Application of the representer method for parameter estimation in numerical reservoir models

A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model. Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method. This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure measurements from a small number of observation wells in between the injection and production wells, but the representer method could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool for applications in reservoir engineering.     

The representer method for two-phase flow in porous media

The representer method is applied to a one-dimensional two-phase flow model in porous media; capillary pressure and gravity are neglected. The Euler–Lagrange equations must be linearized, and one such linearization is presented here. The representer method is applied to the linear system iteratively until convergence, though a rigorous proof of convergence is out of reach. The linearization chosen is easy to calculate but does not converge for certain weights; however, a simple damping restores convergence at the cost of extra iterations. Numerical experiments are performed that illustrate the method, and quick comparison to the ensemble Kalman smoother is made. This research was supported by NSF grant EIA-0121523.     

用多分量感应资料快速重建层状地层的纵横向电阻率和水平界面深度

研究建立用多分量感应测井资料同时快速重建水平层状横向同性介质中横向与纵向电阻率和层界面深度的有效方法。首先,利用电磁场摄动方程、电导率函数与模型参数关系方程以及模式匹配算法得到电磁场并矢Green函数的半解析解,建立多分量感应测井响应的Frèchet导数矩阵的快速算法;在此基础上,借助于规范化处理和奇异值分解技术,给出同时反演水平层状地层中各个地层的纵、横向电阻率以及层界面深度的迭代过程,实现理论合成资料与输入资料的最佳拟合。数值计算证明,该反演算法能够取得较满意的反演效果。     

Computing Petrophysical Properties in Porous Rocks Using a Boundary-Element Technique

An efficient numerical technique has been used to compute the deformation of pores of arbitrary shape embedded in a homogeneous elastic solid under the influence of applied stresses. The scheme is based on the boundary-element method, where single linear elements are used to generate solutions that satisfy prescribed boundary conditions. These solutions can be employed to describe the behavior of elastic moduli and other petrophysical properties in porous rocks. The numerical algorithm allows computation of the stress field induced by the pores in the solid. In this way, the effect of the interactions between pores caused by stress concentrations can be studied from a quantitative point of view. To test the algorithm, some interesting results are compared with existing models, for special cases available in the literature. Also, a model for the compressibility and porosity of sedimentary rocks, as a function of applied hydrostatic stress, was generated by mixing some realistic pore geometries generated with the numerical algorithm. Results were in good agreement with data obtained from selected samples of sandstones.     

基于成矿条件数值模拟和支持向量机算法的深部成矿预测——以粤北凡口铅锌矿为例

随着计算机科学和地质大数据技术的迅猛发展,数值模拟和机器学习已成为当今地学领域定量发展的重要前沿方向。数值模拟综合运用了研究区地质、构造、地球物理、地球化学等多源信息,将成矿条件与过程进行量化模拟分析,对研究成矿动力学演化过程及成矿响应有重要意义,可对已有成矿要素/信息在时空上进行扩展/外推,扩大了成矿预测信息的广度和深度,为解决深部成矿预测中获取深部信息难题提供了一种可能的有效途径。支持向量机是一种重要的机器学习分类算法,它具有简洁、方便、高效和计算结果较稳定等特点,在众多领域中得以成功应用,是成矿预测中多源信息提取与融合的一种可靠的技术手段。为了充分利用数值模拟与机器学习的优势,本文提出将计算机数值模拟方法和机器学习(即支持向量机算法)相结合来进行深部成矿预测的新方法。以粤北凡口超大型铅锌矿为例,首先,对凡口矿区勘探线剖面进行构造应力场模拟;进而,以已知钻孔数据作为训练集和测试集,运用支持向量机算法对模拟结果中的不同参量(也即模拟所得的成矿条件)进行训练学习;最后,建立相应的定量找矿预测模型对研究区(或剖面)外围和深部找矿进行预测评价。研究结果表明,本文所建立的预测模型精确度和召回率都较好,预测结果显示出了三个成矿可能较大的区域,说明数值模拟技术和机器学习算法结合应用的效果较好。这种新的成矿预测方法为深部找矿预测提供了一种可行的新思路和新途径,可以有效地拓展运用到其他矿区、其他类型矿床的深部找矿预测工作中。     

The numerical simulation of seasonal soil drying in an unsaturated clay soil

The results of a numerical simulation of the observed field-drying behaviour of an unsaturated clay are described. In particular, the simulation of soil drying during the summer of 1983 is addressed. Richards' pressure-based unsaturated flow formulation is adopted. Transient numerical solutions are achieved by making use of the finite element method coupled with a finite difference timestepping scheme. The application of the algorithm to the simulation of the problem in hand is described. The initial moisture content distribution represents saturated conditions as indicated by field-measured data. Boundary conditions are determined from an interpretation of meteorological data. A simple method of representing plant root extraction of soil moisture is proposed. Comparisons of numerical results with field-measured data collected by British Gas are presented. Good correlation is obtained. The numerical simulation is shown to be capable of representing the observed field-drying behaviour. The complexity of modelling soil drying, as opposed to infiltration, is clearly illustrated by the work presented.     

