Experiment and simulation of slurry flow in irregular channels to understand proppant transport in complex fractures

Slurry flow and proppant placement in irregular fractures are crucial to evaluate hydraulic fracturing stimulation but need to be better understood. This study aims to investigate how irregular fracture affects proppant transport and distribution using laboratory experiments and micro-scale numerical models. The unresolved method of the computational fluid dynamics (CFD) and the discrete element method (DEM) considers Saffman lift force, Magnus force, and virtual mass force to accurately capture the frequent interaction between proppant and slickwater. Experimental results validated the reliability of the optimized CFD-DEM model and calibrated primary parameters. The effects of crack height and width, bending angle, and distance between the crack and inlet on particle distribution were studied. The results indicated that the improved numerical method could rationally simulate proppant transport in fractures at a scale factor. The small crack height causes downward and upward flows, which wash proppant to the fracture rear and form isolated proppant dunes. A wider region in the fracture is beneficial to build up a large dune, and the high dune can hinder particle transport into the fracture rear. When the crack is close to the inlet, the primary fracture without proppants will close to hinder gas production. The smaller the bending angle, the smaller the proppant dune. A regression model can precisely predict the dune coverage ratio. The results fundamentally understand how complex fractures and natural cracks affect slurry flow and proppant distribution.     

Determination of Hydrogen–Water Relative Permeability and Capillary Pressure in Sandstone: Application to Underground Hydrogen Injection in Sedimentary Formations

This paper presents fundamental analysis and micromechanical understanding of dense slurry behavior during settling in narrow smooth and rough slots. Particularly, this study seeks to contribute toward better understanding of dynamics of particle–particle and particle–wall interactions in viscous fluids using simple experiments. The findings of this study are applicable in a wide variety of problems, for example sediment transport, flow and transport of slurry in pipes, and industrial applications. However, the results interpretation focuses on better understanding of proppant flow and transport in narrow fractures. A sequence of experiments image frames captured by video camera is analyzed with particle image velocimetry (GeoPIV). The measurements include vertical velocities and displacement vectors of singular and agglomerated particles and larger area of formed slurry. Results present novel insights into the formation and effects of agglomerates on general slurry settling, and are supplemented with a comparison with previously published theoretical and empirical relationships. This work also emphasizes a role of particle–particle interactions in promoting agglomeration in viscous fluid. Particularly, a thin layer of viscous fluid between approaching particles dissipates particle kinetic energy due to lubrication effect. Lubrication effect is more pronounced when particles are constrained between two narrow walls and interact frequently with each other. Fluid tends to flow around agglomerated particles, and agglomerates remain stable for prolonged time periods gravitationally moving downward. The relative amount and size of agglomerated affects general settling of the slurry. It was found that fluid viscosity due to lubrication effect promotes agglomeration, and therefore, the overall slurry settling relatively increases at higher fluid viscosities. The results of the presented work have impact on various industrial and engineering processes, such as proppant flow and transport in hydraulic fractures, sand production in oil reservoirs, piping failure of dams and scour of foundation bridges.     

单裂缝中携砂液流动规律研究

裂缝中携砂液流动是一种固液两相流,携砂液的运移与支撑剂的铺置是水力压裂裂缝保持导流能力的关键.本文基于FLUENT流体计算软件,采用双流体模型,将颗粒看作拟流体,携砂液按照牛顿流体处理,分析了支撑剂体积分数α_s、阿基米德数Ar、颗粒雷诺数Re以及裂缝入口边界对流动规律的影响.研究结果表明:携砂液在裂缝中的流动过程中,发展成为支撑剂体积分数不同的四个区域,包括砂堤区、颗粒悬浮区、颗粒滚流区和无砂区;支撑剂的沉降程度随着支撑剂体积分数和阿基米德数的增加而增加,而随着雷诺数增加而降低;入口为网眼型时,进入裂缝后过流面积的增加导致流速突降,使得支撑剂更容易在入口处产生堆积,在同一入口流速下,较均匀入口的工况铺砂高度大.     

