Analyzing core samples extracted from subsurface formations is one of the basic elements of reservoir characterization. Corflooding experiments are conducted routinely for characterization of contaminated aquifers before remediation and in petroleum reservoirs for production planning. They are also necessary when characterizing CO2 storage sites such as deep saline aquifers. We are interested in developing methods for characterizing the sub-core permeability field. In low flow rates, the core properties are rate dependent due to the impact of core heterogeneity and capillary forces. Therefore, knowledge of sub-core heterogeneity will lead to better estimates of the core relative permeability and capillary pressure curves. These studies are part of an ongoing effort to better understand capillary heterogeneity effects.