a second species, j, can be defined as: With the expression above, a membrane system for a binary mixture can be sufficiently defined. it can be seen that the total flow across the membrane is strongly dependent on the relation between the feed and permeate pressures. The ratio of feed pressure (p') over permeate pressure (p") is defined as the membrane pressure ratio (θ). It is clear from the above, that a flow of species i or j across the membrane can only occur when: In other words, the membrane will experience flow across it when there exists a concentration gradient between feed and permeate. If the gradient is positive, the flow will go from the feed to the permeate and species i will be separated from the feed. Therefore, the maximum separation of species i results from: Another important coefficient when choosing the optimum membrane for a separation process is the membrane selectivity αij defined as the ratio of permeability of species i with relation to the species j. This coefficient is used to indicate the level to which the membrane is able to separates species i from j. It is obvious from the expression above, that a membrane selectivity of 1 indicates the membrane has no potential to separate the two gases, the reason being, both gases will diffuse equally through the membrane. In the design of a separation process, normally the pressure ratio and the membrane selectivity are prescribed by the pressures of the system and the permeability of the membrane . The level of separation achieved by the membrane (concentration of the species to be separated) needs to be evaluated based on the aforementioned design parameters in order to evaluate the cost-effectiveness of the system. Membrane performance The concentration of species i and j across the membrane can be evaluated based on their respective diffusion flows across it. In the case of a binary mixture, the concentration of species i across the membrane: This can be further expanded to obtain an expression of the form: Using the relations: The expression can be rewritten as: Then using The solution to the above quadratic expression can be expressed as: Finally, an expression for the permeant concentration is obtained by the following: Along the separation unit, the feed concentration decays with the diffusion across the membrane causing the concentration at the membrane to drop accordingly. As a result, the