页岩有机质纳米孔隙气体吸附与流动规律研究

页岩储层孔隙结构复杂, 气体赋存方式多样. 有机质孔隙形状对受限空间气体吸附和流动规律的影响尚不明确, 导致难以准确认识页岩气藏气体渗流机理. 为解决该问题, 本文首先采用巨正则蒙特卡洛方法模拟气体在不同形状有机质孔隙(圆形孔隙、狭长孔隙、三角形孔隙、方形孔隙)内吸附过程, 发现不同形状孔隙内吸附规律符合朗格缪尔单层吸附规律, 分析了绝对吸附量、过剩吸附浓量、气体吸附参数随孔隙尺寸、压力的变化, 研究了孔隙形状对气体吸附的影响. 在明确不同形状有机质孔隙内气体热力学吸附规律基础上, 建立不同形状有机质孔隙内吸附气表面扩散数学模型和考虑滑脱效应的自由气流动数学模型, 结合分子吸附模拟结果研究了不同孔隙形状、孔隙尺寸有机质孔隙内吸附气流动与自由气流动对气体渗透率的贡献. 结果表明, 狭长孔隙内最大吸附浓度和朗格缪尔压力最高, 吸附气表面扩散能力最弱. 孔隙半径5 nm以上时, 吸附气表面扩散对气体渗透率影响可忽略. 本文研究揭示了页岩气藏实际生产过程中有机质孔隙形状对页岩气吸附和流动能力的影响机制.      

基于Hansbo渗流的圆柱土样Biot固结分析

诸多黏性土渗流试验表明,在低水力梯度下渗流会出现明显偏离Darcy定律的现象.为了分析渗流的非Darcy特性对固结过程的影响,引入Hansbo渗流方程描述圆柱土样内的渗流,重新推导轴对称条件下的Biot固结方程,并给出方程的Crank--Nicolson有限差分格式.通过与Darcy渗流条件下轴对称Biot固结方程解析解的对比,验证计算方法的有效性.然后分析Hansbo模型参数对圆柱土样固结过程的影响.计算结果表明:与Darcy渗流相比,Hansbo渗流会延缓圆柱土样的固结过程.随着Hansbo渗流参数m或I1的增大,在固结前期,Mandel--Cryer效应会更加显著,即孔隙水压力峰值将提高,且达到该峰值的时间会延迟;在固结中后期,孔压消散滞后的现象也更加明显.不过,Hansbo渗流对位移的影响很小.     

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.      

不同滑移边界下的页岩渗透率修正模型

页岩中的孔隙直径通常为纳米量级,基于连续流的达西定律已不能描述纳米级孔隙内的气体流动规律,一般采用附加滑移边界条件的Navier-Stokes方程对其进行描述. 由此可导出与压力相关的渗透率公式(称为"视渗透率"),并用来修正达西定律.因而,渗透率修正方法研究成为页岩气流动研究的热点之一.首先,基于Hagen-Poiseuille 流推导出一般形式二阶滑移模型下的速度分布和流量公式,并推导出相应的渗透率修正公式.该渗透率修正公式基本能将现有的滑移速度模型统一表达为对渗透率的修正. 基于一般形式的渗透率修正公式,重点研究了Maxwell, Hsia, Beskok与Ng 滑移模型速度分布渗透率修正系数、及其对井底压力的影响;提出了基于Ng 滑移速度模型的渗透率修正公式. 基于页岩实际储层温压系统及孔隙分布,计算了Kn 范围及储层条件下页岩气的流动形态,表明页岩气流动存在滑移流、过渡流与分子自由流. 而Ng 模型能描述Kn<88 的滑移流、过渡流、自由分子流的流量规律,因此可以用于描述页岩实际储层中页岩气的流动特征. 计算表明,随着Kn 的增加,不同滑移模型下的渗透率修正系数差异增大.Maxwell与Hsia模型适用于滑移流与过渡流早期,Beskok与Ng 模型可描述自由分子流下的流动规律,但二者在虚拟的孔径均为10nm页岩中,井底压力的差别开始显现;在虚拟的孔径均为1nm页岩中,井底压力的差别开始明显.      

采空区流场非达西渗流一种新的迭代算法

对Bachmat非线性渗流方程求解问题，结合采空区问题的力学特点，提出基于变渗透率达西 (Darcy)渗流求解非线性渗流的迭代算法. 建立了冒落采空区非线性漏风流态的有限元数 值模型，通过对复杂边界采空区的漏风渗流的计算，得到与实际流态更接近的流动规律(风 压等值线和流函数线)和采空区漏风强度分布(速度场). 结果表明，迭代算法是振荡性收 敛的，收敛速度快；与Darcy渗流相比，采空区非线性渗流速度场趋向于平缓，在工作面附 近30\,m范围内最大风速降低到原来的0.61倍，其余大部分区域速度略有增加. 迭代方法满 足工程要求.     

