Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speed-up in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.     

高阶煤煤岩毛管压力曲线新数学模型及关键参数

毛管压力是影响煤层气赋存和开发的重要参数,为建立能够有效表征高阶煤煤岩毛管压力曲线的数学模型,以高阶煤为研究对象,开展了高压压汞实验,系统评价了目前常用的典型毛管压力曲线数学模型的适应性,建立拟合程度更高的数学模型。结果表明,6块高阶煤煤样毛管压力曲线基本没有中间平缓段,整体表现为向左上方凸出的形态,与常规砂岩、低阶煤差异明显;BC模型、贺承祖模型和Li模型均不能很好地拟合高阶煤的毛管压力曲线;建立的新毛管压力曲线数学模型,能够很好地拟合高煤阶煤样毛管压力实验数据,拟合程度达到97%以上;在双对数坐标中,毛管压力和最小毛管压力的对数差与进汞饱和度与最小毛管压力的对数差呈线性关系,可利用该线性关系直接求取毛管压力模型的斜率a和幂指数b,求解步骤较为简单;在其他条件相同时,毛管压力与斜率a和幂指数b均成反比。     

库水位下降时的岸坡非稳定渗流问题研究

水位下降时岸坡的渗流是涉及土体由饱和向非饱和状态过渡的水-气二相流过程,目前相关研究成果大都假设孔隙气压力为0,忽略孔隙气的影响。根据水、空气的质量守恒定律和达西定律,结合多相流理论建立水-气二相流模型,采用高效的积分有限差分法求解,通过变换主要变量,实现饱和（单相）与非饱和（二相）的相互转变,并给出各种边界条件下合理的数学处理方法。通过Muskat渗流问题,验证了上述模型的正确性;并对某土质岸坡水位下降时的非稳定渗流问题进行分析,结果表明,岸坡的基质吸力小于浸润线以上的负孔隙水压力,在浸润线以上的很大区域为毛细管水饱和带,其土体饱和且基质吸力为0,这对边坡稳定十分不利,精确分析水位下降的边坡稳定问题时,孔隙气压力变化的影响值得研究。     

低含水率非饱和高温冻土模型

在低含水率非饱和土模型的基础上,从冻土物理特性出发,只考虑毛细吸力和附加压力的作用,建立了非饱和高温冻土细观结构模型,并结合相关实验数据资料改进了高温冻土未冻水含量的经验关系式,基此推导出孔隙水压力、有效应力以及抗剪强度随温度、含水量的变化关系. 同时,通过理论计算与实验（实测）结果进行对比分析,发现本模型能够很好地反映非饱和高温冻土的相关物理力学特性,尤其在定性上能够与宏观实测结果相吻合. 最后,基于非饱和高温冻土微观模型,对非饱和高温冻土的有效应力、抗剪强度进行了讨论分析,给出了合理的理论解释,并对高温冻土相关物理力学特性做出了定性的理论预测.     

天然气的加速式二次运移过程研究

在静水条件下,游离相天然气运移的主要动力是浮力,阻力是毛细管力。根据前人的实验数据,通过理论计算发现,浮力和毛细管力均受地层温度和压力的影响,气体在储层中上浮的临界高度随地层温度和压力的降低而增大。根据气体状态方程及天然气运移的动力学理论,推导出温度和压力降低前、后气体流速比方程,用其计算了不同储层中临界气体长度并分析不同储层中相同长度的气体在运移途中的变化规律。由此发现,在运载层物性不变的情况下,天然气沿上倾地层向上倾方向运移的过程,是随地层温度和压力不断降低、其运移速度逐渐增大的过程,如果有后续气体的加入,会使气体长度增大,致使运移速度增加得更快。     

Modelling of elastoplastic damage in concrete due to desiccation shrinkage

We present a numerical modelling of elastoplastic damage due to drying shrinkage of concrete in the framework of mechanics of partially saturated porous media. An elastoplastic model coupled with isotropic damage is first formulated. Two plastic flow mechanisms are involved, controlled by applied stress and suction, respectively. A general concept of net effective stress is used in take into account effects of capillary pressure and material damage on stress‐controlled plastic deformation. Damage evolution depends both on elastic and plastic strains. The model's parameters are determined or chosen from relevant experimental data. Comparisons between numerical simulations and experimental data are presented to show the capacity of model to reproduce mains features of concrete behaviour under mechanical loading and during drying shrinkage of concrete. An example of application concerning drying of a concrete wall is finally presented. The results obtained allow to show potential capacity of proposed model for numerical modelling of complex coupling processes in concrete structures. Copyright © 2002 John Wiley & Sons, Ltd.     

