Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Experimental and numerical investigation of droplet flow mechanisms at fracture intersections

Understanding unsaturated flow behaviors in fractured rocks is essential for various applications.A fundamental process in this regard is flow splitting at fracture intersections.However,the impact of geometrical properties of fracture intersections on flow splitting is still unclear.This work investigates the combined influence of geometry(intersection angle,fracture apertures,and inclination angle),liquid droplet length,inertia,and dynamic wetting properties on liquid splitting dynamics at fracture intersections.A theoretical model of liquid splitting is developed,considering the factors mentioned above,and numerically solved to predict the flow splitting behavior.The model is validated against carefullycontrolled visualized experiments.Our results reveal two distinct splitting behaviors,separated by a critical droplet length.These behaviors shift from a monotonic to a non-monotonic trend with decreasing inclination angle.A comprehensive analysis further clarifies the impacts of the key factors on the splitting ratio,which is defined as the percentage of liquid volume entering the branch fracture.The splitting ratio decreases with increasing inclination angle,indicating a decrease in the gravitational effect on the branch fracture,which is directly proportional to the intersection angle.A non-monotonic relationship exists between the splitting ratio and the aperture ratio of the branch fracture to the main fracture.The results show that as the intersection angle decreases,the splitting ratio increases.Additionally,the influence of dynamic contact angles decreases with increasing intersection angle.These findings enhance our understanding of the impact of geometry on flow dynamics at fracture intersections.The proposed model provides a foundation for simulating and predicting unsaturated flow in complex fractured networks.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture networks.This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures.Notably,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry.All geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully automated.The analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming endeavors.The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures.In practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project.The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures.Furthermore,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

Effect of shear-induced contact area and aperture variations on nonlinear flow behaviors in fractal rock fractures

This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 MPa.Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions.The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface.The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots.As the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts in-creases.Based on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.

Modeling unsaturated flow in fractured rocks with scaling relationships between hydraulic parameters

Modeling unsaturated flow in fractured rocks is essential in various subsurface engineering applications,but it remains a great challenge due to the difficulties in determining the unsaturated hydraulic properties of rocks that contain various scales of fractures.It is generally accepted that the van Genuchten(VG)model can be applied to fractured rocks,provided that the hydraulic parameters could be representatively determined.In this study,scaling relationships between the VG parameters(a and n)and hydraulic conductivity(K)across 8 orders of magnitude,from 10^(-10)m/s to 10^(-2)m/s,were proposed by statistical analysis of data obtained from 1416 soil samples.The correlations were then generalized to predict the upper bounds of VG parameters for fractured rocks from the K data that could be obtained more easily under field conditions,and were validated against a limited set of data from cores,fractures and fractured rocks available in the literature.The upper bound estimates significantly narrow the ranges of VG parameters,and the representative values of a and n for fractured rocks at the field scale can then be determined with confidence by inverse modeling using groundwater observations in saturated zones.The proposed methodology was applied to saturated-unsaturated flow modeling in the right-bank slope at the Baihetan dam site with a continuum approach,showing that most of the flow behaviors in fractured rocks in this complex hydrogeological condition could be properly reproduced.The proposed method overcomes difficulties in suction measurement in fractured rocks with strong heterogeneity,and provides a feasible way for modeling of saturated-unsaturated flow in fractured rocks with acceptable engineering accuracy.

Experimental study on the flow behaviour of water-sand mixtures in fractured rock specimens

The study of flow behaviour of water-sand mixtures in fractured rocks is of great necessity to understand the producing mechanism and prevention of water inrush and sand gushing accidents.A self-developed seepage test system is used in this paper to conduct laboratory experiments in order to study the influence of the particle size distribution,the void ratio,and the initial mass of Aeolian sand on the flow behavior.It is concluded that the water flow velocity is insensitive to the initial mass of the Aeolian sand but increases with the power exponent in the Talbot formula and the specimen height.The outflow of the Aeolian sand increases with the power exponent in the Talbot formula,the specimen height,and the initial mass of the Aeolian sand.Besides,the outflow of the Aeolian sand changes exponentially with the water flow velocity.Finally,it is found that the fractured specimen has a maximum sand filtration capacity beyond which the outflow of the Aeolian sand significantly increases with the initial mass of the Aeolian sand.

