{"id":92208,"date":"2026-04-18T13:00:21","date_gmt":"2026-04-18T13:00:21","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92208"},"modified":"2026-04-13T22:59:41","modified_gmt":"2026-04-13T22:59:41","slug":"pollutev10-example-10-landfill-variable-advective-dispersive-transport","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-10-landfill-variable-advective-dispersive-transport\/","title":{"rendered":"POLLUTEv10 Example 10: Time-Varying Advective\u2013Dispersive Transport from a Landfill"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-modeling-hydraulic-gradient-reversal-with-variable-properties\">Modeling Hydraulic Gradient Reversal with Variable Properties<\/h2>\n\n\n\n<p><strong>POLLUTEv10 Example 10<\/strong> demonstrates one of the most powerful capabilities of the model: simulating <strong>time-varying transport conditions<\/strong> using the <strong>Variable Properties<\/strong> feature.<\/p>\n\n\n\n<p>This scenario captures a realistic landfill lifecycle where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Early operation creates a <strong>hydraulic trap (inward gradient)<\/strong><\/li>\n\n\n\n<li>Later conditions cause a <strong>gradient reversal<\/strong><\/li>\n\n\n\n<li>Contaminant transport shifts from <strong>contained \u2192 released<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Problem Overview<\/h2>\n\n\n\n<p>This example models:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>landfill with finite contaminant mass<\/strong><\/li>\n\n\n\n<li>A <strong>conservative species<\/strong> (no sorption, Kd = 0)<\/li>\n\n\n\n<li>A <strong>leachate collection system<\/strong> that is later discontinued<\/li>\n\n\n\n<li>A <strong>clay liner overlying an aquifer<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Key Phases<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>0\u201320 years<\/strong>\n<ul class=\"wp-block-list\">\n<li>Leachate collection active<\/li>\n\n\n\n<li>Inward gradient \u2192 <strong>hydraulic trap<\/strong><\/li>\n\n\n\n<li>No contaminant escape<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>20\u201330 years<\/strong>\n<ul class=\"wp-block-list\">\n<li>Collection stops<\/li>\n\n\n\n<li>Leachate mound builds<\/li>\n\n\n\n<li>Gradient begins to reverse<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>>30 years<\/strong>\n<ul class=\"wp-block-list\">\n<li>Outward flow established<\/li>\n\n\n\n<li>Contaminant begins migrating into aquifer<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Conceptual Model<\/h2>\n\n\n\n<p>The system includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>4 m thick clay layer<\/strong> beneath the landfill<\/li>\n\n\n\n<li>An <strong>underlying aquifer<\/strong><\/li>\n\n\n\n<li>A <strong>finite contaminant source<\/strong> within the landfill<\/li>\n\n\n\n<li>Time-dependent <strong>Darcy velocities (va and vb)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The most critical behavior is the <strong>reversal of hydraulic gradient<\/strong>, which fundamentally changes transport direction.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Key Equations<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Hydrodynamic Dispersion<\/h3>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>D<\/mi><mo>=<\/mo><msub><mi>D<\/mi><mi>m<\/mi><\/msub><mo>+<\/mo><mi>\u03b1<\/mi><mfrac><msub><mi>v<\/mi><mi>a<\/mi><\/msub><mi>n<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">D = D_m + \\alpha \\frac{v_a}{n}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D<\/strong> = hydrodynamic dispersion coefficient<\/li>\n\n\n\n<li><strong>Dm<\/strong> = molecular diffusion coefficient<\/li>\n\n\n\n<li><strong>\u03b1<\/strong> = dispersivity<\/li>\n\n\n\n<li><strong>va<\/strong> = Darcy velocity<\/li>\n\n\n\n<li><strong>n<\/strong> = porosity<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Outflow Velocity Relationship<\/h3>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>v<\/mi><mi>b<\/mi><\/msub><mo>=<\/mo><mn>2<\/mn><mo>+<\/mo><mn>200<\/mn><mo>\u22c5<\/mo><msub><mi>v<\/mi><mi>a<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">v_b = 2 + 200 \\cdot v_a<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At <strong>30 