多种计算方法确定黄土渗透系数的对比分析

渗透系数是工程降水设计重要的水文地质参数之一,由于水文地质本身的复杂性和计算的多样性,致使渗透系数计算值往往存在着较大的差异。而对于渗透系数的计算模型较多,究竟哪种数学计算模型比较接近黄土渗透性的实际情况,不同的专家有不同的观点。以西安地铁四号线火车站地下车站段抽水试验为例,运用了完整井稳定流中的单井法、带观测井法考虑井损的单井法数学计算模型,非完整井稳定流数学计算模型,水位恢复法数学计算模型3种方法综合确定黄土的渗透系数。分析对比了各种数学计算模型优缺点,给出了计算黄土渗透系数较为合理的数学计算模型。     

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.     

Permeability tensors for sedimentary structures

Accurate modeling of fluid flow through sedimentary units is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. Most sedimentary rocks display structure from the mm or cm scale upwards. Flow simulation should therefore begin with grid blocks of this size in order to calculate effective permeabilities for larger structures. In this paper, we investigate several flow models for sandstones, and examine their impact on the calculation of effective permeability for single phase flow. Crossflow arises in some structures, in which case it may be necessary to use a tensor representation of the effective permeability. We establish conditions under which tensors are required, e.g., in crossbedded structures with a high bedding angle, high permeability contrast, and laminae of comparable thickness. Cases where the off-diagonal terms can be neglected, such as in symmetrical systems, are also illustrated. We indicate how the method of calculating tensor permeabilities may be extended to model multiphase flow in sedimentary structures.     

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.     

用试井资料研究低渗透裂缝性油藏渗流模式及演化特征——以准噶尔盆地火烧山油田为例

对于注水开发多年,尤其是多次采取增产增注措施后的油藏,如何准确地判定低渗透非均质储集层渗流特征及其演化规律,难度比较大。针对火烧山低渗透裂缝性油藏,根据不稳定试井曲线识别储层模型,分析了不同开发阶段储层渗流系统的演化规律。由于火烧山油田天然裂缝发育,而且多数井采用压裂方式进行投产,开发初期储层模型主要表现为人工裂缝或双孔模型。开发过程中,随着地层压力的降低及调剖堵水措施的实施,油井渗流特征往单孔模型转变、注水井渗流系统向径向复合模型转变;渗流系统的演化改变了储层的有效渗透率,使其整体上呈现降低的趋势。储层初期有效渗透率场与油井水窜特征基本吻合,有效渗透率的逐步下降与油藏含水上升速度的下降基本吻合,从而为油藏下一步开发调整可行性评价提供了重要依据。     

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Large-scale implementation of geological CO₂ sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO₂ involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO₂ injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO₂ plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical–analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO₂ sequestration problems.     

基于广义径向流模型的非均质孔隙含水层井流试验分析

Theis模型、Dupuit模型等经典井流模型分析非均质含水层井流试验数据有一定的局限性,获取的参数不适合表征非均质含水层特性。而GRF模型可以获取含水层流动特性的数据。相比于Theis模型、Dupuit模型,GRF模型更能表征非均质含水层特性。以黄石东湖新村棋盘洲长江大桥的抽水试验数据为例,采用Theis模型和GRF模型计算含水层渗透系数,结合实际水文地质条件,对比分析不同方法计算的水文地质参数,并计算含水层水流维数和表观压力传导系数（K_f /S_sf）。结果表明:研究区含水层为细砂夹条带状黏土透镜体的非均质含水层,采用GRF模型计算结果更符合实际情况,渗透系数为 4.09×10?3cm/s;含水层水流维数为1.61,地下水为双线性流动状态,含水层对抽水试验的响应主要受黏土条带控制;观测井和抽水主井的K_f /S_sf呈非线性相关,进一步验证了含水层的非均质性。在非均质孔隙含水层中,应用多孔联合非稳定GRF井流试验方法不仅能确定水文地质参数,并且能丰富对含水层特性的认知。     

致密煤层气藏三维全隐式数值模拟

我国煤层普遍存在低渗、低储层压力和低含气饱和度等不利条件,许多研究表明,低渗透多孔介质中的气体运移存在启动压力梯度。为了让数值模拟模型能更加准确地描述致密煤储层中流体的运移特性,基于前人的研究成果,建立了考虑启动压力梯度的致密煤层气藏三维、非平衡吸附、拟稳态条件下气、水两相耦合流动数值模拟模型,并给出了模型的全隐式有限差分格式和数值求解方法。最后利用沁水盆地某生产井的试井资料进行了模拟计算,模拟结果表明,在其他条件相同的情况下,启动压力梯度的存在使得煤层的降压效果变差,且延迟了产气高峰的到来。对比该井的开采资料,模拟结果是合理的,模型能正确反映致密煤层气藏中流体的运移特征。     

