{"id":92347,"date":"2026-04-22T15:00:20","date_gmt":"2026-04-22T15:00:20","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92347"},"modified":"2026-04-27T00:51:34","modified_gmt":"2026-04-27T00:51:34","slug":"migrate-vs-pollute-pure-diffusion","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/migrate-vs-pollute-pure-diffusion\/","title":{"rendered":"MIGRATEv10 vs POLLUTEv10: Pure Diffusion Comparison"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-overview\">Overview<\/h2>\n\n\n\n<p>In this example, we compare pure diffusion results generated using MIGRATEv10 and POLLUTEv10 under identical conditions. The objective is to verify consistency between the two models and highlight key differences in their capabilities.<\/p>\n\n\n\n<p>Both simulations consider contaminant transport through a 4 m thick layer under <strong>pure diffusion<\/strong> (no advection), with constant concentration boundary conditions applied at the top and bottom.<\/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-model-setup\">Model Setup<\/h2>\n\n\n\n<p>The following parameters are identical in both models:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Layer thickness: 4 m<\/li>\n\n\n\n<li>Diffusion coefficient: 0.01 m\u00b2\/a<\/li>\n\n\n\n<li>Porosity: 0.4<\/li>\n\n\n\n<li>Sorption: None (Kd = 0)<\/li>\n\n\n\n<li>Velocity: 0 m\/a (pure diffusion)<\/li>\n\n\n\n<li>Top boundary concentration: 1 mg\/L<\/li>\n\n\n\n<li>Bottom boundary concentration: 0 mg\/L<\/li>\n<\/ul>\n\n\n\n<p>This configuration represents a classical 1D diffusion problem governed by Fick\u2019s Second Law.<\/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-results-comparison\">Results Comparison<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"455\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/migratev10-vs-pollutev10-diffusion-comparison.jpg\" alt=\"Comparison of concentration profiles from MIGRATEv10 and POLLUTEv10 for pure diffusion case\" class=\"wp-image-92348\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/migratev10-vs-pollutev10-diffusion-comparison.jpg 567w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/migratev10-vs-pollutev10-diffusion-comparison-300x241.jpg 300w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-concentration-profiles\">Concentration Profiles<\/h3>\n\n\n\n<p>At all times and depths, the results from MIGRATEv10 and POLLUTEv10 are nearly identical.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-example-concentration-at-100-years\">Example: Concentration at 100 Years<\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Depth (m)<\/th><th>MIGRATEv10 (mg\/L)<\/th><th>POLLUTEv10 (mg\/L)<\/th><\/tr><tr><td>0<\/td><td>1.001<\/td><td>1.000<\/td><\/tr><tr><td>1<\/td><td>0.4795<\/td><td>0.4795<\/td><\/tr><tr><td>2<\/td><td>0.1573<\/td><td>0.1573<\/td><\/tr><tr><td>3<\/td><td>0.0335<\/td><td>0.0335<\/td><\/tr><tr><td>4<\/td><td>0.0000<\/td><td>0.0000<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The minor difference at the surface (1.001 vs 1.000) is due to numerical precision and does not affect interpretation.<\/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-key-observations\">Key Observations<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-excellent-agreement\">1. Excellent Agreement<\/h3>\n\n\n\n<p>Both models produce virtually identical concentration profiles across all times:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>10 years<\/li>\n\n\n\n<li>50 years<\/li>\n\n\n\n<li>100 years<\/li>\n\n\n\n<li>150 years<\/li>\n\n\n\n<li>200 years<\/li>\n<\/ul>\n\n\n\n<p>This confirms that both implementations accurately solve the governing diffusion equation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-2-dimensional-differences\">2. Dimensional Differences<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>POLLUTEv10<\/strong> is a <strong>1D vertical model<\/strong>, providing concentration vs depth only.<\/li>\n\n\n\n<li><strong>MIGRATEv10<\/strong> is <strong>2D (lateral + vertical)<\/strong> and reports results at multiple horizontal distances.<\/li>\n<\/ul>\n\n\n\n<p>In this example, MIGRATEv10 shows symmetric results about the centerline:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x = -100 m \u2192 lower concentration<\/li>\n\n\n\n<li>x = 0 m \u2192 highest concentration<\/li>\n\n\n\n<li>x = +100 m \u2192 identical to -100 m<\/li>\n<\/ul>\n\n\n\n<p>At the centerline (x = 0), MIGRATEv10 results match POLLUTEv10 exactly.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-mass-tracking-migratev10-only\">3. Mass Tracking (MIGRATEv10 Only)<\/h3>\n\n\n\n<p>MIGRATEv10 provides additional insight through mass balance outputs:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass entering the soil increases over time<\/li>\n\n\n\n<li>No mass reaches the base (consistent with zero concentration at 4 m)<\/li>\n<\/ul>\n\n\n\n<p>At 200 years:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass into soil \u2248 128.4 (units consistent with model output)<\/li>\n<\/ul>\n\n\n\n<p>POLLUTEv10 does not explicitly report cumulative mass in this output.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-4-boundary-condition-handling\">4. Boundary Condition Handling<\/h3>\n\n\n\n<p>Although implemented slightly differently:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>MIGRATEv10 uses a zero concentration bottom boundary<\/li>\n\n\n\n<li>POLLUTEv10 specifies a constant concentration of 0 mg\/L<\/li>\n<\/ul>\n\n\n\n<p>These are mathematically equivalent, leading to identical results.<\/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-physical-interpretation\">Physical Interpretation<\/h2>\n\n\n\n<p>Both models show:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Gradual downward migration of contaminants<\/li>\n\n\n\n<li>Smooth concentration gradients typical of diffusion<\/li>\n\n\n\n<li>Increasing penetration depth with time<\/li>\n\n\n\n<li>No breakthrough at the base within 200 years<\/li>\n<\/ul>\n\n\n\n<p>At early times (10 years), diffusion is shallow. By 200 years, concentrations at 3 m depth become significant.<\/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-conclusion\">Conclusion<\/h2>\n\n\n\n<p>This comparison demonstrates that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>MIGRATEv10 and POLLUTEv10 produce equivalent results for pure diffusion problems<\/strong><\/li>\n\n\n\n<li>POLLUTEv10 serves as a reliable <strong>1D benchmark solution<\/strong><\/li>\n\n\n\n<li>MIGRATEv10 extends this capability to <strong>2D systems<\/strong>, while preserving accuracy<\/li>\n<\/ul>\n\n\n\n<p>For problems involving only vertical diffusion, both models are interchangeable. However, MIGRATEv10 provides additional flexibility when lateral transport, source geometry, or mass accounting are important.<\/p>\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-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-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>Overview In this example, we compare pure diffusion results generated using MIGRATEv10 and POLLUTEv10 under identical conditions. The objective is to verify consistency between the two models and highlight key differences in their capabilities. Both simulations consider contaminant transport through a 4 m thick layer under pure diffusion (no advection), with constant concentration boundary conditions [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92349,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1726],"tags":[501,1657,24,821,1721,1689,1636,1627],"class_list":["post-92347","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-pollute-vs-migrate","tag-contaminant-transport","tag-diffusion-modeling","tag-environmental-engineering","tag-hydrogeology","tag-landfill-liners","tag-migratev10","tag-numerical-modeling","tag-pollutev10"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.6 (Yoast SEO v27.6) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>MIGRATEv10 vs POLLUTEv10: Pure Diffusion Comparison - 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