考虑单元劈裂的流-固耦合连续-非连续方法及定向水力压裂模拟

为了更真实地模拟水力压裂过程中的岩石变形、裂缝扩展及流体流动,在自主开发的拉格朗日元与离散元耦合的连续-非连续方法的基础上,发展了一种流-固耦合方法。在该方法中,裂缝可沿四边形单元对角线和单元边界扩展,流体流动满足立方定律。通过与单一裂缝非稳态渗流模型及KGD模型的理论解进行对比,验证了该方法的正确性。由定向射孔水力压裂的模拟结果可以发现,(1)距离射孔越远,流体压力越小;随着时间的增加,裂缝中流体压力降低。(2)随着射孔角度的增加,裂缝起裂和扩展过程中的流体压力及转向距离增加;随着x方向水平应力的增加,裂缝起裂和扩展过程中的流体压力增加;两个方向水平应力之差越大,裂缝转向距离越小。(3)随着时间的增加,裂缝区段数目的增速变慢,这与裂缝体积增加变快有关。     

3-D PTV measurement of Marangoni convection in liquid bridge in space experiment

Microgravity experiments have been conducted on the International Space Station in order to clarify the transition processes of the Marangoni convection in liquid bridges of high Prandtl number fluid. The use of microgravity allows us to generate large liquid bridges, 30?mm in diameter and up to 60?mm in length. Three-dimensional particle tracking velocimetry (3-D PTV) is used to reveal complex flow patterns that appear after the transition of the flow field to oscillatory states. It is found that a standing-wave oscillation having an azimuthal mode number equal to one appears in the long liquid bridges. For the liquid bridge 45?mm in length, the oscillation of the flow field is observed in a meridional plane of the liquid bridge, and the flow field exhibits the presence of multiple vortical structures traveling from the heated disk toward the cooled disk. Such flow behaviors are shown to be associated with the propagation of surface temperature fluctuations visualized with an IR camera. These results indicate that the oscillation of the flow and temperature field is due to the propagation of the hydrothermal waves. Their characteristics are discussed in comparison with some previous results with long liquid bridges. It is shown that the axial wavelength of the hydrothermal wave observed presently is comparable to the length of the liquid bridge and that this result disagrees with the previous linear stability analysis for an infinitely long liquid bridge.     

On Vaporizing Water Flow in Hot Sub-Vertical Rock Fractures

Water injection into unsaturated fractured rock at above-boiling temperatures gives rise to complex fluid flow and heat transfer processes. Examples include water injection into depleted vapor-dominated geothermal reservoirs, and emplacement of heat-generating nuclear wastes in unsaturated fractured rock. We conceptualize fractures as two-dimensional heterogeneous porous media, and use geostatistical techniques to generate synthetic permeability distributions in the fracture plane. Water flow in hot high-angle fractures is simulated numerically, taking into account the combined action of gravity, capillary, and pressure forces, and conductive heat transfer from the wall rocks which gives rise to strong vaporization. In heterogeneous fractures boiling plumes are found to have dendritic shapes, and to be subject to strong lateral flow effects. Fractures with spatially-averaged homogeneous permeabilities tend to give poor approximations for vaporization behavior and liquid migration patterns. Depending on water flow rates, rock temperature, and fracture permeability, liquid water can migrate considerable distances through fractured rock that is at above-boiling temperatures and be only partially vaporized.     