Numerical modeling of the effects of roughness on flow and eddy formation in fractures

The effect of roughness on flow in fractures was investigated using lattice Boltzmann method(LBM).Simulations were conducted for both statistically generated hypothetical fractures and a natural dolomite fracture. The effect of increasing roughness on effective hydraulic aperture, Izbash and Forchheimer parameters with increasing Reynolds number(Re) ranging from 0.01 to 500 was examined. The growth of complex flow features, such as eddies arising near the fracture surface, was directly associated with changes in surface roughness. Rapid eddy growth above Re values of 1, followed by less rapid growth at higher Re values, suggested a three-zone nonlinear model for flow in rough fractures. This three-zone model, relating effective hydraulic conductivity to Re, was also found to be appropriate for the simulation of water flow in the natural dolomite fracture. Increasing fracture roughness led to greater eddy volumes and lower effective hydraulic conductivities for the same Re values.

Convective heat transfer of water flow in intersected rock fractures for enhanced geothermal extraction

Numerous intersected rock fractures constitute the fracture network in enhanced geothermal systems.The complicated convective heat transfer behavior in intersected fractures is critical to the heat recovery in fractured geothermal reservoirs.A series of three-dimensional intersected fracture models is constructed to perform the flow-through heat transfer simulations.The geometry effects of dead-end fractures(DEFs)on the heat transfer are evaluated in terms of intersected angles,apertures,lengths,and the connectivity.The results indicate that annular streamlines appear in the rough DEF and cause an ellipse distribution of the cold front.Compared to plate DEFs,the fluid flow in the rough DEF enhances the heat transfer.Both the increment of outlet water temperatureΔToutand the ratio of heat production Qrpresent the largest at the intersected angle of 90°while decline with the decrease of the intersected angle between the main flow fracture(MFF)and the DEFs.The extension of the length of intersected DEFs is beneficial to heat production while enhancing its aperture is not needed.Solely increasing the number of intersected DEFs induces a little increase of heat extraction,and more significant heat production can be obtained through connecting these DEFs with the MFF forming the flow network.

Mechanisms of fracture propagation from multi-cluster using a phase field based HMD coupling model in fractured reservoir

Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recognized as significant factors affecting hydraulic fracture(HF)propagation,the combined influence of these factors remains poorly understood.To address this knowledge gap,a novel coupled hydromechanical-damage(HMD)model based on the phase field method is developed to investigate the propagation of multi-cluster HFs in fractured reservoirs.The comprehensive energy functional and control functions are established,while incorporating dynamic fluid distribution between multiple perforation clusters and refined changes in rock mechanical parameters during hydraulic fracturing.The HMD coupled multi-cluster HF propagation model investigates various scenarios,including single HF and single NF,reservoir heterogeneity,single HF and NF clusters,and multi-cluster HFs with NF clusters.The results show that the HMD coupling model can accurately capture the impact of approach angle(θ),stress difference and cementation strength on the interaction of HF and NF.The criterion of the open and cross zones is not fixed.The NF angle(a)is not a decisive parameter to discriminate the interaction.According to the relationship between approach angle(θ)and NF angle(a),the contact relationship of HF can be divided into three categories(θ=a,θ<a,andθ>a).The connected NF can increase the complexity of HF by inducing it to form branch fracture,resulting in a fractal dimension of HF as high as2.1280 at angles of±45°.Inter-fracture interference from the heel to the toe of HF shows the phenomenon of no,strong and weak interference.Interestingly,under the influence of NFs,distant HFs from the injection can become dominant fractures.However,as a gradually increases,inter-fracture stress interference becomes the primary factor influencing HF propagation,gradually superseding the dominance of NF induced fractures.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices.Several key aspects of fundamental mechanisms,numerical modeling and engineering applications of flow in fractured rocks are discussed.First,the microscopic mechanisms of fluid flow in fractured rocks,especially under the complex conditions of non-Darcian flow,multiphase flow,rock dissolution,and particle transport,have been revealed through a com-bined effort of visualized experiments and theoretical analysis.Then,laboratory and field methods of characterizing hydraulic properties(e.g.intrinsic permeability,inertial permeability,and unsaturated flow parameters)of fractured rocks in different flow regimes have been proposed.Subsequently,high-performance numerical simulation approaches for large-scale modeling of groundwater flow in frac-tured rocks and aquifers have been developed.Numerical procedures for optimization design of seepage control systems in various settings have also been proposed.Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed.Finally,three case studies are presented to illustrate the applications of the improved theoretical understanding,characterization methods,modeling approaches,and seepage and deformation control strategies to geotechnical engi-neering projects.

