Preprints
https://doi.org/10.5194/hess-2022-298
https://doi.org/10.5194/hess-2022-298
 
17 Oct 2022
17 Oct 2022
Status: this preprint is currently under review for the journal HESS.

Technical note: Displacement variance of a solute particle in heterogeneous confined aquifers with random aquifer thickness fields

Ching-Min Chang1, Chuen-Fa Ni1, Chi-Ping Lin2, and I-Hsien Lee2 Ching-Min Chang et al.
  • 1Graduate Institute of Applied Geology, National Central University, Taoyuan, Taiwan
  • 2Center for Environmental Studies, National Central University, Taoyuan, Taiwan

Abstract. In this work, the problem of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is analyzed in a stochastic framework. A general stochastic methodology for deriving the variance of the displacement of a solute particle is given based on the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation. The variability in solute displacement is attributed to the variability in hydraulic conductivity and aquifer thickness. Explicit results for the solute displacement variance in the mean flow direction are obtained assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances.

Ching-Min Chang et al.

Status: open (until 12 Dec 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-298', Anonymous Referee #1, 08 Nov 2022 reply
  • AC1: 'Comment on hess-2022-298', Chuen-Fa Ni, 11 Nov 2022 reply

Ching-Min Chang et al.

Ching-Min Chang et al.

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Short summary
A general stochastic methodology is developed to describe the variability of regional-scale solute transport. Explicit results for the displacement variance in the mean flow direction are obtained for the case where the random fields of log conductivity and log thickness of the confined aquifer are second-order stationary. The stochastic theory presented here improves quantification of the variance of the solute displacement in natural confined aquifers of random thickness fields.