{"id":92227,"date":"2026-04-16T13:00:49","date_gmt":"2026-04-16T13:00:49","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92227"},"modified":"2026-04-24T01:07:43","modified_gmt":"2026-04-24T01:07:43","slug":"pollutev10-example-13-2d-dispersion-tdast-analytical-comparison","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-13-2d-dispersion-tdast-analytical-comparison\/","title":{"rendered":"POLLUTEv10 Example 13: 2D Plane Dispersion vs Analytical Solution (TDAST)"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-benchmarking-against-analytical-2d-dispersion-models\">Benchmarking Against Analytical 2D Dispersion Models<\/h2>\n\n\n\n<p><strong>POLLUTEv10 Example 13<\/strong> provides another important <strong>model validation case<\/strong>, comparing numerical results from POLLUTEv10 with the analytical solution implemented in <strong>TDAST<\/strong>, developed by P. Javandel and colleagues in 1984.<\/p>\n\n\n\n<p>This example focuses on <strong>2-dimensional plane dispersion<\/strong> in an <strong>infinitely deep porous medium<\/strong>, offering insight into plume spreading under uniform flow conditions.<\/p>\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>The simulation considers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>conservative contaminant<\/strong> (no sorption)<\/li>\n\n\n\n<li>A <strong>constant source concentration<\/strong><\/li>\n\n\n\n<li><strong>Uniform groundwater flow<\/strong><\/li>\n\n\n\n<li><strong>2D dispersion in an infinite domain<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Key Conditions<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Source concentration (<strong>co<\/strong>) = 1.0 g\/L<\/li>\n\n\n\n<li>Time of interest = <strong>4 years<\/strong><\/li>\n\n\n\n<li>Flow is steady and uniform<\/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\">Conceptual Model<\/h2>\n\n\n\n<p>The system represents:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>infinitely thick porous medium<\/strong><\/li>\n\n\n\n<li>A <strong>continuous source<\/strong> releasing contaminant<\/li>\n\n\n\n<li>Transport governed by <strong>advection and diffusion<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Although the domain is infinite:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Results are evaluated over the <strong>top 10 m<\/strong> for comparison<\/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>1.0<\/td><td>m\/a<\/td><\/tr><tr><td>Diffusion Coefficient (D)<\/td><td>0.01<\/td><td>m\u00b2\/a<\/td><\/tr><tr><td>Distribution Coefficient<\/td><td>0.0<\/td><td>cm\u00b3\/g<\/td><\/tr><tr><td>Soil Porosity (n)<\/td><td>1.0<\/td><td>&#8211;<\/td><\/tr><tr><td>Dry Density<\/td><td>0.0<\/td><td>g\/cm\u00b3<\/td><\/tr><tr><td>Soil Thickness (H)<\/td><td>10.0<\/td><td>m<\/td><\/tr><tr><td>Sub-layers<\/td><td>20<\/td><td>&#8211;<\/td><\/tr><tr><td>Source Concentration<\/td><td>1.0<\/td><td>g\/L<\/td><\/tr><tr><td>Time of Interest<\/td><td>4<\/td><td>years<\/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\">Transport Processes<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Advection<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Driven by constant Darcy velocity (<strong>1 m\/a<\/strong>)<\/li>\n\n\n\n<li>Controls plume movement direction<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. Diffusion \/ Dispersion<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Causes plume spreading in all directions<\/li>\n\n\n\n<li>Governed by <strong>D = 0.01 m\u00b2\/a<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. No Sorption<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Conservative contaminant<\/li>\n\n\n\n<li>No retardation effects<\/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\">Analytical Comparison (TDAST)<\/h2>\n\n\n\n<p>The <strong>TDAST model<\/strong> provides an analytical solution for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2D plane dispersion<\/strong><\/li>\n\n\n\n<li><strong>Infinite domain conditions<\/strong><\/li>\n\n\n\n<li><strong>Uniform flow fields<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Purpose of Comparison<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Validate POLLUTEv10 numerical accuracy<\/li>\n\n\n\n<li>Ensure correct implementation of dispersion processes<\/li>\n\n\n\n<li>Benchmark plume geometry and concentration distribution<\/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-depth-vs-concentration\">Graphical Output: Depth vs Concentration<\/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-24.jpg\" alt=\"\" class=\"wp-image-92228\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24.jpg 1007w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24-300x271.jpg 300w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24-768x694.