Modeling Water Leak-off Behavior in Hydraulically Fractured Gas Shale under Multi-mechanism Dominated Conditions

Fracturing-fluid leak-off in fractured gas shale is a complex process involving multiple pore/fluid transports and interactions. However, water leak-off behavior has not been modeled comprehensively by considering the multi-pores and multi-mechanisms in shale with existing simulators. In this paper, we present the development of a comprehensive multi-mechanistic, multi-porosity, and multi-permeability water/gas flow model that uses experimentally determined formation properties to simulate the fracturing-fluid leak-off of hydraulically fractured shale gas wells. The multi-mechanistic model takes into account water transport driven by hydraulic convection, capillary and osmosis, gas transport caused by hydraulic convection, and salt ion transport caused by advection and diffusion. The multi-porosity includes hydraulic fracture millipores, organic nanopores, clay nanopores, and other inorganic micropores. The multi-permeability model accounts for all the important processes in shale system, including gas adsorption on the organics’ surface, multi-mechanistic clay/other inorganic mineral mass transfer, inorganic mineral/hydraulic fracture mass transfer, and injection from a hydraulically fractured wellbore. The dynamic water saturation and pressure profiles within clay and other inorganic matrices are compared, revealing the leak-off behavior of water in rock media with different physicochemical properties. In sensitivity analyses, cases with different clay membrane efficiency, volume proportion of source rock, connate water salinity, and saturation are considered. The impacts of shale properties on water fluxes through wellbore, hydraulic fracture and matrix, and the total injection and leak-off volumes of the well during the treatment of hydraulic fracturing are investigated. Results show that physicochemical properties in both organic and inorganic matrices affect the water leak-off behavior.     

裂隙岩体非稳态渗流数值模型及其应用

为解决裂隙岩体非稳态渗流问题, 发展了一种新的数值模型. 对于单裂隙渗 流求解, 其控制方程是基于一定假设的简化Navier-Stokes方程, 数值方法采用有限差分法 和流体体积法. 在裂隙网络中, 交界处渗流可以由专门的控制方程求解. 计算结果表明, 该 数值模型既可以大幅提高非稳态渗流的计算效率, 还可以避免孤立裂隙所带来的影响. 最后, 通过两个工程算例验证该数值模型的适用性.     

Lattice Boltzmann Simulation of Fluid Flow in Synthetic Fractures

Fractures play an important role in reservoir engineering as they dominate the fluid flow in the reservoir. All evidence suggests that rarely can one model flow and transport in a fractured rock consistently by treating it as a uniform or mildly nonuniform isotropic continuum. Instead, one must generally account for the highly erratic heterogeneity, directional dependence, dual or multicomponent nature and multiscale behavior of fractured rocks. As experimental methods are expensive and time consuming most of the time numerical methods are used to study flow and transport in a fractured rock. In this work, we present results of the numerical computations for single phase flow simulations through two-dimensional synthetically created fracture apertures. These synthetic rock fractures are created using different fractal dimensions, anisotropy factors, and mismatch lengths. Lattice Boltzmann method (LBM), which is a new computational approach suitable to simulate fluid flow especially in complex geometries, was then used to determine the permeability for different fractures. Regions of high velocity and low velocity flow were identified. The resulting permeability values were less than the ones obtained with the cubic law estimates. It has been found that as the mean aperture–fractal dimension ratio increased permeability increased. Moreover as the anisotropy factor increased permeability decreased. Neural network simulations were used to generalize the results.     

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.      

裂隙岩体水力特征数值模拟试验的初步结果

本文利用文献中的数据进行数值模拟试验,结果表明：流量等效和渗透作用力变形效果等效互不包容;不同级别结构面体系难以用连续介质方法处理,同级别结构面体系在工程作用力变化范围内,可由其静态水力特征推演动态特征;工程岩体结构面间充分连通的假设过于粗糙,常规试验手段获取的量值倾向于局部特征的反映。     

非贯通裂隙岩体损伤演化率相关性及变形特征

含非贯通裂隙岩体是自然界中岩体的主要赋存形式,其裂隙几何特征对岩体的强度及变形均产生显著影响。应变率对岩体的损伤演化及黏滞效应也具有显著的率相关性。首先,运用模型元件的方法,将非贯通裂隙岩体动态破坏过程视为具复合损伤、静态弹性特性、动态黏滞特性的非均质点组成,对黏弹性响应的Maxwell体进行改进,将细观损伤体与裂隙损伤演化的宏观损伤体根据等效应变假设并联组成宏细观复合损伤体,构建综合考虑岩体宏细观缺陷的动态损伤模型;其次,基于断裂力学及应变能理论,对岩体宏观裂隙动态扩展的能量机制进行分析,综合考虑初始裂隙应变能、裂隙动态损伤演化过程应变能、裂隙闭合应变能,得到裂隙岩体宏观动态损伤变量计算公式;最后,将模型计算结果与实验结果进行比较,模型计算结果与实验结果吻合较好,证明了模型的合理性,同时利用模型讨论了裂隙倾角、应变率、岩石性质对岩体变形特征的影响规律。     

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.     

