The quantitative evaluation of the three-dimensional (3D) morphology of porous composite materials is important for understanding mass transport phenomena, which further impact their functionalities and durability. Reactive porous paint materials are composites in nature and widely used in arts and technological applications. In artistic oil paintings, ambient moisture and water and organic solvents used in conservation treatments are known to trigger multiple physical and chemical degradation processes; however, there is no complete physical model that can quantitatively describe their transport in the paint films. In the present study, model oil paints with lead white (2PbCO3·Pb(OH)2) and zinc white (ZnO) pigments, which are frequently found in artistic oil paintings and are associated with the widespread heavy metal soap deterioration, were studied using synchrotron X-ray nano-tomography and unilateral nuclear magnetic resonance. This study aims to establish a relationship among the paints' compositions, the 3D morphological properties and degradation. This connection is crucial for establishing reliable models that can predict transport properties of solvents used in conservation treatments and of species involved in deterioration reactions, such as soap formation.