Role of viscous, diffusion and inertial mechanisms in modeling fluid flow through unconventional reservoir

Diffusion forces contribution has been heavily underestimated when modeling fluid flow in porous media especially in UCRs with a general agreement that viscous transport is the predominant controller. This work introduces a new comprehensive flow model suitable for tight UCRs, including viscous, inertia, and diffusion forces, to account for the transport of fluid in the three scales. The new model addressing multi-phase 1-D linear flow in tight UCRs has been mathematically derived and numerically solved, and tested against real cases using MATLAB software. Detailed parametric analysis has been conducted, and very clear profiles and flow patterns of the main flow parameters were identified. It has been established that, with lower permeability of the porous medium and lower viscosity of the flowing fluid, the diffusion mechanism becomes more predominant in controlling flow velocity. The results of the newly derived equations that includes the diffusion term clearly depicted the contribution of diffusivity to the flow in the nano-scaled pore spaces. The comparison between the suggested equation to existing equations and correlations that are used in the field to describe the behavior of the flow in low permeability and low porous medium have been established.