The technology of Micro/Nano-Electro-Mechanical Systems and Micro-Total-Analysis Systems has developed rapidly in the last decade. These miniaturised systems offer the potential to increase yields significantly in chemical, biological and clinical analyses and will lead to significant reductions in process time and reagent consumption. However, there is a major problem in predicting the performance of devices that depend on manipulating gas flows. The thermodynamic quasi-equilibrium hypothesis, on which the Navier-Stokes equations depend, is inappropriate when the mean free path of the gas molecules is comparable to the characteristic dimension of these micro/nano-systems. This research aims to explore whether a mesoscopic lattice Boltzmann equation (LBE) methodology can be established that can predictively model the non-equilibrium gas dynamics in a system with a characteristic length scale between 0.1-1000 microns, which we refer to as a micro/nano-system in the following sections. We will test our LBE model against published observations in a variety of flow configurations and with experimental data provided by BOC Edwards. If successful, the outcomes of this research would contribute to the development of an efficient simulation capability for gas flows in industrially-relevant micro/nano-system geometries.