裂缝性介质多尺度深度学习模型

结合人工神经网络建立裂缝介质多尺度深度学习流动模型.基于一套粗网格和一套细网格,通过在粗网格上训练数据,多尺度神经网络能够以较少的自由度训练出准确的神经网络.并在粗网格上通过求解局部流动问题获得多尺度基函数,结合神经网络进一步得到精细网格的解.基于离散裂缝的流动方程可视为多层网络,网络层数依赖于求解时间步数.阐述裂缝介质多尺度机器学习数值计算格式的建立,介绍如何使用多尺度算法构建离散裂缝模型的多尺度基函数,并采用超样本技术进一步提高计算准确性.数值结果表明,多尺度有限元算法与机器学习结合是一种有效的流体流动模拟算法.     

基于离散裂缝模型的低渗透油藏开发数值模拟

基于低渗透油藏的人工压裂开采的离散裂缝模型,考虑基质岩块中非达西渗流模式,对此类油藏的注水开发进行数值模拟研究.首先对裂缝进行降维处理,建立相应的数学模型;考虑裂缝的复杂几何形状,基于非结构化网格应用控制体积有限差分法进行数值求解,通过数例验证方法的正确性;给出两个注水开发数值算例,分析不同非达西渗流模式对开发效果的影响.     

裂缝诱导TTI双孔隙介质波场传播特征

本文在考虑油藏内流体影响的基础上, 进一步讨论了裂缝诱导各向异性的极化角和方位角的影响, 对裂缝诱导TTI (tilted transverse isotropy)双孔隙介质模型进行了研究. 在裂缝诱导HTI (horizontal transverse isotropy)双孔隙介质理论的基础上, 用Bond变换推导了裂缝诱导TTI双孔隙介质的柔度系数矩阵和耗散系数矩阵, 从而建立了介质的一阶速度应力方程. 采用交错网格高阶有限差分法及PML边界条件, 对xoz平面内的2.5维矢量波动方程进行了数值模拟. 结果表明,裂缝的极化角和方位角的存在都会导致横波分裂, 而在双层裂缝诱导TTI双孔隙介质模型的分界面上,又会产生转换波的分裂和横波的再分裂现象, 这就增加了波场的复杂性, 从而为进一步研究实际地球介质的地震波场传播特征奠定了基础. 关键词： 裂缝诱导TTI 双孔隙 裂缝极化角 裂缝方位角     

裂缝性油藏水平井产能计算方法

根据裂缝性油藏水平井渗流特征,将渗流区域等效为近井区域和远井区域.远井区域视为连续均匀介质.在近井区域,基于势叠加、镜像反映原理和微元线汇思想,建立考虑天然裂缝和水平井生产段共同渗流的耦合模型.组合两个流动区域得到裂缝性油藏水平井产能评价模型,并进行求解.实例计算结果表明,由于考虑了裂缝之间的干扰,用建立的模型计算的水平井产能小于用理论公式计算的水平井的产能,与实际产能比较接近;随着裂缝密度增加,产量逐渐增加,但增加的幅度降低.     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

水平井体积压裂缝网表征及流动耦合模型

针对岩石脆性系数高且发育天然裂缝的储层,提出表征水平井体积压裂形成裂缝网络的三种基本模式,并将渗流过程划分为油藏流动和缝网内部流动.在此基础上,利用势叠加原理导出油藏流动控制方程,利用有限差分方法建立缝网内部有限导流等式;其次,采用星三角变换法处理人工缝与天然缝的交汇流动;最后,耦合两部分流动矩阵方程得到水平井体积压裂缝网渗流数学模型.该模型表明:当水平井改造段长度一定时,压裂段数与段内分簇数是决定产能的最主要因素,其次是人工裂缝半长和人工缝导流能力,而天然裂缝密度和导流能力对产量影响较小.实例应用表明,实际产油量与模型计算值一致,误差较小.     

裂缝性应力敏感油藏流固耦合的数值模拟

以裂缝各向异性全张量渗透率动态耦合渗流模型为基础,建立三维三相裂缝各向异性特低渗透油藏流固耦合数学模型,并运用模块化显示耦合迭代求解建立流固耦合渗流数值模拟方法,编制耦合求解程序.研究表明:对于裂缝性油藏,随着油藏开采过程中压力的变化,岩石变形和储层介质的各向异性应变特性使开发过程中多组裂缝的变形程度不同,引起裂缝渗透率的非线性变化,进而使油藏裂缝渗透率张量主值发生旋转,改变液流方向、影响油藏开发效果.     

