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Development of numerical model to describe water transfer in hygroscopic soil: use of a new method based on off-center upstream principle for convective flux

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Abstract

This manuscript is focused on the mechanisms of water evaporation and the phenomena affecting its migration toward the groundwater. The objective is to estimate the essential parameters which govern the diffusion transfer. The phenomenological parameters used in the model are obtained experimentally and the mass transfer equations have been solved by adopting finite volume method for equations discretization and the eccentric upstream diagram method specifically for convection. The numerical results obtained are in good agreement with experimental results. These results show that the gap between the simulated and the experimental kinetics is less than 2% at the beginning of transfer mechanisms. This gap will decrease very quickly to reach zero. The model can also suitably reproduce water content profiles on the length of the soil column. The difference between experiment and numerical profiles range from 1 to 5% in the upper part and around 2% in the bottom part of the column. Finally we can notice that hygroscopic effects of arid soil can change the transport behavior of water and affect its convective transfer.

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Abbreviations

\({a}_{l}\) :

Liquid activity –

\({D}_{va}\) :

Diffusion coefficient of vapor in free air m2 s−1

\({D}_{v}\) :

Diffusion coefficient of vapor in soil m2 s−1

\({\overrightarrow{F}}_{C}\) :

Capillary forces N

\(\overrightarrow{F}\) :

Gravitational forces N

G :

Gravity acceleration m s−2

\({J}_{l}\) :

Diffusion flux of liquid kg m−2 s−1

\({J}_{v}\) :

Diffusion flux of vapor kg m−2 s−1

\({K}_{ns}\) :

Coefficient of permeability m s−1

\({K}_{sat}\) :

Coefficient of saturated permeability m s−1

\(L\) :

Evaporation coefficient of water kg K s m−5

\({L}_{g}\) :

Average length m

\({L}_{s}\) :

Straight-line length m

\({M}_{l}\) :

Molar weight of liquid kg mol−1

\({P}_{g}\) :

Total pressure of gas Pa

\({P}_{l}\) :

Partial pressure of liquid Pa

\({P}_{v}\) :

Vapor pressure Pa

\({P}_{veq}\) :

Equilibrium vapor pressure Pa

\({P}_{vsat}\) :

Saturated vapor pressure Pa

\(R\) :

Ideal gas constant J K−1 mol−1

s :

Suction Pa

\({s}_{\mathrm{i}}\) :

Intake suction Pa

\({s}_{res}\) :

Residual suction Pa

T :

Temperature of the system K

\({v}_{l}\) :

Liquid velocity m s−1

w :

Water content –

\({w}_{eq}\) :

Equilibrium water content –

\({w}_{r}\) :

Residual water content –

\({w}_{sat}\) :

Saturated water content –

\(\nabla\) :

Divergence operator –

\(\lambda\) :

Empirical parameter –

\(\phi\) :

Porosity of soil %

\({\phi }_{g}\) :

Volume fraction of gas –

\({\rho }_{l}\) :

Apparent density of liquid kg m−3

\({\rho }_{s}\) :

Apparent density of soil kg m−3

\({\rho }_{l}^{*}\) :

Real density of liquid kg m−3

\({\rho }_{s}^{*}\) :

Real density of soil kg m−3

\({\rho }_{v}^{*}\) :

Real density of water vapor kg m−3

\({\widehat{\rho }}_{l}\) :

Source or sink term of liquid kg m−3 s−1

\({\widehat{\rho }}_{v}\) :

Source or sink term of vapor kg m−3 s−1

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Authors and Affiliations

  1. Laboratoire de Physique et de Chimie de l’environnement, UFR-SEA, Université Joseph KI-ZERBO, UFR-SEA/LPCE, 03 BP 7021, Ouaga 03, Burkina Faso

    Samuel Ouoba & Alfa Oumar Dissa

  2. GERME & TI, Université Nazi Boni, Bobo Dioulasso, Burkina Faso

    François Ouedraogo

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  1. Samuel Ouoba
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Contributions

S Ouoba supervised the research and designed the experiments. S Ouoba, AO Dissa and F Ouedraogo analyzed data and co-wrote the paper.

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Correspondence to Samuel Ouoba.

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Ouoba, S., Dissa, A.O. & Ouedraogo, F. Development of numerical model to describe water transfer in hygroscopic soil: use of a new method based on off-center upstream principle for convective flux. Heat Mass Transfer 59, 567–581 (2023). https://doi.org/10.1007/s00231-022-03277-0

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