Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels

We present a new approach to reservoir simulation that gives accurate resolution of both large-scale and fine-scale flow patterns. The method uses a mixed multiscale finite-element method (MMsFEM) to solve the pressure equation on a coarse grid and a streamline-based technique to solve the fluid transport on a fine-scale subgrid. The MMsFEM is based on the construction of special approximation velocity spaces that are adaptive to the local properties of the differential operator. As such, MMsFEM produces a detailed subgrid velocity field that reflects the impact of the fine-scale heterogeneous structures. By combining MMsFEM with rapid streamline simulation of the fluid transport, we aim towards a numerical scheme that facilitates routine reservoir simulation of large heterogeneous geomodels without upscaling. The new method is applied to two different test cases. The first test case consists of two (strongly) heterogeneous quarter five-spot problems in 2D. The second test case is a 3D upscaling benchmark taken from the 10th SPE Comparative Solution Project, a project whose purpose is to compare and validate upscaling techniques. The test cases demonstrate that the combination of multiscale methods and streamlines is a robust and viable alternative to traditional upscaling-based reservoir simulation.     

The <Emphasis Type="Italic">T</Emphasis>-matrix approach for the mathematical modeling of the effective elastic properties of hydrocarbon reservoirs

Various methods of the effective medium theory (EMT)—the T-matrix approach (optical potential approximation and coherent potential approximation), Mori–Tanaka method, generalized singular approximation, etc.—for modeling the effective elastic properties of hydrocarbon reservoir rocks are considered. The relationship of the different approaches (perturbation theory, self-consistent methods, and variational principles) is demonstrated. The classification of the methods by the degree of complexity of solving the inverse problem is suggested. An example of the theoretical modeling of an oil-, gas-, and water-saturated rock with the oriented axis of the fractures is presented. Conclusions about the applicability of different methods for rock modeling are made. In this study we review and compare different methods of the EMT and present the guidelines for determining the effective properties of the medium in rock physics modeling.     

基于叠前反演的流体敏感属性实验研究及应用

提取叠前地震振幅信息的叠前反演技术已成为储层预测的重要手段,其能获得各种岩石弹性参数,丰富储层预测方法.因目标储层的差异性,优选并建立有利的流体敏感参数对储层流体检测尤为重要.本文基于岩石物理实验, 测量并分析了岩石弹性参数随流体饱和度的变化特征, 进一步根据岩石物理理论建立组合流体敏感参数, 达到对油气检测的最佳敏感效果.定义了流体敏感量,定量分析岩石弹性参数的流体敏感性.最后本文在X区块进行了叠前地震反演的应用, 结果表明通过岩石物理实验分析并建立获得的流体敏感参数能明显的提高储层的识别能力.     

Upscaling of flow in heterogeneous porous formations: Critical examination and issues of principle

We consider heterogeneous media whose properties vary in space and particularly aquifers whose hydraulic conductivity K may change by orders of magnitude in the same formation. Upscaling of conductivity in models of aquifer flow is needed in order to reduce the numerical burden, especially when modeling flow in heterogeneous aquifers of 3D random structure. Also, in many applications the interest is in average values of the dependent variables over scales larger or comparable to the conductivity length scales. Assigning values of the conductivity K_b to averaging domains, or computational blocks, is the topic of a large body of literature, the problem being of wide interest in various branches of physics and engineering. It is clear that upscaling causes loss of information and at best it can render a good approximation of the fine scale solution after averaging it over the blocks.The present article focuses on upscaling approaches dealing with random media. It is not meant to be a review paper, its main scope being to elucidate a few issues of principle and to briefly discuss open questions. We show that upscaling can be usually achieved only approximately, and the result may depend on the particular upscaling scheme adopted. The typically scarce information on the statistical structure of the fine-scale conductivity imposes a strong limitation to the upscaling problem. Also, local upscaling is not possible in nonuniform mean flows, for which the upscaled conductivity tensor is generally nonlocal and it depends on the domain geometry and the boundary conditions. These and other limitations are discussed, as well as other open topics deserving further investigation.     

基于计算岩石物理方法的页岩储层弹性参数提取

发展了应用数值计算方法获取页岩储层的速度、各向异性参数的计算岩石物理系列方法.该系列方法包括了大尺度精细地质模型数值建模、计算网格尺度的地球物理建模和地震波数值模拟提取岩石物理弹性参数.本文方法利用储层的统计数据而不是具体岩心的测量数据,可获得储层岩石物理弹性参数的变化规律.相比于基于岩心测试的岩石物理方法,本文方法可精细考虑实际储层的非均匀特征,可得到岩心测试难以求取的与尺寸效应高度相关的弹性参数,也避免了求取弹性参数变化规律时获取不同地质特征岩心的困难.本文发展了计算岩石物理方法,为计算岩石物理面临的大尺度地质建模和计算能力限制问题提供了有效的解决方案.文中以胜利罗家的页岩储层为例,求得了储层TOC含量从3%到21%变化情况下储层的P波、S波速度以及各向异性参数变化规律.     

DETERMINATION OF ELECTRIC ROCK PARAMETERS FROM THE FIELD STRUCTURE OF A MAGNETIC DIPOLE*

In the theoretical part of the present paper, formulas have been analyzed for a magnetic dipole in a homogeneous and unbounded medium. The magnetic field is elliptically polarized in the region between the quasistatic zone and the far field. Since the position and the shape of the polarization ellipses depend on the complex wave number, k, it is possible to determine k by measuring the polarization ellipses. From k, the conductivity and the dielectric constant of the medium are easily calculated. The functions required for the measuring method have been computed and plotted in graphs. In the experimental part it was examined how far the theory may be applied to measurements of propagation through rock at frequencies ranging from 100-1000 kHz. These measurements showed that reasonably defined mean values of rock parameters can be given only if the deviations of the field from the theoretically expected field are not too high. These deviations have been named field distortions and have been examined by means of statistical methods (variance ratio tests). Gallery cavity and inhomogeneity or anisotropy of the medium account for these distortions.     

孔隙压力扩散与水库诱发地震活动性的初步研究

水库诱发地震活动与水的渗透有密切关系,本文认为水库诱发地震中,前震活动主要是由于水的渗透引起孔隙压力扩散,岩石强度弱化所致。由于水库区地下岩石渗透性质的复杂性,将库区岩石介质分为均匀、非均匀渗透的两种情况,利用两相(固、液)多孔介质中孔隙压力扩散理论,分别对水库蓄水所引起的孔隙压力场进行了数值模拟计算,计算结果表明,非均匀渗透模型中水渗透所形成的孔隙压力分布与水库地震发生的空间位置对应得较好,孔隙压力峰值扩散到水库诱发地震的前震震源处的时间(1.8天～45天)与水库蓄水后引起前震活动的滞后时间大体一致。     

Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial‐stacked seismic data are available. The multi‐property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log‐facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock‐physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.     

复杂孔隙储层三维岩石物理模版

复杂孔隙储层往往同时发育孔缝洞等多种孔隙类型,这种孔隙结构的复杂性使得岩石的速度与孔隙度之间的相关性很差.经典的二维岩石物理模版只研究弹性参数与孔隙度和饱和度之间的定量关系,而不考虑孔隙结构的影响,用这样的模版来预测复杂孔隙储层的物性参数时带来很大偏差.本文首先证明多重孔隙岩石的干骨架弹性参数可以用一个等效孔隙纵横比的单重孔隙岩石物理模型来模拟;进而基于等效介质岩石物理理论和Gassmann方程,建立一个全新的三维岩石物理模版,用它来建立复杂孔隙岩石的弹性性质与孔隙扁度及孔隙度和饱和度之间的定量关系;在此基础上,预测复杂储层的孔隙扁度、孔隙度以及孔隙中所包含的流体饱和度.实际测井和地震反演数据试验表明,三维岩石物理模版可有效提高复杂孔隙储层参数的预测精度.     

Reactive transport upscaling at the Darcy scale: A new flow rate based approach raises the unsolved issue of porosity upscaling

This article demonstrates that permeability upscaling, which can require complex techniques, is not necessary to significantly decrease the CPU time in reactive transport modeling. CPU time depends more on the geochemistry than the flow calculation. Flow rate upscaling is proposed as an alternate method to permeability upscaling, which is more suited to time-consuming flow resolution. To apply this method, a finite volume approach is most convenient.Considering the equality of flow as the equivalence criterion, when the coarse grid overlays the fine grid, flow rate upscaling leads, by construction, to the exact results, whereas the accuracy of permeability upscaling methods often depends on specific conditions. Some focus is put on the limitations of a common permeability upscaling technique, the simplified renormalization. In stationary flow, the gain in CPU time is the same for both flow rate upscaling and permeability upscaling. In transient flow, flow rate upscaling is slightly less time-efficient but the ratio between both CPU times decreases when the geochemistry is more complex.Working with an accurate flow rate field in the upscaled case reveals that porosity upscaling is a surprisingly tricky issue. Solution mixing is induced and residence times can be significantly affected. These changes have potentially important consequences on reactive transport modeling. They are not specific to the flow rate upscaling method; they are a general issue. Some simplified cases, assuming a homogeneous mineralogy, are examined. At this stage, a simple heuristic method is proposed, which yields reliable results under particular conditions (high heterogeneity). Porosity upscaling remains an open research field.     