考虑水力压裂缝和天然裂缝动态闭合的三维离散缝网数值模拟

基于嵌入式离散裂缝模型, 提出一种可在三维空间中考虑应力状态影响的裂缝动态闭合表征方法。将任意方向裂缝的开度和渗透率考虑为作用在裂缝平面法向有效应力的函数, 同时用裂缝传导率变化表征支撑剂充填的水力压裂缝与被开启的天然裂缝由于油藏开发过程中地层流体压力下降而发生的动态闭合行为。研究表明: 致密油藏开发以缝控储量为主。对压裂水平井进行产能评价时, 裂缝动态闭合会导致产能的部分损失, 其影响不可忽略; 水力压裂缝的支撑剂材料属性及天然裂缝的刚度是其中的主控因素。因此需要增大支撑剂的浓度、粒径大小并改善支撑剂的性质, 在最大程度上降低裂缝闭合对生产的不利影响。     

裂缝诱导TTI双孔隙介质的纵波偏移成像研究

将交错网格高阶有限差分纵横波分离的方法与逆时偏移成像方法相结合,给出了基于裂缝诱导TTI双孔隙介质模型的纵波逆时偏移成像算法,并对二维水平层状模型的数据进行偏移成像.结果表明,对于裂缝诱导TTI双孔隙介质模型,常规的基于各向同性背景孔隙岩石速度的偏移方法会导致成像结果出现过偏移现象.为研究裂缝参数对过偏移程度的影响,利用Christoffel方程,对裂缝诱导TTI双孔隙介质模型中的相速度公式进行了推导,并在此基础上,分析了裂缝角度和密度参数对介质纵波相速度及成像位置的影响.结果表明,在二维情况下,裂缝极化角增大会减小成像速度与真实速度之间的误差,从而使得成像结果逐渐接近储层的真实位置;而裂缝密度的增大则使得速度误差增大,导致成像结果与真实模型的偏差越来越大.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures

Elastic wave scattering off a layer containing a single set of vertical periodic fractures is examined using a numerical technique based on the work of Hennion et al. [J. Acoust. Soc. Am. 87, 1861-1870 (1990)]. This technique combines the finite element method and plane wave method to simulate three-dimensional scattering off a two-dimensional fractured layer structure. Each fracture is modeled explicitly, so that the model can simulate both discrete arrivals of scattered waves from individual fractures and multiply scattered waves between the fractures. Using this technique, we examine changes in scattering characteristics of plane elastic waves as a function of wave frequency, angle of incidence, and fracture properties such as fracture stiffness, height, and regular and irregular spacing.     

Stop-pass behavior of acoustic waves in a 1D fractured system

This study examines the dispersion and the stop-pass band behavior of acoustic waves propagating across periodically spaced and non periodically spaced parallel fractures. Laboratory ultrasonic wave measurements performed on a stack of synthetic fractures (identical steel plates with roughened interfaces) and numerical propagator matrix simulations show spectra with distinct stop-pass band structures that develop with decreasing fracture stiffness. To understand the physics behind these observations, an exact dispersion equation for wave propagation through an infinite series of equally spaced fractures is derived using displacement-discontinuity boundary conditions to model the constitutive behavior of the fractures and Floquet's (Bloch's) theory for the periodic boundary conditions. Both the measured and numerically simulated stop-pass band structures show good agreement with the theoretical predictions. Furthermore, the theory reveals that the left boundary of the stop-bands contains information about the fracture stiffness, suggesting the possibility of determining the stiffness of the parallel fractures from seismic waves. This paper also discusses the effects of fractured systems with random distributions of fracture spacings and stiffnesses on the stop-pass band structures of seismic waves in fractured rock.     

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.     

Production analysis in shale gas reservoirs based on fracturing-enhanced permeability areas

Hydraulic fracturing has been widely applied in shale gas exploitation because it improves the permeability of the rock matrix.Fracturing stimulation parameters such as the pumping rate, the fracturing sequence, and the fracture spacing significantly influence the distribution of the stimulated reservoir volume(SRV). In this research, we built a numerical model that incorporates the hydraulic fracturing process and predicts gas production. The simulation of fracture propagation is based on the extended finite element method(XFEM), which helps to calculate aspects of the fractures and the SRV; we imported the results into a production analysis model as the initial conditions for production prediction. Using the model, we investigated the effects of some key parameters such as rock cohesion, fracture spacing, pumping rate, and fracturing sequence on the shale gas production.Our results proved that the SRV was distributed in the vicinity of the main fractures, and the SRVs were connected between the fractures in a small fracture spacing. We obtained optimal spacing by analyzing the production increment. High pumping-rate treatment greatly changes the in-situ stress around the hydraulic fractures and enlarges the field of SRV. Simultaneous fracturing treatment improves the flow conductivity of formation more than sequential fracturing. This study provides insights into the hydraulic fracturing design for economical production.     

