Segmentation of X-ray images of rocks is an important step in digital rock technology. Current segmentation methods often suffer from operator bias and can be time-consuming. To overcome these limitations, an automated image segmentation model is created for pore scale images through the use of convolutional neural networks. A dataset of micro-Computed Tomography (CT) images of sandstones is considered. To create the ground truth data for training, Scanning Electron Microscopy 2D and micro-CT 3D images are used to obtain accurate segmentation masks. Three models are trained with the available data: One with limited images, one with the full dataset, and one with augmented data. The data augmentation is achieved by increasing sample size through image partitioning. The data set for each model is divided into training, validation, and testing with a 60/30/10 split, respectively. The U-Net architecture, designed to work with limited training data, is used to develop the models. Further validation of the models is performed on a different dataset unseen by the models. The Minkowski functionals and permeability of the volume generated by the segmented images are computed and compared with the ground truth segmentation. Against the unseen dataset, the models scored a dice coefficient of 0.9479, 0.9518, and 0.9599, respectively. We discuss the potential for improvement by data augmentation and fine-tuning. One limitation of the models is with the deficiency of variety in training data as both SEM and micro-CT is required to obtain the segmentation masks. We also discuss the performance of the model on unseen samples and show the potential improving efficiency in the digital rock technology. The models provide a quick and accurate segmentation for images of sandstones without the influence of operator bias, and the method shows promise for further development and improvement.