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αs、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.     

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.     

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.     

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.

     

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 %.     

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.     

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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.     

Modeling and simulation of the viscoelastic fluid mold filling process by level set method

A model for unifying a viscoelastic fluid and a Newtonian fluid is established, in which the governing equations for the viscoelastic fluid and the Newtonian fluid are successfully united into a system of generalized Navier–Stokes equations. A level set method is set up to solve the model for capturing the moving interface in the mold filling process. The physical governing equations are solved by the finite volume method on a non-staggered grid and the interpolation technique on the collocated grid is used for the pressure-velocity and the stress-velocity decoupling problems. The level set and its reinitialization equation are solved by the finite difference method, in which the spatial derivatives are discretized by the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme, and the temporal derivatives are discretized by the 3rd-order Total Variation Diminishing Runge–Kutta (TVD-R–K) scheme. The validity of the method is verified by some benchmark problems. Then a simulation of viscoelastic fluid mold filling process is pursued with the method. The moving interface and all the information of the physical quantities during the injection process are captured. The die swelling phenomenon is found in the simulation. The influences of elasticity and viscosity on the physical quantities such as stresses etc. in the mold filling process are analyzed. Numerical results show that elastic characteristics such as the stretch and die swelling etc. reinforce accordingly as Weissenberg number increases. Pressures increase continuously in the mold filling process and the pressure maintains the maximum value at the inlet. Injection velocity is proportional to injection pressure. A higher viscosity leads to a higher pressure distribution, that is, the pressure decreases as Reynolds number increases.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon, in order to promote the versatility of gas/oil reservoirs. A numerical simulation of proppants transport at both hydraulic fracture (HF) and natural fracture (NF) intersection is performed to provide a better understanding of key factors which cause, or contribute to proppants transport in HF–NF intersection. Computational fluid dynamics (CFD) in association with discrete element method (DEM) is used to model the complex interactions between proppant particles, host fluid medium and fractured walls. The effect of non-spherical geometry of particles is considered in this model, using the multi-sphere method. All interaction forces between fluid flow and particles are considered in the computational model. Moreover, the interactions of particle–particle and particle–wall are taken into account via Hertz–Mindlin model. The results of the CFD-DEM simulations are compared to the experimental data. It is found that the CFD-DEM simulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data. The results indicate that the HF–NF intersection type, fluid velocity and NF aperture affect the quality of blockage occurrence, presenting a new index, called the blockage coefficient which indicates the severity of the blockage.     

Hydraulic fracture crack propagation driven by a non-Newtonian fluid

The problem of hydraulic fracture crack propagation in a porous medium is considered. The fracture is driven by an incompressible viscous fluid with a power-law rheology of the pseudoplastic type. The fluid seepage is described by an equation generalizing the Darcy law in the hydraulic approximation. It is shown that the system of governing equations has a power-law self-similar solution, whereas, in the limiting cases of low and high fluid saturation in the porous medium, there are some families of power-law or exponential self-similar solutions. The complete self-similar solution is constructed. The effect of the nonlinear rheology of the fracturing fluid on the behavior of the solution is studied. The problem is solved analytically for an arbitrary boundary condition at the crack inlet when the viscous stresses in the non-Newtonian fluid are close to a constant.     

A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains

A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.     

Fractional Dispersion,Lévy Motion,and the MADE Tracer Tests

The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi were conducted in a highly heterogeneous aquifer that violates the basic assumptions of local second-order theories. A governing equation that describes particles that undergo Lévy motion, rather than Brownian motion, readily describes the highly skewed and heavy-tailed plume development at the MADE site. The new governing equation is based on a fractional, rather than integer, order of differentiation. This order (), based on MADE plume measurements, is approximately 1.1. The hydraulic conductivity (K) increments also follow a power law of order =1.1. We conjecture that the heavy-tailed K distribution gives rise to a heavy-tailed velocity field that directly implies the fractional-order governing equation derived herein. Simple arguments lead to accurate estimates of the velocity and dispersion constants based only on the aquifer hydraulic properties. This supports the idea that the correct governing equation can be accurately determined before, or after, a contamination event. While the traditional ADE fails to model a conservative tracer in the MADE aquifer, the fractional equation predicts tritium concentration profiles with remarkable accuracy over all spatial and temporal scales.     

A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

A three-dimensional hydrodynamic model in curvilinear co-ordinates with collocated grid

A three-dimensional hydrodynamic model has been developed for turbulent flows with free surface. In the horizontal x–y-plane, a boundary-fitted curvilinear co-ordinate system is adopted, while in the vertical direction, a σ-co-ordinate transformation is used to represent the free surface and bed topography or lower boundary. Using the finite volume method, the convection terms are discretized using Roe's second-order-accurate scheme. The governing equations are solved in a collocated grid system by a fractional three-step implicit algorithm that has been developed to handle the velocity–pressure–depth coupling problem of free surface incompressible fluid flows. The present study is the extension of previous work to three-dimensional turbulent flows. The model has been applied to three test cases. Comparison with available data shows that the model developed is successful, and is valuable to engineering application. © 1998 John Wiley & Sons, Ltd.     

Fluid velocity based simulation of hydraulic fracture: a penny shaped model—part I: the numerical algorithm

In the first part of this paper, a universal fluid velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of dealing with both the viscosity and toughness dominated regimes, with the fracture being driven by a power-law fluid. The computational approach utilizes two dependent variables; the fracture aperture and the reduced fluid velocity. The latter allows for the application of a local condition of the Stefan type (the speed equation) to trace the fracture front. The obtained numerical solutions are carefully tested using various methods, and are shown to achieve a high level of accuracy.     

The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator.

     

An investigation of hydraulic fracturing. Part I: one-phase flow model

The prediction of the growth of a hydraulic fracture in an oil bearing formation based on the injection rate of fluid is valuable in applications of the waterflood technique in secondary oil recovery. In this paper, the problem of hydraulic fracture growth is studied under the assumption of uniform distribution of pressure in the fracture and unidirectional permeating flow in an infinitely large isothermal linearly elastic porous medium saturated with a one-phase incompressible fluid. The condition of plane strain is imposed in the study. A comparison of the constant fracture toughness criterion based on the asymptotic value for large crack growth with the crack tip ductility criterion for an ideally plastic solid under plane strain and small-scale yielding conditions indicates that the effect of ductility of rock on the crack growth is so small that the steady state value of the energy release rate can be reached within a short period of crack growth. Thus we can employ the constant fracture toughness criterion in our study. The analysis includes the effects of both fracture volume increase and leak-off of fluid from the surface of the fracture. A nonlinear singular integro-differential equation can be formulated for the quasi-static hydraulic fracture growth under a prescribed injection rate. It is solved numerically by a modified fourth order Runge-Kutta method.     

Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution

A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.