Flow Simulations To Evaluate Upscaling of Permeability

We study upscaling of the permeability for porous media flow on a grid with one million blocks. The purpose is to illustrate how flow simulations can be used to evaluate upscaling methods.     

Permeability Upscaling Measured on a Block of Berea Sandstone: Results and Interpretation

To physically investigate permeability upscaling, over 13,000 permeability values were measured with four different sample supports (i.e., sample volumes) on a block of Berea Sandstone. At each sample support, spatially exhaustive permeability datasets were measured, subject to consistent flow geometry and boundary conditions, with a specially adapted minipermeameter test system. Here, we present and analyze a subset of the data consisting of 2304 permeability values collected from a single block face oriented normal to stratification. Results reveal a number of distinct and consistent trends (i.e., upscaling) relating changes in key summary statistics to an increasing sample support. Examples include the sample mean and semivariogram range that increase with increasing sample support and the sample variance that decreases. To help interpret the measured mean upscaling, we compared it to theoretical models that are only available for somewhat different flow geometries. The comparison suggests that the nonuniform flow imposed by the minipermeameter coupled with permeability anisotropy at the scale of the local support (i.e., smallest sample support for which data is available) are the primary controls on the measured upscaling. This work demonstrates, experimentally, that it is not always appropriate to treat the local-support permeability as an intrinsic feature of the porous medium, that is, independent of its conditions of measurement.     

Mortar Upscaling for Multiphase Flow in Porous Media

In mortar space upscaling methods, a reservoir is decomposed into a series of subdomains (blocks) in which independently constructed numerical grids and possibly different physical models and discretization techniques can be employed in each block. Physically meaningful matching conditions are imposed on block interfaces in a numerically stable and accurate way using mortar finite element spaces. Coarse mortar grids and fine subdomain grids provide two-scale approximations. In the resulting effective solution flow is computed in subdomains on the fine scale while fluxes are matched on the coarse scale. In addition the flexibility to vary adaptively the number of interface degrees of freedom leads to more accurate multiscale approximations. This methodology has been implemented in the Center for Subsurface Modeling's multiphysics multiblock simulator IPARS (Integrated Parallel Accurate reservoir Simulator). Computational experiments demonstrate that this approach is scalable in parallel and it can be applied to non-matching grids across the interface, multinumerics and multiphysics models, and mortar adaptivity. Moreover unlike most upscaling approaches the underlying systems can be treated fully implicitly.     

JHomogenizer: a computational tool for upscaling permeability for flow in heterogeneous porous media

This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly.     

Adaptive hierarchical upscaling of flow in heterogeneous reservoirs based on an a posteriori error estimate

This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool.     

Upscaling of elastic properties for large scale geomechanical simulations

Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical Homogenization of Two-Phase Flow in Porous Media

Homogenization has proved its effectiveness as a method of upscaling for linear problems, as they occur in single-phase porous media flow for arbitrary heterogeneous rocks. Here we extend the classical homogenization approach to nonlinear problems by considering incompressible, immiscible two-phase porous media flow. The extensions have been based on the principle of preservation of form, stating that the mathematical form of the fine-scale equations should be preserved as much as possible on the coarse scale. This principle leads to the required extensions, while making the physics underlying homogenization transparent. The method is process-independent in a way that coarse-scale results obtained for a particular reservoir can be used in any simulation, irrespective of the scenario that is simulated. Homogenization is based on steady-state flow equations with periodic boundary conditions for the capillary pressure. The resulting equations are solved numerically by two complementary finite element methods. This makes it possible to assess a posteriori error bounds.     

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

非饱和带水气二相流动参数确定实验研究

对非饱和带水气二相流动的关键参数确定,尤其是二相流动中气相参数确定的实验方法进行了探索,得出了相应的参数结果,建立了气压自动采集系统,为进一步的非饱和带水气二相流动的实验模拟与数值模拟提供了参数依据。     

Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements

In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors.     

ICA及其在气液两相流辨识中的应用

应用独立分量分析（ICA）方法研究气液两相流的辨识问题。根据基于高阶统计量的改进J-H ICA求解算法,利用给定仿真信号及不同流量油、气、水单相流体响应信号,模拟两相、三相混合信源进行分离实验,验证该方法的可靠性,并对生产井实测气液两相流体多路传感器响应信号进行分离。对比及分析分离结果表明,该方法成功地从混合信号中分离出表征气、液特征的源信号,达到了辨识目的。     

非饱和带水-气二相流数值模拟研究进展

通过对近年来水-气二相流数值模拟情况的分析,总结了在水-气二相流模拟过程中,各个主要参数或物理过程的数学概化方法,以及近年来求解水-气二相流方程和污染物运移方程的各种方法,论述了各种方法的优点和不足.并提出了需进一步研究解决的问题.     

A Velocity-Based Approach to Visco-Elastic Flow of Rock

In structural geology, viscous creep is generally recognized as the major deformation mechanism in the folding of rock layers through geological time scales of hundreds of thousands of years. Moreover, since deformation of rock salt by creep takes already place on relatively small time scales—weeks to months, say—creep is a relevant phenomenon when studying salt mining, notably the convergence of mine cavities and the land subsidence caused by it. While creep is the dominant process on relatively long time scales, elasticity plays a dominant role in processes that take place on relatively short time scales. The elastic response to a stress is a displacement; the shape of the rock is deformed instantaneously with respect to its initial shape. However, the viscous response of a rock to a stress is a relatively low velocity in the order of millimeters per months or years, say. In this paper we consider the two deformation phenomena creep and elasticity. In general, elasticity is a compressible phenomenon, while creep is incompressible. Here we approximate creep by the introduction of a negligibly small amount of compressibility, which makes creep velocity calculations similar to conventional elastic displacement calculations. Using this procedure, a standard finite element package for elasticity can be applied to viscous problems, also in combination with elasticity. The method has been demonstrated to upscaling of creep viscosities.     

