双重介质水平井产量递减分析方法

水平井开发特殊类型油气藏有其独到优势,针对双重孔隙介质水平井复杂渗流,以Warren-Root双重介质模型为基础,建立了水平井三维不稳定渗流模型,采用Laplace变换、有限Fourier余弦变换及叠加积分等方法对模型进行求解,获得定产条件下无量纲井底压力解,再利用Duhamel褶积原理将定产条件压力解变换为井底定压条件下的产量解;通过重新定义无量纲量建立McCray型产量积分平均递减方程,结合Stehfest数值反演,获得无量纲产量积分平均递减曲线及其导数曲线图版。计算结果表明,产量积分平均导数曲线上出现双重介质特有的“凹子”, 应用该类图版拟合生产数据可方便进行产量预测及储层动态参数求取。     

时间域航空电磁法2.5维有限元模拟

采用三角网格剖分的有限元法,研究了2.5维航空瞬变电磁法正演模拟问题。利用时频变换数值方法将时间域电磁场转换到拉氏域,再利用傅里叶变换将三维问题降维变为2.5维问题,然后由有限元法求解得到拉氏域二维电磁场,逆拉氏变换后得到时间域航空瞬变响应。为了回避正演模拟中总感应磁场在场源处的奇异性问题,采用异常场算法,场源响应通过在微分方程中施加背景电磁场实现。由于瞬变电磁信号具有较大的动态范围,而且需要经过两次正、逆拉氏变换和傅里叶变换,每个环节的计算精度和速度要严格控制在较高的水平上,否则积累误差会非常大。模型计算表明均匀大地和层状大地模型解析解与数值解吻合很好。这证明该算法是正确可行的,可作为研究二维复杂地质体的方法手段。     

有效应力对裂缝型低渗透砂岩油藏压力响应的影响

为了研究裂缝孔隙型低渗油藏中流体在双重介质之间的渗流规律及其影响,建立了双重介质间流体窜流的数学模型,并利用拉氏变换数值反演方法给出近似解析解;通过数值计算,研究窜流压力的动态特征,分析储容系数及窜流系数对压力响应的影响;通过压敏试验研究了有效应力对双重介质低渗油藏渗流能力的影响。研究结果表明：储容系数主要决定双重介质之间发生窜流现象的早晚,储容系数越大,发生窜流的时间越晚;储容系数越小,发生窜流的时间越早。窜流系数主要决定双重介质之间发生窜流压力的大小,窜流系数越大,发生窜流的压力越小;窜流系数越小,发生窜流的压力越大。有效应力对裂缝型低渗透油藏的渗流能力影响很大,有效应力的增加能够大大降低裂缝型油藏渗透率和孔隙度,以致降低储层的储容系数和窜流系数,从而影响双重介质间窜流压力的动态特征。因此,在裂缝型低渗透砂岩油藏开采中,保持压力、防止储层伤害是非常重要的。     

分布热源作用下裂隙岩体渗流-传热的拉氏变换-格林函数半解析计算方法

以裂隙岩体高放射性核废物地下处置库性能评估为目标,提出了分布热源作用下单裂隙岩体渗流-传热的简化概念模型、控制微分方程和拉氏变换-格林函数半解析法,为进一步采用半解析法计算分布热源作用下多裂隙岩体的渗流-传热问题奠定了基础。针对单裂隙岩体的渗流-传热问题,建立考虑岩石内热源和二维热传导的控制微分方程,利用拉氏变换域微分方程的基本解建立格林函数积分方程,采用解析法处理其中的奇点,通过数值积分和拉氏数值逆变换求解,计算任意时刻裂隙水和岩石的温度分布。通过算例,与基于岩石一维热传导假定的解析解进行了对比,并计算分析了分布热源作用下单裂隙岩体的渗流-传热特征及其对裂隙开度、岩石热传导系数和热流集度的敏感度。算例表明,（1）就裂隙水温度而言,由于考虑了岩石的二维热传导,拉氏变换-格林函数半解析解小于基于岩石一维热传导假定的解析解;（2）裂隙水温度和岩石温度对裂隙开度和热流集度的敏感度较大,对岩石热传导系数的敏感度较小。     

井底应力场对气体钻井井斜的影响

建立了油气井钻井过程中的井底力学模型,该力学模型考虑了井眼内压力、岩石节理、井眼深度、地应力、岩石材料特性、井眼直径等影响因素,并讨论了各个因素对井底应力场的影响,阐明了气体钻井时井底应力场分布变化对井眼井斜的影响。气体钻井时井眼内的压力远小于井眼周围的围压,井底会出现很大的拉应力,岩石容易破坏,因此,气体钻井时钻井速度远远大于钻井液钻井,但拉应力越大,井眼与岩石节理面交接处产生的应力集中越大,应力集中处岩石更容易破坏,也更易产生井斜。气体钻井时井底的应力状态对地层倾角、材料特性、井眼直径、井眼深度及初始地应力的变化较钻井液钻井时更敏感。     

