Influence of Numerical Cementation on Multiphase Displacement in Rough Fractures

We present an application of 3D X-ray computed microtomography for studying the influence of numerical cementation on flow in a cement-lined rough-walled fracture. The imaged fracture geometry serves as input for flow modeling using a combination of the level set and the lattice Boltzmann methods to characterize the capillary-dominated fluid displacement properties and the relative permeability of the naturally cemented fracture. We further numerically add cement to the naturally cement-lined fracture to quantify the effect of increasing cement thickness and diminishing aperture on flow properties. Pore space geometric tortuosity and capillary pressure as a function of water saturation both increase with the numerically increased fracture cement thickness. The creation of unevenly distributed apertures and cement contact points during numerical cement growth causes the wetting and non-wetting fluids to impede each other, with no consistent trends in relative permeability with increasing saturation. Tortuosity of wetting and non-wetting fluid phases exhibits none to poor correlation with relative permeability and thus cannot be used to predict it, contrary to previous findings in smoother fractures.     

Fluid flow in a porous medium containing partially closed fractures

The model of Snow, in which a fracture is represented by two parallel channel walls, has frequently been used to study the flow of fluid in fractured reservoirs. Although this model gives important insight into the flow in fractures, very few naturally occurring fractures have smooth parallel faces. In this paper, a simple model of partially contacting and en-echelon fractures frequently found in geological materials is presented. In this model, a fracture is viewed as a planar region where separation and contact zones both exist. To analyse the fluid flow in a porous medium containing fractures of this type, a planar array of periodically spaced fracture segments is analysed. The flow through a single fracture is deduced by taking the limit as the spacing between neighbouring fractures becomes large. The hydraulic conductivity parallel to the fractures is found to be the parallel combination of the conductivity of the porous matrix and the system of parallel fractures, the individual fracture conductance being a series combination of the hydraulic conductance of the separation and contact zones. This interpretation enables the conductance of the contact zones to be evaluated and the results to be generalised to the case in which the material in the contact regions has a hydraulic conductivity different to that of the matrix. This may arise, for example, from grain-size reduction during fracturing or may result from a partial mineralisation or cementation of the fracture.     

Flow and Transport in Fractured Aquifers: New Conceptual Models Based on Field Measurements

We derived new equations of fracture aperture (or tube diameter) as functions of a tortuosity factor that can be used in discrete models and even in continuum equivalent models to simulate fluid flow and pollutant transport in fractured aquifers. MODFLOW/MT3DMS water velocity predictions have been compared with those obtained using a specific software application which solves flow and transport problems in a 3D set of parallel fissures. The results of a pumping/tracer test carried out in a fractured limestone aquifer in Bari (Southern Italy) have been used to calibrate advective/dispersive tracer fluxes given by the applied models. The mean tracer velocity given by a breakthrough curve was greater than values predicted by continuum models. This discrepancy increased when the hydraulic conductivity of the considered fractured medium decreased. Successful simulations of flow and transport in the fractured limestone aquifer are then achieved by accommodating a new tortuosity factor in models. The importance of the proposed tortuosity factor correction lies in the possibility of taking into account the effective tracer velocity during flow and transport simulations in fractures even when using a continuum model.     

Moving singularities in elasto-diffusive solids with applications to fracture propagation

Solutions are derived for steady-state motion of a singularity class, which includes point sources and dislocations, through a medium in which the elastic stress-field can evolve with time due to the diffusion of an internal second-phase species, such as a pore-fluids and lattice impurity concentrations in a crystalline solid, or the transfer of heat. The technique is to integrate the known influence functions for a stationary singularity. Attention is focused on the most tractable aspect, namely the stress field on the trajectory of motion: this suffices for simulation of growing shear and tensile fractures (e.g. in a porous fluid-saturated solid). Continuous densities of fluid sources and point discontinuities (dislocations) are suitably distributed (as determined by solving the resulting singular integral equations) to satisfy solid stress and fluid pressure or flow conditions on the fracture surfaces. Alternative methods for finding the complete dislocation influence function are discussed and comparisons with existing source solutions are made. Substantial stabilization effects are found in fracture propagation.     

A new computation model of fractured horizontal well coupling with reservoir

Based on Green's functions and Newman's product principle, pressure drop formula was derived for considering simultaneous production of fractures and horizontal wellbore in unsteady state. A reservoir/fractured horizontal well coupling model is developed for finite conductivity condition that can be solved by the combination of quasi‐Newton method and PSO (Particle Swarm Optimization) algorithm. The solution of a practical example shows that lots of factors can affect the productivity of the fractured horizontal well. The number of the fractures has an optimizing range. Different fractures have different flow rates and the production in the central fracture is the lowest. The distribution of production rate in the wellbore has a wave‐like shape due to the influence of fractures. The closer fractures are the lower flow rate in well segments. Considering the horizontal wellbore production, the production rates in the fractures are asymmetric and the corresponding pressure drop curve is smoother. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑诱导缝多段压裂水平井非均质改造压力动态模型研究

