In order to provide the reduction of greenhouse gas emissions needed to attempt to stabilise atmospheric CO₂ concentrations, significant changes in the way energy is produced will have to be implemented and many different options will have to be pursued. Since fossil fuel will remain the main energy source for a number of decades, development of CO₂ capture and storage (CCS) becomes essential. According to the estimate of the Intergovernmental Panel on Climate Change (IPCC), in most CCS systems the cost of capture (including compression) is the largest cost component. As a result, efforts are needed to provide more efficient and cost effective separation options. Recently, Pressure Swing Adsorption (PSA) has attracted attention as a valuable technology for CO₂ capture since it is a more economic and effective alternative to other separation options such as cryogenic, membrane and absorption processes. The aim of our project is the development of computer aided design tools for PSA processes. Our focus is on fast cycle operations which are needed to reduce capital and operating costs. However, both modelling and optimisation of such operations are challenging. The simplest model for a PSA process is based on the assumption of a linear driving force (LDF) to mass transfer between the fluid and the solid adsorbent. It simplifies the model by eliminating the need to describe concentration profiles in the solid. Unfortunately, the LDF model fails to capture the dynamics of fast cycle operations. As a result, we use more detailed diffusion models. These involve coupled nonlinear partial differential and algebraic equations in time and one or two space dimensions. The detailed diffusion models imply more difficulties for optimisers, especially gradient based methods. We are currently investigating the efficiency of direct search methods for the optimization of a PSA process described by the detailed model. The eventual goal is the development of multi-criteria optimization methods for this problem, in order to achieve high efficiency both in terms of costs of the operation and purity/recovery of the products.