A three‐point time discretization technique for parabolic partial differential equations

The Crank–Nicolson scheme has second‐order accuracy, but often leads to oscillations affecting numerical stability. On the other hand, the implicit scheme is free from oscillation, but it has only first‐order accuracy. In this work, a three‐point discretization scheme with variable time step is presented for the time marching of parabolic partial differential equations. The method proposed has second‐order accuracy, is unconditionally stable and dampens spurious oscillations of the numerical results. The application and effectiveness of the new method are demonstrated through several numerical examples. It is shown that, unlike the Crank–Nicolson method, the approach proposed produces no oscillatory response irrespective of the time step adopted. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of Nørsett methods for integrating differential equations in time

Some recently developed implicit time discretizations are discussed whose main application is to solving ordinary differential equations arising from finite element approximations to partial differential equations. Their theoretical properties, computer implementation and numerical behaviour, as observed in tests on simple examples, are compared with well-known discretizations such as the Crank-Nicholson method.     

基于直接生成法的土石混合体三维随机模型构建与数值仿真研究

通过对土石粒径界限、块石分布规律与粒径分布频度的研究,基于直接生成法建立了土石混合体的三维随机模型,形成了一套较为完整的、操作性强的三维随机模型构建方法。在此基础上,将三维随机模型构建方法与FLAC~(3D)随机建模方法相结合,建立与真实土石混合体具有相同统计规律的有限差分模型,开展室内直剪数值仿真试验研究,获取了不同垂直压力下的剪应力-位移曲线和相应的剪切带分布,探讨了土石混合体的剪切破坏特性与土石相互作用机制。剪切过程中由于土体产生的不同程度的剪切变形以及块石在摩擦作用下发生的水平或旋转运动,导致土石混合体的剪切带表现出明显的不规则和不连续特点,其剪应力-位移曲线具有应变硬化特点。研究表明,三维随机模型能够反映土石混合体的宏观力学性质和细观破坏机制,可作为力学性质研究的有效载体。     

泄洪洞整体三维紊流数值模拟

利用实用、高效的泄洪洞整体三维紊流数值模型,对滩坑水电站泄洪洞进行了数值模拟,该模型采用引入VOF方法的k-ε紊流模型,结合通用性强、易扩展的非结构混合网格。为克服网格扭曲给计算精度带来的影响,用一种改进精度的格心格式计算通量,使之具有非结构网格剖分的灵活性,程序的通用性和可扩展性,又有较高的计算精度。数值模拟结果和模型试验数据的对比分析表明,该模型是实用可靠的。     

三维可视化技术在碳酸盐岩储层预测中的应用

近几年,我们充分利用先进的地震技术特别是三维可视化技术、二维和三维交会图分析技术,分析各种三维地震数据的异常特征,从研究古岩溶发育的控制因素(古构造即古地貌、古水系)入手[1],在塔河油田碳酸盐岩储层预测中做了有益的初步尝试,取得了阶段性成果,成果应用于油田勘探开发中获得了很好的效果. 1 基本工作方法 准备数据体 基本数据需有三维地震保幅数据体、偏移数据体、地质层位解释数据体.利用地震处理解释软件从三维地震保幅数据体中提取相干参数数据体,并进行波阻抗反演,得到三维波阻抗数据体. 解释判断标志层 结合区域地质、钻井…     

Unified thermo-compositional-mechanical framework for reservoir simulation

We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositional-mechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems.     

基于随机模拟的堡子湾长6期油层组砂体展布

根据堡子湾长6期油层组区块的沉积环境和沉积相特征,在综合分析研究工区储层成因模式的基础上,结合随机模拟理论与方法,建立了反映堡子湾长6期油层组砂体三维展布规律的空间模型,利用示性点随机模拟技术,对砂体三维展布进行了随机模拟,并对随机模拟数据进行了误差分析。结果表明,三维展布效果良好,精度较高,与工程实际情况较为吻合。     

Exponential time differencing for problems without natural stiffness separation

Computational Geosciences - Explicit numerical schemes are popular in multiphysics and multiscale simulations, yet their use in stiff problems often requires time steps to be so small as to render...     

Fast direct sampling for multiple-point stochastic simulation

Multiple-point statistics simulation has recently attracted significant attention for the simulation of complex geological structures. In this paper, a fast direct sampling (FDS) algorithm is presented based on a fast gradient descent pattern matching strategy. The match is directly extracted from the training image (TI) and so the method does not require intensive preprocessing and database storage. The initial node of the search path is selected randomly but the following nodes are selected in a principled manner so that the path is conducted to the right match. Each node is selected based on the matching accuracy and the behavior of the TI in the previous node. A simple initialization strategy is presented in this paper which significantly accelerates the matching process at the expense of a very naïve preprocessing stage. The proposed simulation algorithm has several outstanding advantages: it needs no (or very limited) preprocessing, does not need any database storage, searches for the match directly in the TI, is not limited to fixed size patterns (the pattern size can be easily changed during simulation), is capable of handling both continuous and categorical data, is capable of handling multivariate data, and finally and more importantly, is a fast method while maintaining high standards for the matching quality. Experiments on different TIs reveal that the simulation results of FDS and DS are comparable in terms of pattern reproduction and connectivity while FDS is far faster than DS.     

