{"id":92286,"date":"2026-04-22T08:00:57","date_gmt":"2026-04-22T08:00:57","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92286"},"modified":"2026-04-16T02:09:21","modified_gmt":"2026-04-16T02:09:21","slug":"migratev10-example-3-pure-diffusion-conservative-contaminant","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/migratev10-example-3-pure-diffusion-conservative-contaminant\/","title":{"rendered":"MIGRATEv10 Example 3: Pure Diffusion of a Conservative Contaminant"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-introduction\">Introduction<\/h2>\n\n\n\n<p>MIGRATEv10 Example 3 presents a simplified but highly instructive case of <strong>pure diffusion<\/strong> of a <strong>conservative contaminant<\/strong> through a porous medium. Unlike previous examples, this scenario excludes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Advection (no groundwater flow in the modeled layer)<\/li>\n\n\n\n<li>Sorption (no retardation effects)<\/li>\n<\/ul>\n\n\n\n<p>This makes it an ideal example for understanding the <strong>fundamental physics of diffusion-controlled transport<\/strong> in subsurface environments.<\/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-conceptual-model-overview\">Conceptual Model Overview<\/h2>\n\n\n\n<p>The modeled system consists of:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>4 m thick homogeneous layer<\/strong><\/li>\n\n\n\n<li>A <strong>constant concentration source at the top boundary<\/strong><\/li>\n\n\n\n<li>An <strong>underlying aquifer acting as a zero-concentration boundary<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-key-simplification\">Key Simplification<\/h3>\n\n\n\n<p>The aquifer is <strong>not explicitly modeled<\/strong> because:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It has a <strong>high flushing velocity<\/strong><\/li>\n\n\n\n<li>Any contaminant reaching it is immediately removed<\/li>\n\n\n\n<li>Therefore, concentration at the base is assumed to be <strong>zero<\/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\" id=\"h-key-modeling-objective\">Key Modeling Objective<\/h2>\n\n\n\n<p>The purpose of this example is to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Demonstrate <strong>diffusion-driven transport<\/strong><\/li>\n\n\n\n<li>Understand concentration gradients over time<\/li>\n\n\n\n<li>Provide a baseline case for comparison with more complex models<\/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-hydrogeologic-concept\">Hydrogeologic Concept<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-boundary-conditions\">Boundary Conditions<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th>Boundary<\/th><th>Condition<\/th><\/tr><tr><td>Top of Layer<\/td><td>Constant concentration<\/td><\/tr><tr><td>Bottom of Layer<\/td><td>Zero concentration<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>This creates a <strong>concentration gradient<\/strong>, which drives diffusion downward.<\/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-governing-process-diffusion\">Governing Process: Diffusion<\/h2>\n\n\n\n<p>Transport is governed entirely by <strong>Fick\u2019s Law of Diffusion<\/strong>, where contaminant flux is proportional to the concentration gradient.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Movement occurs from <strong>high concentration \u2192 low concentration<\/strong><\/li>\n\n\n\n<li>No influence from flow or chemical interactions<\/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-key-assumptions\">Key Assumptions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Conservative contaminant<\/strong> (no decay, no sorption)<\/li>\n\n\n\n<li><strong>Homogeneous porous medium<\/strong><\/li>\n\n\n\n<li><strong>One-dimensional vertical transport<\/strong><\/li>\n\n\n\n<li><strong>Steady boundary conditions<\/strong><\/li>\n\n\n\n<li><strong>Instantaneous removal at aquifer boundary<\/strong><\/li>\n<\/ul>\n\n\n\n<p>These assumptions isolate diffusion as the only active transport mechanism.<\/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-modeling-approach-in-migratev10\">Modeling Approach in MIGRATEv10<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-1-define-geometry\">Step 1: Define Geometry<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Single layer thickness: <strong>4 m<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-2-assign-transport-properties\">Step 2: Assign Transport Properties<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Set diffusion coefficient (user-defined depending on scenario)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-3-configure-boundary-conditions\">Step 3: Configure Boundary Conditions<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Top boundary: <strong>constant concentration source<\/strong><\/li>\n\n\n\n<li>Bottom boundary: <strong>zero concentration<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-4-disable-other-processes\">Step 4: Disable Other