Effects of Heterogeneous Fracture Aperture on Multiphase Production from Shale Reservoirs

Production simulation from fractured shale reservoirs is often performed by simplifying the hydraulic fractures as rectangular planes with homogeneous aperture. This study investigates the effects of heterogeneous fracture aperture and proppant distribution in realistic, non-rectangular fractures on the multi-phase production from shales. The heterogeneous hydraulic fractures are generated with the GEOS multiphysics simulator under realistic 3D stress field. These fractures are embedded into the TOUGH+ multi-phase flow simulator for production simulation. The results emphasize the importance of flow barriers within the hydraulic fractures, due both to low-aperture regions caused by the stress-shadow effect and the settling of proppant. The production rate is particularly sensitive to aperture heterogeneity if the flow barriers are close to the wellbore such that a great portion of fracture volume is isolated from the well. A stage-to-stage comparison reveals that production from different stages could vary significantly because the local stress field leads to different fracture area and aperture. The use of proppant prevents fracture closure, but if the propped regions are far from the well, they do not enhance production because flow barriers between these regions and the well act as bottlenecks. The present study highlights the importance of incorporating aperture heterogeneity into production simulation, provides insights on the relationship between flow barriers, proppant concentration, and well production, and proposes a practical method to mitigate numerical difficulties when modeling heterogeneous fractures.

     

CFD-DEM simulation of the hole cleaning process in a deviated well drilling: The effects of particle shape

We investigate the effect of particle shape on the transportation mechanism in well-drilling using a three-dimensional model that couples computational fluid dynamics (CFD) with the discrete element method (DEM). This numerical method allows us to incorporate the fluid–particle interactions (drag force, contact force, Saffman lift force, Magnus lift force, buoyancy force) using momentum exchange and the non-Newtonian behavior of the fluid. The interactions of particle−particle, particle−wall, and particle−drill pipe are taken into account with the Hertz–Mindlin model. We compare the transport of spheres with non-spherical particles (non-smooth sphere, disc, and cubic) constructed via the multi-sphere method for a range of fluid inlet velocities and drill pipe inclination angles. The simulations are carried out for laboratory-scale drilling configurations. Our results demonstrate good agreement with published experimental data. We evaluate the fluid–particle flow patterns, the particle velocities, and the particle concentration profiles. The results reveal that particle sphericity plays a major role in the fluid–solid interaction. The traditional assumption of an ideal spherical particle may cause inaccurate results.     

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基于射孔完井水平裂缝中支撑剂均匀充填，考虑充填层强度、油层和流体 物性以及裂缝的渗流条件，研究了地应力及渗流引起的附加应力联合作用的支撑剂充填层渗 流模型和力学模型，并进行现场应用. 研究表明，所建立的模型对压裂油井支撑剂回采出砂 状况分析具有较高的符合率，油井总体符合率、不出砂井符合率和出砂井符合率分 别为84.66\%, 84.18\%和88.10\%, 为大庆油田压裂油井防砂措施实施方案制定提 供了决策支持，有利于提高措施有效率.     

Evaluation and Optimization of New Nanocomposite Fiber for Fracturing Technology Based on a New Equipment

The fiber has great advantages in hydraulic fracturing when considering fluid leak off and flow friction, proppant transportation and fracture damage, proppant or sand production, and fracture geometry. However, some drawbacks, such as poor chemical stability, mechanical properties, heat denaturation, and dispersivity, always emerge in oilfield cases. Accordingly, a new type of nanocomposite fiber is used to overcome these shortcomings in our research. Generally, fiber??s conventional performance, dispersivity and proppant suspension capability can be evaluated easily, but reliable evaluation and optimization of fiber applications could not be obtained by normal indoor experimental instruments. So we developed the ??fracture filling model??, a specially designed instrument to evaluate the performances of fracture conductivity, proppant backflow, and sand control. All the performances of the nanocomposite fiber were evaluated, and the length and concentration of the fiber were optimized. The results have great influences on both theoretical study and field treatments of the new nanocomposite fiber.     

