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 discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

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

Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsien Lee

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.

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Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsien Lee

Status: closed

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
    • AC2: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
    • AC4: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
  • AC1: 'Comment on hess-2022-298', Chuen-Fa Ni, 11 Nov 2022
  • RC2: 'Comment on hess-2022-298', Anonymous Referee #2, 18 Dec 2022
    • AC3: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
    • AC5: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023

Status: closed

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
    • AC2: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
    • AC4: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
  • AC1: 'Comment on hess-2022-298', Chuen-Fa Ni, 11 Nov 2022
  • RC2: 'Comment on hess-2022-298', Anonymous Referee #2, 18 Dec 2022
    • AC3: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
    • AC5: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsien Lee
Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsien Lee

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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.