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A continuous time random walk approach to transient flow in heterogeneous porous media
Author(s) -
Cortis Andrea,
Knudby Christen
Publication year - 2006
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 - 10.1029/2006wr005227
Subject(s) - continuous time random walk , random walk , anomalous diffusion , diffusion , porous medium , transient (computer programming) , statistical physics , transient flow , interpretation (philosophy) , diffusion equation , diffusion process , flow (mathematics) , work (physics) , convection–diffusion equation , mathematics , mechanics , physics , porosity , computer science , materials science , thermodynamics , statistics , engineering , meteorology , innovation diffusion , operations management , metric (unit) , knowledge management , composite material , operating system , surge , programming language
We propose a new physical interpretation of the diffusion process for the piezometric head h ( x , t ) in heterogeneous aquifers based on the continuous time random walk (CTRW) theory. For the typical heterogeneities considered in this work, we find that a CTRW based diffusion equation for h ( x , t ) provides better fits to the transient flow simulations than the classical diffusion equation (DE). The DE is found to be a special case of the CTRW diffusion equation. The results of this work have clear implications for the interpretation of pumping tests and what information can be extracted from them.