Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms

  • Avraam D
  • Payatakes A
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Abstract

A parametric experimental investigation of the coupling effects during
steady-state two-phase flow in porous media was carried out using
a large model pore network of the chamber-and-throat type, etched
in glass. The wetting phase saturation,S1, the capillary number,Ca,
and the viscosity ratio,k, were changed systematically, whereas the
wettability (contact angleθe), the coalescence factorCo, and the
geometrical and topological parameters were kept constant. The fluid
flow rate and the pressure drop were measured independently for each
fluid. During each experiment, the pore-scale flow mechanisms were
observed and videorecorded, and the mean water saturation was determined
with image analysis. Conventional relative permeability, as well
as generalized relative permeability coefficients (with the viscous
coupling terms taken explicitly into account) were determined with
a new method that is based on a B-spline functional representation
combined with standard constrained optimization techniques. A simple
relationship between the conventional relative permeabilities and
the generalized relative permeability coefficients is established
based on several experimental sets. The viscous coupling (off-diagonal)
coefficients are found to be comparable in magnitude to the direct
(diagonal) coefficients over board ranges of the flow parameter values.
The off-diagonal coefficients (krij /Μj) are found to be unequal,
and this is explained by the fact that, in the class of flows under
consideration, microscopic reversibility does not hold and thus the
Onsager-Casimir reciprocal relation does not apply. Thecoupling indices
are introduced here; they are defined so that the magnitude of each
coupling index is the measure of the contribution of the coupling
effects to the flow rate of the corresponding fluid. A correlation
of the coupling indices with the underlying flow mechanisms and the
pertinent flow parameters is established.

Author-supplied keywords

  • coupling indices
  • ganglion dynamics
  • relative permeabilities
  • two-phase flow
  • viscous coupling

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