**5. Conclusions**

In this study, a simulation of a membrane plant was discussed. A system of ordinary di fferential equations was developed to accurately simulate the membrane module. The system of equations reflects the change of flow properties along the membrane and incorporates the pressure drop. The steady-state permeate flux presented in [6] is assumed as the governing equation for the filtration process. An economic model including the capital cost as well as the operating cost was used to evaluate the performance of the membrane plant. The e ffect of operating and design parameters, such as recirculation flow rate, inlet pressure, and membrane module geometry, on the economic viewpoint of membrane application was investigated. All the parameters have a critical point which minimizes the annual cost while the other parameters are fixed. The search for an optimum design using genetic algorithm suggests that the system should be operated at high pressure and short channel width. Other parameters should be further investigated so that the cross-flow velocity is maintained at a high value, but does not consume too much energy. It also suggests that the design, selection, and operating strategy strongly depend on the requirement of the process and the permeate flux and its correlation to system parameters. The procedure presented in this study might be extended for the general design of a particular process in which the governing equations are known.

**Author Contributions:** Conceptualization, T.-A.N.; Methodology, T.-A.N.; Supervision, S.Y.; Writing—original draft, T.-A.N.; Writing—review & editing, S.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank Japan International Cooperation Agency (JICA) and Tokyo Institute of Technology for the kind support during the preparation of the manuscript.

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