水平井流入动态计算公式

本文基于欠平衡或过平衡钻井,裸眼完井,割缝衬管完井或套管完井,以及套管完井孔密度及相位角等因素,也给出了已发表过的包含机表皮系数和非达西流动系数的水平井流入动态计算公式,并对其进行了比较,除此之外,给出并比较了含有表皮系数及非达西流动系数的水平井流入动态公式的解析解及数值解。     

越流含水层中抽水井附近非达西流两区模型近似解析解

构建了越流含水层中抽水井附近非达西流动的两区模型,即距离抽水井较近的区域为非达西流,而相对较远区域为达西流,两区之间的临界半径可根据临界雷诺数确定.采用线性化近似方法和Laplace变换相结合分别得到了非达西流区域和达西流区域的水位降深在拉氏空间下的解析解,应用数值Laplace逆变换-Stehfest方法得到其在实空...     

裂隙岩体中的对流扩散研究

揭示一个基于代数拓扑理论的裂隙网络中物质弥散模型，还给出了应用于网络中的对流扩散的对应性原理的证明。应用拓扑理论给出的框架，使其起了一个数据结构的组织者的作用，由此得到网络中每一个分支上的浓度的解。这个解是在拉普拉斯空间上的解析解。网络中任意点在任何时刻的浓度可以很方便地用数值拉氏反变换求出。     

考虑三向地应力差时不同钻井条件下井底应力场研究

井底压差和三向地应力是钻井过程中影响井底岩石应力分布的主要因素,从而影响钻井机械钻速。主要针对欠平衡、平衡、过平衡和气体钻井4种钻井条件下三向地应力对井底应力分布进行定量研究。在井底岩石力学分析的基础上,建立了考虑正断层模型下的三向地应力、液柱压力和孔隙压力因素时的井底岩石流-固耦合模型,采用数值计算方法进行求解。结果表明,三向地应力差相同时,井底面岩石最大主应力与井底压差无关,井底面岩石最小主应力随井底压差增大而增大;不同钻井条件下井底面最小主应力与水平最小地应力无关,且随水平最大地应力增大而减小;不同钻井条件下井底面最大主应力与水平最大地应力无关,当井底压差存在时,其随水平最小主应力增加而减小后逐渐趋于稳定;当气体钻井时,其与水平最小主应力也无关。针对走滑断层和逆断层模型时的井底应力场尚需进一步研究。不同井底压差和三向地应力时井底岩石应力分布的定量化研究为实际钻井条件下钻头破岩机制研究和快速高效破岩提供理论基础。     

侧向有限越流承压含水层中非完整井非稳定流模型及解析解

工程建设中当距离抽水井r=rb处水位基本没有变化或不受抽水影响时,或当此处存在止水帷幕时,含水层系统视为侧向有限延伸,rb为有限半径。为此,构建更加符合工程实际的侧向有限延伸的典型弱透水层-承压水层系统中非完整井非稳定流计算模型,同时考虑井径和井储效应的影响,应用Laplace变换和分离变量法得到了水位降深在拉氏空间下的解析解,并应用拉氏数值逆变换Stehfest法得到真实空间下的水位降深。新建立的解析解可以进一步退化为诸多已有解,并进一步将其与已知解和有限元数值解进行对比,验证了所得解的正确性和可靠性。基于新建解重点分析了侧向边界和井的完整性对承压水层水位降深的影响。结果表明:含水层系统的侧向有限边界仅对抽水后期的水位降深影响明显,含水层系统侧向无限延伸情况下的水位降深要大于情形1(在r=rb处为定水头边界)且明显小于情形2(在r=rb处为不透水边界)下的水位降深,rb越小,两者之间的误差越大;抽水井的完整性对整个抽水期间不同情形下的水位降深均有明显的影响,承压含水层顶板处的水位降深随着抽水井滤管的长度和埋深的增加而减小。     

Development and verification of the comprehensive model for physical properties of hydrate sediment

