total permeant flow (q"out) results from the integration of the diffusion flow across the membrane from the feed inlet (q'in) to feed outlet (q'out). A mass balance across a differential length of the separation unit is therefore: where: Because of the binary nature of the mixture, only one species needs to be evaluated. Prescribing a function n'i=n'i(x), the species balance can be rewritten as: Where: Lastly, the area required per unit membrane length can be obtained by the following expression: Membrane materials for carbon capture in flue gas streams The material of the membrane plays an important role in its ability to provide the desired performance characteristics. It is optimal to have a membrane with a high permeability and sufficient selectivity and it is also important to match the membrane properties to that of the system operating conditions (for example pressures and gas composition). Synthetic membranes are made from a variety of polymers including polyethylene, polyamides, polyimides, cellulose acetate, polysulphone and polydimethylsiloxane. Polymer membranes Polymeric membranes are a common option for use in the capture of CO2 from flue gas because of the maturity of the technology in a variety of industries, namely petrochemicals. The ideal polymer membrane has both a high selectivity and permeability. Polymer membranes are examples of systems that are dominated by the solution-diffusion mechanism. The membrane is considered to have holes which the gas can dissolve (solubility) and the molecules can move from one cavity to the other (diffusion). It was discovered by Robeson in the early 1990s that polymers with a high selectivity have a low permeability and opposite is true; materials with a low selectivity have a high permeability. This is best illustrated in a Robeson plot where the selectivity is plotted as a function of the CO2 permeation. In this plot, the upper bound of selectivity is approximately a linear function of the permeability. It was found that the solubility in polymers is mostly constant but the diffusion coefficients vary significantly and this is where the engineering of the material occurs. Somewhat intuitively, the materials with the highest diffusion coefficients have a more open pore structure, thus losing selectivity. There are two methods that researchers are using to break the Robeson limit, one of these is the use of glassy polymers whose phase transition and changes in mechanical properties make it appear that the material is absorbing molecules and thus surpasses the upper