稳定的二维TTI介质一阶qP波方程RSGFD数值模拟

相比于VTI介质q P波数值模拟方法,考虑倾角因素的TTI介质q P波数值模拟方法能够更加准确地描述各向异性介质中波场的传播特征。常规的声学近似方法往往会造成TTI介质中倾角急剧变化的区域出现数值不稳定,笔者首先引入一个各向异性控制参数,推导了稳定形式的TTI介质二阶q P波方程,保证q P波场的稳定传播;其次,通过引入波场的伪速度分量,推导了其等价的一阶应力—速度形式及相应的PML边界条件,并应用优化的旋转交错网格有限差分(RSGFD)方法实现了精确的数值模拟。数值结果表明:TTI介质一阶q P波方程能够稳定、有效地模拟q P波的运动学特征,利用优化的RSGFD方法可以得到精确的合成地震记录,同时可以相对地提高计算效率。     

Finite element methods for geothermal reservoir simulation

Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.     

A fast marching method for reservoir simulation

We present a fast marching level set method for reservoir simulation based on a fractional flow formulation of two-phase, incompressible, immiscible flow in two or three space dimensions. The method uses a fast marching approach and is therefore considerably faster than conventional finite difference methods. The fast marching approach compares favorably with a front tracking method as regards both efficiency and accuracy. In addition, it maintains the advantage of being able to handle changing topologies of the front structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

A local solution for deterministic and stochastic transport equations

A local method is developed for finding the hydraulic head at an arbitrary point of a soil deposit with conductivity varying randomly in space. The method is said to be local since it delivers the hydraulic head at an arbitrary point of a soil deposit directly rather than extracting it from a field solution. The local method always converges to the exact solution, is ideal for parallel computation, and is simple to implement. The method is applied to solve locally one-dimensional transport equations with mixed boundary conditions, calculate corresponding effective conductivity, and examine size effect in specimens with hydraulic conductivity varying randomly in space.     

水文随机模拟进展

综述了近20年来水文随机模拟的新进展,包括三方面:①随机水文模型改进和创新;②水文随机模拟应用研究新进展;③水文随机模拟认识新进展。并指出了今后的研究重点:①对水文过程的重要物理特性和统计特性作深入的分析;②加强非参数模型和非线性模型的研究;③加强流域系统随机模型的研究;④加强建立模型时如何综合利用多种信息的研究;⑤加强模型的各种检验和合理分析。     

济阳坳陷孤东油田曲流河河道储集层构型三维建模

济阳坳陷孤东油田七区西馆陶组上段为典型的曲流河沉积,其中Ng522单层发育2个大型点坝砂体,在系统的点坝砂体构型表征的基础上,探索了储集层构型界面的几何建模方法,将构型界面模型嵌入到基于三维结构化网格体的相模型中,建立了研究区26-295井区真正意义上的、更符合地下实际的三维储集层构型模型,再现了成因微相内部构型单元及界面的空间分布特征,满足了三维油藏数值模拟的需要。点坝内部的侧积层向废弃河道方向倾斜,延伸到距点坝顶三分之二的位置,点坝砂体表现为“半连通体”特征。建立了点坝内部剩余油分布模式,并指出挖潜措施。该方法在研究区应用效果较好,并可以推广到其他相似油田,这对丰富储集层地质学理论及提高油田开发效率均具有重要意义。     

Robust numerical implementation of a 3D rate-dependent model for reservoir geomechanical simulations

A 3D elasto-plastic rate-dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium “Beyond 2000 in Computational Geotechnics,” pages 249-261, 1999). An original strain-driven algorithm with an Inexact Newton iterative scheme is used to compute the state variables for a given strain increment.The model is validated against laboratory measurements, checked on a simplified test case, and used to simulate land subsidence due to groundwater and hydrocarbon production. The numerical results prove computationally effective and robust, thus allowing for the use of the model on real complex geological settings.     

三维生物礁滩建模及地震数值模拟

基于塔礁、点礁、生物滩等地质体的几何特征及地质特征,采用高精度的三维块状建模方法,建立了适合于复杂地区的三维礁滩复合体模型。该模型不但立体地反映了生物礁、生物滩及地层间的空间展布特征,还可以直观地体现了生物礁滩储层内部的物性差异。此外采用FK域三维波动方程数值模拟方法对其进行了地震波场数值模拟,得到了一系列具有代表性时间剖面上的地震波场响应特征,为正确认识实际生物礁滩的复杂结构和特性提供了依据。     

Geostatistically consistent history matching of 3D oil-and-gas reservoir models

An approach for geostatistically consistent matching of 3D flow simulation models and 3D geological models is proposed. This approach uses an optimization algorithm based on identification of the parameters of the geostatistical model (for example, the variogram parameters, such as range, sill, and nugget effect). Here, the inverse problem is considered in the greatest generality taking into account facies heterogeneity and the variogram anisotropy. The correlation dependence parameters (porosity-to-log permeability) are clarified for each single facies.     

江苏瓦庄油田油藏数值模拟开发技术政策界限研究

针对江苏瓦庄油田窄条状、长井段、多油层、薄互层、多断层的特点,采用地质建模和油藏数值模拟一体化的技术思路,在构造研究、精细地层对比、沉积相分析和测井分析的基础上,建立了三维油藏地质模型,以该模型为静态地质模型进行精细油藏数值模拟研究,在历史拟合成功的基础上,进行了开发层系、油井距断层距离、分层配注的开发技术政策界限研究,得出了该类油田合理的开发政策,为油田的开发生产提供了合理的理论指导。