深部咸水层二氧化碳封存的干化效应及选址启示

将二氧化碳注入到深部咸水层中,形成复杂的多组分、多相流系统。二氧化碳在压力梯度、浓度差作用下不断扩散,逐步带走盐溶液中的水分,导致各组分的相态变化,盐结晶析出,阻塞了咸水层孔隙通道,从而降低了二氧化碳的注入效率,研究该干化效应的影响因素并为工程选址提供依据具有重要意义。采用二维径向模型建立多相流体的流动方程,并结合相对渗透率和毛细压力方程探讨二氧化碳注入速率、咸水层含盐量、毛细压力的特征参数对干化效应的影响,干化效应可用固体饱和度值进行定量描述。结果表明：二氧化碳运移分3个区域：干涸区、气液相混合区及液相咸水区,干化效应主要发生在井周的干涸区。在毛细作用下固体饱和度随注入速率的减小而增大,随咸水层含盐量增大而增大,随毛细作用增大而增大。因此,提高二氧化碳的注入速率,向咸水层中注水稀释含盐量或选择粒径较大的均质咸水层减小毛细作用,均可降低盐结晶对孔隙通道的阻塞,提高注入效率。     

多孔介质两相系统毛细压力与饱和度关系试验研究

两相系统毛细压力-饱和度(h~S)关系曲线的确定是多孔介质多相流动研究的基础。采用简易试验装置对理想和实际介质中水-气和油-水两相系统中的h~S关系曲线进行了测定。试验结果表明,对于相同两相系统,多孔介质孔隙度愈小,同一毛细压力对应的饱和度相应愈大;对于不同两相系统,理想介质的关系曲线在一定毛细压力以下平缓,较大毛细压力时陡直,实际介质关系曲线走势相对较陡。分析结果表明,水-气和油-水两相系统的实测数据符合Parker等提出的基于van Genuchten(1980)关系式的折算理论;应用折算理论,可以在同一多孔介质某一两相系统h~S关系已知的情况下较好地估计同一孔隙度条件下其它两相系统的h~S关系曲线。     

Analysis of A New Model for Unsaturated Flow in Porous Media Including Hysteresis and Dynamic Effects

A new model for unsaturated flow in porous media, including capillary hysteresis and dynamic capillary effects, is analyzed. Existence and uniqueness of solutions are established and qualitative and quantitative properties of (particular) solutions are analyzed. Some results of numerical computations are given. The model under consideration incorporates simple ‘play’-type hysteresis and a dynamic term (time-derivative with respect to water content) in the capillary relation. Given an initial water content distribution, the model determines which parts of the flow domain are in drainage and which parts are in imbibition. The governing equations can be recast into an elliptic problem for fluid pressure and an evolution equation for water content. Standard methods are used to obtain numerical results. A comparison is given between J.R. Philip's semi-explicit similarity solution for horizontal redistribution in an infinite one-dimensional domain and solutions of the new model.     

综合压裂技术在低压致密气藏储层中的研究与应用

大牛地气田储层属于低压致密气层,非均质性强、孔喉直径小、毛管压力高、多层叠置且层间跨度不等导致储层保护和加砂压裂难度大。通过研究提出了采用液氮增能低伤害压裂液体系,降低对储层的伤害,有效地保护了储层;采用大型加砂压裂技术,增加了裂缝长度,扩大了泄气面积,提高了单层产量,气产量由200 m³/d提高到7.23×10⁴ m³/d;采用不动管柱连续分层压裂工艺技术实现了多层叠置气层均衡改造,压裂投产作业时间缩短了近67%,费用降低了20.69%。     

Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.     

