Microstructures are critical for defining material characteristics such as permeability, mechanical, electrical and other physical properties. However, the available techniques for determining compositional microstructures through segmentation of x-ray computed tomography (CT) images are inadequate when there are finer structures than the CT spatial resolution, ie when there is more than one material in each voxel. This is the case for CT imaging of geomaterials characterized with submicron porosity and clay coating that control petrophysical properties of rock. This note outlines our data-constrained modelling (DCM) approach for prediction of compositional microstructures, and our investigation of the feasibility of determining sandstone microstructures using multiple CT data sets with different x-ray beam energies. In the DCM approach, each voxel is assumed to contain a mixture of multiple materials, optionally including voids. Our preliminary comparisons using model samples indicate that the DCM-predicted compositional microstructure is consistent with the known original microstructure under low noise conditions. The approach is quite generic and is applicable to predictions of microstructure of various materials.