Comparative experimental investigation of chemical grouting into a fracture with flowing and static water

We present a series of experimental tests on chemical grouting into a fracture with flowing and static water,using a transparent fracture grouting experimental device.Variations of seepage pressure and grout propagation were compared in our investigation.The results show that flowing water results in drops of seepage pressure,development of penetration radii in the upstream side and drops of propagation area during the same period,compared with grouting in static water.The propagation area in static water is always round before grouts reach the joint boundaries.However,the propagation shape changes from round to an elliptic shape for grouting into a fracture with flowing water.A theoretical model for the grout penetration radius in a fracture considering flowing velocity was developed and validated by our experimental results.These results are helpful in improving understanding of fracture grouting mechanism and in guiding engineering practices.

Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.

Integrated wellbore-reservoir-geomechanics modeling for enhanced interpretation of distributed fiber-optic strain sensing data in hydraulicfracture analysis

Fiber-optic distributed strain sensing(FO-DSS)has been successful in monitoring strain changes along horizontal wellbores in hydraulically fractured reservoirs.However,the mechanism driving the various FO-DSS responses associated with near-wellbore hydraulic fracture properties is still unclear.To address this knowledge gap,we use coupled wellbore-reservoir-geomechanics simulations to study measured strain-change behavior and infer hydraulic fracture characteristics.The crossflow among fractures is captured through explicit modeling of the transient wellbore flow.In addition,local grid refinement is applied to accurately capture strain changes along the fiber.A Base Case model was designed with four fractures of varying properties,simulating strain change signals when the production well is shut-in for 10 d after 240 d of production and reopened for 2 d.Strain-pressure plots for different fracture clusters were used to gain insights into inferring fracture properties using DSS data.When comparing the model with and without the wellbore,distinct strain change signals were observed,emphasizing the importance of incorporating the wellbore in FO-DSS modeling.The effects of fracture spacing and matrix permeability on strain change signals were thoroughly investigated.The results of our numerical study can improve the understanding of the relation between DSS signals and fracture hydraulic properties,thus maximizing the value of the dataset for fracture diagnostics and characterization.

Fracture network types revealed by well test curves for shale reservoirs in the Sichuan Basin,China

Pressure buildup testing can be used to analyze fracture network characteristics and conduct quantitative interpretation of relevant parameters for shale gas wells,thus providing bases for assessing the well productivity and formulating proper development strategies.This study establishes a new well test interpretation model for fractured horizontal wells based on seepage mechanisms of shale reservoirs and proposes a method for identifying fracturing patterns based on the characteristic slopes of pressure buildup curves and curve combination patterns.The pressure buildup curve patterns are identified to represent three types of shale reservoirs in the Sichuan Basin,namely the moderately deep shale reservoirs with high pressure,deep shale reservoirs with ultra-high pressure,and moderately deep shale reservoirs with normal pressure.Based on this,the relationship between the typical pressure buildup curve patterns and the fracture network types are put forward.Fracturing effects of three types of shale gas reservoir are compared and analyzed.The results show that typical flow patterns of shale reservoirs include bilinear flow in primary and secondary fractures,linear flow in secondary fractures,bilinear flow in secondary fractures and matrix,and linear flow in matrix.The fracture network characteristics can be determined using the characteristic slopes of pressure buildup curves and curve combinations.The linear flow in early secondary fractures is increasingly distinct with an increase in primary fracture conductivity.Moreover,the bilinear flow in secondary fractures and matrix and the subsequent linear flow in the matrix occur as the propping and density of secondary fractures increase.The increase in the burial depth,in-situ stress,and stress difference corresponds to a decrease in the propping of primary fractures that expand along different directions in the shale gas wells in the Sichuan Basin.Four pressure buildup curve patterns exist in the Sichuan Basin and its periphery.The pattern of pressure buildup curves of shale reservoirs in the Yongchuan area can be described as 1/2/→1/4,indicating limited stimulated reservoir volume,poorly propped secondary fractures,and the forming of primary fractures that extend only to certain directions.The pressure buildup curves of shale reservoirs in the main block of the Fuling area show a pattern of 1/4/→1/2 or 1/2,indicating greater stimulated reservoir volume,well propped secondary fractures,and the forming of complex fracture networks.The pattern of pressure buildup curves of shale reservoirs in the Pingqiao area is 1/2/→1/4→/1/2,indicating a fracturing effect somewhere between that of the Fuling and Yongchuan areas.For reservoirs with normal pressure,it is difficult to determine fracture network characteristics from pressure buildup curves due to insufficient formation energy and limited liquid drainage.