Pore-Level Observation of Free Gravity Drainage of Oil in Fractured Porous Media

This work presents results from two sets of experiments conducted to study, in pore level, the role of fracture aperture and tilt angle on the stability of liquid bridges and the shape of a front during free gravity drainage process. Glass micromodels of two different aperture sizes were used to monitor the mechanism of gravity drainage of air?Ccrude oil system, rotating around a bottom corner to create different tilting angles. Oil content within the matrix blocks was determined as a function of time using a series of images obtained during the experiments, from which net drainage rate from the upper and lower matrix blocks is calculated. Liquid bridges are more frequent but less stable at early time of drainage. The liquid bridges, which have widths as thin as 50 ??m, can resist instability to maintain continuity. Liquid bridges formed in stacks with higher tilt angles are more stable, enhancing oil drainage from the upper matrix block and causing higher recoveries. Quantitative analysis of the results shows that a wider fracture aperture increases the oil production rate, but reduces the ultimate recovery. Furthermore, stacks with higher tilt angles present larger ultimate recoveries and smaller production rates. The front geometry in the lower block deviates from linearity due to formation of liquid bridges in the middle fracture. The results of this work can be helpful to better understand the interaction between fractures and matrix blocks.     

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

We study the generation and flow of foam through rough-walled, fractured marble rocks that mimic natural fracture systems in carbonate reservoirs. Flow was isolated to the fracture network because of the very low rock permeability of the marble samples and foam generated in situ during co-injection of surfactant solution and gas. The foam apparent viscosities were calculated at steady pressure gradients for a range of gas fractions, and similar to foam flow in porous media, we identified two flow regimes for foam flow in fractures: a high-quality flow regime only dependent on liquid velocity and a low-quality flow regime determined by the gas and liquid velocities. Variations in local fluid saturation during co-injection were visualized and quantified using positron emission tomography combined with computed tomography.

     

Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media

We benchmark a family of hybrid finite element–node-centered finite volume discretization methods (FEFV) for single- and two-phase flow/transport through porous media with discrete fracture representations. Special emphasis is placed on a new method we call DFEFVM in which the mesh is split along fracture–matrix interfaces so that discontinuities in concentration or saturation can evolve rather than being suppressed by nodal averaging of these variables. The main objective is to illustrate differences among three discretization schemes suitable for discrete fracture modeling: (a) FEFVM with volumetric finite elements for both fractures and porous rock matrix, (b) FEFVM with lower dimensional finite elements for fractures and volumetric finite elements for the matrix, and (c) DFEFVM with a mesh that is split along material discontinuities. Fracture discontinuities strongly influence single- and multi-phase fluid flow. Continuum methods, when used to model transport across such interfaces, smear out concentration/saturation. We show that the new DFEFVM addresses this problem producing significantly more accurate results. Sealed and open single fractures as well as a realistic fracture geometry are used to conduct tracer and water-flooding numerical experiments. The benchmarking results also reveal the limitations/mesh refinement requirements of FE node-centered FV hybrid methods. We show that the DFEFVM method produces more accurate results even for much coarser meshes.     

压裂页岩气藏多尺度耦合流动数值模拟研究

在碳达峰的国策背景之下,页岩气成为传统能源向绿色清洁低碳能源转型的重要过渡和能源支点.压后页岩气藏流体流动力学成为高效开发页岩气的关键力学问题.文章将小尺度低导流天然裂缝等效升级为连续介质,建立有机质-无机质-天然裂缝三重连续介质模型,同时对大尺度高导流裂缝采用离散裂缝模型刻画,嵌入天然裂缝连续介质中,构建多重连续/离散裂缝模型.综合考虑吸附气的非平衡非线性解吸附和表面扩散,自由气的黏性流和克努森扩散,给出页岩气在多尺度复杂介质中的非线性耦合流动数学模型.提出多尺度扩展有限单元法对离散裂缝进行显式求解,创新性构建三类加强形函数捕捉离散裂缝的局部流场特征,解决了压后页岩海量裂缝及多尺度流动通道的流动模拟难题.文章提出的模型和方法既能准确刻画高导流裂缝对渗流的影响,又克服了海量多尺度离散裂缝导致计算量增大的问题.通过算例展示了压后页岩各连续介质的压力衰减规律,发现裂缝中自由气、有机质中自由气、无机质中吸附气依次滞后的压力(浓度)扩散现象,重点分析了吸附气表面扩散系数、自由气克努森扩散系数、天然裂缝连续介质渗透率和吸附气解吸附速率对页岩气产量的影响.文章重点解决压后页岩多尺度流动通道的表征和...     

