Percolation model of relative permeability hysteresis

Journal of Applied Mechanics and Technical Physics,  2013, Volume 54, Issue 3, pp 423-432.

V. V. Kadet, A. M. Galechyan

1502. Gubkin Russian State University of Oil and Gas, Moscow, 119991, Russia



A mathematical model of relative permeability hysteresis in drainage and imbibition is constructed on the basis of percolation theory. It is shown that the results are in qualitatively agreement with experimental data. The proposed method can be used to calculate the relative permeability in any a porous medium based only on data on the mineral composition and the pore radius distribution f(r). Experimental studies with core
samples to determine the dependence of the relative permeability on water saturation require considerable time, in contrast to the experimental determination of the dependence f(r). Classifying the types of relative permeability
hysteresis for samples with different mineralogical composition and determining the parameters κ and α for these samples, one can experimentally determine the dependence f(r) and calculate the relative permeability hysteresis using the above procedure.


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