页岩气开采的相关实验、模型和环境效应

页岩气是一种重要的非常规天然气资源,正在改变世界能源、经济和政治格局。渗透率是评价页岩气藏商业开采可行性的重要参数之一,由于页岩的致密性,页岩气的流动机理不同于常规气藏,因此,页岩储层渗透率测试和页岩气流动模型已成为当前国际研究的热点课题之一。在对页岩气开采技术简单介绍的基础上,综述了页岩储层渗透率测试的试验和理论研究现状,分析了气体吸附对页岩渗透率的影响。阐述了页岩气流动模型的最新进展,分析了双重孔隙模型描述气体迁移的准确性,提出了描述均匀储层中页岩气解吸-扩散-渗流多级运移模型。评述了页岩气开采的温室效应和对地下水的影响,并简单介绍了适合页岩气开采的新技术即无水压裂开采技术,即采用CO2对页岩气藏分段压裂,同时将CO2埋存于废弃井中。最后,对页岩储层渗透率测试和页岩气流动模型研究的新发展以及无水压裂技术进行了展望。     

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.     

正常固结软土渗透系数与固结应力关系研究

从固结系数的定义出发,将压缩系数视为变量,建立了渗透系数与固结应力的微分方程,求得了软土正常固结状态时,考虑前期固结压力的渗透系数随固结应力变化关系表达式。利用室内试验数据,将提出的公式与现有渗透系数与固结应力关系式、试验结果进行对比。研究表明,所提出的公式能较好地反映渗透系数随固结应力变化的特点,比未考虑前期固结压力的计算式更接近于实际情况,从而为实际工程中预估固结变形速率提供了一种较为准确的方法。     

Calculation of Well Index for Nonconventional Wells on Arbitrary Grids

Wells are seldom modeled explicitly in large scale finite difference reservoir simulations. Instead, the well is coupled to the reservoir through the use of a well index, which relates wellbore flow rate and pressure to grid block quantities. The use of an accurate well index is essential for the detailed modeling of nonconventional wells; i.e., wells with an arbitrary trajectory or multiple branches. The determination of a well index for such problems is complicated, particularly when the simulation grid is irregular or unstructured. In this work, a general framework for the calculation of accurate well indices for general nonconventional wells on arbitrary grids is presented and applied. The method entails the use of an accurate semianalytical well model based on Green's functions as a reference single phase flow solution. This result is coupled with a finite difference calculation to provide an accurate well index for each grid block containing a well segment. The method is demonstrated on a number of homogeneous example cases involving deviated, horizontal and multilateral wells oriented skew to the grid. Both Cartesian and globally unstructured multiblock grids are considered. In all these cases, the method is shown to provide results that are considerably more accurate compared to results using standard procedures. The method is also applied to heterogeneous problems involving horizontal wells, where it is shown to be capable of approximating the effects of subgrid heterogeneity in coarse finite difference models.     

Upscaled modeling of well singularity for simulating flow in heterogeneous formations

Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine scale solutions in near-well scale-up calculations.     

Uncertainty quantification of two-phase flow problems via measure theory and the generalized multiscale finite element method

The problem of multiphase phase flow in heterogeneous subsurface porous media is one involving many uncertainties. In particular, the permeability of the medium is an important aspect of the model that is inherently uncertain. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and future decisions. In this work, a measure-theoretic framework is employed to quantify uncertainties in a two-phase subsurface flow model in high-contrast media. Given uncertain saturation data from observation wells, the stochastic inverse problem is solved numerically in order to obtain a probability measure on the space of unknown permeability parameters characterizing the two-phase flow. As solving the stochastic inverse problem requires a number of forward model solves, we also incorporate the use of a conservative version of the generalized multiscale finite element method for added efficiency. The parameter-space probability measure is used in order to make predictions of saturation values where measurements are not available, and to validate the effectiveness of the proposed approach in the context of fine and coarse model solves. A number of numerical examples are offered to illustrate the measure-theoretic methodology for solving the stochastic inverse problem using both fine and coarse solution schemes.     

