基于混合方法的二维水力压裂数值模拟

水力压裂在页岩气开采中被广泛使用,采用数值方法研究压裂机理具有重要意义.基于连续-非连续单元法(CDEM) 和中心型有限体积法(FVM),提出解决水力压裂流固耦合问题的二维混合数值计算模型.该混合模型中,使用CDEM 求解应力场和裂缝扩展过程,使用FVM 求解裂隙渗流场.应力场裂缝扩展和渗流场均使用显式迭代求解, 并通过相互之间数据交换实现流固耦合.通过与KGD 理论模型进行对比, 验证数值模型的正确性.通过与颗粒离散元数值结果进行对比,验证数值模型的有效性.通过计算复杂缝网压裂模型,研究水力压裂机理,并说明该数值模型在水力压裂模拟中具有很好的前景.      

致密油藏动态裂缝扩展机理及应用

致密油藏采用注水吞吐补充地层能量取得了一定效果. 但多轮次注水吞吐后, 地层压力和产量降低快. 本文考虑了致密油藏复杂的裂缝形态, 根据艾尔文理论及弹性力学剖析I型裂缝尖端附近的应力场分布, 基于渗流力学、裂缝性致密油藏特征及动态裂缝渗流规律, 建立了多裂缝交叉裂缝扩展渗流模型, 结合注水诱导裂缝扩展机理及断裂力学能量守恒原理, 得到裂缝扩展长度. 依据致密油藏逆向渗吸原理, 提出将注水吞吐转为不稳定脉冲注水. 对比分析注水吞吐、脉冲注水2种能量补充发方式, 预测10年累计采油、压力及剩余油分布. 结果表明, 裂缝净内压随着注水量的增加而升高, 当应力场强度因子达到断裂韧度, 在裂缝尖端会发生扩展. 扩展及延伸的天然裂缝相互沟通, 呈现不规则复杂缝网, 在复杂缝网中主要发生逆向渗吸作用. 脉冲注水累计产油高、注水波及面积广、逆向渗吸作用强. 裂缝性致密油藏水平井注水吞吐转变为脉冲注水方式, 能够充分发挥动态缝网的逆向渗吸及线性驱替作用, 实现有效驱油的目的.      

三维压裂缝网不稳定压力半解析求解方法

受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.      

致密砂岩气藏纳微观结构及渗流特征

随着常规油气资源的减少,致密砂岩气藏逐渐成为勘探开发的热点.然而致密砂岩气高效产出机理研究还相对滞后,已经成为目前制约致密砂岩气大规模经济有效开发的瓶颈.致密砂岩由于其特殊的地质特征, 基质微观结构复杂,天然裂缝一定程度发育, 投产一般需要水力压裂等增产措施,气体在其中渗流存在跨尺度效应.研究揭示出致密砂岩气在多孔介质中的流动分为解吸、扩散、渗流等几个方式,包括浓度场下的扩散、压力场中的渗流等.综述了致密砂岩存在的非常规地质特征及其研究描述方法,并依据克努森数大小, 对致密砂岩气的渗流状态进行流态区域划分,为更好的理解和模拟致密砂岩气的流动状态提供了理论依据,并指出建立一种高效、简洁的微观结构精细描述方法,以及解决致密砂岩气在多尺度条件下的传质优化等是今后研究的重点方向.      

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...     

页岩气藏压裂缝网扩展数值模拟

为探究页岩气藏水力压裂复杂裂缝网络的形成机理,开展了缝网扩展的数值模拟研究.考虑应力阴影和天然裂缝作用,建立了井筒和裂缝中流体流动模型,利用位移不连续方法求解应力与位移不连续量,然后构建了压力与裂缝宽度的迭代方程,并采用牛顿迭代法求解.通过比较数值解经典模型解析解,验证了模型和迭代解法的正确性.多簇裂缝同步扩展时裂缝间距越小,压裂液分配到各条裂缝越不均匀,靠近井筒跟部的裂缝的分流量越大,从而裂缝宽度越大;考虑天然裂缝作用时,逼近角越小或者应力各向异性越弱,水力裂缝越容易发生转向扩展,裂缝网络越复杂.      