On the capillary stress tensor in wet granular materials

This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based on numerical experiments using the discrete element method, compared with a microstructural elastoplastic model. Water effects are taken into account by adding capillary menisci at contacts and their consequences in terms of force and water volume are studied. Simulations of triaxial compression tests are used to investigate both macro and micro‐effects of a partial saturation. The results provided by the two methods appear to be in good agreement, reproducing the major trends of a partially saturated granular assembly, such as the increase in the shear strength and the hardening with suction. Moreover, a capillary stress tensor is exhibited from capillary forces by using homogenization techniques. Both macroscopic and microscopic considerations emphasize an induced anisotropy of the capillary stress tensor in relation with the pore fluid distribution inside the material. Insofar as the tensorial nature of this fluid fabric implies shear effects on the solid phase associated with suction, a comparison has been made with the standard equivalent pore pressure assumption. It is shown that water effects induce microstructural phenomena that cannot be considered at the macro level, particularly when dealing with material history. Thus, the study points out that unsaturated soil stress definitions should include, besides the macroscopic stresses such as the total stress, the microscopic interparticle stresses such as the ones resulting from capillary forces, in order to interpret more precisely the implications of the pore fluid on the mechanical behaviour of granular materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

Recovery from incompletely water-wet fractured reservoirs can be extremely low. A reason for the low recovery is related to wetting issues, whereas the reason for slow recovery can be the non-equilibrium behavior of capillary pressure. One of the non-equilibrium theories is developed by Barenblatt et al. and it modifies both capillary pressure and relative permeabilities. The other theory is developed by Hassanizadeh et al. and it only deals with non-equilibrium effects for capillary pressure. To incorporate non-equilibrium in larger-scale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the non-equilibrium effects are included. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use simulations to determine the range of delay times and capillary-damping coefficients for which discernable effects occur in terms of oil recovery. It is shown that at low Peclet numbers, i.e., when the residence time of the fluids in the fracture is long with respect to the imbibition time, incorporation of delay times of the order of few months have no significant effect on the oil recovery. However, when the Peclet number is large, the delay times reduce the rate of oil recovery. We discuss for which values of the delay time (Barenblatt) and capillary-damping coefficient (Hassanizadeh), significant delays in oil production occur.     

Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible,three-phase flow with gravity

Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model). Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation). The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities. The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/ sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of nonlinear compressible multiphase flow in strongly heterogeneous formations.     

Dynamic capillary effects in heterogeneous porous media

In standard multi-phase flow models on porous media, a capillary pressure saturation relationship developed under static conditions is assumed. Recent experiments have shown that this static relationship cannot explain dynamic effects as seen for example in outflow experiments. In this paper, we use a static capillary pressure model and a dynamic capillary pressure model based on the concept of Hassanizadeh and Gray and examine the behavior with respect to material interfaces. We introduce a new numerical scheme for the one-dimensional case using a Lagrange multiplier approach and develop a suitable interface condition. The behavior at the interface is discussed and verified by various numerical simulations.     

利用核磁共振T2分布构造毛管压力曲线的新方法

根据实验分析,提出一种新的构建方法,该方法对单峰T2 谱,用单一幂函数构造毛管压力曲线;利用核磁共振(NMR)T2 分布与孔隙结构直接相关,可以利用T2分布来构建毛管压力曲线.对双峰T2 谱则用两种不同的幂函数在小孔和大孔处分段构造毛管压力曲线.分别利用线性方法和幂函数方法构建毛管压力曲线,与实验测量得到的毛管压力曲线相对比,新方法对于毛管压力曲线的构造精度有明显改进.     

