Modeling Fluid Flow in Tight Unconventional Reservoirs: Micro/Nano Scale Approach

The need for a tool to predict transport phenomena in petroleum unconventional tight reservoirs is placing more stringent demand on establishing more realistic models beyond the currently used viscous and inertial dependent models. Since diffusion is the principal mechanism in tight unconventional reservoirs that take place in both Micro and Nano scales, a diffusive term was added to the diffusivity model that operates both viscous and inertial forces, introduced by (Belhaj, et al., 2003). This diffusive term is a modified Fick’s 1st Law. It counts for the flow velocity caused by the diffusion process. Using the three-term model as a rate equation, in addition to the continuity equation and the EOS, a new model (a form of PDE) has been developed. The new model works ideally in unconventional tight reservoirs where oil and/or gas flow. The model has been numerically solved and tested. A comprehensive parametric study has been conducted and revealed clear trends. It has been concluded that diffusion mechanism contribution to flow increases with low permeability of the medium and low viscosity of the flowing fluid. An index (a combination of permeability and viscosity) has been developed and used to verify the influence and impact of the diffusion forces.