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.     

分形裂缝性页岩气藏多段压裂水平井瞬态压力特征

基于分形理论和连续性假设,考虑页岩气吸附解吸、基质-裂缝窜流等机制,建立分形裂缝性页岩气藏多段压裂水平井试井解释模型,并通过拉氏变换、点源函数及压降叠加原理等方法得到模型的解.绘制无因次压力随时间变化的双对数曲线,研究分形裂缝性页岩气藏多段压裂水平井的压力特征,分析分形指数、分形维数等参数对压力动态的影响.结果表明：分形裂缝性页岩气藏多段压裂水平井的压力动态可划分为7个流动阶段;分形指数越大或分形维数越小,晚期径向流直线段的斜率越大;其它参数对水平井的压力动态也有一定的影响.     

使用混合网格计算非达西渗流

针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解.     

一种基于预估-修正策略的非定常流网格自适应加密/稀疏方法

给出一种非定常流动数值模拟的网格自适应处理方法.在"求解流动方程-自适应调整网格"的流程中,引入预估-修正步.根据自适应周期内每个时间步上的流场预估解,计算单元上的事后误差估算值.建立考虑解演变的网格自适应指示器,并进行多层次单元加密-稀疏的动态网格自适应处理.在自适应网格上重新计算流场.每个自适应周期中,流动演变区域的网格获得加密;而前一个周期中的特征现象已离开区域的网格被稀疏.应用边界非协调的当地DFD(Domain-Free Discretization)方法求解流动方程.为验证网格自适应处理方法,针对静止圆柱和自推进游鱼的流动进行了数值实验.     

天然裂缝储层压裂定向井稳态产量的蒙特卡洛计算

针对各向异性天然裂缝储层,蒙特卡洛随机模拟天然裂缝分布,从统计学角度表征天然裂缝参数,根据势叠加原理,把天然裂缝和人工裂缝当成独立的源进行势叠加,考虑天然裂缝和人工裂缝的耦合作用,建立压裂定向井稳态产量计算公式.计算结果表明,基于蒙特卡洛的天然裂缝模拟能从统计学角度反映产量变化趋势,能快速分析压裂定向井稳态产能.     

低渗透油藏压裂水平井井筒与油藏耦合的非稳态模型

推导低渗透各向异性油藏压裂水平井井筒与盒式油藏耦合的非稳态模型,并给出求解方法.模型考虑摩阻和加速度的影响,并可以使用不同类型的约束条件.实例计算表明,压裂水平井的流动可分为非稳态阶段和拟稳态阶段.在非稳态阶段,各条裂缝的产量相差不大,总产量随着裂缝条数的增加呈线性增加;在拟稳态阶段,两端裂缝产量高于中部裂缝的产量.受摩阻和加速度压降的影响,空间上位置对称的裂缝在流量上呈现不对称性.井筒内压力损失的存在将使水平井的产量降低,并使井筒内的压力分布不均匀.在最小井底流压的基础上固定流量时,裂缝条数越多,稳产期也越长.     

表面细分技术在二维声辐射和声散射中的应用

把表面细分技术应用于求解边界积分方程，既能把CAD模型直接用于边界元分析，又能精确描述复杂的边界几何形状，实现网格自动加密和形函数自动升阶，满足误差要求。把它应用于简单的二维声辐射和声散射，结果表明对提高边界元方法的计算精度是有效的。     

各向异性油藏水平井多角度人工裂缝线性单元计算方法

考虑各向异性油藏渗透率张量的表征,利用Green函数和拉普拉斯变换建立裂缝流动的一维单元,裂缝的流量分布采用节点线性插值,裂缝内的流动处理为线性积分,耦合地层与人工裂缝的流动,建立有限导流裂缝井底压力的求解方法.结果表明:多裂缝压裂水平井存在压裂裂缝线性流、地层线性流、系统径向流3种流动形态,压裂裂缝条数越多,相同的生产时间,无因次井底压降越小;裂缝条数对流动影响明显.随着裂缝条数的增加,压降变化减小;裂缝长度和导流能力有相似的变化.人工裂缝与井筒角度越大,产能越大,当裂缝垂直于井筒时,产量最大;地层最大渗透率方向垂直于人工裂缝时产量最大,平行裂缝时产量最小.当人工裂缝垂直于井筒,并同时垂直于地层最大渗透率方向时,达到最大产量值.     

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.     

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。     

Advances in multi-domain lattice Boltzmann grid refinement

Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed to pass form the coarse to the fine grid. In this context, we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation. We show this operation to be extremely important, because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high Reynolds numbers. Then we demonstrate that to reconstruct the information, a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice Boltzmann method.These two fundamental extra-steps are validated on two classical 2D benchmarks, the 2D circular cylinder and the 2D dipole–wall collision. The latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high Reynolds number of 5000. A very good agreement is found between the single grid and the refined grid cases.The proposed grid refinement strategy has been implemented in the parallel open-source library Palabos.     