BIOT’S CONSOLIDATION ANALYSIS FOR CYLINDRICAL SOIL-SAMPLE BASED ON HANSBO’S FLOW1)

诸多黏性土渗流试验表明,在低水力梯度下渗流会出现明显偏离Darcy定律的现象. 为了分析渗流的非Darcy特性对固结过程 的影响,引入Hansbo渗流方程描述圆柱土样内的渗流,重新推导轴对称条件下的Biot固结方程,并给出方程的Crank--Nicolson有限 差分格式. 通过与Darcy渗流条件下轴对称Biot固结方程解析解的对比,验证计算方法的有效性. 然后分析Hansbo模型参数对圆柱 土样固结过程的影响. 计算结果表明：与Darcy渗流相比,Hansbo渗流会延缓圆柱土样的固结过程. 随着Hansbo渗流参数m或I¹的增大,在固结前期,Mandel--Cryer效应会更加显著,即孔隙水压力峰值将提高,且达到该峰值的时间 会延迟;在固结中后期,孔压消散滞后的现象也更加明显. 不过,Hansbo渗流对位移的影响很小.     

低渗透煤层气藏中气-水两相不稳定渗流动态分析

针对低渗透煤层渗流问题,考虑启动压力梯度及其引起的动边界和动边界内吸附气解吸作用的渗流模型研究目前仅限于单相流,而更符合实际的气-水两相渗流动边界模型未见报道.本文综合考虑了煤层吸附气的解吸作用、气-水两相渗流、非达西渗流、地层应力敏感等影响因素,进行了低渗透煤层的气-水两相渗流模型研究.采用了试井技术中的"分相处理"方法,修正了两相渗流的综合压缩系数和流度,并基于含气饱和度呈线性递减分布的假设,建立了煤层气藏的气-水两相渗流耦合模型.该数学模型不仅可以描述由于低渗透煤层中渗流存在启动压力梯度而产生的可表征煤层有效动用范围随时间变化的移动边界,还可以描述煤层有效动用范围内吸附气的解吸现象以及吸附气解吸作用所引起的煤层含气饱和度的上升;为了提高模型精度,控制方程还保留了二次压力梯度项.采用了稳定的全隐式有限差分方法进行了模型的数值求解,并验证了数值计算方法的正确性,获得了模型关于瞬时井底压力与压力导数响应的双对数特征曲线,由此分析了各渗流参数的敏感性影响.本文研究结果可为低渗透煤层气藏开发的气-水两相流试井技术提供渗流力学的理论基础.     

页岩基质解吸-扩散-渗流耦合实验及数学模型

采用川南地区龙马溪组页岩样品,设计了页岩基质解吸-扩散-渗流耦合物理模拟实验,揭示了页岩基质气体流动特征以及压力传播规律.推导了页岩气解吸-扩散-渗流耦合数学模型并且利用有限差分法对数学模型进行数值求解,与实验结果相比较表明该数学模型能够很好地描述气体在页岩基质中的流动规律.同时对页岩基质气体流动的影响因素进行了分析,认为页岩基质的渗透率、扩散系数、解吸附常数等因素均能影响页岩基质气体的流量和压力传播规律,在页岩气藏的开发过程中需要考虑这些参数的影响,该数学模型为页岩气井产能计算提供了更准确的计算方法.      

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.      

水力压裂中裂纹扩展的数值模拟

水力压裂是在高压粘滞流体或清水作用下地层内裂缝起裂与扩展的过程。由于包含岩石断裂和流-固耦合等复杂问题,对该过程的数值模拟具有相当大的挑战性。本文建立基于有限元与离散元混合方法的裂纹模型,模拟岩石裂纹扩展,实现了连续向非连续的转化;建立双重介质流动模型,裂隙流作为孔隙渗流的压力边界,孔隙渗流反作用裂隙的压力求解,处理了流体在基岩与人工裂缝中的协调流动;将裂纹模型与流体流动模式进行结合,建立断裂-应力-渗流耦合形式的力学模型,进一步分析了水力压裂的基本过程,综合多种数值计算方法,编写程序,在验证岩体裂纹模型与双重介质流动模型有效性的基础上,对压裂过程进行复现,将模拟结果与文献结果进行了对比,并讨论了所构建模型的优缺点。     

Apparent Permeability and Gas Flow Behavior in Carboniferous Shale from the Qaidam Basin,China: An Experimental Study

