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Streamline simulations have been extensively used due to their computational speed and invulnerability to numerical dispersion. However, many works have been applied to transport modeling without considering dispersive transport. A new term, advection-dispersion ratio, is introduced, which is defined as a relative extent of advection to dispersion along a streamline. By using the advection-dispersion ratio, analytical solution to the advection-dispersion equation is mapped onto streamlines so that dispersive transport can be effectively modeled by streamline simulation. With the advection-dispersion ratio incorporated, streamline simulation was applied to model transport in an artificially fractured sample, and validated by comparing with an experiment. It is observed that the tracer breakthrough curve from the simulation matches well with that from the experiment.
By allocating variable advection-dispersion ratios to streamlines, streamline simulations were performed on various fields generated by sequential Gaussian simulation in order to analyze the effect of the advection-dispersion ratio on transport modeling. The results were then compared with the simulation results using a single representative advection-dispersion ratio over the entire flow domain. The simulation results indicate that a representative advection-dispersion ratio is applicable when the advection-dispersion ratio is high. On the other hand, different advection-dispersion ratio should be allocated to each streamline according to the characteristics of the streamline, in the case where the representative advection-dispersion ratio is low. Moreover, similar values of permeability cluster spatially in a field of high correlation length, which result in more diverse and contrastable streamline characteristics from the standpoint of advection-dispersion ratio. This explains why the results using a single representative advection-dispersion ratio differ from those using variable advection-dispersion ratios along individual streamlines.
Acknowledgments
This work was supported by Korea Research Foundation Grant (KRF-2002-003-D00468) and conducted through the Research Institue of Engineering Science at Seoul National University, South Korea.