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Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations
Author(s) -
Severino Gerardo,
De Bartolo Samuele,
Toraldo Gerardo,
Srinivasan Gowri,
Viswanathan Hari
Publication year - 2012
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 - 10.1029/2012wr012608
Subject(s) - péclet number , porous medium , hydraulic conductivity , mechanics , flow (mathematics) , function (biology) , aquifer , probability density function , anisotropy , gaussian , clogging , envelope (radar) , domain (mathematical analysis) , statistical physics , physics , geotechnical engineering , geology , porosity , mathematics , mathematical analysis , soil science , groundwater , computer science , statistics , history , archaeology , biology , telecommunications , quantum mechanics , evolutionary biology , soil water , radar
Diverging radial flow takes place in a heterogeneous porous medium where the log conductivity Y = ln K is modeled as a stationary random space function (RSF). The flow is steady, and is generated by a fully penetrating well. A linearly sorbing solute is injected through the well envelope, and we aim at computing the average flux concentration ( breakthrough curve ). A relatively simple solution for this difficult problem is achieved by adopting, similar to Indelman and Dagan (1999), a few simplifying assumptions: (i) a thick aquifer of large horizontal extent, (ii) mildly heterogeneous medium, (iii) strongly anisotropic formation, and (iv) large Peclet number. By introducing an appropriate Lagrangian framework, three‐dimensional transport is mapped onto a one‐dimensional domain ( τ , t ) where τ and t represent the fluid travel and current time, respectively. Central for this approach is the probability density function of the RSF τ that is derived consistently with the adopted assumptions stated above. Based on this, it is shown that the travel time can be regarded as a Gaussian random variable only in the far field. The breakthrough curves are analyzed to assess the impact of the hydraulic as well as reactive parameters. Finally, the travel time approach is tested against a forced‐gradient transport experiment and shows good agreement.