电磁波场数值计算中时间域有限差分法与时间域伪谱法的对比研究

为提高电磁波场数值计算精度,对时间域有限差分法与时间域伪谱法进行了对比研究。时间域有限差分法是一种目前流行的电磁场时域数值计算方法,已被广泛应用于求解与时间有关的偏导数方程。对于大规模数值计算,时间域有限差分法需要较多的内存空间。时间域伪谱法基于时间域有限差分法,该方法使用快速傅里叶度换来计算麦克斯韦方程中的空间导数。由于傅里叶变换的准确性,时间域伪谱法使计算精度提高,数值计算时所需的格子数大大减少,这极大地节省了计算机内存空间,适合于大规模正反演问题的数值计算。     

Automatic Variogram Modeling by Iterative Least Squares: Univariate and Multivariate Cases

In this paper, we propose a new methodology to automatically find a model that fits on an experimental variogram. Starting with a linear combination of some basic authorized structures (for instance, spherical and exponential), a numerical algorithm is used to compute the parameters, which minimize a distance between the model and the experimental variogram. The initial values are automatically chosen and the algorithm is iterative. After this first step, parameters with a negligible influence are discarded from the model and the more parsimonious model is estimated by using the numerical algorithm again. This process is iterated until no more parameters can be discarded. A procedure based on a profiled cost function is also developed in order to use the numerical algorithm for multivariate data sets (possibly with a lot of variables) modeled in the scope of a linear model of coregionalization. The efficiency of the method is illustrated on several examples (including variogram maps) and on two multivariate cases.     

混沌控制反演系统构造及算法逻辑设计

给出了适用于非线性反演的混沌控制反演系统构造方法及求解控制矩阵的算法逻辑设计。该方法在迭代反演控制参数和迭代反演输出结果之间建立耦合关系，通过时时修改控制参数保证迭代稳定收敛到预期的解空间。在求解过程中，应用数据结构方法分析了混沌控制理论中计算控制矩阵的数据结构，采用树形结构表述出控制矩阵计算过程中下标的取值逻辑，利用可以复读栈中元素的中序遍历来遍历每一棵树，寻找各元素的组合序列，给出的数值算例说明了混沌控制反演方法及其算法的有效性。     

基于复杂地质体的地应力场智能识别方法研究

初始地应力是地下开采及施工所需要考虑的重要影响因素,地应力值的准确获得通常采用现场测量与反演计算结合实现。针对某铜镍矿复杂地质体,在已有监测数据的基础上建立三维正交数值模型,获得监测点的地应力计算值。利用遗传规划程序,回归地应力监测点的地应力与各自变量的函数关系。建立地应力实测值和计算值之差的平方和最小的目标优化函数,使用遗传算法智能算法对目标函数进行优化,最终获得了矿区的原岩应力场。检测样本验证结果显示,计算值与实测值的误差控制在10%以内,一定程度上证明了该地应力场智能识别方法的可靠性,可为以后复杂地质体矿区地应力场的计算提供较为可行的研究方法。     

Multi-frequency synthesis of VLBI images using a generalized maximum entropy method

A new multi-frequency synthesis algorithm for reconstructing images from multi-frequency VLBI data is proposed. The algorithm is based on a generalized maximum entropy method, and makes it possible to derive an effective spectral correction for images over a broad frequency bandwidth, while simultaneously reconstructing the spectral-index distribution over the source. The results of numerical simulations demonstrating the capabilities of the algorithm are presented.     

Influence of vertical ground motion on seismic-induced displacements of gravity structures

A method enabling assessment of seismic-induced movements of gravity block is proposed. This method is based on dynamic analysis of the block subjected to both horizontal and vertical ground accelerations, and resultant forces acting on the block. There are two kinds of the motion. The first one is trivial, as it is a common motion of the block and subsoil. The second is a relative motion of the block with respect to subsoil, depending on combination of ground accelerations and the resultant of horizontal forces. Attention is focused on the influence of vertical ground motion on seismic-induced displacements of the structure. Experimental investigations performed in order to validate a numerical algorithm are described, and then experimental data are compared with numerical predictions. A good agreement is obtained. Then, the dynamics analysis of the block is presented for harmonic and pseudo-stochastic ground motions in order to illustrate the algorithm proposed. The results of computations show that, for some typical data and ground accelerations corresponding to strong earthquakes, large permanent displacements of the block take place, as observed in real conditions.     

