Integrated modeling of fracturing-flowback-production dynamics and calibration on field data:Optimum well startup scenarios

We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.

An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition.This paper proposes a new randomized fixed-precision algorithm which for a given third-order tensor and a prescribed approximation error bound,it automatically finds the tubal rank and corresponding low tubal rank approximation.The algorithm is based on the random projection technique and equipped with the power iteration method for achieving better accuracy.We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.

MERACLE:Constructive Layer-Wise Conversion of a Tensor Train into a MERA

In this article,two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz(MERA).The Tucker core tensor is never explicitly computed but stored as a tensor train instead,resulting in both computationally and storage efficient algorithms.Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error.In addition,an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors,which are a crucial component in the construction of a low-rank MERA.Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.

Conceptual Method of Temperature Sensation in Bionic Hand by Extraordinary Perceptual Phenomenon

Lack of temperature sensation of myoelectric prosthetic hand limits the daily activities of amputees.To this end,a noninvasive temperature sensation method is proposed to train amputees to sense temperature with psychophysical sensory substitution.In this study,22 healthy participants took part besides 5 amputee participants.The duration time of the study was 31 days with five test steps according to the Leitner technique.An adjustable temperature mug and a Peltier were used to change the temperature of the water/phantom digits to induce temperature to participants.Also,to isolate the surroundings and show colors,a Virtual Reality(VR)glass was employed.The statistical results conducted are based on the response of participants with questionnaire method.Using Chi-square tests,it is concluded that participants answer the experiment significantly correctly using the Leitner technique(P value<0.05).Also,by applying the“Repeated Measures ANOVA”,it is noticed that the time of numbness felt by participants had significant(P value<0.001)difference.Participants could remember lowest and highest temperatures significantly better than other temperatures(P value<0.001);furthermore,the well-trained amputee participant practically using the prosthesis with 72.58%could identify object’s temperature with only once time experimenting the color temperature.

Incorporating microgrids coupling with utilization of flexible switching to enhance self-healing ability of electric distribution systems

Electric distribution networks have to deal with issues caused by natural disasters. These problems possess unique characteristics, and their severity can make load restoration methods impotent. One solution that can help in alleviating the aftermath is the use of microgrids (MGs). Employing the cumulative capacity of the generation resources through MG coupling facilitates the self-healing capability and leads to better-coordinated energy management during the restoration period, while the switching capability of the system should also be considered. In this paper, to form and schedule dynamic MGs in distribution systems, a novel model based on mixed-integer linear programming (MILP) is proposed. This approach employs graph-related theories to formulate the optimal formation of the networked MGs and management of their proper participation in the load recovery process. In addition, the Benders decomposition technique is applied to alleviate computability issues of the optimization problem. The validity and applicability of the proposed model are evaluated by several simulation studies.

Efficient Flexible Boundary Conditions for Long Dislocations

We present a novel efficient implementation of the flexible boundary condition(FBC)method,initially proposed by Sinclair et al.,for large single-periodic problems.Efficiency is primarily achieved by constructing a hierarchical matrix(H-matrix)representation of the periodic Green matrix,reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms.In addition,our implementation is supported by various other tools from numerical analysis,such as a residual-based transformation of the boundary conditions to accelerate the convergence.We assess the method for a comprehensive set of examples,relevant for predicting mechanical properties,such as yield strength or ductility,including dislocation bow-out,dislocation-precipitate interaction,and dislocation cross-slip.The main result of our analysis is that the FBC method is robust,easy-to-use,and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems,the periodic array of dislocations(PAD)method,in terms of the required number of per-atom force computations when both methods give similar accuracy.This opens new prospects for large-scale atomistic simulations—without having to worry about spurious image effects that plague classical boundary conditions.