Fractal model equation for spontaneous imbibition

D. Samayoa, L. A. Ochoa Ontiveros, L. Damián Adame, E. Reyes de Luna, L. Álvarez Romero, G. Romero-Paredes


A new analytic model of fractal imbibition in porous media is derived. The topological Hausdorff dimension is used as a fractal parameter in
the proposed model. The fractal formulation is based on the model introduced by Li and Zhao to predict the production rate by spontaneous
imbibition. Cantor Tartans and Menger sponge fractals are used to simulate fractal porous media with different ramifications. Results of
illustrative examples are presented in the form of a set of curves, which reveal the features of enhanced oil recovery of the model under
consideration. The results are compared with the experimental behaviour found on core samples of previous publications.


Topological Hausdorff dimension, spontaneous imbibition, Cantor Tartan, Menger Sponge

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