{"id":92232,"date":"2026-04-16T07:00:20","date_gmt":"2026-04-16T07:00:20","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92232"},"modified":"2026-04-13T23:00:51","modified_gmt":"2026-04-13T23:00:51","slug":"pollutev10-example-14-passive-sink-landfill-model","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-14-passive-sink-landfill-model\/","title":{"rendered":"POLLUTEv10 Example 14: Modeling a Landfill with Primary and Secondary Leachate Collection Using Passive Sink"},"content":{"rendered":"\n

Introduction<\/h2>\n\n\n\n

POLLUTEv10 Example 14 demonstrates an advanced application of contaminant transport modeling using the Passive Sink special feature<\/strong>. This scenario simulates a landfill equipped with both primary and secondary leachate collection systems<\/strong>, incorporating layered hydrogeologic conditions and a finite contaminant source.<\/p>\n\n\n\n

The example is particularly useful for environmental engineers and hydrogeologists seeking to understand how engineered systems influence contaminant migration in subsurface environments.<\/p>\n\n\n\n

\n\n\n\n

Conceptual Model Overview<\/h2>\n\n\n\n

The model represents a hypothetical landfill<\/strong> with the following characteristics:<\/p>\n\n\n\n

    \n
  • Finite mass of a conservative contaminant<\/strong><\/li>\n\n\n\n
  • Primary and secondary leachate collection systems<\/strong><\/li>\n\n\n\n
  • Underlying aquifer with fixed outflow<\/strong><\/li>\n\n\n\n
  • Use of a passive sink<\/strong> to simulate leachate removal<\/li>\n<\/ul>\n\n\n\n

    Key Assumptions<\/h3>\n\n\n\n
      \n
    • Peak leachate concentration is reached early<\/li>\n\n\n\n
    • No increase in concentration over time<\/li>\n\n\n\n
    • Flow conditions are steady-state<\/li>\n\n\n\n
    • Transport includes advection and diffusion<\/strong><\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Source Term Characterization<\/h2>\n\n\n\n

      The landfill contains waste with the following properties:<\/p>\n\n\n\n

        \n
      • Waste thickness: 6.25 m<\/strong><\/li>\n\n\n\n
      • Waste density: 600 kg\/m\u00b3<\/strong><\/li>\n\n\n\n
      • Contaminant fraction: 0.2%<\/strong><\/li>\n<\/ul>\n\n\n\n

        Total Contaminant Mass per Unit Area<\/h3>\n\n\n\n

        m<\/mi>t<\/mi>c<\/mi><\/mrow><\/msub>=<\/mo>0.002<\/mn>\u00d7<\/mo>600<\/mn>\u00d7<\/mo>6.25<\/mn>=<\/mo>7.5<\/mn>\u2009<\/mtext>kg\/m<\/mtext>2<\/mn><\/msup><\/mrow>m_{tc} = 0.002 \\times 600 \\times 6.25 = 7.5 \\, \\text{kg\/m}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

        Reference Height of Leachate<\/h3>\n\n\n\n

        H<\/mi>r<\/mi><\/msub>=<\/mo>m<\/mi>t<\/mi>c<\/mi><\/mrow><\/msub>c<\/mi>0<\/mn><\/msub><\/mfrac>=<\/mo>7.5<\/mn>1<\/mn><\/mfrac>=<\/mo>7.5<\/mn>\u2009<\/mtext>m<\/mtext><\/mrow>H_r = \\frac{m_{tc}}{c_0} = \\frac{7.5}{1} = 7.5 \\, \\text{m}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

        Where:<\/p>\n\n\n\n

          \n
        • c<\/mi>0<\/mn><\/msub>=<\/mo>1000<\/mn>\u2009<\/mtext>mg\/L<\/mtext><\/mrow>c_0 = 1000 \\, \\text{mg\/L}<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n

          Because peak concentration occurs early:<\/p>\n\n\n\n

            \n
          • Rate of increase in concentration: c<\/mi>r<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>c_r = 0<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            Leachate Generation and Collection<\/h2>\n\n\n\n

            The water balance in the landfill is defined as:<\/p>\n\n\n\n

              \n
            • Infiltration through cover: 0.3 m\/a<\/strong><\/li>\n\n\n\n
            • Exfiltration through base: 0.01 m\/a<\/strong><\/li>\n<\/ul>\n\n\n\n

              Volume of Leachate Collected<\/h3>\n\n\n\n

              Q<\/mi>c<\/mi><\/msub>=<\/mo>q<\/mi>0<\/mn><\/msub>\u2212<\/mo>v<\/mi>a<\/mi><\/msub>=<\/mo>0.3<\/mn>\u2212<\/mo>0.01<\/mn>=<\/mo>0.29<\/mn>\u2009<\/mtext>m\/a<\/mtext><\/mrow>Q_c = q_0 – v_a = 0.3 – 0.01 = 0.29 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

              This collected leachate is managed by the primary system<\/strong>, while the secondary system<\/strong> is modeled using a passive sink.<\/p>\n\n\n\n

              \n\n\n\n

              Hydrogeologic Stratigraphy<\/h2>\n\n\n\n

              The subsurface consists of:<\/p>\n\n\n\n

              Layer<\/th>Description<\/th>Thickness<\/th><\/tr><\/thead>
              Layer 1<\/td>Clay layer<\/td>1 m<\/td><\/tr>
              Layer 2<\/td>Granular layer (secondary LCS)<\/td>0.3 m<\/td><\/tr>
              Layer 3<\/td>Aquitard<\/td>2 m<\/td><\/tr>
              Aquifer<\/td>Flowing groundwater zone<\/td>1 m<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
              \n\n\n\n

