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The world's water shortage problem has drawn immense attention and many researchers have tried to solve the problem by introducing water purification and seawater desalination. It is widely accepted that a reverse osmosis (RO) process is more effective in terms of separation capability and its simple installation and requires less energy than any other water purification and seawater desalination processes. However, its specific energy consumption is still higher than the theoretical minimum energy and there is scope for further improvement. Spiral wound modules are the most commonly used in large RO desalination plants, in which flat sheet membranes and spacers are alternately arranged and wrapped around a centre pipe. Feed spacers play an important role by keeping membrane sheets separate and enhancing mixing near membrane surfaces. This thesis focusses on identifying opportunities for enhancement of membrane performance, reductions in energy consumption and other costs via predictive modelling and model-based scenario studies. Firstly, a new mathematical model for a spiral wound module is developed by accounting for its unique geometric features. The performance of the spiral model is compared with existing models based on the plate-and-frame approach. The spiral model is then used to investigate the effects of geometric parameters on module performance and energy consumption, and further extended to simulate a large-scale RO process with multiple modules. Secondly, computational fluid dynamics (CFD) models for spacer-filled feed channels are built using two-dimensional geometric representations and simulated under a wide range of operating and geometric conditions. A new boundary condition is introduced in the CFD models by reformulating the solution-diffusion model in order to describe permeable membrane walls. As a result, the effects of different operating and geometric conditions in the presence of spacers can be assessed in terms of key performance indicators such as water flux, concentration polarisation modulus and pressure drop. A large number of numerical simulations have been carried out and the results are used to derive empirical correlations for concentration polarisation and pressure loss in a feed channel, in order to facilitate the incorporation of the impact of spacers in a process model. The new correlations are implemented in a process model and compared with existing correlations that were experimentally derived in terms of predicted performance and energy consumption. Finally, three-dimensional CFD models for various spacer designs are developed by varying filament configuration, mesh angle and flow attack angle. By implementing the proposed boundary condition for permeable membrane walls, the CFD models presented here can be utilised to predict membrane performance for a given feed spacer type and geometry.