动载荷作用下裂隙岩体的止裂机理分析

为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC（tunnel with single radial crack）构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。     

Modeling Free-Surface Seepage Flow in Complicated Fractured Rock Mass Using a Coupled RPIM-FEM Method

The prediction of the free-surface seepage flow behavior in fractured rock mass is of significance in geotechnical engineering. There are two major issues in solving the seepage flow in complicated fractured rock mass based on the fractured porous medium (FPM) flow model, in which groundwater is assumed to flow simultaneously in both rock matrix and embedded fractures: One is the mesh generation of rock mass in the presence of the fracture network, especially when there exist a large number of stochastic fractures; the other is that a robust iteration algorithm is required since the free surface is unknown at the beginning of solution. Aiming at these two issues, this paper proposes a novel numerical method by coupling radial point interpolation method (RPIM) and finite element method (FEM), in which RPIM is utilized to model the rock matrix and FEM is utilized to model the fractures. On the basis of the variational inequality (VI) theory for free-surface seepage analysis, the computation formulations of the numerical method are derived and the corresponding computation program is developed. Three examples are solved with the present method. It is found that the VI theory can be extended to solve the free-surface seepage problem based on the FPM flow model. A crucial advantage of the present method is that the mesh generation can be greatly simplified. The present method has been verified to be a robust, efficient and reliable method for modeling the groundwater flow in complicated fractured rock mass.     

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.     

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。     

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.     

一种预测颗粒增强复合材料界面力学性能的新方法

界面在颗粒增强复合材料中起到传递载荷的关键作用, 界面性能对复合材料整体力学行为产生重要影响. 然而由于复合材料内部结构较为复杂, 颗粒与基体间的界面强度和界面断裂韧性难以确定, 尤其是法向与切向界面强度的分别预测缺乏有效方法. 本文以氧化锆颗粒增强聚二甲基硅氧烷(PDMS)复合材料为研究对象, 提出一种预测颗粒增强复合材料界面力学性能的新方法. 首先, 实验获得纯PDMS基体材料及单颗粒填充PDMS试样的单轴拉伸应力$\!-\!$应变曲线, 标定出PDMS基体材料的单轴拉伸超弹性本构关系; 其次, 建立与单颗粒填充试样一致的有限元模型, 选择特定的黏结区模型描述界面力学行为, 通过样品不同阶段拉伸力学响应的实验与数值结果对比, 分别给出颗粒与基体界面的法向强度、切向强度及界面断裂韧性; 进一步应用标定的界面力学参数, 开展不同尺寸及不同数目颗粒填充试样的实验与数值结果比较, 验证界面性能预测结果的合理性. 本文提出的界面力学性能预测方法简便、易操作、精度高, 对定量预测颗粒增强复合材料的力学性能具有一定帮助, 亦对定量预测纤维增强复合材料的界面性能具有一定参考意义.      

水力压裂中裂纹扩展的数值模拟

水力压裂是在高压粘滞流体或清水作用下地层内裂缝起裂与扩展的过程。由于包含岩石断裂和流-固耦合等复杂问题,对该过程的数值模拟具有相当大的挑战性。本文建立基于有限元与离散元混合方法的裂纹模型,模拟岩石裂纹扩展,实现了连续向非连续的转化;建立双重介质流动模型,裂隙流作为孔隙渗流的压力边界,孔隙渗流反作用裂隙的压力求解,处理了流体在基岩与人工裂缝中的协调流动;将裂纹模型与流体流动模式进行结合,建立断裂-应力-渗流耦合形式的力学模型,进一步分析了水力压裂的基本过程,综合多种数值计算方法,编写程序,在验证岩体裂纹模型与双重介质流动模型有效性的基础上,对压裂过程进行复现,将模拟结果与文献结果进行了对比,并讨论了所构建模型的优缺点。     

Displacement of Cr(III)–Partially Hydrolyzed Polyacrylamide Gelling Solution in a Fracture in Porous Media

