User's guide of Proceessing Modflow 5.0

288 Processing Modflow
6.6 Solute Transport
6.6.1 One-Dimensional Dispersive Transport
Folder: \pm5\examples\transport\transport1\
Overview of the Problem
This example demonstrate the use of numerical model and compares the numerical results with
the analytical solution.
A uniform flow with a hydraulic gradient of 2‰ exists in a sand column. The hydraulic
conductivity of the sand column is 100 m/d. The effective porosity is 0.2. The longitudinal
dispersivity is 1 m. A point source of 1 g is injected into the sand column.
Your task is to construct an one-dimensional numerical model and calculate the
breakthrough curve (concentration - time curve) at 20 m downstream of the point source.
Calculate the breakthrough curve by using a longitudinal dispersivity of 4 m and compare these
two curves. Will the peak arrival time of the concentration be changed if only the longitudinal
dispersivity is changed?
Modeling Approach and Simulation Results
The numerical model of this example consists of one layer, one row and 51 columns. The
thickness of the layer and the width of the row and column is 1 m. To obtain of hydraulic
gradient of 2‰, the first cell and the last cell of the model are specifed as fixed-head cells with
an initial hydraulic heads of 1.1 m and 1.0 m, respectively. The initial head of all other cells is
1.0 m. A steady-state flow simulation is performed for a stress period length of 100 days.
3
The injected mass of 1 [g] is simulated by assigning an initial concentration of 5 [g/m ] to
the cell [10, 1, 1]. Using the Boreholes and Observations dialog box, an observation borehole
is set in the center of the cell [30, 1, 1]. The breakthrough curves for the dispersivity of 1 m and
4 m are shown in Fig. 6.58. It is interesting to see that the concentration peak arrives earlier
(with a lower concentration value) when the value of dispersivity is getting higher. At the first
glance, this result is somewhat confusing because the center of the mass must travel with the
same velocity, regardless of the value of dispersivity. Because of a higher dispersivity, the front
of the concentration plume travels faster and at the same time the intensity of the concentration
drops down with a higher rate. This combination has caused this phenomenon.
Analytical solutions for solute transport involving advection, dispersion and first-order
6.6.1 One-Dimensional Dispersive Transport