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。     

两套节点格林元嵌入式离散裂缝模型数值模拟方法

对于原始嵌入式离散裂缝模型(EDFM), 在计算包含裂缝单元的基质网格内的压力分布时采用了线性分布假设, 这导致了油藏开发早期对非稳态窜流量的计算精度不足. 因此, 本文提出了一种两套节点格林元法的EDFM数值模拟方法. 两套节点格林元法的核心思想是将压力节点与流量节点区分开, 一套压力节点设置在单元顶点, 另一套流量节点设置在网格边的中点, 满足局部物质守恒、具有二阶精度的同时, 可适用于任意网格类型. 本文将两套节点格林元法与EDFM耦合, 采用了非稳态渗流控制方程的边界积分形式推导了基质网格与裂缝网格之间传质量的新格式, 代替了线性分布假设以提高模拟精度; 此外, 修正后的EDFM能适应任意形态的基质网格剖分, 拓展了原始EDFM仅适用于矩形基质网格、难以考虑复杂油藏边界的局限性. 研究表明: 通过对比商业模拟软件tNavigator? LGR模块与原始EDFM, 验证了本文模型具有较高的早期计算精度; 以复杂油藏边界?缝网?SRV分区模型为例, 通过对比SFEM-COMSOL商业模拟软件, 验证了本文模型处理复杂问题的适应性. 本文研究可用于裂缝性油藏开发动态的精确模拟.      

裂缝介质渗流多尺度混合有限元数值模拟研究

针对裂缝介质具有多尺度特点,建立了Darcy/Stokes-Brinkman多尺度耦合模型,采用多尺度混合有限元方法,对裂缝介质渗流问题进行了研究.阐述了多尺度混合有限元方法的基本原理,并推导得到Darcy/Stokes-Brinkman方程的多尺度混合有限元计算格式.数值计算结果表明,大尺度Darcy模型能够捕捉到小尺度上裂缝网络渗流特征;与网格粗化、传统有限元方法相比,多尺度混合有限元方法的基函数具有能反映单元内参数变化的优点,在保证计算精度的同时能够减少计算量,对于裂缝油藏具有良好的适用性.     

非常规油气资源渗流力学进展专题序

《力学学报》本次组织的《非常规油气资源渗流力学进展专题》包含12篇研究型或综述型论文, 涉及页岩油气、煤层气、致密油气及天然气水合物等非常规资源, 旨在反映国内高校、科研院所及企业的科研人员在非常规油气资源开发渗流力学领域取得的最新进展, 以促进学术交流, 供从事相关领域的读者参考, 期望能有所启迪.      

基于离散裂缝的多段压裂水平井数值试井模型及应用

水平井压裂技术已经成为开发低渗透油气藏、页岩气藏和致密气场等非常规油气藏的关键技术。基于离散裂缝模型,对裂缝进行简化,建立了二维多段压裂水平井有限导流数值试井模型,利用有限元方法求解模型,获得多段压裂水平井试井理论曲线和压力场特征。分析表明:多段压裂水平井的试井理论曲线一共分为七个阶段:井筒储存段、裂缝线性流段、裂缝-地层双线性流段、裂缝干扰段、地层线性流段、系统径向流段和边界作用段,其中裂缝-地层双线性流段和裂缝干扰是其典型特征。分析了裂缝数量、裂缝间距、裂缝不对称、裂缝不等长和裂缝部分缺失等因素对试井理论曲线的影响,结果表明:裂缝数量和裂缝间距对试井理论曲线的影响最大。较多的裂缝、较大裂缝间距、对称的裂缝和等长的裂缝有利于降低压裂水平井井底的流动阻力,提高产能。将建立的数值试井模型应用于四川盆地一口多段压裂水平井的压力恢复测试的数值试井解释,结果表明:本文建立的模型可以较好的拟合压力恢复测试数据,可以获得裂缝的导流能力和裂缝长度,为压裂效果评价和压裂设计提供指导。      

Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore

Multi-stage fracturing is the current preferred method of completion of horizontal wells in unconventional hydrocarbon reservoirs. Its core component consists in simultaneously initiating and propagating an array of hydraulic fractures. We develop a numerical model for the initiation and growth of an array of parallel radial hydraulic fractures. The solution accounts for fracture growth, coupling between elastic deformation and fluid flow in the fractures, elastic stress interactions between fractures and fluid flow in the wellbore. We also take into account the presence of a local pressure drop (function of the entering flow rate) at the connection between the well and the fracture, i.e., a choke-like effect due to current well completion practices, also referred to as entry friction. The partitioning of the fluid into the different fractures at any given time is part of the solution and is a critical indicator of simultaneous (balanced fluid partitioning) versus preferential growth. We validate our numerical model against reference solutions and a laboratory experiment for the initiation and growth of a single radial hydraulic fracture. We then investigate the impact of stress interaction on preferential growth of a subset of fractures in the array. Our results show that a sufficiently large local entry friction provides a strong feedback in the system and thus can counteract elastic stress interaction between fractures, thereby ensuring simultaneous growth. We propose a dimensionless number capturing the competition between stress interaction and local entry friction. This dimensionless number is a function of rock properties, fracture spacing and injection parameters. We verify that it captures the transition from the case of simultaneous growth (entry friction larger than interaction stress) to the case of preferential growth of some fractures (interaction stress larger than entry friction). We also discuss the implication of these results for multi-stage fracturing engineering practices.     

