This computational study focuses on the application of pervaporation for the removal of low concentrations of water from organic solvents. A classic chemical engineering approach is employed using mass and energy balances combined with an empirical expression for flux, to address a number of important problems in the area of pervaporation design and analysis. For both composition-independent and composition-dependent fluxes, expressions are obtained for the ideal average flux, and hence the ideal membrane area, of single-stage adiabatic pervaporation membrane modules. These expressions which take the form of integrals are then approximated by easy-to-use shortcut methods suitable for rapid conceptual design calculations. Ideal isothermal pervaporation modules are analysed. The actual module efficiency of an industrial-scale pervaporation system is determined. The range of economically feasible values of the activation energy is established. This allows the full range of typical industrial operating conditions to be determined thereby allowing validation of shortcut methods. Novel equations are developed for determining feed flowrate and composition as functions of recycle. The optimisation of multi-stage systems is addressed and isothermal pervaporation, a limiting case of multi-stage adiabatic operation, is modelled. Permeate composition is assumed to be constant within a module: this assumption is usually only valid for water concentrations greater than 2 wt%. The models developed assume ideal behaviour and do not allow for concentration polarisation, temperature polarisation or poor flow distribution. Novel performance metrics for pervaporation modules are proposed. The performance of industrial-scale systems is analysed. Finally, a novel metric, the Pervaporation Membrane Index (PMI) is proposed: this metric gives appropriate weighting to flux and separation. Areas requiring further research are identified including the analysis of industrial systems, the use of multiple types of membrane within a single system and optimisation of multi-stage pervaporation systems.