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This paper considers the fluid flow through a porous medium containing intersecting fractures and presents three main analytical findings, namely: (1) mass exchange between fractures and surrounding matrix at the fracture intersection;(2) fluid potential solution (pressure field) within the whole domain under the form of a single singular integral equation; and (3) closed-form solutions of fluid flow in and around a crack disc under a far field pressure gradient. The crack is represented mathematically by a 2D smooth surface (i.e., zero thickness) within a 3D porous medium, while physically by a constant aperture. The fluid flow within the crack obeys Poisseuille's law, while Darcy's law is used to represent the fluid flow in the surrounding matrix. The general solution of pressure field for the general case of multiple intersecting cracks is firstly derived under a singular integral equation form. The mass exchange between the porous matrix and the crack, as well as the mass conservation at the intersection between cracks are the keys to obtaining this general solution. Then, the general solution is written for the case of a single crack. Rigorous derivation of the latter equation allows obtaining a closed-form solution of flow through a single crack. Introducing this solution of flow into the general equation gives the pressure field around the crack. The solution derived in this paper for a crack disk with Poisseuille's flow is slightly different from the well-known Eshelby's solution for the case of flattened inclusion in which the flow obeys Darcy's law.

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With the rise of industrial artificial intelligence (AI), smart sensing, and the Internet of Things (IoT), companies are learning how to use their data not only for analysing the past but also for predicting the future. Maintenance is a crucial area that can drive significant cost savings and production value around the world. Predictive maintenance (PdM) is a technique that collects, cleans, analyses, and utilises data from various manufacturing and sensing sources like machines usage, operating conditions, and equipment feedback. It applies advanced algorithms to the data, automatically compares the fed data and the information from previous cases to anticipate or predict equipment failure before it happens, thus helping optimise equipment utilisation and maintenance strategies, improve performance and productivity, and extend equipment life. Robust PdM tools enable organisations to leverage and maximise the value of their existing data to stay ahead of potential breakdowns or disruptions in services, and address them proactively instead of reacting to issues as they arise. Therefore, it has attracted more and more attention of specialists in recent years. This paper provides a comprehensive review of the recent advancements of machine learning (ML) techniques widely applied to PdM by classifying the research according to the ML algorithms, machinery and equipment used in data acquisition. Important contributions of the researchers are highlighted, leading to some guidelines and foundation for further studies. Currently, BIENDONG POC is running some pilot PdM projects for critical equipment in Hai Thach - Moc Tinh gas processing plant.