Modeling Non-Darcian Single- and Two-Phase Flow in Transparent Replicas of Rough-Walled Rock Fractures

While it is generally assumed that in the viscous flow regime, the two-phase flow relative permeabilities in fractured and porous media depend uniquely on the phase saturations, several studies have shown that for non-Darcian flows (i.e., where the inertial forces are not negligible compared with the viscous forces), the relative permeabilities not only depend on phase saturations but also on the flow regime. Experimental results on inertial single- and two-phase flows in two transparent replicas of real rough fractures are presented and modeled combining a generalization of the single-phase flow Darcy’s law with the apparent permeability concept. The experimental setup was designed to measure injected fluid flow rates, pressure drop within the fracture, and fluid saturation by image processing. For both fractures, single-phase flow experiments were modeled by means of the full cubic inertial law which allowed the determination of the intrinsic hydrodynamic parameters. Using these parameters, the apparent permeability of each fracture was calculated as a function of the Reynolds number, leading to an elegant means to compare the two fractures in terms of hydraulic behavior versus flow regime. Also, a method for determining the experimental transition flow rate between the weak inertia and the strong inertia flow regimes is proposed. Two-phase flow experiments consisted in measuring the pressure drop and the fluid saturation within the fractures, for various constant values of the liquid flow rate and for increasing values of the gas flow rate. Regardless of the explored flow regime, two-phase flow relative permeabilities were calculated as the ratio of the single phase flow pressure drop per unit length divided by the two-phase flow pressure drop per unit length, and were plotted versus the measured fluid saturation. Results confirm the dependence of the relative permeabilities on the flow regime. Also the proposed generalization of Darcy’s law shows that the relative permeabilities versus fluid saturation follow physical meaningful trends for different liquid and gas flow rates. The presented model fits correctly the liquid and gas experimental relative permeabilities as well as the fluid saturation.     

Simulation of Fluid Flow on Fractures and Implications for Reactive Transport Simulations

The diverse numerical simulation techniques employed to predict fluid flow properties of fractures yield differing results which limits their applicability for reactive transport simulations. Basically the fluid flow simulation techniques can be divided in two groups: (i) techniques that yield average fluid flow characteristics and (ii) techniques that produce space-resolved properties. These differences may have substantial impact on the reactive transport simulations but may also depend on the fracture characteristics. For this reason, a sensitivity analysis of the geometrical properties of fractures on the fluid flow properties is conducted and evaluated with respect to their impact on reactive transport modeling. Although employing space-resolved simulation techniques, the results of the tests show average values for permeability and fluid velocity that are comparable to previous studies that used other simulation techniques. Observed fluid flow channeling appears to be related to fracture surfaces matching and anisotropy. However, average flow velocities at potential sites for reactive transport differ up to a factor of five from the average ones for the entire fracture. Furthermore, extreme values at reactive transport sites may differ even more and the flow may be directed against the applied pressure gradient. For studies concerned with simulation of reactive transport, these deviations are crucial and should be explicitly considered in the calculations. Hence space-resolved fluid flow simulations should be employed for the simulation of reactive transport.     

Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys

The dynamic thermomechanical response of a tungsten heavy alloy is investigated via modeling and numerical simulation. The material of study consists of relatively stiff pure tungsten grains embedded within a more ductile matrix alloy comprised of tungsten, nickel, and iron. Constitutive models implemented for each phase account for finite deformation, heat conduction, plastic anisotropy, strain-rate dependence of flow stress, thermal softening, and thermoelastic coupling. The potentially nonlinear volumetric response in tungsten at large pressures is addressed by a pressure-dependent effective bulk modulus. Our framework also provides a quantitative prediction of the total dislocation density, associated with cumulative strain hardening in each phase, and enables calculation of the fraction of plastic dissipation converted into heat energy. Cohesive failure models are employed to represent intergranular fracture at grain and phase boundaries. Dynamic finite element simulations illustrate the response of realistic volume elements of the polycrystalline microstructure subjected to compressive impact loadings, ultimately resulting in spallation of the material. The relative effects of mixed-mode interfacial failure criteria, thermally-dependent fracture strengths, and grain shapes and orientations upon spall behavior are weighed, with interfacial properties exerting a somewhat larger influence on the average pressure supported by the volume element than grain shapes and initial lattice orientations within the bulk material. Spatially resolved profiles of particle velocities at the free surfaces of the volume elements indicate the degree to which the incident and reflected stress waves are altered by the heterogeneous microstructure.     

