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This paper aims to employ a multivariate nonlinear regression analysis to establish a predictive model for the final fracture area, while accounting for the impact of individual parameters.

This analysis is based on the numerical simulation data obtained, using the hybrid finite element–discrete element (FE–DE) method. The forecasting model was compared with the numerical results and the accuracy of the model was evaluated by the root mean square (RMS) and the RMS error, the mean absolute error and the mean absolute percentage error.

The multivariate nonlinear regression model can accurately predict the nonlinear relationships between injection rate, leakoff coefficient, elastic modulus, permeability, Poisson’s ratio, pore pressure and final fracture area. The regression equations obtained from the Newton iteration of the least squares method are strong in terms of the fit to the six sensitive parameters, and the model follow essentially the same trend with the numerical simulation data, with no systematic divergence detected. Least absolutely deviation has a significantly weaker performance than the least squares method. The percentage contribution of sensitive parameters to the final fracture area is available from the simulation results and forecast model. Injection rate, leakoff coefficient, permeability, elastic modulus, pore pressure and Poisson’s ratio contribute 43.4%, −19.4%, 24.8%, −19.2%, −21.3% and 10.1% to the final fracture area, respectively, as they increased gradually. In summary, (1) the fluid injection rate has the greatest influence on the final fracture area. (2)The multivariate nonlinear regression equation was optimally obtained after 59 iterations of the least squares-based Newton method and 27 derivative evaluations, with a decidability coefficient R2 = 0.711 representing the model reliability and the regression equations fit the four parameters of leakoff coefficient, permeability, elastic modulus and pore pressure very satisfactorily. The models follow essentially the identical trend with the numerical simulation data and there is no systematic divergence. The least absolute deviation has a significantly weaker fit than the least squares method. (3)The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.

A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.

The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R²) is 0.93 for the validation set, and the R² for the test set A and test set B are 0.93 and 0.94, respectively.

This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

Multi-well hydrofracturing is an important technology to create new fractures and expand existing fractures to increase reservoir permeability. The propagation morphology of the fracture network is affected by the disturbance between the fractures initiation sequences and spacings between adjacent wells. However, it remains unclear how well spacing and initiation sequences lead to fracture propagation, deflection and connection.

In this study, the thermal-hydro-mechanical coupling effect in the hydrofracturing process was considered, to establish a finite element-discrete element model of multistage hydrofracturing in a horizontal well. Using typical cases, the unstable propagation of hydraulic fractures in multiple horizontal wells was investigated under varying well spacing and initiation sequences. Combined with the shear stress shadow caused by in situ stress disturbed by fracture tip propagation, the quantitative indexes of fracture propagation such as length, volume, displacement vector, deflection and unstable propagation behavior of the hydrofracturing fracture network were analyzed.

The results show that the shear stress disturbance caused by multiple hydraulic fractures is a significant factor in multi-well hydrofracturing. Reducing the spacing between multiple wells increases the stress shadow area and aggravates the mutual disturbance and deflection between the fractures. The quantitative analysis results show that a decrease of well spacing reduces the total length of hydraulic fractures but increases the total volume of the fracture; compared with sequential and simultaneous fracturing, alternate fracturing can effectively reduce stress shadow area, alleviate fracture disturbance and generate larger fracture propagation length and volume.

The numerical models and results of the unstable propagation and stress evolution of the hydraulic fracture network under thermal-hydro-mechanical coupling obtained in this study can provide useful guidance for the evaluation and design of rock mass fracture networks in deep unconventional oil and gas reservoirs.

Background: Geostatistics focuses on spatial or spatiotemporal datasets. Geostatistics was initially developed to generate probability distribution predictions of ore grade in the mining industry; however, it has been successfully applied in diverse scientific disciplines. This technique includes univariate, multivariate, and simulations. Kriging geostatistical methods, simple, ordinary, and universal Kriging, are not multivariate models in the usual statistical function. Notwithstanding, simple, ordinary, and universal kriging techniques utilize random function models that include unlimited random variables while modeling one attribute. The coKriging technique is a multivariate estimation method that simultaneously models two or more attributes defined with the same domains as coregionalization.

