{"id":92193,"date":"2026-04-19T13:00:44","date_gmt":"2026-04-19T13:00:44","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92193"},"modified":"2026-04-13T23:36:23","modified_gmt":"2026-04-13T23:36:23","slug":"pollutev10-example-7-radioactive-fractured-rock","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-7-radioactive-fractured-rock\/","title":{"rendered":"POLLUTEv10 Example 7: Lateral Migration of a Radioactive Contaminant in Fractured Rock"},"content":{"rendered":"\n<p>This example demonstrates how <strong>POLLUTEv10<\/strong> can be used to simulate the <strong>lateral migration of a radioactive contaminant<\/strong> in a <strong>fractured porous rock system<\/strong>. It focuses on transport along a <strong>single set of parallel fractures<\/strong>, incorporating <strong>advection, dispersion, matrix diffusion<\/strong>, and <strong>radioactive decay<\/strong>.<\/p>\n\n\n\n<p>The scenario is particularly relevant for <strong>nuclear waste disposal assessments<\/strong>, deep geological repositories, and long-term contaminant fate modeling.<\/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 model assumes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>fractured rock domain extending effectively infinitely<\/strong> from the source<\/li>\n\n\n\n<li>Transport occurring primarily <strong>along fractures (fast pathways)<\/strong><\/li>\n\n\n\n<li><strong>Diffusion into the surrounding rock matrix (slow storage zone)<\/strong><\/li>\n\n\n\n<li>A <strong>radioactive contaminant<\/strong> that undergoes <strong>decay over time<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The analysis focuses on:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>First 50 m of transport distance<\/strong><\/li>\n\n\n\n<li><strong>Time period of 30 years<\/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-assumptions\">Key Modeling Assumptions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial source concentration: <strong>co = 1 (normalized unit)<\/strong><\/li>\n\n\n\n<li>The source is <strong>constant (no depletion)<\/strong> due to large supply<\/li>\n\n\n\n<li><strong>Radioactive decay occurs continuously<\/strong><\/li>\n\n\n\n<li><strong>No sorption<\/strong> in fractures or matrix (Kf = Km = 0)<\/li>\n\n\n\n<li>Transport is governed by:\n<ul class=\"wp-block-list\">\n<li><strong>Advection<\/strong><\/li>\n\n\n\n<li><strong>Dispersion<\/strong><\/li>\n\n\n\n<li><strong>Matrix diffusion<\/strong><\/li>\n\n\n\n<li><strong>First-order radioactive decay<\/strong><\/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-governing-radioactive-decay\">Governing Radioactive Decay<\/h2>\n\n\n\n<p>The decay of the contaminant follows first-order kinetics:<\/p>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo stretchy=\"false\">(<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>C<\/mi><mn>0<\/mn><\/msub><msup><mi>e<\/mi><mrow><mo>\u2212<\/mo><mi>\u03bb<\/mi><mi>t<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">C(t)=C_0 e^{-\\lambda t}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo stretchy=\"false\">(<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">C(t)<\/annotation><\/semantics><\/math>= concentration at time <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math>t<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_0<\/annotation><\/semantics><\/math> = initial concentration<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03bb<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda<\/annotation><\/semantics><\/math> = decay constant<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> = time (years)<\/li>\n<\/ul>\n\n\n\n<p>The decay constant is related to half-life:<\/p>\n\n\n\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>ln<\/mi><mo>\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><msub><mi>t<\/mi><mrow><mn>1<\/mn><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>0.693<\/mn><mn>100<\/mn><\/mfrac><mo>\u2248<\/mo><mn>0.00693<\/mn><mtext>\u2009<\/mtext><msup><mtext>a<\/mtext><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda = \\frac{\\ln(2)}{t_{1\/2}} = \\frac{0.693}{100} \\approx 0.00693 \\, \\text{a}^{-1}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>This means that over 30 years, only modest decay occurs, making <strong>transport processes dominant<\/strong> in plume evolution.<\/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-input-parameters\">Input Parameters<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-hydraulic-and-transport-properties\">Hydraulic and Transport Properties<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Symbol<\/th><th>Value<\/th><th>Units<\/th><\/tr><\/thead><tbody><tr><td>Darcy Velocity<\/td><td>va<\/td><td>0.08<\/td><td>m\/a<\/td><\/tr><tr><td>Dispersion in fractures<\/td><td>Df<\/td><td>6<\/td><td>m\u00b2\/a<\/td><\/tr><tr><td>Matrix diffusion coefficient<\/td><td>Dm<\/td><td>0.0018<\/td><td>m\u00b2\/a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-fracture-geometry\">Fracture Geometry<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr><td>Fracture spacing (2H1)<\/td><td>0.05 m<\/td><\/tr><tr><td>Fracture aperture (2h1)<\/td><td>10 \u03bcm<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>These closely spaced fractures create <strong>highly efficient lateral pathways<\/strong> for contaminant migration.