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-example13.pdf&amp;embedded=true&amp;hl=en\" title=\"Embedded Document\" class=\"ead-iframe\" style=\"width: 100%;height: 100%;border: none;position: absolute;left: 0;top: 0;visibility: hidden;\"><\/iframe><\/div>\t\t\t<div class=\"ead-document-loading\" style=\"width:100%;height:100%;position:absolute;left:0;top:0;z-index:10\">\n\t\t\t\t<div class=\"ead-loading-wrap\">\n\t\t\t\t\t<div class=\"ead-loading-main\">\n\t\t\t\t\t\t<div class=\"ead-loading\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/loading.svg\" width=\"55\" height=\"55\" alt=\"Loader\">\n\t\t\t\t\t\t\t<span>Loading&#8230;<\/span>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"ead-loading-foot\">\n\t\t\t\t\t\t<div class=\"ead-loading-foot-title\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/EAD-logo.svg\" alt=\"EAD Logo\" width=\"36\" height=\"23\"\/>\n\t\t\t\t\t\t\t<span>Taking too long?<\/span>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<p>\n\t\t\t\t\t\t\t<div class=\"ead-document-btn ead-reload-btn\" role=\"button\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/reload.svg\" alt=\"Reload\" width=\"12\" height=\"12\"\/> Reload document\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<span>|<\/span>\n\t\t\t\t\t\t\t<a href=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/pollute-example13.pdf\" class=\"ead-document-btn\" target=\"_blank\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/open.svg\" alt=\"Open\" width=\"12\" height=\"12\"\/> Open in new tab\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div><\/div>\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Key Insights<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analytical solutions remain essential for <strong>model verification<\/strong><\/li>\n\n\n\n<li>2D dispersion produces <strong>predictable plume geometries<\/strong><\/li>\n\n\n\n<li>Infinite domain assumptions simplify boundary effects<\/li>\n\n\n\n<li>POLLUTEv10 can accurately simulate <strong>multi-dimensional transport<\/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 Discretization<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>20 sub-layers<\/strong> used for vertical resolution<\/li>\n\n\n\n<li>Adequate for capturing concentration gradients over 10 m<\/li>\n<\/ul>\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\">Increasing sub-layers improves resolution for sharper gradients or shorter time scales<\/p>\n<\/blockquote>\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 relevant for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Groundwater contamination assessments<\/strong><\/li>\n\n\n\n<li><strong>Plume migration prediction<\/strong><\/li>\n\n\n\n<li><strong>Model calibration and validation<\/strong><\/li>\n\n\n\n<li><strong>Regulatory and environmental 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 13 demonstrates the model\u2019s capability to accurately reproduce <strong>2D contaminant transport behavior<\/strong> and match analytical solutions such as TDAST.<\/p>\n\n\n\n<p>Key takeaways:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Advection controls plume direction<\/li>\n\n\n\n<li>Diffusion governs plume spreading<\/li>\n\n\n\n<li>Analytical comparisons build confidence in model results<\/li>\n<\/ul>\n\n\n\n<p>This example reinforces POLLUTEv10 as a reliable tool for <strong>groundwater contaminant transport modeling<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-learn-more-about-our-contaminant-transport-modeling-solutions\">Learn more about our Contaminant Transport Modeling Solutions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.gaeatech.com\/pollute.php\" target=\"_blank\" rel=\"noreferrer noopener\">POLLUTE and MIGRATE Contaminant Modeling and Landfill Design<\/a><\/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-pollute-examples\">POLLUTE Examples<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-1-modeling-a-u-s-rcra-subtitle-d-landfill\/\">POLLUTEv10 Example 1: Modeling a U.S. RCRA Subtitle D Landfill<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-2-pure-diffusion-soil-model\/\">POLLUTEv10 Example 2: Pure Diffusion in a Soil Layer (No Sorption)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-3-advection-diffusion-aquifer-mixing\/\">POLLUTEv10 Example 3: Advection + Diffusion with Aquifer Mixing<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-4-finite-mass-leachate-collection\/\">POLLUTEv10 Example 4: Finite Mass Source with Leachate Collection System<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-5-hydraulic-trap-upward-flow\/\">POLLUTEv10 Example 5: Hydraulic Trap (Upward Flow into the Landfill)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-6-fractured-till-sorption\/\">POLLUTEv10 Example 6: Fractured Layer with Sorption and Reactive Transport<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-7-radioactive-fractured-rock\/\">POLLUTEv10 Example 7: Lateral Migration of a Radioactive Contaminant in Fractured Rock<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-8-potassium-diffusion-clay\/\">POLLUTEv10 Example 8: Laboratory Diffusion of Potassium in Clay<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-9-phenol-diffusion-freundlich-sorption\/\">POLLUTEv10 Example 9: Diffusion with Freundlich Non-Linear Sorption (Phenol in Clay)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-10-landfill-variable-advective-dispersive-transport\/\">POLLUTEv10 Example 10: Time-Varying Advective\u2013Dispersive Transport from a Landfill<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-11-time-varying-source-chloride-diffusion\/\">POLLUTEv10 Example 11: Time-Varying Source Concentration with Diffusion (Chloride in Clay)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-12-fractured-media-transport-analytical-solution\/\">POLLUTEv10 Example 12: Fractured Media Transport vs Analytical Solution (Tang et al., 1981)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-14-passive-sink-landfill-model\/\">POLLUTEv10 Example 14: Modeling a Landfill with Primary and Secondary Leachate Collection Using Passive Sink<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-15-leachate-system-failure-variable-properties\/\">POLLUTEv10 Example 15: Modeling Leachate Collection System Failure Using Variable Properties and Passive Sink<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-16-monte-carlo-leachate-system-failure\/\">POLLUTEv10 Example 16: Monte Carlo Simulation of Leachate Collection System Failure Timing<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-17-composite-liner-landfill-model\/\">POLLUTEv10 Example 17: Modeling a Landfill with Composite Liners and Dual Leachate Collection Systems<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-18-phase-change-leachate-system\/\">POLLUTEv10 Example 18: Modeling Phase Change in a Secondary Leachate Collection System<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-19-multiphase-diffusion-toluene\/\">POLLUTEv10 Example 19: Multiphase Diffusion of Toluene Through a Geomembrane System<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-20-sensitivity-analysis-leachate-system\/\">POLLUTEv10 Example 20: Sensitivity Analysis of Primary Leachate Collection System Failure<\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-comparison-between-pollute-and-migrate\">Comparison between POLLUTE and  MIGRATE<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/migrate-vs-pollute-pure-diffusion\/\">MIGRATEv10 vs POLLUTEv10: Pure Diffusion Comparison<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/migrate-vs-pollute-advective-diffusive-transport\/\">MIGRATEv10 vs POLLUTEv10: Advective\u2013Diffusive Transport Comparison<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/wp-admin\/post.php?post=91707&amp;action=edit\">MIGRATEv10 vs POLLUTEv10: Finite Mass Source Comparison<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/migrate-vs-pollute-hydraulic-trap\/\">MIGRATEv10 vs POLLUTEv10: Hydraulic Trap (Finite Mass Source) Comparison<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gaeatech.com\/knowledge-center\/migrate-vs-pollute-fractured-layer-sorption\/\">MIGRATEv10 vs POLLUTEv10: Fractured Layer with Sorption Comparison<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Benchmarking Against Analytical 2D Dispersion Models POLLUTEv10 Example 13 provides another important model validation case, comparing numerical results from POLLUTEv10 with the analytical solution implemented in TDAST, developed by P. Javandel and colleagues in 1984. This example focuses on 2-dimensional plane dispersion in an infinitely deep porous medium, offering insight into plume spreading under uniform [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92230,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1632],"tags":[1670,1669,501,24,469,821,1636,1236,1627,1671],"class_list":["post-92227","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-pollute-examples","tag-2d-dispersion","tag-analytical-solution","tag-contaminant-transport","tag-environmental-engineering","tag-groundwater-modeling","tag-hydrogeology","tag-numerical-modeling","tag-plume-migration","tag-pollutev10","tag-tdast"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.5 (Yoast SEO v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>2D Dispersion Modeling \u2013 POLLUTEv10 Example 13 Insights - 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