Objective: This study investigates the impact of populations on traffic volumes as a variable. The additional variable determines the strength or accuracy obtained when data integration is adopted. In addition, this is to help improve the estimation of annual average daily traffic (AADT).

Methods procedures, process: The investigation adopts the coKriging technique with AADT data from 2009 to 2016 from Montana, Minnesota, and Washington as primary attributes and population as a controlling factor (second variable). CK is implemented for this study after reviewing the literature and work completed by comparing it with other geostatistical methods.

Results, observations, and conclusions: The Investigation employed two variables. The data integration methods employed in CK yield more reliable models because their strength is drawn from multiple variables. The cross-validation results of the model types explored with the CK technique successfully evaluate the interpolation technique's performance and help select optimal models for each state. The results from Montana and Minnesota models accurately represent the states' traffic and population density. The Washington model had a few exceptions. However, the secondary attribute helped yield an accurate interpretation. Consequently, the impact of tourism, shopping, recreation centers, and possible transiting patterns throughout the state is worth exploring.

This paper aims to consider the potential implications of the layering of regulation in relation to hydraulic fracturing (fracking) at the borders between the nations of the UK.

This paper uses a qualitative research method grounded in particular in legal geography to examine the existing approaches to regulating hydraulic fracturing and identify the places and their features that are constructed as a result of their intersection at the borders of the nations comprising the UK.

The current regulatory framework concerning hydraulic fracturing risks restricts the places in which the practice can occur in such a manner as to potentially cause greater environmental harm should the process be used. The regulations governing the process are not aligned in relation to the surface and subsurface aspects of the process to enable their management, once operational, as a singularly constructed place of extraction. Strong regulation at the surface can have the effect of influencing placement of the site only in relation to the place at which the resource sought reaches the surface, whilst having little to no impact on the environmental harms, which will result at the subsurface or relative to other potential surface site positions, and potentially even increasing them.

This paper is limited by uncertainty as to the future use of hydraulic fracturing to extract oil and gas within the UK. The issues raised within it would also be applicable to other extractive industries where a surface site might be placed within a radius of the subsurface point of extraction, rather than having to be located at a fixed point relative to that in the subsurface. This paper therefore raises concerns that might be explored more generally in relation to the regulation of the place of resource extraction, particularly at legal borders between jurisdictions, and the impact of regulation, which does not account for the misalignment of regulation of spaces above and below the surface that form a single place at which extraction occurs.

This paper considers the potential impacts of misaligned positions held by nations in the UK in relation to environmentally harmful practices undertaken by extractive industries, which are highlighted by an analysis of the extant regulatory framework for hydraulic fracturing.

Whilst the potential for cross internal border extraction of gas within the UK via hydraulic fracturing and the regulatory consequences of this has been highlighted in academic literature, this paper examines the implications of regulation for the least environmentally harmful placement of the process.

The purpose of this study is to investigate the impact of the construction and operation of underground gas storage (UGS) facilities, under the prism of the recent rise in energy prices. The focus is on developing energy markets interconnected with gas producers through pipelines and has access to liquefied natural gas (LNG) facilities in parallel.

Through a focal market in Europe, the authors estimate the economic value for both stakeholders and consumers by introducing a methodology, appropriately adjusted to the specificities of the domestic energy market. The Transmission System Operator, the Energy Market Regulator, the Energy Exchange and Eurostat are the main data sources for our calculations and conclusions.

The authors investigate the perspectives of UGS facilities, identifying financial challenges considering specific energy market conditions which are barriers to new storage facilities. Nevertheless, the energy price rocketing coupled with the security of gas supply issues, which arose in autumn 2021 and were continuing in 2022 due to the Russia–Ukraine crisis, highlight that gas storage remains, at least for the midterm, at the core of European priorities.

The paper emphasizes on developing markets toward green transition, proposing tangible policy recommendations regarding gas storage. A new methodological approach is proposed, appropriate to quantify the economic value of UGSs in such markets. Last, a mix of energy policy options is suggested which include regulatory reforms, support schemes and new energy infrastructures that could make the gas storage investments economically viable.