Shale can act as an unconventional gas reservoir with low permeability and complex seepage characteristics. Study of the apparent permeability and percolation behavior of shale gas is important in understanding the permeability of shale reservoirs, to evaluate formation damage, to develop gas reservoirs, and to design wells. This study simulated methane percolation at 298.15 K under inlet pressures ranging from 0.2 to 4 MPa and a constant outlet pressure of 0.1 MPa to investigate shale gas percolation behavior and apparent permeability. Five representative shale cores from the Carboniferous Hurleg and Huitoutala formations in the eastern Qaidam Basin, China, were analyzed. Each experiment measured the volume flow rate of methane and the inlet pressure. Pseudopressure approach was used to analyze high-velocity flow in shale samples, and apparent permeability at different pressures was calculated using the traditional method. A nonlinear apparent permeability model that considers diffusion and slippage is established from theory and experimental data fitting, and the shale gas flow characteristics affected by slippage and diffusion are analyzed. The results indicate that the pseudopressure formulation that considers the effect of gas properties on high-velocity flow produces a more accurate linear representation of the experimental data. The apparent gas permeability of shale consists of contributions from Darcy permeability, slippage, and diffusion. The apparent permeability and gas flow behavior in the studied shales strongly depended on pressure. The diffusion contribution increased greatly as pressure decreased from 2 to 0.2 MPa, and the smaller the shale permeability, the greater the relative contribution of diffusion flow. At pressures greater than 2 MPa, slip flow contributes \(\sim \)20% of the total flux, Darcy flow contributes up to 70%, and diffusion makes only a minor contribution. This study provides useful information for future studies of the mechanism of shale gas percolation and the exploration and development of Qaidam Basin shale gas specifically.     

Pressure Transient Analysis for Multi-stage Fractured Horizontal Wells in Shale Gas Reservoirs

This article presents the PTA on the multi-stage fractured horizontal well in shale gas reservoirs incorporating desorption and diffusive flow in the matrix. Currently, most PTA models are simply based on Darcy flow both in natural fractures and matrix without considering the mechanisms of desorption and diffusion in shale matrix. Source function and Laplace transform with the numerical discrete method are employed to solve the mathematical model. The solution is presented in the Laplace domain so that the wellbore storage effect and skin factor can be easily incorporated by convolution. Type curves are plotted with Stehfest algorithm and different flow regimes are identified. The presented model could be used to interpret pressure signals more accurately for shale gas reservoirs.     

基于REV尺度格子Boltzmann方法的页岩气流动数值模拟

结合页岩扫描电镜图像,提出页岩气藏物理模型,采用表征单元体积(representative elementary volume,REV)尺度格子Boltzmann方法,考虑滑脱效应,模拟页岩气在页岩气藏中的流动.模拟结果表明,页岩气主要沿着天然裂缝窜进,但在有机质和无机质中也存在缓慢的流动,且有机质中的流速要略大于无机质中的流速.通过改变地层压力,研究地层压力对页岩气渗流特性的影响.研究结果表明,整个流场的速度和渗透率均随着地层压力的下降而增加.     

A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems

Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.     

Laboratory Investigation of LNAPL Migration in Double-Porosity Soil Under Fractured Condition Using Digital Image Analysis

Gas production from shale gas reservoirs plays a significant role in satisfying increasing energy demands. Compared with conventional sandstone and carbonate reservoirs, shale gas reservoirs are characterized by extremely low porosity, ultra-low permeability and high clay content. Slip flow, diffusion, adsorption and desorption are the primary gas transport processes in shale matrix, while Darcy flow is restricted to fractures. Understanding methane diffusion and adsorption, and gas flow and equilibrium in the low-permeability matrix of shale is crucial for shale formation evaluation and for predicting gas production. Modeling of diffusion in low-permeability shale rocks requires use of the Dusty gas model (DGM) rather than Fick’s law. The DGM is incorporated in the TOUGH2 module EOS7C-ECBM, a modified version of EOS7C that simulates multicomponent gas mixture transport in porous media. Also included in EOS7C-ECBM is the extended Langmuir model for adsorption and desorption of gases. In this study, a column shale model was constructed to simulate methane diffusion and adsorption through shale rocks. The process of binary \(\hbox {CH}_{4}{-}\hbox {N}_{2}\) diffusion and adsorption was analyzed. A sensitivity study was performed to investigate the effects of pressure, temperature and permeability on diffusion and adsorption in shale rocks. The results show that methane gas diffusion and adsorption in shale is a slow process of dynamic equilibrium, which can be illustrated by the slope of a curve in \(\hbox {CH}_{4}\) mass variation. The amount of adsorption increases with the pressure increase at the low pressure, and the mass change by gas diffusion will decrease due to the decrease in the compressibility factor of the gas. With the elevated temperature, the gas molecules move faster and then the greater gas diffusion rates make the process duration shorter. The gas diffusion rate decreases with the permeability decrease, and there is a limit of gas diffusion if the permeability is less than \(1.0\,\times \,10^{-15}\, \hbox { m}^{2}\). The results can provide insights for a better understanding of methane diffusion and adsorption in the shale rocks so as to optimize gas production performance of shale gas reservoirs.     

