## 1 Introduction  
Petroleum reservoirs are structures in the earth's subsurface that consist of pores and a fracture network that can store hydrocarbons [1]. In fractured reservoirs, the fractures can increase the porosity and permeability of the reservoir, affecting fluid flow and transport [2]; therefore, understanding these physical parameters could improve oil extraction mechanisms [3]. The irregular and complex geometry of fractures is the main factor affecting fluid flow. The complexity of the geometry is due to the surface roughness and varying aperture widths [4]. Previous studies have shown that this irregular geometry significantly impacts fluid mobility within fractures [5,6].  
Determination of the physical parameters of fractures is complex, generally achieved through laboratory tests, for example, by injecting a fluid through a rock fracture sample by maintaining the pressure and temperature conditions [7]. Numerical simulations are also widely used, employing the X-ray micro-computed tomography technique to create three-dimensional fracture geometry [8] for numerical fluid flow simulations, enablingus to obtain the physical parameters [9]. One of the numerical simulation methods often used for fractures to obtain fluid flow parameters in porous media and fractures is the Lattice Boltzmann method [10; 11; 12]. However, both these methods are time-consuming and resource-intensive [13].  
The recently developed machine learning methods have been applied to resolve many problems in technology, industry, and science [14], including the optimisation of hydrocarbon production [15], well-log data analysis [16], and the estimation of physical parameters related to porous rocks and fractures. For example, the toughness of a fracture has been estimated using regression trees and neural networks [17], physical properties of two-dimensional porous media properties have been predicted [18], and the estimation of porous media porosity, permeability, and tortuosity [13]. Deep learning models are commonly applied to handle complex problems using artificial neural networks consisting of multiple layers of neurons which mimic the neurons in the human brains, with weights that are adjusted throughout the training process. A variant of the deep learning model is the convolutional neural network (CNN). The CNN has been used for image pattern recognition due to its ability to learn complex features from images [19; 20]. CNN models have been used in research on fractures, for example, to estimate permeability in fracture networks [21], as well as for the estimation of physical parameters in two-dimensional fractures [22]. There are also pre-trained models that use transfer learning, which have yielded accurate results in estimating porous media parameters when working with small datasets [23]. Beyond the CNN, other deep learning models, such as transformers-based deep learning models, have been used to improve the prediction of permeability in porous media by leveraging their self-attention mechanisms to capture complex spatial correlations and heterogeneity [24].  
CNN models were utilised in this study to predict the physical properties of three-dimensional singular fractures, including permeability, surface roughness, and mean aperture. Permeability refers to the ability of a medium to allow fluids to pass through it. Surface roughness refers to the roughness of the internal surface of fractures, and mean aperture is the mean aperture width of fractures. This study builds upon our previous work [22], which focused on estimating two-dimensional fracture properties using machine learning. This study advances from our previous one by transitioning to three-dimensional fracture geometries. Five CNN models were evaluated, two models developed specifically for this study, referred to as CNN-1 and CNN-2, and three pre-trained models consisting of DenseNet201, VGG16, and Xception to estimate the physical parameters of three-dimensional fractures.