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Low-carbon production is a vital solution for many environmental problems, as is consumers’ consciousness about carbon playing a more important role and ultimately passing upstream. Supply chains are eager to seek sustainable development via appropriate decision making with data-driven methods. Consistent with this aim, we investigated decisions toward lower carbon efforts and prices in a two-echelon supply chain via a game theoretical approach. The decision-making scenarios of decentralized, centralized, and cost-sharing contracts were investigated and compared. The results show that the level of improvement in environmental performance is positively correlated with the degree of cooperation between partners. Cooperation between partners would be even more significant with an increase in consumers’ low carbon awareness. Furthermore, cost-sharing contracts improve the performance of the entire supply chain compared with decentralized cases. Finally, we implemented numerical experiments to verify the modeling results. Therefore, this study provides theoretical support toward sustainable operations for supply chains concerning low carbon awareness.

The natural microdefects of shale and the expansion of microcracks under hydration and overlying rock loadings are important for the wellbore stability. According to the conservation of energy, the force of the microdefects and microcracks under finite deformation is studied by the method of configuration force through the migrating control volume in the spatial observer. Under the hydration stress and rock pressure, the equation of hydration stress and its work in reference configuration has been obtained, and the equations of configuration forces and configuration moment have been established as a consequence of invariance under changes. The relationship between the configuration and deformation forces is determined by the second law. The energy dissipation equation of the crack tip has been deduced, which shows that the projection of the concentrated internal configuration body force at the crack tip in the opposite direction of the crack is equal to the energy dissipation of the crack tip per unit length. The inertial and internal parts of the concentrated configuration body force at the crack tip have been derived; it is indicated that the internal configuration force plays a leading role in the irreversible fracture process. Moreover, the energy release rate of shale under hydration is proved to depend on constitutive responses and hydration stress. In the theoretical system of configuration force, the migrating control volume at the crack tip contains inclusions, microcracks, microvoids, and heterogeneity of the rock itself. We use the configuration force theory to solve the problem of rock crack propagation and rock fracture. The factors considered are more comprehensive, which can better reflect the actual situation and provide a theoretical basis for the study of wellbore stability.

A model is set up to calculate shale formation fracturing pressure based on the theory of elastic-plastic fracture mechanics, physicochemical rock fracture mechanics and the maximum tensile stress criterion. The model takes into account such factors as the total stress field and the crustal stress, physicochemical factors including temperature field, shale porosity and the mechanism of seepage of the drilling fluid. The model was verified by field studies of formation fracturing and laboratory investigations of the stress field in triaxial compression of shale core samples with different water contents. The error of the values calculated using the model came to 3.85%, which is close to the measured fracturing pressure. Curves of the dependence of tensile stress and fracturing pressure on water saturation were also obtained. Results show that both the fracturing pressure and the tensile strength decrease with increasing water saturation of the sample, i.e., mechanical characteristics of the rock deteriorate with increasing hydration.

In this paper, a comprehensive model to calculate the rock fracture pressure by the theory of double effective stress of porous medium is established, which considers such effective factors as the crustal stress field, hydration stress field, temperature field, tectonic stress field, the porosity of rock, and additional stress field generated by seepage of drilling fluid. This new model is applicable to predict the fracture pressure of different types of rocks. Using the experimental parameters of field fracturing and the experimental results of three-axis compression of rock cores with different water contents, we may get the calculated fracture pressure. Compared with the measured fracture pressure in the oilfield, the result calculated in the present study shows good agreement. Besides, the effects of water contents on the tensile strength and fracture pressure are analyzed. Results show that both the tensile strength and fracture pressure decrease with the increase of water contents, which is due to the reduction of the mechanical properties of rocks by hydration.

Oil drilling rig is an important equipment for oil and gas drilling operations. There is a great risk in the process of its use. If the risk factors are not well managed, it will cause great loss. In order to prevent accidents, the safety evaluation index and evaluation model of the oil drilling rig system are established by the extension theory. We qualified and normalized each index, determined the classical domain and the joint domain, then calculated the correlation coefficient of the evaluation index by the association function of the extension set. The weight of all the system indexes is determined by the improved analytic hierarchy process. By the characteristic value of the level variable, the grade of the failure probability of the oil drilling rig system is judged. The feasibility of the model is verified by experiments, and the safety evaluation of the oil drilling rig system is carried out. It provides a new and effective way to study the safety evaluation of the oil drilling rig system.

In this paper, we build an aggregative model to calculate the rock fracture pressure by the theory of double effective stress of porous medium; it takes into account such factors as the crustal stress field, chemical field, temperature field, the porosity of rock, seepage of drilling fluid, and so on. As the parameters of the model take different values, the model can predict the fracture pressure of different types of rocks under different geological conditions. Combined with the experimental data of field fracturing and the experimental results of three-axial compression of rock core with different water contents, the results show that the error of the this paper’s model is 4.39% compared with the measured value, which provides technical support for drilling engineering.