Keyur, thanks for the advise. Both images were generated with the same mesh controls, except with a reduced tunnel size. With that knowledge, and the knowledge that the mesher gives the following warning:
---- Warning--- Inner wrap for void material point fluid-region-1 is not created. There is no leakage at global min size.
I feel confindent the only way there could be leakage is when it squeezes through the tunnel wall because there is no "imprint".
What I have found that helps is using the Extract Edge Features. It is located under Advanced under Describe Geometry and Flow. Here I can set the edge-group to be "collective" between my surface and the tunnel walls. Then one can use the Preview to view the extracted edges in the viewer in Pink. This seems to help, but I am having trouble with a couple other things at the moment, so I am trying to work through those first and will update later.