Thermal fractures initiated under cooling at the surfaces of a 2-D or 3-D structure propagate, arrest and coalesce, leading to its structural failure and material-property changes, while the same processes can happen in the rock mass between parallel hydraulic fractures filled with cold fluid, leading to enhanced fracture connectivity and permeability.

This study used a 2-D plane strain fracture model for mixed-mode thermal fractures from two parallel cooling surfaces. Fracture propagation was governed by the theory of linear elastic fracture mechanics, while the displacement and temperature fields were discretized using the adaptive finite element method. This model was validated using two numerical benchmarks with strong fracture curvature and then used to simulate the propagation and coalescence of thermal fractures in a long rock mass.

Modeling results show two regimes: (1) thermal fractures from a cooling surface propagate and arrest by following the theoretical solutions of half-plane fractures before the unfractured portion decreases to 20% rock-mass width and (2) some pairs of fractures from the opposite cooling surfaces tend to eventually coalesce. The fracture coalescence time is in a power law with rock-mass width.

These findings are relevant to both subsurface engineering and material engineering: structure failure is a key concern in the latter, while fracture coalescence can enhance the connectivity of thermal and hydraulic fractures and thus reservoir permeability in the former.

The aim of this study is to understand the environmental benefits and economic savings associated with adoption of circular economy in the construction sector. The research findings will support different stakeholders and decision makers to develop business models based on responsible consumption of resources and build sustainable business models.

The research uses mixed methodology wherein inventory for life cycle assessment and life cycle costing for environmental and economic impacts is based on primary data using on-site visits for qualitative and quantitative data.

Different types of land transportation infrastructures are compared for their environmental impacts. It is found that bridges have the highest environmental impacts as compared to tunnels, roads and railways. Further, the results affirm the environmental and economic benefits of adopting circular economy practices.

This is one of a kind research that compares the environmental and economic tradeoffs of adopting circular economy in different types of land transportation infrastructures.

The crude oil supply chain (COSC) is one of the most complex and largest supply chains in the world. It is easily vulnerable to extreme events. Recently, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (often known as COVID-19) pandemic created a massive imbalance between supply and demand which caused significant price fluctuations. The purpose of this study is to explore the influential factors affecting the international COSC in terms of consumption, production and price. Furthermore, it develops a model to predict the international crude oil price during disease outbreaks using Random Forest (RF) regression.

This study uses both qualitative and quantitative approaches. A qualitative study is conducted using a literature review to explore the influential factors on COSC. All the data are extracted from Web sources. In addition to COVID-19, four other diseases are considered to optimize the accuracy of predictive results. A principal component analysis is deployed to reduce the number of variables. A forecasting model is developed using RF regression.

The findings of the qualitative analysis characterize the factors that influence international COSC. The findings of quantitative analysis emphasize that production and consumption have a higher contribution to the variance of the data set. Also, this study found that the impact caused to crude oil price varies with the region. Most importantly, the model introduced using the RF technique provides a high predictive ability in short horizons such as infectious diseases. This study delivers future directions and insights to researchers and practitioners to expand the study further.

This is one of the few available pieces of research which uses the RF method in the context of crude oil price forecasting. Additionally, this study examines international COSC in the events of emergencies, specifically disease outbreaks using machine learning techniques.

The purpose of this paper is to develop a coupled lattice Boltzmann model for the simulation of the freezing process in unsaturated porous media.

In the developed model, the porous structure with complexity and disorder was generated by using a stochastic growth method, and then the Shan-Chen multiphase model and enthalpy-based phase change model were coupled by introducing a freezing interface force to describe the variation of phase interface. The pore size of porous media in freezing process was considered as an influential factor to phase transition temperature, and the variation of the interfacial force formed with phase change on the interface was described.

The larger porosity (0.2 and 0.8) will enlarge the unfrozen area from 42 mm to 70 mm, and the rest space of porous medium was occupied by the solid particles. The larger specific surface area (0.168 and 0.315) has a more fluctuated volume fraction distribution.

The concept of interfacial force was first introduced in the solid–liquid phase transition to describe the freezing process of frozen soil, enabling the formulation of a distribution equation based on enthalpy to depict the changes in the water film. The increased interfacial force serves to diminish ice formation and effectively absorb air during the freezing process. A greater surface area enhances the ability to counteract liquid migration.