全拖曳式深海直流电阻率法三维任意各向异性正演模拟

高精度、高效率的深海勘探是当前国家海洋资源勘探开发的研究热点之一,设计观测效率高、勘探成本低的探测方式,开发可精确计算海底复杂电性环境的正演模拟算法有助于推进该研究的进展。本文基于前人的研究经验,引入了全拖曳式深海直流电阻率观测方式,同时考虑到海底沉积环境的电各向异性,开发了基于非结构有限元方法的三维任意各向异性深海直流电阻率正演算法,实现了对海底任意电各向异性情况的仿真模拟。本文算法与层状一维模型半解析解的对比验证了算法的精度。对典型各向异性电性模型的仿真模拟和分析,证明了全拖曳式深海探测方式对海底沉积层和矿产资源电各向异性的高分辨率。在此基础上,总结了电导率各向异性主轴沿笛卡尔坐标旋转时视电阻率分布也发生同方向旋转的视电阻率分布特征,并根据海底地形对各向异性探测的影响进行了简单探讨。     

Contaminant transport with non‐equilibrium processes in unsaturated soils and implicit characteristic Galerkin scheme

A non‐equilibrium sorption—advection—diffusion model to simulate miscible pollutant transport in saturated–unsaturated soils is presented. The governing phenomena modelled in the present simulation are: convection, molecular diffusion, mechanical dispersion, sorption, immobile water effect and degradation, including both physical and chemical non‐equilibrium processes. A finite element procedure, based on the characteristic Galerkin method with an implicit algorithm is developed to numerically solve the model equations. The implicit algorithm is formulated by means of a combination of both the precise and the traditional numerical integration procedures. The stability analysis of the algorithm shows that the unconditional stability of the present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results illustrate good performance of the present algorithm in stability and accuracy, and in simulating the effects of all the mentioned phenomena governing the contaminant transport and the concentration distribution. Copyright © 2000 John Wiley & Sons, Ltd.     

成层土场地地震效应的时程算法研究

成层土场地是一类常见的建筑场地,覆盖土层的厚度、刚度、地层顺序等是影响地震动特性的主要因素,动力时程方法是分析此类问题的一个有效手段。但常规的动力时程方法计算求解复杂,不仅费时、费力,而且还可能因为算法的不 稳定性而无法得到预期的结果。为了获得一种高效简便的动力时程算法,根据地震波在层状弹性介质中的传播原理,采用 弹性波叠加方法,提出一种计算成层土场地地震响应的快速时程算法。该方法是一种级数逼近算法,无需剖分网格进行数 值法计算,极大地提高了计算效率。应用该算法进行了模型试算,并将计算结果与相关文献进行对比,验证了此算法的正确性。     

Taking into account general boundary conditions in upscaling absolute permeability

Upscaling methods that need to solve local problems subject to boundary conditions are addressed in this article. We define a new upscaling method based on optimization problems, which can take into account general boundary conditions applied to local problems. The determination of upscaled permeability leads to minimizing the difference of dissipated energies (or averaged velocity) at fine and large scale. Using optimal control techniques, we obtain an effective computing algorithm that allows us to recover, with classical boundary conditions, the well-known results. The uniqueness issue is tackled for the optimization problems introduced in our approach. We show that the method is stable with respect to G-convergence, a property that establishes a link with homogenization theory, and finally, 2D numerical experiments are presented.     

An efficient matrix-free algorithm for the ensemble Kalman filter

In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states, and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis. Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free implementation outperforming an singular value decomposition-based implementation in computational time.     

基于ν-SVR和改进PSO算法的反分析方法及应用

岩土工程反分析面临着多元化、复杂化和精确化的挑战,反分析方法要求能在少而精的正分析基础上结合监测数据快速反馈出数值计算参数.充分发挥支持向量回归机ν-SVR和改进的变邻域PSO算法的优势,建立起岩土工程反分析的流程和方法.同时,将其应用于锦屏左岸边坡的反分析问题,选择稳定问题非常突出的II1-II1剖面作为分析对象,根据监测资料反馈设计关键岩体的力学参数,并与监测数据比对,反演成果合理准确,进一步验证了该方法的的正确性和有效性.     

A coupled time integration algorithm for discontinuous deformation analysis using the numerical manifold method

To improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial-domain coupled explicit-implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration-based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.     

碳酸盐岩喀斯特溶洞和裂缝系统的地震模拟与预测

提出了有助于确定碳酸盐岩裂缝带和喀斯特溶洞系统空间分布的地震正演模拟和预测方法。地震正演方法包含两个关键步骤，一是利用弹性波动方程计算含缝洞介质的有效弹性参数，另一步骤是根据有效弹性参数构成的等效地质模型，用单程声学波动方程进行波场延拓。数值模拟和实际地震数据的例子说明，将地震正演剖面与地震偏移剖面相结合进行对比分析有可能识别和预测碳酸盐岩地层中的缝洞发育带。