THE SIGNIFICANCE OF PORE THROAT LENGTH IN PORE-SCALE FLUID FLOW FROM THE PERSPECTIVE OF BOUNDARY LAYER THEORY

A predictive understanding of fluid flow through rocks is fundamental in making inferences about subsurface geological activities. This is important in resource exploration and production as well as in environmental protection and management. A key factor in understanding fluid flow is permeability. Generally, the role of pore throat length (PTL) is neglected in empirical models. That said, PTL is accounted for in numerical models via Poiseuille’s law which shows an inverse relationship between PTL and permeability. However, the scale of Poiseuille’s experiments is orders of magnitude larger than typical pore-throat sizes. Taking the boundary layer theory into account, we hypothesize that PTL in pore microstructures could be small enough to have a nonlinear relationship between permeability and PTL. According to the boundary layer theory (in geologic terms), internal flow through a pore throat is divided into hydrodynamic entrance region and fully developed region. The hydrodynamic entrance region is the zone through which the boundary layer is still growing from the rock surface; hence, the velocity profile is still developing. A fully developed region is formed when the velocity profile no longer changes because the boundary layer from all sides merge at the flow axis. Consequently, if the PTL is within the hydrodynamic entrance region, the varying thickness of the boundary layer could have profound effect on permeability that would not be captured by Poiseuille’s equation. Hence, disobeying the linear relationship from Poiseuille’s law. To test our hypothesis, we investigate the effect of PTL on permeability of stochastically generated pore microstructures using pore-scale numerical flow simulations. Our results show that PTL has a nonlinear relationship with permeability at pore scale and potentially plays a key role in fluid flow at continuum scale. A simulation of fluid displacement shows the same result where longer PTL restrict the displacement of immiscible fluids through rocks by up to 45 % increase in discharge time. The findings from this study can help improve the development of pore scale modelling of fluid flow.