Processes<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>No advection (Darcy velocity = 0)<\/li>\n\n\n\n<li>No sorption (distribution coefficient = 0)<\/li>\n\n\n\n<li>No decay<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-5-run-simulation\">Step 5: Run Simulation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Evaluate concentration profiles over time<\/li>\n\n\n\n<li>Observe diffusion front progression<\/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=\"804\" height=\"881\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-34.jpg\" alt=\"\" class=\"wp-image-92287\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-34.jpg 804w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-34-274x300.jpg 274w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-34-768x842.jpg 768w\" sizes=\"auto, (max-width: 804px) 100vw, 804px\" \/><\/figure>\n\n\n\n<p><\/p>\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%2Fmigrate-example3.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\/migrate-example3.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<h2 class=\"wp-block-heading\" id=\"h-interpretation-of-results\">Interpretation of Results<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-development-of-concentration-gradient\">1. Development of Concentration Gradient<\/h3>\n\n\n\n<p>A smooth gradient forms from the top (high concentration) to the bottom (zero concentration).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-2-time-dependent-diffusion\">2. Time-Dependent Diffusion<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Early time: steep gradients near the source<\/li>\n\n\n\n<li>Later time: deeper penetration into the layer<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-steady-state-behavior\">3. Steady-State Behavior<\/h3>\n\n\n\n<p>Over long periods, the system may approach a <strong>steady-state profile<\/strong>, depending on conditions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-4-role-of-aquifer-boundary\">4. Role of Aquifer Boundary<\/h3>\n\n\n\n<p>The zero-concentration boundary ensures continuous downward flux, preventing accumulation.<\/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-why-this-example-matters\">Why This Example Matters<\/h2>\n\n\n\n<p>Although simple, this case is critical because it:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Establishes a <strong>baseline for diffusion-only transport<\/strong><\/li>\n\n\n\n<li>Helps validate model setup and parameters<\/li>\n\n\n\n<li>Provides insight into <strong>mass transfer without flow<\/strong><\/li>\n\n\n\n<li>Serves as a comparison for more complex scenarios involving:\n<ul class=\"wp-block-list\">\n<li>Advection<\/li>\n\n\n\n<li>Sorption<\/li>\n\n\n\n<li>Decay<\/li>\n<\/ul>\n<\/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-key-takeaways\">Key Takeaways<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Diffusion is driven solely by <strong>concentration gradients<\/strong><\/li>\n\n\n\n<li>Boundary conditions strongly control system behavior<\/li>\n\n\n\n<li>Conservative species simplify analysis by removing reactions<\/li>\n\n\n\n<li>MIGRATEv10 can isolate individual transport processes effectively<\/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-final-thoughts\">Final Thoughts<\/h2>\n\n\n\n<p>MIGRATEv10 Example 3 is a foundational case that highlights the importance of understanding <strong>basic transport mechanisms<\/strong> before introducing additional complexity. While real-world systems rarely involve pure diffusion alone, this example provides critical insight into how contaminants behave in low-flow or stagnant environments.<\/p>\n\n\n\n<p>In practice, this type of model is useful for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Low-permeability soils<\/li>\n\n\n\n<li>Barrier systems<\/li>\n\n\n\n<li>Early-stage conceptual modeling<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>Introduction MIGRATEv10 Example 3 presents a simplified but highly instructive case of pure diffusion of a conservative contaminant through a porous medium. Unlike previous examples, this scenario excludes: This makes it an ideal example for understanding the fundamental physics of diffusion-controlled transport in subsurface environments. Conceptual Model Overview The modeled system consists of: Key Simplification [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92289,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1690],"tags":[1693,1657,24,1694,1695,1689],"class_list":["post-92286","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-migrateexamples","tag-conservative-contaminant","tag-diffusion-modeling","tag-environmental-engineering","tag-ficks-law","tag-groundwater-transport","tag-migratev10"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>MIGRATEv10 Example 3 Diffusion Model Overview - Knowledge Center<\/title>\n<meta name=\"description\" content=\"Learn 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