              Flow Conditions<\/h2>\n\n\n\n

              Vertical Flow<\/h3>\n\n\n\n
                \n
              • From landfill to secondary system: v<\/mi>a<\/mi><\/msub>=<\/mo>0.01<\/mn>\u2009<\/mtext>m\/a<\/mtext><\/mrow>v_a = 0.01 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
              • From secondary system to aquifer: v<\/mi>a<\/mi><\/msub>=<\/mo>0.0<\/mn>\u2009<\/mtext>m\/a<\/mtext><\/mrow>v_a = 0.0 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n

                This implies the water table is located at the base of the secondary system<\/strong>.<\/p>\n\n\n\n

                \n\n\n\n

                Horizontal Flow in Passive Sink Layer<\/h3>\n\n\n\n

                The passive sink (granular layer) induces lateral flow:v<\/mi>s<\/mi><\/msub>=<\/mo>(<\/mo>v<\/mi>a<\/mi>1<\/mn><\/mrow><\/msub>\u2212<\/mo>v<\/mi>a<\/mi>2<\/mn><\/mrow><\/msub>)<\/mo>\u00d7<\/mo>L<\/mi><\/mrow>h<\/mi><\/mfrac><\/mrow>v_s = \\frac{(v_{a1} – v_{a2}) \\times L}{h}<\/annotation><\/semantics><\/math>v<\/mi>s<\/mi><\/msub>=<\/mo>(<\/mo>0.01<\/mn>\u2212<\/mo>0.0<\/mn>)<\/mo>\u00d7<\/mo>200<\/mn><\/mrow>0.3<\/mn><\/mfrac>=<\/mo>6.67<\/mn>\u2009<\/mtext>m\/a<\/mtext><\/mrow>v_s = \\frac{(0.01 – 0.0) \\times 200}{0.3} = 6.67 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

                This represents efficient lateral drainage<\/strong> within the secondary leachate collection system.<\/p>\n\n\n\n

                \n\n\n\n

                Aquifer Flow<\/h3>\n\n\n\n
                  \n
                • Upgradient inflow: 4 m\/a<\/strong><\/li>\n\n\n\n
                • Down-gradient outflow:<\/li>\n<\/ul>\n\n\n\n

                  v<\/mi>b<\/mi><\/msub>=<\/mo>4<\/mn>+<\/mo>200<\/mn>1<\/mn><\/mfrac>\u00d7<\/mo>0.0<\/mn>=<\/mo>4<\/mn>\u2009<\/mtext>m\/a<\/mtext><\/mrow>v_b = 4 + \\frac{200}{1} \\times 0.0 = 4 \\, \\text{m\/a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

                  Thus, aquifer flow remains constant beneath the landfill.<\/p>\n\n\n\n

                  \n\n\n\n

                  Passive Sink Layer Configuration<\/h2>\n\n\n\n

                  The Passive Sink option divides the system into three computational layers:<\/p>\n\n\n\n

                    \n
                  1. Layer 1 (Clay Layer)<\/strong>\n
                      \n
                    • Vertical flow only: 0.01 m\/a downward<\/strong><\/li>\n\n\n\n
                    • No horizontal flow<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                    • Layer 2 (Granular Secondary LCS)<\/strong>\n
                        \n
                      • Horizontal flow: 6.67 m\/a<\/strong><\/li>\n\n\n\n
                      • Represents leachate collection<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • Layer 3 (Aquitard)<\/strong>\n
                          \n
                        • No advective flow<\/li>\n\n\n\n
                        • Diffusion dominates transport<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
                          \n\n\n\n

                          Model Parameters<\/h2>\n\n\n\n
                          Property<\/th>Symbol<\/th>Value<\/th>Units<\/th><\/tr><\/thead>
                          Darcy Velocity<\/td>va<\/td>Variable<\/td>m\/a<\/td><\/tr>
                          Sink Velocity<\/td>vs<\/td>Variable<\/td>m\/a<\/td><\/tr>
                          Diffusion Coefficient<\/td>D<\/td>Variable<\/td>m\u00b2\/a<\/td><\/tr>
                          Distribution Coefficient<\/td>Kd<\/td>0<\/td>cm\u00b3\/g<\/td><\/tr>
                          Soil Porosity<\/td>n<\/td>0.4<\/td>–<\/td><\/tr>
                          Granular Porosity<\/td>n<\/td>0.3<\/td>–<\/td><\/tr>
                          Dry Density<\/td>\u03c1d<\/td>1.5<\/td>g\/cm\u00b3<\/td><\/tr>
                          Source Concentration<\/td>c\u2080<\/td>1000<\/td>mg\/L<\/td><\/tr>
                          Ref. Height<\/td>Hr<\/td>7.5<\/td>m<\/td><\/tr>
                          Leachate Collected<\/td>Qc<\/td>0.29<\/td>m\/a<\/td><\/tr>
                          Landfill Length<\/td>L<\/td>200<\/td>m<\/td><\/tr>
                          Aquifer Velocity<\/td>vb<\/td>4<\/td>m\/a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                          \n\n\n\n

                          Graphical Output: Concentration vs Time<\/h2>\n\n\n\n
                          \"\"<\/figure>\n\n\n\n
                          \n\n\n\n

                          PDF Report<\/h2>\n\n\n