Fig 1.
Three-dimensional numerical grid geometry.
Example of the grid geometry used in the numerical simulation of a three-phase fluid flow (water + LNAPL + air) with a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 × 22 m, at the initial time t = 0 s. The red box is the continuous source of an immiscible contaminant at the top of the parallelepiped in the z − x plane (left-hand side) and the z − y plane (right-hand side), respectively.
Table 1.
List of parameters used for the three-dimensional numerical simulations of LNAPL and DNAPL in variably saturated zones.
Fig 2.
Saturation contours of LNAPL (continuous source) at different times.
Three-dimensional numerical results on the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a continuous source of LNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. Left-hand side shows the saturation contours in the (z − x) plane. Right-hand side shows the saturation contours in the (y − x) one. Notice how the LNAPL moves in the unsaturated zone, although initially, it goes a bit down with respect to the groundwater table (-5 m) being a continuous contaminant spill. On the other hand, the first two rows show no contamination since the plane is located at the groundwater table.
Fig 3.
Depth vs. saturation of LNAPL (continuous source) at different times.
Three-dimensional numerical simulation results of the depth as a function of the water saturation Sw (blue points), LNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a continuous leak of LNAPL of Fig 2. Initially, at t = 0 s, there is a sharp front of contaminant saturation situated on top of the grid, rapidly reaching zero when the height decreases. At the same time, it is filled by the air saturation (green point) in the unsaturated zone and water saturation in the saturated zone. Notice that the sum of the three-phase saturations is always one. For later times is being observed how the contaminant (red points) moves toward the saturated zone and remains floating while moving with the direction of the groundwater flow.
Fig 4.
Pressure vs. Depth for LNAPL (continuous source) at different times.
Three-dimensional numerical simulation results of the pressure as a function of the depth for a constant leak of LNAP at different times. Initially, at a time equal to zero (blue points), the pressure is equal to one atmosphere in the unsaturated zone composed by air-contaminant. It increases up to 220 KPa in the saturated zone. For later times (green points), the pressure slightly increases also in the unsaturated zone when the LNAPL arrives at the saturated zone.
Fig 5.
Saturation contours of DNAPL (continuous source) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a continuous source of DNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. The left-hand side shows the saturation contours in the (z − x) plane. The right-hand side shows the saturation contours in the (z − y) one. Notice how the DNAPL migrates through the saturated zone while moving in the left direction (where it is positioned a gravity at 15 degrees in the z–x plane, left-hand side). The difference between the previous case (Fig 2) is that now the continuous leak of DNAPL keeps moving to the bottom (aquiclude) of the saturated zone while moving in the left direction due to the pressure gradient.
Fig 6.
Depth vs. saturation of DNAPL (continuous source) at different times.
Three-dimensional numerical simulation results of the depth as a function of the water saturation Sw (blue points), DNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a continuous leak of DNAPL in Fig 5. Initially, at t = 0 s, a front of contaminant saturation is situated on top of the grid, which rapidly goes to zero. At the same time, it is filled by the air saturation (green point) in the unsaturated zone and water saturation in the saturated one. Notice how the sum of the three-phase saturations is always one. For later times the contaminant (red points) is immersed into the saturated zone.
Fig 7.
Pressure vs. Depth for DNAPL (continuous source) at different times.
Three-dimensional numerical result on the pressure as a function of the depth for a continuous leak of DNAPL at different times. Initially, at t = 0 s (blue points), the pressure is equal to one atmosphere in the unsaturated zone composed of air and the contaminant. Then the pressure increases as the contaminant goes downward the groundwater table to the bottom, up to a value of 220 KPa.
Fig 8.
Saturation contours of DNAPL (small source) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a small volume source of DNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. Left-hand side shows the saturation contours in the (z − x) plane. Right-hand side shows the saturation contours in the (z − y) one. Notice how the DNAPL migrates through the saturated zone while moving in the left direction (where it is positioned a gravity at 15 degrees in the z–x plane, left-hand side) at different times.
Fig 9.
Depth vs. saturation of DNAPL (small source) at different times.
Three-dimensional numerical simulation results of a depth as a function of the water saturation Sw (blue points), DNAPL saturation Sn (red points), and air saturation Sa (green points) (plane x = 0) at various times for a small leak of DNAPL of Fig 8. Initially, at t = 0 s, there is a sharp front of contaminant saturation (red points) situated in the unsaturated zone at z = [4.0, 7.0] m. The unsaturated zone comprises the contaminant and air (green points). Later, the contaminant starts to move downward, and the saturation starts to decrease in the unsaturated zone (center). Contextually, the air phase begins to occupy the space left by the contaminant (green points). Finally, (left-hand side) the contaminant arrives at the groundwater table and enters the saturated zone (see also Fig 8, same time).