years<\/strong>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>v<\/mi><mi>b<\/mi><\/msub><mo>=<\/mo><mn>6.2<\/mn><mtext>\u2009<\/mtext><mtext>m\/a<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">v_b = 6.2 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Input Parameters<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><th>Units<\/th><\/tr><\/thead><tbody><tr><td>Darcy Velocity (va)<\/td><td>Variable<\/td><td>m\/a<\/td><\/tr><tr><td>Diffusion Coefficient (Dm)<\/td><td>0.02<\/td><td>m\u00b2\/a<\/td><\/tr><tr><td>Distribution Coefficient<\/td><td>0.0<\/td><td>cm\u00b3\/g<\/td><\/tr><tr><td>Dispersivity (va &lt; 0)<\/td><td>0.0<\/td><td>m<\/td><\/tr><tr><td>Dispersivity (va &gt; 0)<\/td><td>0.4<\/td><td>m<\/td><\/tr><tr><td>Soil Porosity (n)<\/td><td>0.4<\/td><td>&#8211;<\/td><\/tr><tr><td>Dry Density<\/td><td>1.5<\/td><td>g\/cm\u00b3<\/td><\/tr><tr><td>Soil Thickness<\/td><td>4.0<\/td><td>m<\/td><\/tr><tr><td>Sub-layers<\/td><td>12<\/td><td>&#8211;<\/td><\/tr><tr><td>Source Concentration<\/td><td>1000<\/td><td>mg\/L<\/td><\/tr><tr><td>Leachate Height (Hr)<\/td><td>7.5<\/td><td>m<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Aquifer Properties<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><th>Units<\/th><\/tr><\/thead><tbody><tr><td>Length (L)<\/td><td>200<\/td><td>m<\/td><\/tr><tr><td>Width (W)<\/td><td>1<\/td><td>m<\/td><\/tr><tr><td>Thickness (h)<\/td><td>1<\/td><td>m<\/td><\/tr><tr><td>Porosity (nb)<\/td><td>0.3<\/td><td>&#8211;<\/td><\/tr><tr><td>Outflow Velocity<\/td><td>Variable<\/td><td>m\/a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Finite Mass Source Calculation<\/h2>\n\n\n\n<p>The contaminant mass per unit area:<\/p>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>m<\/mi><mrow><mi>t<\/mi><mi>c<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>0.002<\/mn><mo>\u00d7<\/mo><mn>600<\/mn><mo>\u00d7<\/mo><mn>6.25<\/mn><mo>=<\/mo><mn>7.5<\/mn><mtext>\u2009<\/mtext><msup><mtext>kg\/m<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">m_{tc} = 0.002 \\times 600 \\times 6.25 = 7.5 \\, \\text{kg\/m}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>This yields the <strong>reference leachate height<\/strong>:<\/p>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>H<\/mi><mi>r<\/mi><\/msub><mo>=<\/mo><mn>7.5<\/mn><mtext>\u2009<\/mtext><mtext>m<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">H_r = 7.5 \\, \\text{m}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>This ensures the model represents a <strong>finite, depleting contaminant source<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Time-Varying Flow Conditions<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Infiltration &amp; Collection<\/h3>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>Q<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><msub><mi>q<\/mi><mi>o<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>v<\/mi><mi>a<\/mi><\/msub><mo>=<\/mo><mn>0.3<\/mn><mo>\u2212<\/mo><msub><mi>v<\/mi><mi>a<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Q_c = q_o &#8211; v_a = 0.3 &#8211; v_a<\/annotation><\/semantics><\/math>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>qo = 0.3 m\/a<\/strong> (infiltration through cover)<\/li>\n\n\n\n<li><strong>va = exfiltration through base<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Variable Dispersivity Behavior<\/h2>\n\n\n\n<p>A key feature of this example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>va &lt; 0 (inward flow):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Dispersivity = 0<\/li>\n\n\n\n<li>Transport = diffusion only<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>va > 0 (outward flow):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Dispersivity = 0.4 m<\/li>\n\n\n\n<li>Transport = advection + dispersion<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>This reflects real-world physics:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>No plume spreading during containment<\/li>\n\n\n\n<li>Significant plume spreading after release<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-graphical-output-concentration-vs-time\">Graphical Output: Concentration vs