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<p>A general analytical solution is worked out for the classical one-dimensional steady-state advection dispersion equation (ADE) for a heterogeneous soil with a compressible advective fluid. The solution can account for any well-defined boundary conditions at the ends of a transport space and can also consider any arbitrary nonlinear coefficients in the decay and sorption terms of the ADE. It can also accommodate any user specified spatial variations of the parameters of the ADE, including spatial variations of the degradation rates in the liquid and solid phases as well as spatial variations of the source term in the liquid phase. The validity of the proposed solution is extensively checked by comparing with analytical and experimental works of others for a few relatively simple transport situations. Also, a numerical check on it has also been carried out utilizing the HYDRUS-1D numerical codes. The study shows that advection dispersion transport of a solute in a heterogeneous soil may be greatly impacted by the spatial variations of the soil-hydraulic parameters of the soil; thus, the assumption of soil homogeneity in a heterogeneous soil for modelling solute transport through it may lead to substantial modelling errors at times. The developed solution also shows that steady-state solute transport dynamics in a soil is quite sensitive to the parameters of the ADE like advective velocity, partition coefficient, degradation rates in the liquid and solid phases and zero order production rate, and that a slight change in either of these parameters may affect the transport process on the soil in a significant way. The study has revealed that solute transport dynamics with a compressible fluid in many instances may be significantly different from that with an incompressible one. The study also showed that the nature of the sorption isotherm associated with a transport process alone may affect it in a significant way. Further, the study, expectedly, has also shown that the solute concentration profile of a transport process is fairly sensitive to the Peclet number associated with it and that the concentration profile of an advection dominated process may be substantially higher than that of a diffusion dominated process.</p>

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An analytical solution of the one-dimensional steady-state advection-dispersion equation of a compressible fluid for a heterogeneous soil

  • 期刊论文

  • 发表日期：

    2025年1月9日

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  • Bhargov Phukan,
  • Gautam Barua

摘要

A general analytical solution is worked out for the classical one-dimensional steady-state advection dispersion equation (ADE) for a heterogeneous soil with a compressible advective fluid. The solution can account for any well-defined boundary conditions at the ends of a transport space and can also consider any arbitrary nonlinear coefficients in the decay and sorption terms of the ADE. It can also accommodate any user specified spatial variations of the parameters of the ADE, including spatial variations of the degradation rates in the liquid and solid phases as well as spatial variations of the source term in the liquid phase. The validity of the proposed solution is extensively checked by comparing with analytical and experimental works of others for a few relatively simple transport situations. Also, a numerical check on it has also been carried out utilizing the HYDRUS-1D numerical codes. The study shows that advection dispersion transport of a solute in a heterogeneous soil may be greatly impacted by the spatial variations of the soil-hydraulic parameters of the soil; thus, the assumption of soil homogeneity in a heterogeneous soil for modelling solute transport through it may lead to substantial modelling errors at times. The developed solution also shows that steady-state solute transport dynamics in a soil is quite sensitive to the parameters of the ADE like advective velocity, partition coefficient, degradation rates in the liquid and solid phases and zero order production rate, and that a slight change in either of these parameters may affect the transport process on the soil in a significant way. The study has revealed that solute transport dynamics with a compressible fluid in many instances may be significantly different from that with an incompressible one. The study also showed that the nature of the sorption isotherm associated with a transport process alone may affect it in a significant way. Further, the study, expectedly, has also shown that the solute concentration profile of a transport process is fairly sensitive to the Peclet number associated with it and that the concentration profile of an advection dominated process may be substantially higher than that of a diffusion dominated process.