致密砂岩气藏储层流动单元划分方法及随机模拟

针对致密砂岩气藏开发中所面临的难题,以及流动单元划分中存在的问题,提出了一套致密砂岩储层流动单元划分新方法。根据流动单元的定义及其地质意义,在取心井定性和定量分析的基础上,确定了孔隙度、渗透率、流动层指数和Winland r35 四个参数作为流动单元划分的指标。应用储层层次分析的研究思路,结合致密砂岩气藏的工业气流标准,识别了渗流屏障,并通过聚类分析、判别分析等统计学方法建立了连同体内部流动单元的定量识别模式,实现了流动单元由取心井到非取心井的定量识别,最后利用序贯指示模拟方法建立了流动单元的三维地质模型。进一步研究表明,应用储层流动单元方法不仅精细地刻画了河流相储层的空间非均质性,而且不同的流动单元对应着不同的开发效果。其中,A类流动单元开发效果最好,B类流动单元开发效果次之,是挖潜的主要目标,C类流动单元开发效果最差。     

Identifying the Representative Elementary Volume for Permeability in Heterolithic Deposits Using Numerical Rock Models

Using a range of realistic 3D numerical lithofacies (dm-scale) models of ripple laminated sandstone intercalated with mudstone we evaluate how single-phase permeability varies as a function of sample support. The models represent a range of mudstone content which is typical for tidal deposits. Furthermore, the spatial distribution of flow barriers (i.e. mudstone) is not random, but governed by sedimentological rules giving a variable anisotropy ratio as a function of mudstone content. Both vertical and horizontal permeability are found to vary at small sample volumes, but these fluctuations reduce as the sample volume increases. The vertical permeability increases while the horizontal permeability is nearly constant as a function of sample support for small mudstone contents. For higher mudstone content, the horizontal permeability decreases while the vertical permeability is nearly constant as a function of sample support. We propose a criterion, based on a normalised standard deviation, to determine the Representative Elementary Volume (REV). The size of the REV is dependent on both the property measured (vertical and horizontal permeability) and the correlation lengths of the lithological elements (i.e. lithofacies). Based on this we identify three flow upscaling regimes that each require a different method for upscaling: (1) layered systems where the arithmetic and harmonic averages are appropriate, (2) systems close to the percolation threshold where a percolation model should be used, and (3) discontinuous systems where an effective medium method provides the best estimate of permeability. The work gives, by using numerical experiments on a range of heterogeneous systems, a new insight in determination of the REV for permeability at the lithofacies scale and its relation to sedimentological parameters.     

Numerical simulation of groundwater flowing to horizontal seepage wells under a river

A horizontal seepage well, consisting of an interconnected vertical well, galleries, chambers and small-diameter radiating bores, is used to acquire relatively clean water that has been filtered through natural alluvial deposits in a riverbed. It has wide application, especially in arid and semi-arid areas. The lack of calculation formulae or models for horizontal seepage wells, up until now, has resulted in several false applications. Based on the analysis of groundwater flow characteristics, it has been concluded that several flow regimes coexist and hydraulic head loss exists in the horizontal seepage well. To avoid the difficulty of confirming the flux or head distribution in such a complex system, the model boundary of the whole horizontal seepage well has been moved to that of just the vertical well, and the well-aquifer system was treated as a heterogeneous medium, where the horizontal seepage well itself is a highly permeability medium. A mathematical model has been developed, based on the coupled seepage-pipe flow, by the introduction of equivalent hydraulic conductivity according to different flow regimes. Then a three-dimensional finite difference numerical model, based on the mathematical model, was developed and applied to a horizontal seepage well in China. The numerical model verified the groundwater flow characteristics of the horizontal seepage well. An erratum to this article can be found at     

Immiscible two-phase Darcy flow model accounting for vanishing and discontinuous capillary pressures: application to the flow in fractured porous media

Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom.     

Production rate analysis of multiple-fractured horizontal wells in shale gas reservoirs by a trilinear flow model

Most multiple-fractured horizontal wells experience long-term linear flow due to the ultralow permeability of shale gas reservoirs. Considering the existence of natural fractures caused by compression and shear stresses during the process of tectonic movement or the expansion of high-pressure gas, a shale gas reservoir can be more appropriately described by dual-porosity medium. Based on the assumption of slab dual-porosity, this paper uses the trilinear flow model to simulate the transient production behavior of multiple-fractured horizontal wells in shale gas reservoirs, which takes the desorption of adsorbed gas, Knudsen diffusion and gas slippage flow in the shale matrix into consideration. Production decline curves are plotted with the Stehfest numerical inversion algorithm, and sensitivity analysis is done to identify the most influential reservoir and hydraulic fracture parameters. It was found that the density and permeability of the natural fracture network are the most important parameters affecting the production dynamics of multiple-fractured horizontal wells in shale gas reservoirs. The higher the density and permeability of the natural fractures are, the shorter the time is required to exploit the same amount of reserve, which means a faster investment payoff period. The analytical model presented in this paper can provide some insight into the reserve evaluation and production prediction for shale gas reservoirs.