为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化,建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型,耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解,对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性.基于压力导数曲线特征进行流动阶段划分和参数敏感性分析,得到以下结果:和常规压裂水平井井底压力导数曲线相比较,理想模式下,考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝“补充”阶段、储层线性流动阶段和拟边界控制流阶段.诱导缝条数的增加加剧了综合线性流阶段的持续时间,降低了流体渗流阻力,早期阶段压力曲线越低;当诱导缝与压裂裂缝导流能力一定时,裂缝导流能力越大,线性流持续时间越长;当所有压裂裂缝不在一个区域时,沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段,因此,沿井筒方向两端区域渗透率越低,早期阶段压力曲线越高;当所有压裂裂缝在一个区域时,渗透率变化只影响径向流阶段之后压力曲线形态,外区渗透率越低,早期径向流阶段之后压力曲线越高.通过实例验证,表明该模型和方法的实用性和准确性.     

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed.Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model(DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density.The pressure propagation is slower in the direction of larger fracture density.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

变开度岩体裂隙多相渗流实验与有效渗透率模型

岩体裂隙的有效渗透率是描述岩体非饱和或多相渗流的关键参数,而裂隙开度是影响有效渗透率的重要因素.通过自主研发的粗糙裂隙多相渗流可视化实验平台,针对天然岩体裂隙复制而成的裂隙模型开展变开度条件下的多相渗流可视化实验,研究开度变化对多相渗流流动结构以及有效渗透率的影响.研究表明:非湿润相流体运动通道,在低流量比条件下呈现出气泡流流动结构,而在高流量比条件下呈现较为稳定的通道流流动结构.随着开度的增加,非湿润相流动通道的分支变少、等效宽度增加,两相流体的有效渗透率均增大,流动结构趋于稳定.可视化结果还阐明了柱塞流流动结构下,两相流体交替占据裂隙空间的竞争机制:当非湿润相流体通道由连续转变为不连续时,裂隙进出口压差显著增加;反之,当该通道由不连续转变为连续时,压差显著减小.最后,基于分形理论以及渗透率统计建模方法,建立了考虑开度效应的岩体裂隙多相渗流有效渗透率理论模型,并通过实验测定的有效渗透率数据验证了该模型的正确性与有效性.     

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model (Maxwell model) for two-phase porous materials is presented, serving an explicit thermo-physical basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combination of reduced effective heat flow area and elongated heat transfer distance (thermal tortuosity).     

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...     

A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions

A directional crack growth criterion in a compressed elastic perfectly plastic material is considered. The conditions at the crack-tip are evaluated for a straight stationary crack with a small incipient kink. Remote load is a combined hydrostatic pressure and pure shear applied via a boundary layer. Crack surfaces in contact are assumed to develop homogenous Coulomb friction.The crack opening displacement of an extended kink is examined in a finite element analysis to judge the risk of opening mode failure. It has been found that the direction that maximizes the crack opening displacement of an extended kink tip coincides very well with a prediction of the crack growth direction obtained by using a criterion for continued crack growth direction discussed by the authors elsewhere [Int. J. Fract. 108 (2001) 351].Moreover, the by the model predicted incipient crack growth directions are qualitatively comparable with reported crack paths obtained in ductile materials in a limited number of experiments performed under a combined load of in-plane shear and compression.     

New Correlative Models to Improve Prediction of Fracture Permeability and Inertial Resistance Coefficient

Presence of fracture roughness and occurrence of nonlinear flow complicate fluid flow through rock fractures. This paper presents a qualitative and quantitative study on the effects of fracture wall surface roughness on flow behavior using direct flow simulation on artificial fractures. Previous studies have highlighted the importance of roughness on linear and nonlinear flow through rock fractures. Therefore, considering fracture roughness to propose models for the linear and nonlinear flow parameters seems to be necessary. In the current report, lattice Boltzmann method is used to numerically simulate fluid flow through different fracture realizations. Flow simulations are conducted over a wide range of pressure gradients through each fracture. It is observed that creeping flow at lower pressure gradients can be described using Darcy’s law, while transition to inertial flow occurs at higher pressure gradients. By detecting the onset of inertial flow and regression analysis on the simulation results with Forchheimer equation, inertial resistance coefficients are determined for each fracture. Fracture permeability values are also determined from Darcy flow as well. According to simulation results through different fractures, two parametric expressions are proposed for permeability and inertial resistance coefficient. The proposed models are validated using 3D numerical simulations and experimental results. The results obtained from these two proposed models are further compared with those obtained from the conventional models. The calculated average absolute relative errors and correlation coefficients indicate that the proposed models, despite their simplicity, present acceptable outcomes; the models are also more accurate compared to the available methods in the literature.     

