Tracer Injection into Aquifer

This two dimensional model describes the transient concentration distribution of trichloroethylene (TCE), which is injected as a tracer into a vertical well completed into a sandstone aquifer. Initially the whole system is at equilibrium at the far field pressure, and the tracer concentration is zero.
The well is cased and perforated, and completed with a concentric screen (modeled here as a porous medium). The annular gap is gravel-packed up to three quarters of the considered well length. Water is injected through the top of the base pipe, which feeds into the screen pipe. The equidistant perforation tunnels are also sand-packed.

The fluid flow equations solved are the stationary Navier-Stokes in the free domains, and the Brinkman equations for the porous ones (screen, sand pack, and aquifer matrix). Inertial effects are considered for the sand pack, and described via the Ergun correlation for the beta factor. The sand pack permeability is also determined with the Ergun model. All materials are considered incompressible and at constant temperature.
The convective solute transport equations for the tracer are fully coupled with those for fluid flow.

The applied fluid boundary conditions are constant pressure at the base pipe inlet, constant pressure at the reservoir far field outlet, and no flow on the other outer boundaries of the model. The wellbore connects hydraulically to the reservoir only through the sand-packed perforation tunnels. The TCE tracer is injected for the first 10 minutes, at constant concentration c0 = 10 g/liter, and TCE-free water continues to be injected afterwards.

Figure 1. The domain geometry and mesh. The inset provides a close-up of the section of the completion indicated by the dashed magenta rectangle.

The length of the well is 1.5 m, the outer and inner diameters of the screen and casing are 3.32 inch and 6.63 inch, respectively, and the modeled aquifer extends to 15 ft away from the axis of the well. The borehole has a diameter of 9.5 inch, while the seven perforation tunnels are 0.75 inch-wide. The screen assembly hydraulically connects the interior of the screen pipe to the well annulus.

The sand pack consists of particles 400 micron in diameter, with a porosity of 30%. The Ergun correlations lead therefore to a permeability Ksand = 59.55 Darcy and a beta factor of 1.13E5 m-1. The permeability and porosity of the aquifer are 100 mD and 20%, respectively. The screen assembly is modeled as a porous medium of porosity equal to unity and 1000 Darcy permeability, without inertial effects.

The animated Figure 2 below depicts the distribution of the fractional TCE concentration (relative to c0) for the first 30 minutes of injection time.

Figure 2. Fractional TCE concentration distribution during the first 30 minutes of injection.
Figure 2. Fractional TCE concentration distribution during the first 30 minutes of injection.

Figure 3 shows the time evolution of the average fractional TCE concentration within the screen pipe, the sand pack, the nearby aquifer section, and the rest of the considered porous matrix (solid blue, green, red, and cyan curves, respectively). The dashed black line corresponds to the tracer concentration at the base pipe inlet.

Figure 3.
Figure 3. Time evolution of the average fractional TCE concentration within the screen pipe, the sand pack, the nearby aquifer section, and the rest of the considered porous matrix (solid blue, green, red, and cyan curves, respectively). The dashed black line corresponds to the tracer concentration at the injection boundary.

The capabilities featured by this model can be employed for computational analysis of field tracer tests.

 

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