[case] CubicLawPermeability

Hydraulic aperture equals the mechanical aperture s.t. multiplication of the permeability by the mechanical aperture yields the cubic law. The volumetric flux of incompressible fluid flow in a laminar regime within a fracture consisting of two parallel and smooth surfaces is given by the cubic law:

\[ Q = W/(u L) b^3/12 \Delta p,\]

where, \(Q\) is the volumetric flux normal to the flow direction, \(W\) is the fracture width, \(u\) is the fluid viscosity, \(L\) is the fracture length, \(p\) is the fluid pressure, and \(b\) is the fracture hydraulic aperture.

In the context of Darcy’s law, the fracture permeability becomes:

\[ k_f = b^2/12,\]


Ref: He, Xupeng, et al. "A corrected cubic law for single-phase laminar flow through rough-walled fractures." Advances in Water resources 154 (2021): 103984.

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