As repositories for CO(2) and radioactive waste, as oil and gas reservoirs, and as contaminated sites needing remediation, rock formations play a central role in energy and environmental management. The connectivity of the rock's porespace strongly affects fluid flow and solute transport. This work examines pore connectivity and its implications for fluid flow and chemical transport. Three experimental approaches (imbibition, tracer concentration profiles, and imaging) were used in combination with network modeling. In the imbibition results, three types of imbibition slope [log (cumulative imbibition) vs. log (imbibition time)] were found: the classical 0.5, plus 0.26, and 0.26 transitioning to 0.5. The imbibition slope of 0.26 seen in Indiana sandstone, metagraywacke, and Barnett shale indicates low pore connectivity, in contrast to the slope of 0.5 seen in the well-connected Berea sandstone. In the tracer profile work, rocks exhibited different distances to the plateau porosity, consistent with the pore connectivity from the imbibition tests. Injection of a molten metal into connected pore spaces, followed by 2-D imaging of the solidified alloy in polished thin sections, allowed direct assessment of pore structure and lateral connection in the rock samples. Pore-scale network modeling gave results consistent with measurements, confirming pore connectivity as the underlying cause of both anomalous behaviors: imbibition slope not having the classical value of 0.5, and accessible porosity being a function of distance from the edge. A poorly connected porespace will exhibit anomalous behavior in fluid flow and chemical transport, such as a lower imbibition slope (in air-water system) and diffusion rate than expected from classical behavior.