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The purpose of this paper is to develop a numerical method to model the simultaneous propagation of multiple hydraulic fractures (HFs) with fluid lags driven from a horizontal wellbore.

Fracture propagation in solid medium is modeled with the extended finite element method and fluid flow is modeled with finite volume method. Three iteration loops are introduced to solve the nonlinear system within each time increment, i.e. a Newtonian iteration to solve the solid-fluid coupling system, a Picard iteration to determine fluid front positions and a secant iteration to update fracture lengths.

The propagation of one single HF with a fluid lag is simulated and agrees well with semi-analytical solutions or other numerical results in the literature. The simultaneous propagation of two HFs are then investigated, which demonstrates the ability of the proposed method in capturing the hydraulic fracturing process with multiple fractures and fluid lags.

With the proposed method, one can simulate the simultaneous propagation of multiple HFs with fluid lags, which play a significant role during early-time propagation or when the confinement stress is relatively low (shallow HFs). Solid deformation and fracturing, fluid flow in fractures and in the wellbore are fully coupled, and three iteration loops are introduced to solve the nonlinear system.

The unstable dynamic propagation of multistage hydrofracturing fractures leads to uneven development of the fracture network and research on the mechanism controlling this phenomenon indicates that the stress shadow effects around the fractures are the main mechanism causing this behaviour. Further studies and simulations of the stress shadow effects are necessary to understand the controlling mechanism and evaluate the fracturing effect.

In the process of stress-dependent unstable dynamic propagation of fractures, there are both continuous stress fields and discontinuous fractures; therefore, in order to study the stress-dependent unstable dynamic propagation of multistage fracture networks, a series of continuum-discontinuum numerical methods and models are reviewed, including the well-developed extended finite element method, displacement discontinuity method, boundary element method and finite element-discrete element method.

The superposition of the surrounding stress field during fracture propagation causes different degrees of stress shadow effects between fractures and the main controlling factors of stress shadow effects are fracture initiation sequence, perforation cluster spacing and well spacing. The perforation cluster spacing varies with the initiation sequence, resulting in different stress shadow effects between fractures; for example, the smaller the perforation cluster spacing and well spacing are, the stronger the stress shadow effects are and the more seriously the fracture propagation inhibition arises. Moreover, as the spacing of perforation clusters and well spacing increases, the stress shadow effects decrease and the fracture propagation follows an almost straight pattern. In addition, the computed results of the dynamic distribution of stress-dependent unstable dynamic propagation of fractures under different stress fields are summarised.

A state-of-art review of stress shadow effects and continuum-discontinuum methods for stress-dependent unstable dynamic propagation of multiple hydraulic fractures are well summarized and analysed. This paper can provide a reference for those engaged in the research of unstable dynamic propagation of multiple hydraulic structures and have a comprehensive grasp of the research in this field.

This paper aims to explore how resilience is evident in healthcare supply chains in the public sector when faced with pandemic disruption and to identify any learnings to inform recovery and future-readiness phases.

An exploratory case study was conducted, consisting of seven semi-structured interviews with public sector supply chain actors in the healthcare personal protective equipment supply chain. The data included document analysis.

Key findings show how specific resilience strategies such as agility, collaboration, flexibility and redundancy, contributed to supply chain resilience during the COVID-19 pandemic response. Collaboration is identified as a key mechanism for resilience with public sector networks viewed as facilitating this. Established collaborative relationships with suppliers pre-pandemic did not support increased visibility of tiers within the supply chain.

This is one of the first papers to provide in-depth resilience insights through an example of healthcare supply chains during the COVID-19 pandemic.

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.

The purpose of this study is to investigate the unstable propagation of parallel hydraulic fractures induced by interferences of adjacent perforation clusters and thermal diffusion. Fracture propagation in the process of multistage fracturing of a rock mass is deflected owing to various factors. Hydrofracturing of rock masses in deep tight reservoirs involves thermal diffusion, fluid flow and deformation of rock between the rock matrix and fluid in pores and fractures.

To study the unstable propagation behaviours of three-dimensional (3D) parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion, a 3D engineering-scale numerical model is established under different fracturing scenarios (sequential, simultaneous and alternate fracturing) and different perforation cluster spacings while considering the thermal-hydro-mechanical coupling effect. Stress disturbance region caused by fracture propagation in a deep tight rock mass is superimposed and overlaid with multiple fractures, resulting in a stress shadow effect and fracture deflection.

