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The ever-increasing quest to identify, secure, access and operate oil and gas fields is continuously expanding to the far corners of the planet, facing extreme conditions towards exploring, securing and deriving maximum fluid benefits from established and unconventional fossil fuel sources alike: to this end, the unprecedented geological, climatic, technical and operational challenges have necessitated the development of revolutionary drilling and production methods. This review paper focuses on a technological field of great importance and formidable technical complexity -that of well drilling for fossil fuel production. A vastly expanding body of literature addresses design and operation problems with remarkable success: what is even more interesting is that many recent contributions rely on multidisciplinary approaches and reusable Process Systems Engineering (PSE) methodologies -a drastic departure from ad hoc/one-use tools and methods of the past.The specific goals of this review are to first, review the state of art in active fields within drilling engineering, and explore currently pressing technical problems, which are in dire need, or have recently found, PSE-and/or CFD-relevant solutions. Then, we illustrate the methodological versatility of novel PSE-based approaches for optimization and control, with an emphasis on contemporary problems.Finally, we highlight current challenges and opportunities for truly innovative research contributions, which require the combination of best-in-class methodological and software elements in order to deliver applicable solutions of industrial importance. Well drilling in the oil and gas industryThe annual increase in global energy demand and the diverse applications of conventional & unconventional oil and gas resources are indicative of the fact that these resources will continuously remain relevant to humanity in the far future. With increasing climate change concerns, natural gas already provides a promising transition between some oil-based fuels and renewables in the long run, despite its well-known transportation difficulties. 1 It can be further argued that natural gas represents an economically attractive option for electricity generation (particularly in the US where shale gas is naturally abundant) with significantly reduced greenhouse gas emissions compared to coal; thus increasing its market demand. 2 These reasons have warranted the advancements in technologies of

Accurate prediction of the flow behaviour of drill cuttings carried by a non-Newtonian fluid in an annular geometry is important for the successful and efficient design, operation, and optimisation of drilling operations. Although it is widely recognised that practical drilling operations hardly involve perfectly spherical cuttings, the relative ease in mathematical description coupled with speedy computation are the main reasons for the prevalence of this simplifying assumption. The possibilities offered by the modification of the interphase exchange coefficient of the Syamlal-O'Brien model as well as its scarce implementation in literature have motivated the authors to delve into this area of research as far as the transport phenomena of non-spherical drill cuttings is concerned. Another aspect of this work was influenced by the need to understand the flow dynamics around bends (horizontal to inclined and inclined to vertical sections) during deviated drilling operations using two high viscosity muds (0.5% CMC and 0.5% CMC + 4% Bentonite mud). The Eulerian-Eulerian model was adopted for this study while considering particle sphericities of 0.5, 0.75 and 1 and diameters of 0.002 m, 0.003 m, 0.004 m, 0.005 m and 0.008 m respectively. It was discovered that particle deposition intensifies at the inclined-to-vertical bend compared to other locations in the flow domain. We also observe increased dispersion effects and transport velocities of non-spherical particles compared to particles of a perfectly spherical geometry. Furthermore, an improvement in the rheological properties of the drilling mud shows a remarkable increase in cuttings transport efficiency especially with the smaller particles. However, increased deposition of larger particles still poses a challenge to the wellbore cleaning process despite this rheological enhancement. The proposed CFD modelling methodology is thus capable of providing critical insight into the dynamics of cuttings transport, and the resulting computational observations are consistent with relevant experimental investigations.