Electric effects on the rheology of insulating oils in electrodes with flocked fabric

The rheological behavior of insulating oils is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabric. Although the oils show no electrorheological effects in uniform fields between metal electrodes with smooth surfaces, the flocked fabric leads to a striking increase of viscosity in steady shear. The viscosity enhancement increases with decreasing zero-field viscosity and decreasing conductivity of oils. In the limit of zero shear rate, the oils with low conductivity behave as solids with yield stress. When a very small quantity of fine particles is introduced into electrified oils without shear, a rapid and large-scale motion of particles is observed between the tips of fibers and the plate electrode. The local motion of fluids in high electric fields is referred to as electrohydrodynamic (EHD) convection. Periodic patterns of circulation flow are formed in static oils. The electric energy which is dissipated during the circulation motion contributes to holding the periodic flow in static oils. When the stress is very low, the periodic patterns are not broken down. The yield stress corresponds to the force required to rupture the domain structures of EHD convection. In shear fields, the additional energy may be required to change the periodic patterns of EHD convection. The striking increase of viscosity in steady shear can be attributed to the interactions between EHD convection and external shear. Received: 31 August 1998 Accepted: 17 February 1999     

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。     

Simulation of Pressure Transient Behavior for Asymmetrically Finite-Conductivity Fractured Wells in Coal Reservoirs

Based on Fick’s law in matrix and Darcy flow in cleats and hydraulic fractures, a new semi-analytical model considering the effects of boundary conditions was presented to investigate pressure transient behavior for asymmetrically fractured wells in coal reservoirs. The new model is more accurate than previous model proposed by Anbarci and Ertekin, SPE annual technical conference and exhibition, New Orleans, 27–30 Sept 1998 because new model is expressed in the form of integral expressions and is validated well through numerical simulation. (1) In this paper, the effects of parameters including fracture conductivity, coal reservoir porosity and permeability, fracture asymmetry factor, sorption time constant, fracture half-length, and coalbed methane (CBM) viscosity on bottomhole pressure behavior were discussed in detail. (2) Type curves were established to analyze both transient pressure behavior and flow characteristics in CBM reservoir. According to the characteristics of dimensionless pseudo pressure derivative curves, the process of the flow for fractured CBM wells was divided into six sub-stages. (3) This paper showed the comparison of transient steady state and pseudo steady state models. (4) The effects of parameters including transfer coefficient, wellbore storage coefficient, storage coefficient of cleat, fracture conductivity, fracture asymmetry factor, and rate coefficient on the shape of type curves were also discussed in detail, indicating that it is necessary to keep a bigger fracture conductivity and fracture symmetry for enhancing well production and reducing pressure depletion during the hydraulic fracturing design.     

基于XFEM-MBEM的嵌入式离散裂缝模型流固耦合数值模拟方法

离散缝网的表征与模拟是目前国内外研究的热点. 在非常规油气开发过程中, 由于地应力场的存在会对裂缝的流动属性产生显著影响, 若将裂缝视为静态对象, 与矿场数据会出现极大偏差, 因此要基于动态裂缝做更深入的研究. 本文针对致密油藏应力场?渗流场耦合力学问题, 提出了一种高效的混合数值离散化方法, 其中采用扩展有限元法 (XFEM) 求解岩石的弹性形变, 采用了混合边界元法 (MBEM) 精确计算基岩与裂缝间的非稳态窜流, 这两种数值格式是完全耦合的, 并对整体计算格式的时间项进行了全隐式求解, 可准确表征致密油藏开采过程中的裂缝变形及流体流动机理. 此外, 本文采用了嵌入式离散裂缝前处理算法显式表征大尺度水力压裂缝, 并考虑了支撑剂的作用; 采用了双孔有效应力原理和双重介质隐式裂缝表征方法, 可捕捉基质与小尺度天然裂缝的动态信息; 由此, 本文所提出的混合模型综合表征了基质?天然裂缝?水力压裂缝共同组成的致密油藏复杂渗流环境, 并通过几个实例论证了模型的准确性, 研究表明: 对致密油藏压裂水平井进行产能评价时, 应力场所引起渗流参数的改变及裂缝开度降低的影响不可忽略. 本文研究可为非常规油气资源的开发提供理论指导.      

裂隙岩体渗透系数确定方法研究

裂隙岩体渗透系数以及渗透主方向的确定对研究岩体渗透性大小及各向异性具有重要意义。高放废物地质处置库介质岩体的渗透性能将直接影响其使用安全性。本文运用离散裂隙网络模拟的方法对我国高放废物处置库甘肃北山预选区3#钻孔附近裂隙岩体进行了渗透性质分析。通过对3#钻孔1715～1780m段压水试验数据的反演,标定了离散裂隙网络渗流模型中的裂隙渗透参数(导水系数T)。利用标定的离散裂隙网络模型对场区裂隙岩体进行了渗流模拟,确定了该区域裂隙岩体的渗流表征单元体(REV)的尺寸大小以及渗透主值和主渗透方向。运用离散裂隙网络模型计算得出的渗透主值的几何均值与现场压水试验计算结果较接近,证明了计算结果的有效性。     

Radial Flow of Non-Newtonian Power-Law Fluid in a Rough-Walled Fracture: Effect of Fluid Rheology

Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots.     

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.