{"id":92259,"date":"2026-04-14T13:00:56","date_gmt":"2026-04-14T13:00:56","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92259"},"modified":"2026-04-24T01:15:58","modified_gmt":"2026-04-24T01:15:58","slug":"pollutev10-example-19-multiphase-diffusion-toluene","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-19-multiphase-diffusion-toluene\/","title":{"rendered":"POLLUTEv10 Example 19: Multiphase Diffusion of Toluene Through a Geomembrane System"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-introduction\">Introduction<\/h2>\n\n\n\n<p>POLLUTEv10 Example 19 models a <strong>multiphase diffusion experiment<\/strong> originally conducted by <em>Buss et al. (1995)<\/em>. This example is particularly useful for understanding how volatile organic compounds (VOCs), such as <strong>toluene<\/strong>, migrate through engineered barrier systems that include <strong>geomembranes, airspaces, and aqueous reservoirs<\/strong>.<\/p>\n\n\n\n<p>The simulation demonstrates how POLLUTEv10 can accurately reproduce laboratory-scale results by incorporating <strong>diffusion coefficients<\/strong>, <strong>phase partitioning<\/strong>, and <strong>layered transport mechanisms<\/strong> across multiple media.<\/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-background-of-the-experiment\">Background of the Experiment<\/h2>\n\n\n\n<p>The experimental setup consists of three primary components:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>HDPE geomembrane (barrier layer)<\/strong><\/li>\n\n\n\n<li><strong>Air-filled void space<\/strong><\/li>\n\n\n\n<li><strong>Well-mixed water reservoir (receptor)<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Toluene migrates from a <strong>constant concentration source<\/strong>, diffusing sequentially through each medium before reaching the receptor.<\/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 includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>constant source of toluene<\/strong><\/li>\n\n\n\n<li>A <strong>0.1 cm thick HDPE geomembrane<\/strong><\/li>\n\n\n\n<li>An <strong>18.2 cm thick airspace<\/strong><\/li>\n\n\n\n<li>A <strong>12.3 cm water reservoir<\/strong>, assumed to be fully mixed<\/li>\n<\/ul>\n\n\n\n<p>This layered configuration allows simulation of <strong>multiphase transport<\/strong>, where contaminant movement is governed by both diffusion and partitioning between phases.<\/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-input-parameters\">Key Input Parameters<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-geomembrane-properties-hdpe\">1. Geomembrane Properties (HDPE)<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th>Parameter<\/th><th>Value<\/th><\/tr><tr><td>Thickness<\/td><td>0.1 cm<\/td><\/tr><tr><td>Diffusion Coefficient<\/td><td>6 \u00d7 10\u207b\u2078 cm\u00b2\/s<\/td><\/tr><tr><td>Phase Coefficient<\/td><td>43.8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The high phase coefficient reflects strong partitioning of toluene into the geomembrane material.<\/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-airspace-properties\">2. Airspace Properties<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Parameter<\/td><td>Value<\/td><\/tr><tr><td>Thickness<\/td><td>18.2 cm<\/td><\/tr><tr><td>Diffusion Coefficient<\/td><td>0.088 cm\u00b2\/s<\/td><\/tr><tr><td>Phase Coefficient<\/td><td>0.27<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The airspace provides relatively rapid diffusion compared to the geomembrane, acting as a transport pathway between layers.<\/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-water-reservoir-receptor\">3. Water Reservoir (Receptor)<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Parameter<\/td><td>Value<\/td><\/tr><tr><td>Thickness<\/td><td>12.3 cm<\/td><\/tr><tr><td>Mixing Condition<\/td><td>Well-mixed<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The assumption of a well-mixed reservoir simplifies the model by treating the receptor concentration as uniform at any given time.<\/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-assumptions\">Modeling Assumptions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Constant concentration source<\/strong> of toluene<\/li>\n\n\n\n<li><strong>Diffusion-dominated transport<\/strong> (no advection)<\/li>\n\n\n\n<li><strong>Phase equilibrium<\/strong> at layer interfaces<\/li>\n\n\n\n<li><strong>Well-mixed receptor boundary<\/strong><\/li>\n\n\n\n<li>No degradation or reaction processes considered<\/li>\n<\/ul>\n\n\n\n<p>These assumptions align with the controlled laboratory conditions of the original experiment.