Pore Scale Modeling (PSM) for describing fluid flow through porous medium: Is it significantly different from Darcy’s macroscopic-scale modelling?
Variations of fluid velocity and pore-geometry at the pore-scale or nano-scale remains completely different from that at the Darcy’s scale.
Establishing hydraulic connectivity – isolating the dead-end pores – at the pore-scale / nano-scale remains challenging.
Role on roughness of the solid grains associated with the pore-geometry may significantly alter the resultant fluid flow regime between pore-scale and Darcy’s scale fluid flow.
Application of no-slip boundary condition at the pore-scale seems very remote.
Conservation of fluid mass at the pore-scale seems to be complicated.
Darcy’s approach has no relevance with the fluid mass exchange by capillary imbibition at the pore-scale. In addition, wetting properties of the fluid mass and its associated inter-facial tension that govern the shape and migration of the phase boundaries are out of Darcy’s domain.
Dear Suresh,
These are completely different models. At the pore scale you use Stokes or Navier-Stokes equations, at the Darcy scale you use... Darcy :) You can view the latter as an averaged version of the former, which can be obtained e.g. by homogenization techniques. Then you can also derive the Darcy-scale properties of the medium, based on pore-scale properties, including the geometry, roughness, etc.
Besides, I am speaking about the simplest models, where the medium is fully saturated with one fluid phase (e.g. water), which occupies the entire pore space. When you consider more than one phase, or the flow is more rapid, or other processes are taken into account (deformations, adsorption/desorption, heat transfer - to name a few) the situation gets more complex.
Good luck,
Sorin
Sorin,
Suresh is asking about the scale and not about the Darcy model. I think Darcy law can be applied at the pore scale (in general pore scale=mesoscopic scale). At the nanoscale, there are other models that should be incorporated. Nanoscale and pore scales are different.. We use the term macroscopic scale, when we consider domains of larger size than the mesoscopic...
Pore scale modelling uses realistic description of the pores. Normally one solves Stokes flow. Darcy's flow is at the macroscopic scale, you do not have any description of the pores, but you account for their presence by porosity and permeability, which are functions defined at each point of the domain. You can look at the book by Withaker or that of Bear.
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