页岩气藏体积压裂有效改造体积计算方法

页岩气藏矿场压裂实践表明,储层有效改造体积（effective stimulated reservoir volume,简称ESRV）是影响页岩气藏体积压裂水平井生产效果的关键因素,ESRV的准确计算对页岩气藏压裂方案评价与体积压裂水平井产量预测具有重要作用.基于页岩储层改造体积（stimulated reservoir volume,简称SRV）多尺度介质气体运移机制,建立了SRV区域正交离散裂缝耦合双重介质基质团块来表征单元体渗流模型（representation elementary volume,简称REV）,并结合北美页岩储层实例研究了次生裂缝间距、宽度等缝网参数对页岩气藏气体运移规律的影响.在此基础上根据SRV区域次生裂缝分布特征,采用分形质量维数定量表征裂缝间距分布规律,结合页岩气藏次生裂缝间距对基质团块内流体动用程度的影响规律,得到了页岩气藏体积压裂ESRV计算方法.结果表明SRV区域次生裂缝间距对基质团块内吸附及自由气影响较大,次生裂缝间距小于0.20 m时可以实现SRV区域基质团块内流体向各方向裂缝的"最短距离"渗流.选取北美典型页岩储层生产井体积压裂数据进行ESRV计算,页岩气藏目标井ESRV占体积压裂SRV的37.78%.因此ESRV受改造区域次裂缝分布规律及SRV有效裂缝间距界限的影响,是储层固有性质及人工压裂因素综合作用的结果.      

页岩储层体积压裂裂缝扩展机制研究

页岩储层天然裂缝、水平层理发育,水力压裂过程中可能形成复杂的体积裂缝。针对页岩储层体积裂缝扩展问题,基于流-固耦合基本方程和损伤力学原理,建立了页岩储层水力压裂体积裂缝扩展的三维有限元模型。将数值模型的模拟结果与页岩储层裂缝扩展室内试验结果进行对比,二者吻合较好,从而证明了数值模型的可靠性。通过一系列数值模拟发现：（1）水力压裂过程中水平层理可能张开,形成水平缝,水平与垂直缝相互交错,形成复杂的体积裂缝网络;（2）水平主应力差增大,体积裂缝的分布长度（水平最大主应力方向压裂裂缝的展布距离）增加、分布宽度（水平最小主应力方向压裂裂缝的展布距离）减小,体积裂缝的长宽比增加;（3）压裂施工排量增大,体积裂缝的分布长度减小、宽度增加,压裂裂缝的长宽比降低;（4）天然裂缝的残余抗张强度增大,体积裂缝分布宽度减小、分布长度增加,体积裂缝的长宽比增加。研究成果可以为国内的页岩气的压裂设计和施工提供一定的参考和借鉴。     

页岩水平井体积压裂设计的一种新方法

页岩水平井常采用体积压裂技术获得产能,压裂形成的缝网体积、渗透率是影响压裂效果的关键因素。目前页岩体积压裂设计借用产能预测模型优化缝网参数,此模型较复杂,不便于现场应用。根据等效渗流原理,将页岩储层压裂后形成的缝网系统等效为一个高渗透带,建立了体积压裂缝网参数与施工规模关系模型,提出了体积压裂设计的3个步骤:体积压裂可行性研究、数值模拟优化缝网参数和施工参数优化。根据QY2页岩油水平井特征,进行了体积压裂设计和现场实施。结果表明:压裂形成的高渗透带对产能的贡献最大;高渗透带数量、体积和渗透率增加,压裂后的累积产量和采出程度逐渐增加,存在最优的高渗透带参数。现场应用表明这种设计方法方便实用,可以推广。     

An analytical model for multiple fractured shale gas wells considering fracture networks and dynamic gas properties

Multi-stage fractured horizontal wells play an important role in developing shale gas reservoirs by significantly improving productivity. By considering fracture networks, gas desorption, stress-sensitive fracture permeability, and pressure-dependent gas PVT properties, an analytical model is developed for shale gas wells. Fracture networks are handled based on transient linear flow, gas desorption is handled by defining a new total compressibility, stress-dependent hydraulic fracture permeability is handled by variable substitution, and pseudo-pressure and pseudo-time are used to handle pressure-dependent PVT properties. After obtaining the solution of the linearized model, a material balance method and successive substitution iteration procedure are proposed to convert the pseudo-time into real time and calculate the production contribution from gas desorption. The results show that induced fractures also have a great impact on the production of the well. Production contribution from free gas and adsorbed gas could be quantified using the proposed material balance principle and iterative method. The rank of parameters that influence the ultimate recovery is the following: half-length of hydraulic fracture, induced fracture length/hydraulic fracture spacing, hydraulic fracture spacing, conductivity of induced fractures, conductivity of hydraulic fracture, and induced fracture spacing.     

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。     

Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs

The state of the art of modeling fluid flow in shale reservoirs is dominated by dual-porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano-pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual-porosity models and Darcy’s law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of the complex flow mechanisms occurring in these reservoirs. This paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three porosity systems: inorganic matter, organic matter (mainly kerogen), and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nano-pores and micro-pores in kerogen are incorporated into the simulator. The multiple-porosity model is built upon a unique tool for simulating general multiple-porosity systems in which several porosity systems may be tied to each other through arbitrary connectivities. This new model allows us to better understand complex flow mechanisms and eventually is extended into the reservoir scale through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual-porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple-porosity simulation.     

埋深对深部煤层气储层物性及开发效果的影响: 以鄂尔多斯盆地东南缘延川南区块为例

近几年全国深部煤层气基于精细地质研究和水平井多段加砂压裂取得重大突破,部分井日产气量高达十万方,给煤层气产业重新树立了信心。但是,由于深部煤储层处于高地应力、高地温、高孔隙压力、低渗透率的复杂地质环境,不同深度煤储层典型参数和煤层气赋存方式的分布特征以及对储量和产量的影响亟需揭示。基于Langmuir等温吸附式、亨利定律及物质平衡原理,考虑吸附层和溶解气的影响,建立了深部煤层气游离气饱和度计算模型;以国内鄂尔多斯盆地大宁−吉县区块深部煤层气藏为例,分析不同深度深部煤层气赋存方式及分布特征,并评价游离气饱和度对深部煤层气储量、产量与合理配产的影响。研究认为：当煤层埋深大于溶解饱和对应的深度,游离气才会出现,且随着埋深的增加,游离气饱和度先快速增加后缓慢增加,目标区块埋深1 875 m处才出现游离气,在埋深2 800 m处游离气饱和度高达90%,游离气的占比高达17.3%。游离气饱和度对深部煤层气储量计算、产气特征和合理配产影响很大,随着游离气饱和度的增大,煤层气储量线性增大,累产气量持续上升但后期上升幅度逐渐变缓,深部煤层气井最优配产增加,井底流压下降速度加快,压裂改造区的内外压差降低,未改造区动用程度增加。目标区块主力开发煤层埋深位于2 100~2 300 m,游离气饱和度介于48%~68%,游离气占比介于10%~13%,建议气井合理配产介于(4~10)×10⁴ m³/d。研究结果可为深部煤层气进一步开发提供理论依据和方法支撑。

     

Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media

We consider a system of nonlinear partial differential equations that arises in the modeling of two-phase flows in a porous medium. The phase velocities are modeled using a Brinkman regularization of the classical Darcy’s law. We propose a notion of weak solution for these equations and prove existence of these solutions. An efficient finite difference scheme is proposed and is shown to converge to the weak solutions of this system. The Darcy limit of the Brinkman regularization is studied numerically using the convergent finite difference scheme in two space dimensions as well as using both analytical and numerical tools in one space dimension. The results suggest that the Brinkman regularization may not approximate the accepted entropy solutions of the Darcy model and raise fundamental questions about the use of Brinkman type models in two-phase flows.     

向斜成藏理论及其石油地质意义

传统的石油成藏理论适用于中高渗透储层,流体的渗流特征是达西渗流,主要作用力是浮力,油气分布在构造高部位或砂体高部位,主要是寻找圈闭。但是在低超低渗透储层和致密储层中,流体的渗流特征是非达西渗流,传统理论不再适用,油水不能发生正常的重力分异,流体在超压作用下以幕式排烃方式发生初次运移,石油在储层中运移要以非达西渗流方式通过变形才能缓慢通过,这种运移必然降低流速产生滞留效应导致石油在低部位大量滞留并聚集成连续油藏。这种滞留油藏的产生,可以形成背斜区圈闭含油、斜坡区相对高部位含水、而相对低部位却连续含油的油水倒置现象。由于滞留油藏无需构造和岩性边界圈闭,无需统一压力系统和油水边界,改变了传统上的圈闭找油模式,拓展了油气藏的概念,形成了低超低渗透储层、非常规、致密油等成藏研究的理论基础。向斜成藏理论的提出,是对传统石油成藏理论的重要补充,拓展了油气勘探领域,使油气勘探从构造高部位转向构造低部位,增大了石油资源量,对勘探开发具有重要的指导作用。     

A semi-analytical solution to consolidation of unsaturated soils with the free drainage well

Based on Fredlund’s one-dimensional consolidation equation for unsaturated soil, Darcy’s law and Fick’s law, a semi-analytical solution was presented to the free drainage well with a finite thickness under application of uniform vertical loading and the boundary of the top and bottom surfaces impermeable to water and air. According to the polar governing equations of water and air phases and the boundary and initial conditions, the excess pore-air and pore-water pressures and the soil layer settlement in the Laplace transformed domain are obtained by performing the Laplace transform and utilizing the Bessel functions. Crump’s method is used to perform the inversion of Laplace transform in order to obtain numerical solutions in the real time domain. Finally, a typical example is given to illustrate the changes in the excess pore-air and pore-water pressures and soil layer settlement with time factor at different ratios of air–water permeability coefficient and/or different distances from the well.     

煤层气运移产出气水固三相耦合模型

根据达西渗流理论 ,结合Langmuir等温吸附定律和Fick第一定律描述了煤层气由煤基质解吸经扩散进入煤层裂隙系统 ,由裂隙运移至生产井筒产出的气水二相渗流过程 ,又将其和由渗流作用引起的煤体变形场耦合起来 ,形成了煤层气运移产出的气水固三相耦合模型 ,并采用全隐式联立求解方法同时隐式求出了气、水产量和饱和度值 ,实现了模型求解的无条件稳定。在沁水盆地 3 # 煤层气井开采潜能的评价预测中 ,应用该方法分别预测了将该井的动液面置于 3 # 煤底和 15 # 煤底的气、水产量 ,效果良好。     

储层地震反演在辽河油田大民屯凹陷的应用

针对大民屯凹陷构造复杂、薄互层储层横向变化快等特殊地质条件, 在叠前时间偏移和叠后高分辨处理的地震资料基础上, 利用以已知地质规律和测井资料为约束的储层地震反演新技术, 对地下岩层空间结构和物理性质进行反演、综合岩性解释、定量预测和描述储层空间分布及变化规律.通过叠前高分辨地震资料波阻抗反演、测井多属性反演方法的研究和应用, 提高了该区储层预测的纵向分辨率, 加强了对薄互层砂体的识别能力, 提高了储层预测的可靠性, 落实了有利的岩性圈闭, 获得了较好的地质效果, 为该区隐蔽油气藏的勘探做了有意义的探索.      

裂缝性致密油藏直井体积改造产能评价模型

针对裂缝性致密油藏,基于拉普拉斯变换及Stehfest数值反演, 建立了一种可用于直井体积改造产能评价的半解析两区复合模型,模型内区包含有限条无限导流水力裂缝,外区是经典的Warren-Root双重介质系统. 并分析了导压系数比α、裂缝传导率比β、储容比ω、窜流系数λ以及改造半径r_eD等参数敏感性,绘制了产量递减图版。结果表明：从产量递减曲线,可以看出体积改造直井产能遵循“L”形递减规律;导压系数比越大,初期产量越高;裂缝传导率比对整个生产周期的产能都有影响,裂缝传导率比越大,单井产量越高,同时还会伴有明显的复合边界流特征;储容比和窜流系数分别影响双重介质基质-裂缝系统窜流发生的程度和时间;内区人工主裂缝条数越多或改造渗透率越大,复合边界流越明显,产能也越高,这说明改造程度与改造体积对产能的增加都很重要,应注意两者的合理优化。矿场实例验证了该模型在裂缝性封闭边界油藏直井多次压裂改造以及裂缝性致密油藏直井体积改造方面的适用性和实用性。     

Study on Effects of Low Viscosity Fluid Pre-injection on Hydraulic Fracture Complexity in Tight Heterogeneous Glutenite Reservoirs

Tight heterogeneous glutenite reservoir is typically not easy to form complex hydraulic fracture (HF) due to its poor physical properties, poor matrix seepage capacity, and small limit discharge radius and undeveloped natural fracture system. To improve the HF complexity and the stimulated reservoir volume (SRV), a novel stimulation technology called CO₂ miscible fracturing has been introduced and its fracturing mechanism has been studied. The CO₂ miscible fracturing modifies the in situ stress field by injecting low viscosity fluid to increase the HF complexity and SRV. Therefore, a series of numerical simulations based on a hydro-mechanical-damage model were carried out to study the effects of low viscosity fluid pre-injection on pore pressure, stress field, and fracturing effect in tight heterogeneous glutenite reservoirs. The results indicate that the low viscosity fluid injection can effectively increase the pore pressure around the wellbore and reduce the effective stress of the glutenite. The FCI and SRV increase with the increase of the pre-injection amount of the low viscosity fluid. The HF complexity and SRV can be improved by pre-injecting low viscosity fluid to transform the in situ stress field. The field application of this technology in a well of Shengli Oilfield showed that low-viscosity fluid pre-injection can effectively increase the width of the fractured zone, improve the SRV, and optimize the fracturing effect.

     

柴达木盆地东部石炭系页岩气储层渗流特征研究

页岩气是一种潜在资源量巨大的非常规天然气资源,页岩气藏具有多尺度的孔渗结构及多种渗流形态,研究页岩气藏储渗特征能够为页岩气的勘探开发提供理论支撑。该研究选取了柴达木盆地东部石炭系克鲁克组与怀头他拉组的页岩钻井岩心共5个样品,应用氩离子抛光扫描电镜实验与孔径分布测试(包括压汞法、氮气吸附法、二氧化碳吸附法)对页岩的孔隙结构特征进行定性定量测试。基于页岩气质量流量渗流模型,给出页岩表观渗透率与平均压力的关系。通过甲烷渗流模拟实验测定页岩的表观渗透率。从表观渗透率随平均压力的变化特征出发,分析页岩储层中的气体渗流规律。研究结果表明：页岩气的渗流形态包括滑脱流、扩散流及达西流。在低压情况下,渗透率低的页岩中以扩散流为主,其次为滑脱流。随渗透率的增大,渗流主要形式转变为滑脱流。当压力大于2 MPa时渗流形态以达西流为主,滑脱与扩散行为不明显。研究区内页岩微孔与中孔发育较多,达西渗透率与大孔的孔隙体积相关性较大,扩散流对表观渗透率的贡献与50 nm以下的孔隙孔体积比例有一定的相关性。低压下扩散流对表观渗透率的贡献较大,扩散流是一种非常重要的页岩气运移形式。     

水平井开采煤层气藏生产动态计算新数学模型

基于朗格缪尔模型、菲克第二扩散定律和达西定律,综合考虑重力和气体压缩效应的影响,推导出描述煤层气和水渗流规律的基本偏微分方程组(并给出定解条件),且利用有限差分法对该数学模型进行了数值求解。计算结果表明,该模型能够有效模拟煤层气水平井的生产动态。通过对比是否考虑非稳态扩散和气体压缩效应时不同裂隙渗透率下的产气动态可知,忽略非稳态扩散和压缩效应,将人为缩短达到气体峰值产量的时间,增大产气峰值;将降低气体膨胀能,低估气井后期产能。煤岩裂隙渗透率越高,气井产能受渗透率回归效应影响越大,峰值产量的持续时间越短且产量下降速度快。因此在煤层气藏开采过程中,应根据气井的产气动态调整井底流压,建立合理的储层压力系统,以降低渗透率回归效应带来的不利影响。     

Analysis of subdiffusion in disordered and fractured media using a Grünwald-Letnikov fractional calculus model

The increasing applications of fractional calculus in simulating the anomalous transport behavior in disordered and fractured heterogeneous porous media has grown rapidly over the past decade. In the present study, a temporal fractional flux relationship is employed as a constitutive equation to relate the volumetric flow rate to the gradient of the pore pressure. The novelty of this paper entails interpreting the time fractional derivative operator in the flux relationship by the Grünwald-Letnikov (G-L) definition as opposed to the Caputo interpretation which has been widely considered. Subsequently, a numerical scheme based on the block-centered finite-difference discretization is formulated to handle the resulting non-linear fractional diffusion model. In addition, a linear stability analysis is successfully performed to establish the stability criterion of the developed numerical scheme. An expression for the modified incremental material balance index was derived to assess the effectiveness of the numerical discretization process. Finally, numerical experiments were performed to provide qualitative insights into the nature of pressure evolution in a hydrocarbon reservoir under the influence subdiffusion. In summary, the results establish that subdiffusion regime results in the development of higher pressure drop in the reservoir. This paper will provide a strong foundation for researchers interested in investigating anomalous diffusion phenomena in porous media.     

Optimization and Evaluation of Multiple Hydraulically Fractured Parameters in Random Naturally Fractured Model Blocks: An Experimental Investigation

Researchers have recently realized that the non-tectonic natural fractures are developed in shale formations and significant for the exploitation of shale gas. Studies have shown that the tectonic fractures in naturally fractured reservoirs have influences on the maximization of stimulated reservoir volume (SRV) during hydraulic fracturing. However, the effect of the non-tectonic randomly natural fractures on the fracturing network propagation is not well understood. Laboratory experiments are proposed to study the evolution of fracturing network in naturally fractured formations with specimens that contain non-tectonic random fractures. The influences of the dominating factors were studied and analyzed, with an emphasis on natural fracture density, stress ratio, and injection rate. The response surface methodology was employed to perform the multiple-factor analysis and optimization in the maximization of the SRV. A sensitivity study reveals a number of interesting observations resulting from these parameters on the fracturing network evaluation. It is suggested from the geometry morphology of fracturing network that high natural fracture density and injection rate tend to maximize the fracturing network. The influence of stress contrast on fracturing network is nonlinear; an optimal value exists resulting in the best hydraulic fracturing effectiveness.     

Analytical solution to one-dimensional consolidation in unsaturated soils under loading varying exponentially with time

This note presents an analytical solution to one-dimensional consolidation in unsaturated soils with a finite thickness under confinement in the lateral direction and vertical loading varying exponentially with time. The boundary conditions are that the top surface is permeable to water and air and the bottom is impermeable to water and air. The transfer relationship between the state vectors at the top surface and any depth is gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial and boundary conditions. By performing the inverse Laplace transforms, the analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement are obtained in the time domain.     

Cluster spacing optimization of multi-stage fracturing in horizontal shale gas wells based on stimulated reservoir volume evaluation

The multi-stage fracturing in horizontal well is a common technique for shale gas reservoir exploitation, in which cluster spacing governs the fracturing performance. Undersized cluster spacing might make the stimulated reservoir volume (SRV), activated by the respective hydraulic fracture, excessively overlap with each other, while oversized cluster spacing might leave a large unstimulated volume between neighboring hydraulic fractures; in either case, fracturing would be inefficient. Previous design of cluster spacing has failed to maximize the SRV due to the absence of a dynamic SRV evaluation model. A numerical model of SRV evaluation in shale reservoir was established by integrating four main modules, including fracture propagation, reservoir pressure distribution, formation stress distribution, and natural fracture failure criterion. Then, a method to optimize cluster spacing was developed with the goal of maximizing SRV. In order to validate this method, it was applied in Fuling shale gas reservoir in Southwest China to determine the optimal cluster spacing. The sensitivity of key parameters on the optimal cluster spacing has been analyzed. This research proposed a compelling cluster spacing optimization method, which could reduce the uncertainty in cluster spacing design, and provides some new insights on the optimal design of multi-stage fracturing in horizontal shale gas well.