Effect of gap and flow orientation on two-phase flow in an oil-wet gap: Relative permeability curves and flow structures

Naturally fractured reservoirs contain about 25–30% of the world supply of oil. In these reservoirs, fractures are the dominant flow path. Therefore, a good understanding of transfer parameters such as relative permeability as well as flow regimes occurring in a fracture plays an important role in developing and improving oil production from such complex systems. However, in contrast with gas–liquid flow in a single fracture, the flow of heavy oil and water has received less attention. In this research, a Hele-Shaw apparatus was built to study the flow of water in presence of heavy oil and display different flow patterns under different flow rates and analyze the effect of fracture orientations on relative permeability curves as well as flow regimes. The phase flow rates versus phase saturation results were converted to experimental relative permeability curves. The results of the experiments demonstrate that, depending on fracture and flow orientation, there could be a significant interference between the phases flowing through the fracture. The results also reveal that both phases can flow in both continuous and discontinuous forms. The relative permeability curves show that the oil–water relative permeability not only depends on fluid saturations and flow patterns but also fracture orientation.     

Modeling of Solute Transport in a 3D Rough-Walled Fracture–Matrix System

Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.     

Effective Permeability of a Porous Medium with Spherical and Spheroidal Vug and Fracture Inclusions

Vugs and fractures are common features of carbonate formations. The presence of vugs and fractures in porous media can significantly affect pressure and flow behavior of a fluid. A vug is a cavity (usually a void space, occasionally filled with sediments), and its pore volume is much larger than the intergranular pore volume. Fractures occur in almost all geological formations to some extent. The fluid flow in vugs and fractures at the microscopic level does not obey Darcy’s law; rather, it is governed by Stokes flow (sometimes is also called Stokes’ law). In this paper, analytical solutions are derived for the fluid flow in porous media with spherical- and spheroidal-shaped vug and/or fracture inclusions. The coupling of Stokes flow and Darcy’s law is implemented through a no-jump condition on normal velocities, a jump condition on pressures, and generalized Beavers–Joseph–Saffman condition on the interface of the matrix and vug or fracture. The spheroidal geometry is used because of its flexibility to represent many different geometrical shapes. A spheroid reduces to a sphere when the focal length of the spheroid approaches zero. A prolate spheroid degenerates to a long rod to represent the connected vug geometry (a tunnel geometry) when the focal length of the spheroid approaches infinity. An oblate spheroid degenerates to a flat spheroidal disk to represent the fracture geometry. Once the pressure field in a single vug or fracture and in the matrix domains is obtained, the equivalent permeability of the vug with the matrix or the fracture with matrix can be determined. Using the effective medium theory, the effective permeability of the vug–matrix or fracture–matrix ensemble domain can be determined. The effect of the volume fraction and geometrical properties of vugs, such as the aspect ratio and spatial distribution, in the matrix is also investigated. It is shown that the higher volume fraction of the vugs or fractures enhances the effective permeability of the system. For a fixed-volume fraction, highly elongated vugs or fractures significantly increase the effective permeability compared with shorter vugs or fractures. A set of disconnected vugs or fractures yields lower effective permeability compared with a single vug or fracture of the same volume fraction.     