Understanding Oil and Gas Flow Mechanisms in Shale Reservoirs Using SLD–PR Transport Model

More and more attention has been paid to the oil and gas flow mechanisms in shale reservoirs. The solid–fluid interaction becomes significant when the pores are in the nanoscale. The interaction changes the fluid’s physical properties and leads to different flow mechanisms in shale reservoirs from those in conventional reservoirs. By using a Simplified Local Density–Peng Robinson transport model, we consider the density and viscosity profiles, which result from solid–fluid interaction. Gas rarefaction effect is negligible at high pressure, so we assume it is viscous flow. Considering the density- and viscosity-changing effects, we proposed a slit permeability model. The velocity profiles are obtained by this newly established model. This proposed model is validated by matching the density profile and velocity profile from molecular dynamic simulation. Then, the effects of pressure and pore size on gas and oil flow mechanisms are also studied in this work. The results show that both gas and oil exhibit enhanced flow rates in nanopores. Gas-phase flow in nanopores is dominated by the density-changing effect (adsorption), while the oil-phase flow is mainly controlled by the viscosity-changing effect. Both gas and oil permeability quickly decrease to the Darcy permeability when the slit aperture becomes large. The results reported in this work are representative and should significantly help us understand the mechanisms of oil and gas flow in shale reservoirs.     

Parameter Determination Using 3D FIB-SEM Images for Development of Effective Model of Shale Gas Flow in Nanoscale Pore Clusters

A large amount of nano-pores exists in pore clusters in shale gas reservoirs. In addition to the multiple transport regimes that occur on the nanoscale, the pore space is another major factor that significantly affects the shale gas recoverability. An investigation of the pore-scale shale gas flow is therefore important, and the results can be used to develop an effective cluster-scale pore network model for the convenient examination of the process efficiency. Focused ion beam scanning electron microscope imaging, which enables the acquisition of nanometre-resolution images that facilitate nano-pore identification, was used in conjunction with a high-precision pore network extraction algorithm to generate the equivalent pore network for the simulation of Darcy and shale gas flows through the pores. The characteristic parameters of the pores and the gas transport features were determined and analysed to obtain a deeper understanding of shale gas flow through nanoscale pore clusters, such as the importance of the throat flux–radius distribution and the variation of the tortuosity with pressure. The best parameter scheme for the proposed effective model of shale gas flow was selected out of three derived schemes based on the pore-scale prediction results. The model is applicable to pore-scale to cluster-scale shale gas flows and can be used to avoid the multiple-solution problems in the study of gas flows. It affords a foundation for further study to develop models for shale gas flows on larger scales.     

Comprehensive Seepage Simulation of Fluid Flow in Multi-scaled Shale Gas Reservoirs

Shale gas seepage behaviour is a multi-field/-scale problem and makes transient pressure analysis a very challenging task. Non-Darcy flow in nanopores is prominent due to the broken of continuity hypothesis. Slippage effect and Knudsen diffusion are two important seepage mechanisms in nanopores, while recent studies show surface diffusion is another important transporting mechanism on surface of nanopores. Porous kerogen system contains large amounts of dissolved gas, which should not be overlooked. In this study, a comprehensive mathematical model was established by pseudo-quadruple porosity medium conception, coupling the effects of slippage flow, Knudsen diffusion, surface diffusion, ad-/desorption and gas transferring from kerogen to nanopore system, while fluid flow in fractures/macropores is described by Darcy’s law. Transient pressure behaviours of a multiple fractured horizontal well in box-shaped shale gas reservoir were studied, with nine possible flow regimes divided and parameters sensitivity analysed. Adsorbed constant and dissolved constant were defined to reflect the amount of adsorbed gas and dissolved gas, respectively. Research shows that adsorbed gas and dissolved gas are two important gas storage forms, neither of which should be neglected. The study can not only help us understand fluid flow mechanisms in nanopores from microscopic perspective, but enable us to analyse production performance and determine key operational parameters from macroscopic perspective.