Petrophysical inversion of AVA data

We investigate the interactions between the elastic parameters, V_P, V_S and density, estimated by non-linear inversion of AVA data, and the petrophysical parameters, depth (pressure), porosity, clay content and fluid saturation, of an actual gas-bearing reservoir. In particular, we study how the ambiguous solutions derived from the non-uniqueness of the seismic inversion affect the estimates of relevant rock properties. It results that the physically admissible values of the rock properties greatly reduce the range of possible seismic solutions and this range contains the actual values given by the well. By means of a statistical inversion, we analyse how approximate a priori knowledge of the petrophysical properties and of their relationships with the seismic parameters can be of help in reducing the ambiguity of the inversion solutions and eventually in estimating the petrophysical properties of the specific target reservoir. This statistical inversion allows the determination of the most likely values of the sought rock properties along with their uncertainty ranges. The results show that the porosity is the best-resolved rock property, with its most likely value closely approaching the actual value found by the well, even when we insert somewhat erroneous a priori information. The hydrocarbon saturation is the second best-resolved parameter, but its most likely value does not match the well data. The depth of the target interface is the least-resolved parameter and its most likely value is strongly dependent on a priori information. Although no general conclusions can be drawn from the results of this exercise, we envisage that the proposed AVA–petrophysical inversion and its possible extensions may be of use in reservoir characterization.     

礁滩储层内部孔隙结构模型模拟与孔隙度预测

地下岩石是由岩石基质和孔隙流体组成的双相介质,其有效弹性参数受岩石基质、孔隙度、孔隙结构及孔隙流体的影响,因此为了得到孔隙度与岩石有效弹性参数之间的关系,必须消除其他因素对孔隙度的影响.本文首先引进等效体的概念和Eshelby椭球包体裂缝理论,然后在合理的假设前提下,运用Gassman流体替换方程,推导并建立了生物礁滩...     

水渗透引起的应力场调整及岩石强度弱化的初步研究

本文采用二维线弹性的两相多孔介质理论,对水库蓄水后由水渗透引起的耦合应力变化及岩石强度弱化进行了数值模拟计算。结果表明,由于水的渗透使得岩石中的孔隙压力增大,耦合应力随之减小,从而导致岩石的有效应力减小,同时抗剪强度也相应减小,其减小的量值可以与地震时断层面上的应力降相比。根据计算结果,本文讨论了由水渗透引起地震的可能机制。     

Application of alternative digital rock physics methods in a real case study: a challenge between clean and cemented samples

High‐resolution three‐dimensional images are used in digital rock physics to numerically compute rock physical properties such as permeability and elastic moduli. These images are not widely available, and their preparation is both expensive and time consuming. All of these issues highlight the importance of alternative digital rock physics methods that are based on two‐dimensional images and use different approaches to compute effective properties of three‐dimensional samples. In addition, the scale of study in both standard and alternative digital rock physics is very small, which applications of its results are questionable at wells or reservoir scale. The aim of this study is to use two‐dimensional images and alternative digital rock physics techniques for computing seismic wave velocity and permeability, which are compared with well and laboratory data. For this purpose, data from one well in a reservoir located in the southwestern part of Iran are used. First, two clean (carbonate) and two cemented (limy sandstone) samples were collected from well cores at different depths. Then, two‐dimensional images by scanning electron microscope and conventional microscope were captured. In the next step, two alternative digital rock physics methods, namely, empirical relations and conditional reconstruction, have been employed to compute P‐wave velocity and permeability of a three‐dimensional medium. Results showed that, in clean (mono‐mineral) samples, velocity values were reasonably close to well data. However, permeability values are underestimated compared with laboratory data because laboratory data were obtained at ambient pressure, whereas alternative digital rock physics results are more representative of reservoir pressure conditions. Nevertheless, permeability–porosity trends are valid for both samples. In the case of cemented samples, a two‐scale procedure, along with a method for two‐scale computation and grain‐cement segmentation, is presented and developed. Results showed that P‐wave velocity is overestimated probably due to random sampling in this method. However, velocity–porosity trends are in agreement with well data. Moreover, permeability results obtained for cemented samples were also similar to those obtained for the clean samples.     