<\/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-matrix-properties\">Matrix Properties<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr><td>Matrix porosity (nm)<\/td><td>0.05<\/td><\/tr><tr><td>Distribution coefficient (Km)<\/td><td>0 cm\u00b3\/g<\/td><\/tr><tr><td>Dry density<\/td><td>2 g\/cm\u00b3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>With <strong>no sorption<\/strong>, the matrix acts purely as a <strong>diffusive sink<\/strong>, not a reactive barrier.<\/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-domain-and-simulation-setup\">Domain and Simulation Setup<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr><td>Fractured rock thickness (HT)<\/td><td>50 m<\/td><\/tr><tr><td>Number of sub-layers<\/td><td>5<\/td><\/tr><tr><td>Source concentration (co)<\/td><td>1<\/td><\/tr><tr><td>Half-life<\/td><td>100 years<\/td><\/tr><tr><td>Simulation time<\/td><td>30 years<\/td><\/tr><tr><td>Distance of interest<\/td><td>50 m<\/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\" id=\"h-special-feature-maximum-sublayer-thickness\">Special Feature: Maximum Sublayer Thickness<\/h2>\n\n\n\n<p>This example highlights a <strong>POLLUTEv10 special feature<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ability to define <strong>sublayers thicker than the default 5 units<\/strong><\/li>\n\n\n\n<li>Allows efficient modeling of <strong>large domains (50 m)<\/strong> with fewer layers<\/li>\n\n\n\n<li>Maintains numerical stability while improving computational efficiency<\/li>\n<\/ul>\n\n\n\n<p>This is especially useful in <strong>regional-scale fractured rock simulations<\/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-transport-processes-explained\">Transport Processes Explained<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-advective-dispersive-flow-in-fractures\">1. Advective\u2013Dispersive Flow in Fractures<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Advection<\/strong> drives the contaminant forward along fractures<\/li>\n\n\n\n<li><strong>Dispersion<\/strong> spreads the plume longitudinally<\/li>\n\n\n\n<li>Results in <strong>rapid lateral migration over tens of meters<\/strong><\/li>\n<\/ul>\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-matrix-diffusion\">2. Matrix Diffusion<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Contaminants diffuse from fractures into the rock matrix<\/li>\n\n\n\n<li>Acts as a <strong>temporary storage mechanism<\/strong><\/li>\n\n\n\n<li>Slows peak concentrations in fractures<\/li>\n\n\n\n<li>Leads to <strong>long-term back-diffusion<\/strong><\/li>\n<\/ul>\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-radioactive-decay\">3. Radioactive Decay<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Reduces total contaminant mass over time<\/li>\n\n\n\n<li>Less significant over 30 years due to long half-life (100 years)<\/li>\n\n\n\n<li>Becomes more important in <strong>long-term (>100 year) simulations<\/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-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-18.jpg\" alt=\"\" class=\"wp-image-92194\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-18.jpg 1007w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-18-300x271.jpg 300w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-18-768x694.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-example7.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-example7.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<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-engineering-and-environmental-insights\">Engineering and Environmental Insights<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fractured rock systems can enable <strong>fast contaminant migration<\/strong>, even with low matrix permeability<\/li>\n\n\n\n<li><strong>Matrix diffusion is critical<\/strong> for realistic long-term predictions<\/li>\n\n\n\n<li><strong>Radioactive decay alone is insufficient<\/strong> for short-term attenuation<\/li>\n\n\n\n<li>This type of modeling is essential for:\n<ul class=\"wp-block-list\">\n<li><strong>Nuclear waste repository design<\/strong><\/li>\n\n\n\n<li><strong>Risk assessment of radioactive contaminants<\/strong><\/li>\n\n\n\n<li><strong>Long-term groundwater protection strategies<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\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>This example demonstrates how POLLUTEv10 can be used to simulate the lateral migration of a radioactive contaminant in a fractured porous rock system. It focuses on transport along a single set of parallel fractures, incorporating advection, dispersion, matrix diffusion, and radioactive decay. The scenario is particularly relevant for nuclear waste disposal assessments, deep geological repositories, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92196,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1632],"tags":[1652,501,1654,685,1655,1650,469,821,1648,1653,1236,1627,1651],"class_list":["post-92193","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-decay-modeling","tag-environmental-modeling","tag-fracture-flow","tag-fractured-rock","tag-groundwater-modeling","tag-hydrogeology","tag-matrix-diffusion","tag-nuclear-waste","tag-plume-migration","tag-pollutev10","tag-radioactive-contaminants"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - 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