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、PKN两类等高解析模型对主控因素的参数敏感性进行分析,直观、快速、可靠地获得水压裂缝扩展长度、张开度动态演化行为的量化数值．研究发现,压裂持续开展过程中水压裂缝扩展长度呈线性增长、开度逐渐趋于稳定,高流体动力粘度导致裂缝难扩展、形成较大裂缝开度,通过增加压裂液流体注入流速可同时增加裂缝扩展长度和开度,较高的岩石剪切模量将降低水压裂缝的开度．通过对比两类解析模型在不同参数下的水压裂缝扩展结果,分析压裂参数与裂缝扩展的相关性和敏感系数,讨论水力压裂解析模型的裂缝扩展参数敏感性．     

Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method

Capillary dominated flow or imbibition—whether spontaneous or forced—is an important physical phenomena in understanding the behavior of naturally fractured water-driven reservoirs (NFR’s). When the water flows through the fractures, it imbibes into the matrix and pushes the oil out of the pores due to the difference in the capillary pressure. In this paper, we focus on modeling and quantifying the oil recovered from NFR’s through the imbibition processes using a novel fully implicit mimetic finite difference (MFD) approach coupled with discrete fracture/discrete matrix (DFDM) technique. The investigation is carried out in the light of different wetting states of the porous media (i.e., varying capillary pressure curves) and a full tensor representation of the permeability. The produced results proved the MFD to be robust in preserving the physics of the problem, and accurately mapping the flow path in the investigated domains. The wetting state of the rock affects greatly the oil recovery factors along with the orientation of the fractures and the principal direction of the permeability tensor. We can conclude that our novel MFD method can handle the fluid flow problems in discrete-fractured reservoirs. Future works will be focused on the extension of MFD method to more complex multi-physics simulations.

     

页岩气和致密砂岩气藏微裂缝气体传输特性

页岩气和致密砂岩气藏发育微裂缝,其开度多在纳米级和微米级尺度且变化大,因此微裂缝气体传输机理异常复杂.本文基于滑脱流动和努森扩散模型,分别以分子之间碰撞频率和分子与壁面碰撞频率占总碰撞频率的比值作为滑脱流动和努森扩散的权重系数,耦合这两种传输机理,建立了微裂缝气体传输模型. 该模型考虑微裂缝形状和尺度对气体传输的影响. 模型可靠性用分子模拟数据验证.结果表明:(1)模型能够合理描述微裂缝中所有气体传输机理,包括连续流动,滑脱流动和过渡流动;(2)模型能够描述不同开发阶段,微裂缝中各气体传输机理对传输贡献的逐渐变化过程;(3)微裂缝形状和尺度影响气体传输,相同开度且宽度越大的微裂缝,气体传输能力越强,且在高压和微裂缝大开度的情况下表现更明显.      

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.     

Acid Leakoff Mechanism in Acid Fracturing of Naturally Fractured Carbonate Oil Reservoirs

In acid fracturing, excessive acid leakoff is thought to be the main reason that limits fracture propagation and live acid penetration distance. Since most carbonates are naturally fractured, we developed a new model in this paper to simulate acid leakoff into a naturally fractured carbonate oil reservoir during acid fracturing. Our model incorporates the acid-rock reaction, fracture width variation due to rock dissolution on the fractured surfaces, and fluid flow in naturally fractured carbonate oil reservoirs. Given the information of the reservoir, injected acid, and pressure in the hydraulic facture and the reservoir, the model predicts acid leakoff with time. In this study, we found that acid leakoff mechanism in naturally fractured carbonates is much different from that in reservoirs without natural fractures. Widened natural fractures by acid-rock reaction act as high-conductivity conduits allowing leakoff acid to penetrate deeper into the formation, resulting in serious leakoff. Wide natural fractures have a dominant effect on acid leakoff compared to micro-fractures and matrix.     

A Fractal Model for Oil Transport in Tight Porous Media

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.     

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.