Numerical investigation of Herschel–Bulkley fluid flows in 2D porous media: Yielding behaviour and tortuosity

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

“…Such dependence exists only within the range of injection velocities in which the shear-thinning fluid exhibits a Newtonian plateau viscosity in certain pores, but not in all pores. Moreover, the directional nature of shear-thinning behavior resulted in decreased tortuosity values as compared to the flow of Newtonian fluids, in agreement with previous results in 2D media [14] and rough-walled fractures [13].…”

“…This dependency is stronger as the shear-thinning behaviour becomes more pronounced (higher values of C p ). These results are in good agreement with the previous numerical results dealing with the flow of yield stress fluids through 2D porous media [14]. The tortuosity of the streamlines is always lower in the case of the shear-thinning fluid as compared to the Newtonian fluid, which is due to the directional nature of shear-thinning behavior.…”

“…T is commonly defined as the ratio between the average length of the actual fluid flow path through the porous matrix, L e , and the apparent length of the porous medium, L. In the absence of recirculation zones during the flow of an incompressible fluid, the surface average of L e /L weighted by the local flux over a reference surface perpendicular to the main flow direction is equivalent to the ratio between the surface average of the velocity magnitude field u j j À and the surface average of the component of velocity in the main flow direction u x À [46]. By taking the previous observation into account, T was calculated from the velocity maps obtained in the current simulations by using the following expression [14,46,47,48]:…”

“…DNS were also used in the past to show that shear-thinning fluids exhibit high values of local viscosity in the microscopic conduits of the porous media in which the pressure gradient is low, which results in flow being diverted from these zones. This is the case of the pore channels that are oriented nearly perpendicularly to the main flow direction On this topic, previous research works showed that the average macro-scopic tortuosity of flow paths was lower during flow of shearthinning and yield stress fluids as compared to the flow of a Newtonian fluids, both in rough-walled fractures [13] and 2D porous with varying levels of microstructural disorder media [14]. However, the conclusions of these works have not yet been extended to the case of 3D porous media, which is mainly due to the demanding requirements in terms of computational resources to perform DNS for the flow of complex fluids.…”

Upscaling non-Newtonian rheological fluid properties from pore-scale to Darcy’s scale

“…The reason could be [11] (i) the porous medium has complex geometry compared to rheometers; (ii) the presence of many expansion and contraction in the porous medium expose polymer to the various amount of shear stress [3]; (iii) mechanical retention and adsorption of the polymer change the geometry of the porous medium. To describe polymeric fluid behaviour in porous medium, apparent viscosity or Darcy viscosity is a commonly used terms in the literature [11,3,12,13,14].…”