# Performance Analysis of an Eductor-Based Membrane Distillation Unit

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Technology and Mechanism Description

#### 2.1. Eductor

_{r}is the entrainment ratio, ${\dot{\mathrm{m}}}_{\mathrm{s}}$ is the suction mass flow rate, ${\dot{\mathrm{m}}}_{\mathrm{p}}$ is the primary (motive fluid) mass flow rate, and P

_{r}is the pressure ratio. P

_{b}is the back pressure that can be controlled by opening or closing a valve at the outlet of the eductor (beyond the pressure rising diffuser). P

_{s}is the suction pressure that is experienced by the secondary fluid, and it is measured at an inlet to the suction port. P

_{i}is the inlet pressure, i.e., the pressure at which the motive fluid (primary fluid) is supplied to the eductor.

_{go}is the specific enthalpy of vapor at the nozzle inlet, h

_{g2}is the specific enthalpy of the primary nozzle outlet, and V

_{g2}is the outlet velocity of the nozzle.

_{c}) is defined by [10] as:

_{fg}is the latent heat, v

_{g}is the specific volume of vapor, v

_{l}is the specific volume of liquid, T

_{g}is the temperature of vapor, and T

_{l}is the temperature of liquid.

_{g}/dt) within the eductor as follows [11]:

#### 2.2. Mechanism of Membrane Distillation (MD)

#### 2.2.1. Heat Transfer

_{f}(W·m

^{−2}·K

^{−1}), T

_{f}(K), and T

_{mf}(K) are the convective heat transfer coefficient on the feed side, the bulk feed temperature, and the membrane surface temperature on the feed side, respectively. The bulk fluid temperature on the feed side is estimated based on the feed inlet temperature (T

_{f,in}) and the feed outlet temperature (T

_{f,out}) as in Equation (7):

_{w}(kg·m

^{−2}·s

^{−1}) and $\Delta {\mathrm{H}}_{\mathrm{v},\mathrm{w}}$ (kJ/kg) are the permeate flux and latent heat of vaporization, respectively. $\Delta {\mathrm{H}}_{\mathrm{v},\mathrm{w}}$ can be evaluated at the mean membrane surface temperature Tm(K) using the Equation (10) [17,20]:

_{g}and k

_{p}are the thermal conductivity of the gas phase inside the membrane pores and the thermal conductivity of the membrane material, respectively.

_{p}(W·m

^{−2}·K

^{−1}), T

_{p}(K), and T

_{mp}(K) are the convective heat transfer coefficient on the permeate side, bulk permeate temperature, and membrane surface temperature on the permeate side, respectively. The bulk temperature on the permeate side is estimated based on the permeate inlet temperature (T

_{p,in}) and the permeate outlet temperature (T

_{p,out}), and is determined using Equation (14):

_{h}is the hydraulic diameter calculated based on spacer characteristics, L is the characteristic length, ${\mathrm{R}}_{\mathrm{e}}$ Reynolds number, and ${\mathrm{P}}_{\mathrm{rd}}$ Prandtl number.

#### 2.2.2. Mass Transfer Mechanism

_{w}) and vapor pressure difference (∆P

_{v}), expressed by Equation (21) [22]:

_{v,mf,}and P

_{v,mp}are the partial pressures of water vapor at the feed–membrane interface and permeate–membrane interface, respectively. These pressures can be estimated at T

_{m,f,}and T

_{m,p}by using Sharqawy’s equation [23].

_{v,mp}) in Equation (21) can be assumed to be equal to the vacuum pressure for simplified calculation [17]. As a result, Equation (21) can be written for VMD, as showed in Equation (22):

_{w}) can be calculated using Equation (24) [13,17].

_{e}, d

_{p}, P

_{m}, and k

_{B}, are Collison diameters of water vapor, pore diameter, mean pressure within the membrane pores, and the Boltzman constant, respectively.

_{m}, ε

_{m}, r, R, µ, M, P

_{a}, and p, are membrane tortuosity, membrane thickness, membrane porosity, mean pore size radius, gas constant, fluid viscosity, the molecular weight of water, entrapped air pressure, and average pressure in the pore, respectively. T is the absolute temperature in the pore and Tm is the average temperature across the membrane. P is the total pressure in the pore and D is the diffusion coefficient.

_{f}, C

_{m,f}, ρ

_{f}, and k

_{s}are the bulk solution concentration, solution concentration at the membrane surface, solution density, and mass transfer coefficient respectively. To determine the mass transfer coefficient, the Sherwood number correlation is used, as shown in Equation (32) [17]:

^{2}·s

^{−1}) and Sc

_{f}are the diffusion coefficient of the solute and the Schmidt number, which are determined in Equations (33) and (34), respectively [26]. To simplify the modelling, it is assumed that the proposed system will operate at low salinities and the effect of salinity on the diffusion coefficient will be negligible, hence the following equation of the diffusion coefficient has been used.

## 3. Eductor-Based Membrane Distillation

#### 3.1. Concept Discussion

#### 3.2. Experimental Set-Up Description

## 4. Results and Discussion

#### 4.1. Capacity Assessment of the Eductor

_{s}, has been considered as the primary factor required to plan for the operational parameters of the final water production unit.

_{i}, and outlet, P

_{b}) and secondary fluid pressure (suction, P

_{s}). The measurements were taken at constant inlet pressure and varying outlet pressure (also referred to as back pressure) and maintaining constant volume condition at the inlet to the suction port by closing the valve. Maintaining a constant volume condition at the suction port provided the opportunity to estimate maximum suction pressure at different back pressures (P

_{b}). At the critical point (choked flow), a constant P

_{s}of 3.4 kPa (absolute) was measured for a P

_{b}/P

_{i}ratio of 0.27. Past this critical back pressure to inlet pressure ratio, the vacuum generation capacity of the eductor started to decrease, i.e., absolute pressure at the suction port started to increase. This continued until the P

_{b}/P

_{i}ratio of 0.382, where the pressure at the suction port was observed to rise above the atmospheric pressure, this indicates a flow reversal (back flow) condition where the secondary flow ceases and the motive (primary) fluid enters the suction port. Therefore, it is recommended that the proposed system be operated at sub-critical P

_{b}/P

_{i}ratio to ensure forward flow of the permeate from the feed to the motive fluid direction, and higher efficiency.

^{3}is shown. This aids the interpretation of the observation in Figure 6, as it provides a more descriptive depiction of the influence of P

_{b}/P

_{i}on the degassing rate. A piezo-resistive pressure transducer was installed in the chamber, which recorded time-dependent pressure data at a frequency of 5 Hz. The inter-relationship between back pressure and forward moving flow contributes to both momentum and thermal energy exchange within the flow path of the eductor. When the back pressure is increased at constant inlet pressure (i.e., increasing P

_{b}/P

_{i}), it obstructs the forward path of two-phase flow. This results in the compression of the secondary fluid until the physical limit, and eventually reduces entraining mass flow rate to cause reverse flow. Figure 6 describes the process during the compression. The average time required for complete degassing i.e., reaching a pressure of 4.2 kPa absolute, is 5.42 min.

#### 4.2. Performance of Desalination Module

#### 4.2.1. Impact of Feed Temperature

_{fi}): 50 °C, 60 °C, 70 °C, and 80 °C. The mass flux (J) and instantaneous vacuum pressure (P

_{s}) were plotted against P

_{b}/P

_{i}. The difference in operation before and after the critical point is clearly visible in all four cases, with a larger flux before the critical back pressure is reached and a sudden decline in flux after. The maximum flux for the feed temperatures of 50 °C, 60 °C, 70 °C and 80 °C are 23.1 kg·hr

^{−1}·m

^{−2}, 27.6 kg·hr

^{−1}·m

^{−2}, 33.8 kg·hr

^{−1}·m

^{−2}, and 43.12 kg·hr

^{−1}·m

^{−2}, respectively.

_{b}/P

_{i}ratio results in a rapid increase in the total pressure in the suction chamber. This is due to a decrease in the velocity of the motive fluid and hence the dynamic pressure of the motive fluid in the suction chamber. This results in the observed rise in the static pressure in the suction chamber and decreases the trans-membrane pressure that drives the vapor transfer. The average absolute suction pressure at the critical points for the feed temperatures of 50 °C, 60 °C, 70 °C, and 80 °C are 7.32 kPa, 8.71 kPa, 11.52 kPa, and 13.6 kPa, respectively. Considering the utilization of mechanical energy, the region of operation around the critical point is more efficient.

#### 4.2.2. Impact of Feedwater Flow Rate

_{fi}) on freshwater production rate of flux (J). This relationship is shown in Figure 9. The plot is for two different feed temperatures, 70 °C and 80 °C. The observations were noted for flow rates ranging from 1 LPM to 5.2 LPM. For 80 °C, at 1.1 LPM a flux of 32.5 kg·hr

^{−1}·m

^{−2}was observed, which sharply increases to 41.2 kg·hr

^{−1}·m

^{−2}for a Q

_{f}of 3.18 LPM and then shows only a small variation past this point. Similarly, for the case of 70 °C, for Q

_{f}= 1.21 LPM, a flux of 18.1 kg·hr

^{−1}·m

^{−2}was noted, which then increased sharply up to 34.5 kg·hr

^{−1}·m

^{−2}for Q

_{f}= 3.3 LPM, and then showed only minute variations for further increases in Q

_{f}. This indicates the presence of an optimum feedwater flow rate, and shows that for operation beyond this rate, not much change in yield can be achieved. The identification of or selection of this point through design will be advantageous from both a thermal and electrical energy usage point of view. The average specific thermal energy consumption (STEC) was estimated to be around 3000 kJ/kg of permeate produced.