P-and SV-wave dispersion and attenuation in saturated microcracked porous rock with aligned penny-shaped fractures

P-and SV-wave dispersion and attenuation have been extensively investigated in saturated poroelastic media with aligned fractures.However,there are few existing models that incorporate the multiple wave attenuation mechanisms from the microscopic scale to the macroscopic scale.Hence,in this work,we developed a unified model to incorporate the wave attenuation mechanisms at different scales,which includes the microscopic squirt flow between the microcracks and pores,the mesoscopic wave-induced fluid flow between fractures and background(FB-WIFF),and the macroscopic Biot's global flow and elastic scattering(ES)from the fractures.Using Tang's modified Biot's theory and the mixed-boundary conditions,we derived the exact frequency-dependent solutions of the scattering problem for a single penny-shaped fracture with oblique incident P-and SV-waves.We then developed theoretical models for a set of aligned fractures and randomly oriented fractures using the Foldy approximation.The results indicated that microcrack squirt flow considerably influences the dispersion and attenuation of P-and SV-wave velocities.The coupling effects of microcrack squirt flow with the FB-WIFF and ES of fractures cause much higher velocity dispersion and attenuation for P waves than for SV waves.Randomly oriented fractures substantially reduce the attenuation caused by the FB-WIFF and ES,particularly for the ES attenuation of SV waves.Through a comparison with existing models in the limiting cases and previous experimental measurements,we validated our model.

Flow behavior and fracture of Al−Mg−Si alloy at cryogenic temperatures

The tensile and fracture behaviors of AA6061 alloy were investigated in order to provide quantitative data about this alloy at cryogenic temperatures.Specimens of AA6061 alloy were solution heat treated before tensile tests at 298,173 and 77 K and tested at strain rates in the range from 0.1 to 0.0001 s^(−1).The results indicate the suppression of the Portevin−Le Chatelier(PLC)effect and dynamic strain aging(DSA)at 77 K.In contrast,at 298 K,a remarkable serrated flow,characteristic of the PLC effect,is observed.Furthermore,the tensile behavior at 77 K,compared with that observed at 173 and 298 K,shows a simultaneous increase in strength,uniform elongation,modulus of toughness,strain-hardening exponent and strain rate sensitivity,which is related to a decrease in the dynamic recovery rate at low temperature.These responses are reflected on the fracture morphology,since the dimple size decreases at 77 K,while the area covered by dimples increases.Comparisons of the Johnson−Cook model show that a good agreement can be obtained for tests at 173 and 77 K,in which DSA is suppressed.

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.

Assessments of the effects of various fracture surface morphology on single fracture flow: A review

Natural rock joint permeability deviates from the classic fluid flow governing equations due to the inher-ent fracture surface roughness(i.e.,contact points,spatial correlation,matching,varying aperture,iso-lated voids,infilling material,tortuosity and channellings)and engineering disturbance such as excavations.To improve the accuracy of fracture permeability evaluation,many efforts have been made in analytical,experimental,and numerical methods.This study reviews the modified mathematical gov-erning equations of fluid flow and classifies them based on different influencing factors,such as friction factor,aperture,tortuosity,inertia,and various in situ stress effects.Various experimental and simulation techniques for the coupled normal-and shear-stress flow problems were assessed,and their advantages and disadvantages were also analysed.Furthermore,different surface roughness descriptions and their impacts on mechanical and hydraulic behaviours were discussed,followed by the potential research directions for fracture flow problems.