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.     

Numerical experiments on the efficiency of local grid refinement based on truncation error estimates

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.     

使用AMR型背景网格的并行SPH方法

在分布式并行SPH方法中根据网格范围内粒子最大光滑长度调整网格尺度的AMR（Adaptive Mesh Refinement）背景网格,确保网格内粒子的相邻粒子位于同一个网格或者相邻的同尺寸网格范围内.与统一尺寸的背景网格相比,在光滑长度空间分布不均匀和随时间变化的情况下能够应用并减小搜索量,提高计算效率.数值结果表明,基于AMR型背景网格的并行SPH方法应用到粒子光滑长度变化很大的数值计算时能有效地降低搜索复杂度.     

Mesh refinement algorithms in an unstructured solver for multiphase flow simulation using discrete particles

This study developed spray-adaptive mesh refinement algorithms with directional sensitivity in an unstructured solver to improve spray simulation for internal combustion engine application. Inadequate spatial resolution is often found to cause inaccuracies in spray simulation using the Lagrangian–Eulerian approach due to the over-estimated diffusion and inappropriate liquid–gas phase coupling. Dynamic mesh refinement algorithms adaptive to fuel sprays and vapor gradients were developed in order to increase the grid resolution in the spray region to improve simulation accuracy. The local refinement introduced the coarse-fine face interface that requires advanced numerical schemes for flux calculation and grid rezoning with moving boundaries. To resolve the issue in flux calculation, this work implemented the refinement/coarsening algorithms into a collocated solver to avoid tedious interpolations in solving the momentum equations. A pressure correction method was applied to address unphysical pressure oscillations due to the collocation of pressure and velocity. An edge-based algorithm was used to evaluate the edge-centered quantities in order to account for the contributions from all the cells around an edge at the coarse-fine interface. A quasi-second-order upwind scheme with strong monotonicity was also modified to accommodate the coarse-fine interface for convective fluxes. To resolve the issue related to grid rezoning, rezoning was applied to the initial baseline mesh only and the new locations of the refined grids were obtained by interpolating the updated baseline mesh. The time step constraints were also re-evaluated to account for the change resulting from mesh refinement. The present refinement algorithm was used in simulating fuel sprays in an engine combustion chamber. It was found that the present approach could produce the same level of results as those using the uniformly fine mesh with substantially reduced computer time. Results also showed that this approach could alleviate the artifacts related to the Lagrangian discrete modeling of spray drops due to insufficient spatial resolution.     

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.     

Multi-scale method study of nano-void under the shock wave

The dynamic behavior of nano-void in metal Al under shock loading is simulated by using the multi-scale numerical simulation method. This method couples the molecular dynamics method used in local defect domain and the finite element method overall domain. The macroscopic failure of material is analyzed based on the microscopic dynamic behavior of nano-void. Our results show that the collapse of nano-void depends on the shock strength. Both a high and a low stress region are formed in the region of void after void collapse, whereas only a low stress region is formed under no collapse. The local hot spot is displayed in the temperature field, and a detailed analysis reveals that the hot point initiation is caused by recompression of atoms in void.     

双水平井电磁测距径向距离计算方法的ANSYS仿真研究

基于旋转磁场测距(RMRS)的基本理论,借助ANSYS有限元分析软件,研究了金属套管条件下双水平井电磁测距径向距离计算方法。首先建立SAGD双水平井RMRS井下传播模型,通过设定单元属性、划分网格、加载边界条件等对模型进行求解;然后研究套管厚度、直径、相对磁导率等对双水平电磁测距系统中磁场轴向分量的影响;最后利用实验室现有的旋转磁场测距模拟装置对仿真结果进行了验证。研究结果表明：随着套管厚度、直径、相对磁导率的增加,探管接收到的磁感应强度会逐渐减小,但双水平井径向间距计算仍可采用均匀介质中的理论测距导向计算方法。此结论可为套管的选取、磁导向仪器的研究及测量资料解释提供理论参考。     

Euler及N-S方程的二维四边形/叉树混合网格自适应算法

描述了一种基于直角叉树网格的Euler和N-S方程自适应算法.由于考虑了粘性的作用,提出并使用了四边形叉树混合网格的方法,在几何表面附近生成贴体的四边形网格,外流场使用直角叉树网格.采用中心有限体积法,对Euler及N-S方程进行数值求解,对N-S方程的计算中加入了B-L代数湍流模型.在流场中,运用了网格自适应算法,提高了数值计算对激波、流动分离等特性的捕捉和分辨能力.采用上述方法,数值分析了单段和多段翼型的绕流问题.