The results show that the size of the stress shadow areas and the interaction between fractures increase with decreasing multiple perforation cluster spacing in horizontal wells. Alternate fracturing can produce more fracture areas and improve the fracturing effect compared with those of sequential and simultaneous fracturing. The larger the temperature gradient between the fracturing fluid and rock matrix, the stronger the thermal diffusion effect, and the effect of thermal diffusion on the fracture propagation is significant.

This study focuses on the behaviours of the unstable dynamic propagation of 3D parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion. Further, the temperature field affects the fracture deflection requires could be investigated from the mechanisms; this paper is to study the unstable propagation of fractures in single horizontal well, which can provide a basis for fracture propagation and stress field disturbance in multiple horizontal wells.

Simultaneous hydrofracturing of multiple perforation clusters in vertical wells has been applied in the stimulation of hydrocarbon resources reservoirs. This technology is significantly impeded due to the challenges in its application to the multilayered reservoirs that comprise multiple interlayers. One of the challenges is the accurate understanding and characterization of propagation and deflection of the multiple hydraulic fractures between reservoirs and embedded interlayers.

Numerical models of the tight multilayered reservoirs containing multiple interlayers were established to study hydrofracturing of multiple perforation clusters and its influencing factors on unstable propagation and deflection of hydraulic fractures. Brittle and plastic multilayered reservoirs fully considering the influences of different in situ stress ratio and physical attributes for reservoir and interlayer strata on propagations of hydraulic fractures were investigated. The combined finite element–discrete element method and mesh refinement strategy were adopted to guarantee the accuracy of stress solutions and reliability of fracture path in computation.

Results show that the shear stress fields between adjacent multiple hydraulic fractures are superposed to cause fractures deflection. Stress shadows induce the shielding effects of hydraulic fractures and inhibit fractures growth to emerge unstable propagation behaviors, and a main single fracture and several minor fractures develop. As the in situ stress ratio increases, hydraulic fractures more easily deflect toward the direction of maximum in situ stress, and stress shadow and mutual interaction effects between them are intensified. Compared to brittle reservoir, plastic-enhanced reservoir may limit fracture growth and cannot form long fracture length; nevertheless, plastic properties of reservoir are prone to induce more microseismic events with larger magnitude.

The obtained fracturing behaviors and mechanisms based on engineering-scale multilayered reservoir may provide effective schemes for controlling and estimating the unstable propagation of multiple hydraulic fractures.

Multi-well hydrofracturing is a key technology in engineering, and the evaluation, control and optimization of the fracturing network determine the recovery rate of unconventional oil and gas production. In engineering terms, altering well spacing and perforation initiation sequences changes fracture propagation behavior. Fracture propagation can result in fracture-to-fracture and well-to-well interactions. This may be attributed to the interference between fractures caused by squeezing of the reservoir strata. Meanwhile, the stratal movement caused by the propagation of the fractures may lead to either the secondary fracturing of wells with primary fractures or perforation to begin fracturing. Besides, the stratal compression and squeeze of multi-well hydrofracturing will cause earthquakes; the fracture size is different owing to the different fracturing scenarios, and the occurrence of induced microseismic events is still unknown; microseismic events also affect fracture orientation and deflection. If the mechanism of the above mechanical behavior cannot be clarified, optimizing the fracture network and reduce the induced microseismic disaster becomes difficult.

In this study, combined finite element-discrete element models were used to simulate the multi-well hydrofracturing. Numerical cases compared the fracture network, dynamic stratal movement and microseismic events at 50, 75 and 100 m well spacings, respectively, and varying initiation sequence of multiple horizontal wells.

From the results, fracture propagation in multi-well hydrofracturing may simulate the propagation and deflection of adjacent fractures and induce fracture-to-fracture and well-to-well interactions. As the well spacing increases, the effect of fracturing-induced stratal movement and squeezing deformation decrease. In alternate fracturing, starting from a well located in the middle can effectively reduce the influence of stratal movement on fracturing, and the fracturing scenario with cross-perforation can minimize the influence of stratal movement. The stratal movement between multiple wells is positively correlated to microseismic events, which behaviors can be effectively weakened by reducing the strata movement.

The fracture network, thermal-hydro-mechanical coupling, fracturing-induced stratal movement and microseismic events were analyzed. This study analyzed the intersection and propagation behavior of fractures in multi-well hydrofracturing, which can be used to evaluate and study the mechanism of hydrofracturing fracture network propagation in multiple horizontal wells and conduct fracture optimization research to form an optimized hydrofracturing scheme by reasonably arranging the spacing between wells and initiation sequences of perforation clusters.