Comparison of upscaling methods to estimate hydraulic conductivity

A hydraulic field test program was performed at a hard rock laboratory (Asp? HRL) on the Swedish east coast to test upscaling theories. The test program investigated the rock volume around a borehole located at a depth of approximately 340 m below sea level. Hydraulic packer tests were performed at various scales, from 2 m to the entire borehole length of 296 m. From this set of data the predictive ability of different upscaling methods could be evaluated. The comparison of the evaluated "true" field scale hydraulic conductivity with the upscaled hydraulic conductivity yielded that the majority of the upscaling methods tested in this paper predict the large scale values with significant accuracy. However, the ability to predict rapidly decreases when the variance of the natural logarithm of hydraulic conductivity of the subsamples is larger than one. Such a variance is consistently found in the crystalline rocks at the tested site at the 2 m scale. However, at scales of 10 m and larger, a variance larger than one is uncommon. Therefore, it is concluded that there exists a smallest possible scale for use of hydraulic pumping test results for estimating the effective hydraulic conductivity at scales typical for regional flow.     

Biofilm growth in porous media: Experiments,computational modeling at the porescale,and upscaling

Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution of such properties is difficult both at the porescale where the phase morphology can be distinguished, as well as during upscaling to the corescale effective properties. Experimental data on biofilm growth is also limited because its collection can interfere with the growth, while imaging itself presents challenges.In this paper we combine insight from imaging, experiments, and numerical simulations and visualization. The experimental dataset is based on glass beads domain inoculated by biomass which is subjected to various flow conditions promoting the growth of biomass and the appearance of a biofilm phase. The domain is imaged and the imaging data is used directly by a computational model for flow and transport. The results of the computational flow model are upscaled to produce conductivities which compare well with the experimentally obtained hydraulic properties of the medium. The flow model is also coupled to a newly developed biomass–nutrient growth model, and the model reproduces morphologies qualitatively similar to those observed in the experiment.     

Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification

The transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete fracture networks methods can provide detailed solutions to the problem of modeling the contaminant transport in fractured media. However, within the framework of the performance assessment (PA) of radioactive waste repositories, the computational efforts required are not compatible with the repeated calculations that need to be performed for the probabilistic uncertainty and sensitivity analyses of PA. In this paper, we present a novel upscaling approach, which consists in computing the detailed numerical fractured flow and transport solutions on a small scale and use the results to derive the equivalent continuum parameters of a lean, one-dimensional dual-permeability, Monte Carlo simulation model by means of a genetic algorithm search. The proposed upscaling procedure is illustrated with reference to a realistic case study of $ {}^{239}{\text{Pu}} $ migration taken from literature.     

细观非均匀性对岩石破裂过程和微震序列类型影响的数值试验研究

运用岩石破裂过程分析RFPA2D系统，研究了岩石介质细观非均匀性对宏观力学行为的影响和微震序列特征. 通过对不同均质度系数m=1.1，1.5，2，3，5的5个样本进行破裂过程的模拟，发现均质度不同会产生不同地震序列类型，主要有：前震-主震-余震型、主震型和震群型. 此外，对5种不同均质度系数的岩石样本破裂过程的模拟表明，岩石介质的非均匀性不仅对岩样宏观强度和宏观变形非线性行为有显著的影响，而且也显著地影响试样破裂模式. 随着均质度系数的提高，主破裂呈现脆断模式. 同时介质的细观结构随机性，也对试样宏观破裂模式产生重要影响.     

Statistical facies classification from multiple seismic attributes: comparison between Bayesian classification and expectation–maximization method and application in petrophysical inversion

We present here a comparison between two statistical methods for facies classifications: Bayesian classification and expectation–maximization method. The classification can be performed using multiple seismic attributes and can be extended from well logs to three‐dimensional volumes. In this work, we propose, for both methods, a sensitivity study to investigate the impact of the choice of seismic attributes used to condition the classification. In the second part, we integrate the facies classification in a Bayesian inversion setting for the estimation of continuous rock properties, such as porosity and lithological fractions, from the same set of seismic attributes. The advantage of the expectation–maximization method is that this algorithm does not require a training dataset, which is instead required in a traditional Bayesian classifier and still provides similar results. We show the application, comparison, and analysis of these methods in a real case study in the North Sea, where eight sedimentological facies have been defined. The facies classification is computed at the well location and compared with the sedimentological profile and then extended to the 3D reservoir model using up to 14 seismic attributes.     

裂缝诱导双相HTI介质地震波场错格伪谱法模拟与波场特征分析

裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征.