s) | 0.0027 |

Feed-water flow rate, ${M}_{f}$ (kg/s) | 0.003 |

Brine flow rate, ${M}_{b}$ (kg/s) | n/a |

Product-water salinity, ${C}_{p}$ (g/kg) | 1 |

Feed-water salinity, ${C}_{f}$ (g/kg) | 100 |

Brine salinity, ${C}_{b}$ (g/kg) | n/a |

Actual recovery ratio, $R$ | 0.91 |

Family Outputs | |

Specific energy, ${E}_{des}$ (kWh/m^{3}) | Scenario 1: 986_{el}, 53_{th}Scenario 2: 1039 _{el} |

Motive-steam flow rate, ${M}_{p}$ (kg/s) | 2.37 × 10^{−4}/n/a |

Gain ratio, $GR$ | 11.4/n/a |

Sp. cooling-water flow rate, $s{M}_{cw}$ (kg/kg) | n/a |

Specific Outputs | |

Atomized water-and-air temp., ${T}_{3}$ (°C) | 75 |

Atomized water-and-air rel. hum., ${\mathsf{\varphi}}_{3}$ (−) | 0.69 |

Solid salt-product flow rate., ${m}_{s}$ (kg/s) | 2.94 × 10^{−4} |

Compressor power, ${W}_{comp}$ (kW) | 9.6 |

Evaporator heat required, ${Q}_{e}$ (kW) | 3.3 |

Condenser heat available, ${Q}_{c}$ (kW) | 7.3 |

Superheater heat, $d{H}_{sup}$ (kW) | 0.5 |

System Type | MDT | MDT | ROX | ROX |
---|---|---|---|---|

Plant Location | Jeddah, KSA | Jamnagar, IN | Bimini, BS | Cát Bà, VT |

${M}_{d}$ (kg/s) | 55 | 284 | 12 | 17 |

${C}_{f}$ (g/kg) | 41.5 | 42 | 39 | 33 |

${T}_{in}$ (°C) | 30 | 26 | 29 | 32 |

${M}_{b}$ (kg/s) | 109 | 409 | 12 | 20 |

${C}_{b}$ (g/kg) | 62.5 | 70 | 78.9 | 62.9 |

${T}_{b}$ (°C) | 46 | 43 | 39 | 33 |

${E}_{des}$ (kWh/m^{3}) | 132_{th} | 76_{th} | 2.7_{el} | 2.4_{el} |

${Q}_{req}$ (kW) | 26,132 | 77,619 | n/a | n/a |

${W}_{pump}$ (kW) | n/a | n/a | 110 | 149 |

$RR$ (-) | 0.34 | 0.41 | 0.50 | 0.47 |

STEWARD Replacement | ||||

Total ${M}_{d}$ (kg/s) | 55 | 284 | 12 | 17 |

Units in Parallel | 20,385 | 105,170 | 4449 | 6306 |

${E}_{des}/unit$ (kWh/m^{3}) | 1036 | 1036 | 1036 | 1012 |

${W}_{comp}/unit$ (kW) | 9.6 | 9.6 | 9.6 | 9.6 |

$d{H}_{sup}/unit$ (kW) | 0.5 | 0.5 | 0.5 | 0.5 |

${Q}_{req}/unit$ (kW) | 3.0 | 2.9 | 1.6 | 2.1 |

$RR/unit$ (-) | 0.96 | 0.96 | 0.96 | 0.97 |

STEWARD Complement | ||||

Total ${M}_{d}$ (kg/s) | 109 | 409 | 12 | 20 |

Units in Parallel | 40,344 | 151,520 | 4442 | 7403 |

${E}_{des}/unit$ (kWh/m^{3}) | 1067 | 1069 | 1092 | 1072 |

${W}_{comp}/unit$ (kW) | 9.98 | 9.98 | 10.2 | 9.98 |

$d{H}_{sup}/unit$ (kW) | 0.5 | 0.5 | 0.5 | 0.5 |

${Q}_{req}/unit$ (kW) | 1.3 | 1.7 | 1.1 | 1.4 |

$RR/unit$ (-) | 0.94 | 0.93 | 0.93 | 0.94 |

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Romo, S.A.; Elhashimi, M.; Abbasi, B.; Srebric, J. Mapping of a Novel Zero-Liquid Discharge Desalination System Based on Humidification–Dehumidification onto the Field of Existing Desalination Technologies. *Water* **2022**, *14*, 2688.
https://doi.org/10.3390/w14172688

**AMA Style**

Romo SA, Elhashimi M, Abbasi B, Srebric J. Mapping of a Novel Zero-Liquid Discharge Desalination System Based on Humidification–Dehumidification onto the Field of Existing Desalination Technologies. *Water*. 2022; 14(17):2688.
https://doi.org/10.3390/w14172688

**Chicago/Turabian Style**

Romo, Sebastian A., Mohammed Elhashimi, Bahman Abbasi, and Jelena Srebric. 2022. "Mapping of a Novel Zero-Liquid Discharge Desalination System Based on Humidification–Dehumidification onto the Field of Existing Desalination Technologies" *Water* 14, no. 17: 2688.
https://doi.org/10.3390/w14172688