Natural gas hydrate is widely distributed all over the world and may be a potential resource in the near future, whereas hydrate dissociation during the development affects wellbore stability and drilling safety. However, the present modeling of hydrate reservoir parameters ignored the influence of effective stress and only considered the hydrate saturation. In this paper, a series of stress sensitivity experiments for the unconsolidated sandstone were carried out, and the influence of mean effective stress on physical parameters was obtained; a comprehensive model for the physical parameters of hydrate reservoir was developed subsequently. With the help of ABAQUS finite element software, the established comprehensive model was verified by the use of the wellbore stability numerical model of hydrate reservoir. The verification results show that ignoring the effect of mean effective stress on the parameters of hydrate formation aggravates the invasion of drilling fluid into the hydrate formation. Besides, ignoring the stress sensitivity of reservoir physical parameters will underestimate the wellbore instability during hydrate drilling, which will be a threat to the safety of gas hydrate drilling. At the end of the drilling operation, the maximum plastic strain of the model for considering and not considering stress sensitivity was 0.0145 and 0.0138, respectively. Therefore, the established comprehensive model will provide a theoretical support for accurately predicting the engineering geological disasters in hydrate development process.     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part II: verification and numerical example

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models.     

基于微地震数据的增强型地热储层参数及采热的数值模拟研究

发展清洁、稳定、可再生的干热岩型地热资源对于缓解能源危机、减轻环境污染、改善人类健康具有重要意义。增强型地热系统(Enhanced Geothermal System,EGS)是一项改造干热岩天然储层,高效开发地热能资源的先进技术。以澳大利亚库珀盆地地热储层为研究对象,基于水力压裂实测微震数据,建立了三维分区均质渗透率模型和非均质渗透率模型,分别进行储层温度场、流场及采热性能变化的研究,并对比其差异。结果表明：在同样的注采流量下,由于非均质模型中微震事件集中于井口附近,进而形成明显的优势流动通道,流体从注入井更快流向生产井,温度下降速度相对更快,分区均质模型中优势流动通道没有非均质模型明显,温度下降速度较慢;地热模型运行期间分区均质模型的采热量变化相对稳定,降幅为3.74%,非均质模型采热量降幅较大,为12.72%。分区均质模型的模拟结果相比于非均质模型,温度下降幅度小、采热量高;但实际储层中的渗透率分布不均,分区均质模型的模拟采热量相比实际采热量偏高,因此在实际应用中,非均质模型的模拟结果对实际工程更具参考意义。     

A mathematical model of permeability alteration around wells

This paper presents an analytical solution of the permeability alteration problem around the wellbore. This alteration may be a permeability reduction due to drilling fluid invasion or mudcake formation around the wellbore. On the other hand, the alteration may be a permeability increase resulting from stimulation by acidizing the formation matrix around the well. This permeability discontinuity in a reservoir forms a composite reservoir system. With the composite model, both the degree and the radial extent of permeability alteration can be adequately predicted. The conventional skin concept is inadequate and physically unrealistic in most of these cases. This paper describes the application of an automatic weighted constrained least-squares parameter estimation technique and the analytical model for pressure transient analysis. The parameters of the composite reservoir system are determined from a match of the pressure transient data. The behaviour of the pressure transient in such composite systems is presented using the analytical solution.     

高温热田井筒热力学及地层参数计算方法

在高温热田的井孔施工及测试实践中,通常由于高温热水在地层或井简内闪蒸汽化,形成复杂的两相流动而无法直接从单井放喷资料中计算地层参数。西藏羊八井属于高温热水型地热田,第四系热储内热液温度约介于140—155℃之间,埋藏深度大略为70—200米左右,井口闭井压力大多在2—4个大气压之间。热储流体在上述深度、温度和压力的配置下,在地层内处于单相液态,而在开发动态下则在大部分井筒上部达到饱和点而汽化,形成相对稳定的汽化面,构成双相流和单相流之间的界面。     

Modeling semi-steady state near-well flow performance for horizontal wells in anisotropic reservoirs

This paper presents a novel methodology to model semi-steady state horizontal well flow performance in an anisotropic reservoir taking into account flow in the near-well region for an arbitrary well trajectory. It is based on an analytical productivity model describing coupled axial reservoir flow and radial well inflow. In order to apply this model in an anisotropic reservoir, the permeability field relative to the radial direction perpendicular to the well trajectory and the axial direction along the well trajectory must first be determined. A classical space transformation is used in concert with rotational transforms to obtain a virtual isotropic model. The transformation preserves the volumes and pressures. It is not a novel concept, but different from previous approaches in the sense that it is only applied in the near-well domain to formulate an equally isotropic media. As a result, the use of this virtual isotropic model requires the Dietz shape factor for an ellipse, transformed from the original cylindrical near-well domain. The Dietz shape factors are determined numerically in this research. The semi-steady state well/near-well model is implemented in a numerical simulator incorporating formation anisotropy and wellbore hydraulics. The specific productivity index along the well trajectory is generated using the virtual configuration. Numerical results for different anisotropy ratios and also incorporating frictional losses in the well are presented. Furthermore, the well/near-well model is applied in coupling with streamline reservoir model for a water flooding case. This appears to be the first coupling of a well hydraulics model and a streamline simulator. It presents the application of the well/near-well model in integrated reservoir simulation in an efficient and accurate manner. The results demonstrate that the coupling approach with a streamline reservoir model and the well/near-well is of great potential for advanced well simulation efficiently.     