Experimental Study on the Pore Structure Fractals and Seepage Characteristics of a Coal Sample Around a Borehole in Coal Seam Water Infusion

In this study, a two-dimensional fully coupled computational model is developed for simulation of proppant settlement in hydro-fractures with the use of the extended finite element framework. The porous domain is governed by the well-known \((\mathbf{u}-p)\) formulation, which consists of the momentum balance equation of the bulk, in conjunction with the momentum balance and continuity equations of the pore fluid. The hydro-fracture inflow is modeled as a 1D flow on the basis of the Darcy law, in which fracture permeability is incorporated by means of the cubic law. Contact constraints are elaborated to eliminate the overlap of fracture edges and the leak-off flow. Proppant settlement is conducted on the basis of Stokes’ law for particle terminal velocity, in which the effects of fracture walls, concentration, viscosity and bridging are incorporated into the model. A fixed-point algorithm is introduced to achieve the optimum combination for the proppant injection. Using the extended finite element method, the strong discontinuity in the displacement field due to crack body, as well as the weak discontinuity in the pressure field due to leakage, is included in the model with the use of the Heaviside and modified level set enrichment functions, respectively. The robustness and versatility of the proposed numerical algorithm in determining the optimum proppant injection is examined through several numerical simulations.     

Experimental Study of Fracture Permeability for Stimulated Reservoir Volume (SRV) in Shale Formation

“Stimulated reservoir volume”(SRV) makes shale gas production economic through new completion techniques including horizontal wells and multiple hydraulic fractures. However, the mechanism behind these treatments that provide sufficient permeability is not well understood. The effects of different stimulation treatments need to be further explored. To understand the effects of fracture surface roughness, fracture registration, confining pressure, proppant type and distribution mode, fiber and acidizing treatment on fracture permeability, a series of laboratory permeability experiments were performed on fractured cores from shale formation of Shengli Oilfield. The results of this study demonstrate that sedimentary bedding of shale has important influence on matrix permeability. At 35 MPa confining pressure, the permeability of aligned fracture (unpropped and without fracture offset) can increase about 1–3 orders of magnitude over shale matrix. The permeability of displaced fracture can increase about 1–2 orders of magnitude over the aligned fracture. The permeability of fracture propped with proppant can increase about 2–4 orders of magnitude over unpropped fracture. The greater the fracture surface roughness, the higher the permeability. The increasing degree of displaced fracture permeability is not proportional to the amount of fracture offset. In the microfracture of shale, the effect of ceramic proppant is still better than that of quartz sand, and the permeability of a centralized fairway distribution of proppant is about 1.2 times better than an even monolayer distribution of proppant. Under high pressure, proppant is easy to cause the break of fracture faces of brittle shale, and increase local fracture permeability to some extent. However, quartz sand are more easily broken to embed and block microcracks just made, which results in fracture permeability lower than that of ceramic proppant. At the same time, the argillation phenomenon is easy to happen on propped fracture faces of shale, which is one of the main factors that leads to a substantial decline in fracture permeability. The permeability of displaced fracture propped with proppant is greater than that of aligned fracture propped with proppant. Because of added fiber presence, the permeability of microfractures presented in SRV is greatly reduced. The pressure dependence of aligned fractures in shale obeys Walsh’s theory, but the pressure dependence of propped and displaced fractures in shale obeys Walsh’s law over a limited range of pressures. Deviations reflect proppant seating, proppant embedding and breaking. For shale formation with the high carbonate content, acidizing treatment should be carefully implemented. Experimental results may provide more valuable information for effective design of hydraulic fracturing in shale reservoir.     

Fully resolved simulations of viscoelastic suspensions by an efficient immersed boundary-lattice Boltzmann method

An efficient immersed boundary-lattice Boltzmann method (IB-LBM) is proposed for fully resolved simulations of suspended solid particles in viscoelastic flows. Stress LBM based on Giesekus and Oldroyd-B constitutive equation are used to model the viscoelastic stress tensor. A boundary thickening-based direct forcing IB method is adopted to solve the particle–fluid interactions with high accuracy for non-slip boundary conditions. A universal law is proposed to determine the diffusivity constant in a viscoelastic LBM model to balance the numerical accuracy and stability over a wide range of computational parameters. An asynchronous calculation strategy is adopted to further improve the computing efficiency. The method was firstly applicated to the simulation of sedimentation of a single particle and a pair of particles after good validations in cases of the flow past a fixed cylinder and particle migration in a Couette flow against FEM and FVM methods. The determination of the asynchronous calculation strategy and the effect of viscoelastic stress distribution on the settling behaviors of one and two particles are revealed. Subsequently, 504 particles settling in a closed cavity was simulated and the phenomenon that the viscoelastic stress stabilizing the Rayleigh–Taylor instabilities was observed. At last, simulations of a dense flow involving 11001 particles, the largest number of particles to date, were performed to investigate the instability behavior induced by elastic effect under hydrodynamic interactions in a viscoelastic fluid. The elasticity-induced ordering of the particle structures and fluid bubble structures in this dense flow is revealed for the first time. These simulations demonstrate the capability and prospects of the present method for aid in understanding the complex behaviors of viscoelastic particle suspensions.     