During waterflooding of a fractured formation, water may channel through the fracture or interconnected network of fractures, leaving a large portion of oil bearing rock unswept. One remedial practice is injection of a gelling solution into the fracture. Such placement of a gelling mixture is associated with leak-off from the fracture face into the adjoining matrix. Design of a gel treatment needs understanding of the flow of gelling mixture in and around the fracture. This flow is addressed here for Cr(III)–partially hydrolyzed polyacrylamide formulation through experiments and conceptual model. A fractured slab was used to develop a lab-model, where the flow along the fracture and simultaneous leak-off into the matrix can be controlled. Also, the fracture and matrix properties had to be evaluated individually for a meaningful analysis of the displacement of gelling solution. During this displacement, the gelling fluid leaked off from the fracture into the matrix as a front, resulting in a decreasing velocity (and pressure gradient) along the fracture. With pressure in the fracture held constant with time, the leak-off rate decreased as the viscous front progressed into the matrix. The drop in leak-off rate was rapid during the initial phase of displacement. A simple model, based on the injection of a viscous solution into the dual continua, could explain the displacement of Cr(III)–polyacrylamide gelling mixture through the fractured slab. This study rules out any major complication from the immature gelling fluid, e.g., build-up of cake layer on the fracture face. The model, due to its simplicity may become useful for quick sizing of gel treatment, and any regression-based evaluation of fluid properties in a fracture for other applications.     

水力压裂解析模型裂缝扩展参数敏感性分析

水力压裂形成复杂裂缝网络是致密储层油气开采的重要技术,掌握水压裂缝扩展机理是控制压裂行为和优化压裂效果的关键.水压裂缝动态扩展行为涉及储层岩体、注入压裂液、压裂实施工艺等方面,其中水力压裂扩展时间、压裂液流体动力粘度系数、压裂液流体注入流速、储层岩石剪切模量成为决定裂缝扩展长度和裂缝开度的重要因素.本研究采用KGD、P...     

Characterization of Single-Phase Flow Through Carbonate Rocks: Quantitative Comparison of NMR Flow Propagator Measurements with a Realistic Pore Network Model

We report here the quantitative comparisons between the measured NMR flow propagator of a carbonate rock and the flow propagator calculated with a porous network extracted from the micro-CT image of the twin plug. We developed a numerical model based on a particle tracking algorithm in pore space. The particle tracking in throats is described using the first arrival time distribution. As pores have an important volume fraction in the sample considered, we implemented a time-delay mechanism for particle transport in the pores. We consider that the nodes have volume and there is a transport of the tracking particles inside the nodes, which leads to an “apparent” time-delay. Simulations of flow propagator show good agreement with low field NMR experiments performed on the twin plug of the sample used for pore network extraction with a single adjustable parameter (that describes the dynamics in the pores). These results lead us to a better understanding of the connection between pore structure and the behavior of NMR flow propagator in fluid-saturated rocks and are essential in interpreting the experimental data and correlating NMR parameters to petrophysical properties.     

脆性岩石破裂过程损伤与渗流耦合数值模型研究

大量的实验结果表明，脆性岩石的渗透性不是一个常量，而是应力和应力诱发损伤破裂的函数．建立了一个描述非均匀岩石渗流-应力-损伤耦合数学模型(FSD Model)，开发出岩石破裂过程渗流-应力-损伤耦合分析计算系统(F-RFPA^2D)．在该系统中，单元的力学、水力学性质根据统计分布而变化，以体现材料的随机不均质性，材料在开裂破坏过程中流体压力传递通过单元渗流-损伤耦合迭代来实现．该系统能够对岩石试件在孔隙水压力和双轴荷载作用下裂纹的萌生、扩展过程中渗透率演化规律及其渗流-应力耦合机制进行模拟分析．最后，给出两个算例：算例1模拟载荷作用下岩石应力应变-渗透率全过程．模拟结果表明，非均匀性对岩石的应力峰值强度、峰值前后其渗透性演化规律及其破裂机制影响十分明显，模拟结果和实验结果较为一致；算例2模拟孔隙水压力作用下岩石拉伸断裂过程，通过和物理实验对比验证，验证了模型计算结果的可靠性。     

裂缝性低渗透油藏流-固耦合理论与数值模拟

根据裂缝性低渗油藏的储层特征,建立适合裂缝性砂岩油藏渗流的等效连续介质模型。将渗流力学与弹塑性力学相结合,建立裂缝性低渗透油藏的流-固耦合渗流数学模型,并给出其数值解.通过数值模拟对一实际井网开发过程中孔隙度、渗透率的变化以及开发指标进行计算,并和刚性模型以及双重介质模型的计算结果进行了分析比较.     

Transient Pressure Behavior of Reservoirs with Discrete Conductive Faults and Fractures

Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior.