Friedrichs systems for systems of wave equations and shear waves in a three-dimensional elastic medium

This paper considers a two-dimensional hydraulic model which describes gas or oil flow to a horizontal well with hydraulic fractures and takes into account the reservoir geometry and fluid flow between the reservoir and the well. A computational algorithm is proposed, and calculations for gas and oil reservoirs are performed. A comparison of the calculation results and the solutions of the corresponding problems in a three-dimensional formulation show that the calculations using the approximate hydraulic model yield reasonably accurate results.     

海陆过渡相页岩气藏不稳定渗流数学模型

海陆过渡相页岩常与煤层和砂岩呈互层状产出, 储层连续性较差、横向变化快、非均质性强, 水力压裂技术是其获得经济产量的关键手段. 然而, 目前缺乏有效的海陆过渡相页岩气藏不稳定渗流数学模型, 对其渗流特征分析及储层参数评价不利. 针对这一问题, 首先建立海陆过渡相页岩气藏压裂直井渗流数学模型, 其次采用径向复合模型来反映强非均质性, 采用Langmuir等温吸附方程来描述气体的解吸和吸附, 分别采用双重孔隙模型和边界元模型模拟天然裂缝和水力裂缝, 建立并求解径向非均质的页岩气藏压裂直井不稳定渗流数学模型, 分析海陆过渡相页岩气藏不稳定渗流特征, 并进行数值模拟验证和模型分析应用. 分析结果表明, 海陆过渡相页岩气藏不稳定渗流特征包括流动早期阶段、双线性流、线性流、内区径向流、页岩气解吸、内外过渡段、外区径向流及边界控制阶段. 将本模型应用在海陆过渡相页岩气试井过程中, 实际资料拟合效果较好, 其研究成果可为同类页岩气藏的压裂评价提供一些理论支撑, 具有较好应用前景.      

Numerical solution of the coefficient inverse problems on nonstationary filtration to a well intersected by a hydraulic fracture

A computational algorithm is proposed to determine the reservoir and hydraulic fracture properties from the results of nonstationary hydrodynamic studies of vertical wells. The problem of oil flow to a well intersected by a fracture is solved numerically. Averaged permeabilities are used for cells through which the fracture propagates.     

基于离散裂缝的多段压裂水平井数值试井模型及应用

水平井压裂技术已经成为开发低渗透油气藏、页岩气藏和致密气场等非常规油气藏的关键技术。基于离散裂缝模型,对裂缝进行简化,建立了二维多段压裂水平井有限导流数值试井模型,利用有限元方法求解模型,获得多段压裂水平井试井理论曲线和压力场特征。分析表明:多段压裂水平井的试井理论曲线一共分为七个阶段:井筒储存段、裂缝线性流段、裂缝-地层双线性流段、裂缝干扰段、地层线性流段、系统径向流段和边界作用段,其中裂缝-地层双线性流段和裂缝干扰是其典型特征。分析了裂缝数量、裂缝间距、裂缝不对称、裂缝不等长和裂缝部分缺失等因素对试井理论曲线的影响,结果表明:裂缝数量和裂缝间距对试井理论曲线的影响最大。较多的裂缝、较大裂缝间距、对称的裂缝和等长的裂缝有利于降低压裂水平井井底的流动阻力,提高产能。将建立的数值试井模型应用于四川盆地一口多段压裂水平井的压力恢复测试的数值试井解释,结果表明:本文建立的模型可以较好的拟合压力恢复测试数据,可以获得裂缝的导流能力和裂缝长度,为压裂效果评价和压裂设计提供指导。      

页岩气藏压裂水平井试井分析

页岩气藏资源丰富,开发潜力巨大,已成为目前研究的热点.与常规气藏相比,页岩气藏运移机制复杂,流动模式呈非线性,有必要考虑页岩气的吸附解吸,天然微裂缝的应力敏感性,人工裂缝内的非达西流等非线性因素对压裂水平井压力响应的影响. 基于双重介质和离散裂缝混合模型,分别采用Langmuir等温吸附方程描述吸附解吸,渗透率指数模型描述应力敏感,Forchheimer方程描述非达西效应,建立页岩气藏压裂水平井数值试井模型. 运用伽辽金有限元法对模型进行求解.根据试井特征曲线,划分流动阶段,着重分析非线性因素对压力响应的影响.结果表明:页岩气藏压裂水平井存在压裂裂缝线性流、压裂裂缝径向流、地层线性流、系统径向流及封闭边界影响5 种流动阶段.吸附解吸的影响发生窜流之后,Langmuir吸附体积增大,拟压力导数曲线凹槽更加明显,系统径向流出现时间与压力波传播到边界时间均延迟;天然裂缝系统的应力敏感性主要影响试井曲线的晚期段,拟压力和拟压力导数曲线均表现为上翘,应力敏感效应越强,上翘幅度越大;高速非达西效应对早期段影响较大,非达西效应越强,拟压力降幅度越大,试井曲线上翘.与解析解的对比以及矿场实例验证了模型的正确性与适用性.      

Numerical modeling of the process of oil displacement from reservoirs with zonal nonuniformity

In extracting oil from nonuniform reservoirs a considerable fraction remains unrecovered from the zones of lesser permeability. The mechanism of displacement of oil from reservoirs with zonal nonuniformity is investigated within the framework of the two-dimensional Muskat-Meres model of combined oil, water and gas flow [1]. A wholly conservative difference scheme implicit in the saturations and pressure is used for the calculations. Various reservoir exploitation regimes are considered with the object of seeking means of improving the characteristics of the process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1987.     

基于XFEM-MBEM的嵌入式离散裂缝模型流固耦合数值模拟方法

离散缝网的表征与模拟是目前国内外研究的热点. 在非常规油气开发过程中, 由于地应力场的存在会对裂缝的流动属性产生显著影响, 若将裂缝视为静态对象, 与矿场数据会出现极大偏差, 因此要基于动态裂缝做更深入的研究. 本文针对致密油藏应力场?渗流场耦合力学问题, 提出了一种高效的混合数值离散化方法, 其中采用扩展有限元法 (XFEM) 求解岩石的弹性形变, 采用了混合边界元法 (MBEM) 精确计算基岩与裂缝间的非稳态窜流, 这两种数值格式是完全耦合的, 并对整体计算格式的时间项进行了全隐式求解, 可准确表征致密油藏开采过程中的裂缝变形及流体流动机理. 此外, 本文采用了嵌入式离散裂缝前处理算法显式表征大尺度水力压裂缝, 并考虑了支撑剂的作用; 采用了双孔有效应力原理和双重介质隐式裂缝表征方法, 可捕捉基质与小尺度天然裂缝的动态信息; 由此, 本文所提出的混合模型综合表征了基质?天然裂缝?水力压裂缝共同组成的致密油藏复杂渗流环境, 并通过几个实例论证了模型的准确性, 研究表明: 对致密油藏压裂水平井进行产能评价时, 应力场所引起渗流参数的改变及裂缝开度降低的影响不可忽略. 本文研究可为非常规油气资源的开发提供理论指导.      

Calculation of Groundwater Flows in Coastal Pressurized Reservoirs

A model of a fresh groundwater flow through a rectangular horizontal pressurized reservoir toward a salt-water sea (basin, reservoir, trench, etc.) is examined within the framework of two-dimensional steady-state flow theory. In order to study the model, a mixed multi-parameter boundary value problem of the theory of analytic functions is formulated and solved using the Polubarinova-Kochina method. The structure and the characteristic features of the simulated process and the effect of all the determining physical parameters of the model on the nature of the flow are analyzed using the analytic dependences obtained and numerical calculations. An approximate hydraulic solution of the problem is compared with the exact solution obtained.     

Analytical model of the linear inflow to a horizontal well with hydraulic fractures in low-permeability reservoirs

At present, increasing attention has been concentrated on low-permeability deposits whose development is tightly related with technologies of horizontal drilling and hydraulic fracturing of the reservoir. However, the simultaneous presence of a horizontal section of the well and hydraulic fractures in the reservoir impedes the process of flow of reservoir liquids and gases through the porous medium and complicates simulation of such flows. In the present study a new analytical model of the linear inflow to a horizontal well with hydraulic fractures in low-permeability reservoirs is proposed. This is a generalizing model which takes into account both situations when there exists a linear flow in the direction perpendicular to the borehole of a horizontal well in the distant sections of the reservoir and when there is a linear flow in the direction parallel to the borehole of a horizontal well. The use of the model is not restricted by the shape of the flow domain. The new model proposed has a wide application field and does not require complex computations.     

裂缝性低渗透油藏流-固耦合理论与数值模拟

根据裂缝性低渗油藏的储层特征,建立适合裂缝性砂岩油藏渗流的等效连续介质模型。将渗流力学与弹塑性力学相结合,建立裂缝性低渗透油藏的流-固耦合渗流数学模型,并给出其数值解.通过数值模拟对一实际井网开发过程中孔隙度、渗透率的变化以及开发指标进行计算,并和刚性模型以及双重介质模型的计算结果进行了分析比较.     

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基于射孔完井水平裂缝中支撑剂均匀充填，考虑充填层强度、油层和流体 物性以及裂缝的渗流条件，研究了地应力及渗流引起的附加应力联合作用的支撑剂充填层渗 流模型和力学模型，并进行现场应用. 研究表明，所建立的模型对压裂油井支撑剂回采出砂 状况分析具有较高的符合率，油井总体符合率、不出砂井符合率和出砂井符合率分 别为84.66\%, 84.18\%和88.10\%, 为大庆油田压裂油井防砂措施实施方案制定提 供了决策支持，有利于提高措施有效率.     

考虑多重运移机制耦合页岩气藏压裂水平井数值模拟

页岩作为典型的微纳尺度多孔介质,游离气与吸附气共存,传统的达西定律已无法准确描述气体在页岩微纳尺度的运移规律.基于双重介质模型和离散裂缝模型构建页岩气藏分段压裂水平井模型,其中基岩中考虑气体的黏性流、Knudsen 扩散以及气体在基岩孔隙表面的吸附解吸,吸附采用Langmuir等温吸附方程;裂缝中考虑黏性流和Knudsen扩散,在此基础上建立基岩-裂缝双重介质压裂水平井数学模型并采用有限元方法对模型进行求解.结果表明,基岩固有渗透率越小,表面扩散和Knudsen扩散的影响越大,反之则越小;人工裂缝的性质包括条数、开度、半长以及间距,主要影响压裂水平井生产早期,随着人工裂缝参数值的增加,压裂水平井产能增加,累产气量也越大.其次,页岩气藏压裂诱导缝和天然裂缝的发育程度对页岩气藏的产能有很大的影响,水平井周围只有人工裂缝,周围天然裂缝不开启或不发育时,页岩气藏的水平井的产能较低.      

Seepage effects of dissolving rock by acid action on carbonate oil-bearing formations

The displacement of oil by an aqueous acid solution in the neighborhood of a well and a hydraulic fracture is considered with allowance for the kinetics of acid dissolution of a carbonate rock. The penetration of the active admixture and the variation of the seepage characteristics of the reservoir in the course of the reactant injection and after stoppage for reaction are investigated on the basis of the model proposed. The effect of the acid treatment, the reaction time, and the depth of penetration of the solution into the formation are estimated. Analytic estimates and numerical calculations are carried out for real examples.     

油页岩原位注热开采储层有效热解区变化规律分析

针对油页岩原位注热开采过程中储层有效热解区变化规律不清,实际热解效果无法准确判断难题,采用数值模拟方法,以抚顺油页岩储层为研究对象,建立了油页岩原位注热开采热流固耦合力学模型,与前人结果对比,验证了模型可靠性。重点考察水力压裂裂缝通道短路问题,分析得到了油页岩原位注热开采过程中储层有效热解区、储层有效热解区中地应力、注汽压力及沉降量随注热时间变化规律。结果表明,过热蒸汽沿水力压裂裂缝流动不会出现裂缝通道短路现象,过热蒸汽可通过水力压裂裂缝加速油页岩储层热解;采用过热蒸汽对流加热油页岩储层效率高,只需1年能使96%的油页岩储层达到热解所需温度;油页岩储层有效热解区中部形成应力集中区,最大地应力为21.6 MPa;热解后靠近注热井处岩层发生沉降,热解2年后最大沉降量达0.85 m。所得结论对现场油页岩原位注热开采有参考意义。     

页岩气在超低渗介质中的渗流行为

基于页岩气藏复杂孔隙结构和页岩气在纳米孔隙表面的滑脱和吸附-解吸附等现象,通过引入表观渗透率,修正Darcy渗流模型,得到了页岩气渗流本构方程. 将计算结果与Darcy模型计算结果进行了比照,结果表明,在产量定常情形下,基于非Darcy渗流模型得到的井底压力高于Darcy流结果; Darcy流模型得到的压力衰减速度较快,改进后的渗流模型更能准确描述与表征页岩气渗流过程;研究结果可为页岩气藏的经营与管理提供基础参数.      

Bingham’s model in the oil and gas industry

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.     

Dynamic Relative Permeability and Simulation of WAG Injection Processes

In this work, we investigate the impact of mobility changes due to flow reversals from co-current to counter-current flow on the displacement performance of water alternating gas (WAG) injection processes. In WAG processes, the injected gas will migrate toward the top of the formation while the injected water will migrate toward the bottom of the formation. The segregation of gas, oil and water phases will result in counter-current flow occurring in the vertical direction in some portions of the reservoir during the displacement process. Previous experimental and theoretical studies of counter-current flow have shown that the relative mobility of each of the phases in a porous medium is considerably less when counter-current flow prevails as compared to co-current flow settings. A reduction of the relative permeability in the vertical direction results in a dynamic anisotropy in phase mobilities. This effect has, to the best of our knowledge, not previously been considered in the modeling and simulation of WAG processes. A new flow model that accounts for flow reversals in the vertical direction has been implemented and tested in a three-phase compositional reservoir simulator. In order to investigate the impact of flow reversals, results from the new flow model are compared to cases where counter-current flow effects on the phase mobilities are ignored. A range of displacement settings, covering relevant slug sizes, have been investigated to gauge the impact of mobility reductions due to flow reversals. Significant differences, in terms of saturation distribution, producing GOR and oil recovery, are observed between the conventional flow model (ignoring mobility reductions due to counter-current flow) and the proposed new model that accounts for reductions in phase mobility during counter-current flow. Accordingly, we recommend that an explicit representation of flow transitions between co-current and counter-current flow (and the related impact on phase mobilities) should be considered to ensure accurate and optimal design of WAG injection processes.     

High-viscosity oil flow in a formation with a hydraulic fracture under the action of a high-frequency electromagnetic field

The results of numerical investigations of high-viscosity oil flow in a low-permeability reservoir under high-frequency electromagnetic action in combination with hydraulic fracturing are presented. The fluid flow toward a solitary vertical sand-filled fracture with high permeability, much higher than the permeability of the formation, is considered. The electrophysical and thermal characteristics of the formation and fracture both saturated with formation fluid are assumed to be identical. The unsteady fluid pressure, temperature and viscosity fields near the hydraulic fracture are calculated and the efficiencies of high-viscosity oil extraction are compared for different electromagnetic radiation powers and “cold” fluid withdrawal.     

页岩气储层压裂数值模拟技术研究进展

页岩气储层水力压裂数值模拟既要考虑页岩储层岩石的特性,又要兼顾水平外分段压裂施工工艺,是一个非常棘手的力学难题.本文简述了页岩气储层岩石具有的地质力学特征和页岩气储层开发常用的水平井分段压裂技术;详述了扩展有限元、边界元、离散元在水力压裂裂缝模拟上的应用现状,指出了它们在处理裂缝问题的局限性和优越性,总结出边界元三维位移不连续法是模拟多裂缝扩展的有效方法.