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Capillary effects in steady-state flow in heterogeneous cores

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Abstract

Effects of capillary heterogeneity at the macroscopic scale have previously been analyzed for static conditions or in the context of outflow end-effects. This paper presents a systematic study for the case of one-dimensional, steady-state flow, that complements recent work on transient displacement. We consider the saturation response to various forms of heterogeneity. Included are analytical results for certain model cases, some general results, and numerical solutions for variously correlated spatial variations. The sensitivity to process parameters, such as rate, heterogeneity length scale and correlation, is studied. Physical interpretations are offered and potential applications in the estimation of heterogeneity are discussed.

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Abbreviations

F :

fractional flow, dimensionless

f w :

fractional flow, dimensionless

J :

Leverett function, dimensionless

k :

absolute permeability, L2

L :

heterogeneity length, L

M :

mobility ratio, dimensionless

p :

pressure, L−1MT−2

q :

flow rate, LT−1

S :

saturation, dimensionless

t :

time, T

u :

normalized water saturation, dimensionless

x :

distance, L

γ:

interfacial tension, MT−2

ε:

macroscopic capillary number, dimensionless

μ :

viscosity, L−1MT−1

τ:

normalized square root of permeability, dimensionless

φ :

porosity, dimensionless

c :

capillary

D :

dimensionless

i :

injection

o :

oil

w :

water

or :

oil residual

ro :

relative to oil

rw :

relative to water

wc :

connate water

+:

downstream

−:

upstream

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Authors and Affiliations

  1. Department of Petroleum Engineering, University of Southern California, 90089-1211, Los Angeles, CA, USA

    Y. C. Yortsos & Jincai Chang

  2. Department of Chemical Engineering, USA

    Y. C. Yortsos

Authors
  1. Y. C. Yortsos
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  2. Jincai Chang
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Yortsos, Y.C., Chang, J. Capillary effects in steady-state flow in heterogeneous cores. Transp Porous Med 5, 399–420 (1990). https://doi.org/10.1007/BF01141993

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  • DOI: https://doi.org/10.1007/BF01141993

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