Pore to pore validation of pore network modelling against micromodel experiment results

Pore network modelling (PNM) has been widely used to study the multiphase flow and transport in porous media. Although a number of recent papers discussed the PNM validation on core-scale parameters such as permeability, relative permeability and capillary pressure; quantitative predictive potential of PNM on pore by pore basis has rarely been studied. The aim of this paper is to present a direct comparison between PNM simulations and corresponding micro-model experiments at the same scale and the same geometry. A number of well-defined and constrained two-phase flow in porous medium experimental scenarios were utilized to validate the physics solving part in PNM (filling rules, capillary and viscous pressure). This work validates that a dynamic pore network flow solver can predict two-phase flow displacements for these experiments for drainage situations at both pore and plug scales. A glass-etched micro-model is used to quantify the accuracy of a dynamic PNM solver on pore and core levels. Two-phase drainage micro fluidic experiments at different flow conditions are performed on micro-models. PNM simulations are performed on the same pattern and flow conditions as used in micro-model experiments. The two-phase distribution extracted from experiment images is registered onto rsults of PNM simulations for direct pore to pore comparison. Pore-scale matching level is found at around 75 % for all three test cases. The matching level of core-scale parameters such as S _{w c} and oil-phase permeability varies from case to case; the relative error to micro-model experiment measurements varies from 15 to 60 %. Possible reasons leading to discrepancies on core-scale parameters are discussed: missing considerations during validation of the combination of uncertainty in both simulator input parameters and experiments are seen as the principal factors.     

非离子表面活性剂对两相系统毛细压力和饱和度关系的影响

表面活性剂至水相的引入将对原先包含纯水两相系统的毛细压力和饱和度关系存在影响.对含有非离子表面活性剂Triton X-100的水-气和水-油两相系统中的毛细压力-饱和度关系曲线进行了试验测定.试验结果表明,同不含表面活性剂的纯水系列相比,在同一饱和度情况下,含有表面活性剂的Triton X-100(0.1%)系列对应的毛细压力水头值都有不同程度的减小,说明在Triton X-100存在的情况下,驱替出同样数量的湿润相体积所需的毛细压力值较小.以van Genuchten关系式为基础的拟合结果表明,在已知纯水系列毛细压力饱和度关系的情况下,对于Triton X-100-气系统的毛细压力饱和度关系,考虑界面张力降低作用引入折算系数得到的拟合值更接近于真实值;而对于Triton X-100-油系统拟合值接近真实值的程度则随多孔介质的不同而有所不同.     

辽河油田东部凹陷火成岩储层孔隙结构评价

对火成岩储层的核磁共振测井资料和实验室压汞资料进行对比,采用插值法建立地层孔隙流体的横向弛豫时间T_2与压汞曲线的压力P_C之间的关系,发现它们之间满足对数关系,并用T_2谱构造毛管压力曲线。分别利用线性方法和对数方法构造毛管压力曲线,对数方法构造的毛管压力曲线与实验测量的毛管压力曲线更接近。将研究结果应用于辽河油田东部凹陷火成岩储层孔隙结构的评价中,发现分选系数小、孔喉歪度大、最大进汞饱和度高和平均孔喉半径大的毛管应力曲线对应的孔隙结构较好。     

南堡凹陷1号构造断层垂向封闭能力定量评价

通过对断裂带内部结构及其特征研究发现,断层岩是断层构成的重要部分,断层垂向封闭能力的强弱关键取决于油气运移方向断层岩与下伏储层岩石的排替压力差.若断层岩排替压力大于等于储层岩石,断层垂向封闭,其封闭能力的大小取决于二者排替压力差值的大小,差值越大,断层垂向封闭能力越强;反之断层垂向开启.断层岩的排替压力大小受泥质含量、压实成岩程度、岩石结构方向性等因素的影响,其泥质含量越高、压实成岩程度越大、断面方向与铅直方向夹角越小,断层岩排替压力越大.基于断层垂向封闭机理及影响因素,综合实验室不同角度泥岩样品排替压力测试结果与岩石力学分解关系,在确定与目标点断层岩具有相同压实成岩程度围岩地层的基础上,建立了一套定量评价断层垂向封闭能力的方法,并将其应用于渤海湾盆地南堡凹陷1号构造内典型断层垂向封闭能力评价中,结果表明:f1断层在不同测线处的断-储排替压力差为-0.114~1.035 MPa,除L7~L11测线处其他测线内断层岩排替压力均大于储层岩石,断层垂向封闭,与油气分布吻合关系较好.通过与未考虑岩石结构方向性方法的比较,证实该方法具有更好的可行性和更高的可信度.