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Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures
Author(s) -
Cvetkovic Vladimir,
Gotovac Hrvoje
Publication year - 2013
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2013wr014213
Subject(s) - flow (mathematics) , gaussian , matrix (chemical analysis) , advection , diffusion , mathematics , residence time (fluid dynamics) , fluid dynamics , fracture (geology) , mechanics , geology , fluid queue , statistical physics , geometry , geotechnical engineering , statistics , physics , materials science , thermodynamics , queueing theory , quantum mechanics , composite material
Diffusive mass transfer in rock fractures is strongly affected by fluid flow in addition to material properties. The flow‐dependence of matrix diffusion is quantified by a random variable (“transport resistance”) denoted as β [ T / L ] and computed from the flow field by following advection trajectories. The numerical methodology for simulating fluid flow is mesh‐free, using Fup basis functions. A generic statistical model is used for the transmissivity field, featuring three correlation structures: (i) highly connected non‐multi‐Gaussian; (ii) poorly connected (or disconnected) non‐multi‐Gaussian; and (iii) multi‐Gaussian. The moments of β are shown to be linear with distance, irrespective of the structure, after approximately 10 integral scales of ln T . Percentiles of β are found to be linear with the mean β when considering all three structures. Taking advantage of this property, a potentially useful relationship is presented between β percentiles and the fracture mean water residence time that integrates all structures with high variability; it can be used in discrete fracture network simulations where T statistical data on individual fractures are not available.