<\/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-simulation-setup-in-pollutev10\">Simulation Setup in POLLUTEv10<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-1-define-layer-geometry\">Step 1: Define Layer Geometry<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Layer 1: HDPE geomembrane (0.1 cm)<\/li>\n\n\n\n<li>Layer 2: Airspace (18.2 cm)<\/li>\n\n\n\n<li>Layer 3: Water reservoir (12.3 cm)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-2-assign-material-properties\">Step 2: Assign Material Properties<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Input diffusion coefficients and phase coefficients for each layer<\/li>\n\n\n\n<li>Ensure units are consistent (cm\u00b2\/s)<\/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>Apply a <strong>constant concentration source<\/strong><\/li>\n\n\n\n<li>Define the receptor as a <strong>well-mixed boundary<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-4-set-simulation-time\">Step 4: Set Simulation Time<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total simulation duration: <strong>600 hours<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-step-5-run-model\">Step 5: Run Model<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Track concentration breakthrough in the water reservoir<\/li>\n\n\n\n<li>Compare simulated results with observed data<\/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-30.jpg\" alt=\"\" class=\"wp-image-92260\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-30.jpg 1007w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-30-300x271.jpg 300w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-30-768x694.jpg 768w\" sizes=\"auto, (max-width: 1007px) 100vw, 1007px\" \/><\/figure>\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-example19.pdf&amp;embedded=true&amp;hl=en\" title=\"Embedded Document\" class=\"ead-iframe\" style=\"width: 100%;height: 100%;border: 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id=\"h-interpretation-of-multiphase-diffusion\">Interpretation of Multiphase Diffusion<\/h2>\n\n\n\n<p>This example highlights several important concepts:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-barrier-performance-of-hdpe\">1. Barrier Performance of HDPE<\/h3>\n\n\n\n<p>The very low diffusion coefficient demonstrates the effectiveness of geomembranes in limiting contaminant migration.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-2-role-of-phase-partitioning\">2. Role of Phase Partitioning<\/h3>\n\n\n\n<p>The high phase coefficient in the geomembrane indicates strong sorption, which slows transport.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-rapid-transport-in-air\">3. Rapid Transport in Air<\/h3>\n\n\n\n<p>Diffusion in air is orders of magnitude faster than in solids, making the airspace a critical pathway.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-4-importance-of-interface-conditions\">4. Importance of Interface Conditions<\/h3>\n\n\n\n<p>Accurate modeling of phase equilibrium at interfaces is essential for realistic 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-key-takeaways\">Key Takeaways<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>POLLUTEv10 can effectively simulate <strong>multiphase diffusion systems<\/strong><\/li>\n\n\n\n<li>Geomembranes play a critical role in <strong>contaminant containment<\/strong><\/li>\n\n\n\n<li><strong>Phase coefficients<\/strong> are just as important as diffusion coefficients<\/li>\n\n\n\n<li>Laboratory validation strengthens confidence in model predictions<\/li>\n\n\n\n<li>This example bridges <strong>experimental data and numerical modeling<\/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-final-thoughts\">Final Thoughts<\/h2>\n\n\n\n<p>Example 19 provides a strong foundation for modeling <strong>VOC transport through engineered barrier systems<\/strong>, particularly in landfill and containment applications. By reproducing a controlled laboratory experiment, it demonstrates the reliability of POLLUTEv10 in handling <strong>complex, multi-layer, multiphase diffusion problems<\/strong>.<\/p>\n\n\n\n<p>However, real-world applications require careful consideration of:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Temperature effects<\/li>\n\n\n\n<li>Material variability<\/li>\n\n\n\n<li>Field-scale heterogeneity<\/li>\n<\/ul>\n\n\n\n<p>As always, <strong>site-specific calibration and expert judgment<\/strong> are essential.<\/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-13-2d-dispersion-tdast-analytical-comparison\/\">POLLUTEv10 Example 13: 2D Plane Dispersion vs Analytical Solution (TDAST)<\/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-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>Introduction POLLUTEv10 Example 19 models a multiphase diffusion experiment originally conducted by Buss et al. (1995). This example is particularly useful for understanding how volatile organic compounds (VOCs), such as toluene, migrate through engineered barrier systems that include geomembranes, airspaces, and aqueous reservoirs. The simulation demonstrates how POLLUTEv10 can accurately reproduce laboratory-scale results by incorporating [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92262,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1632],"tags":[501,24,1686,1687,1627,1685,1631],"class_list":["post-92259","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-pollute-examples","tag-contaminant-transport","tag-environmental-engineering","tag-geomembrane-modeling","tag-multiphase-diffusion","tag-pollutev10","tag-toluene-transport","tag-voc-migration"],"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>POLLUTEv10 Example 19 Multiphase Diffusion Model Overview - 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