There is a uniform flow with a velocity of v=nV in an unbounded homogeneous isotropic aquifer. Let the x direction be consistent with the v direction and the y direction be perpendicular to it. At the moment t > 0, the tracer is injected in the whole aquifer thickness range passing through the coordinate origin (0,0), and the injection mass per unit thickness is m, and then it stops, thus two-dimensional dispersion occurs. Assuming that the aquifer initially contains no injected tracer, the source-sink term is zero (see Figure 3-5-4). The mathematical model of this problem can be expressed as:

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Figure 3-5-4 Two-dimensional dispersion of tracer injected at instantaneous point

Figure 3-5-5 Variation of Isoconcentration Curve with Time in Instantaneous Point Injection of Tracer

The solution of the above mathematical model is (Sun, 1988):

hydrogeochemistry

Ignoring the molecular diffusion in porous media, substituting DL=αL V and DT=αT V into the formula (3-5-2 1) gives:

hydrogeochemistry

Where αL and αT are longitudinal and transverse dispersion respectively. According to formula (3-5-22), the temporal and spatial distribution of tracer under given conditions can be easily obtained, and the calculation results at different times are shown in Figure 3-5-5.