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Steady-state two-phase flow through planar and nonplanar model porous media

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Abstract

A comparative experimental study of ‘steady-state’ two-phase flow in two types of model porous media is made to determine the effects of nonplanarity on the flow mechanisms and the mesoscopic flow behavior. The two model porous media have virtually the same pore geometry, but one has a planar network skeleton, whereas the other has a nonplanar (two-layer) skeleton. The latter is a new type of model porous medium that permits detailed visual observation and quantitative measurements without sacrificing the 3D character of the pore network topology. The capillary number and the flowrate ratio are changed systematically, whereas the viscosity ratio and the wettability (contact angle) are kept constant. Conventional relative permeabilities are determined and correlated with the porescale flow phenomena. In the range of parameter values investigated, the flow mechanism observed was ganglion dynamics (intrinsically unsteady, but giving a time-averaged steady-state). The nonplanarity is shown to have small qualitative but significant quantitative effects. In the nonplanar porous medium, the ganglion size distribution is wider, the mean ganglion size larger, and the stranded ganglia are fewer than those in the planar one, under the same flow conditions.

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Abbreviations

A i :

total cross-sectional area of thei model (i=2D or 3D), m2

Ca:

capillary number, Ca=Μ w v w /σ

Bo:

Bond number, Bo=(ρ w −ρ o )gd 2/4σ

d :

diameter of perpendicular throats, m

f d :

number distribution of depths of etched pores

f w :

fraction of wetting phase in the flowing stream,f w =q w /(q w +q o

g :

acceleration of gravity, m/s2

k i :

absolute permeability (i=2D or 3D), m2 or Darcy

k ro :

relative permeability of nonwetting phase

k rw :

relative permeability of wetting phase

l :

length of periodicity (node-to-node distance), m

L :

distance of the pressure taps along the pore network, m

p c :

capillary pressure, Pa

q o :

flowrate of nonwetting phase, m3/s

q w :

flowrate of wetting phase, m3/s

r :

flowrate ratio,q o /q w

S :

mercury saturation

S o :

‘steady-state’ nonwetting phase saturation

S′ o :

modified ‘steady-state’nonwetting phase saturation

S w :

‘steady-stat’ wetting phase saturation

x :

Cartesian coordinate, direction of macroscopic flow

δp :

pressure drop, Pa

θ :

equilibrium contact angle, measured in aqueous phase

κ :

viscosity ratio,κ=Μ o /Μ w

Μ o :

viscosity of nonwetting phase, Pa s

Μ w :

viscosity of wetting phase, Pa s

ρ o :

density of nonwetting phase, kg/m3

ρ w :

density of wetting phase, kg/m3

σ :

interfacial tension, N/m

2D:

planar or two-dimensional or one-layer

3D:

non-planar or three-dimensional or two-layer

ro :

relative to nonwetting phase

rw :

relative to wetting phase

o :

nonwetting (oleic) phase

w :

wetting (aqueous) phase

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Patras and Institute of Chemical Engineering and High Temperature Chemical Processes, PO Box 1414, GR-265 00, Patras, Greece

    D. G. Avraam, G. B. Kolonis, T. C. Roumeliotis, G. N. Constantinides & A. C. Payatakes

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  1. D. G. Avraam
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  2. G. B. Kolonis
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  3. T. C. Roumeliotis
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  4. G. N. Constantinides
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  5. A. C. Payatakes
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Avraam, D.G., Kolonis, G.B., Roumeliotis, T.C. et al. Steady-state two-phase flow through planar and nonplanar model porous media. Transp Porous Med 16, 75–101 (1994). https://doi.org/10.1007/BF01059777

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