Multiscale ensemble filtering for reservoir engineering applications

Reservoir management requires periodic updates of the simulation models using the production data available over time. Traditionally, validation of reservoir models with production data is done using a history matching process. Uncertainties in the data, as well as in the model, lead to a nonunique history matching inverse problem. It has been shown that the ensemble Kalman filter (EnKF) is an adequate method for predicting the dynamics of the reservoir. The EnKF is a sequential Monte-Carlo approach that uses an ensemble of reservoir models. For realistic, large-scale applications, the ensemble size needs to be kept small due to computational inefficiency. Consequently, the error space is not well covered (poor cross-correlation matrix approximations) and the updated parameter field becomes scattered and loses important geological features (for example, the contact between high- and low-permeability values). The prior geological knowledge present in the initial time is not found anymore in the final updated parameter. We propose a new approach to overcome some of the EnKF limitations. This paper shows the specifications and results of the ensemble multiscale filter (EnMSF) for automatic history matching. EnMSF replaces, at each update time, the prior sample covariance with a multiscale tree. The global dependence is preserved via the parent–child relation in the tree (nodes at the adjacent scales). After constructing the tree, the Kalman update is performed. The properties of the EnMSF are presented here with a 2D, two-phase (oil and water) small twin experiment, and the results are compared to the EnKF. The advantages of using EnMSF are localization in space and scale, adaptability to prior information, and efficiency in case many measurements are available. These advantages make the EnMSF a practical tool for many data assimilation problems.     

Behaviour of Coupled Modes in a Simple Nonlinear Air-Sea Interaction Model

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Localized multi-scale energy and vorticity analysis: II. Finite-amplitude instability theory and validation

A novel localized finite-amplitude hydrodynamic stability analysis is established in a unified treatment for the study of real oceanic and atmospheric processes, which are in general highly nonlinear, and intermittent in space and time. We first re-state the classical definition using the multi-scale energy and vorticity analysis (MS-EVA) developed in Liang and Robinson [Liang, X.S., Robinson, A.R., 2005. Localized multiscale energy and vorticity analysis. I. Fundamentals. Dyn. Atmos. Oceans 38, 195–230], and then manipulate certain global operators to achieve the temporal and spatial localization. The key of the spatial localization is transfer-transport separation, which is made precise with the concept of perfect transfer, while relaxation of marginalization leads to the localization of time. In doing so the information of transfer lost in the averages is retrieved and an easy-to-use instability metric is obtained. The resulting metric is field-like (Eulerian), conceptually generalizing the classical formalism, a bulk notion over the whole system. In this framework, an instability has a structure, which is of particular use for open flow processes. We check the structure of baroclinic instability with the benchmark Eady model solution, and the Iceland–Faeroe Frontal (IFF) intrusion, a highly localized and nonlinear process occurring frequently in the region between Iceland and Faeroe Islands. A clear isolated baroclinic instability is identified around the intrusion, which is further found to be characterized by the transition from a spatially growing mode to a temporally growing mode. We also check the consistency of the MS-EVA dynamics with the barotropic Kuo model. An observation is that a local perturbation burst does not necessarily imply an instability: the perturbation energy could be transported from other processes occurring elsewhere. We find that our analysis yields a Kuo theorem-consistent mean–eddy interaction, which is not seen in a conventional Reynolds stress framework. Using the techniques of marginalization and localization, this work sets up an example for the generalization of certain geophysical fluid dynamics theories for more generic purposes.     

Role of anthropogenic volatile organic compounds and nitrogen oxides as ozone precursors in the wintertime over East Asia

As an exercise in model sensitivity, the Models-3 Community Multiscale Air Quality (CMAQ) modeling system with meteorological fields from the Regional Atmospheric Modeling System (RAMS) was applied to study the response of photochemical oxidants to systematic increases in anthropogenic volatile organic compounds (VOC) and nitrogen oxides (NO_x) emissions in January 1997 over East Asia. Three simulations-one base case and two sensitivity simulations were carried out. Two sensitivity simulations were performed by assuming a 35% separate increase in anthropogenic VOC and NO_x emissions comparing with the base case. Biogenic VOC emissions were held constant across the sensitivity simulations. To evaluate the model performance, ozone mixing ratios (O₃) from the base case simulation were compared with surface observations at five remote sites in Japan, and it was found that the model reproduces most of the important features in the observations. Monthly average O₃ concentrations in the daytime were examined to gain an understanding of how the increase in anthropogenic emissions affected the overall chemical system for each sensitivity simulation.     

