*3.6. Process Simulation Using MATLAB at Pilot Scale*

At this point, using the MATLAB software [33], the obtained results for the modified membrane at the laboratory scale were simulated at the pilot scale as shown in Table 1.

**Table 1.** Comparing the results of the operational parameters at the pilot and laboratory scales.


What is noticeable in the simulation is the low temperature of the feed (below 50 ◦C) at the pilot scale. Another point to note is the ability of this method to remove high concentrations of nitrate at the pilot scale. According to the data obtained from the simulation, a small area of the modified membrane (0.5 m<sup>2</sup> ) is enough to remove nitrate from water with the concentration of 35 g/kg in a low temperature (48.33 ◦C) with the flow rate of 1 Kg/s and cross-membrane flux (0.96 Kgm−2h −1 ). The reason for the reduction of flux at the pilot scale may be the decrease of the driving force temperature difference). With the increase of temperature difference, the flux will probably increase (Figure S3; Video S1).

## **4. Conclusions**

The PVDF membrane was coated in two steps with TiO<sup>2</sup> nanoparticles and 1H,1H, 2H,2H-Perfluorododecyltrichlorosilane. The hierarchical structure of the membrane with a multilayer roughness resulted in an increase in the contact angle of the membrane from 89◦ ± 8 ◦ to 174◦ ± 10◦ . The membrane performance was evaluated by the direct contact membrane distillation method using 5 wt % potassium nitrate at the laboratory scale. The electrical conductivity of the feed containing nitrate increased, while the electrical conductivity of the permeate remained constant during the entire process. Furthermore, the low temperature and high flux at the simulated pilot-scale indicate that this method is highly efficient.

At the pilot-scale, using the membrane distillation method and 0.5 m<sup>2</sup> of the modified membrane, it is possible to treat water polluted with nitrate with the concentration of 35 g/Kg at the low temperature of 48.33 ◦C and the flow rate of 1 Kg/s with the cross-membrane flux (0.96 Kgm−2h −1 ).

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4360/12/12/2774/s1, Figure S1: Lab scale setup of Direct Contact Membrane Distillation, Table S1: List of input conditions to software, Table S2: List of the output conditions from running the application, Figure S2: 4. Simulation output at pilot scale with PVDF-TiO2 -FTCS membrane; Figure S3: Schematic presentation of membrane distillation by superhydrophobic membrane. Video S1: Live cover.

**Author Contributions:** Conceptualization, A.R. and Y.O.; Experiments and analyses, F.E.; writing—original draft preparation F.E.; writing—review and editing, Y.O. and A.R.; funding acquisition, Y.O. and A.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by grant numbers 163020139, 164020247 and 163020211.

**Acknowledgments:** The authors hereby express their thanks for the support rendered by University of Isfahan and Nanjing Forestry University.

**Conflicts of Interest:** The authors declare no conflict of interest.