A model for the constant-head pumping test conducted in vertically fractured media

An analytical model for the constant-head pumping test is developed for a partially penetrating well that has a finite thickness skin, and intersects a single vertical fracture. In the model, the fracture is fully confined and flow occurs only in the fracture. The model is developed using Laplace transform and finite Fourier transform methods. The model is to be used for analysing well test data from vertically fractured media and for verifying numerical models. Dimensionless curves are used to study the effects of a finite thickness skin and a partially penetrating wellbore. In the presence of a finite thickness skin, or a partially penetrating wellbore, a typical flow response for the constant-head pumping test has three distinct periods of flow corresponding to small-, intermediate- and large-time. Small- and large-time approximations are presented for the model. For tests where the wellbore is fully penetrating, or the partial penetration ratio is known, these approximations can be used to analyse field data.     

Hydro-mechanical coupled analysis of near-wellbore fines migration from unconsolidated reservoirs

Oil or gas production from unconsolidated reservoirs could be hampered by sand migration near the wellbore. This paper presents a numerical investigation of production-induced migration of fine sands towards a wellbore drilled in a gap-graded sediment. The solid–fluid interaction is simulated by coupling the discrete element method and the dynamic fluid mesh. With the merit of DEM and a dynamic mesh, the model is capable of naturally capturing particle movements and spatiotemporal variations of hydraulic properties of the sediment at the pore scale. The results show that fine particles are mobilized by radial flow under an imposed hydraulic gradient, and the increase in the hydraulic gradient causes an increase in the fines production. The microscopic pattern of sand migration is clearly visualized through the simulation. The presence of fine particles affects the process of fines migration through two competing mechanisms. Under a low fine content, fine sands mainly serve as the fines production source, and thus, fines production is enhanced as the fine content increases up to a critical value, beyond which fines production is weakened with a further increase in the fine content since the blocking effect gradually dominates. A barrier layer is likely formed during sand migration due to settling and jamming of fine sands at the throats of pores, as fine sands migrate with the radial flow towards the wellbore. This layer is helpful to slow down sand migration, while it could impede production due to reduced permeability in the affected reservoir.

     

基于等效介质理论的碳酸盐岩储层地震数值模拟

综合考虑碳酸盐岩储层孔隙度、孔隙类型对储层物性参数的影响,对常规的Xu-White模型等效介质理论进行了改进,采用K-T理论增加多种不同类型的孔隙(如粒间孔隙、刚性孔隙、裂隙等),得到了一种新的改进的Xu-White模型等效介质理论,并提出了一套新的适用于碳酸盐岩储层的地震数值模拟方法。该方法首先采用改进的Xu-White模型等效介质理论,来计算碳酸盐岩储层的等效参数,将各向异性的储层转换为均匀介质;然后再采用声学波动方程进行地震数值模拟。模型试验的结果表明,该方法不仅计算效率高,而且可以得到高信噪比的模拟记录,其主要地层的反射波场特征与弹性波方程数值模拟完全一致,是一种简单高效的适用于碳酸盐岩储层的地震数值模拟方法。     

A scalable multistage linear solver for reservoir models with multisegment wells

Wellbore flow and interactions between wells and the reservoir can be complex. Accurate modeling of these behaviors is especially important for multilateral and other advanced wells. This paper describes a new scalable linear solver for flow simulation of detailed reservoir models with advanced wells and well groups. A general purpose research simulator serves as the computational platform, in which a multisegment well (MsWell) model is used to describe wellbore flow. In the MsWell model, the wellbore is discretized into a number of segments. Hence, the MsWell model adds a large number of equations and unknowns, which are fully coupled to the reservoir model. Operating constraints on groups of wells add one more level of complexity to the system. The new linear solver is a generalized two-stage constrained pressure residual preconditioner. A global pressure system is obtained algebraically in the first stage. The system represents the pressure coupling between the reservoir and wells accurately. The well groups are disaggregated into individual multisegment wells, which then are further reduced to a standard well-like form. The two-stage scheme serves as the inner loop of a generalized minimum residual solver. Algebraic multigrid is used to compute the first-stage pressure solution; a special block-based incomplete lower–upper preconditioner is used for the second stage. We demonstrate the superior performance of this new solver compared with state-of-the-art methods using a variety of highly detailed reservoir models with complex wells and well groups.