Argon is a noble gas that has many diverse applications, including welding of metals, steelmaking and semiconductor manufacture. High-purity argon is conventionally produced as a co-product of cryogenic air separation units (ASUs) producing oxygen. In ASUs, argon is separated from oxygen at temperatures below -180 Â°C. Argon and oxygen have very similar boiling points and the required purity for argon is high; as a result, the conventional technology requires distillation columns with over 150 stages and reflux ratios as high as 30 to 40. This, together with the need for expensive low-temperature refrigeration, results in high capital and operating costs. Membrane-assisted distillation potentially represents an economically attractive alternative to conventional technology, possibly leading to significant reductions in capital and energy costs. Therefore, this project develops membrane-assisted cryogenic distillation processes to improve the energy efficiency of argon production from air. Novel process flowsheets for argon production are developed, screened and evaluated using process models. This thesis is the first comprehensive study, to the best of our knowledge, to investigate such synergy between the membrane and distillation units for argon production. Two types of membrane materials--polymeric and carbon molecular sieve membranes--are identified as promising candidates for the proposed process from the open literature. The novel hybrid configurations are evaluated systematically by simultaneous simulation and optimisation. The performance of hybrid flowsheets is evaluated in terms of compression power savings, per unit of argon produced, compared to that of conventional cryogenic distillation. The process configurations and operating conditions offering the highest energy savings are identified. Air separation units producing argon, and the membrane separations, are modelled in the commercial process simulator Aspen Plus. Air separation units co-producing argon are highly complex due to heat integration and coupling between the distillation columns, with stringent operational constraints. Therefore, an optimisation-based solution approach is proposed for modelling and simulation of air separation units to minimise the energy consumption (i.e. compressor power demand) of the process while satisfying the operational constraints. The SQP optimisation algorithm available in Aspen Plus is used to optimise operating conditions. The multicomponent membrane model developed by Shindo et al. (1985) is used for modelling of polymer and CMS membranes. A robust solution technique that guarantees fast and stable convergence is proposed. The membrane model is incorporated within Aspen Plus via a Fortran subroutine. The process models are used to identify important degrees of freedom. Decision variables, including the membrane feed flow rate, stage cut, locations of column feed, side-feeds and side-draws and reflux ratio are optimised to give the highest energy savings. The results show that the synergy between distillation and membranes can reduce energy consumption per unit of argon produced. The optimum location for the membrane side-draw is close to the feed stage of the column. Polymeric membranes can give 12% power savings and a 32% reduction could be achieved with a carbon molecular sieve membrane operating at low temperatures (-110Â°C). However, the latter membranes have not yet been commercialised due to poor stability and high cost. Overall, the results suggest that the proposed hybrid process has a high potential for industrial implementation; development of the advanced membrane materials is key to success.