A method for determining in-situ relationships between physical properties of a porous medium from a sample thereof includes acquiring a three-dimensional image of the sample and segmenting the image into pixels representing pore space and pixels representing rock grain. A plurality of sub-volumes are selected from the segmented image, and a porosity is calculated for each of the sub-volumes. A digital simulation is conducted on each of the sub-volumes to obtain a selected physical property for the sub-volume. A relationship is determined between porosity and the selected physical property using relationship data comprising the calculated porosity and the simulated physical property for each of the sub-volumes. The method includes at least one of storing and displaying the relationship.