Development of CASRock for modeling multi-fracture interactions in rocks under hydro-mechanical conditions

The interaction between multiple fractures is important in the analysis of rock fracture propagation,fracture network evolution and stability and integrity of rocks under hydro-mechanical(HM)coupling conditions.At present,modeling the mechanical behavior of multiple fractures is still challenging.Under the condition of multiple fractures,the opening,closing,sliding,propagation and penetration of fractures become more complicated.In order to simulate the HM coupling behavior of multi-fracture system,the paper presents a novel numerical scheme,including mesh reconstruction and topology generation algorithm,to efficiently and accurately represent fractures and their propagation process,and a potential function-based algorithm to address contact problem.The fracture contact algorithm does not need to set contact pairs and thus is suitable for complex contact situations from small to large deformations induced by HM loading.The topology of fracture interfaces is constructed by the dynamic adding algorithm,which makes the mesh reconstruction more rapid in the modeling of fracturing process,especially in the case of multiple fractures intersections.The numerical scheme is implemented in CASRock,a self-developed numerical code,to simulate the propagation process of rock fractures and the interaction of multiple fractures under the condition of HM coupling.To verify the suitability of the code,a series of tests were performed.The code was then applied to simulate hydraulic fracture propagation and fracture interactions caused by fluid injection.The ability of this method to study fracture propagation,multi-fracture interaction and fracture network evolution under hydro-mechanical coupling conditions is demonstrated.

Multi-fracture interactions during two-phase flow of oil and water in deformable tight sandstone oil reservoirs

Tight oil reservoirs are complex geological materials composed of solid matrix,pore structure,and mixed multiple phases of fluids,particularly for oil reservoirs suffering from high content of in situ pressurized water found in China.In this regard,a coupled model considering two-phase flow of oil and water,as well as deformation and damage evolution of porous media,is proposed and validated using associated results,including the oil depletion process,analytical solution of stress shadow effect,and physical experiments on multi-fracture interactions and fracture propagation in unsaturated seepage fields.Then,the proposed model is used to study the behavior of multi-fracture interactions in an unsaturated reservoir in presence of water and oil.The results show that conspicuous interactions exist among multiple induced fractures.Interaction behavior varies from extracted geological profiles of the reservoir due to in situ stress anisotropy.The differential pressures of water and that of oil in different regions of reservoir affect interactions and trajectories of multi-fractures to a considerable degree.The absolute value of reservoir average pressure is a dominant factor affecting fracture interactions and in favor of enhancing fracture network complexity.In addition,difference of reservoir average pressures in different regions of reservoir would promote the fracturing effectiveness.Factors affecting fracture interactions and reservoir treatment effectiveness are quantitatively estimated through stimulated reservoir area.This study confirms the significance of incorporating the two-phase flow process in analyses of multifracture interactions and fracture trajectory predictions during tight sandstone oil reservoir developments.

A numerical method for simulating planar 3D multi-fracture propagation in multi-stage fracturing of horizontal wells

To resolve the issue of design for multi-stage and multi-cluster fracturing in multi-zone reservoirs, a new efficient algorithm for the planar 3 D multi-fracture propagation model was proposed. The model considers fluid flow in the wellbore-perforation-fracture system and fluid leak-off into the rock matrix, and uses a 3 D boundary integral equation to describe the solid deformation. The solid-fluid coupling equation is solved by an explicit integration algorithm, and the fracture front is determined by the uniform tip asymptotic solutions and shortest path algorithm. The accuracy of the algorithm is verified by the analytical solution of radial fracture, results of the implicit level set algorithm, and results of organic glass fracturing experiment. Compared with the implicit level set algorithm(ILSA), the new algorithm is much higher in computation speed. The numerical case study is conducted based on a horizontal well in shale gas formation of Zhejiang oilfield. The impact of stress heterogeneity among multiple clusters and perforation number distribution on multi-fracture growth and fluid distribution among multiple fractures are analyzed by numerical simulation. The results show that reducing perforation number in each cluster can counteract the effect of stress contrast among perforation clusters. Adjusting perforation number in each cluster can promote uniform flux among clusters, and the perforation number difference should better be 1-2 among clusters. Increasing perforation number in the cluster with high in situ stress is conducive to uniform fluid partitioning. However, uniform fluid partitioning is not equivalent to uniform fracture geometry. The fracture geometry is controlled by the stress interference and horizontal principal stress profile jointly.

Evolution mechanism of optical fiber strain induced by multi-fracture growth during fracturing in horizontal wells

A forward model for optical fiber strain was established based on a planar 3D multi-fracture model. Then the forward method calculating distributed fiber strain induced by multi-fracture growth was proposed. Based on this method, fiber strain evolution during fracturing of the horizontal well was numerically simulated. Fiber strain evolution induced by fracture growth can be divided into three stages: strain increasing, shrinkage convergence, and straight-line convergence, whereas the evolution of fiber strain rate has four stages: strain rate increasing, shrinkage convergence, straight-line convergence, and strain rate reversal after pumping stops. Fiber strain does not flip after pumping stop, while the strain rate flips after pumping stop so that strain rate can reflect injection dynamics. The time when the fracture extends to the fiber and inter-well pressure channeling can be identified by the straight-line convergence band of distributed fiber strain or strain rate, and the non-uniform growth of multiple fractures can be evaluated by using the instants of fractures reaching the fiber monitoring well.When the horizontal section of the fiber monitoring well is within the height range of a hydraulic fracture, the instant of the fracture reaching the fiber can be identified;otherwise, the converging band is not apparent. In multi-stage fracturing, under the influence of stress shadow from previous fracturing stages, the tensile region of fiber strain may not appear, but the fiber strain rate can effectively show the fracture growth behavior in each stage. The evolution law of fiber strain rate in single-stage fracturing can be applied to multi-stage fracturing.

A new approach for flow simulation in complex hydraulic fracture morphology and its application:Fracture connection element method

Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.

Fifty years of finite elements——a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.

Productivity model for gas reservoirs with open-hole multi-fracturing horizontal wells and optimization of hydraulic fracture parameters

Multi-fractured horizontal wells are commonly employed to improve the productivity of low and ultra-low permeability gas reservoirs.However,conventional productivity models for open-hole multi-fractured horizontal wells do not consider the interferences between hydraulic fractures and the open-hole segments,resulting in significant errors in calculation results.In this article,a novel productivity prediction model for gas reservoirs with open-hole multi-fractured horizontal wells was proposed based on complex potential theories,potential superimposition,and numerical analysis.Herein,an open-hole segment between two adjacent fractures was regarded as an equivalent fracture,which was discretized as in cases of artificial fractures.The proposed model was then applied to investigate the effects of various parameters,such as the angle between the fracture and horizontal shaft,fracture quantity,fracture length,diversion capacity of fractures,horizontal well length,and inter-fracture distance,on the productivity of low permeability gas reservoirs with multi-fractured horizontal wells.Simulation results revealed that the quantity,length,and distribution of fractures had significant effects on the productivity of low permeability gas reservoirs while the effects of the diversion capacity of fractures and the angle between the fracture and horizontal shaft were negligible.Additionally,a U-shaped distribution of fracture lengths was preferential as the quantity of fractures at shaft ends was twice that in the middle area.