分形低渗透缝洞型油藏非线性渗流规律

引入分形理论,建立考虑低速非达西效应的分形三重介质缝洞型油藏数学模型,通过Laplace变换及Stehfest数值反演方法求出井底压力,借助Matlab编程绘制压力动态曲线,划分渗流阶段,分析渗流规律,进行非线性参数敏感性分析.最后结合实际算例,验证模型的正确性.结果表明：分形三重介质油藏渗流过程分为早期纯井储,过渡流,缝洞窜流,拟径向流,基质与溶洞、裂缝窜流及总体径向流6个渗流阶段;低速非达西效应对渗流的影响随时间的推移逐渐增大;启动压力梯度越大,总径向流阶段压力动态曲线上翘幅度越大;分形系数影响整个渗流过程,随着分形系数的增大,裂缝迂曲程度随之增大,致使渗流阻力增加,引起压力动态曲线整体上移幅度增大.     

高速通道压裂裂缝的高导流能力分析及其影响因素研究

高速通道压裂是近年在非常规致密油气资源开采中出现的新工艺, 已在世界范围内推广实施, 并取得了良好的增产效果. 该技术可使支撑剂在人工压裂缝中形成簇团式分布, 从而形成油气高速流动通道, 提高裂缝的导流能力. 但目前对于高速通道压裂裂缝高导流能力的形成机理及其影响因素尚不清楚. 对此, 本文从流体力学理论出发, 首先将高速通道压裂裂缝内形成的支撑剂簇团视为渗流区域, 簇团间的大通道视为自由流动区域; 然后基于Darcy-Brinkman方程建立了裂缝内的流动数学模型, 采用均匀化理论对该流动数学模型进行了尺度升级, 推导得到了高速通道压裂裂缝的渗透率, 揭示了其高导流能力的形成机理; 并以此为基础, 分析了不同支撑剂簇团形状、大小以及分布方式等因素对其导流能力的影响, 可为高速通道压裂工艺参数设计与优化提供基础.     

缝洞型介质流动模拟的多尺度分解法

缝洞型介质通常具有非均质性强、结构多尺度的特征.传统数值方法在解决此类多尺度流动问题时,难以兼顾计算精度与计算效率,无法实际应用.对此,本文提出了多孔介质流体流动的多尺度分解法,并应用于缝洞介质流动模拟,能够大幅减小计算的复杂度,同时,可以通过控制均化程度控制计算精度.该方法将求解空间分为若干个子空间的正交直和,从而获得一个近线性的计算复杂度;以分层计算的方式实现了快速计算,另外这种方法是一种无网格方法,具有较好的地层适应性.同时,采用离散缝洞模型简化缝洞结构,进一步提高了计算效率.详细阐述了基于多尺度分解法的多孔介质流体流动数值计算格式的建立,重点介绍了如何在不同的层次上计算基函数.数值结果表明,本文提出的计算方法不仅能够准确捕捉多孔介质中的精细流动特征,而且具有很高的计算效率,是一种有效的流动模拟方法.     

An efficient multi-point flux approximation method for Discrete Fracture–Matrix simulations

We consider a control volume discretization with a multi-point flux approximation to model Discrete Fracture–Matrix systems for anisotropic and fractured porous media in two and three spatial dimensions. Inspired by a recently introduced approach based on a two-point flux approximation, we explicitly account for the fractures by representing them as hybrid cells between the matrix cells. As well as simplifying the grid generation, our hybrid approach excludes small cells in the intersection of the fractures and hence avoids severe time-step restrictions associated with small cells. Excluding the small cells also reduces the condition number of the discretization matrix. For examples involving realistic anisotropy ratios in the permeability, numerical results show significant improvement compared to existing methods based on two-point flux approximations. We also investigate the hybrid method by studying the convergence rates for different apertures and fracture/matrix permeability ratios. Finally, the effect of removing the cells in the intersections of the fractures are studied. Together, these examples demonstrate the efficiency, flexibility and robustness of our new approach.     

Poroelastic modeling of seismic boundary conditions across a fracture

Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.     

Numerical modelling of radionuclide transport through a water saturated rock massif

The paper deals with the introduction to combined schemes for numerical modelling of water transport of radionuclides through a rock massif modelled as a system of fractures. Inside the fracture system, Darcy flow of water is supposed. The combined schemes for solution of convective-reactive-diffusive transport of radionuclides with sorption and radioactive decay in the fracture flow field are mentioned and referenced and results of numerical computations are presented.