NUMERICALLY MODELED TRACER MOVEMENT THROUGH A CONDUIT-MATRIX SYSTEM

Modeling groundwater flow through karst systems is a difficult task due to contrasts in hydraulic properties of the conduits and the matrix. One possible solution is to model flow strictly through the conduits using a pipe-flow model. The applicability of a pipe-flow model depends on the fluid movement between the conduit and the matrix. It is hypothesized that conduits serve as the primary pathway, with minimal fluid transfer to the matrix. To assess the validity of the hypothesis, a numerical model was developed to examine contaminant transport within a conduit-porous matrix system.

The model design examined whether differences between hydraulic properties of the conduit and the matrix limited fluid/tracer interchange between the two media. The model uses a cylindrical coordinate expression of the diffusion-convection mass transport equation. The difference between the governing equations of the two subsystems is that convective velocity is assumed negligible within the matrix, but important within the conduit. The diffusion in both the conduit and matrix subsystems is described by using Fick's First Law. The governing equations were solved using an alternate direction implicit method.

Results indicate that the tracer is moving predominately through the conduit. Very little tracer is migrating into the matrix. Simulations were performed representing the different hydraulic conditions between the conduit and matrix. One simulation used a two-order magnitude difference in the Peclet number between the matrix and conduit. The results show that the highest simulated concentrations in the matrix after 50 time-steps is over 1000 times smaller than the concentrations observed in the conduit. If the identical Peclet number was used for both the conduit and matrix, the simulated results generated the same outcome; the tracer moved through the conduit. The results produced by the model simulations indicate that the velocity of the fluid through the conduits is the fundamental mechanism for tracer movement through the system. The lack of tracer movement into the matrix reinforces the hypotheses that the conduit is the primary pathway, and since the principle flow occurs within the conduit, a pipe-flow model may be an appropriate model to simulate a conduit system.