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Effect of hydrodynamic forces on capillary pressure and relative permeability

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Because of the influence of hydrodynamic forces, the capillary pressure measured at static equilibrium may be different from that which pertains during flow. If such is the case, it may not be permissible to use steady-state relative permeabilities to predict unsteady-state flow. In this paper, the idea that the total flux of a given phase may be partitioned into several individual fluxes, together with a new pressure difference equation, is used to explore the possible impact that the hydrodynamic forces might have on capillary pressure and, as a consequence, relative permeability. This exploration reveals that, provided the pressure difference equation is implemented properly, capillarity has no impact on the relative permeability curves for the homogeneous, water-wet porous media considered. Moreover, it is demonstrated that, if the hydrodynamic effects are neglected, very little error is introduced into the analysis.

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a :

parameter in Equation (25)

c i :

constant of proportionality for phasei;i=1, 2

k :

absolute permeability; m2

k i :

effective permeability to phasei;i=1, 2, m2

k ij :

generalized effective permeability for phasei;i, j=1, 2, m2

k ri :

k i/k =relative permeability to phasei;i=1, 2

M r :

endpoint mobility ratio

p d :

p 2p 1=difference in pressure between two flowing phases, N/m2

p i :

pressure for phasei;i=1, 2, N/m2

P c :

static capillary pressure, N/m2

R 12 :

function defined by Equation (25)

S :

normalized saturation

u :

total flux, m3/m2/s

u i :

flux of phasei;i=1, 2, m3/m2/s

x :

distance in direction of flow, m

ε R :

relative error

λ c :

mobility associated with flux due to imbibition, m2/Pa·s

λ i :

k i /Μ i =mobility of phasei;i=1, 2, m2/Pa·s

λ ij :

k ij /Μ j =generalized mobility of phasei;i, j=1, 2, m2/Pa·s

Μ i :

viscosity of phasei;i=1, 2, Pa·s


countercurrent flow


pure countercurrent flow


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Bentsen, R.G. Effect of hydrodynamic forces on capillary pressure and relative permeability. Transp Porous Med 17, 121–132 (1994). https://doi.org/10.1007/BF00624728

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Key words

  • Capillary pressure
  • relative permeability
  • immiscible
  • two-phase flow
  • hydrodynamic forces