青藏铁路多年冻土区热棒的施工技术

青藏铁路要穿越550 km长的多年冻土区,其中年平均地温>-1.0℃的高温多年冻土路段275 km,高含冰量冻土类型路段长221 km.为确保路基工程的整体稳定,部分地段采用了热棒处理措施.热棒路基利用自然能源,在温差作用下驱动内部制冷工质的汽液两相对流循环,通过蒸发段蒸发吸热作用降低周围冻土温度,增加冻土本身的冷储量,提高热稳定性,保护多年冻土.热棒技术是一种有着广阔应用前景的新技术,尤其是在全球气温升高大环境下,其作用更为明显.针对热棒的工作原理和施工技术进行了系统的总结分析,实践证明,热棒能够很好的防止多年冻土的融沉、冻胀病害,已在青藏铁路、公路多年冻土区路基试验段取得重要的阶段成果,以后将会在多年冻土区施工中逐步推广应用.     

流体性质转换机制在重力流沉积体系分析中应用初探

自1950年Kuenen发表"浊流形成粒序层理"一文至今,深水重力流研究取得了长足发展。然而,目前很多学者不仅对浊流理论分歧很大,而且对浊流概念、术语的使用也有不同的观点,这严重制约了重力流的分类及重力流沉积体系的识别。本文在重力流沉积过程和流态研究的基础上,提出了基于"流体性质转换"理论的重力流沉积体系分析方法。研究认为,重力流在形成、发展和消亡过程中不仅存在多个流体阶段,而且存在着多种流态之间的转换。这种流体发育的最终阶段特征决定了重力流沉积体系的形态与类别,而流态共存与转换的特性造成了深水紊流成因的浊积岩与其他流体成因的岩相共存的沉积特征。根据这一理论对牵引流—碎屑流成因的扇三角洲体系、浊流成因的近岸水下扇体系和碎屑流成因的斜坡裙体系进行成因分析与特征对比,阐述了"流体性质转换"理论在沉积体系识别中的作用。     

中温UBF与UASB两相厌氧系统处理垃圾渗滤液的实验研究

针对石碑岭垃圾场渗滤液水质特性,采用以高效生物陶粒为填料的UBF反应器作酸化相,以UASB反应器作甲烷相的两相厌氧系统进行了处理垃圾渗滤液的实验研究.实验结果表明:在系统进水CODCr和BOD5质量浓度分别为3 887 mg/L和819 mg/L,UBF与UASB的HRT分别控制在10.3 h和61.7 h时,CODCr和BOD5总去除率分别为85.4%和90.1%,UBF酸化率达42.9%,BOD5/CODCr比值由0.21提高到0.39.     

用估算热收支的方法评价热棒制冷效果

利用青藏铁路路基地质钻孔资料和地温资料,通过计算随地温变化的热收支、来自近地表的热量、来自深部的热量、以及冻土上限变化引起的相变热,来估算测温孔在水平方向的热收支.通过对比热棒路基、普通路基的右路肩孔以及天然孔水平热收支的差异,来描述热棒的工作效果.之后,对比了热棒路基左路肩孔(阳坡)和右路肩孔(阴坡)水平热收支的差异,并给出解释.最后,以热棒路基右路肩孔水平热收支为基础估算了整个路基的水平热收支,进而给出了单个热棒的平均"产冷量".     

油气成藏流体动力系统分析原理及应用

阐述了油气成藏流体动力系统分析的基本原理,把油气成藏流体动力系统分为重力驱动型、压实驱动型、滞流型和封存型四种类型。结合国内外的研究实例,分析了不同类型流体动力系统油气藏形成和分布的规律,强调在不同类型的流体动力系统中,油气藏形成的机理不同,在成藏动力学研究中有不同的侧重点。加强重力驱动型和封存型流体动力系统动力系统油气成藏条件研究对我国南方海相盆地和其它勘探程度较高的盆地深部的油气勘探具有重要意义。     

Prediction of Flowing Bottomhole Pressures for Two-Phase Coalbed Methane Wells

A method is proposed to predict the flowing bottomhole pressures(FBHPs)for two-phase coalbed methane(CBM)wells.The mathematical models for both gas column pressure and two-phase fluid column pressure were developed based on the well liquid flow equation.FBHPs during the production were predicted by considering the effect of entrained liquid on gravitational gradients.Comparison of calculated BHPs by Cullender-Smith and proposed method was also studied.The results show that the proposed algorithm gives the desired accuracy of calculating BHPs in the lowproductivity and low-pressure CBM wells.FBHP is resulted from the combined action of wellhead pressure,gas column pressure and fluid column pressure.Variation of kinetic energy term,compressibility and friction factors with depth increments and liquid holdup with velocity should be considered to simulate the real BHPs adequately.BHP is a function of depth of each column segment.The small errors of less than 1.5%between the calculated and measured values are obtained with each segment within 25 m.Adjusting BHPs can effectively increase production pressure drop,which is beneficial to CBM desorption and enhances reservoir productivity.The increment of pressure drop from 5.37 MPa2 to 8.66 MPa2 leads to an increase of CBM production from 3270 m3/d to 6700 m3/d and is attributed to a decrease in BHP from 2.25 MPa to 1.33 MPa.