Fractal Prediction Model of Spontaneous Imbibition Rate

• Published in: Transport in porous media Vol. 91; no. 2; pp. 363 - 376
• Main Authors: Li, Kewen, Zhao, Haiyang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2012; Springer; Springer Nature B.V
• Subjects: Capillary pressure; Chalk; Civil Engineering; Classical and Continuum Physics; Data recovery; Dimensional measurements; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Exact sciences and technology; Fractal analysis; Fractal geometry; Fractal models; Fractals; Geotechnical Engineering & Applied Earth Sciences; Geysers; Greywacke; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Imbibition; Industrial Chemistry/Chemical Engineering; Intrusion; Mathematical models; Media; Porous media; Rocks; Sandstone; Sedimentary rocks; Spontaneous; Stone; Fractal dimension; Spontaneous imbibition; Production model; experimental studies; carbonate rocks; mercury; mathematical models; permeability; fractal dimension; ground water; recovery; transport; sandstone; intrusions; fractals; natural gas; sedimentary rocks; water-rock interaction; chalk; prediction; capillary pressure; porous media; clastic rocks
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-011-9848-0

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.