Wetting Phase Bridges Establish Capillary Continuity Across Open Fractures and Increase Oil Recovery in Mixed-Wet Fractured Chalk

The effect of fractures on oil recovery and in situ saturation development in fractured chalk has been determined at near neutral wettability conditions. Fluid saturation development was monitored both in the matrix and in the fractures and the mechanisms of fracture crossing were determined using high spatial resolution MRI. Capillary continuity across open oil-filled fractures was verified by imaging the water bridges established within the fracture. Despite an alternate escape fracture for the water, separate water bridges were shown to be stable for the entire duration of the experiments. The established capillary contact resulted in oil recovery exceeding the spontaneous imbibition potential in the outlet-isolated cores by ca. 10% PV. This is explained by viscous recovery provided by water bridges across open fractures. The size of the bridges seemed to be controlled by the wettability of the rock and not by the differential pressure applied across the open fracture.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media

Over the past few decades, significant progress of assessing chemical transport in fractured rocks has been made in laboratory and field investigations as well as in mathematic modeling. In most of these studies, however, matrix diffusion on fracture–matrix surfaces is considered as a process of molecular diffusion only. Mathematical modeling based on this traditional concept often had problems in explaining or predicting tracer transport in fractured rock. In this article, we propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity. The proposed model incorporates an additional matrix-diffusion process, induced by rapid fluid flow along fractures. According to the boundary-layer theory, fracture-flow-enhanced matrix diffusion may dominate mass-transfer processes at fracture–matrix interfaces, where rapid flow occurs through fractures. The new conceptual model can be easily integrated with analytical solutions, as demonstrated in this article, and numerical models, as we foresee. The new conceptual model is preliminarily validated using laboratory experimental results from a series of tracer breakthrough tests with different velocities in a simple fracture system. Validating of the new model with field experiments in complicated fracture systems and numerical modeling will be explored in future research.     

Intermittent gas-liquid flow in upward inclined pipes

Experimental measurements of flow patterns. pressure gradients and liquid holdup for intermittent two-phase flow in upward inclined pipes are reported. Comparison of this new experimental evidence is made with the Taitel & Dukler theory and the intermittent flow model as modified by Nicholsonet al.     

Development of hot dry rocks by hydraulic stimulation: Natural fracture network simulation

This paper presents an advanced computational modelling of natural fracture networks in HDR (hot dry rock) reservoirs. The model stochastically simulates discrete properties of natural fractures, utilizing multi-set orientation and fractal mathematics. The simulated fracture networks are essential for further stimulation and fluid flow studies. The model has been verified using the data of actual fracture stimulation programs conducted by Gas Research Institute and Department of Energy at the multi-site. It is validated that the simulated fracture distribution is sufficiently similar to that observed in the reservoir. This paper also examines the detrimental effects of the simulated natural fracture network on the stimulated fluid flow capacity. The effective permeability enhancement (due to hydraulic stimulation) is found almost proportional to the density of the reservoir natural fractures.     

Fluid Flow Through Single Fractures With Directional Shear Dislocations

This paper numerically investigates the fluid flow behavior through single fractures with directional shear dislocations. Synthetic fractures are generated with directional shear dislocations, and the lattice Boltzmann method is used to simulate the fracture flow. With an ignorance of tortuosity effect, a notable overestimation of hydraulic conductivity is observed when the simplified local cubic law is used. During the closure process, the decreasing rate of conductivity is found to be highly related to the roughness of fractures. The conductivity of smoother fractures decreases faster than that of rougher fractures. By conducting simulations on fractures with a constant shear displacement, the effective conductivity is found to vary with the shear directions. The results show that the conductivity of rougher fractures is less sensitive to the shear directions than that of smoother fractures. As fracture surfaces come into contact, a sharp decrease in effective conductivity is observed and the decreasing trend flattens as the contact ratio continues to increase. A new model is proposed based on the bottleneck model to predict the conductivity of sheared fractures. By integrating the tortuosity and channeling effects into the original model, the proposed new model shows a better performance in predicting the conductivity, especially for fractures with rougher surfaces.     

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.