#### 4.3. Performance of the Eductor

_{r}) against the pressure ratio (P

_{r}) for different temperatures of feedwater. The collective mechanical and thermal performance of the eductor can be visualized. Although the experiments were performed until reversed flow was observed, the graph only summarizes data for the conditions until critical chocking occurred. The variation in P

_{r}is a result of changes in back pressure, which indicates the compressible nature of the process.

_{r}of 0.0053, 0.0039, 0.0034, and 0.0027 was recorded for 80 °C, 70 °C, 60 °C, and 50 °C, respectively. The critical points for 80 °C, 70 °C, 60 °C, and 50 °C were observed at P

_{r}of 0.244, 0.25, 0.251, and 0.262 respectively.

## 5. Practicality of Modified Eductor Based VMD (E-MD)

^{−2}·hr

^{−1}while for the theoretical VMD model it was 27.83 kg·m

^{−2}·hr

^{−1}. In comparison to conventional VMD (indirect condensation), the direct contact condensation in modified VMD or E-MD is clearly more effective [29], as there is no thermal resistance at the interface like there is in a traditional condenser. This simultaneous thermal and mechanical activity of the cooling fluid in E-MD enhances the performance of the system compared to standard VMD. Although it does not use a vacuum pump, the energy consumption is relatively high compared to other technologies because of the amount of energy required for mechanical operation in the eductor.

_{f}). The GOR-Critical is based on the average value of flux at the critical point, and GOR-subcritical is based on the flux after the critical point. The value of GOR-Critical ranges from 0.72 to 0.87 while the value of GOR-Subcritical ranges from 0.29 to 0.31. Increasing feedwater temperature has a positive influence on the value of GOR. The value of the temperature polarization coefficient (TPC) was calculated based on the iterative process for calculating membrane surface temperature in Equations (17)–(20). The TPC was calculated to be 0.92 for 50 °C and 0.85 for 80 °C. The value of TPC decreases with increasing T

_{f}.

## 6. Sensitivity Analysis

_{ei}reduces the mass transfer rate, and hence allows accumulation of vapor in the suction track, which reduces the P

_{r}due to the increase in P

_{s}. The experiment was conducted for about 60 min without active cooling of the motive fluid. During this experiment, T

_{ei}increased from 27.6 °C to 42.1 °C. As a result, the value of P

_{r}decreased from 0.17 to 0.162. This significantly reduced both the mechanical and thermal performance of the eductor. This experiment was conducted for T

_{fi}= 80 °C, with the chiller turned off, and all other conditions were as per the description in Table 4. For a multiphase same-species heat transfer device like an eductor, the motive fluid temperature is an important influencing parameter that needs to be considered. In addition, the design temperature needs to be set to an easily achievable value from a work input perspective.

^{−1}·m

^{−2}to 42 kg.h

^{−1}·m

^{−2}. The average experimental uncertainty of all the experiments results was around ±5.4%. The variation in the flux over the SG range of 1.005 to 1.01 was within the uncertainty and it could be said that at these low salinities, the effect of the concentration was negligible on the flux.

## 7. Conclusions

^{−1}·m

^{−2}was calculated, which is significantly higher than conventional VMD under similar operating conditions. The value of J is dependent on Q

_{f}, hence the optimum value is to be selected to ensure the highest energy efficiency. The operation of the eductor is segregated into critical and sub-critical regions separated by a critical point. It is always recommended to operate the eductor at the critical point.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Degassing rate of eductor at different P

_{b}/P

_{i}for initialization of distillation desalination.

**Figure 8.**Mass flux (J) with respect to P

_{b}/P

_{i}at different T

_{fi}(cold side temperature constant at T

_{p}= 15 °C).

Mass Transfer Mechanism | MD Coefficient (B_{m}) | Eq No. | Condition |
---|---|---|---|

Molecular diffusion | ${\mathrm{B}}_{\mathrm{m}}^{M}=\frac{{\mathsf{\epsilon}}_{\mathrm{m}}}{{\mathsf{\tau}\times \mathsf{\delta}}_{\mathrm{m}}}\frac{\mathrm{PD}}{{\mathrm{P}}_{\mathrm{a}}}\frac{\mathrm{M}}{\mathrm{RT}}$ | (25) | Kn < 0.01 |

