Osmotically driven membrane processes, like forward osmosis and pressure retarded osmosis, may hold key advantages when integrated with reverse osmosis for seawater desalination. The spiral-wound membrane platform in which these processes are applied has inherent disadvantages that need to be explored. Maintaining proper operating pressure in both of the fluid channels of a spiral-wound membrane requires the feed and draw streams to be operated at different flow rates, often as drastic as a 1:10 ratio. This affects the thermodynamic equilibrium of the system and drastically affects potential water and energy recovery. In this work, a model was created to rigorously represent spiral-wound membranes to increase modeling accuracy. A process configuration that features periodic recharging of the stream inside of the envelope is proposed to mitigate the effects of the flow rate difference. The model is used to compare the multi-stage design to single-stage configurations for both forward osmosis and pressure retarded osmosis by testing various feed and draw flow rate ratios, between 1:10 to 1:1, operated by each process as well as important membrane characteristics such as channel height and water and salt permeability. The multi-stage design shows an increase in wastewater utilization from 62.6% to 90% when compared to the single-stage designs for forward osmosis. Additionally, the multi-stage configuration increases the pressure retarded osmosis specific energy recovery from 0.13 kWh/m3 to 0.55 kWh/m3. However, the increased effectiveness of these multi-staged designs comes with a reduction in average water flux and power density, which leads to the requirement of more membrane area and capital investment for potential system implementation.