Environmental issues have been stricken our planet in different areas. Current worldwide problems, for instance, water shortage and the increasing demand for energy can be mitigated by employing technological mechanisms, such as a well-established osmotic process for salt water desalination known as reverse osmosis (RO), and a promising technology for generating power from salinity gradient sources, called pressure retarded osmosis (PRO). This work aims to mathematically model the core component of RO and PRO systems, which is the membrane module, working in different conditions and graphically characterize its efficiency using performance indicators to support researchers and people in industry to design and implement RO and PRO systems in a less complex and more reliable way. To reach this goal, segmented mathematical models of a 5-inch scale Toyobo HP5255SI-H3K hollow fibers membrane module were developed for the RO and PRO processes using the solution-diffusion and friction-concentration polarization transport models, mass balances and pressure drop equations. After validating the models and performing simulations, the performance curves obtained were able to provide the optimum values of inlet parameters for both RO and PRO processes that led to generate the best results in terms of volume flow rate and salinity of permeate, recovery ratio, salt rejection rate, power density and net power output. In addition, some interesting discoveries were acquired from the results such as an unused portion of membrane area in the radial direction and the influence of flow velocities on entropy generation, salt and water fluxes within the membrane module in the RO process, as well as how input parameters as hydraulic pressures and flow rates impact power generation in PRO systems and how to mitigate the reverse salt flux in this process. Finally, the possibility of integrating RO and PRO systems to desalinate salt water and produce power from the resulting permeate and brine solutions is also discussed and arguments on the reasons why such systems would not work with current technology are presented.