A fractional derivative perspective on transient pulse test for determining the permeability of rocks. (January 2019)

• Record Type: Journal Article
• Authors: Yang, S.; Zhou, H.W.; Zhang, S.Q.; Ren, W.G.
• Is Part Of: International journal of rock mechanics and mining sciences. Volume 113(2018)
• Page Start: 92
• Page End: 98
• Publication Date: 2019-01
• Subjects: Transient pulse test -- Permeability -- Fractional derivative -- Mittag-Leffler law -- Granite; Rock mechanics -- Periodicals; Soil mechanics -- Periodicals; Mining engineering -- Periodicals; Roches, Mécanique des -- Périodiques; Sols, Mécanique des -- Périodiques; Technique minière -- Périodiques; 624.151305
• DOI: 10.1016/j.ijrmms.2018.11.013
• Languages: English
• ISSNs: 1365-1609

Abstract

Abstract: This work presents a fractional relaxation equation that, in the full respect of the time-dependent behavior of flow transport and under appropriate simplifying assumptions, leads to an accurate description of the differential pressure decay in transient pulse test by the Mittag-Leffler function. The permeability of granite at different water pressures is measured. Moreover, the results of experimental data interpretation illustrate that the transient pulse test based on the Mittag-Leffler law fitting provides a much better determination of permeability than the conventional exponential decay model. The relationship between the presented fractional relaxation equation and fractional diffusion equation is also discussed in the framework of continuous time random walk.