Time<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1007\" height=\"910\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-21.jpg\" alt=\"\" class=\"wp-image-92209\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-21.jpg 1007w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-21-300x271.jpg 300w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-21-768x694.jpg 768w\" sizes=\"auto, (max-width: 1007px) 100vw, 1007px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-pdf-report\">PDF Report<\/h2>\n\n\n<div class=\"ead-preview\"><div class=\"ead-document\" style=\"position: relative;padding-top: 90%\"><div class=\"ead-iframe-wrapper\"><iframe src=\"\/\/docs.google.com\/viewer?url=https%3A%2F%2Fgaeatech.com%2Fknowledge-center%2Fwp-content%2Fuploads%2F2026%2F04%2Fpollute-example10.pdf&amp;embedded=true&amp;hl=en\" title=\"Embedded Document\" 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has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Key Insights<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Hydraulic traps are temporary<\/strong> if conditions change<\/li>\n\n\n\n<li><strong>Leachate collection systems are critical<\/strong> for containment<\/li>\n\n\n\n<li>Gradient reversal can trigger <strong>sudden contaminant release<\/strong><\/li>\n\n\n\n<li>Dispersion becomes significant only during <strong>outward flow<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Importance of Sub-Layer Resolution<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"has-small-font-size\">Accuracy depends on the number of sub-layers when using Variable Properties.<\/p>\n<\/blockquote>\n\n\n\n<p>Why?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time-dependent parameters require <strong>fine numerical resolution<\/strong><\/li>\n\n\n\n<li>Velocity reversals create <strong>sharp transitions<\/strong><\/li>\n\n\n\n<li>Coarse meshes may miss key behaviors<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Best Practice<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>\u2265 12 sub-layers<\/strong> (minimum)<\/li>\n\n\n\n<li>Increase for sensitivity analysis<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Practical Applications<\/h2>\n\n\n\n<p>This example is highly relevant for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Landfill design and risk assessment<\/strong><\/li>\n\n\n\n<li><strong>Long-term contaminant migration modeling<\/strong><\/li>\n\n\n\n<li><strong>Leachate collection system evaluation<\/strong><\/li>\n\n\n\n<li><strong>Regulatory compliance studies<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p>POLLUTEv10 Example 10 highlights the complexity of <strong>time-dependent transport systems<\/strong>, demonstrating that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Flow conditions can <strong>change dramatically over time<\/strong><\/li>\n\n\n\n<li>Containment strategies must consider <strong>future scenarios<\/strong><\/li>\n\n\n\n<li>Variable properties modeling is essential for <strong>realistic predictions<\/strong><\/li>\n<\/ul>\n\n\n\n<p>This example is a powerful tool for understanding how <strong>engineering controls and hydrogeology interact<\/strong> to influence contaminant fate.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Modeling Hydraulic Gradient Reversal with Variable Properties POLLUTEv10 Example 10 demonstrates one of the most powerful capabilities of the model: simulating time-varying transport conditions using the Variable Properties feature. This scenario captures a realistic landfill lifecycle where: Problem Overview This example models: Key Phases Conceptual Model The system includes: The most critical behavior is the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92211,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1632],"tags":[1652,501,24,469,1665,821,675,1666,1636,1627],"class_list":["post-92208","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-pollute-examples","tag-advective-dispersive-transport","tag-contaminant-transport","tag-environmental-engineering","tag-groundwater-modeling","tag-hydraulic-gradient","tag-hydrogeology","tag-landfill-modeling","tag-leachate","tag-numerical-modeling","tag-pollutev10"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - 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