Experimental Method to Simulate Coal Fines Migration and Coal Fines Aggregation Prevention in the Hydraulic Fracture

A simple and effective experimental method is proposed to simulate coal fines migration through the proppant pack; such migration inevitably occurs during the process of fracturing fluid flowback or dewatering and gas production in coalbed methane (CBM) reservoirs. The damage to conductivity caused by coal fines migration in the pack and the factors affecting such migration are analyzed. A dispersion agent of coal fines applicable to hydraulic fracturing in CBM is optimized, consequently solving the problem of coal fines aggregation and retention in the proppant pack. Discharging coal fines with water or water-based fracturing fluid from the proppant pack can be difficult because of the adsorption and hydrophobicity of coal fines. Thus, coal fines are likely to aggregate and be retained in the proppant pack, thereby resulting in pore throat plugging, which causes serious damage to fracture conductivity. Two percent coal fines can reduce propped fracture conductivity by 24.4 %. The mobility and retention of coal fines in the proppant pack are affected by proppant size, proppant type, flowback rate, and coal fines property. When flowback rate exceeds the critical value, coal fines can be discharged from the pack, consequently reducing damage to propped fracture conductivity. More importantly, the steady discharging of coal fines requires steady dewatering and gas production to avoid flow shock, which causes pressure disturbance to drive coal fines in a remote formation. The optimized dispersant FSJ-02 employed in this paper can effectively change the wettability and surface potential of coal fines to improve their suspension and dispersion in water-based fracturing fluid. The recovery rate of coal fines increased by 31.5 %, whereas conductivity increased by 13.3 %.     

Effects of particle migration on suspension flow in a hydraulic fracture

An asymptotic model of a hydraulic-fracture flow of a sedimenting concentrated suspension is formulated on the basis of the two-fluid approach with account of transverse particle migration. In the thin-layer approximation, a two-dimensional system of equations averaged across the fracture is constructed with account for a nonuniform distribution of the particle concentration. As compared to the similar model without particle migration, the averaged two-dimensional equations contain modified coefficients which explicitly depend on the width of the flow core occupied by the particles. Using the model constructed, a numerical simulation is performed, which shows that the particle migration towards the fracture center results in the increase in the depth of particle penetration into the fracture and the suppression of gravitational convection in the vicinity of the leading front. The calculations are compared with available experimental data and an analytical formula for the height of the dense packed sediment. A good agreement between the analytical theory, the experiments, and the two-dimensional calculations is attained.     

水力劈裂问题的态型近场动力学建模

将态型近场动力学理论引入水力劈裂问题的模拟。构建了能反映岩土类材料准脆性断裂特征的态型近场动力学本构模型,并在物质点间相互作用力模型中加入等效水压力项,以实现在新生裂纹面上跟踪施加水压力。同时,考虑裂纹面间的接触,引入物质点间的短程排斥力作用,并设计了相应的接触算法。通过自编程序将模型和算法应用于含初始裂纹、不含初始裂纹以及含坝基软弱结构面的混凝土重力坝在高水头作用下的水力劈裂过程模拟,并与扩展有限元等模拟结果对比,验证了本文模型和算法的可行性和准确性。     

Particle fracture in high-volume-fraction ceramic-reinforced metals: Governing parameters and implications for composite failure

