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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v14.i12.30
pages 1077-1086

DEPENDENCE OF SINGLE-PHASE AND MULTIPHASE PERMEABILITY ON CAPILLARY PRESSURE: A UNIFIED APPROACH

B. Markicevic
Department of Mechanical Engineering, Kettering University, Flint, Michigan 48504, USA
Ned Djilali
Institute for Integrated Energy Systems and Department of Mechanical Engineering, University of Victoria, PO Box 1700, Victoria, BC V8W 2Y2, Canada

ABSTRACT

We present a formulation to predict simultaneously the porous medium (single-phase) permeability, and the multiphase flow permeability of a non-wetting liquid in the limit of slow flow. The formulation is based on a new set of mixing rules in which weighting coefficients are obtained from the capillary pressure in the breakthrough point. These weights are calculated by mixing the harmonic average capillary pressure of the actual heterogeneous sample and the capillary pressure of a corresponding homogeneous medium. The porous medium (single phase) and the phase permeability are, on the other hand, found using two length scales: the first determined from the capillary pressure in the breakthrough point and the second calculated again using the homogeneous sample. This formulation is successfully validated for a slow drainage using capillary network simulations based on the invasion percolation mechanism with phase trapping. In the numerical simulations, both network heterogeneity and network size are varied. The simulations reveal that with increasing medium heterogeneity, the porous medium permeability (single phase) decreases, whereas for multiphase flow, the mobile phase permeability and the capillary pressure increase. For a sufficiently large domain (network) size, all three parameters are independent of domain size. The analytical mixing rules capture all of these dependencies, and very good agreement between analytical and numerical results is found.


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