This paper aims to develop supply chain strategies for the fashion retail supply chain (FRSC), likely to be disrupted by the current pandemic (COVID-19) under physical and online retail stores. The resilient retail supply chain design is proposed under budget allocation and merchandise capacity constraints.

This paper utilises the theory of constraint (ToC) and goal programming (GP) to address the COVID-19 impact on FRSC. The budgetary and capacity constraints are formulated with a constraint optimisation model and tested with six different priorities to deal with the physical and online stores. Next, all priorities are developed under different FRSC business scenarios. The ToC-GP-based optimisation model is validated with one of the Indian fashion retail supply chains.

The proposed optimisation model presents the optimal retailing strategies for selling fashion goods over physical and online platforms. The multiple scenarios are presented for developing trade-offs among different strategies to maximise the retailer's merchandise performance. This paper also highlighted the strategic movement from high merchandise density stores to low merchandise density stores. This implies a reduction of sales targets and aspiration levels of both online and physical fashion stores.

The proposed model is validated with one of the fashion retailers in India. Other nations or multiple fashion retailers might be considered for more generalisation of findings in the future.

This research helps fashion retail supply chain managers deal with consumer demand uncertainty over physical and online stores in pandemic times. Limitation: Other nations or multiple fashion retailers might be considered for more generalisation of findings in the future.

This is the first study that considered the impact of COVID-19 on the retail fashion supply chain. The effect of physical and online platforms is mainly discussed from consumer marketing perspectives, but an inventory and resilience perspective is missing in earlier studies. The role of merchandise planning is highlighted in this study.

In most commercial processors, enhancing the speed of multiplication using radix-8 booth encoding is the preferred option. In radix-8 architecture, the 3X(= 2X + X) multiple generation is a major bottleneck. This paper aims to propose a parallel implementation scheme recognizing the symmetry in the carry recurrence equations of 3X multiples. The proposed architecture evaluates the odd (H) and even (K) carry signals separately. As prefix tree structure offers fast carry propagation, the parallel implementation is based on a hybrid style of two popular prefix architectures.

The performance of the proposed architecture is evaluated using Cadence TSMC 180 nm library. A comparison of performance parameters with other architectures has been carried out to highlight the architectural advantages of the proposed architecture.

A comparison of performance parameters with others shows that the proposed architecture has a reduced critical path and a commensurate improvement in delay for a bit width of 64. It is shown that up to 32 bits, this parallel architecture has a superior performance and would be the appropriate choice for Application Specific Integrated Circuit (ASIC) implementation. It has also been suggested that higher-order bit widths could be implemented using a modular arrangement.

This paper proposes a new parallel architecture for hard multiple (3X) generation in Radix-8 Booth encoding. As the multiplication is the key operation in digital signal processors, this type of high-speed architectures gains importance in the future processor design. Defence applications such as target finding and multiple target recognitions and image processing applications necessitate this type of high-speed multipliers. Also, it is appropriate for the ASIC implementation. The authors would like to mention that this paper is not yet published anywhere, and it is the research paper of Dr R. Nirmaladevi.

With the development of fracturing technology, the research of multi-well hydrofracturing becomes the key issue. Frac-hits in multi-well hydrofracturing has an important effect on fracture propagation and final production of fractured well; in the process of hydrofracturing, there are many implement parameters that can affect frac-hits, and previous studies in this area have not systematically targeted the influence of a single parameter on multi-well hydrofracturing. Therefore, it is of great significance to study the occurrence rule and influence of frac-hits for optimizing the design of fracturing wells.

Based on the proposed numerical models, the effects of different fracturing implement parameters (perforation cluster spacing, well spacing and injection rate) on frac-hits are compared in numerical cases. Through the analysis of fracture network, stress field and microseismic, the effects of different fracturing implement parameters on frac-hits and connections are compared.

The simulation results show that the effect of perforation cluster spacing and well spacing on frac-hits is greater than that of injection rate. Smaller well spacing makes it easier for fractures between adjacent wells to interact with each other, which increases the risk of frac-hits and reduces the risk of fracture connections. Smaller perforation cluster spacing results in larger individual fracture lengths and greater deflection angles, which makes the possibility of frac-hits and connections greater. The lower the injection rate, the lower the probability of frac-hits.

In this study, the influence of different fracturing implement parameters on frac-hits and connections in multi-well hydrofracturing is studied, and the mechanism of frac-hits and connections is analyzed through fracture network, stress field and microseismic analysis. Different simulation results are compared to optimize fracturing well parameter design and provide reference for engineering application.