Weibull parameters of angular alumina particles are determined from experimental tensile test data on high-ceramic-content metal matrix composites using a micromechanical model that accounts for internal damage in the form of particle cracking, the dominant damage mode in these composites. The fraction of broken particles is assessed from the drop of Young's modulus and particle fracture is assumed to be stress controlled. Two extreme load-sharing modes, namely a purely local and a global load-sharing mode, are considered to account for the load redistribution due to particle fracture. Consistent powder strength parameters can be thus “back-calculated” for particles that are embedded in different Al-Cu matrices. On the other hand, this calculation fails for pure Al matrix composites, which exhibit a much larger strain to failure than Al-Cu matrix composites. It is shown that for Al matrix composites, the role of plastic (composite) strain on particle fracture constitutes a second parameter governing particle damage. This finding is rationalized by particle-particle interactions in these tightly packed ceramic particle-reinforced composites, and by the increase of matrix stress heterogeneity that is brought with increasing plastic strain. Failure of the alloyed matrix composites is well described by the (lower bound) local load-sharing micromechanical model, which predicts a catastrophic failure due to an avalanche of damage. The same model predicts failure of pure aluminium matrix composites to occur at the onset of tensile instability, also in agreement with experimental results once the role of plastic strain on damage accumulation is accounted for.     

Particle deposition in channels with permeablewalls

The filling of a channel with solid particles is considered in connection with the problem of preserving the geometry of a slot produced by hydraulic fracturing in a petroleum reservoir. The channel walls are permeable for the fluid. In the study, an experimental model of the channel (slot) in a permeable porous medium is used, on the periphery of which a constant pressure is sustained. The conditions of particle deposition on the permeable channel walls are determined. It is shown that in the case considered the initial stage of the particle deposition is independent of the viscosity and velocity of the fluid and is determined by the particle size and the specific permeability of the channel walls. It is found that the particles moving in the fluid stop at a certain distance and fill the fracture closely, forming a slug which loses stability as the pressure difference on its edges increases. The loss of the stability of the slug is accompanied by the appearance of a wavy channel, devoid of the particles and propagating in the flow direction.     

Numerical investigation of the temperature field in a reservoir with a hydraulic fracture

The temperature distribution in a reservoir with a hydraulic fracture is studied by numerical modeling of transient temperature fields taking into account the Joule–Thomson effect and the adiabatic effect. It is shown that the presence of a hydraulic fracture in the reservoir leads to a nonmonotonic change in the reservoir temperature: as the well pressure decreases, the temperature first decreases due to the adiabatic expansion of the fluid and then increases due to the Joule–Thomson effect. As the water–oil displacement front approaches the wellbore, the temperature decreases slightly due to heat exchange in the fracture–reservoir system.     

Steady suspension flows into two-dimensional horizontal and inclined channels

In this study a model which was developed previously is used to theoretically investigate the steady flow of a particulate suspension into two-dimensional horizontal and inclined channels. The continuity equation for the fluid and the simplified two-dimensional Navier-Stokes equations are then solved together with a particle concentration equation. This latter equation is formulated by considering the balance between the particle flux due to gravity with the corresponding particle fluxes due to convection and shear-induced diffusion. The resulting coupled system of equations is solved numerically using a specialised finite-difference method. It is found, for the parameter range for flows of proppants in hydraulic fractures, that when the suspension enters the channel with a uniform velocity profile it almost instantaneously becomes parabolic. In addition, the effects of particle sedimentation are most dominant in the entrance region, but further downstream such effects are balanced as shear-induced particle diffusion becomes more important. It is also shown that the suspension flow depends critically on the choice of the parameters used, e.g. the ratio of the particle radius to the height of the channel.     

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles

This study develops an extended unresolved CFD-DEM coupling method for simulation of the fluid–solid flow with non-spherical particles. The limitation of fluid grid size is discussed, by simulating the settling of a cylinder in a Newtonian fluid based on the resolved and unresolved CFD-DEM coupling method. Then, the calculation of porosity and the fluid–particle relative velocity based on the particle shape enlargement method for simulation of non-spherical particles is proposed. The availability of the particle shape enlargement method for the simulation of non-spherical particles with different sphericity is discussed in this work, by comparing it with the results from the equivalent diameter enlargement method. The limitation of the equivalent diameter enlargement method for non-spherical particles is revealed from the simulation results. Several typical cases are employed to elaborate and verify the extended unresolved CFD-DEM method based on particle shape enlargement method, by presenting a good consistency with the experimental results. It proves that the extended unresolved CFD-DEM method is suitable for different CFD grid size ratios, and consolidates that it is a universal calculation method for CFD-DEM coupling simulation.