中国大陆地壳密度差异多尺度反演

利用小波分析方法原理,在对中国布格重力异常多尺度分解的基础上,反演了各种尺度意义下中国大陆地壳的密度差异,给出了中国大陆地壳中相对密度差异的空间分布,为研究中国大陆地壳构造、进行深部地质研究提供了新结果．     

Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations

Subsurface flow models can exhibit strong full-tensor anisotropy due to either permeability or grid nonorthogonality effects. Upscaling procedures, for example, generate full-tensor effects on the coarse scale even for cases in which the underlying fine-scale permeability is isotropic. A multipoint flux approximation (MPFA) is often needed to accurately simulate flow for such systems. In this paper, we present and apply a different approach, nonlinear two-point flux approximation (NTPFA), for modeling systems with full-tensor effects. In NTPFA, transmissibility (which provides interblock connections) is determined from reference global flux and pressure fields for a specific flow problem. These fields can be generated using either fully resolved or approximate global simulations. The use of fully resolved simulations leads to an NTPFA method that corresponds to global upscaling procedures, while the use of approximate simulations gives a method corresponding to recently developed local–global techniques. For both approaches, NTPFA algorithms applicable to both single-scale full-tensor permeability systems and two-scale systems are described. A unified framework is introduced, which enables single-scale and two-scale problems to be viewed in a consistent manner. Extensive numerical results demonstrate that the global and local–global NTPFA techniques provide accurate flow predictions over wide parameter ranges for both single-scale and two-scale systems, though the global procedure is more accurate overall. The applicability of NTPFA to the simulation of two-phase flow in upscaled models is also demonstrated.     

Multiscale simulations of porous media flows in flow-based coordinate system

In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system.     

ROY—A multiscale magnetospheric mission

The scientific rationale of the ROY multi-satellite mission addresses multiscale investigations of plasma processes in the key magnetospheric regions with strong plasma gradients, turbulence and magnetic field annihilation in the range from electron inertial length to MHD scales.The main scientific aims of ROY mission include explorations of:

(a)

turbulence on a non-uniform background as a keystone for transport processes;

(b)

structures and jets in plasma flows associated with anomalously large concentration of kinetic energy; their impact on the energy balance and boundary formation;

(c)

transport barriers: plasma separation and mixing, Alfvenic collapse of magnetic field lines and turbulent dissipation of kinetic energy;

(d)

self-organized versus forced reconnection of magnetic field lines;

(e)

collisionless shocks, plasma discontinuities and associated particle acceleration processes.

In the case of autonomous operation, 4 mobile spacecrafts of about 200 kg mass with 60 kg payload equipped with electro-reactive plasma engines will provide 3D measurements at the scales of 100-10000 km and simultaneous 1D measurements at the scales 10-1000 km. The latter smaller scales will be scanned with the use of radio-tomography (phase-shift density measurements within the cone composed of 1 emitting and 3 receiving spacecrafts).We also discuss different opportunities for extra measurement points inside the ROY mission for simultaneous measurements at up to 3 scales for the common international fleet.Combined influence of intermittent turbulence and reconnection on the geomagnetic tail and on the nonlinear dynamics of boundary layers will be explored in situ with fast techniques including particle devices under development, providing plasma moments down to 30 ms resolution.We propose different options for joint measurements in conjunction with the SCOPE and other missions:

•

simultaneous sampling of low- and high-latitudes magnetopause, bow shock and geomagnetic tail at the same local time;

•

tracing of magnetosheath streamlines from the bow shock to near-Earth geomagnetic tail;

•

passing “through” the SCOPE on the inbound orbit leg;

•

common measurements (with SCOPE and other equatorial spacecraft) at distances of ∼ few thousand km for durations of ∼several hours per orbit.

The orbit options and scientific payload of possible common interest are discussed in this work, including FREGAT cargo opportunities for extra payload launching and the “Swarm” campaigns with ejection of nano- and pico-satellites.     

2008年1月中国南方低温雨雪期间异常阻塞高压事件的多尺度动力过程分析

2008年1月,中国南方发生了罕见的低温雨雪灾害,造成这次灾害的关键系统之一是乌拉尔山以东地区的异常阻塞高压（阻高）。基于NCEP再分析资料,利用新发展的多尺度子空间变换和重构分析了这一期间阻高的多尺度特征,发现其源头来自欧洲地区,强度减弱后东移,在乌拉尔山—贝加尔湖地区重新增强并得以维持相当长的时间。结果表明,两次阻高过程本质上是同一过程在不同阶段的表现。为探讨上述过程的动力学机制,利用基于多尺度子空间变换的局地多尺度能量分析方法以及正则传输理论对其进行了分析,发现此次异常阻高过程源自32 d以下尺度系统的动能强迫,具体地说,能量来自32 d以下尺度系统向32—128 d低频尺度系统的正压正则传输,而且这种正则传输在阻高环流的东、西两侧不对称,西侧在强度上远大于东侧。分析表明,上述非对称的强迫作用由动能空间输运来平衡,平流将西侧获得的32—128 d低频尺度动能向东侧输运,以此来维持阻高环流的整体稳定和均一。上述两种内部的物理过程是高压环流在东移的过程中得以重新增强并长时间维持的机制。      

A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms

In this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods [23]. These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction.