On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field
Monotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional n...
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2024-10-01
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| author | Yaniv Edery Shaul Sorek |
| author_facet | Yaniv Edery Shaul Sorek |
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| description | Monotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>, from the macroscopic Darcian-based flow equation. The derived <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> theoretically classifies the flow equation to be hyperbolic or parabolic, according to the hydraulic head gradient length scale, and the hydraulic conductivity slope and mean. This flow classification is explored numerically, while its effect on the transport is explored by Lagrangian particle tracking (LPT). The numerical simulations show the transition from hyperbolic to parabolic flow, which manifests in the LPT transition from advective to dispersive transport. This classification is also applied to an interpolation of tilled soil from the literature, showing that, indeed, there is a transition in the transport. These results indicate that in a monotonously stratified porous medium, very low conducting (impervious) formations may still allow unexpected contamination leakage, specifically for the parabolic case. This classification of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> to the flow and transport pattern provides additional insight without solving the flow or transport equation only by knowing the hydraulic conductivity distribution. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2024-10-01 |
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| series | Entropy |
| spelling | doaj-art-b9fc92d1a5454d9f89651a9ea3f73f6c2024-11-26T18:02:57ZengMDPI AGEntropy1099-43002024-10-01261190410.3390/e26110904On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity FieldYaniv Edery0Shaul Sorek1Faculty of Civil and Environmental Engineering, Technion, Haifa 32000, IsraelZuckerberg Institute for Water Research, J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion 8499000, IsraelMonotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>, from the macroscopic Darcian-based flow equation. The derived <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> theoretically classifies the flow equation to be hyperbolic or parabolic, according to the hydraulic head gradient length scale, and the hydraulic conductivity slope and mean. This flow classification is explored numerically, while its effect on the transport is explored by Lagrangian particle tracking (LPT). The numerical simulations show the transition from hyperbolic to parabolic flow, which manifests in the LPT transition from advective to dispersive transport. This classification is also applied to an interpolation of tilled soil from the literature, showing that, indeed, there is a transition in the transport. These results indicate that in a monotonously stratified porous medium, very low conducting (impervious) formations may still allow unexpected contamination leakage, specifically for the parabolic case. This classification of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>h</mi><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> to the flow and transport pattern provides additional insight without solving the flow or transport equation only by knowing the hydraulic conductivity distribution.https://www.mdpi.com/1099-4300/26/11/904flow and transport through a monotonously stratified porous mediumLagrangian particle tracking (LPT)stochasticity and dispersion of transport through a monotonously stratified porous medium |
| spellingShingle | Yaniv Edery Shaul Sorek On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field Entropy flow and transport through a monotonously stratified porous medium Lagrangian particle tracking (LPT) stochasticity and dispersion of transport through a monotonously stratified porous medium |
| title | On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field |
| title_full | On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field |
| title_fullStr | On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field |
| title_full_unstemmed | On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field |
| title_short | On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field |
| title_sort | on the scaling of transport phenomena at a monotonously changing hydraulic conductivity field |
| topic | flow and transport through a monotonously stratified porous medium Lagrangian particle tracking (LPT) stochasticity and dispersion of transport through a monotonously stratified porous medium |
| url | https://www.mdpi.com/1099-4300/26/11/904 |
| work_keys_str_mv | AT yanivedery onthescalingoftransportphenomenaatamonotonouslychanginghydraulicconductivityfield AT shaulsorek onthescalingoftransportphenomenaatamonotonouslychanginghydraulicconductivityfield |