Combined Knudsen-molecular diffusion | ${\mathrm{B}}_{\mathrm{m}}^{K-M}=\frac{1}{{\mathrm{RT}\mathsf{\delta}}_{\mathrm{m}}}{\left(\frac{3\mathsf{\tau}}{{2\mathsf{\epsilon}}_{\mathrm{m}}\mathrm{r}}{\left(\frac{\mathsf{\pi}\mathrm{M}}{8\mathrm{RT}}\right)}^{1/2}+\frac{{\mathrm{P}}_{\mathrm{a}}\times \mathsf{\tau}}{{\mathsf{\epsilon}}_{\mathrm{m}}\mathrm{PD}}\right)}^{-1}$ | (26) | 0.01 < Kn < 1 |

Knudsen flow model | ${\mathrm{B}}_{\mathrm{m}}^{\mathrm{K}}=\frac{2}{3\mathrm{RT}}\frac{{\mathsf{\epsilon}}_{\mathrm{m}}\mathrm{r}}{{\mathsf{\tau}\times \mathsf{\delta}}_{\mathrm{m}}}{\left(\frac{8\mathrm{RT}}{\mathsf{\pi}\mathrm{M}}\right)}^{1/2}$ | (27) | Kn > 1 |

$\mathsf{\tau}=\frac{1}{{\mathsf{\epsilon}}_{\mathrm{m}}}$ $\mathrm{PD}=1{.895\times 10}^{-5}{\mathrm{T}}_{\mathrm{m}}^{2.072}$ |

**Table 2.**Estimation of membrane distillation coefficient (Bm) in VMD [17].

Mass Transfer Mechanism | MD Coefficient (B_{m}) | Eq No. | Condition |
---|---|---|---|

Viscous flow model | ${\mathrm{B}}_{\mathrm{m}}^{V}=\frac{1}{RT{\delta}_{m}}\frac{{\epsilon}_{m}{r}^{2}}{8\tau \mu}p$ | (28) | Kn < 0.01 |

Combined Knudsen-viscous mechanism | ${\mathrm{B}}_{\mathrm{m}}^{K-V}=\frac{1}{{\mathrm{RT}\mathsf{\delta}}_{\mathrm{m}}}\left[\frac{2}{3}\frac{{\mathsf{\epsilon}}_{\mathrm{m}}r}{\tau}{\left(\frac{8RT}{\pi M}\right)}^{1/2}+\frac{{\mathsf{\epsilon}}_{\mathrm{m}}{r}^{2}}{8\tau \mu}p\right]$ | (29) | 0.01 < Kn < 10 |

Knudsen flow model | ${\mathrm{B}}_{\mathrm{m}}^{\mathrm{K}}=\frac{2}{3\mathrm{RT}}\frac{{\mathsf{\epsilon}}_{\mathrm{m}}\mathrm{r}}{{\mathsf{\tau}\times \mathsf{\delta}}_{\mathrm{m}}}{\left(\frac{8\mathrm{RT}}{\mathsf{\pi}\mathrm{M}}\right)}^{1/2}$ | (30) | Kn > 10 |

Particular | Description | Units | Symbols |
---|---|---|---|

Membrane Module | |||

Width | 2 | mm | W |

Length | 180 | mm | L |

Breadth | 180 | mm | B |

Membrane | |||

Material | PTFE | ||

Pore size | 0.22 | µm | d_{p} |

Thickness | 190–240 | µm | δt |

Porosity | 80 | % | |

Eductor | |||

Inlet diameter | 12 | mm | D_{ed,in} |

Outlet diameter | 12 | mm | D_{ed,out} |

Suction diameter | 12 | mm | D_{ed,suc} |

Eductor length | 114 | mm | L_{ed} |

Particular | Description | Units | Symbols |
---|---|---|---|

Membrane Module operating parameter | |||

Feed flow | 5.02 | LPM | Q_{f,in} |

Feed temperature | 50, 60, 70 & 80 (+/−2) | °C | T_{f} |

Eductor operating parameter | |||

Eductor inflow | 4.85 | LPM | Q_{e,in} |

Eductor inlet Temperature | 15 | °C | T_{e,in} |

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**MDPI and ACS Style**

Koirala, R.; Ve, Q.L.; Rupakheti, E.; Inthavong, K.; Date, A. Performance Analysis of an Eductor-Based Membrane Distillation Unit. *Water* **2022**, *14*, 3624.
https://doi.org/10.3390/w14223624

**AMA Style**

Koirala R, Ve QL, Rupakheti E, Inthavong K, Date A. Performance Analysis of an Eductor-Based Membrane Distillation Unit. *Water*. 2022; 14(22):3624.
https://doi.org/10.3390/w14223624

**Chicago/Turabian Style**

Koirala, Ravi, Quoc Linh Ve, Eliza Rupakheti, Kiao Inthavong, and Abhijit Date. 2022. "Performance Analysis of an Eductor-Based Membrane Distillation Unit" *Water* 14, no. 22: 3624.
https://doi.org/10.3390/w14223624