Fig 10.
Saturation contours of LNAPL (small source) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a small volume source of LNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. Notice how the LNAPL migrates through the saturated zone while moving in the left direction due to a pressure gradient and remains entirely on the capillary fringe zone.
Fig 11.
Depth vs. saturation of LNAPL (small source) at different times.
Numerical simulation results of a depth as a function of the water saturation Sw (blue points), LNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a small leak of LNAPL of Fig 10. Initially, at t = 0 s, there is a sharp front of contaminant saturation (red points) situated in the unsaturated zone at z = [4.0,7.0] m. Later, the contaminant moves downward, and the saturation decreases (center). On the right-hand side, the contaminant reaches the groundwater table and does not enter the saturated zone except in a small quantity.
Fig 12.
Saturation contours of DNAPL (with an impermeable lens) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a continuous source of DNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. The DNAPL leak encounters an impermeable obstacle (depicted in green) situated at z = [2.0,6.0]m, x = [−10.0, +10.0]m, y = [−10.0, +10.0]m. After seven days and 2.7 hours the contaminant has reached the saturated (aquifer) zone at x = −10 m depth.
Fig 13.
Depth vs. saturation of DNAPL (with an impermeable lens) at different times.
Three-dimensional numerical simulation results of a depth as a function of the water saturation Sw (blue points), DNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a continuous leak of DNAPL of Fig 12 (plane x = 0). The DNAPL leak encounters an impermeable obstacle (depicted in green in Fig 12). The left-hand side shows a sharp front of contaminant saturation (red points) situated in the unsaturated zone at z = [8.0,10.0] m. At later times, (center) after two days and 8.9 hours, the contaminant saturation increases to 1.0 due to an accumulation on top of the impermeable zone while part of it reaches the saturated zone. This situation remains almost invariable for later times (right-hand side) since we plot the x = 0 plane.
Fig 14.
Saturation contours of DNAPL (with a smaller impermeable lens) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a continuous source of DNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times (plane x = 0). The continuous source of DNAPL encounters an impermeable obstacle (depicted in green), smaller than the one in Fig 12, situated at z = [2.0,4.0]m, x = [−5.0, +5.0]m, y = [−5.0, +5.0]m. After arriving at the groundwater table, the continuous source of DNAPL keeps going downward and moving to the left direction on both sides.
Fig 15.
Depth vs. saturation of DNAPL (with a smaller impermeable lens) at different times.
Three-dimensional numerical simulation results of a depth as a function of the water saturation Sw (blue points), DNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a continuous leak of DNAPL of Fig 14 (plane x = 0). The DNAPL leak encounters an impermeable obstacle (depicted in green in Fig 14). After 5.7 hours, there is a sharp front of contaminant saturation (red points) situated in the unsaturated zone at z = [8.0,10.0] m. The DNAPL saturation increases from 0.9 to one at later times since it accumulates on top of the impermeable parallelepiped. Then abruptly goes to zero and finally increases in the saturated zone (right-hand side). Notice that the DNAPL and water saturation sum is one for a fixed depth value.
Fig 16.
Saturation iso-surface of DNAPL (with an impermeable lens) at time 8.15 days.
The three-dimensional visualization of the numerical simulation results of the contaminant saturation iso-surface at time 8.15 days. Notice the impermeable parallelepiped zone just below the contaminant released on top of the grid. This figure was generated using VisIt (an open-source post-processing) and the three-dimensional saturation data of Fig 14.
Fig 17.
Saturation contours of DNAPL (with an impermeable in the groundwater) at different times.
Three-dimensional numerical simulation results of the saturation contours (σn = Snϕ) of a three-phase immiscible fluid flow (water + a continuous source of DNAPL + air) using a spatial grid resolution of 0.50 m and a grid dimension of 80 m × 32 m × 22 m, at different times. The DNAPL encounters an impermeable obstacle (depicted in green), situated at z = [−5.0, −2.0]m, x = [−10.0, +10.0]m, y = [−10.0, +10.0]m.
Fig 18.
Depth vs. saturation of DNAPL (with an impermeable lens in the groundwater) at different times.
Three-dimensional numerical simulation results of a depth as a function of the water saturation Sw (blue points), DNAPL saturation Sn (red points), and air saturation Sa (green points) at various times for a continuous leak of DNAPL of Fig 17 (plane x = 0). The continuous source of DNAPL encounters an impermeable obstacle (depicted in green in Fig 17). Initially, the contaminant (red points) is situated on the parallelepiped (left-hand side). Then the sharp front starts to move downward (middle) until it arrives at the saturated zone where the impermeable obstacle causes the contaminant to accumulate just below the groundwater table (right-hand side).